- Turbulence, Combustion, Turbulence Modelling, Large Eddy Simulation, Cavitation, Aerospace Engineering, and 14 moreComputational Fluid Dynamics, Direct Numerical Simulation, Shock Turbulence Interaction, Shock Waves Boundary Layer Interaction, Implicit LES, Laminar to Turbulence Transitions, Immersed Boundary Methods, Heat Transfer, Turbulence modeling, Transport Phenomena in Porous Media, Multiphase flows, Fluid Dynamics, Numerical and Experimental Methods in Fluid Dynamics, and INCA CFDedit
- Stefan Hickel is Professor of Computational Fluid Dynamics and Chair of Aerodynamics at the Faculty of Aerospace Engi... moreStefan Hickel is Professor of Computational Fluid Dynamics and Chair of Aerodynamics at the Faculty of Aerospace Engineering of TU Delft. He obtained his PhD from TU Munich for research into the design of consistent numerical methods and turbulence models for large-eddy simulation in 2008 and was appointed full professor at TU Delft in 2015. Professor Hickel and his students develop models and methods for high-performance computational thermo-fluid dynamics with which they perform numerical experiments on a broad range of turbulent flows. Typical applications are, for example, waves and turbulence within Earth’s atmosphere, shock-turbulence interactions in supersonic aircraft and rockets, interactions of high-speed fluid flows with elastic structures such as aircraft wings, and turbulence in chemically reacting, multiphase and supercritical fluids, such as fuel injection and combustion in rocket or car engines. Professor Hickel serves the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC) as Chairman of the Scientific Programme Committee and TU Delft as Director of the Graduate School of Aerospace Engineering.edit
The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at Ma = 1.7 and Re ∞ = 1.3718 × 10 7 m −1 are investigated using a well-resolved large-eddy simulation. The instantaneous flow field illustrates... more
The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at Ma = 1.7 and Re ∞ = 1.3718 × 10 7 m −1 are investigated using a well-resolved large-eddy simulation. The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. Görtler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady Görtler-like vortices are affected by fluctuations in the incoming boundary layer. Compared with SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.
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We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES)... more
We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by 19.6 •. The Reynolds number based on the incoming boundary-layer thickness of Re δ 0 ≈ 203 × 10 3 is considerably higher than in previous LES studies. The very long integration time of 3805δ 0 /U 0 allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.
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The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach... more
The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of Ma=2. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of Ma=3 confirm the existence of the dual-solution domain predicted by theory.
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Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a... more
Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a reference experiment. Details of the experiment, such as planar side walls, are taken into account, all wall boundary layers are well-resolved and no wall model is used. The Adaptive Local Deconvolution Method (ALDM) with shock sensor is employed for subgrid-scale turbulence modeling and shock capturing. The LES results are validated against experimental wall-pressure measurements and schlieren pictures. A detailed discussion of the complex flow phenomena of three-dimensional shock-wave–boundary-layer interaction, including corner vortices and recirculation zones, is presented. Limitations of RANS approaches are discussed with reference to the LES results.
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In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by Ma=1.05,Ma=1.2, and Ma=1.5 shock waves interacting with a perturbed planar interface between air and SF6. At the lowest... more
In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by Ma=1.05,Ma=1.2, and Ma=1.5 shock waves interacting with a perturbed planar interface between air and SF6. At the lowest shock Mach number the fluids slowly mix due to viscous diffusion, whereas at the highest shock Mach number the mixing zone becomes turbulent. When a minimum critical Taylor microscale Reynolds number is exceeded, an inertial range spectrum emerges, providing further evidence of transition to turbulence. The scales of turbulent motion, i.e., the Kolmogorov length scale, the Taylor microscale, and the integral length, scale are presented. The separation of these scales is found to increase as the Reynolds number is increased. Turbulence statistics, i.e., the probability density functions of the velocity and its longitudinal and transverse derivatives, show a self-similar decay and thus that turbulence evolving from RMI is not fundamentally different from isotropic turbulence, though nominally being only isotropic and homogeneous in the transverse directions.
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We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer–Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma= 1.5. The prescribed initial conditions define a deterministic... more
We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer–Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma= 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Well-resolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ${\sim } t^{7/12}$ before re-shock and ${\sim } (t-t_0)^{2/7}$ long after re-shock. The decay rate of turbulence kinetic energy is consistently ${\sim } (t-t_0)^{-10/7}$ at late times, where the molecular mixing fraction approaches an asymptotic limit $\varTheta \approx 0.85$. The anisotropy measure $\langle a \rangle _{xyz}$ approaches an asymptotic limit of ${\approx }0.04$, implying that no full recovery of isotropy within the mixing zone is obtained, even after re-shock. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. The probability density function of the heavy-gas mass fraction and vorticity reveal that the light–heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity.
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We present results of well-resolved direct numerical simulations (DNS) of the turbu-lent flow evolving from Richtmyer-Meshkov instability (RMI) in a shock-tube with square cross section. The RMI occurs at the interface between a mixture... more
We present results of well-resolved direct numerical simulations (DNS) of the turbu-lent flow evolving from Richtmyer-Meshkov instability (RMI) in a shock-tube with square cross section. The RMI occurs at the interface between a mixture of O 2 and N 2 (light gas) and SF 6 and acetone (heavy gas). The interface between the light and heavy gas is accelerated by a Ma = 1.5 planar shock wave. RMI is triggered by a well-defined multimodal initial disturbance at the interface. The DNS exhibit grid-resolution inde-pendent statistical quantities and support the existence of a Kolmogorov-like inertial range with a k −5/3 scaling unlike previous simulations found in the literature. The results are in excellent agreement with the experimental data of Weber et al. ["Turbu-lent mixing measurements in the Richtmyer-Meshkov instability," Phys. Fluids 24, 074105 (2012)].
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Two-dimensional simulations of the single-mode Richtmyer–Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005 Phys. Fluids 17 034105). The employed adaptive central-upwind sixth-order... more
Two-dimensional simulations of the single-mode Richtmyer–Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005 Phys. Fluids 17 034105). The employed adaptive central-upwind sixth-order weighted essentially non-oscillatory (WENO) scheme (Hu et al 2010 J. Comput. Phys. 229 8952–65) introduces only very small numerical dissipation while preserving the good shock-capturing properties of other standard WENO schemes. Hence, it is well suited for simulations with both small-scale features and strong gradients. A generalized Roe average is proposed to make the multicomponent model of Shyue (1998 J. Comput. Phys. 142 208–42) suitable for high-order accurate reconstruction schemes. A first sequence of single-fluid simulations is conducted and compared to the experiment. We find that the WENO-CU6 method better resolves small-scale structures, leading to earlier symmetry breaking and increased mixing. The first simulation, however, fails to correctly predict the global characteristic structures of the RMI. This is due to a mismatch of the post-shock parameters in single-fluid simulations when the pre-shock states are matched with the experiment. When the post-shock parameters are matched, much better agreement with the experimental data is achieved. In a sequence of multifluid simulations, the uncertainty in the density gradient associated with transition between the fluids is assessed. Thereby the multifluid simulations show a considerable improvement over the single-fluid simulations.
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We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma∞=2.3 and a Reynolds number based on the incoming... more
We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma∞=2.3 and a Reynolds number based on the incoming boundary-layer thickness of Reδ0=60 500 by means of large-eddy simulation (LES). The compressible Navier–Stokes equations in conservative form are solved using the adaptive local deconvolution method (ALDM) for physically consistent subgrid scale modeling. Emphasis is placed on the correct description of turbulent inflow boundary conditions, which do not artificially force low-frequency periodic motion of the reflected shock. The control configuration combines suction inside the separation zone and blowing upstream of the interaction region by a pressure feedback through a duct embedded in the wall. We vary the suction location within the recirculation zone while the injection position is kept constant. Suction reduces the size of the separation zone with strongest effect when applied in the rear part of the separation bubble. The analysis of wall-pressure spectra reveals that all control configurations shift the high-energy low-frequency range to higher frequencies, while the energy level is significantly reduced only if suction acts in the rear part of the separated zone. In that case also turbulence production within the interaction region is significantly reduced as a consequence of mitigated reflected shock dynamics and near-wall flow acceleration.
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The unsteady behavior in shockwave turbulent boundary layer interaction is investi- gated by analyzing results from a LES of a supersonic turbulent boundary layer over a compression-expansion ramp. The interaction leads to a... more
The unsteady behavior in shockwave turbulent boundary layer interaction is investi- gated by analyzing results from a LES of a supersonic turbulent boundary layer over a compression-expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analyzed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analyzed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward-backward motion of the shock.
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Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compression–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same... more
Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compression–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same flow conditions. The compression–expansion ramp has a deflection angle of β = 25°. The flow is characterized by a free-stream Mach number of Ma∞ = 2.88 and the Reynolds number based on the incoming boundary layer thickness is Reδ0=132840. The Navier Stokes equations for compressible flows are solved on a cartesian collocated grid. About 32.5 × 106 grid points are used to discretize the computational domain. Subgrid scale effects are modeled implicitly by the adaptive local deconvolution method (ALDM). A synthetic inflow-turbulence technique is used, which does not introduce any low frequency into the domain, therefore avoiding any possible interference with the shock/boundary layer interaction system. Statistical samples are gathered over 800 characteristic time scales δ0/U∞. The numerical data are in good agreement with the experiment in terms of mean surface-pressure distribution, skin-friction, mean velocity profiles, velocity and density fluctuations. For the first time the full compression–expansion ramp configuration was taken into account. The computational results confirm theoretical and experimental findings on fluctuation-amplification across the shockwave/boundary layer interaction region and on turbulence damping through the interaction with rarefaction waves. The LES provide evidence of the existence of Görtler-like structures originating from the recirculation region and traveling downstream along the ramp. An analysis of the wall pressure field clearly shows the presence of a low frequency motion of the shock and strong influence of the Görtler-like vortices on the wall pressure spectra.
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We present Implicit Large-Eddy Simulations of a shockwave-turbulent boundary layer interaction with and without localized heat addition. The flow is complex and involves boundary layer separation under the adverse pressure gradient... more
We present Implicit Large-Eddy Simulations of a shockwave-turbulent boundary layer interaction with and without localized heat addition. The flow is complex and involves boundary layer separation under the adverse pressure gradient imposed by the shock, turbulence amplification across the interaction and low frequency oscillation of the reflected shock. For an entropy spot generated ahead of the shock, baroclinic vorticity production occurs when the resulting density peak passes the shock. The objective of the present study is to analyze the shock-separation interaction and turbulence structure of such a configuration. The effect of the addition of an entropy spot to the flow field is assessed in terms of turbulence amplification.
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We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a... more
We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a polynomial chaos expansion to propagate the initial-data uncertainties to the output quantities of interest. The initial flow configuration follows previous experimental and numerical works of the shock accelerated heavy-gas cylinder. We investigate three main initial- data uncertainties, (i) shock Mach number, (ii) contamination of SF6 with acetone, and (iii) initial deviations of the heavy-gas region from a perfect cylindrical shape. The impact of initial-data uncertainties on the mixing process is examined. The results suggest that the mixing process is highly sensitive to input variations of shock Mach number and acetone contamination. Additionally, our results indicate that the measured shock Mach number in the experiment of Tomkins et al. [“An experimental investigation of mixing mechanisms in shock-accelerated flow,” J. Fluid. Mech. 611, 131 (2008)] and the estimated contamination of the SF6 region with acetone [S. K. Shankar, S. Kawai, and S. K. Lele, “Two-dimensional viscous flow simula- tion of a shock accelerated heavy gas cylinder,” Phys. Fluids 23, 024102 (2011)] exhibit deviations from those that lead to best agreement between our simulations and the experiment in terms of overall flow evolution.
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We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric... more
We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.
Research Interests: Chemical Engineering, Computational Physics, Phase Transformations, Computational Fluid Dynamics, Reservoir Engineering, and 15 moreMultiphase Flow, Two Phase Flow, GAS TURBINE, Oil and gas, Molecular Thermodynamics of Fluid Phase Equilibria, Rocket Propulsion, Reservoir Simulation, Multiphase flows, Chemical Engineering Process Design, Vapor liquid equilibrium, Diesel engines, Fuel injection, Oil and Gas Reservoir Characterization, Fluid phase equilibria, and Chemical and Process Systems Engineering
Large-eddy simulations (LES) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of... more
Large-eddy simulations (LES) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models – the Smagorinsky model, the Vreman model and the Adaptive Local Deconvolution Method – shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid's thermodynamic state. The injected fluid is either in a supercritical or in a transcritical state and undergoes a pseudo-boiling process during mixing. Such flows typically exhibit strong density gradients that delay the instability growth and can lead to a redistribution of turbulence kinetic energy from the radial to the axial flow direction. We evaluate novel volume-translation methods on the basis of the cubic Peng-Robinson equation of state in the framework of LES. At small extra computational cost, their application considerably improves the simulation results compared to the standard formulation. Furthermore, we found that the choice of inflow temperature is crucial for the reproduction of the experimental results, and that heat addition within the injector can affect the mean flow field in comparison to results with an adiabatic injector.
Research Interests: Cryogenics, Computational Fluid Dynamics, Turbulence, Cubic Equations of State, Supercritical fluids, and 9 moreLarge Eddy Simulation, Turbulence modeling, Supercritical fluid science and technology, OpenFOAM, Mixing Rules for Equations of State, Fuel injection, Turbulent Mixing, Compressible Flows, and INCA CFD
We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can... more
We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component sub-critical two-phase states via a homogeneous mixture approach. Well-resolved LES results for the Spray A benchmark case of the Engine Combustion Network (ECN) and three additional operating conditions are found to agree very well with available experimental data. We also address well-known numerical challenges of trans-and supercritical fluid mixing and compare a fully conservative formulation to a quasi-conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi-conservative formulation on typical LES grids.
Research Interests: Computational Fluid Dynamics, Turbulence, Multiphase Flow, Supercritical fluids, Large Eddy Simulation, and 9 moreNumerical Analysis, Numerical Modelling, Marine Diesel Engines, Multiphase flows, Turbulence modeling, Modeling and Simulation of Diesel Engine, Diesel engines, Fuel injection, and INCA CFD
Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation... more
Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation processes of an initially supercritical fluid due to the interaction with its surrounding. N-hexane was injected into a chamber filled with pure nitrogen at 5 MPa and 293 K and three different test cases were selected such that they cover regimes in which the thermodynamic non-idealities, in particular the effects that stem from the potential phase separation, are significant. Simultaneous shadowgraphy and elastic light scattering experiments were conducted to capture both the flow structure as well as the phase separation. In addition, large-eddy simulations with a vapor-liquid equilibrium model were performed. Both experimental and numerical results show phase formation for the cases, where the a-priori calculation predicts two-phase flow. Moreover, qualitative characteristics of the formation process agree well between experiments and numerical simulations and the transition behaviour from a dense-gas to a spray-like jet was captured by both.
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We report on recent developments within the field of real gas thermodynamics models with particular emphasis on volume translation methods for cubic equations of state. On the basis of the generalized form of a cubic equation of state, a... more
We report on recent developments within the field of real gas thermodynamics models with particular emphasis on volume translation methods for cubic equations of state. On the basis of the generalized form of a cubic equation of state, a mathematical framework for applying volume translations is provided, allowing for an unified and thermodynamically consistent formulation in the context of computational fluid dynamics simulations. This generalized methodology is applied to two selected volume translation methods that were recently proposed: the method of Abudour et al. (Fluid Phase Equilibria, 2012) and the method of Baled et al. (Fluid Phase Equilibria, 2012). In particular, the consistent integration of both methods in the evaluation of the caloric properties is investigated, showing that for Abudour et al.’s method one has to apply numerical integration whereas an analytical solution exists for Baled et al.’s method. The results of both volume translations are compared with those of the untranslated equations of state as well as with reference data. The density predictions of Abudour et al.’s method proved to be superior to those of the other approaches, whereas we observe a decreased accuracy for caloric properties. To evaluate the applicability of both methods in the context of real-gas computational fluid dynamics simulations, we performed well-resolved large-eddy simulations for the coaxial injection of cryogenic and gaseous nitrogen into a supercritical nitrogen atmosphere. A qualitative comparison of the numerical results with the available experimental backlight image shows a good agreement and a comparison of different volume translation methods demonstrates the effect of the thermodynamic model on the flow field.
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Large-eddy simulations are carried out for the coaxial injection of liquid nitrogen and preheated hydrogen at supercritical pressures. The conditions are similar to that in typical liquid-propellant rocket combustors. By using nitrogen as... more
Large-eddy simulations are carried out for the coaxial injection of liquid nitrogen and preheated hydrogen at supercritical pressures. The conditions are similar to that in typical liquid-propellant rocket combustors. By using nitrogen as a model gas, the mixing process is studied without the interference with chemical reactions. An analysis of the thermodynamic conditions that arise in the shear layer reveals that local phase separation may occur if the injection condition is transcritical. A novel volume-translation method on the basis of the cubic Peng–Robinson equation of state is introduced for the use in multispecies large-eddy simulations and is tested for both trans- and supercritical injection conditions. The new thermodynamic model corrects the deficiencies of the Peng–Robinson equation of state in the transcritical regime at minimal extra computational cost. Two independently developed large- eddy simulation codes are used for the simulations and the results are compared. The outcome indicates that the flowfield is mainly controlled by the turbulence on the resolved scales, and an accurate model for the fluid’s thermodynamic state is more important than the subgrid-scale turbulence model or the details of the code architecture. A comparison with available experimental data shows that important flow features are well predicted.
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ABSTRACT Rising performance demands on future rocket combustion engines and growing financial restrictions increase the need for the aid of computational fluid dynamics during the development process of such an engine. Our ultimate goal... more
ABSTRACT Rising performance demands on future rocket combustion engines and growing financial restrictions increase the need for the aid of computational fluid dynamics during the development process of such an engine. Our ultimate goal is to simulate a whole rocket combustion chamber by means of CFD. In the presented work, different LES simulations were conducted with two different CFD codes, an in-house code and OpenFOAM. The implicit LES method ALDM and the explicit Smagorinsky Model were validated against DNS simulations of a non-reacting mixing layer of counter-flowing hydrogen and oxygen. ALDM gave good results and OpenFOAM showed its capability to simulate such kinds of flows. A focus of our future work will be the optimization of the LES models for real gas flows and the subsequent simulation of the whole combustion process.
The pressure in modern combustion chambers can exceed 10 MPa which is above the critical pressure of both hydrogen and oxygen. The fluids thereby become supercritical at injection, hence a real gas equation of state and extended transport... more
The pressure in modern combustion chambers can exceed 10 MPa which is above the critical pressure of both hydrogen and oxygen. The fluids thereby become supercritical at injection, hence a real gas equation of state and extended transport equations have to be ...
The coaxial injection of cryogenic, liquid nitrogen (LN2) and preheated hydrogen (GH2) at supercritical pressures is studied using Large-Eddy Simulation (LES). The focus of the present work lies on the evaluation of real-gas... more
The coaxial injection of cryogenic, liquid nitrogen (LN2) and preheated hydrogen (GH2) at supercritical pressures is studied using Large-Eddy Simulation (LES). The focus of the present work lies on the evaluation of real-gas thermodynamics models for binary mix- tures at conditions that are similar to that in LOx/GH2 liquid rocket combustors. A novel volume-translation method on the basis of the cubic Peng-Robinson equation of state is introduced for the use in multi-species LES and is tested for both trans- and supercritical injection conditions. The new method corrects the deficiencies of the Peng-Robinson equa- tion of state in the transcritical regime at minimal extra computational cost. A comparison with available experimental data is encouraging.
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We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric... more
We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective. K E Y W O R D S constant volume flash, reduction method, vapor-liquid equilibrium, volume function 1 | INTRODUCTION Robust, computationally efficient and accurate phase splitting or flash calculations play a crucial role in many engineering disciplines, such as chemical-process and reservoir simulations. In Computational Fluid Dynamics (CFD) simulations of realistic multi-component vapor-liquid fluid flows, millions of phase equilibrium calculations are required every time step in the form of either the VT-flash or UV-flash, depending on the chosen formulation of the governing equations: The VT-flash is needed in cases where the overall specific volume, temperature and composition are known, such as for the carbon dioxide injection into subsurface reservoirs. 1,2 Methods that solve the com-pressible Navier-Stokes equations based on the conservation laws for mass, linear momentum and total energy, such as applied for the simulation of the trans-critical vaporization of liquid fuels, 3-6 require a UV-flash, where the input is the overall specific internal energy, volume , and composition. The calculation of thermodynamic equilibrium properties of multi-component multi-phase mixtures typically consumes more than three quarters of the total computational time 7,8 and thus imposes severe limitation on the tractable space-time resolution or even the computational feasibility of such numerical simulations. At the same time, flash algorithms for CFD applications have to be fault tolerant and robust, because even a method that fails to converge only once in a billion will eventually spoil the entire simulation. The simplest case and workhorse of most phase-equilibrium calculations is the so-called PT-flash, where the equilibrium pressure and temperature of the mixture are already given. Most methods for calculating the isobaric-isothermal equilibrium volume fractions and
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We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating... more
We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben et al. (Exp. Fluids, 2010). While a diesel-like test fuel was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for water and vapor and a simple phase-change model based on equilibrium assumptions. Our LES resolve all wave dynamics in the compressible fluid and the turbulence production in shear layers. The numerical results are in good agreement with available experimental data. This work represents, to our knowledge, the first successful LES of a cavitating two-phase flow with a compressible fluid model.
Research Interests:
In this paper, we investigate the high-speed dynamics of symmetric and asymmetric cavitation bubble-collapse. For this purpose, a sharp-interface numerical model is employed, that includes a numerically effi-cient evaporation/condensation... more
In this paper, we investigate the high-speed dynamics of symmetric and asymmetric cavitation bubble-collapse. For this purpose, a sharp-interface numerical model is employed, that includes a numerically effi-cient evaporation/condensation model. The underlying assumption is that phase change occurs in thermal non-equilibrium and that the associated timescale is much larger than that of the wave-dynamics described by the interfacial Riemann problem. The sharp-interface model allows for an accurate tracking of the interface evolution throughout collapse and rebound. With a first set of simulations, we investigate the influence of the non-equilibrium on the relaxation behaviour of an oscillating vapour bubble. We observe that a good prediction of the phase-change rate is essential. Of high practical interest is the col-lapse of cavitation bubbles near walls under high ambient-pressure conditions. We investigate the differ-ences in collapse evolution for detached and attached bubbles. It is shown that the maximum wall pressure strongly depends on the symmetry of the collapse mechanisms, and regions with a high proba-bility of bubble rebound are identified. Asymmetric attached bubbles lead to significantly different topol-ogy changes during collapse than symmetric bubbles but exhibit roughly the same range of maximum pressures.
Research Interests:
In most technical applications involving cavitation, vapor bubbles occur in clouds, and their collapse is affected by the interaction with neighboring bubbles. One ap- proach to study the influence of these interactions is the... more
In most technical applications involving cavitation, vapor bubbles occur in clouds, and their collapse is affected by the interaction with neighboring bubbles. One ap- proach to study the influence of these interactions is the investigation of the collapse of cavity arrays in water under shock wave loading. We describe in detail the collapse mechanisms during the collapse of a horizontal cavity array, with particular consid- eration of maximum pressures. As general trend, we find a pressure amplification in consecutive cavity collapses. However, by increasing the number of cavities, we are able to demonstrate that the amplification is not monotonic. A parameter study of the bubble separation distance in horizontal arrays shows that a smaller distance generally, but not necessarily, results in larger collapse pressure. Exceptions from the general trend are due to the very complex shock and expansion-wave interac- tions and demonstrate the importance of using state-of-the-art numerical methods. By varying boundary conditions, we illustrate the significance of large test sec- tions in experimental investigations, as the expansion wave emitted at a free surface has a large effect on the collapse dynamics.
Research Interests:
We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are... more
We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics. The thermodynamic model is embedded into an implicit large-eddy simulation (LES) environment. The considered configuration follows the general setup of a reference experiment and is a generic reproduction of a scaled-up fuel injector or control valve as found in an automotive engine. Due to the experimental conditions, it operates, however, at significantly lower pressures. LES results are compared to the experimental reference for validation. Three different operating points are studied, which differ in terms of the development of cavitation regions and the jet break-up characteristics. Observed differences between experimental and numerical data in some of the investigated cases can be caused by uncertainties in meeting nominal parameters by the experiment. The investigation reveals that three main mechanisms promote primary jet break-up: collapse-induced turbulent fluctuations near the outlet, entrainment of free gas into the nozzle, and collapse events inside the jet near the liquid-gas interface.
Research Interests:
Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of... more
Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.
Research Interests:
We investigate a reacting shock–bubble interaction through three-dimensional numerical simulations with detailed chemistry. The convex shape of the bubble focuses the shock and generates regions of high pressure and temperature, which are... more
We investigate a reacting shock–bubble interaction through three-dimensional numerical simulations with detailed chemistry. The convex shape of the bubble focuses the shock and generates regions of high pressure and temperature, which are sufficient to ignite the diluted stoichiometric H 2 −O 2 gas mixture inside the bubble. We study the interaction between hydrodynamic instabilities and shock-induced reaction waves at a shock Mach number of Ma = 2. 83. The chosen shock strength ignites the gas mixture before the shock-focusing point, followed by a detonation wave, which propagates through the entire bubble gas. The reaction wave has a significant influence on the spatial and temporal evolution of the bubble. The misalignment of density and pressure gradients at the bubble interface, caused by the initial shock wave and the subsequent detonation wave, induces Richtmyer–Meshkov and Kelvin–Helmholtz instabilities. The growth of the instabilities is highly affected by the reaction wave, which significantly reduces mixing compared to an inert shock–bubble interaction. A comparison with two-dimensional simulations reveals the influence of three-dimensional effects on the bubble evolution, especially during the late stages. The numerical results reproduce experimental data in terms of ignition delay time, reaction wave speed and spatial expansion rate of the bubble gas. We observe only a slight divergence of the spatial expansion in the long-term evolution.
Research Interests:
We present numerical simulations for a reactive shock–bubble interaction with detailed chemistry. The convex shape of the bubble leads to shock focusing, which generates spots of high pressure and temperature. Pressure and temperature... more
We present numerical simulations for a reactive shock–bubble interaction with detailed chemistry. The convex shape of the bubble leads to shock focusing, which generates spots of high pressure and temperature. Pressure and temperature levels are sufficient to ignite the stoichiometric H 2 –O 2 gas mixture. Shock Mach numbers between Ma = 2. 13 and Ma = 2. 90 induce different reaction wave types (deflagration and detonation). Depending on the shock Mach number low-pressure reactions or high-pressure chemistry are prevalent. A deflagration wave is observed for the lowest shock Mach number. Shock Mach numbers of Ma = 2. 30 or higher ignite the gas mixture after a short induction time, followed by a detonation wave. An intermediate shock strength of Ma = 2. 19 induces deflagration that transitions into a detonation wave. Richtmyer–Meshkov and Kelvin–Helmholtz instability evolutions exhibit a high sensitivity to the reaction wave type, which in turn has distinct effects on the spatial and temporal evolution of the gas bubble. We observe a significant reduction in mixing for both reaction wave types, wherein detonation shows the strongest effect. Furthermore, we observe a very good agreement with experimental observations.
Research Interests:
We analyse results of numerical simulations of reactive shock-bubble interaction with detailed chemistry. The interaction of the Richtmyer–Meshkov instability and shock-induced ignition of a stoichiometric H 2-O 2 gas mixture is... more
We analyse results of numerical simulations of reactive shock-bubble interaction with detailed chemistry. The interaction of the Richtmyer–Meshkov instability and shock-induced ignition of a stoichiometric H 2-O 2 gas mixture is investigated. Different types of ignition (deflagration and detonation) are observed at the same shock Mach number of Ma = 2. 30 upon varying initial pressure. Due to the convex shape of the bubble, shock focusing leads to a spot with high pressure and temperature. Initial pressures between p 0 = 0. 25 − 0. 75 atm exhibit low pressure reactions, dominated by H , O , OH production and high pressure chemistry driven by HO 2 and H 2 O 2. Deflagration is observed for the lowest initial pressure. Increasing pressure results in smaller induction times and ignition, followed by a detonation wave. The spatial and temporal evolution of the gas bubble is highly affected by the type of ignition. The Richtmyer–Meshkov instability and the subsequent Kelvin–Helmholtz instabilities develop with a high reaction sensitivity. Mixing is significantly reduced by both reaction types. The strongest effect is observed for detonation.
Research Interests:
Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low-and high-fidelity models... more
Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low-and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high-and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES-RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES-RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.
Research Interests:
We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic... more
We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence statistics that are very similar to the implicit LES results. However, while the explicit LES requires a tailored high-order low-dissipative numerical method that applies numerical dissipation only in shock normal direction, no such ad hoc adjustments are necessary with the proposed implicit LES method.
Research Interests:
Research Interests:
Approaches to large eddy simulation where subgrid-scale model and numerical discretization are fully merged are called implicit large eddy simulation (ILES). Recently, we have proposed a systematic framework for development, analysis, and... more
Approaches to large eddy simulation where subgrid-scale model and numerical discretization are fully merged are called implicit large eddy simulation (ILES). Recently, we have proposed a systematic framework for development, analysis, and optimization of nonlinear discretization schemes for ILES [ Hickel et al., J. Comput. Phys. 213, 413(2006) ]. The resulting adaptive local deconvolution method (ALDM) provides a truncation error which acts as a subgrid-scale model consistent with asymptotic turbulence theory. In the present paper ALDM is applied to incompressible, turbulent channel flow to analyze the implicit model for wall-bounded turbulence. Computational results are presented for Reynolds numbers, based on friction velocity and channel half-width, of Reτ = 180, Reτ = 395, Reτ = 590, and Reτ = 950. All simulations compare well with direct numerical simulation data and yield better results than the dynamic Smagorinsky model at the same resolution. The results demonstrate that the implicit model ALDM provides an accurate prediction for wall-bounded turbulence although model parameters have been calibrated for the infinite Reynolds number limit of isotropic turbulence. The near-wall accuracy can be further improved by a simple modification which is described in the paper.
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The objective of this project was the analysis and the control of local truncation errors in large eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic... more
The objective of this project was the analysis and the control of local truncation errors in large eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a non-linear discretization method is developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model which accurately represents the effects of unresolved turbulence.
Research Interests:
The adaptive local deconvolution method (ALDM) is proposed as a new nonlinear discretization scheme designed for implicit large-eddy simulation (ILES) of turbulent flows. In ILES the truncation error of the discretization of the... more
The adaptive local deconvolution method (ALDM) is proposed as a new nonlinear discretization scheme designed for implicit large-eddy simulation (ILES) of turbulent flows. In ILES the truncation error of the discretization of the convective terms functions as a subgrid-scale model. Therefore, the model is implicitly contained within the discretization, and an explicit computation of model terms becomes unnecessary. The discretization is based on a solution-adaptive deconvolution operator which allows to control the truncation error. Deconvolution parameters are determined by an analysis of the spectral numerical viscosity. An automatic optimization based on an evolutionary algorithm is employed to obtain a set of parameters which results in an optimum spectral match for the numerical viscosity with theoretical predictions for isotro- pic turbulence. Simulations of large-scale forced and decaying three-dimensional homogeneous isotropic turbulence show an excellent agreement with theory and experimental data and demonstrate the good performance of the implicit model. As an example for transitional flows, instability and breakdown of the three-dimensional Taylor–Green vortex are considered. The implicit model correctly predicts instability growth and transition to developed turbulence. It is shown that the implicit model performs at least as well as established explicit models.
Research Interests:
A new approach for the construction of implicit subgrid-scale models for large-eddy simulation based on adaptive local deconvolution is proposed. An approximation of the unfiltered solution is obtained from a quasi-linear combination of... more
A new approach for the construction of implicit subgrid-scale models for large-eddy simulation based on adaptive local deconvolution is proposed. An approximation of the unfiltered solution is obtained from a quasi-linear combination of local interpolation polynomials. The physical flux function is modeled by a suitable numerical flux function. The effective subgrid-scale model can be determined by a modified-differential equation analysis. Discretization pa- rameters which determine the behavior of the implicit model in regions of developed turbulence can be adjusted so that a given explicit subgrid-scale model is recovered to leading order in filter width. Alternatively, improved discretization parameters can be found directly by evolutionary optimization. Computational results for stochastically forced and decaying Burgers turbulence are provided. An assessment of the computational experiments shows that results for a given explicit subgrid-scale model can be matched by computations with an implicit representation. A considerable improvement can be achieved if instead of the parameters matching an explicit model discretization parameters determined by evolutionary optimization are used.
Research Interests:
Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain... more
Further development of Large Eddy Simulation (LES) faces as major obstacle the strong coupling between subgrid-scale (SGS) model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. In this paper, we explore how implicit SGS models can be derived systematically and propose a procedure for design, analysis, and optimization of nonlinear discretizations. Implicit LES can be made rigorous by requiring that the numerical dissipation approximates the SGS dissipation obtained from the analysis of nonlinear interactions in turbulence.
Research Interests:
We propose a method for quantifying the effective numerical dissipation rate and effective numerical viscosity in Computational Fluid Dynamics (CFD) simulations. Different from previous approaches that were formulated in spectral space,... more
We propose a method for quantifying the effective numerical dissipation rate and effective numerical viscosity in Computational Fluid Dynamics (CFD) simulations. Different from previous approaches that were formulated in spectral space, the proposed method is developed in a physical-space representation and allows for determining numerical dissipation rates and viscosities locally, that is, at the individual cell level, or for arbitrary subdomains of the computational domain. The method is self-contained and uses only the results produced by the Navier-Stokes solver being investigated. As no further information is required, it is suitable for a straightforward quantification of numerical dissipation as a post-processing step. We demonstrate the method’s capabilities on the example of implicit large-eddy simulations of a three-dimensional Taylor-Green vortex flow, serving as a test flow going through laminar, transitional, and turbulent stages of time evolution. For validation, we compare results for the effective numerical dissipation rate with exact reference data we obtained with an accurate, spectral-space approach.
Research Interests:
The subgrid-scale (SGS) modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been recently extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has... more
The subgrid-scale (SGS) modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been recently extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed ...
Research Interests:
Further development of Large-Eddy Simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing... more
Further development of Large-Eddy Simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The term implicit LES is used to indicate approaches that merge SGS model and numerical discretization. In this paper, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) is extended to LES of passive-scalar mixing. The resulting method is discussed with respect to its numerical and turbulence-theoretical background. We demonstrate that implicit LES allows for reliable predictions of the turbulent transport of passive scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers
Research Interests:
Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing... more
Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The name “implicit LES” is used for approaches that merge the SGS model and numerical discretization. In this paper, the implicit SGS modeling environment provided by the adaptive local deconvolution method is extended to LES of passive-scalar mixing. The resulting adaptive advection algorithm is discussed with respect to its numerical and turbulence-theoretical background. We demonstrate that the new method allows for reliable predictions of the turbulent transport of passive scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers.
Research Interests:
The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme's... more
The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme's truncation error and the subgrid-scale model are linked, which ...
Research Interests:
Turbulence modeling and the numerical discretization of the NavierStokes equations are strongly coupled in large-eddy simulations (LES). The trunca-tion error of common approximations for the convective terms can outweigh the effect of a... more
Turbulence modeling and the numerical discretization of the NavierStokes equations are strongly coupled in large-eddy simulations (LES). The trunca-tion error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale (SGS) ...
Research Interests:
We correct a data processing error in the article ‘‘Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex” by Dieter Fauconnier, Chris De Langhe and... more
We correct a data processing error in the article ‘‘Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex” by Dieter Fauconnier, Chris De Langhe and Erik Dick published in the Journal of Computational Physics 228 (2009), pp. 8053–8084.
Research Interests:
Research Interests:
Research Interests:
Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and... more
Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. Relevant dis- cretizations are e.g. finite-volume schemes with a nonlinear regularization to maintain nonlinear stability. Whereas previous approaches in implicit subgrid-scale (SGS) model- ing employed available discretization schemes without analyzing the effective SGS model, and not incorporating physical modeling approaches into the implicit model, we have de- veloped an approach where a full coupling of SGS model and discretization scheme is accomplished. The ALDM (Adaptive Local Deconvolution Method) approach is introduced as an implicit subgrid-scale modeling environment and discussed with respect to its nu- merical and turbulence-theoretical background. We summarize recent accomplishments in terms of complex flows computed successfully with ALDM and provide a brief outlook on future work.
Research Interests:
The adaptive local deconvolution method (ALDM) [9] provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Exploiting numerical truncation errors, the subgrid scale (SGS) model of ALDM is... more
The adaptive local deconvolution method (ALDM) [9] provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Exploiting numerical truncation errors, the subgrid scale (SGS) model of ALDM is implicitly contained within the discretization. An explicit computation of model terms therefore becomes unnecessary. Subject of the present paper is a modification of the numerical algorithm that allows for reducing the amount of computational operations without affecting the quality of the results. Computational results for isotropic turbulence and plane channel flow show that the simplified adaptive local deconvolution (SALD) method performs similarly to the original method ALDM and at least as well as established explicit models.
Research Interests:
The adaptive local deconvolution method (ALDM) provides a system- atic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Ex- ploiting numerical truncation errors, the subgrid scale model of ALDM is implicitly... more
The adaptive local deconvolution method (ALDM) provides a system- atic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Ex- ploiting numerical truncation errors, the subgrid scale model of ALDM is implicitly contained within the discretization. An explicit computation of model terms there- fore becomes unnecessary. Subject of the present paper is the efficient implemen- tation and the application to large-scale computations of this method. We propose a modification of the numerical algorithm that allows for reducing the amount of computational operations without affecting the quality of the LES results. Computa- tional results for isotropic turbulence and plane channel flow show that the proposed simplified adaptive local deconvolution (SALD) method performs similarly to the original ALDM and at least as well as established explicit models.
Research Interests:
The numerical truncation error of vortex-in-cell methods is analyzed a-posteriori through the effective spectral numerical viscosity for simulations of three-dimensional isotropic turbulence. The interpolation kernels used for... more
The numerical truncation error of vortex-in-cell methods is analyzed a-posteriori through the effective spectral numerical viscosity for simulations of three-dimensional isotropic turbulence. The interpolation kernels used for velocity-smoothing and re-meshing are identified as the most relevant components affecting the shape of the spectral numerical viscosity as a function of wave number. A linear combination of well-known standard kernels leads to new kernels assigned to the specific use for implicit large-eddy simulation of turbulent flows, i.e. their truncation errors acts as subgrid-scale model. Numerical results are provided to show the potential and drawbacks of the approach.
Research Interests:
Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and... more
Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. Relevant discretizations are e.g. finite-volume schemes with a nonlinear regularization to maintain nonlinear stability. Whereas previous approaches in implicit subgrid-scale (SGS) model- ing employed available discretization schemes without analyzing the effective SGS model, and not incorporating physical modeling approaches into the implicit model, we have developed an approach where a full coupling of SGS model and discretization scheme is accomplished. The ALDM (Adaptive Local Deconvolution Method) approach is introduced as an implicit subgrid-scale modeling environment and discussed with respect to its numerical and turbulence-theoretical background. We summarize recent accomplishments in terms of complex flows computed successfully with ALDM and provide a brief outlook on future work.
Research Interests:
Research Interests:
Subgrid-scale models in LES operate on a range of scales which is marginally resolved by the discrete approximation. Accordingly, the discrete approximation method and the subgrid-scale model are linked. One can exploit this link by... more
Subgrid-scale models in LES operate on a range of scales which is marginally resolved by the discrete approximation. Accordingly, the discrete approximation method and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or vice versa. Approaches where SGS models and numerical discretizations are fully linked are called implicit SGS models. Different approaches to SGS modeling can be taken. Mostly, given nonlinearly stable discretizations schemes for the convective fluxes are used as main element of implicit SGS models. Recently we have proposed to design nonlinear discretization schemes in such a way that their truncation error functions as SGS model in regions where the flow is turbulent and as a second-order accurate discretization in regions where the flow is laminar. In this paper we review the current status on this so-called adaptive local deconvolution method (ALDM) and provide some application results.
Research Interests:
In an implicit subgrid-scale modeling the truncation error of a numerical scheme is used to model the effects of the unresolved scales. It has been previously shown that dissipative properties of a truncation error for an arbitrary... more
In an implicit subgrid-scale modeling the truncation error of a numerical scheme is used to model the effects of the unresolved scales. It has been previously shown that dissipative properties of a truncation error for an arbitrary numerical scheme can be expressed in a form of a spectral numerical viscosity. We employ an extended WENO scheme where the effective model depends on six free parameters through the solution-adaptive weights. To determine physically appropriate values of the free parameters for the scheme we minimize, by means of an automatic optimization that employs an evolutionary algorithm, the r.m.s. deviation of its averaged numerical viscosity from the spectral eddy viscosity predicted by the analytical theories of turbulence. The method selects a set of parameters which yield an excellent match with the theoretical requirements: the numerical eddy viscosity exhibits a low-wavenumber plateau at the correct level and a cusp near the cut-off wavenumber close to the theoretical shape and with a correct amplitude. To validate the choice of the parameters we have performed simulations of forced and freely decaying three-dimensional homogeneous isotropic turbulence with vanishing molecular viscosity. After the Kolmogorov cascade has been established from the initial state, the energy spectrum decays in a self similar manner, preserving -5/3 slope up to the largest wavenumbers and with a value of the Kolmogorov constant of about 1.8.
Research Interests:
Large-Eddy Simulation has been recognized as one of the major tools for the numerical simulation of complex turbulent flows, in events when more accessible alternative approaches, such as statistically averaged Navier-Stokes equations... more
Large-Eddy Simulation has been recognized as one of the major tools for the numerical simulation of complex turbulent flows, in events when more accessible alternative approaches, such as statistically averaged Navier-Stokes equations (Reynolds-averaged Navier-Stokes equations - RANS), fail. This is in particular the case, when complex flow phenomena (reaction, fluid-structure interaction, interfaces, shocks) introduce additional non-turbulent temporal or spatial scales. It is known since quite some time that the nonlinear truncation error of some classes of discretization schemes for the Navier-Stokes equations not only interferes with explicitly added subgrid-scale (SGS) models but also can provide some SGS closure when no model is added at all. More recent analyses of such schemes have outlined the way to a more systematic procedure for such no-model approaches, leading to what is called now implicit LES (ILES). With ILES no subgrid-scale model is added to the discretized Navier- Stokes equations, and SGS modeling is left solely to the numerical truncation error. In this contribution we will outline a theory of ILES which allows for physically motivated modeling of the nonlinear truncation error, called adaptive local deconvolution method (ALDM), and demonstrate its feasibility for reliable LES of a wide range of turbulent flow configurations.
Research Interests:
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural... more
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance equations. Upon each linearization step, the number of unknowns is strongly decreased by using modal reduction, which leads to a substantial gain in computational efficiency. Through adaptive re-calibration and truncation augmentation whenever a non-dimensional deformation threshold is exceeded, we ensure that the reduced modal basis maintains arbitrary accuracy for small and large deformations. Our novel model is embedded into a partitioned, loosely coupled finite volume-finite element framework, in which the structural interface motion within the Eulerian fluid solver is accounted for by a conservative cut-element immersed-boundary method. Applications to the aeroelastic instability of a flat plate at supersonic speeds, to an elastic panel placed within a shock tube, and to the shock induced buckling of an inflated thin semi-sphere demonstrate the efficiency and accuracy of the method.
Research Interests: Mechanical Engineering, Computational Physics, Computational Fluid Dynamics, Fluid structure interaction, Large Eddy Simulation, and 7 moreShock Waves, Immersed Boundary Methods, Reduced order modeling, Gas Dynamics, Aeroelastic Flutter, Adaptive Mesh Refinement, and Fluid Structure Interaction (FSI)
Research Interests:
Research Interests:
The conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on Cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving... more
The conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on Cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries. We demonstrate that an approximation of moving interfaces by a level-set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water. By introducing an exact reconstruction of the cut-cell properties directly based on a surface triangulation of the immersed boundary, we are able to recover the correct flow evolution free of numerical artifacts. The new method is based on cut-elements. It provides sub-cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner. We validate our method with canonical flows around oscillating cylinders. We demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects. In particular, we show that the cavitating flow through a closing fuel injector control valve, which is an example for a complex application with interaction of stationary and moving parts, can be predicted by the method.
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We present a loosely-coupled approach for the solution of the thermo-fluid-structure interaction problem, based on Dirichlet-Neumann partitioning. A cartesian grid finite volume scheme, with conservative interface method is used for the... more
We present a loosely-coupled approach for the solution of the thermo-fluid-structure interaction problem, based on Dirichlet-Neumann partitioning. A cartesian grid finite volume scheme, with conservative interface method is used for the fluid and a finite-element scheme for the thermo-structure problem. Special attention is given to the transfer of forces, temperatures and to the structural positions. The structural surface is repre- sented by a level set function in the fluid code. The velocity and temperature field required for the coupling are interpolated from structural values on the zero-contour level set surface. Data transfer between the two codes is performed via message passing interface. The proposed method is tested for a cooling-process of a heated metal bar by mean of an external laminar boundary layer flow. Results show that the presented approach is able to handle the complexity of the three-field problem.
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We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume... more
We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume discretization of the incompressible Navier–Stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained. A level-set technique is used for description and tracking of the interface geometry, so that an extension of the method to moving boundaries and flexible walls is straightforward. Numerical stability is ensured for small cells by a conservative mixing procedure. Discrete conservation and sharp representation of the fluid–solid interface render the method particularly suitable for Large-Eddy Simulations of high-Reynolds number flows. Accuracy, second- order grid convergence and robustness of the method is demonstrated for several test cases: inclined channel flow at Re = 20, flow over a square cylinder at Re = 100, flow over a circular cylinder at Re = 40, Re = 100 and Re = 3900, as well as turbulent channel flow with periodic constrictions at Re = 10,595.
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The success of Large-Eddy Simulations (LES) of wall-bounded turbulence depends strongly on an accurate representation of the flow near the boundaries. Since in implicit LES the truncation error of the numerical discretization itself... more
The success of Large-Eddy Simulations (LES) of wall-bounded turbulence depends strongly on an accurate representation of the flow near the boundaries. Since in implicit LES the truncation error of the numerical discretization itself functions as SGS model, the order of accuracy of the discretization should be maintained near the boundary. In this paper, we analyze the performance of implicit LES for predicting turbulent flows along complex geometries. For the representation of wall-boundaries two different approaches are compared: (A) the case of body-fitted grids, and (B) a novel second-order accurate Conservative Immersed Interface Method (CIIM) for representing boundaries of arbitrary shape on Cartesian grids. The need for mapping domain boundaries on the grid raises the question whether a comparable accuracy with body-fitted grids can be achieved. In both (A) and (B) we employ the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The assessment is carried out on the example of the flow over a circular cylinder at Re = 3900. Two simulations with comparable numerical resolution are performed and com- pared to experimental reference data. Both methods result in similar accuracy for turbulent statistics and mean integral quantities. This demonstrates that ALDM on Cartesian grids is a feasible and efficient approach to simulate turbulent flows on complex domains.
Research Interests:
Implicit Large Eddy Simulation (ILES) has shown considerable potential for the efficient representation of physically complex flows, see e.g. [4]. In ILES the truncation error of the discretization of the convective terms acts as a... more
Implicit Large Eddy Simulation (ILES) has shown considerable potential for the efficient representation of physically complex flows, see e.g. [4]. In ILES the truncation error of the discretization of the convective terms acts as a subgrid-scale model which is therefore implicit to the discretization. In this context, the Adaptive Local Deconvolution Method (ALDM) [5,6] uses a discretization based on solution-adaptive deconvolution which allows to control the nonlinear truncation error. Deconvolution parameters are determined by an analysis of the spectral numerical viscosity. ALDM is incorporated into finite volume numerical solver for the incompressible Navier–Stokes equations based on finite volumes on a staggered grid. Applications to generic configurations, such as isotropic turbulence [5], plane channel flow [7], and turbulent boundary layer separation [4], show excellent agreement with the corresponding results from theory, experiments, or direct numerical simulations. Given this performance the motivation is to use ALDM for the investigation of complex flow configurations of practical relevance.
Research Interests:
Computational fluid dynamics for complex industrial applications up to now usually refers to RANS (Reynolds-Averaged Navier Stokes) simulations with appropriate statistical turbulence models. Existing RANS turbulence models, however,... more
Computational fluid dynamics for complex industrial applications up to now usually refers to RANS (Reynolds-Averaged Navier Stokes) simulations with appropriate statistical turbulence models. Existing RANS turbulence models, however, often fail to accurately predict separated and reattached flows. Better results but higher computational costs are expected from Large-Eddy Simulations (LES). It is therefore a common interest to develop efficient and robust LES approaches for the prediction of complex flows with industrial relevance. An efficient representation of physically complex flows can be achieved with an Implicit LES approach, where the truncation error of the numerical discretization itself functions as turbulence model. We employ an Adaptive Local Deconvolution Method (ALDM) implemented in a solver for the incompressible Navier-Stokes equations where the domain is discretized on a Cartesian grid. Boundaries of arbitrary shape are represented by a second-order accurate Conservative Immersed Interface Method (CIIM). In this report we point out the computational aspects of CIIM in the framework of ILES on the example of the flow over a circular cylinder at Re = 3,900. As benchmark an ILES with ALDM on body-fitted grids and with a usual formulation of the wall-boundary condition is taken. Two simulations with similar numerical resolution are compared with experimental reference data. Also compared are their computational cost.
Research Interests:
ABSTRACT On the application of WKB theory for the simulation of multi-scale gravity wave interactions
Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of... more
Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.
Research Interests:
The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment,... more
The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure. Both models employ an implicit parameterization of the subgrid-scale turbulence by the Adaptive Local Deconvolution Method (ALDM). One part of the laboratory procedure, which is commonly neglected in simulations, is the annulus spin-up. During this phase the annulus is accelerated from a state of rest to a desired angular velocity. We use a simple modelling approach of the spin-up to investigate whether it increases the agreement between experiment and simulation. The model validation compares the azimuthal mode numbers of the baroclinic waves and does a principal component analysis of time series of the temperature field. The Eady model of baroclinic instability provides a guideline for the qualitative understanding of the observations.
Research Interests:
The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature... more
The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain “benchmarks” have been created that can later be used as test cases for atmospheric numerical model validation.
Research Interests:
A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis... more
A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.
Research Interests:
The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity... more
The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.
Research Interests:
The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional... more
The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and time-dependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problem that occurs in WKB ray-tracing models when the wave number becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volume method and a Lagrangian ‘phase-space ray tracer’ that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wave number. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model, as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parametrizations of atmospheric gravity waves in weather and climate models.
Research Interests:
We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters... more
We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.
Research Interests:
Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of... more
Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.
Research Interests:
Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series... more
Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.
Research Interests:
The dynamics of three-dimensional turbulence under the influence of density stratification can be classified in different regimes that differ fundamentally; see Brethouwer et al. (2007) for a good review. Up to now, strongly stratified... more
The dynamics of three-dimensional turbulence under the influence of density stratification can be classified in different regimes that differ fundamentally; see Brethouwer et al. (2007) for a good review. Up to now, strongly stratified turbulent flows were mainly studied by direct numerical simulations (DNS). The available computer resources, however, limit the application of DNS to Reynolds numbers that are too small for studying the regime of real scale atmospheric problems. Large Reynolds number flows in general can be simulated efficiently by large- eddy simulation (LES). However, most subgrid-scale (SGS) models for LES are not suitable for stratified flows, as local isotropy of the SGS turbulence is assumed, and therefore require ad-hoc modifications. We propose an implicit subgrid-scale model that handles anisotropic turbulence in a straight forward way without any limiting assumptions.
We solve the non-linear Boussinesq equations for a fluid with a constant background stratification using a finite- volume solver. DNS are performed with a 4th order centered scheme. The implicit sub-grid scale model is based on the Adaptive Local Deconvolution Method (ALDM) for the incompressible Navier-Stokes equations (Hickel et al. 2006) and the ALDM for passive scalar transport (Hickel et al. 2007). The turbulence theoretical background of ALDM and the numerical details will be given in the full paper.
Two generic test cases are considered. First, we computed the temporal evolution of a 3D Taylor-Green-vortex (Brachet 1991) under the influence of stratification. We ran several fully resolved simulations with up to 7683 cells and corresponding implicit LES with 643 cells. The LES show good agreement with a fully resolved DNS. The total dissipation rate is predicted correctly and also the proportions of kinetic and potential energy are well estimated. We repeated the LES and DNS at a number of different Froude and Reynolds numbers. In all cases we found good agreement between LES and DNS.
As a second test case, we computed homogeneous stratified turbulence (Brethouwer et al. 2007) at different Froude numbers. The Boussinesq equations are supplemented by a volume force that acts on the large horizontal scales only. Three-dimensional structures with finite vertical length scale develop only due to stratification. To ensure complete resolution of the smallest scales, the DNS domain contained about 900 million cells. We studied the influence of varying stratification on the averaged longitudinal kinetic energy spectra in the vertical and horizontal directions.
We will discuss the energy budget, dissipation rates, spectra of turbulence, turbulence length scales, and anisotropy of the DNS and draw conclusions with respect to SGS modeling. Our computational results support that implicit LES with ALDM can be a suitable tool for the investigation of stratified turbulence. This will enable us to compute and characterize atmospheric turbulence beyond the reach of DNS with reasonable accuracy at low computational costs.
We solve the non-linear Boussinesq equations for a fluid with a constant background stratification using a finite- volume solver. DNS are performed with a 4th order centered scheme. The implicit sub-grid scale model is based on the Adaptive Local Deconvolution Method (ALDM) for the incompressible Navier-Stokes equations (Hickel et al. 2006) and the ALDM for passive scalar transport (Hickel et al. 2007). The turbulence theoretical background of ALDM and the numerical details will be given in the full paper.
Two generic test cases are considered. First, we computed the temporal evolution of a 3D Taylor-Green-vortex (Brachet 1991) under the influence of stratification. We ran several fully resolved simulations with up to 7683 cells and corresponding implicit LES with 643 cells. The LES show good agreement with a fully resolved DNS. The total dissipation rate is predicted correctly and also the proportions of kinetic and potential energy are well estimated. We repeated the LES and DNS at a number of different Froude and Reynolds numbers. In all cases we found good agreement between LES and DNS.
As a second test case, we computed homogeneous stratified turbulence (Brethouwer et al. 2007) at different Froude numbers. The Boussinesq equations are supplemented by a volume force that acts on the large horizontal scales only. Three-dimensional structures with finite vertical length scale develop only due to stratification. To ensure complete resolution of the smallest scales, the DNS domain contained about 900 million cells. We studied the influence of varying stratification on the averaged longitudinal kinetic energy spectra in the vertical and horizontal directions.
We will discuss the energy budget, dissipation rates, spectra of turbulence, turbulence length scales, and anisotropy of the DNS and draw conclusions with respect to SGS modeling. Our computational results support that implicit LES with ALDM can be a suitable tool for the investigation of stratified turbulence. This will enable us to compute and characterize atmospheric turbulence beyond the reach of DNS with reasonable accuracy at low computational costs.
Research Interests:
ABSTRACT A systematic approach to the direct numerical simulation (DNS) of breaking upper-mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector... more
ABSTRACT A systematic approach to the direct numerical simulation (DNS) of breaking upper-mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25000, relevant to breaking waves in the upper mesosphere, make the three-dimensional DNS tractable with present day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.
Research Interests:
ABSTRACT The dynamics of internal gravity waves is modelled using WKB theory in position wavenumber phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a... more
ABSTRACT The dynamics of internal gravity waves is modelled using WKB theory in position wavenumber phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and time-dependent horizontal-mean horizontal wind. The mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problem that occurs in WKB ray-tracing models when the wavenumber becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volume method, and a Lagrangian “phase-space ray tracer” that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wavenumber. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet, and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parameterizations of atmospheric gravity waves in weather and climate models.
Research Interests:
Research Interests:
Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of... more
Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate
simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with
direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.
simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with
direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.
Research Interests:
We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters... more
We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.
Research Interests:
Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyancy forces make the energy spectra anisotropic and change the way in which energy is converted and transported within the spectrum. Based on... more
Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyancy forces make the energy spectra anisotropic and change the way in which energy
is converted and transported within the spectrum. Based on results of direct numerical simulations of homogeneous stratified turbulence, we show two–dimensional energy spectra at different intensities of stratification. Additionally, we analyze the spectral contribution of the different terms in the energy transport equations to the overall energy budget and trace the flow energy through all its conversions and transport in spectral
space from the injection at large scales to the molecular dissipation on small scales.
is converted and transported within the spectrum. Based on results of direct numerical simulations of homogeneous stratified turbulence, we show two–dimensional energy spectra at different intensities of stratification. Additionally, we analyze the spectral contribution of the different terms in the energy transport equations to the overall energy budget and trace the flow energy through all its conversions and transport in spectral
space from the injection at large scales to the molecular dissipation on small scales.
Research Interests:
A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis... more
A systematic approach to the direct numerical simulation (DNS) of breaking upper
mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is
presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase
velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and
structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional
velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is
then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to
three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the
computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to
breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day
computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave,
a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity
wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of
the wave and generation of turbulence is faster in three dimensions, but the results are otherwise
qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the
domain and initial condition are chosen properly.
mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is
presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase
velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and
structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional
velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is
then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to
three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the
computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to
breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day
computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave,
a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity
wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of
the wave and generation of turbulence is faster in three dimensions, but the results are otherwise
qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the
domain and initial condition are chosen properly.
Research Interests:
Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been... more
Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulence-theoretical background by Hickel et al., 2007. Results demonstrate that this method allows for reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. We now use this new method to perform LES of a confined rectangular-jet reactor and compare obtained results with experimental data available in the literature.
Research Interests:
Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been... more
Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulence-theoretical background by Hickel et al., 2007. Results demonstrate that this method allows for reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. We now intend to use this new method to perform LES of a confined rectangular-jet reactor and compare obtained results to experimental data available in the literature.
Research Interests:
The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the sub- grid-scalemodel are linked. One can... more
The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the sub- grid-scalemodel are linked. One can exploit this link by developing discretizationmethods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGSmodel. The resulting so-called adaptive local deconvolutionmethod (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper,ALDMis evaluated for the separated flowthrough a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2, 808 and Re = 10, 595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered phys- ically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.
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"Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble... more
"Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, wind turbines, and propellers consist of a laminar boundary layer near the leading edge that is often followed by a laminar separation bubble and transition to turbulence further downstream. Typical RANS turbulence models are inadequate for such flows. Direct numerical simulation (DNS) is the most reliable, but is also the most computationally expensive alternative. This work assesses the capability of Immersed Boundary (IB) methods and Large Eddy Simulations (LES) to reduce the computational requirements for such flows and still provide high quality results. Two-dimensional and three-dimensional simulations of a laminar separation bubble on a NACA-0012 airfoil at Re = 50 000 at 5 degrees of incidence have been performed with an IB code and a commercial code using body fitted grids. Several Subgrid Scale (SGS) models have been implemented in both codes and their performance evaluated. For the two-dimensional simulations with the IB method the results show good agreement with DNS benchmark data for the pressure coefficient Cp and the friction coefficient Cf but only when using dissipative numerical schemes. There is evidence that this behavior can be attributed to the ability of dissipative schemes to damp numerical noise coming from the IB. For the three-dimensional simulations the results show a good prediction of the separation point, but inaccurate prediction of the reattachment point unless full DNS resolution is used. The commercial code shows good agreement with the DNS benchmark data in both two and three-dimensional simulations, but the presence of significant, unquantified numerical dissipation prevents a conclusive assessment of the actual prediction capabilities of very coarse LES with low order schemes in general case."
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The presented investigation includes a combined experimental-numerical approach to quantify the wake vortex system of a high-agility aircraft from the near field up to the far field. Detailed near-field data are obtained by low-speed... more
The presented investigation includes a combined experimental-numerical approach to quantify the wake vortex system of a high-agility aircraft from the near field up to the far field. Detailed near-field data are obtained by low-speed wind-tunnel tests on a delta-canard configuration of 1:15 scale. The measurements are performed at several angles of attack applying advanced hot-wire anemometry. For a wake distance of up to 16 wing spans, mean and turbulent velocity fields are measured. The upstream data are used to initialize implicit large-eddy simulations aimed to compute the velocity fields of the wake vortex system over a wake distance of up to 50 spans. Here, a validation case is shown comparing measured and calculated wake data over a distance from 4 to 16 spans, with the implicit large-eddy simulations initialized by the measured quantities at a position of two wing spans. Compared with the experimental data, the numerical results show the expected lateral and vertical movement of the wake vortex system due to the interaction of the single vortices. The distributions of axial vorticity, crossflow velocities, and turbulence intensities match well with the experimental data. In addition, the dissipation process can be observed, resulting in a reduction of circulation. In the context of this study, the measured and computed velocity fields will be used to determine unsteady aerodynamic loads acting on a fighter aircraft encountering the wake. This is of great importance as wake induction may result in critical structural dynamic loads.
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Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing... more
Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The adaptive local deconvolution method (ALDM) is an approach to LES of turbulent flows that represents a full coupling of SGS model and discretization scheme. To provide evidence for the validity of this new SGS model, well resolved large-eddy simulations of a fully turbulent flat-plate boundarylayer flow subjected to a constant adverse pressure gradient are conducted. Flow parameters are adapted to an available experiment. The Reynolds number based on the local free-stream velocity and momentum thickness is 670 at the inflow and 5100 at the separation point. Clauser’s pressure-gradient parameter
increases monotonically from 0 up to approximately 100 since a constant pressure gradient is prescribed. The adverse pressure gradient leads to a highly unsteady and massive separation of the boundary layer. The numerical predictions agree well with theory and experimental data.
increases monotonically from 0 up to approximately 100 since a constant pressure gradient is prescribed. The adverse pressure gradient leads to a highly unsteady and massive separation of the boundary layer. The numerical predictions agree well with theory and experimental data.
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3D-PIV and 2D-LDA measurements in a fully turbulent boundary with adverse pressure gradient have been performed. Two types of surfaces were investigated: a smooth surface and a surface with riblets aligned in main flow direction. Particle... more
3D-PIV and 2D-LDA measurements in a fully turbulent boundary with adverse pressure gradient have been performed. Two types of surfaces were investigated: a smooth surface and a surface with riblets aligned in main flow direction. Particle image velocimetry was used to determine the influence of the surface structure on large-scale structures in the near wall region whereas profiles of mean and fluctuating velocity inside the boundary layer were acquired by laser Doppler anemometry. Significant changes of size and location of near-wall vortex structures were found ongoing with a deformation of the mean-velocity profile due to the riblet surface.
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The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme’s truncation error and the subgrid-scale... more
The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme’s truncation error and the subgrid-scale model are linked, which raises the question of how accurate the computational results are. The link between the SGS model and truncation error can be beneficially exploited by developing discretization methods for subgrid-scale modeling, or vice versa. Approaches where the SGS model and the numerical discretization scheme are fully merged are called implicit LES (ILES) methods.
In order to improve on modeling uncertainties, a systematic framework is proposed for design, analysis, and optimization of nonlinear discretization schemes for implicit LES. The resulting adaptive local deconvolution method (ALDM) for implicit LES is a finite volume method based on a nonlinear deconvolution operator and a numerical flux function. Free parameters inherent to the discretization allow to control the truncation error. They are calibrated in such a way that the truncation error acts as a physically motivated SGS model. An automatic optimization based on an evolutionary algorithm is employed to obtain a set of parameters that results in an optimum match between the spectral numerical viscosity and theoretical predictions of the spectral eddy viscosity for isotropic turbulence. The method is formulated for LES of turbulent flows governed by the incompressible Navier-Stokes equations and for passive-scalar mixing.
ALDM has shown the potential for providing a reliable, accurate, and efficient method for LES. Various applications, such as three-dimensional homogeneous isotropic turbulence, transitional and turbulent plane channel flow, and turbulent boundary-layer separation, demonstrate the good performance of the implicit model. Computational results agree well with theory and experimental data and show that the implicit SGS model performs at least as well as established explicit models, for most considered applications the performance is even better. This is possible because physical reasoning is incorporated into the design of the discretization scheme and discretization effects are fully taken into account within the SGS model formulation.
In order to improve on modeling uncertainties, a systematic framework is proposed for design, analysis, and optimization of nonlinear discretization schemes for implicit LES. The resulting adaptive local deconvolution method (ALDM) for implicit LES is a finite volume method based on a nonlinear deconvolution operator and a numerical flux function. Free parameters inherent to the discretization allow to control the truncation error. They are calibrated in such a way that the truncation error acts as a physically motivated SGS model. An automatic optimization based on an evolutionary algorithm is employed to obtain a set of parameters that results in an optimum match between the spectral numerical viscosity and theoretical predictions of the spectral eddy viscosity for isotropic turbulence. The method is formulated for LES of turbulent flows governed by the incompressible Navier-Stokes equations and for passive-scalar mixing.
ALDM has shown the potential for providing a reliable, accurate, and efficient method for LES. Various applications, such as three-dimensional homogeneous isotropic turbulence, transitional and turbulent plane channel flow, and turbulent boundary-layer separation, demonstrate the good performance of the implicit model. Computational results agree well with theory and experimental data and show that the implicit SGS model performs at least as well as established explicit models, for most considered applications the performance is even better. This is possible because physical reasoning is incorporated into the design of the discretization scheme and discretization effects are fully taken into account within the SGS model formulation.
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The dynamics of the interaction between a shock wave and a turbulent boundary layer in a supersonic flow are investigated by analyzing an LES database that was developed for the flow of a supersonic turbulent boundary layer along a... more
The dynamics of the interaction between a shock wave and a turbulent boundary layer in a supersonic flow are investigated by analyzing an LES database that was developed for the flow of a supersonic turbulent boundary layer along a compression-...
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The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the... more
The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the inter...
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The unsteadiness of shock wave-boundary layer interactions is investigated in a transitional backward-facing step flow at Ma=1:7 and Red0 =13718 using large eddy simulation. The mean and instantaneous flow shows that the laminar inflow... more
The unsteadiness of shock wave-boundary layer interactions is investigated in a transitional backward-facing step flow at Ma=1:7 and Red0 =13718 using large eddy simulation. The mean and instantaneous flow shows that the laminar inflow undergoes a laminar-to-turbulence transition in which Kelvin-Helmholtz vortices form, distort and eventually break down into small hairpin-like vortices. The interaction system features broadband frequency oscillations in a range f d0=u¥ = 0:03 _ 0:23 based on the spectral and statistical analysis. The results of dynamic mode decomposition indicate that the medium-frequency motions centered at f d0=u¥ = 0:06 are related to the shock winkling and the shedding of large coherent vortices, while the lower (centered at f d0=u¥ _ 0:01) and higher ( f d0=u¥ _ 0:1) frequency unsteadiness is associated with the periodical dilatation and shrinking of separation system and the convection of upstream K-H vortices respectively.
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Adaptive mesh refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). Adjoint methods, which are able to localize error... more
Adaptive mesh refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). Adjoint methods, which are able to localize error contributions, can be used to optimize the mesh for computing a physical quantity of interest (e.g. lift, drag) during AMR. When adjoint-based AMR techniques are applied to LES, primal flow solutions are needed to solve the adjoint problem backward in time due to the nonlinearity of Navier-Stokes equations. However, the resources required to store primal flow solutions can be huge, even prohibitive, in practical problems because of the long averaging time for computing statistical quantities. In this paper, a Reduced-Order Model (ROM) based upon Proper Orthogonal Decomposition (POD) is introduced to circumvent this issue. First, an adjoint-based error estimation procedure is verified using a manufactured solution. Then a ROM-driven AMR strategy is studied usin...
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We perform direct numerical simulations of turbulent flow at friction Reynolds number $$Re_\tau \approx 500{-}2000$$ R e τ ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter $$d^+\approx 40-160$$ d +... more
We perform direct numerical simulations of turbulent flow at friction Reynolds number $$Re_\tau \approx 500{-}2000$$ R e τ ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter $$d^+\approx 40-160$$ d + ≈ 40 - 160 and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.
Research Interests: Engineering and Physics
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We present well-resolved RANS simulations of a high-aspect-ratio generic cooling duct configuration consisting of an adiabatic straight feed line followed by a heated straight section ending with a 90° bend. The configuration is... more
We present well-resolved RANS simulations of a high-aspect-ratio generic cooling duct configuration consisting of an adiabatic straight feed line followed by a heated straight section ending with a 90° bend. The configuration is asymmetrically heated with a temperature difference of ∆T = 40 K. As fluid liquid water is used at a Reynolds number of Re b = 110 × 10^3 . The setup follows an experimental reference case, which has also been investigated using a well-resolved LES. The current investigation focuses on the prediction capabilities of different RANS turbulence closure models for the duct flow field, defined by the interaction of secondary flows and turbulent heat transfer. In the straight duct only turbulence-induced secondary flow is present, which becomes weaker along the heated duct due to the viscosity reduction, leading in turn to a reduced mixing. In the curved section, the stronger pressure-induced secondary flow superimposes the turbulence-induced one increasing the mixing of hot and cold fluid. A well-resolved LES serves as comparison database for the straight duct results.
Research Interests: Mechanics and Turbulence
Turbulence in the atmosphere is generally affected by rotation and stratification. The combination of these two effects endows the atmosphere with wavelike motions, which are particularly relevant for the mixing processes in the middle... more
Turbulence in the atmosphere is generally affected by rotation and stratification. The combination of these two effects endows the atmosphere with wavelike motions, which are particularly relevant for the mixing processes in the middle and upper atmosphere. Gravity-waves, for instance, can transfer energy over large distances, carrying energy from where they are created to regions thousands of kilometers away (Fritts and Alexander (2003)). Due to wave instabilities, they break and induce small scale turbulence in the overall large scale flow, thus contributing to the mixing process. In current general circulation models, however, small scale motion is not resolved and instead only parametrized. Hence, understanding the breaking process can potentially lead to improved parametrization models and predictions. Depending on their frequency, gravity-waves can be classified as high-frequency gravity-waves (HGWs) and low-frequency inertia-gravity waves (IGWs). The breaking behavior of IGWs...
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Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic... more
Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/e = 1. In this work, we propose an improved EASSM design that does not involve this precalibration and retains the ratio P/e as a space and time dependent variable. Our model is based on the partial differential evolution equation for the SGS kinetic energy ksgs and the assumption that the ratio P/e evolves slower in time than ksgs. Computational results for simple cases of forced isotropic turbulence show that the new model is able to track the evolution of the SGS kinetic energy significantly better than the dynamic and non-dynamic EASSMs of Marstorp et al. (2009). Also the predicted kinetic energy spectra and resolved dissipation evol...
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Micro-ramps are deployed to prevent boundary layer separation by creating a momentum excess close to the wall. Through Direct Numerical Simulations (DNS) of the base, instantaneous and mean flow, we identify that the perturbation dynamics... more
Micro-ramps are deployed to prevent boundary layer separation by creating a momentum excess close to the wall. Through Direct Numerical Simulations (DNS) of the base, instantaneous and mean flow, we identify that the perturbation dynamics in the wake of the microramp play an essential role in creating the near-wall momentum excess. To identify the origin of the perturbations, we deploy BiGlobal stability analysis on the laminar base flow. We demonstrate that the amplification of the most unstable linear mode is closely related to the time-averaged amplitude of the unsteady perturbations. The flow structure corresponding to this mode has a varicose symmetry with respect to the symmetry plane and matches with the early development of the hairpin vortices in the instantaneous flow field. It is concluded that the varicose instability supported by the laminar base flow represents the mechanism that generates the hairpins.
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We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large-Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and... more
We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large-Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and homogeneous rotating turbulence. We focus on the performance of three models: the dynamic Smagorinsky (DSM) and the standard and dynamic explicit algebraic models as in Marstorp et al. (2009), here refereed to as SEA and DEA. By comparing correlation coefficients, we show that the subgrid scale (SGS) stress tensor is better captured by the EA models. Overall, the DEA leads to the best performance, which is evidenced by comparing how each model reproduces the probability density function (p.d.f.) of the SGS kinetic energy production. Next, we evaluate the approximations that are inherent to EA models such as the model for the pressure-strain correlation. We analyze the performance of three pressure-strain models commonly employed in the RANS framewor...
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The path of laminar-to-turbulent transition behind a backward-facing step (BFS) in the supersonic regime at Ma = 1.7 and Reδ0 = 13718 is investigated using a very well-resolved large eddy simulation (LES). Five distinct stages are... more
The path of laminar-to-turbulent transition behind a backward-facing step (BFS) in the supersonic regime at Ma = 1.7 and Reδ0 = 13718 is investigated using a very well-resolved large eddy simulation (LES). Five distinct stages are identified in the transition process by the visualisation of instantaneous flow. The transition is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the distorted K-H vortices, leading to Λ-shaped vortices, hair-pin vortices and finally to a fully turbulent state around the reattachment location. Spectral analysis and proper orthogonal decomposition (POD) reveal that the low-frequency breathing dynamics also plays a major role in the transition process.
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We present numerical simulations of a reacting shock–bubble interaction with detailed chemistry. The interaction between the Richtmyer-Meshkov instability and shock-induced ignition of a \( {\mathrm{H}}_2-{\mathrm{O}}_2 \) gas mixture is... more
We present numerical simulations of a reacting shock–bubble interaction with detailed chemistry. The interaction between the Richtmyer-Meshkov instability and shock-induced ignition of a \( {\mathrm{H}}_2-{\mathrm{O}}_2 \) gas mixture is investigated. Shock wave Mach numbers in the range of \( Ma=2.13-2.50 \) at a constant initial pressure of \( {p}_0=0.50 \) atm trigger different reaction wave types. Deflagration is induced by a shock wave Mach number of \( Ma=2.13 \) and detonation by \( Ma=2.50 \). The spatial expansion of the bubble, the Richtmyer-Meshkov instability, and the subsequent Kelvin Helmholtz instabilities develop with a high reaction wave sensitivity. Mixing is significantly decreased by both reaction waves types, with detonation waves resulting in the strongest damping.
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The unsteadiness of shock wave-boundary layer interactions is investigated in a transitional backward-facing step flow at Ma= 1.7 and Reδ0 = 13718 using large eddy simulation. The mean and instantaneous flow shows that the laminar inflow... more
The unsteadiness of shock wave-boundary layer interactions is investigated in a transitional backward-facing step flow at Ma= 1.7 and Reδ0 = 13718 using large eddy simulation. The mean and instantaneous flow shows that the laminar inflow undergoes a laminar-to-turbulence transition in which Kelvin-Helmholtz vortices form, distort and eventually break down into small hairpin-like vortices. The interaction system features broadband frequency oscillations in a range f δ0/u∞ = 0.03 ∼ 0.23 based on the spectral and statistical analysis. The results of dynamic mode decomposition indicate that the medium-frequency motions centered at f δ0/u∞ = 0.06 are related to the shock winkling and the shedding of large coherent vortices, while the lower (centered at f δ0/u∞ ≈ 0.01) and higher ( f δ0/u∞ ≈ 0.1) frequency unsteadiness is associated with the periodical dilatation and shrinking of separation system and the convection of upstream K-H vortices respectively.
Research Interests: Engineering, Physics, Computational Physics, Mechanics, Computational Fluid Dynamics, and 11 moreFluid Mechanics, System Dynamics Modeling, Large Eddy Simulation, Turbulent Flows, Shock Waves, Fourier Analysis, Turbulent boundary layer, Mathematical Sciences, Dynamic Systems and Control, Shock Waves Boundary Layer Interaction, and Boundary Layer
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The injection of cryogenic nitrogen with a coflow of warm hydrogen into a supercritical nitrogen atmosphere is studied numerically by means of well resolved large-eddy simulation (LES). The conditions resemble those in liquid-propellant... more
The injection of cryogenic nitrogen with a coflow of warm hydrogen into a supercritical nitrogen atmosphere is studied numerically by means of well resolved large-eddy simulation (LES). The conditions resemble those in liquid-propellant rocket engines. By substituting oxygen with the inert gas nitrogen the setup allows for an isolated view on binary mixing processes near the injector without the influence of combustion. The thermodynamic model is based on the cubic Peng-Robinson equation of state. The LES results are compared with available experimental data demonstrating that the numerical method is suitable to study turbulent binary mixing at transcritical conditions. The following detailed analysis of the thermodynamic conditions that arise in the shear layer reveals that local phase separation may occur for the present injection conditions. The resulting effect on the flow is quantified by an a-posteriori calculation of the two-phase equilibrium conditions in the shear layer. The result indicates a maximum density variation of up to 25% compared to the single-phase calculation.
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Research Interests: Mechanical Engineering, Applied Mathematics, Physics, Computational Physics, Computational Fluid Dynamics, and 12 moreFluid structure interaction, Large Eddy Simulation, Shock Waves, Immersed Boundary Methods, Reduced order modeling, Gas Dynamics, Aeroelastic Flutter, Adaptive Mesh Refinement, Fluid Structure Interaction (FSI), Interdisciplinary Engineering, Compressible Flow, and Immersed Boundary Method
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Micro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around... more
Micro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around a micro-ramp immersed in a quasi-incompressible boundary layer at supercritical roughness Reynolds number. Results of our Direct Numerical Simulations (DNS) are compared with results of BiLocal stability analysis on the DNS base flow and independent tomographic Particle Image Velocimetry (tomo-PIV) experiments. We analyse relevant flow structures developing in the micro-ramp wake and assess their role in the micro-ramp functionality, i.e., in increasing the near-wall momentum. The main flow feature of the base flow is a pair of streamwise counter-rotating vortices induced by the micro-ramp, the so-called primary vortex pair. In the instantaneous transitional flow, the primary vortex pair breaks up into large-scale hairpin vortices, which arise due ...
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We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of $Re_{b}=110\times 10^{3}$ and an average Nusselt number of $Nu_{xz}=371$... more
We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of $Re_{b}=110\times 10^{3}$ and an average Nusselt number of $Nu_{xz}=371$ . The geometry and boundary conditions follow an experimental reference case and good agreement with the experimental results is achieved. The current investigation focuses on the influence of asymmetric wall heating on the duct flow field, specifically on the interaction of turbulence-induced secondary flow and turbulent heat transfer, and the associated spatial development of the thermal boundary layer and the inferred viscosity variation. The viscosity reduction towards the heated wall causes a decrease in turbulent mixing, turbulent length scales and turbulence anisotropy as well as a weakening of turbulent ejections. Overall, the secondary flow strength becomes increasingly less intense along the length of the spatially resolved heated duct as...
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Research Interests: Engineering, Materials Science, Computational Fluid Dynamics, Turbulence, Multiphase Flow, and 14 moreSupercritical fluids, Large Eddy Simulation, Numerical Analysis, Numerical Modelling, Marine Diesel Engines, Multiphase flows, Turbulence modeling, Modeling and Simulation of Diesel Engine, Diesel engines, Fuel injection, Large Eddy Simulation(LES), Supercritical, Transcritical, and INCA CFD
We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES)... more
We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by$19.6^{\circ }$. The Reynolds number based on the incoming boundary-layer thickness of$Re_{\unicode[STIX]{x1D6FF}_{0}}\approx 203\times 10^{3}$is considerably higher than in previous LES studies. The very long integration time of$3805\unicode[STIX]{x1D6FF}_{0}/U_{0}$allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise...
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We performed wall modeled large eddy simulation of the flow field around a delta wing with sweep angle of \(65^{\circ }\) and round leading edge at angles of attack of \(13^{\circ }\), \(18^{\circ }\), and \(23^{\circ }\). Qualitatively,... more
We performed wall modeled large eddy simulation of the flow field around a delta wing with sweep angle of \(65^{\circ }\) and round leading edge at angles of attack of \(13^{\circ }\), \(18^{\circ }\), and \(23^{\circ }\). Qualitatively, the numerical simulations correctly predict the flow phenomena for all angles of attack considered. Quantitatively, the results show reasonable agreement with experimental measurements of steady and unsteady surface pressures, velocity distributions, and vortex breakdown position and frequency.
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A scramjet is an air breathing jet engine for hypersonic flight, in which combustion takes place at supersonic flow velocity. Fast mixing of fuel and the compressed air flow is thus essential for the efficient operation. Because the... more
A scramjet is an air breathing jet engine for hypersonic flight, in which combustion takes place at supersonic flow velocity. Fast mixing of fuel and the compressed air flow is thus essential for the efficient operation. Because the penetration depth of fuel injection perpendicular to the main flow direction is very small, strut injectors that are positioned directly within the supersonic core flow are usually used in large chambers. We performed large-eddy simulations for a generic strut-injector geometry. The main objective of this paper is the analysis of the pilot injection for flame stabilisation.
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Research Interests: Engineering, Physics, Mechanics, Turbulence, Two Phase Flow, and 14 moreLarge Eddy Simulation, Mathematical Sciences, Cavitation, Physical sciences, Phase Change, Water Jet, Multi phase Flows, Fuel injection, Jet Breakup, Physics of Fluids, Computational Fluids Dynamics (CFD), Large Eddy Simulations, Injector Nozzle, and Nozzle
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Research Interests: Engineering, Physics, Cryogenics, Computational Fluid Dynamics, Turbulence, and 15 moreCubic Equations of State, Supercritical fluids, Large Eddy Simulation, Turbulence modeling, Mathematical Sciences, Supercritical fluid science and technology, Physical sciences, OpenFOAM, Mixing Rules for Equations of State, Fuel injection, Turbulent Mixing, Physics of Fluids, Compressible Flows, Supercritical Fluid, and INCA CFD
Abstract We analyse results of numerical simulations of reactive shock-bubble interaction with detailed chemistry. The interaction of the Richtmyer–Meshkov instability and shock-induced ignition of a stoichiometric H 2 - O 2 gas mixture... more
Abstract We analyse results of numerical simulations of reactive shock-bubble interaction with detailed chemistry. The interaction of the Richtmyer–Meshkov instability and shock-induced ignition of a stoichiometric H 2 - O 2 gas mixture is investigated. Different types of ignition (deflagration and detonation) are observed at the same shock Mach number of M a = 2.30 upon varying initial pressure. Due to the convex shape of the bubble, shock focusing leads to a spot with high pressure and temperature. Initial pressures between p 0 = 0.25 − 0.75 atm exhibit low pressure reactions, dominated by H, O, OH production and high pressure chemistry driven by HO 2 and H 2 O 2 . Deflagration is observed for the lowest initial pressure. Increasing pressure results in smaller induction times and ignition, followed by a detonation wave. The spatial and temporal evolution of the gas bubble is highly affected by the type of ignition. The Richtmyer–Meshkov instability and the subsequent Kelvin–Helmholtz instabilities develop with a high reaction sensitivity. Mixing is significantly reduced by both reaction types. The strongest effect is observed for detonation.