Matteo Parsani

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurat...

In this study, the generation of airfoil trailing edge broadband noise that arises from the interaction of turbulent boundary layer with the airfoil trailing edge is investigated. The primary objectives of this work are: (i) to apply a wall-modelled large-eddy simulation (WMLES) approach to predict the flow of air passing a controlled-diffusion blade, and (ii) to study the blade broadband noise that is generated from the interaction of a turbulent boundary layer with a lifting surface trailing edge. This study is carried out for two values of the Mach number, $${{\rm Ma}}_{\infty } = 0.3$$Ma∞=0.3 and 0.5, two values of the chord Reynolds number, $${{\rm Re}}=8.30 \times 10^5$$Re=8.30×105 and $$2.29 \times 10^6$$2.29×106, and two angles of attack, AoA $$=4^\circ$$=4∘ and $$5^\circ$$5∘. To examine the influence of the grid resolution on aerodynamic and aeroacoustic quantities, we compare our results with experimental data available in the literature. We also compare our results with t...

In this study, a new set of direct numerical simulations is generated and used to examine the influence of mixture composition heterogeneities on the propagation of a premixed iso-octane/air spherical turbulent flame, with a representative chemical description. The dynamic effects of both turbulence and combustion heterogeneities are considered, and their competition is assessed. The results of the turbulent homogeneous case are compared with those of heterogeneous cases which are characterized by multiple stratification length scales and segregation rates in the regime of a wrinkled flame. The comparison reveals that stratification does not alter turbulent flame behaviors such as the preferential alignment of the convex flame front with the direction of the compression. However, we find that the overall flame front propagation is slower in the presence of heterogeneities because of the differential on speed propagation. Furthermore, analysis of different displacement speed componen...

In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well-known methods. We perform a general analysis of internal error propagation, emphasizing that it depends significantly on how the method is implemented. We show that for a fixed method, essentially any set of internal stability polynomials can be obtained by modifying the implementation details. We provide bounds on the internal error amplification constants for some classes of methods with many stages, including strong stability preserving methods and extrapolation methods. These results are used to prove error bounds in the presence of roundoff or other internal errors.

ABSTRACT Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier–Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although dis- continuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, dis- continuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

ABSTRACT We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion ...

The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower–upper symmetric Gauss–Seidel (LU-SGS ...

ABSTRACT The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modeled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm. The SD-LES method provides the acoustic sources for aerodynamic sound field simulation in the time domain. The numerical noise simulation is based on the Ffowcs-Williams Hawkings (FW-H) approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 103 and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional (3D) turbulent flow in a muffler at Re = 46,650 and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately.

The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. The implicit method addresses the stiffness in the discrete Navier–Stokes equations associated with stretched meshes. The LU-SGS algorithm is then used as a smoother for a ...

1, 2, 3 Vrije Universiteit Brussel, Department of Mechanical Engineering, Fluid Dynamics and Thermodynamics Research Group Triomflaan 43, B-1050 Brussels, Belgium 1 mparsani@ vub. ac. be, 2 kvdabeel@ vub. ac. be, 3 chris. lacor@ vub. ac. be Key Words: Spectral Volume Method, LU-SGS Algorithm, p− Multigrid.

Abstract: Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge-Kutta schemes available in literature. Furthermore, they have a small principal error norm and admit a low-storage implementation.

ABSTRACT This paper presents the development of a two- and three-dimensional high-order solver with an unstructured spectral difference (SD) method coupled with the nonlinear lower-upper symmetric Gauss-Seidel method to solve the algebraic systems arising from SD discretizations with a second-order backward difference formula for time marching. The solver employs the formulations of Sun et al. [1] and Van den Abeele et al. [2]. This method is used to solve the 2D flow around a circular cylinder at Re = 300, 800, 1000 and M = 0.05, the NACA0012 airfoil at Re = 50000 and M = 0.4 at zero angle of attack and the 2D flow around a square cylinder at Re = 10000 and M = 0.05. The obtained results are compared with reference solutions.

The main goal of this paper is to develop an efficient numerical algorithm to compute the radiated far field noise provided by an unsteady flow field from bodies in arbitrary motion. The method computes a turbulent flow field in the near fields using a high-order spectral difference method coupled with large-eddy simulation approach. The unsteady equations are solved by advancing in time using a second-order backward difference formulae scheme. The nonlinear algebraic system arising from the time discretization is solved with ...