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Int. J. Turbomach. Propuls. Power, Volume 9, Issue 2 (June 2024) – 12 articles

Cover Story (view full-size image): A central aspect within the development of frequency-domain methods for turbomachinery flows is the ability to accurately predict rotor–rotor and stator–stator interactions in a single-passage domain. To simulate such interactions, state-of-the-art frequency-domain approaches require one fundamental interblade phase angle, and therefore it can be necessary to resort to multi-passage configurations or neglect the cross-coupling of different harmonics. This paper shows how to overcome these issues by using multidimensional Fourier transforms in time. View this paper
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29 pages, 22049 KiB  
Article
Predicting Erosion Damage in a Centrifugal Fan
by Adel Ghenaiet
Int. J. Turbomach. Propuls. Power 2024, 9(2), 23; https://doi.org/10.3390/ijtpp9020023 - 17 Jun 2024
Viewed by 854
Abstract
Erosion damage can occur in fans and blowers during industrial processes, cooling, and mine ventilation. This study focuses on investigating erosion caused by particulate air flows in a centrifugal fan with forward-inclined blades. This type of fan is particularly vulnerable to erosion due [...] Read more.
Erosion damage can occur in fans and blowers during industrial processes, cooling, and mine ventilation. This study focuses on investigating erosion caused by particulate air flows in a centrifugal fan with forward-inclined blades. This type of fan is particularly vulnerable to erosion due to its radial flow component and flow recirculation. The flow field was solved separately, and the data transferred to the particle trajectory and erosion code. This in-house code implements the Lagrangian approach and the random walk algorithm, including statistical descriptions of particle sizes, release positions, and restitution factors. The study involved two types of dust particles, with a concentration between 100 and 500 μg/m3: The first type is the Saharan (North Africa) dust, which has a finer size between 0.1 and 100 microns. The second type is the Coarse Arizona Road Dust, also known as AC-coarse dust, which has a larger size ranging from 1 to 200 microns. The complex flow conditions within the impeller and scroll, as well as the concentration and size distribution of particles, are shown to affect the paths, impact conditions, and erosion patterns. The outer wall of the scroll is most heavily eroded due to high-impact velocities by particles exiting the impeller. Erosion is more pronounced on the pressure side of the full blades compared to the splitters and casing plate. The large non-uniformities of erosion patterns indicate a strong dependence with the blade position around the scroll. Therefore, the computed eroded mass is cumulated and averaged for all the surfaces of components. These results provide useful insights for monitoring erosion wear in centrifugal fans and selecting appropriate coatings to extend the lifespan. Full article
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<p>Centrifugal fan (<b>left</b>) and impeller (<b>right</b>).</p>
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<p>Computational domain.</p>
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<p>Meshing of the (<b>a</b>) impeller and (<b>b</b>) scroll tongue region.</p>
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<p>Distribution of <span class="html-italic">y</span><sup>+</sup>: (<b>a</b>) impeller and (<b>b</b>) scroll.</p>
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<p>Grid size independence verification.</p>
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<p>Computed performance compared with reference (dashed line).</p>
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<p>Static pressure at (<b>a</b>) mid-span and (<b>b</b>) near blade tip.</p>
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<p>Flow velocity at the meridional plane halving the fan components.</p>
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<p>Flow velocity at (<b>a</b>) mid-span and (<b>b</b>) near blade tip.</p>
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<p>Meridional flow velocities near (<b>a</b>) the exit from the scroll and (<b>b</b>) tongue.</p>
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<p>Flow structures at cross-sections of the impeller.</p>
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<p>Flow streamlines.</p>
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<p>Turbulent kinetic energy.</p>
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<p>Impact conditions.</p>
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<p>Dust particle size distributions.</p>
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<p>Release positions and sizes of Saharan dust particles at the highest concentration for two randomness factors.</p>
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<p>Samples of particle (1 μm) trajectories coloured by velocity: (<b>a</b>) top view and (<b>b</b>) side view.</p>
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<p>Samples of particle (100 μm) trajectories coloured by velocity: (<b>a</b>) top view and (<b>b</b>) side view.</p>
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<p>Trajectories of Saharan dust (0.1–100 microns) colored by (<b>a</b>) the particle diameter, (<b>b</b>) side view, and (<b>c</b>) Stokes number.</p>
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<p>Erosion with the blades’ positions, caused by Saharan dust (0.1–100 microns) of the concentration 500 μg/m<sup>3</sup>: impeller blades, casing plate, and volute.</p>
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<p>EMPH with blades’ positions caused by Saharan dust (0.1–100 microns) of the concentration 500 μg/m<sup>3</sup>: (<b>a</b>) full blades, (<b>b</b>) splitters, (<b>c</b>) impeller, (<b>d</b>) casing plate, and (<b>e</b>) scroll.</p>
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<p>Erosion patterns in the impeller, caused by Saharan dust (0.1–100 microns) of the concentration 500 μg/m<sup>3</sup>, operating at (<b>a</b>) the nominal flow rate and (<b>b</b>) maximum discharge.</p>
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<p>Erosion patterns in the impeller, caused by AC-coarse dust (1–200 microns) of the concentration 500 μg/m<sup>3</sup>, operating at (<b>a</b>) the nominal flow rate and (<b>b</b>) maximum discharge.</p>
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<p>Erosion rate density in the scroll, caused by Saharan (0.1–100 microns) of the concentration 500 μg/m<sup>3</sup>, operating at (<b>a</b>) the nominal flow rate and (<b>b</b>) maximum discharge.</p>
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<p>Erosion rate density (mg/s·mm<sup>2</sup>) in the scroll, caused by AC-coarse dust (1–200 microns) of the concentration 500 μg/m<sup>3</sup>, operating at (<b>a</b>) the nominal flow rate and (<b>b</b>) maximum discharge.</p>
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<p>Erosion rate density (mg/s·mm<sup>2</sup>) in the scroll, caused by AC-coarse dust (1–200 microns) of the concentration 500 μg/m<sup>3</sup>, operating at (<b>a</b>) the nominal flow rate and (<b>b</b>) maximum discharge.</p>
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<p>EMPH (mg/h) of the impeller, caused by (<b>a</b>) Saharan dust (0.1–100 microns) and (<b>b</b>) AC-coarse dust (1–200 microns).</p>
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<p>EMPH (mg/h) of centrifugal fan parts, caused by (<b>a</b>) Saharan dust (0.1–100 microns) and (<b>b</b>) AC-coarse dust (1–200 microns).</p>
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21 pages, 23685 KiB  
Article
Numerical Investigation of Forced Response in a Transonic Compressor Stage—Highlighting Challenges Using Experimental Validation
by Nicklas Kilian, Fabian Klausmann, Daniel Spieker, Heinz-Peter Schiffer and Mauricio Gutiérrez Salas
Int. J. Turbomach. Propuls. Power 2024, 9(2), 22; https://doi.org/10.3390/ijtpp9020022 - 6 Jun 2024
Viewed by 985
Abstract
An experiment-supported simulation process chain is set up to perform numerical forced response analyses on a transonic high-pressure compressor front stage at varying operating conditions. A wake generator is used upstream of the rotor to excite a specific resonance within the operating range [...] Read more.
An experiment-supported simulation process chain is set up to perform numerical forced response analyses on a transonic high-pressure compressor front stage at varying operating conditions. A wake generator is used upstream of the rotor to excite a specific resonance within the operating range of the compressor. Thereby, extensive aerodynamic and structural dynamic experimental data, obtained from state-of-the-art rig testing at the Transonic Compressor Darmstadt test facility at the Technical University of Darmstadt, are used to validate numerical results and ensure realistic boundary conditions. In the course of this, five-hole-probe measurements at steady operating conditions close to the investigated resonance enable a validation of the steady aerodynamics. Subsequently, numerically obtained aeroelastic quantities, such as resonance frequency, and damping, as well as maximum alternating blade stresses and tip deflections, are compared to experimental blade tip timing data. Experimental trends in damping can be confirmed and better explained by considering numerical results regarding the aerodynamic wall work density and secondary flow phenomena. The influence of varying loading conditions on the resonance frequency is not observed as distinctly in numerical, as in experimental results. Generally, alternating blade stresses and deflections appear to be significantly lower than in the experiments. However, similar to the aerodynamic damping, numerical results contribute to a better understanding of experimental trends. The successive experimental validation shows the capabilities of the numerical forced response analysis setup and enables the highlighting of challenges and identification of potential further adaptations. Full article
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<p>Test rig and compressor core configuration (A) including the investigated resonance crossing and vibration mode shape (B).</p>
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<p>Schematic compressor map illustrating conducted measurements with five-hole probe (A) and blade tip timing (B).</p>
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<p>Numerical simulation process chain.</p>
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<p>Numerical domain and measurement sections within the test rig.</p>
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<p>Experimental total pressure ratio circumferential profiles and 2D flow fields at N87 PE.</p>
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<p>Experimental and numerical rotor inlet and outlet total pressure radial profiles at N87 PE.</p>
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<p>Experimental Campbell diagram of M1 EO3 resonance crossings at varying loading conditions.</p>
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<p>Comparison of experimental and numerical resonance frequencies.</p>
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<p>Comparison and assessment of experimental and numerical damping including the distribution of aerodynamic wall work over the blade (A) for the investigated mode shape (B).</p>
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<p>Assessment of the aerodynamic forcing based on numerical results.</p>
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<p>Comparison of experimental and numerical maximum alternating blade stresses (<b>a</b>) and deflections (<b>b</b>).</p>
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<p>Unintended structural frequency mistuning of the investigated blisk rotor.</p>
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15 pages, 4989 KiB  
Article
Numerical Investigation of the Excitation Characteristics of Contaminated Nozzle Rings
by Michaela R. Beierl, Damian M. Vogt, Magnus Fischer, Tobias R. Müller and Kwok Kai So
Int. J. Turbomach. Propuls. Power 2024, 9(2), 21; https://doi.org/10.3390/ijtpp9020021 - 4 Jun 2024
Viewed by 1045
Abstract
The deposition of combustion residues in the nozzle ring (NR) of a turbocharger turbine stage changes the NR geometry significantly in a random manner. The resultant complex and highly asymmetric geometry induces low engine order (LEO) excitation, which may lead to resonance excitation [...] Read more.
The deposition of combustion residues in the nozzle ring (NR) of a turbocharger turbine stage changes the NR geometry significantly in a random manner. The resultant complex and highly asymmetric geometry induces low engine order (LEO) excitation, which may lead to resonance excitation of rotor blades and high cycle fatigue (HCF) failure. Therefore, a suitable prediction workflow is of great importance for the design and validation phases. The prediction of LEO excitation is, however, computationally expensive as high-fidelity, full annulus CFD models are required. Previous investigations showed that a steady-state computational model consisting of the volute, the NR, and a radial extension is suitable to reduce the computational costs massively and to qualitatively predict the level of LEO forced response. In the current paper, the aerodynamic excitation of 69 real contaminated NRs is analyzed using this simplified approach. The results obtained by the simplified simulation model are used to select 13 contaminated NR geometries, which are then simulated with a model of the entire turbine stage, including the rotor, in a transient time-marching manner to provide high-fidelity simulation results for the verification of the simplified approach. Furthermore, two contamination patterns are analyzed in a more detailed manner regarding their aerodynamic excitation. It is found that the simplified model can be used to identify and classify contamination patterns that lead to high blade vibration amplitudes. In cases where transient effects occurring in the rotor alter the harmonic pressure field significantly, the ability of the simplified approach to predict the LEO excitation is not sufficient. Full article
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<p>Contamination level distribution.</p>
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<p>Scanned blade geometry with equidistant axial sections (<b>left</b>) and tuned vane section fitted into a contaminated section (<b>right</b>).</p>
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<p>An unwrapped view of the averaged contamination pattern derived from all measured NR vanes.</p>
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<p>Flow chart of the workflow to assess the LEO excitation using a simplified computational approach.</p>
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<p>Numerical Isolated Nozzle Ring (INR) model.</p>
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<p>Excitation potential vs. contamination level.</p>
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<p>Influence of operating point on aerodynamic excitation.</p>
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<p>Grouping according to the level of excitation potential.</p>
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<p>Comparison of the NR outflow field spectra determined with the INR and TM model.</p>
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<p>Comparison of excitation potential with different models.</p>
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<p>Instantaneous Mach number distribution at 90% span for two different nozzle rings.</p>
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<p>Standard deviation of the pressure at 90% span.</p>
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<p>Harmonic pressure amplitude at EO6 at 90% span.</p>
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<p>Harmonic pressure amplitude at EO6.</p>
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<p>Modal pressure amplitude at EO6.</p>
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14 pages, 5084 KiB  
Article
Rotating Stall Inception Prediction Using an Eigenvalue-Based Global Instability Analysis Method
by Shenren Xu, Caijia Yuan, Chen He, Dongming Cao, Dakun Sun, Carlos Martel, Huihao Chen and Dingxi Wang
Int. J. Turbomach. Propuls. Power 2024, 9(2), 20; https://doi.org/10.3390/ijtpp9020020 - 4 Jun 2024
Viewed by 862
Abstract
The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and [...] Read more.
The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice. Full article
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<p>NASA Rotor 67, the test configuration at 50% blade span, and the computation domain.</p>
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<p>Speed lines for grid independence study (eigenanalyses were performed at the three near stall operating points of A, B and C).</p>
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<p>Eigen-spectra obtained from eigenvalue analyses.</p>
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<p>Reconstructed snapshots (<b>left</b>) and time traces (<b>right</b>) for mode 3.</p>
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<p>Reconstructed snapshots (<b>left</b>) and time traces (<b>right</b>) for mode 4.</p>
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<p>Reconstructed snapshots (<b>left</b>) and time traces (<b>right</b>) for mode 5.</p>
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<p>Correlation between rotating speed in the stationary frame of reference and nodal diameter of the eigenmodes.</p>
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<p>A snapshot of the axial velocity field at 3.2 s.</p>
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<p>Dot products between eleven right and left eigenvectors (at a logarithmic scale).</p>
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<p>Evolutions of projections onto the selected modes.</p>
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<p>Evolutions of projections onto mode 2 and mode 5 with introduced perturbations.</p>
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17 pages, 6793 KiB  
Article
Physics of the Unsteady Response of Turbine Cascade to Pulsed Flow Conditions
by Pierre Bertojo, Nicolas Binder and Jeremie Gressier
Int. J. Turbomach. Propuls. Power 2024, 9(2), 19; https://doi.org/10.3390/ijtpp9020019 - 27 May 2024
Viewed by 899
Abstract
The present contribution is in direct continuation of previous work which aimed at demonstrating the possible benefit of the unsteady feeding of turbines. Some numerical analyses of the flow inside a skeletal cascade revealed that instantaneous overloading occurs on the blades. However, such [...] Read more.
The present contribution is in direct continuation of previous work which aimed at demonstrating the possible benefit of the unsteady feeding of turbines. Some numerical analyses of the flow inside a skeletal cascade revealed that instantaneous overloading occurs on the blades. However, such an academic case is far from a realistic configuration. The present paper investigates the influence of a simplified thickness distribution to check whether the instantaneous benefit is still observed. Based on numerical simulations, an analysis of the physical origin of the overloading is proposed on a single blade. It results in the choice of a triangular thickness distribution, which should promote the physical phenomena responsible for the overloading. A parametric study of such a distribution demonstrates that it is possible to obtain instantaneous performance very close to the optimum of the flat plate. Conclusions drawn from the single-blade analysis are extended to cascades and stator–rotor configurations and show an increase in the complexity of physical phenomena. Ultimately, the aim is to optimize the geometric shape to obtain maximum overloading. Consequently, the same type of study was carried out for the expansion phase, and similar results were obtained. Full article
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<p>Basic illustration of the reflection (r) induced by an incident shock wave (i) propagating along a flat plate. The black arrows represent the velocity vector in reference to the moving shock wave.</p>
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<p>Illustration of the diffraction phenomenon at the trailing edge (extracted from Hermet [<a href="#B6-ijtpp-09-00019" class="html-bibr">6</a>]).</p>
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<p>(<b>Left</b>): Geometric configuration. (<b>Right</b>): Different configurations (flat plate, skeletal configuration and the triangular one).</p>
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<p>Illustration of boundary conditions on the triangular profile.</p>
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<p>Illustration of boundary conditions on the skeletal profile.</p>
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<p>Illustration of boundary conditions on the flat plate profile.</p>
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<p>Pressure distribution over flat plate configuration (shock wave propagation). (<b>a</b>–<b>e</b>) correspond to five instants.</p>
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<p>Normalized lift evolution along time in flat plate configuration. (<b>a</b>–<b>e</b>) correspond to the same instants as in <a href="#ijtpp-09-00019-f007" class="html-fig">Figure 7</a>.</p>
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<p>Design of experiment results. Instantaneous overloading for different configurations.</p>
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<p>Design of experiment results. Integral load for different configurations.</p>
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<p>Design of experiment results. (<b>a</b>) corresponds to the projection at <math display="inline"><semantics> <msup> <mi>β</mi> <mo>*</mo> </msup> </semantics></math> fixed, (<b>b</b>) the projection at <math display="inline"><semantics> <mi>α</mi> </semantics></math> fixed, (<b>c</b>) the projection at <math display="inline"><semantics> <msup> <mi>l</mi> <mo>*</mo> </msup> </semantics></math> fixed.</p>
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<p>Best configuration pressure distribution (shock wave propagation) (<b>a</b>–<b>f</b>).</p>
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<p>Instantaneous loading for the three geometries.</p>
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<p>Influence of the solidity on the best configuration (7).</p>
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<p>Pressure distribution over the triangular turbine stage (<b>a</b>–<b>f</b>).</p>
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<p>Instantaneous loading for the stator case and the rotor case (including the sliding interface) (<b>a</b>–<b>f</b>).</p>
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<p>Flat plate configuration pressure distribution (expansion wave) for four instants (<math display="inline"><semantics> <msub> <mi>t</mi> <mn>1</mn> </msub> </semantics></math>−<math display="inline"><semantics> <msub> <mi>t</mi> <mn>4</mn> </msub> </semantics></math>).</p>
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<p>The <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> representation for flat plate case (pressure field). (I): Initial expansion wave, (R1) (R2): Reflections due to interaction with geometry and boundary condition, (S): Source Term, (C): Reflection with converging–diverging term.</p>
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<p>Instantaneous loading with expansion.</p>
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19 pages, 11401 KiB  
Article
Design and Characterization of Highly Diffusive Turbine Vanes Suitable for Transonic Rotating Detonation Combustors
by Sergio Grasa and Guillermo Paniagua
Int. J. Turbomach. Propuls. Power 2024, 9(2), 18; https://doi.org/10.3390/ijtpp9020018 - 9 May 2024
Viewed by 1344
Abstract
In rotating detonation engines the turbine inlet conditions may be transonic with unprecedented unsteady fluctuations. To ensure an acceptable engine performance, the turbine passages must be suited to these conditions. This article focuses on designing and characterizing highly diffusive turbine vanes to operate [...] Read more.
In rotating detonation engines the turbine inlet conditions may be transonic with unprecedented unsteady fluctuations. To ensure an acceptable engine performance, the turbine passages must be suited to these conditions. This article focuses on designing and characterizing highly diffusive turbine vanes to operate at any inlet Mach number up to Mach 1. First, the effect of pressure loss on the starting limit is presented. Afterward, a multi-objective optimization with steady RANS simulations, including the endwall and 3D vane design is performed. Compared to previous research, significant reductions in pressure loss and stator-induced rotor forcing are obtained, with an extended operating range and preserving high flow turning. Finally, the influence of the inlet boundary layer thickness on the vane performance is evaluated, inducing remarkable increases in pressure loss and downstream pressure distortion. Employing an optimization with a thicker inlet boundary layer, specific endwall design recommendations are found, providing a notable improvement in both objective functions. Full article
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<p>Starting limit: red dashed lines mark the minimum throat-to-inlet area ratio for different pressure loss levels.</p>
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<p>Optimization Strategy.</p>
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<p>Camber line and Suction side parametrization.</p>
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<p>Meridional law and Endwall contour parametrization.</p>
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<p>Outlet angle radial distribution: (<b>a</b>) Solver Verification. (<b>b</b>) Grid Independence.</p>
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<p>Computational domain of baseline geometry with detailed view of grid topology.</p>
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<p>Optimization results: (<b>a</b>) Pressure loss coefficient versus pressure distortion. (<b>b</b>) Effect of throat-to-inlet area ratio on pressure loss coefficient.</p>
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<p>IND 497: Pitch-wise averaged Mach number contour (<b>top</b>) and axial evolution of local-to-inlet area ratio (<b>bottom</b>).</p>
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<p>IND 497: 50% span Mach number contour (<b>left</b>), 90% span Mach number contour (<b>center</b>), Isentropic Mach number distribution at 50–90% span (<b>right</b>).</p>
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<p>IND 497: Pitch-wise averaged Mach number contour with 5.5% BL thickness at passage inlet plane.</p>
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<p>Iso-surface of <span class="html-italic">V<sub>ax</sub></span> = −1 for IND 497 with zero (<b>left</b>) and 5.5% (<b>right</b>) inlet BL thickness.</p>
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<p>Optimization with 5.5% inlet BL. Pressure loss coefficient versus pressure distortion.</p>
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<p>Evolution of local-to-inlet area ratio (<b>top</b>) and endwall contour angle (<b>bottom</b>) for optimized designs with different inlet BL thicknesses.</p>
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<p>Optimized geometry: Pitch-wise averaged Mach number contour and iso-surface of <span class="html-italic">V<sub>ax</sub></span> = −1 for on-design conditions (<b>top</b>) and for Mach 1 inflow (<b>bottom</b>).</p>
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<p>Optimized geometry: Three-dimensional Mach number contours (<span class="html-italic">P</span><sub>01</sub><span class="html-italic">/P</span><sub>2</sub> = 2.1).</p>
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20 pages, 2038 KiB  
Article
Simulation of Indexing and Clocking with a New Multidimensional Time Harmonic Balance Approach
by Laura Junge, Christian Frey, Graham Ashcroft and Edmund Kügeler
Int. J. Turbomach. Propuls. Power 2024, 9(2), 17; https://doi.org/10.3390/ijtpp9020017 - 8 May 2024
Viewed by 1653
Abstract
Alongside the capability to simulate rotor–stator interactions, a central aspect within the development of frequency-domain methods for turbomachinery flows is the ability of the method to accurately predict rotor–rotor and stator–stator interactions on a single-passage domain. To simulate such interactions, state-of-the-art frequency-domain approaches [...] Read more.
Alongside the capability to simulate rotor–stator interactions, a central aspect within the development of frequency-domain methods for turbomachinery flows is the ability of the method to accurately predict rotor–rotor and stator–stator interactions on a single-passage domain. To simulate such interactions, state-of-the-art frequency-domain approaches require one fundamental interblade phase angle, and therefore it can be necessary to resort to multi-passage configurations. Other approaches neglect the cross-coupling of different harmonics. As a consequence, the influence of indexing on the propagation of the unsteady disturbances is not captured. To overcome these issues, the harmonic balance approach based on multidimensional Fourier transforms in time, recently introduced by the authors, is extended in this work to account for arbitrary interblade phase angle ratios on a single-passage domain. To assess the ability of the approach to simulate the influence of indexing on the steady, as well as on the unsteady, part of the flow, the proposed extension is applied to a modern low-pressure fan stage of a civil aero engine under the influence of an inhomogeneous inflow condition. The results are compared to unsteady simulations in the time-domain and to state-of-the-art frequency-domain methods based on one-dimensional discrete Fourier transforms. Full article
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<p>Passage indices for <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <msub> <mi>S</mi> <mn>1</mn> </msub> </msub> <mo>/</mo> <msub> <mi>B</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mn>2</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> correspond to real stator positions. (<b>a</b>) Sampling points. (<b>b</b>) Sampling phases.</p>
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<p>Fan with inlet distortion. (<b>a</b>) Distorted relative total pressure distribution on fan stage entry plane. (<b>b</b>) Full annulus setup of the fan stage.</p>
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<p>Unfolded bi-dimensional frequency–time domain. (<b>a</b>) Frequency interblade phase angle combinations. (<b>b</b>) Sampling point combinations.</p>
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<p>Instantaneous entropy distribution at <math display="inline"><semantics> <mrow> <mo>∼</mo> <mn>90</mn> <mo>%</mo> </mrow> </semantics></math> relative radial height. (<b>a</b>) HB MDFT, (<b>b</b>) HB DFT, (<b>c</b>) HB HS, (<b>d</b>) time domain.</p>
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<p>Instantaneous entropy distribution at <math display="inline"><semantics> <mrow> <mo>∼</mo> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math> relative radial height. (<b>a</b>) HB MDFT, (<b>b</b>) HB DFT, (<b>c</b>) HB HS, (<b>d</b>) time domain.</p>
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<p>Instantaneous entropy distribution in front of the stator. (<b>a</b>) HB MDFT, (<b>b</b>) HB HS, (<b>c</b>) HB DFT, (<b>d</b>) time domain.</p>
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<p>Instantaneous Mach number over the circumference at <math display="inline"><semantics> <mrow> <mo>∼</mo> <mn>90</mn> <mo>%</mo> </mrow> </semantics></math> relative radial height and slice position A.</p>
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<p>Instantaneous inflow angle over the circumference at <math display="inline"><semantics> <mrow> <mo>∼</mo> <mn>90</mn> <mo>%</mo> </mrow> </semantics></math> relative radial height and slice position A.</p>
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<p>Performance map for design speed.</p>
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23 pages, 3122 KiB  
Article
Wall-Proximity Effects on Five-Hole Probe Measurements
by Adrien Vasseur, Nicolas Binder, Fabrizio Fontaneto and Jean-Louis Champion
Int. J. Turbomach. Propuls. Power 2024, 9(2), 16; https://doi.org/10.3390/ijtpp9020016 - 8 May 2024
Viewed by 1372
Abstract
Wall proximity affects the accuracy of pressure probe measurements with a particularly strong impact on multi-hole probes. The wall-related evolution of the calibration of two hemispheric L-shaped 3D-printed five-hole probes was investigated in a low-speed wind tunnel. Pressure measurements and 2D particle image [...] Read more.
Wall proximity affects the accuracy of pressure probe measurements with a particularly strong impact on multi-hole probes. The wall-related evolution of the calibration of two hemispheric L-shaped 3D-printed five-hole probes was investigated in a low-speed wind tunnel. Pressure measurements and 2D particle image velocimetry were performed. The wall proximity causes the probe to measure a flow diverging from the wall, whereas the boundary layer causes the probe to measure a velocity directed towards the wall. Both angular calibration coefficients are affected in different manners. The error in angle measurement can reach 7°. These errors can be treated as calibration information. Acceleration caused by blockage is not the main reason for the errors. Methods to perform measurements closer to the wall are suggested. Full article
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Figure 1
<p>Lee’s probe head details and probe shape [<a href="#B15-ijtpp-09-00016" class="html-bibr">15</a>].</p>
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<p>The VKI L-12 wind tunnel.</p>
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<p>Mounting gear and test section.</p>
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<p>The probes used for the experiment and details of the head. The heads were 3D printed and assembled with the masts in VKI. They were coated in black paint to be less reflective.</p>
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<p>Illustration of the probe positions and angle conventions.</p>
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<p>Naming convention of the probe holes in this document.</p>
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<p>Representation of evolution of the flow angle measurement during a traverse.</p>
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<p>Evolution of the flow angle reading error.</p>
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<p>The top hole (hole number 1), crossed in red, comes closer to the wall when the probe has a negative pitch. The head centre cannot reach the 0.5 d wall distance when the probe has a positive pitch (blue).</p>
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<p>Comparison of the angle coefficient’s behaviour near the wall, reported by Lee et al. [<a href="#B15-ijtpp-09-00016" class="html-bibr">15</a>] for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.028</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>35</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>, and from this work for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>16</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The solid lines are from Lee [<a href="#B15-ijtpp-09-00016" class="html-bibr">15</a>], and the lines with error bars are from this work.</p>
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<p>Angle coefficient’s behaviour near the wall, as measured in this work, for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>16</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Calibration map evolution for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>16</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The grey dots are the (<math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>y</mi> <mi>a</mi> <mi>w</mi> </mrow> </msub> </semantics></math>,<math display="inline"><semantics> <msub> <mi>k</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>c</mi> <mi>h</mi> </mrow> </msub> </semantics></math>) calculated from the pressure data as functions of wall proximity for a given probe orientation. The yellow map representing the calibration data 0.525 diameters away from the wall is incomplete. The reason is that the head bend prevented the head from getting close to the wall for positive pitches; see <a href="#ijtpp-09-00016-f009" class="html-fig">Figure 9</a>.</p>
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<p>Fit of the <math display="inline"><semantics> <msubsup> <mi>k</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>c</mi> <mi>h</mi> </mrow> <mo>*</mo> </msubsup> </semantics></math> traverse from this work when the probe has a mechanical pitch and yaw of 10°.</p>
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<p>Fit of the <math display="inline"><semantics> <msubsup> <mi>k</mi> <mrow> <mi>y</mi> <mi>a</mi> <mi>w</mi> </mrow> <mo>*</mo> </msubsup> </semantics></math> traverse from this work when the probe has a mechanical pitch and yaw of 0° and 10°, respectively.</p>
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<p>Pitch coefficient evolution for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The black line marks where the probe reaches the edge of the theoretical boundary layer.</p>
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<p>Pitch coefficient evolution for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The black line marks where the probe reaches the edge of the theoretical boundary layer.</p>
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<p>BL component in pitch coefficient for −10° pitch and 10° yaw for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.34</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>16</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The star marks the probe’s entrance into the boundary layer.</p>
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<p>BL component in pitch coefficient for 0° pitch and 0° yaw for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The star marks the probe’s entrance into the boundary layer.</p>
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<p>BL component in yaw coefficient for 10° pitch and 10° yaw for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The star marks the probe’s entrance into the boundary layer.</p>
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<p>BL component in yaw coefficient for −10° pitch and 10° yaw for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.34</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>16</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>. The star marks the probe’s entrance into the boundary layer.</p>
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<p>The velocity field from the PIV results can help simulate a probe traverse.</p>
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<p>Simulation of a calibration map evolution without probe intrusivity or wall-proximity effect.</p>
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<p>Calibration map evolution for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Perceived direction with vertical probes.</p>
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<p>Perceived direction with −10° pitch and 10° yaw.</p>
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<p>PIV velocity field for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>y</mi> <mo>*</mo> </msup> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>. The green dashed line is where the maximum velocity was extracted to build <a href="#ijtpp-09-00016-t007" class="html-table">Table 7</a>. The red dashed line is the wall. The grey area was not analysed because of the probe’s shadow. The blue zone around the head is a space polluted by laser reflections on the probe’s head.</p>
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<p>Calibration map evolution for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>.</p>
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<p>Perceived direction for lower Mach numbers.</p>
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<p>Comparison of the PIV pitch angle profile, the probe results, and the results corrected for the distance between the probe holes for <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mn>99</mn> </msub> <mo>/</mo> <msub> <mi>d</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>8</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>, 0° pitch, and 0° yaw.</p>
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<p>Summary of the wall-proximity and boundary layer main effects on calibration maps. Green arrows stand for the boundary layer effects and red arrows stand for the wall proximity effect.</p>
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65 pages, 7774 KiB  
Review
Unsteady Flows and Component Interaction in Turbomachinery
by Simone Salvadori, Massimiliano Insinna and Francesco Martelli
Int. J. Turbomach. Propuls. Power 2024, 9(2), 15; https://doi.org/10.3390/ijtpp9020015 - 5 Apr 2024
Cited by 1 | Viewed by 2698
Abstract
Unsteady component interaction represents a crucial topic in turbomachinery design and analysis. Combustor/turbine interaction is one of the most widely studied topics both using experimental and numerical methods due to the risk of failure of high-pressure turbine blades by unexpected deviation of hot [...] Read more.
Unsteady component interaction represents a crucial topic in turbomachinery design and analysis. Combustor/turbine interaction is one of the most widely studied topics both using experimental and numerical methods due to the risk of failure of high-pressure turbine blades by unexpected deviation of hot flow trajectory and local heat transfer characteristics. Compressor/combustor interaction is also of interest since it has been demonstrated that, under certain conditions, a non-uniform flow field feeds the primary zone of the combustor where the high-pressure compressor blade passing frequency can be clearly individuated. At the integral scale, the relative motion between vanes and blades in compressor and turbine stages governs the aerothermal performance of the gas turbine, especially in the presence of shocks. At the inertial scale, high turbulence levels generated in the combustion chamber govern wall heat transfer in the high-pressure turbine stage, and wakes generated by low-pressure turbine vanes interact with separation bubbles at low-Reynolds conditions by suppressing them. The necessity to correctly analyze these phenomena obliges the scientific community, the industry, and public funding bodies to cooperate and continuously build new test rigs equipped with highly accurate instrumentation to account for real machine effects. In computational fluid dynamics, researchers developed fast and reliable methods to analyze unsteady blade-row interaction in the case of uneven blade count conditions as well as component interaction by using different closures for turbulence in each domain using high-performance computing. This research effort results in countless publications that contribute to unveiling the actual behavior of turbomachinery flow. However, the great number of publications also results in fragmented information that risks being useless in a practical situation. Therefore, it is useful to collect the most relevant outcomes and derive general conclusions that may help the design of next-gen turbomachines. In fact, the necessity to meet the emission limits defined by the Paris agreement in 2015 obliges the turbomachinery community to consider revolutionary cycles in which component interaction plays a crucial role. In the present paper, the authors try to summarize almost 40 years of experimental and numerical research in the component interaction field, aiming at both providing a comprehensive overview and defining the most relevant conclusions obtained in this demanding research field. Full article
(This article belongs to the Special Issue Advances in Critical Aspects of Turbomachinery Components and Systems)
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Figure 1

Figure 1
<p>Secondary flow visualization in a high-pressure turbine blade.</p>
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<p>Visualization of the horseshoe vortex and of the tip leakage vortex in a high-pressure turbine blade along with the non-dimensional static pressure map on the lower end-wall.</p>
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<p>Hot spot generation in a lean-burn combustor coupled with a high-pressure turbine vane.</p>
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<p>Aerothermal field on the combustor/turbine interface (adapted from [<a href="#B25-ijtpp-09-00015" class="html-bibr">25</a>,<a href="#B26-ijtpp-09-00015" class="html-bibr">26</a>,<a href="#B27-ijtpp-09-00015" class="html-bibr">27</a>]).</p>
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<p>Definition of slip velocity components in turbine stages.</p>
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<p>Segregation effect generated by positive and negative jet.</p>
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<p>Typical residual swirl and temperature profile at the exit of a lean-burn gas turbine combustor [<a href="#B75-ijtpp-09-00015" class="html-bibr">75</a>].</p>
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<p>Effect of residual swirl on isentropic Mach number distribution at 15% of blade span (<b>a</b>) and at 85% of blade span (<b>b</b>) of a high-pressure turbine vane [<a href="#B75-ijtpp-09-00015" class="html-bibr">75</a>].</p>
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<p>Distributions of turbulence intensity on the combustor/turbine interface plane [<a href="#B92-ijtpp-09-00015" class="html-bibr">92</a>].</p>
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<p>Numerical Schlieren visualization of the shock system occurring in the CT3 high-pressure turbine stage at mid-span (adapted from [<a href="#B123-ijtpp-09-00015" class="html-bibr">123</a>]).</p>
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<p>Rotating stall mechanism in axial compressors.</p>
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<p>Domain coupling with overlapping regions (adapted from [<a href="#B92-ijtpp-09-00015" class="html-bibr">92</a>]).</p>
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<p>Unsteady coupling methodology with different time steps [<a href="#B25-ijtpp-09-00015" class="html-bibr">25</a>].</p>
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<p>Unsteady simulation of a blunt trailing edge test case with domain coupling and different treatments of Domain 1 outlet (adapted from [<a href="#B92-ijtpp-09-00015" class="html-bibr">92</a>]).</p>
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<p>Unsteady simulation of a turbulent pipe flow with domain coupling and different treatments for Domain 1 (SAS) and Domain 2 (URANS) [<a href="#B204-ijtpp-09-00015" class="html-bibr">204</a>].</p>
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<p>Geometrical modifications generated by domain scaling at mid-span of the CT3 blade (red–dotted lines represent the unscaled geometry) [<a href="#B123-ijtpp-09-00015" class="html-bibr">123</a>].</p>
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<p>Time-averaged non-dimensional static pressure distribution at CT3 blade mid-span calculated using 2D CFD with both domain scaling and phase lag techniques (adapted from [<a href="#B123-ijtpp-09-00015" class="html-bibr">123</a>]).</p>
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<p>Relative position between vane and blade for a generic blade count (adapted from [<a href="#B123-ijtpp-09-00015" class="html-bibr">123</a>]).</p>
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<p>Phase-shifted periodicity to be applied to single-passage simulations of turbine stages (adapted from [<a href="#B123-ijtpp-09-00015" class="html-bibr">123</a>]).</p>
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17 pages, 10631 KiB  
Article
Relationship between Casing Pressure and Non-Synchronous Vibration in an Axial Compressor
by Valerie Hernley, Aleksandar Jemcov, Jeongseek Kang, Matthew Montgomery and Scott C. Morris
Int. J. Turbomach. Propuls. Power 2024, 9(2), 14; https://doi.org/10.3390/ijtpp9020014 - 2 Apr 2024
Cited by 2 | Viewed by 1340
Abstract
The relationship between aerodynamic forcing and non-synchronous vibration (NSV) in axial compressors remains difficult to ascertain from experimental measurements. In this work, the relationship between casing pressure and blade vibration was investigated using experimental observations from a 1.5-stage axial compressor under off-design conditions. [...] Read more.
The relationship between aerodynamic forcing and non-synchronous vibration (NSV) in axial compressors remains difficult to ascertain from experimental measurements. In this work, the relationship between casing pressure and blade vibration was investigated using experimental observations from a 1.5-stage axial compressor under off-design conditions. The wavenumber-dependent auto-spectral density (ASD) of casing pressure was introduced to aid in understanding the characteristics of pressure fluctuations that lead to the aeromechanical response. Specifically, the rotor blade’s natural frequencies and nodal diameters could be directly compared with the pressure spectra. This analysis indicated that the rotating disturbances coincided with the first bending (1B) and second bending (2B) vibration modes at certain frequencies and wavenumbers. The non-intrusive stress measurement system (NSMS) data showed elevated vibration amplitudes for the coincident nodal diameters. The amplitude of the wavenumber-dependent pressure spectra was projected onto the single-degree-of-freedom (SDOF) transfer function and was compared with the measured vibration amplitude. The results showed a near-linear relationship between the pressure and vibration data. Full article
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Figure 1
<p>(<b>a</b>) Schematic of the 10 MW compressor rig at the Notre Dame Turbomachinery Lab. (<b>b</b>) Schematic of unsteady pressure and blade vibration instrumentation, where blue squares indicate 12 equally spaced pressure transducers (XTL-190(M) Kulites) at 5% axial chord upstream of the rotor leading edge and red circles indicate 8 non-equally spaced non-intrusive stress measurement system (NSMS) probes at the rotor leading edge.</p>
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<p>Compressor characteristic showing total-to-total pressure ratio (PR) versus corrected mass flow for a part-speed, IGV-partially-closed operating condition, as measured by a throttle transient experiment (black) and throttle steady-state experiments (colored circles). All values were normalized by the full-speed design point values.</p>
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<p>Leading-edge casing unsteady pressure ASD, <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </semantics></math>, during the throttle transient computed using moving windows of 0.002 s with 50% overlap. Numbers at the top correspond to steady experiments with the same corrected mass flow rate as a given time in the transient (<a href="#ijtpp-09-00014-f002" class="html-fig">Figure 2</a>).</p>
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<p>Instantaneous vibration amplitudes measured by NSMS during the transient experiment for mode families (<b>a</b>) 1B and (<b>b</b>) 2B for the nodal diameters, <span class="html-italic">p</span>, with the highest amplitude vibration. Numbers at the top correspond to steady experiments with the same corrected mass flow rate as a given time in the transient (<a href="#ijtpp-09-00014-f002" class="html-fig">Figure 2</a>).</p>
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<p>Vibration amplitude measured by NSMS for (<b>a</b>) 1B, <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>=</mo> <mo>−</mo> <mn>7</mn> </mrow> </semantics></math> and (<b>b</b>) 2B, <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>=</mo> <mn>9</mn> </mrow> </semantics></math> at steady operating points (<b>a</b>) OP11 and (<b>b</b>) OP3, respectively.</p>
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<p>Mean vibration amplitude, <math display="inline"><semantics> <msub> <mi>μ</mi> <mi>A</mi> </msub> </semantics></math>, measured by NSMS for mode families (<b>a</b>) 1B and (<b>b</b>) 2B. Colors correspond to the 11 steady operating points shown in <a href="#ijtpp-09-00014-f002" class="html-fig">Figure 2</a>.</p>
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<p>Contour plot of the casing pressure wavenumber-dependent ASD, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, for select steady operating points. Vibration modes overlaid via Equation (<a href="#FD7-ijtpp-09-00014" class="html-disp-formula">7</a>) are shown by the red circles (1B) and red squares (2B), and red arrows indicate select nodal diameters for each mode.</p>
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<p>Scatter plot of mean vibration amplitude from NSMS, <math display="inline"><semantics> <msub> <mi>μ</mi> <mi>A</mi> </msub> </semantics></math>, versus the SDOF-projected pressure amplitude, <math display="inline"><semantics> <mover accent="true"> <mi>P</mi> <mo>˜</mo> </mover> </semantics></math> (Equation (<a href="#FD8-ijtpp-09-00014" class="html-disp-formula">8</a>)), for each of the 11 steady operating points. Colors correspond to different nodal diameters, <span class="html-italic">p</span>, for mode families (<b>a</b>) 1B and (<b>b</b>) 2B.</p>
Full article ">
19 pages, 11703 KiB  
Article
Numerical and Experimental Study of Flutter in a Realistic Labyrinth Seal
by Oscar Bermejo, Juan Manuel Gallardo, Adrian Sotillo, Arnau Altuna, Roberto Alonso and Andoni Puente
Int. J. Turbomach. Propuls. Power 2024, 9(2), 13; https://doi.org/10.3390/ijtpp9020013 - 1 Apr 2024
Cited by 1 | Viewed by 1519
Abstract
Labyrinth seals are commonly used in turbomachinery in order to control leakage flows. Flutter is one of the most dangerous potential issues for them, leading to High Cycle Fatigue (HCF) life considerations or even mechanical failure. This phenomenon depends on the interaction between [...] Read more.
Labyrinth seals are commonly used in turbomachinery in order to control leakage flows. Flutter is one of the most dangerous potential issues for them, leading to High Cycle Fatigue (HCF) life considerations or even mechanical failure. This phenomenon depends on the interaction between aerodynamics and structural dynamics; mainly due to the very high uncertainties regarding the details of the fluid flow through the component, it is very hard to predict accurately. In 2014, as part of the E-Break research project funded by the European Union (EU), an experimental campaign regarding the flutter behaviour of labyrinth seals was conducted at “Centro de Tecnologias Aeronauticas” (CTA). During this campaign, three realistic seals were tested at different rotational speeds, and the pressure ratio where the flutter onset appeared was determined. The test was reproduced using a linearised uncoupled structural-fluid methodology of analysis based on Computational Fluid Dynamics (CFD) simulations, with results only in moderate agreement with experimental data. A procedure to adjust the CFD simulations to the steady flow measurements was developed. Once this method was applied, the matching between flutter predictions and the measured data improved, but some discrepancies could still be found. Finally, a set of simulations to retain the influence of the external cavities was run, which further improved the agreement with the testing data. Full article
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<p>Test rig assembly (baseline geometry).</p>
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<p>Schematics of testing procedure.</p>
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<p>Geometries tested in the E-Break project.</p>
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<p>Uncoupled structural-fluid linearised methodology.</p>
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<p>FEM model mesh and boundary conditions.</p>
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<p>CFD domains and associated grids. (<b>a</b>) Computational mesh for the simplified domain. (<b>b</b>) Computational mesh for the complete domain. (<b>c</b>) Detail of the computational mesh in the fin-clearance region.</p>
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<p>Contour of static radial displacements (m) of the baseline geometry. Shaft speed of 0 rpm (<b>left</b>), 1500 rpm (<b>centre</b>) and 2900 rpm (<b>right</b>).</p>
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<p>Modal and acoustic frequencies at 1500 rpm.</p>
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<p>Contour plot of the modal displacement module for the baseline geometry and torsion centre position. ND 1 (<b>left</b>), ND 3 (<b>centre</b>) and ND 5 (<b>right</b>).</p>
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<p>Contour plot of the modal displacement module for the 2-fin geometry and torsion centre position. ND 1 (<b>left</b>), ND 3 (<b>centre</b>) and ND 5 (<b>right</b>).</p>
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<p>Steady solution from CFD. Baseline geometry operating at 2900 rpm, ΔP = 0.1251 (MPa). Arrows indicate the flow direction, from right to left. (<b>a</b>) Static pressure (MPa). (<b>b</b>) Mach number. (<b>c</b>) Detail of the left-most (last) fin clearance. Mach number.</p>
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<p>Unsteady pressure field (MPa) at inter-fin cavities for the baseline geometry, simplified domain and nominal (0.3 mm) gaps. Operating point: 1500 rpm, ΔP = 0.1513 MPa.</p>
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<p>Baseline geometry experimental SG readings (CTA Campaign).</p>
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<p>Two-fin geometry experimental SG readings (CTA Campaign).</p>
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<p>Fin clearances influence on critical aerodynamic damping ratio. (<b>a</b>) Baseline geometry operating at 0 rpm and ΔP = 0.1674 MPa. (<b>b</b>) Two-fin geometry operating at 1500 rpm and ΔP = 0.0968.</p>
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<p>Unsteady pressure in external cavities for ND 0 (MPa).</p>
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<p>Influence of external cavities in the critical aerodynamic damping ratio. Simulations with adjusted gaps. (<b>a</b>) Baseline geometry operating at 1500 rpm and ΔP = 0.1513 MPa. (<b>b</b>) Two-fin geometry operating at 1500 rpm and ΔP = 0.0968 MPa.</p>
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16 pages, 4744 KiB  
Article
Modelling Method for Aeroelastic Low Engine Order Excitation Originating from Upstream Vanes’ Geometrical Variability
by Marco Gambitta, Bernd Beirow and Sven Schrape
Int. J. Turbomach. Propuls. Power 2024, 9(2), 12; https://doi.org/10.3390/ijtpp9020012 - 1 Apr 2024
Viewed by 1247
Abstract
The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical [...] Read more.
The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical variability affects the flow traversing it. This impacts the downstream rotor, especially when considering the aeroelastic excitation forces. Optical surface scans coupled with a parametrisation method allow for acquiring the information relative to the real aerofoils geometries. The measured data are included in a multi-passage and multi-stage CFD setup to represent the mistuned flow. In particular, low excitation harmonics on the rotor vane are introduced due to the geometrical deviations of the upstream stator. The introduced low engine orders, as well as their amplitude, depend on the stator geometries and their order. A method is proposed to represent the phenomena in a reduced CFD domain, limiting the size and number of solutions required to probabilistically describe the rotor excitation forces. The resulting rotor excitation forces are reconstructed as a superposition of disturbances due to individual stator aerofoils geometries. This indicates that the problem is linear in the combination of disturbances from single passages. Full article
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<p>Radial sections used for the parametric description of a VSV’s optical surface scan.</p>
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<p>Vibration mode shapes of interest for the second stage rotor.</p>
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<p>Numerical and experimental steady state results on VSV1, R2 and VSV2 at 90% nominal mechanical speed: (<b>a</b>) numerical relative Mach number at 90% channel height; (<b>b</b>) numerical and experimental total pressure’s radial distribution upstream of the variable stator vanes [<a href="#B20-ijtpp-09-00012" class="html-bibr">20</a>].</p>
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<p>Stator–Rotor–Stator (SRS) configuration forced response: (<b>a</b>) MPMR representation of the investigated test rig for the SRS setup; (<b>b</b>) excitation forces amplitude spectra of the two vibration modes, comparing the FA and the MPMR CFD results for the tuned nominal geometry SRS setup.</p>
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<p>Full Annulus (FA) comparison between tuned and mistuned setups: (<b>a</b>) geometry comparison between the FA of the tuned setup and the mistuned VSV1 setup; (<b>b</b>) spectra of the two vibration modes, comparing the FA tuned setup and the FA mistuned VSV1 setup CFD results.</p>
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<p>Mixture of the local forcing function <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>f</mi> </mrow> <mrow> <mi>b</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> with respect to blade <span class="html-italic">b,</span> with the modal forcing computed for the neighbouring blades <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Modal forcing mixture method: (<b>a</b>) CFD domain used for the MPMR forcing mixture individual solutions; (<b>b</b>) comparison of the forcing spectra between a FA CFD and the MPMR mixture results.</p>
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<p>MPMR superposition method’s FA disturbances for a set of aerofoils with considered geometrical deviations (rotor mode <span class="html-italic">m</span>); the vertical dotted lines indicate the wake position for blade <span class="html-italic">b</span>.</p>
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<p>Modal forcing superposition method (<math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>): (<b>a</b>) CFD domain used for the individual MPMR solutions computed for the forcing superposition; (<b>b</b>) comparison of the forcing spectra between a FA CFD and the MPMR superposition results.</p>
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<p>Excitation forces <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>F</mi> </mrow> <mrow> <mi>e</mi> </mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in the time domain for the investigated vibration modes; comparison between the FA CFD and the MPMR superposition results.</p>
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<p>Modal forcing superposition method on extended sector (<math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>): (<b>a</b>) CFD domain used for the individual MPMR solutions computed for the forcing superposition; (<b>b</b>) comparison of the forcing spectra between a FA CFD and the MPMR superposition results.</p>
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