Compressible Large Eddy Simulation Research Articles

Incompressible versus compressible large eddy simulation for the identification of premixed flame dynamics

The present work compares the respective advantages and disadvantages of compressible and incompressible computational fluid dynamics (CFD) formulations when used for the estimation of the acoustic flame response. The flame transfer function of a turbulent premixed swirl-stabilized burner is determined by applying system identification (SI) to time series data extracted from large eddy simulation (LES). By analyzing the quality of the results, the present study shows that incompressible simulations exhibit several advantages over their compressible counterpart with equal prediction of the flame dynamics. On the one hand, the forcing signals can be designed in such a way that desired statistical properties can be enhanced, while maintaining optimal values in the amplitude. On the other hand, computational costs are reduced and the implementation is fundamentally simpler due to the absence of acoustic wave propagation and corresponding resonances in the flame response or even self-excited acoustic oscillations. Such an increase in efficiency makes the incompressible CFD/SI modeling approach very appealing for the study of a wide variety of systems that rely on premixed combustion. In conclusion, the present study reveals that both methodologies predict the same flame dynamics, which confirms that incompressible simulation can be used for thermoacoustic analyses of acoustically compact velocity-sensitive flames.

Adaptative finite element simulation of unsteady turbulent compressible flows on unstructured meshes

The simulation of high-speed turbulent compressible flows using Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and a mesh adaptation strategy is presented in this work. A compressible dynamic Smagorinsky model is employed for the compressible LES model and the CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes. An accurate mesh adaptation scheme is frequently applied along the simulation including mesh refinement, mesh coarsening, edge or face swapping and a vertex smoothing technique in order to control the interpolation error and the mesh size. A feature-based error estimation is employed considering multi-scale and multi-metric intersection in order to capture turbulence effects. Two and three-dimensional applications are evaluated in order to investigate the capabilities of the present approach for evaluating external turbulent and compressible aerodynamics problems. The turbulent transonic flow around a circular cylinder in 2D and 3D domains and the turbulent supersonic flow past a blunt cylinder-flare model are investigated. Aerodynamic coefficients, frequency analysis and pressure distributions are compared against experimental data and other numerical simulations.

The noise-generating mechanism of rod-airfoil configuration and the effect of spanwise length on noise prediction

The wake-blade interaction in turbo-engines is the primary source of broadband noise. In this work, the noise mechanism of a benchmark rod-airfoil configuration is exhaustively analyzed using compressible Large Eddy Simulation (LES) and Ffowcs Williams-Hawkings (FW-H) methods. The baseline model with a spanwise length shortened by 7d (d is the rod diameter) is simulated under periodic boundary conditions, and the effect of spanwise lengths on noise prediction and correlation is investigated in combination with two other models (3d and 1d). In terms of the baseline model, the noise predicted by different FW-H surfaces is compared first, and the noise radiated from different chordwise and spanwise regions of the airfoil surface reveal the generating mechanism of the main dipolar noise and the effect of periodic boundary conditions on noise prediction, respectively. Additionally, the fluctuating surface pressure characterized at four frequency bands confirms that the wake-airfoil interaction dominates the leading-edge noise at low frequencies. The characteristic frequencies of the noise and transient velocity fields reveal that the primary broadband noise source is the interaction of large-scale vortices with the airfoil surface at the leading-edge region. Finally, the effect of spanwise length on noise prediction and correlation is studied for three models. The differences in the flow structures lead to different features of their coherence coefficients. The results presented in this work provide a comprehensive understanding of the noise-generating mechanism of wake-airfoil interaction in turbomachinery and the practical application of simplified models in the future numerical simulations.

Investigation of soot formation in turbulent spray flame burning real fuel

This work uses Large Eddy Simulation (LES) combined with an accurate chemical description to predict soot formation in a turbulent spray flame burning real fuel at atmospheric conditions. Understanding and being able to predict soot formation in practical configurations burning complex liquid fuel is essential for the design of engines meeting present and future environmental requirements. The prediction of soot formation with numerical simulations has been mostly limited to academic configurations burning light gaseous fuel. This is explained by the numerical cost of (i) the fuel oxidation chemistry including soot precursors like Polycyclic Aromatic Hydrocarbons (PAH), and (ii) the modeling of two dispersed phases, i.e., the liquid fuel spray and the soot particles. In this work, an Analytically Reduced Chemistry (ARC) for real fuels is proposed to allow a direct integration of accurate combustion chemistry including PAH in the compressible LES solver AVBP. The ARC model is coupled with a Lagrangian particle tracking approach for both the fuel droplets and the soot, including for the latter the description of the complex physical and chemical processes driving the particle evolution. Validation is first performed in a one-dimensional ethylene/air flame configuration, experimentally studied in the literature at several operating points. The numerical profiles of both the soot volume fraction and the soot diameter are in good agreement with measurements. This allows to apply the LES methodology to the sooting swirled turbulent liquid JetA-1/air combustor measured at UTIAS. Very satisfying predictions for both the flow dynamics and the soot production are obtained. The analysis of the results brings valuable new insights on the interaction between fuel droplets, turbulent combustion, PAH and soot evolution in such complex flames.

Large Eddy Simulation of a Pistonless Constant Volume Combustor: A New Concept of Pressure Gain Combustion

Abstract Classical gas turbine thermodynamic cycle has undergone no change over the last decades. The most important efficiency improvements have been obtained by reducing thermal losses and raising the overall pressure ratio and peak temperature. Pressure gain combustion (PGC) represents an increasingly interesting solution to break out current technological limits. Indeed cycle models show that a pressure raise across the combustion process would reduce fuel consumption, increasing efficiency. Providing an efficiency close to the corresponding detonative technological concepts, constant volume combustion (CVC) represents a viable solution that still needs to be studied. In this work, the CV2 (constant-volume combustion vessel) installed at the Pprime laboratory (France) is numerically investigated using the high-fidelity compressible large eddy simulation (LES) solver AVBP. All the successive phases of the CVC cycle, i.e., air intake, fuel injection, spark-ignited combustion, and exhaust, are considered in the LES. Intake and exhaust valves are properly represented by novel boundary conditions able to mimic the valves impact on the flow without the need to directly consider their presence and dynamics during the simulation, reducing the computational costs. The spark ignition is modeled as an energy deposition term added to the energy equation. The combustion phase is treated by the dynamic version of the thickened flame model (DTFLES) extended to deal with nonconstant pressure combustion. Time-resolved particle imaging velocimetry (PIV) and pressure measurement inside the chamber reveal that cold and reactive turbulent flow are well captured in all the phases, showing the reliability of the approach and the models used.

Numerical study on the aeroacoustics and interaction of two distributed-propulsion propellers in co- and counter-rotations

Driven by increasing demands for a sustainable and eco-friendly future in aviation, distributed electric propulsion (DEP) systems have received much attention for their high aerodynamic efficiency. DEP systems of lower noise emissions are desired by customers and policymakers and therefore it is important to understand the aeroacoustics and interaction of distributed propeller systems. In this paper, the aeroacoustics of a simplified DEP system is numerically investigated. The system consists of two Mejzlik 2-blade-9 × 9-inch propellers that are distributed side by side, with a tip-to-tip distance of 10 mm. Their rotating speed and freestream velocity are set as 6500 RPM and 12 m/s, respectively. The configurations of both co- and counter-rotation are considered. Compressible Large-eddy simulations are performed to obtain the flow solutions, and the Ffowcs Williams and Hawkings (FW-H) method is used to calculate the corresponding far-field acoustic solutions. The results present interaction effects for both configurations and compare against isolated propeller results. First, the thrust and the induced sound of each propeller are examined and secondly the impact of the interaction effects on the aerodynamic and acoustic performance is investigated. Finally, sound interference in the acoustic fields is assessed and compared for both co- and counter-rotation configurations.

Numerical investigation on aerodynamic forces and flow patterns of high-speed trains from open air into long tunnel

Method of sliding mesh and segregated compressible large eddy simulation was used to simulate the flow field of a 1/25 scale eight-coach China Railway train running from open air into long tunnel, validated by the same scale Intercity Express 2 (ICE2) train. Side force fluctuation increases greatly when train enters tunnel. Short-time Fourier transform on side force coefficients of Coach 5 and 8 presents the peak frequency at about 95Hz. The hunting motion of laterally swinging airflow in lower space near the train is analyzed. Correlation analyses of pressure time histories reflect its traveling mode. Propagating velocity is 57–62% in open air, and 75–80% in tunnel of the operating speed. Wavelength is both in the range of 0.3–0.6m. Spectral Proper Orthogonal Decomposition (SPOD) and POD extract the transverse pattern of hunting motion. Total POD energy increases when hunting motion appears. Consistent to side force spectrums, SPOD energy spectrums present peak frequencies at 95Hz, where energy is larger in tunnel than open air. Mode 1 of POD and SPOD under peak frequencies presents similar spatial distribution: anti-symmetrical streamwise velocity fluctuation, vortex pairs outside bogie cavities and large-scale circulation. The relation between coherent structures and side forces is well established by SPOD.

Numerical investigation of whistling sound in narrow-gap flow of automobile side mirror

It is frequently reported that a high-frequency whistling noise is generated by airflow through the narrow gap of a vehicle’s side mirror under certain driving conditions. The aim of the present study is to identify the generation mechanism of the narrow gap whistling of a side mirror, which is considered one of the most challenging problems due to too the small dimensions and complex geometry of the gap. A wind tunnel test was performed to find the flow conditions where the whistling sound is generated. The relative directions and speeds of the airflow were identified for the onset of the whistling sound and its frequency. A numerical analysis of the external and internal flows of the side mirror was then conducted using compressible Large Eddy Simulation (LES) techniques with high-resolution grids to capture the generation mechanism of the whistling sound, which is generally based on a feedback mechanism between the vortex and sound waves. The numerical result was validated through a comparison of the predicted sound pressure spectrum with the measured ones. The main aerodynamic sources were identified using the vortex sound sources, and a generation mechanism of the whistling sound based on the feedback mechanism was revealed. This was done by visualizing the standing wave pattern in the narrow gap, which was coupled with the identified vortex sound sources.

Numerical Aeroacoustic Analysis of a Linear Compressor Cascade with Tip Gap

A wall-resolved compressible large-eddy simulation is performed on a linear compressor cascade with tip gap to investigate the tip-leakage noise sources. The cascade is composed of eight 4%-thick modified circular-arc blades with a 254 mm chord and a 235 mm spacing. The chord-based Reynolds number is , and the Mach number is 0.07. The gap considered in this study is 4.0 mm (1.6% chord). An aerodynamic analysis of the tip-leakage flow coupled with a Ffowcs-Williams and Hawkings analogy to compute the noise in the far field allows identifying the main tip-noise mechanisms. The acoustic contribution of the tip-leakage flow is highlighted by comparison with the trailing-edge noise contribution obtained with a 25 mm slice configuration at midspan without tip gap. This small-span configuration is also simulated using large-eddy simulation and allows computing the blade trailing-edge noise. A dynamic mode decomposition performed on the full configuration close to the tip highlights the main noise source, located around 75% chord with a propagation frequency between 5 and 6 kHz. The acoustic waves propagate mostly downstream of the cascade and on the pressure side. This study provides the first high-fidelity wall-resolved compressible simulation of a linear compressor cascade comprising a comprehensive investigation of the tip-leakage noise sources, which is a necessary first step toward fan tip-noise prediction.

Surface pressure spectrum variation with Mach number on a CD airfoil

The surface pressure spectrum characteristics are studied on a Controlled Diffusion airfoil at varying Mach numbers and a fixed Reynolds number. Compressible large eddy simulation datasets have been used for this analysis. The study focusses on the noise generation mechanism and the source locations responsible for it. A mid-high frequency hump is observed for the higher Mach number cases in the pressure spectrum and the amplitude of this observed hump increases with Mach number. To investigate the cause of this hump, different hydrodynamic and acoustic pressure modes traveling at specific speeds are obtained by a wavenumber–frequency decomposition. The acoustic component originating from the separation bubble region near the leading edge is found to be responsible for the hump in the pressure spectrum. The interaction of hydrodynamic and acoustic waves also plays a significant role in the appearance of the hump in the spectrum. There is also an increase in the amplitude of the high frequency region in the acoustic spectrum as we go towards the trailing edge for higher Mach number which can be attributed to an increase in turbulent fluctuation amplitude in the leading edge region. Furthermore, stability analysis has been performed on one-dimensional mean boundary-layer profiles. The higher reverse velocity in the separation bubble with increasing Mach number seems to be causing higher growth rates of instabilities, ultimately resulting in the significant surface spectrum variations. The directivity in the farfield also confirms a significant contribution of the hump in the spectrum in the overall sound pressure level.

Non-Equilibrium Time-Relaxation Kinetic Model for Compressible Turbulence Modeling

For the first time, the non-equilibrium time-relaxation kinetic model (NTRKM) is proposed for compressible turbulence modeling on unresolved grids. Within the non-equilibrium time-relaxation framework, NTRKM is extended in the form of modified Bhatnagar-Gross-Krook model. Based on the first-order Chapman-Enskog expansion, NTRKM connects with the six-variable macroscopic governing equations. The first five governing equations correspond to the conservative laws in mass, momentum and total energy, while the sixth equation governs the evolution of unresolved turbulence kinetic energy Kutke. The unknowns in NTRKM, including turbulent relaxation time and source term, are determined by essential gradient-type assumption and standard dynamic modeling approach. Current generalized kinetic model on unresolved grids consequently offers a profound mesoscopic understanding for one-equation subgrid-scale turbulence kinetic energy Ksgs model in compressible large eddy simulation. To solve NTRKM accurately and robustly, a non-equilibrium gas-kinetic scheme is developed, which succeeds the well-established gas-kinetic scheme for simulating Navier-Stokes equations. Three-dimensional decaying compressible isotropic turbulence and temporal compressible plane mixing layer on unresolved grids are simulated to evaluate the generalized kinetic model and non-equilibrium gas-kinetic scheme. The performance of key turbulent quantities up to second-order statistics confirms that NTRKM is comparable with the widely-used eddy-viscosity Smagorinsky model (SM) and dynamic Smagorinsky model (DSM). Specifically, compared with the DNS solution in temporal compressible plane mixing layer, the performance of NTRKM is much closer with DSM and better than SM. This study provides a workable approach for compressible turbulence modeling on unresolved grids.

Comparative Analysis of Surface Pressure Fluctuations of High-Speed Train Running in Open-Field and Tunnel Using LES and Wavenumber-Frequency Analysis

The interior noise of a high-speed train due to the external flow disturbance is more than ever a major problem for product developers to consider during a design state. Since the external surface pressure field induces wall panel vibration of a high-speed train, which in turn generates the interior sound, the first step for low interior noise design is to characterize the surface pressure fluctuations due to external disturbance. In this study, the external flow field of a high-speed train cruising at a speed of 300 km/h in open-field and tunnel are numerically investigated using high-resolution compressible LES (large eddy simulation) techniques, with a focus on characterizing fluctuating surface pressure field according to surrounding conditions of the cruising train, i.e., open-field and tunnel. First, compressible LES schemes with high-resolution grids were employed to accurately predict the exterior flow and acoustic fields around a high-speed train simultaneously. Then, the predicted fluctuating pressure field on the wall panel surface of a train was decomposed into incompressible and compressible ones using the wavenumber-frequency transform, given that the incompressible pressure wave induced by the turbulent eddies within the boundary layer is transported approximately at the mean flow and the compressible pressure wave propagated at the vector sum of the sound speed and the mean flow velocity. Lastly, the power levels due to each pressure field were computed and compared between open-field and tunnel. It was found that there is no significant difference in the power levels of incompressible surface pressure fluctuations between the two cases. However, the decomposed compressible one in the tunnel case is higher by about 2~10 dB than in the open-field case. This result reveals that the increased interior sound of the high-speed train running in a tunnel is due to the compressible surface pressure field.

Numerical analysis of indirect noise generated by compositional inhomogeneities using large eddy simulation

In the present work, indirect noises generated by compositional disturbances in a non-isotropic convergent nozzle are studied using Large Eddy Simulations (LESs). An in-house compressible LES code, Boundary Fitted Flow Integrator-LESc, is utilized to simulate the noise generation in the system. A non-reflective outlet boundary condition is used to eliminate numerical reflections and to ensure the reproduction of the operating conditions in the experiments. The experiments are designed to feature two configurations with different injection positions, which enable the separation of direct and indirect noises. Different operating conditions are investigated, including different injection gases and air mass flow rates. This present paper compares computational results with the experimental measurements. The results revealed that the processes of direct and indirect noise generation are successfully reproduced in the LES, with the noise magnitudes in good agreement with those in the measurements. Injection of gases with smaller (He) and larger (CO2) molar masses compared to air is found to generate negative and positive indirect noises, respectively, in the LES, which is consistent with the experimental findings. The effect of different air mass flow rates is also investigated and discussed, and the direct noise and indirect noise amplitudes are both found to be closely related to the air mass flow rate.

A combined oscillation cycle involving self-excited thermo-acoustic and hydrodynamic instability mechanisms

The paper examines the combined effects of several interacting thermo-acoustic and hydrodynamic instability mechanisms that are known to influence self-excited combustion instabilities often encountered in the late design stages of modern low-emission gas turbine combustors. A compressible large eddy simulation approach is presented, comprising the flame burning regime independent, modeled probability density function evolution equation/stochastic fields solution method. The approach is subsequently applied to the PRECCINSTA (PREDiction and Control of Combustion INSTAbilities) model combustor and successfully captures a fully self-excited limit-cycle oscillation without external forcing. The predicted frequency and amplitude of the dominant thermo-acoustic mode and its first harmonic are shown to be in excellent agreement with available experimental data. Analysis of the phase-resolved and phase-averaged fields leads to a detailed description of the superimposed mass flow rate and equivalence ratio fluctuations underlying the governing feedback loop. The prevailing thermo-acoustic cycle features regular flame liftoff and flashback events in combination with a flame angle oscillation, as well as multiple hydrodynamic phenomena, i.e., toroidal vortex shedding and a precessing vortex core. The periodic excitation and suppression of these hydrodynamic phenomena is confirmed via spectral proper orthogonal decomposition and found to be controlled by an oscillation of the instantaneous swirl number. Their local impact on the heat release rate, which is predominantly modulated by flame-vortex roll-up and enhanced mixing of fuel and oxidizer, is further described and investigated. Finally, the temporal relationship between the flame “surface area,” flame-averaged mixture fraction, and global heat release rate is shown to be directly correlated.

LES – DFSD modelling of vented hydrogen explosions in a small-scale combustion chamber

Accidental explosions are a plausible danger to the chemical process industries. In the event of a gas explosion, any obstacles placed within the path of the flame generate turbulence, which accelerates the transient flame and raises explosion overpressure, posing a safety hazard. This paper presents numerical studies using an in-house computational fluid dynamics (CFD) model for lean premixed hydrogen/air flame propagations with an equivalence ratio of 0.7. A laboratory-scale combustion chamber is used with repeated solid obstacles. The transient compressible large eddy simulation (LES) modelling technique combined with a dynamic flame surface density (DFSD) combustion model is used to carry out the numerical simulations in three-dimensional space. The study presented uses eight different baffle configurations with two solid obstructions, which have area blockage ratios of 0.24 and 0.5. The flame speed, maximum rate of pressure-rise as well as peak overpressure magnitude and timing are presented and discussed. Numerical results are validated against available published experimental data. It is concluded that, increasing the solid obstacle area blockage ratio and the number of consecutive baffles results in a raised maximum rate of pressure rise, higher peak explosion overpressure and faster flame propagation. Future model development would require more experimental data, probably in a more congested configuration.

Modelling of sound-vortex interaction for the flow through an annular aperture

The acoustic characteristics of bluff-body burners play a critical role in the combustion stability for combustors using this type of burners. The acoustic modelling of an axisymmetric bluff-body burner entails properly capturing the sound-vortex interaction for the flow through the annular aperture of the burner. Such a problem pertaining to annular apertures can also be of relevance to other engineering applications, such as acoustic dampers or turbofan duct systems. The methodology of combining suitable acoustic Green’s functions with a vortex sheet model has been applied extensively in previous theoretical studies of the acoustic response of a short circular orifice with a mean flow passing through it. In this work, the Green’s function and vortex sheet model theory is generalised in order to efficiently predict the acoustic characteristics of thin annular apertures sustaining a mean flow, which effectively emulate the typical axisymmetric bluff-body burner configurations in realistic combustors. This requires the incorporation of multiple Kutta conditions for modelling the vortex shedding and multiple vortex sheets for modelling the interaction of the shed vorticity and the acoustics. A high-resolution compressible Large Eddy Simulation (LES) of a simplified representative geometry is performed for validation; the analytical prediction and numerical findings show very good agreement, and the LES further provides key insights into the speed with which vortical disturbances convect downstream.

Low-Noise Synthetic Turbulence Tailored to Lateral Periodic Boundary Conditions

The present work is dedicated to turbulence synthesis tailored to lateral periodic boundary conditions for direct noise computations through compressible large eddy simulations. Synthetic turbulence can be essential for aeroacoustic applications when computing airfoil turbulent inflow noise or for accurately capturing the behavior of boundary layers. This behavior determines both trailing edge noise and complex flow structures such as laminar separation bubbles. For airfoil simulation purposes, spanwise periodic boundary conditions are usually considered. If synthetic perturbations are injected without observing the periodicity rule, strong spurious pressure waves are emitted and pollute the entire computational domain. In this work, the random Fourier modes method for turbulence generation is adapted in order to respect the spanwise periodicity constraint right at the computational domain inlet. This approach does not affect the turbulence properties such as the spectral shape and the turbulent kinetic energy decay. Since the emphasis is put on the generation and convection of the turbulence, only the turbulence convection region between the inlet and the airfoil is considered in this paper, without the airfoil. Two geometrical configurations are tested: the first one is a simple box with a constant mesh size, and the second one concentrates the fine cells on the area in front of the airfoil. In the second configuration, the computational cost is reduced by up to 25%, but more spurious noise is present because of interpolation areas between different grids using the Chimera method. Finally, the results’ reproducibility is assessed using different turbulence realizations.

On the use of a two-layer model for large-eddy simulations of supersonic boundary layers with separation

The two-layer modeling approach has become one of the most promising and successful methodology for simulating turbulent boundary layers in the past ten years. In the present study, a mixed wall model for large-eddy simulations (LES) of high-speed flows is proposed which combine two approaches; the thin-Boundary Layer Equations (TBLE) model of Kawai and Larsson (1994) and the analytical wall-layer model of Duprat et al. (2011) for streamwise pressure gradients. The new hybrid model has been efficiently implemented into a three-dimensional compressible LES solver and validated against DNS of a spatially-evolving supersonic boundary layer (BL) under moderate and strong pressure gradients, before being employed for the prediction of nozzle flow separations at different flow conditions, ranging from weakly to highly over-expanded regimes. A good agreement is obtained in terms of mean and fluctuating quantities compared to the DNS results. Particularly, the current wall-modeled LES results are found to perfectly match the DNS data of supersonic BL with/out pressure gradient. It is also shown that the model can account for the effect of the large-scale turbulent motions of the outer layer, indicating a good interaction between the inner and the outer part of the wall layer. In terms of simulations costs and improvements of computing power, the obtained results highlight the capability of the current wall-modeling LES strategy in saving a considerable amount of computational time compared to the wall-resolved LES counterpart, allowing to push further the simulations limits. Furthermore, the application of these computationally low-costly LES simulations to nozzle flow separation allows to clearly identify the origin of the shock unsteadiness, and the existence of broadband and energetically-significant low-frequency oscillations (LFO) in the vicinity of the separation region.

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence II: Coarse-graining analysis of compressible Ksgs budget

The direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime with Mat=1.2 has been investigated by the high-order gas-kinetic scheme (HGKS) (Cao et al. (2019) [8]). In this study, the DNS on a much higher initial turbulent Mach number up to Mat=2.0 is performed by HGKS, which confirms the super robustness of HGKS. The coarse-graining analysis of subgrid-scale (SGS) turbulent kinetic energy Ksgs budget is fully analyzed for constructing one-equation SGS model in the compressible large eddy simulation (LES). The exact compressible SGS turbulent kinetic energy Ksgs transport equation is derived with density weighted filtering process. Based on the compressible Ksgs transport equation, the coarse-graining processes are implemented on three sets of unresolved grids with the Box filter. The coarse-graining analysis of compressible Ksgs budgets shows that all unresolved source terms are dominant in the current system. Especially, the magnitude of SGS pressure-dilation term is on the order of SGS solenoidal dissipation term within the initial acoustic time scale. Therefore, the SGS pressure-dilation term cannot be neglected as that in the previous work. The delicate coarse-graining analysis of SGS diffusion terms in compressible Ksgs equation also confirms that both the fluctuation velocity triple correlation term and the pressure-velocity correlation term are dominant terms. The current analysis provides an indication on the order of magnitude of all SGS terms in compressible Ksgs budget, which provides a solid basis for compressible LES modeling of high Mach number turbulent flow.

Aerodynamic investigation of a linear cascade with tip gap using large-eddy simulation

The flow in a linear compressor cascade with tip gap is simulated using a wall-resolved compressible Large-Eddy Simulation. The cascade is based on the Virginia Tech Low Speed Cascade Wind Tunnel. The Reynolds number based on the chord is 3.88 x 10⁵ and the Mach number is 0.07. The gap considered in this study is 4.0 mm (2.9% of axial chord). An aerodynamic analysis of the tip-leakage flow allow us identifying the main mechanisms responsible for the development and the convection of the tip-leakage vortex downstream of the cascade. A region of high turbulence and vorticity levels is located along an ellipse that borders the top of the tip-leakage vortex. The influence of the airfoil suction side boundary layer development on the tip-leakage vortex is highlighted by tripping the flow. A tripped boundary layer induces a stronger and larger tip-leakage vortex that tends to move further away from the airfoil suction side and from the endwall compared with an untripped flow. The boundary layer turbulent state influences the tip-leakage flow development.