Eddy Simulation Of Compressible Flows Research Articles

Extension of the local domain-free discretization method to large eddy simulation of compressible flows

Most of the flow problems encountered in practical engineering are wall-bounded turbulent flows at high Reynolds numbers. Wall-modeled large eddy simulation (WMLES) is one of the most viable approaches for predicting these realistic flows. Immersed boundary (IB) approach is an efficient computational technique to solve flow problems involving complex and/or moving geometries. This work extends a sharp-interface IB method, named the local domain-free discretion (DFD), to WMLES of compressible flows at high Reynolds numbers. An equilibrium wall model based on solving the simplified compressible turbulent boundary layer equations is utilized to alleviate the requirement of high near-wall mesh resolution. In conjunction with the approximate boundary conditions prescribed by the modeled wall shear stress and wall heat flux, the tangential velocity and temperature at an exterior dependent node are evaluated. Then, the closure of the discrete form of governing equations at an interior node in the immediate vicinity of the immersed wall is accomplished. A simple non-equilibrium correction of the wall shear stress provided by the equilibrium wall model is introduced explicitly. The WMLES/DFD method is applied to a supersonic zero-pressure-gradient turbulent boundary layer flow, a shock wave/flat-plate boundary layer interaction, a supersonic compression ramp flow and high-speed turbulent Couette flows with various thermal boundary conditions. The influence of grid resolution is investigated in the simulation of zero-pressure-gradient turbulent boundary layer flow. By comparing the computed results with the referenced experimental data and/or numerical results, the accuracy and ability of the WMLES/DFD method to simulate compressible turbulent flows are verified.

Hysteresis of aeroacoustic sound generation in the articulation of [s

A fricative consonant (e.g., [s]) is known to be pronounced by a turbulent jet flow inside the oral cavity. In this study, the effects of tongue motion on the aeroacoustic sound generation during the articulation of [s] were investigated through the large eddy simulation of compressible flow using a simplified vocal tract model. The walls of the simplified model were expressed using a volume penalization approach as an immersed boundary method, and the tongue geometry was ascended and descended from the position of /u/ to /s/ with tongue speeds of 40 mm/s, 60 mm/s, and 80 mm/s. The simulated acoustic pressure at a far-field sampling point was compared with previous experimental measurements, and the acoustic characteristics of the simulated sound reasonably agreed with those of the experiment. The overall acoustic amplitudes increased and decreased in accordance with tongue ascent and descent, and these transitions in amplitudes were almost the same for the different tongue speeds. Meanwhile, we found a hysteresis effect on the overall acoustic amplitudes between tongue ascent and tongue descent. This hysteresis was caused by the larger velocity fluctuations and vortices near the upper and lower teeth during tongue descent, and the results indicated that these flow differences occurred owing to the inertia of the turbulent flow structures and the aerodynamic pressures over the constriction of the vocal tract. This study suggests that these phenomena cause a delay in the sound generation of [s].

An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows

In this work we present an a posteriori high-order finite volume scheme for the computation of compressible turbulent flows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the flow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical flux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of the proposed numerical scheme.

Effects of vocal tract geometrical differences on flow and sound of sibilant fricatives

Sibilant fricatives are known to be produced by controlling a turbulent jet flow in a front part of the vocal tract. However, the manner of the control in each individual is still unclear. In this study, the vocal tract geometries of sibilant fricatives /s/ and /∫/ were extracted from magnetic resonance imaging (MRI) and large eddy simulation was conducted to clarify the relationship among the vocal tract geometries, flows, and acoustic characteristics. Five male Japanese subjects assumed a supine position in the MR machine, and images of the vocal tract were corrected while the subject was sustaining /s/ and /∫/. From the corrected images, computational grids were constructed, and large eddy simulation of compressible flow was applied to simulate both the turbulent flow and sound generation. Results of the simulations showed that the configuration of jet flow in each vocal tract was different, and the maximum amplitude of sound source distributed in different positions in the front part of the vocal tracts. By extracting the characteristic dimensions of each vocal tract, we found that a space between lower incisor and tongue constriction is important for the formation of individual acoustic characteristics of sibilant fricatives.

A consistent multi-level subgrid scale closure for large eddy simulation of compressible flow using adaptive mesh refinement

A novel subgrid closure model is proposed for performing Large Eddy Simulation (LES) of turbulent compressible flows with block structured Adaptive Mesh Refinement (AMR) strategy. The new approach, henceforth called as AMRLES, is an improvement over the well-established one-equation based subgrid turbulent kinetic energy model with corrections proposed to consistently handle the total resolved turbulent kinetic energy across a multi-level AMR grid hierarchy. The proposed correction for the subgrid kinetic energy is based on an explicit on-the-fly filtering operation from finer grids to underlying coarser grids. The effect of the inter-grid correction is demonstrated by investigating advection of decaying isotropic turbulence across a coarse/fine and fine/coarse AMR grid interface. In the case of fine-to-coarse transition, the multi-level model is shown to correctly recover the subgrid turbulent kinetic energy. AMRLES is then applied to study the canonical problem of shock turbulent interaction. Two different Reynolds numbers are considered and the behavior of the inter-grid corrections on the subgrid turbulent kinetic energy and the subgrid turbulent stresses are analyzed for both the cases. Comparison with filtered DNS results indicates that AMRLES is able to predict the behavior of turbulent statistics across the shock in a satisfactory manner.

Detached eddy simulation of compressible flow with rapid expanded divergent contour

Detached eddy simulation of compressible flow with rapid expanded divergent contour

A locally p-adaptive approach for Large Eddy Simulation of compressible flows in a DG framework

We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high-order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already employed in the literature. The resulting locally adaptive approach allows to achieve significant reductions in computational cost of representative LES computations.

High-order implicit residual smoothing time scheme for direct and large eddy simulations of compressible flows

Restrictions on the maximum allowable time step of explicit time integration methods for direct and large eddy simulations of compressible turbulent flows at high Reynolds numbers can be very severe, because of the extremely small space steps used close to solid walls to capture tiny and elongated boundary layer structures. A way of increasing stability limits is to use implicit time integration schemes. However, the price to pay is a higher computational cost per time step, higher discretization errors and lower parallel scalability. In quest for an implicit time scheme for scale-resolving simulations providing the best possible compromise between these opposite requirements, we develop a Runge–Kutta implicit residual smoothing (IRS) scheme of fourth-order accuracy, based on a bilaplacian operator. The implicit operator involves the inversion of scalar pentadiagonal systems, for which efficient parallel algorithms are available. The proposed method is assessed against two explicit and two implicit time integration techniques in terms of computational cost required to achieve a threshold level of accuracy. Precisely, the proposed time scheme is compared to four-stages and six-stages low-storage Runge–Kutta method, to the second-order IRS and to a second-order backward scheme solved by means of matrix-free quasi-exact Newton subiterations. Numerical results show that the proposed IRS scheme leads to reductions in computational time by a factor 3 to 5 for an accuracy comparable to that of the corresponding explicit Runge–Kutta scheme.

Dynamic models for Large Eddy Simulation of compressible flows with a high order DG method

The impact of dynamic models for applications to LES of compressible flows is assessed in the framework of a numerical model based on high order discontinuous finite elements. The projections onto lower dimensional subspaces associated with lower degree basis functions are used as LES filter, along the lines proposed in Variational Multiscale templates. Comparisons with DNS results available in the literature for plane and constricted channel flows at Mach numbers 0.2, 0.7 and 1.5 show clearly that the dynamic models are able to improve the prediction of most key features of the flow with respect to the Smagorinsky models employed so far in a VMS-DG context.

Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction

We derive and analyze a model for implicit Large Eddy Simulation (LES) of compressible flows that is applicable to a broad range of Mach numbers and particularly efficient for LES of shock-turbulence interaction. Following a holistic modeling philosophy, physically sound turbulence modeling and numerical modeling of unresolved subgrid scales (SGS) are fully merged, in a manner quite different from that of traditional implicit LES approaches. The implicit subgrid model is designed in such a way that asymptotic consistency with incompressible turbulence theory is maintained in the low Mach number limit. Compressibility effects are properly accounted for by a novel numerical flux function, which can capture strong shock waves in supersonic flows and also ensures an accurate representation of smooth waves and turbulence without excessive numerical dissipation. Simulations of shock-tube problems, Noh's three-dimensional implosion problem, large-scale forced and decaying three-dimensional homogeneous isotropic turbulence, supersonic turbulent boundary layer flows, and a Mach = 2.88 compression-expansion ramp flow demonstrate the good performance of the SGS model; across this range of flows, predictions are in excellent agreement with theory, direct numerical simulations, and experimental reference data. Results for implicit LES of canonical shock-turbulence interaction are compared with results of explicit LES using the dynamic Smagorinsky model. The analysis shows that details of the numerical method used for shock capturing clearly outweigh the effect of different turbulence modeling strategies in explicit and implicit LES. The implicit LES model recovers the ideal 2nd-order grid convergence of shock-capturing errors that has been predicted using Rapid Distortion Theory. The dynamic Smagorinsky model in conjunction with a hybrid method that combines sixth-order central differences with a seventh-order weighted essentially non-oscillatory scheme yields turbulence statistics that are very similar to the implicit LES results. However, while the explicit LES requires a tailored high-order low-dissipative numerical method that applies numerical dissipation only in shock normal direction, no such ad hoc adjustments are necessary with the proposed implicit LES method.

An immersed volume method for Large Eddy Simulation of compressible flows using a staggered-grid approach

This article suggests a new and efficient method, called Immersed Volume Method (IVM) to compute compressible viscous flows with complex stationary geometries using finite difference codes with a staggered cartesian grid formulation. A background cartesian mesh is generated for each staggered variable and a finite volume approach is adopted in the layer near the immersed boundaries according to the well known cut cell method. Accurate description of the real three-dimensional geometry inside the cut cell volume is preserved by means of a triangulated surface description instead of approximating it by a plane. The overall spatial accuracy of the base solver (2nd order in this article) is preserved by means of high order flux reconstruction in the cut cells. In particular, the code adopted here to test the suggested technique adopts a 2nd order centered scheme in space and 3rd order Runge–Kutta scheme in time. The code is parallelized using domain decomposition and message passing interface. The robustness and accuracy of the method is proved simulating, at first, a laminar flow past a sphere at Re=50,200,250, then a turbulent nonreacting flow past a sphere with a sting at Re=51500 and a turbulent premixed, stoichiometric CH4/air flame anchored by means of a cubic bluff body at Re=3200, both adopting the Large Eddy Simulation approach. Numerical results are compared with available experimental data.

The residual-based variational multiscale formulation for the large eddy simulation of compressible flows

The residual-based variational multiscale formulation is applied to develop a large eddy simulation (LES) model for compressible flows. In addition, a mixed model, in which a deviatoric Smagorinsky subgrid stress term is added to the RBVM terms to better model the Reynolds stresses is proposed. These models, along with the dynamic Smagorinsky–Yoshizawa eddy diffusivity model are tested in predicting the decay of homogenous turbulence. For most relevant measures, it is observed that the RBVM models are more accurate than the dynamic Smagorinsky-type model.

An explicit filtering method for large eddy simulation of compressible flows

A method for large eddy simulation (LES) is presented in which the sub-grid-scale modeling is achieved by filtering procedures alone. The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity. The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter. This filter should be an almost perfect low pass filter below a cut-off wavenumber and then fall off smoothly. The procedure has been applied to a pressure-velocity-entropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data. Mach numbers are 1.5 and 3.0, and Reynolds numbers are 3000 and 6000, respectively. Effects of filter cut-off location, choice of differentiation scheme (a fifth-order compact upwind formula and a symmetric sixth-order compact formula were used), and grid refinement are examined. The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter. All simulations demonstrate a uniform convergence towards their respective DNS solutions.