Dynamic Large Eddy Simulation Model Research Articles

Scale-resolving simulations and investigations of the flow in a hydraulic retarder considering cavitation

Cavitation has a significant influence on the accurate control of the liquid filling rate and braking performance of a hydraulic retarder; however, previous studies of the flow field in hydraulic retarders have provided insufficient information in terms of considering cavitation. Here, the volume of fluid (VOF) method and a scale-resolving simulation (SRS) were employed to numerically and more comprehensively calculate and analyze the flow field in a retarder considering the cavitation phenomenon. The numerical models included the improved delayed detached eddy simulation (IDDES) model, stress-blended eddy simulation (SBES) model, dynamic large eddy simulation (DLES) model, and shear stress transport (SST) model in the Reynolds-averaged Navier-Stokes (RANS) model. All the calculations were typically validated by the brake torque in the impeller rather than the internal flow. The unsteady flow field indicated that the SBES and DLES models could better capture unsteady flow phenomena, such as the chord vortex. The SBES and DLES models could also better capture bubbles than the SST and IDDES models. Since the braking torque error of the SBES model was the smallest, the transient variation of the bubble volume fraction over time on a typical flow surface was analyzed in detail with the SBES model. It was found that bubbles mainly appeared in the center area of the blade suction surface, which coincided with the experiments. The accumulation of bubbles resulted in a larger bubble volume fraction in the center of the blade over time. In addition, the temperature variations of the pressure blade caused by heat transfer were further analyzed. More bubbles precipitated in the center of the blade, leading to a lower temperature in this area.

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured, Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re = 5000, the turbulent channel flow at Reτ = 587, the circular cylinder in cross-flow at ReD = 3900, the square cylinder in cross-flow at ReD = 22400 and the channel with periodic constrictions at Reh = 10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.

A study on the numerical dissipation of the Spectral Difference method for freely decaying and wall-bounded turbulence

Abstract This paper aims at understanding the numerical dissipation mechanisms related to the Spectral Difference (SD) method in the context of three-dimensional (3D) turbulence. The numerical dissipation stemming from the discretization of the convective terms is studied by performing inviscid computations of the transitional Taylor–Green vortex and isotropic turbulence configurations. The Taylor–Green vortex computations show that the increase in the order of accuracy restricts the numerical dissipation to smaller scales which, in turn, leads to a better representation of transitional mechanisms. However, isotropic turbulence computations using a fifth-order accuracy or above show obvious manifestations of under-resolution (such as the onset of oscillations and numerical noise), which suggests that the high-order numerical dissipation alone is unable to mimic the dissipation originating from sub-grid scales in the case freely decaying turbulence. Computations of the channel flow configuration at R e τ = 1000 at typical large-eddy simulation resolutions show that under-resolved SD discretizations using a high order of accuracy (fifth and sixth) lead to an excellent prediction of the wall-friction, the velocity profiles, the turbulent structures near the wall and the energy spectra, while lower order discretizations lead to an underestimation of the wall-friction and globally a poor representation of wall-bounded turbulence. The present study emphasizes the benefit of using high-order SD discretizations for an accurate representation of turbulent phenomena (namely, transitional and wall-bounded turbulence) but also the necessity of combining this approach with dynamic large-eddy simulation models or appropriate regularization techniques which would activate only where needed to recover physically consistent results, e.g. , in regions where fully developed turbulence is present.

A New Inlet Boundary Conditon for LES

It is known that the inlet boundary condition is still a problem for tubulence simulation. In this paper a numerical procedure to generate inflow turbulence based on the digital filter technique (Autoregressive Moving Average (ARMA) model) is presented suitable for Large Eddy Simulation (LES) models and validated to realize the inflow turbulence and this approach is adopted to investigate the flow characteristics in the empty domain based on standard and dynamic LES models.

Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Comparison of Turbulence Modeling Strategies for Indoor Flows

Turbulence modeling techniques are compared for the simulation of low speed indoor air flow in a simple room. The effect of inlet turbulence intensity on the flow field is investigated using the constant coefficient large eddy simulation (LES) model with uniform mean inlet conditions at several levels of inlet turbulence intensities. The results show significant differences between the simulations with laminar inflow conditions and those in which turbulence was introduced at the inlet. For simulations with turbulent inlet conditions, it is noticed that the jet transitions to a state of fully developed turbulence wherein the dynamics of the flow become nearly insensitive to any further increase in the level of inlet turbulence. For laminar flow conditions, it is seen that the jet slowly spreads and mixes with the quiescent room air. As a result, the jet reaches a fully developed turbulent state further away from the inlet relative to the simulations with inlet turbulence. The effect of using experimental inlet profiles is also investigated. It is seen that, close to the inlet, the flow is sensitive to the inflow details, whereas further away from the inlet, these effects become less pronounced. The results from the constant coefficient and the dynamic LES models are compared. The most noticeable differences in the flow occur at the locations where the subgrid-scale’s contribution to the turbulent kinetic energy is highest. Finally, the results from the dynamic LES and the k-ϵ models are compared. It is found that there are significant differences between the two models for the zero inlet turbulence limit where the flow is most probably transitional in nature and turbulence has not yet reached a fully developed state. It is seen that in the laminar inflow case the k-ϵ model predicts a fully turbulent jet very close to the inlet and thus fails to capture the slow development of the jet found in LES. Accordingly, the k-ϵ model results are nearly insensitive to the level of inlet turbulence especially far from the origin of the flow. It is also seen that for cases with nonzero inlet turbulence level, the k-ϵ model predicts the general features of the mean flow reasonably well; however, the k-ϵ model overpredicts the jet spreading rate and the turbulent kinetic energy close to the inlet. Furthermore, the k-ϵ model under predicts the turbulence level near the corner of the ceiling as it fails to capture the complicated mean velocity and turbulent kinetic energy, most likely because of the highly intermittent flow pattern found there in LES.

Applications of a variational multiscale method for large eddy simulation of turbulent flows on moving/deforming unstructured grids

In this paper, the three-level formulation of a variational multiscale (VMS) large eddy simulation (LES) method for compressible flow computations [B. Koobus, C. Farhat, A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes—application to vortex shedding, Comput. Methods Appl. Mech. Eng. 193 (2004) 1367–1384; C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691] is extended for applications involving moving/deforming grids. A consistent method to improve the VMS-LES method by computing the small scale Smagorinsky constant ( C s ′ ) dynamically [C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691; A. Rajasekharan, Variationally consistent multiscale formulations and ALE time integrators for large eddy simulation of turbulent flows on dynamic grids, Ph.D. Dissertation, Stanford University, 2008] as the flow develops (dynamic VMS-LES) is also extended for dynamic grid applications. Two applications of VMS-LES for the simulation of separated flow over moving NACA-0012 extruded airfoil is then presented. The first application involves a qualitative simulation exploring the Knoller–Betz effect [K.D. Jones, C.M. Dohring, M.F. Platzer, Experimental and computational investigation of the Knoller–Betz effect, AIAA J. 36(7) (1998) 1240–1246] of the heaving airfoil at high Strouhal number. The second application is that of the pitching airfoil undergoing dynamic stall. The results predicted by the dynamic VMS-LES method are compared to those obtained with other turbulence models and to experimental data and it is found that the dynamic VMS-LES performs better than the other considered static and dynamic LES models.

Compressible Wall-Injection Flows in Laminar, Transitional, and Turbulent Regimes: Numerical Prediction

Numerical simulations of compressible rocket flows are conducted in laminar, transitional, and turbulent regimes. The laminar simulation is carried out on a planar rocket flow without nozzle using the unsteady two-dimensional Navier-Stokes system. The transitional and turbulent flows are performed in three-dimensional on an extended rocket geometry with a divergent outlet using compressible large eddy simulation (LES) models. In both cases, the compressibility effect plays an important role. In the laminar case, pressure oscillation is forced at the outflow boundary. The time-averaged part of the solution is compared with the inviscid theory of compressible rocket flow of Balakrishnan et al. (Balakrishnan, G., Linan, A., and Williams F. A., Compressibility Effects in Thin Channels with Injection, AIAA Journal, Vol.29, No. 12, 1991, pp. 2149-2154) and the oscillatory part with the acoustic layer model of Majdalani and Van Moorhem (Majdalani, J., and Van Moorhem, W. K., Improved Time-Dependent Flowfield Solution for Solid Rocket Motors, AIAA Journal, Vol. 36, No. 2, 1998, pp. 241-248). The mean flow from the present numerical result is in better agreement with the compressible theory than the conventional Taylor's profiles (Taylor, G. I., Fluid Flow in Regions Bounded by Porous Surfaces, Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 234, 1956, pp. 456-475), as expected. The oscillatory part of the flow agrees well in the first quarter of the axial extent, near the head end. Farther downstream, the discrepancies develop rapidly between the numerical result and the acoustic-layer model. Possible causes of the difference are the effect of compressibility, which alters the local speed of sound, hence, acoustic properties, and the interference of hydrodynamic instabilities. In the transition and turbulent regimes, the dynamic LES model is applied on different resolutions. The measurements data of Traineau et al. (Traineau, J. C., Hervat, P., and Kuentzmann, P., Cold Flow Simulation of a Two Dimensional Nozzleless Solid Rocket Motor, AIAA Paper 86-1447, June 1986) are employed for comparison purposes. The refinement study by comparison with the measurement data suggests the importance of resolving the laminar and transition region for a reliable application of LES in transitional flows. With the consideration of this aspect, LES with efficient grid size can produce resonable accuracy. Forcing hydrodynamic instabilities and a more realistic injection fluctuations model are recommended.

Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations

The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large-eddy simulation of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5 % for c_s^2), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics.

Convergence of cognitive and adaptive decline in chronic schizophrenia

In this paper, the three-level formulation of a variational multiscale (VMS) large eddy simulation (LES) method for compressible flow computations [B. Koobus, C. Farhat, A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes—application to vortex shedding, Comput. Methods Appl. Mech. Eng. 193 (2004) 1367–1384; C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691] is extended for applications involving moving/deforming grids. A consistent method to improve the VMS-LES method by computing the small scale Smagorinsky constant (Cs′) dynamically [C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691; A. Rajasekharan, Variationally consistent multiscale formulations and ALE time integrators for large eddy simulation of turbulent flows on dynamic grids, Ph.D. Dissertation, Stanford University, 2008] as the flow develops (dynamic VMS-LES) is also extended for dynamic grid applications. Two applications of VMS-LES for the simulation of separated flow over moving NACA-0012 extruded airfoil is then presented. The first application involves a qualitative simulation exploring the Knoller–Betz effect [K.D. Jones, C.M. Dohring, M.F. Platzer, Experimental and computational investigation of the Knoller–Betz effect, AIAA J. 36(7) (1998) 1240–1246] of the heaving airfoil at high Strouhal number. The second application is that of the pitching airfoil undergoing dynamic stall. The results predicted by the dynamic VMS-LES method are compared to those obtained with other turbulence models and to experimental data and it is found that the dynamic VMS-LES performs better than the other considered static and dynamic LES models.

Response of the dynamic LES model to heat release induced effects

The response of the dynamic large eddy simulation (LES) subgrid model to heat release effects is investigated. Nonpremixed turbulent flames are considered in the case of large Damköhler number combustion in homogeneous and isotropic flows. The subgrid fluctuations of mixture fraction are accounted for through a presumed probability density function approach. In this work, dynamic LES includes a procedure minimizing, over flow path lines, the error in the determination of the parameters entering the turbulence model [Meneveau, Lund, and Cabot, Proceedings of the 1994 Summer Program (CTR, Stanford, CA, 1994), pp. 271–299]. Both direct numerical simulation (DNS) and LES are performed. It is found that the flux of turbulent kinetic energy toward the subgrid is correctly represented by the dynamic LES model in the presence of heat release.

A Lagrangian dynamic subgrid-scale model of turbulence

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.