Soshi Kawai

Wall-modeling in large eddy simulation: Length scales, grid resolution, and accuracy

This paper addresses one of the most persistent errors in wall-modeled large eddy simulation: the inevitable presence of numerical and subgrid modeling errors in the first few grid points off the wall, which leads to the so-called “log-layer mismatch” with its associated 10-15% error in the predicted skin friction. By considering the behavior of turbulence length scales near a wall, the source of these errors is analyzed, and a method that allows for the log-layer mismatch to be removed, thereby yielding accurately predicted skin friction, is proposed.

Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows

The localized artificial diffusivity method is investigated in the context of large-eddy simulation of compressible turbulent flows. The performance of different artificial bulk viscosity models are evaluated through detailed results from the evolution of decaying compressible isotropic turbulence with eddy shocklets and supersonic turbulent boundary layer. Effects of subgrid-scale (SGS) models and implicit time-integration scheme/time-step size are also investigated within the framework of the numerical scheme used. The use of a shock sensor along with artificial bulk viscosity significantly improves the scheme for simulating turbulent flows involving shocks while retaining the shock-capturing capability. The proposed combination of Ducros-type sensor with a negative dilatation sensor removes unnecessary bulk viscosity within expansion and weakly compressible turbulence regions without shocks and allows it to localize near the shocks. It also eliminates the need for a wall-damping function for the bulk viscosity while simulating wall-bounded turbulent flows. For the numerical schemes used, better results are obtained without adding an explicit SGS model than with SGS model at moderate Reynolds number. Inclusion of a SGS model in addition to the low-pass filtering and artificial bulk viscosity results in additional damping of the resolved turbulence. However, investigations at higher Reynolds numbers suggest the need for an explicit SGS model. The flow statistics obtained using the second-order implicit time-integration scheme with three sub-iterations closely agrees with the explicit scheme if the maximum Courant-Friedrichs-Lewy is kept near unity.

Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes

A simple and efficient localized artificial diffusivity scheme is developed for the purpose of capturing discontinuities on curvilinear and anisotropic meshes using a high-order compact differencing scheme. The artificial diffusivity is dynamically localized in space to capture different types of discontinuities such as a shock wave, contact surface or material discontinuity. The method is intended for use with large-eddy simulation of compressible transitional and turbulent flows. The method captures the discontinuities on curvilinear and anisotropic meshes with minimum impact on the smooth flow regions. The amplitude of wiggles near a discontinuity and the number of grid points used to capture the discontinuity do not depend on the mesh size. The comparisons between the proposed method and high-order shock-capturing schemes illustrate the advantage of the method for the simulation of flows involving shocks, turbulence and their interactions. The multi-dimensional formulation is tested on a variety of 1D and 2D, steady and unsteady, different types of discontinuity-related problems on curvilinear and anisotropic meshes. A simplification of the method which reduces the computational cost does not show any major detrimental effect on the discontinuity capturing under the conditions examined.

Computational Study of a Supersonic Base Flow Using Hybrid Turbulence Methodology

Large-eddy simulation/Reynolds-averaged Navier-Stokes (LES/RANS) hybrid methodology is applied to a high-Reynolds-number supersonic axisymmetric base flow. Accurate predictions of the base flowfield and base pressure are successfully achieved by using the LES/RANS hybrid methodology with less computational cost than that of pure LES and monotone integrated large-eddy simulation (MILES) approaches. Both the efficiency and reliability of the present LES/RANS hybrid methodology for the prediction of massively separated high-Reynolds-number flows are identified by comparison with the results obtained by LES, MILES, RANS, and the experiments in detail. The LES/RANS hybrid simulation accurately resolves the physics of unsteady turbulent motions, such as shear-layer rollup, large-eddy motions in the downstream region, small-eddy motions inside the recirculating region, and formation of large mushroom-shaped patterns in the end view

Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers

A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on equilibrium boundary layers and a non-equilibrium shock/boundary-layer interaction problem. The proposed method builds on the prior non-equilibrium wall-models of Balaras et al. [AIAA J. 34, 1111–1119 (1996)]10.2514/3.13200 and Wang and Moin [Phys. Fluids 14, 2043–2051 (2002)]10.1063/1.1476668: the failure of these wall-models to accurately predict the skin friction in equilibrium boundary layers is shown and analyzed, and an improved wall-model that solves this issue is proposed. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer, the grid resolution, and the resolution-characteristics of numerical methods. The proposed model yields accurate resolved turbulence, both in terms of structure and statistics for both the equilibrium and non-equilibrium flows without the use of ad hoc corrections. Cr...

Compact Scheme with Filtering for Large-Eddy Simulation of Transitional Boundary Layer

Bypass transition induced by freestream turbulence is numerically simulated by compressible large-eddy simulation and implicit large-eddy simulation using a compact differencing scheme with spatial filtering. Simulated transitional flowfields qualitatively reproduce the physics of the transition and are appropriate for the discussion of transitional flowfields. Key coherent structures, such as low-speed streaks, longitudinal vortex pairs, and hairpin vortices, which play important roles in determining the behavior of transition, need to be directly resolved to properly simulate the physics of transition. Only a slight numerical damping of these coherent structures by the spatial filtering procedure causes the delay of transition. On the other hand, once the flow develops into a fully turbulent state, the spatial filtering has little influence on the flowfield. At the late stage of transition, the coherent structures break down into finer scales which require finer grid resolution to accurately resolve. However, the underresolution of the finer scale structures has little influence on the overall results if the key coherent structures are adequately resolved. Under the condition examined, the tenth-order filtering with α f = 0.495 does not act as an implicit subgrid-scale model. The present results reasonably illustrate the capability of compact/filter-based compressible large-eddy simulation and the guidelines regarding how to properly simulate transitional boundary layers using the large-eddy simulation.

Mechanisms of Jet Mixing in a Supersonic Crossflow: A Study Using Large-Eddy Simulation

High-order compact differencing/filtering schemes are coupled with recently developed localized artificial diffusivity methodology in the context of large-eddy simulation (LES) to obtain insights into the physics of an under-expanded sonic jet injection into a supersonic crossflow. The flow conditions of the experiment by Santiago and Dutton [J. Prop. Power. 13 (1997) 264–273] are selected for detailed simulation. The present LES qualitatively reproduce the unsteady dynamics of both barrel shock and bow shock as observed in the experiment. It found that pressure fluctuation inside the upstream recirculation region induces unsteadiness of windward jet shear layer and causes large-scale dynamics of the barrel shock and front bow shock. Statistics obtained by the LES also show good agreement with the experiment. With regard to the processes controlling the jet mixing we studied the dynamics of vortex structures in the flow. Two regions of vortex formation which form hairpin-like structure are identified in the windward and leeward jet boundaries. These vortices play an important role in determining the behavior of jet fluid stirring and subsequent mixing. Also noted is the entrainment of rolled-up windward shear layer by the upstream recirculating flow.

Large-Eddy Simulation of an Oblique Shock Impinging on a Turbulent Boundary Layer

Large-eddy simulation (LES) of an oblique shock impinging on a supersonic turbulent boundary layer is carried out with a high-order compact differencing scheme using localized artificial diffusivity (LAD) for shock capturing. Flow conditions attempt to match those of the tomographic particle image velocimetry (PIV) experiments conducted at the Delft University of Technology (M∞ = 2.05 and φ = 8°). However, due to computational cost, the Reynolds number is taken to be Reδ = 20,000 (1/30 th of the experimental Reynolds number), and an attempt is made to geometrically match the interaction parameters. Inflow conditions are generated by an improved recycling/rescaling method to eliminate the non-physical “tones” associated with standard recycling/rescaling. The numerical scheme is first validated by simulating a two-dimensional laminar shock wave / boundary layer interaction (SWBLI). Next, a three-dimensional simulation with progressive mesh refinement is conducted to investigate flow physics and establish confidence in the ability of the computational method to accurately and efficiently simulate complex supersonic flow phenomena. Mean and fluctuating profiles of velocity, pressure, and skin friction provide good indication of grid convergence between the two highest levels of refinement. Instantaneous data fields are analyzed, and observations are made regarding “flapping” motion caused by boundary layer turbulence and spanwise variation in shock location. Additionally, the range of spatial and temporal scales captured by the present work is quantified by analyzing spanwise wavenumber and frequency spectra at various locations in the flow. Through analysis of the frequency spectra of the wall pressure signal, low-frequency motion of the separation bubble with a time scale ~O(100δ/u∞) is observed and described. Through direct comparison, we additionally observe that standard recycling/rescaling inflow conditions may result in different low-frequency behavior.

High-Resolution Numerical Method for Supercritical Flows with Large Density Variations

is introduced with the aim of simulating jet mixing under supercritical pressure environments. The nonlinear localized artificial diffusivity provides the stability to capture different types of discontinuity, such as shock wave, contact surface, and material interface, whereas the high-order compact difference scheme resolves broadband scales in the rest of the domain. The present method is tested on several one-dimensional discontinuity-related problems under super/transcritical conditions and a comparatively more illustrative two-dimensional lowtemperature planar jet problem under a supercritical pressure condition. The localized artificial diffusivity, especially artificial thermal conductivity for temperature gradients, effectively suppresses numerical wiggles near the interfaces. The effects of the artificial thermal conductivity on numerical stability and accuracy are examined. Comparisons between the present method and a conventional low-order scheme demonstrate the superior performance of the present method for resolving a wide range of flow scales while successfully capturing large density/temperature variations at interfaces.

Computational Study of a Supersonic Base Flow Using LES/RANS Hybrid Methodology

Large-Eddy Simulation (LES)/Reynolds-Averaged Navier-Stokes (RANS) hybrid methodology is applied to the high Reynolds number supersonic axisymmetric base flow. Both the reliability and capability of the hybrid method are investigated by the comparison with the LES, Monotone Integrated Large-Eddy Simulation (MILES), RANS simulation and the experiments. The idea of LES/RANS hybrid methodology is that RANS model is used in boundary layer, and LES model is used in massively separated regions where unsteady flow structures are precisely captured. The subgrid-scale (SGS) stresses are computed using the compressible form of the Smagorinsky model while the Baldwin-Lomax (BL) model is applied to the RANS region near the body surface because of their robustness and low computational cost. The LES/RANS hybrid simulations accurately capture the physics of unsteady turbulent flows within acceptable computational cost. The reverse flow behind the base separation shows satisfactory agreement with the measurements. The base pressure distribution, which is the primary parameter from the engineering interest, is in excellent agreement with the experiment. Dependency of the value of the Smagorinsky constant to the base pressure prediction is also investigated. The results suggest that the LES/RANS hybrid methodology is a reliable tool for the prediction of wall bounded high Reynolds number flows with the lower computational cost than that of the LES and MILES approaches.