Sangsan Lee

A dynamic subgrid-scale model for compressible turbulence and scalar transport

The dynamic subgrid‐scale (SGS) model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

Subgrid-scale backscatter in turbulent and transitional flows

Most subgrid‐scale (SGS) models for large‐eddy simulations (LES) are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Recent work on the LES of transitional flows [Piomelli et al., Phys. Fluids A 2, 257 (1990)] has shown that failure to account for this phenomenon can cause inaccurate prediction of the growth of the perturbations. Direct numerical simulations of transitional and turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomenon. In all flows considered roughly 50% of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much...

Simulation of spatially evolving turbulence and the applicability of Taylor's hypothesis in compressible flow

For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor’s hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor’s hypothesis, space‐time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space‐time correlation of dilatation fluctuations is explained via a wave propagation model.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number M t of the upstream turbulence and the shock strength M 2 1 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ M t ≤ 0.110 and 1.05 ≤ M 1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations. Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M 2 t a ( M 2 1 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term. Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M 2 t a ( M 2 1 — 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M 2 t > a ( M 2 1 — 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

Eddy shocklets in decaying compressible turbulence

The existence of eddy shocklets in three‐dimensional compressible turbulence is controversial. To investigate the occurrence of eddy shocklets, numerical simulations of temporally decaying isotropic turbulence are conducted. Dilatation statistics from simulations with different initial fluctuation Mach numbers, Mt, show that dilatation is more intermittent and more negatively skewed for higher Mt. By studying instantaneous flow fields, shocklets are found and verified to have all the characteristics of a typical shock wave, such as proper jumps in pressure and density along with a local entropy peak inside the high‐compression zone. Although overall compressible dissipation contributes to less than one‐tenth of the total dissipation, compressible dissipation around shocklets is about an order of magnitude larger than typical values of incompressible dissipation. In the zones of eddy shocklets, pressure is highly correlated with dilatation to convert kinetic energy into internal energy. These mechanisms ne...

Direct numerical simulation and analysis of shock turbulence interaction

Two kinds of linear analysis, rapid distortion theory (RDT) and linear interaction analysis (LIA), were used to investigate the effects of a shock wave on turbulence. Direct numerical simulations of two-dimensional isotropic turbulence interaction with a normal shock were also performed. The results from RDT and LIA are in good agreement for weak shock waves, where the effects of shock front curvature and shock front unsteadiness are not significant in producing vorticity. The linear analyses predict wavenumber-dependent amplification of the upstream one-dimensional energy spectrum, leading to turbulence scale length scale decrease through the interaction. Instantaneous vorticity fields show that vortical structures are enhanced while they are compressed in the shock normal direction. Entrophy amplfication through the shock wave compares favorably with the results of linear analyses.

Compressible Turbulence and Shock Waves

If the velocity scale associated with the turbulent fluctuations is a substantial fraction of the mean speed of sound, compressibility effects are expected to arise. This direct effect of compressibility, which is also the most well documented, appears to be responsible for the reduced spreading rate of turbulent mixing layers under compressible conditions, and the slower decay of hypersonic wakes. A different circumstance where the compressibility effects can become significant occurs when an otherwise quasi-incompressible turbulent flow is subjected to a rapidly changing environment. For example a turbulent flow passing through a shock wave or a steep expansion wave may suddenly enter in a state of disequilibrium. The sudden change may also generate significant fluctuations of acoustic and entropy modes. Thus the recovery of the turbulence from this disequilibrium may also exhibit compressibility effects. Other phenomena where the global behavior of the flow is strongly affected by compressibility include shock induced separations of a turbulent flow, phenomena involving the Ranque-Hilsh effect and other effects requiring chemical or thermodynamic nonequilibrium. The problem of shock wave boundary layer interaction in a hypersonic free-stream involves all of the above processes.