Zhaorui Li

Compressible Scalar Filtered Mass Density Function Model for High-Speed Turbulent Flows

The scalar filtered mass density function model is further extended and employed for large-eddy simulations of high-speed turbulent mixing and reacting flows. The model is implemented through a hybrid mathematical/ computationalmethodology. In thismethodology, the filtered compressible Navier–Stokes equations in a curvilinear coordinate system are solved with a generalized, high-order, multiblock, finite difference scheme for the turbulent velocity and pressure. However, the scalar mixing and combustion are computed with the compressible scalar filteredmass density function. The pressure effect in the energy equation, as needed in high-speedflows, is included in the filtered mass density function formulation. The new compressible large-eddy simulation/filtered mass density function model is used for the simulations of flows in a rapid compression machine, in a shock tube and in a supersonic coaxial jet. The numerical results indicate that the model is able to correctly capture the scalar mixing in compressible subsonic and supersonic turbulent flows.

Numerical investigations of shock wave interactions with a supersonic turbulent boundary layer

Direct numerical simulations (DNS) are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. The accuracies of DNS calculations are established by checking the convergence of flow statistics for various grids, by comparing the generated results with those in the literature and also by the balance of contributing terms in the turbulent kinetic energy equation. Instantaneous flow visualizations show the significant effect of shock on turbulence structure in the shock-boundary layer interaction zone and also in the flow downstream of the interaction region. The separation bubbles exhibit highly unsteady and three-dimensional behavior and are larger for stronger shocks but the maximum probability of flow separation is found to be independent of the shock strength. The differences between Reynolds- and Favre-averaged quantities are also observed to be small and largely independent of the shock intensity. The turbulent kinetic energy is...

Subgrid-Scale Models for Large-Eddy Simulations of Shock-Boundary-Layer Interactions

Direct numerical simulation and large-eddy simulation of a flat-plate supersonic turbulent boundary layer interacting with an oblique incident shock wave are conducted for a priori and a posteriori assessments of subgrid-scale models. The incident shock is strong enough to generate a marginal separation in the boundary layer near the interaction region providing the subgrid-scale models with a nontrivial challenge. The governing equations for direct numerical simulation and large-eddy simulation are solved by a new seventh-order monotonicity-preserving scheme for inviscid fluxes and a sixth-order compact finite-difference scheme for the viscous terms. The effect of subgrid-scale stress term on the resolved velocity field is shown to be significant and shock-dependent. The subgrid-scale models tested include the mixed-time-scale model, the dynamic Smagorinsky model, the dynamic mixed model and a new dynamic model termed the compressible serial-decomposition model. A priori analysis indicate that the new dy...

Turbulence-interface interactions in a two-fluid homogeneous flow

The two-way interactions between the turbulent velocity field and the interface in an incompressible two-fluid homogeneous turbulent flow are studied with a recently developed Lagrangian–Eulerian interfacial particle level-set method. The numerical results confirm that the rate of change of the interface area is directly related to the work done by the surface tension force. While the surface tension damps the surrounding turbulence in the “interface stretching period” to oppose the increase in interface area, it is shown to actually increase the turbulent kinetic energy when the interface experiences compression. Additionally, the surface tension force is found to generate strong vortical motions close to the interface through the baroclinic torque effects. There is also an increase in strain rate and the viscous dissipation rate of turbulent kinetic energy in the interface region. The effect of interface on the surrounding turbulence appears primarily in the direction perpendicular to the interface. Ana...

Large-Eddy Simulation of Turbulent Boundary Layer Interaction with an Oblique Shock Wave

Large eddy simulations (LES) of an incident shockwave interacting with a supersonic turbulent boundary layer have been performed via a new high-order Monotonicity-Preserving scheme. The LES results with four subgrid-scale (SGS) models, namely, the modified Smagorinksy model, the hybrid scale-similarity model, the modified kinetic energy viscosity model and the dynamic Smagorinsky model, are compared with the direct numerical simulation (DNS) results. The shock strength is strong enough to induce a small separation region in the vicinity of shock impingement location. However, all SGS models are shown to overpredict the length of separation region and LES and DNS predictions of flow statistics are shown to differ more near this region. Overall, LES with the dynamic Smagorinsky model is in agreement with DNS and is able to reproduce main features of the flow.

Subgrid-scale backscatter after the shock-turbulence interaction

The statistics of the subgrid scales (SGS) are studied in the context of Large Eddy Simulations (LES) of turbulence after the interaction with a nominally normal shock wave. In general, in practical applications, the shock wave width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J. Fluid Mech., 756, R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). By using LIA to alleviate the need to resolve the shock wave, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number ≈ 180 are used for an analysis of the SGS backscatter properties. In particular, it is shown that the interaction with the shock wave decreases the asymmetry of the SGS dissipation Probability Density Function (PDF) as the shock Mach number increases, with a sign...

Numerical simulation of multi-fluid shock-turbulence interaction

Accurate numerical simulation of multi-fluid Shock-Turbulence Interaction (STI) is conducted by a hybrid monotonicity preserving-compact finite difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Comparison of multi-fluid and single-fluid data indicates that the turbulent kinetic energy is amplified more and the scalar mixing is enhanced more by the shock in flows involving two different fluids/densities when compared with those observed in single-fluid flows.

Large Eddy Simulation of Turbulent Combustion via Filtered Mass Density Function

This paper provides a brief review of the scalar filtered mass density function (FMDF) model. The FMDF is a subgrid-scale probability density function (PDF) model for large eddy simulation (LES) of turbulent combustion and is obtained by the solution of a set of stochastic differential equations by a Lagrangian Monte Carlo method. The applicability and the validity of the LES/FMDF are established by simulating various low and high speed, single- and two-phase turbulent reacting flows. The LES/FMDF results are found to be consistent and comparable to DNS and experimental results for different flows.

Numerical Investigations of Shock-Turbulence Interactions in a Planar Mixing Layer

Direct numerical simulation (DNS) and large-eddy simulation (LES) of spatially developing supersonic mixing layer, interacting with an oblique shock wave are conducted with a new high-order Monotonicity-Preserving scheme. Without the incident shock, the mixing layer grows linearly and exhibits self-similar behavior after the transition. With the shock, significant small-scale turbulence is generated just behind the shock. With an increase in shock angle, the intensity of the shock-generated turbulence is increased and its peak position shifts away from the mixing layer centerline. The effects of turbulence on the shock are also shown to be very significant, such that normal shocklets and large adverse pressure gradients are created in some conditions. Comparison with the DNS data indicates that the LES with the modified kinetic energy viscosity (MKEV) subgrid stress model is able to predict the main features of the flow and shock-turbulence interactions.

Large-Scale Simulations of High Speed Turbulent Flows

This paper briefly describes a new class of high-order Monotonicity-Preserving (MP) finite difference methods recently developed for direct numerical simulation (DNS) and large-eddy simulation (LES) of high-speed turbulent flows. The MP method has been implemented together with high-order compact (COMP) and weighted essentially nonoscillatory (WENO) methods in a generalized three-dimensional (3D) code and has been applied to various 1D, 2D and 3D problems. For the LES, compressible versions of the gradient-based subgrid-scale closures are employed. Detailed and extensive analysis of various flows indicates that MP schemes have less numerical dissipation and faster grid convergence than WENO schemes. Simulations conducted with high-order MP schemes preserve sharp changes in flow variables without spurious oscillations and capture the turbulence at the smallest simulated scales. The non-conservative form of the scalar equation solved with MP schemes are shown to generate the same results as COMP schemes for supersonic mixing problems involving shock waves.