Session BB: Turbulence Simulations II

Supersonic turbulent boundary layer on a surface with distributed roughness

Knowledge of heat load on the surface of vehicles (re-)entering a planetary atmosphere is important for heat-shield design. However, due to the heat-shield material itself or as a result of ablation during flight, the surface of a heat shield is often not smooth. The surface roughness may strongly influence the heat flux, but the details of this influence are presently not well understood. We carry out numerical simulations of a flat-plate boundary layer with small distributed roughness at a supersonic Mach number. Time-accurate solutions to the compressible Navier-Stokes equations are obtained by an overall fourth-order finite-difference method with explicit time stepping for a calorically perfect gas. In the computation, the rough wall is modelled by an immersed boundary method. The boundary-layer is tripped to turbulence upstream of the rough surface. Its downstream evolution will be compared between a smooth flat-plate and the rough-wall case. This approach shall allow to identify physical mechanisms that lead to a possible enhancement in heat load caused by distributed roughness.   

LES of an inclined jet into a supersonic cross-flow at Mach 3.6

The objective of this work is to capture the main flow physics of an inclined jet (He, $M=1.0$) into a supersonic cross-flow (Air, $M=3.6$) using LES. The jet to free-stream momentum flux ratio is $\overline{q}=1.75$. The flow parameters are the same of the experimental study of Maddalena {\em et al.} ({\em J. of Prop. and Power 2006}). Large-eddy simulation with sub-grid scale was performed using the stretched vortex model of turbulent and scalar transport developed by Pullin and co-workers. The governing equations are solved on a Cartesian mesh with adaptive mesh refinement (AMR). The level-set approach with the ghost-fluid method is used to treat the complex boundary where no-slip and adiabatic-wall conditions are applied. The numerical method is a hybrid approach with low numerical dissipation that uses tuned centered finite differences (TCD), and weighted essentially non-oscillatory (WENO) scheme around discontinuities, ghost-fluid boundaries (Hill \& Pullin, {\em J. Comput. Phys. 2004}; Pantano {\em et al., J. Comput. Phys. 2007}), and low pressure regions ($<2000$Pa). The results show that the main flow features are well captured: bow shock, barrel shock, Mach disk, shear layers, counter-rotating vortices, and large-scale structures.   

Assessment of Shock-Capturing Schemes and Subgrid-Scale Models for Large-Eddy Simulation of Highly Compressible Turbulence

We assess recent weighted essentially non-oscillatory (WENO) schemes with lower dissipation for large-eddy simulations (LES) of highly compressible forced isotropic turbulence. In particular, we test both linearly [1] and linearly-nonlinearly [2] optimized WENO schemes. We compute dissipation budgets to compare the energy removal due to numerical dissipation with that due to the subgrid-scale terms. In addition, we assess traditional dynamic eddy viscosity and mixed models as well as approximate deconvolution models (ADM) [3] in highly compressible turbulence. Finally, the benefits and/or drawbacks of shock-confining filters to modify the LES filtering operation and avoid filtering across discontinuities are assessed. [1] Martin, M.P., Taylor, E.M., Wu, M., and Weirs, V.G., J. Comp. Phys. 220(1), 270-289, 2006. [2] Taylor, E.M., Wu, M., and Martin, M.P., J. Comp. Phys. 223(1), 384-397, 2007. [3] Stolz, S., Adams, N.A., and Kleiser, L., Phys. Fluids 13(10), 2985-3001, 2001. This work is sponsored by NASA Grant \#{}NCC3-989.   

Grid-independence and convergence of statistics in an LES of turbulent mixing

Grid resolution, or the turbulence resolution length scale, is an important parameter in large-eddy simulation (LES). For a predictive LES model, turbulence statistics should become independent of grid-resolution, for sufficiently refined calculations. In the work presented, the dependence of the statistics on grid-resolution is studied for a case of mixing of a passive scalar in a high Reynolds number recirculating shear flow. The stretched-vortex LES--SGS model is used for both subgrid momentum and scalar transport. In order to investigate convergence, simulations where performed at three grid-resolutions differing by a factor of 2 in each direction between them. The effect of grid-resolution on the mean flow fields, probability density functions of the passive scalar and spectra is discussed and the resolution requirements are quantified. Turbulence statistics are also compared against experimental measurements.   

Numerical Errors in Scalar Variance Models for LES

Large eddy simulation (LES) has emerged as an indispensable tool for modeling turbulent combustion. While large-scale mixing is accurately captured by LES, the small-scale combustion process itself has to be modeled. Developing LES models is further complicated by the interaction of discretization errors with the models. Most numerical methods, due to their dissipative nature, preferentially impact the smallest resolved scales that are critical for modeling combustion and can undermine the predictive accuracy of LES. The focus of this work is to evaluate the impact of numerical methods on subfilter modeling. A key quantity in combustion modeling is the subfilter conserved scalar variance that determines the level of mixing between fuel and oxidizer at the subfilter level. The study here demonstrates that conventional notions about truncation errors and accuracy of higher-order methods are invalid in the context of subfilter modeling. In particular, it is demonstrated that the commonly used dynamic procedure counteracts numerical diffusion associated with computing derivatives, thereby reducing the model error. When using transport equation based variance models, it is shown that certain model forms cancel numerical errors, giving superior performance in the context of LES modeling.   

Buoyant Turbulent Jets with Off-Source Heating. Part I: ILES Simulations

Bhat and Narasimha (JFM 1996) presented an investigation of a novel laboratory experiment analogous to latent heat release during cloud formation. An acidic jet was injected into a deionized ambient, and electrodes were used to selectively heat the conducting jet fluid. We use high-resolution three-dimensional implicit LES simulations to investigate the experiment numerically. The ILES approach uses non-oscillatory finite-volume schemes to capture the inviscid cascade of kinetic energy through the inertial range, while the inherent numerical dissipation acts as an implicit sub-grid model. We first consider the implications of using the ILES approach for turbulent jets and plumes, and then examine the complex interaction between momentum, buoyancy and (acid) concentration for a turbulent jet with off-source heating. The simulations provide valuable insight into the flow structure, and motivate a reinterpretation of the experimental data.   

Large Eddy Simulation of a Turbulent Buoyant Helium Plume

Numerical simulations of fires remain challenging because of the complex coupled physics including buoyancy effects, turbulence, combustion, and soot formation. The present work focuses on a turbulent buoyant helium plume as a canonical test reflecting some of the important features of fires. In this configuration, small scale structures are formed due to Rayleigh-Taylor instabilities. Then, these structures start to interact with large scale features of the flow resulting in a puffing cycle. The simulation of this 1-meter diameter helium plume is performed using Large Eddy Simulation (LES). The simulation is shown to reproduce the main features of the turbulent plume, such as puffing frequency and the development of Rayleigh-Taylor instabilities. Furthermore, comparison of numerical results with experimental measurements shows good agreement not only for mean quantities but also for velocity and scalar fluctuations. Finally, the effects of mesh resolution and subgrid scale modeling are analyzed by considering different meshes and models.   

Large Eddy Simulation Analysis of Turbulent Combustion in a Jet-Engine Combustor

Large-eddy simulation is performed to understand turbulent mixing, cooling, and combustion dynamics in a jet-engine combustor. An LES technique conserving discrete mass, momentum, and kinetic energy on arbitrary shaped unstructured grids is coupled with a Lagrangian particle tracking method for liquid fuel atomization and evaporation, and a presumed probability density function approach for turbulent combustion. A systematic analysis of the mean and turbulent flow fields is carried out to elucidate dynamics of important flow structures and mechanisms for turbulent mixing and cooling. The present LES is found to predict flow splits through the injector swirler and inner and outer dilution shrouds that are in excellent agreement with experimental measurements. The mean temperature, temperature profile, and NO mole fraction at the exit of the combustor are also found to be in favorable agreement with experimental data. The dilution jets produce significant magnitudes of the derivatives of the mean radial and circumferential velocity components, thereby dominating turbulent kinetic energy production. Combustor exit flow consists of fine-scale velocity fluctuations and intermittent large-scale high temperature flow structures.   

Implementation of the Joint Frequency-Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows

The recently developed methodology ``frequency-velocity-scalar filtered mass density function'' (FVS-FMDF) is implemented for large eddy simulation (LES) of turbulent reacting flows. The FVS-FMDF, takes account of unresolved subgrid scales by considering the joint probability density function (PDF) of the frequency, velocity and scalar fields. A transport equation for FVS-FMDF is derived in which the effects of convection and chemical reaction appear in closed forms. The unclosed terms in this equation are modeled in a fashion similar to PDF methods. The modeled FVS-FMDF transport equation is solved by a Lagrangian Monte Carlo method. This is the most comprehensive form of the filtered density function for turbulent reacting flows to date. The methodology is implemented to simulate turbulent shear flows. The LES results are compared with the direct numerical simulation (DNS) data of the same layer. The LES predictions show close agreements with DNS data.