Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L8: Compressible Flows II |
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Chair: Medhi Nik, University of Pittsburgh Room: 311 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L8.00001: Low-dissipation hybrid schemes for simulations of compressible multicomponent flows Pooya Movahed, Eric Johnsen In the present work an efficient hybrid scheme is proposed for numerical simulations of compressible multicomponent flows. The algorithm is based on a high-order accurate weighted essentially non-oscillatory (WENO) scheme for shock capturing and a non-dissipative central scheme in the split form for smooth regions. The central-difference method results in a reasonable speed up and exhibits better resolution properties for turbulence. The shock capturing is handled using the AUSM+up Riemann solver with a WENO reconstruction of the primitive variables. A new sensor based on the first norm of the difference of WENO weights from the ideal weights is used at the beginning of each Runge-Kutta step for a smooth transition between the central and WENO fluxes at interfaces. The scheme is shown to prevent spurious pressure oscillations at interfaces. The performance of the method is presented for a set of problems including the Sod shock tube problem, the Shu-Osher problem and the planar Richtmyer-Meshkov instability with particular emphasis on mixing at early and late times. This research was supported in part by the DOE NNSA under the Predictive Science Academic Alliance Program by grant DEFC52- 08NA28616. [Preview Abstract] |
Monday, November 21, 2011 3:48PM - 4:01PM |
L8.00002: A Novel A Posteriori Investigation of Scalar Flux Models for Passive Scalar Dispersion in Compressible Boundary Layer Flows Kalen Braman, Venkat Raman A novel direct numerical simulation (DNS) based a posteriori technique has been developed to investigate scalar transport modeling error. The methodology is used to test Reynolds-averaged Navier-Stokes turbulent scalar flux models for compressible boundary layer flows. Time-averaged DNS velocity and turbulence fields provide the information necessary to evolve the time-averaged scalar transport equation without requiring the use of turbulence modeling. With this technique, passive dispersion of a scalar from a boundary layer surface in a supersonic flow is studied with scalar flux modeling error isolated from any flowfield modeling errors. Several different scalar flux models are used. It is seen that the simple gradient diffusion model overpredicts scalar dispersion, while anisotropic scalar flux models underpredict dispersion. Further, the use of more complex models does not necessarily guarantee an increase in predictive accuracy, indicating that key physics is missing from existing models. Using comparisons of both a priori and a posteriori scalar flux evaluations with DNS data, the main modeling shortcomings are identified. Results will be presented for different boundary layer conditions. [Preview Abstract] |
Monday, November 21, 2011 4:01PM - 4:14PM |
L8.00003: The conservative cascade of kinetic energy in compressible turbulence Hussein Aluie, Shengtai Li, Hui Li We use a coarse-graining approach to analyze inter-scale transfer of kinetic energy in compressible turbulence. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional ``conversion'' scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum, $E^{PD}(k)$, where we provide the first numerical evidence that it decays at a rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to imply that mean pressure dilatation acts primarily at large-scales and that kinetic and internal energy budgets statistically decouple beyond a transitional scale-range. Our analysis establishes the existence of an ensuing inertial range over which mean SGS kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion despite not being an invariant. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L8.00004: Energy-Pressure-Velocity-Scalar Filtered Mass Density Function Mehdi B. Nik, Peyman Givi, Cyrus Madnia, Stephen B. Pope The ``Energy-Pressure-Velocity-Scalar Filtered Mass Density Function'' (EPVS-FMDF) is a new subgrid scale (SGS) model developed for large eddy simulation of high speed turbulent flows. This is an extension of the previously developed ``velocity-scalar filtered mass density function'' method [1] in low speed flows. In the EPVS-FMDF formulation, compressibility effects are accounted for by including two additional thermodynamic variables: the pressure and the internal energy. This is the most general form of the FDF for high speed flow simulations. The EPVS-FMDF is obtained by solving its transport equation, in which the effects of convection for velocity and scalar field appear in a closed form. The unclosed terms are modeled in a fashion similar to that in RANS-PDF methods. The modeled EPVS-FMDF transport equation is solved by a Lagrangian Monte Carlo method and is employed for LES of a temporally developing mixing layer at several values of the convective Mach number. The predicted results are assessed by comparison with direct numerical simulation (DNS) data.\\[4pt] [1] Sheikhi, M. R. H., Givi, P., and Pope, S. B., Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Turbulent Reacting Flows, Phys. Fluids, 19(9): 095196 1-21 (2007) [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L8.00005: Small-scale intermittency in compressible turbulence Diego Donzis, Shriram Jagannathan While the effects of compressibility on low-order quantities such as the mean turbulent kinetic energy and dissipation in decaying turbulence have been extensively investigated, little is known about the scaling of fine intermittent structures and how they scale with Reynolds and turbulent Mach numbers. It is thus unclear how the intermittent behavior of energy dissipation rate, for example, in compressible flows compares with its incompressible counterpart. Massive direct numerical simulations of isotropic compressible turbulence at finer-than-usual grid resolutions were conducted to investigate the scaling of small-scale intermittency at a range of Reynolds and turbulent Mach numbers. Large-scale forcing is applied to attain a stationary state which permits better statistical sampling of intermittent activity and, at the same time, provides results independent of initial conditions. Scaling exponents for energy dissipation rate are computed and compared to theoretical models. While low-order moments of dissipation show weak dependence on compressibility levels and thus possess scaling exponents similar to the incompressible case, high-order moments depend on the turbulent Mach number. Differences in the scaling of solenoidal and dilatational components are related to the structure of the most intense events for each type of motion. The consequences of the finidings are discussed in the context of high Reynolds number flows. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L8.00006: A numerical method for DNS/LES of high--enthalpy turbulent flows Shankar Ghosh, Krishnan Mahesh A numerical method is developed for simulation of high-- enthalpy turbulent flows. A non-dissipative algorithm is used for accurate flux reconstruction at the cell faces. The method is combined with a predictor corrector based shock capturing scheme to simulate strong shock waves encountered in high-- enthalpy flows. A non--linear limiter is used to limit the application of shock capturing only to the vicinity of the shock wave to minimize dissipation. The Navier-Stokes equations are suitably modified to represent various thermo--chemical processes occurring in high--enthalpy flows. A five species model for air is considered. To account for finite rate chemical reactions, individual mass conservation equations are solved for every species. An equation for conservation of vibrational energy is also solved to account for vibrational excitation. Species diffusion is modeled through Fick's law. Transport properties are computed taking high temperature effects into account. The numerical method is evaluated using test problems. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L8.00007: Modeling Compressed Turbulence with BHR Daniel Israel Turbulence undergoing compression or expansion occurs in systems ranging from internal combustion engines to supernovae. One common feature in many of these systems is the presence of multiple reacting species. Direct numerical simulation data is available for the single-fluid, low turbulent Mach number case. Wu, et al. (1985) compared their DNS results to several Reynolds-averaged Navier-Stokes models. They also proposed a three-equation $k-\varepsilon-\tau$ model, in conjunction with a Reynolds-stress model. Subsequent researchers have proposed alternative corrections to the standard $k-\varepsilon$ formulation. Here we investigate three variants of the BHR model (Besnard, 1992). BHR is a model for multi-species variable-density turbulence. The three variants are the linear eddy-viscosity, algebraic-stress, and full Reynolds-stress formulations. We then examine the predictions of the model for the fluctuating density field for the case of variable-density turbulence. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L8.00008: Differential Reynolds stress closure modeling of compressible shear flows Carlos Gomez, Sharath Girimaji The most important difference between turbulence in high and low Mach number flows stems from the changing role and action of pressure at different speed regimes. In the rapidly distorted turbulence regime, this effect is well captured by rapid distortion theory (RDT) which shows that gradient Mach number characterizes the role/action of pressure very accurately. Thus motivated, we develop a new rapid pressure-strain correlation model for high-speed compressible shear flows in which the closure coefficients are functions of the local gradient Mach number. The functional dependence of the model coefficients on the Mach number is obtained by comparison against RDT data. This closure naturally leads to a pressure-dilatation closure model. Further analysis reveals that a modification of the dissipation equation is also mandatory to accommodate the pressure-dilatation closure physics. Full differential Reynolds stress closure calculations of plane supersonic mixing layers are performed and comparison with the experimental data of Goebel and Dutton shows that the model exhibits good overall agreement without any further model calibration. [Preview Abstract] |
Monday, November 21, 2011 5:19PM - 5:32PM |
L8.00009: {\it A Priori} Assessment of the FDF Sub-Closures in Compressible Turbulence Navid S. Vaghefi, Mehdi B. Nik, Patrick Pisciuneri, Peyman Givi, Cyrus K. Madnia Results are presented of {\it a priori} assessment of some of the sub-closures required in LES via FDF in compressible turbulent flows. This is done via assessment of DNS of several turbulent flow configurations at varying compressibility levels and Reynolds numbers. Optimum model parameters are calculated by maximizing the correlation coefficients between the SGS exact and modelled terms. The effects of the filter width are also assessed for some of the sub-closures. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L8.00010: Application of gradient limiters for computation of viscous fluxes in an unstructured compressible flow solver J.P. Strodtbeck, K. Weber, J.M. McDonough HYDRA, an unstructured finite-volume CFD code used internally by Rolls--Royce LLC, evaluates viscous fluxes using a characteristic-based scheme in which the characteristic variables are modified with a pseudo-Laplacian smoothing introduced in the doctoral dissertation of Moinier (Oxford University, 1999). Since the pseudo-Laplacian scheme is inadequate for removing numerical oscillations in a variety of situations, a replacement scheme is proposed and implemented with characteristic variables approximated using a smoothed flux limiter based on a traditional minmod scheme. Formally, the method retains second-order accuracy except near oscillations. Convergence plots and comparisons with data demonstrate that the limiter technique provides improvement compared with baseline simulations. Convergence plot comparisons show improved mass flow conservation, removal of oscillations, and the capability of converging to machine zero without sacrificing overall accuracy. Besides this specific application to shock capturing in compressible flows, similar flux limiters may also be appropriate for use in implicit LES for incompressible flows where other limiters and/or filters are currently used in a similar pseudo-Laplacian manner, and also for compressible LES. [Preview Abstract] |
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