Publications

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The Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics (MGD) has been used for more than 50 years to simulate rarefied gas flows. Modern supercomputers have brought higher-density near-continuum flows within range. In the present paper, DSMC is used to study compressible turbulence in the Taylor-Green (TG) vortex flow. The DSMC results are compared to available numerical results from Direct Numerical Simulation (DNS) of the (continuum) Navier-Stokes equations.

Direct numerical simulations (DNS) were conducted to characterize the pressure fluctuations under the turbulent portion of the boundary layer over a sharp 7◦ half-angle cone at a nominal freestream Mach number of 8 and a unit Reynolds number of Reunit = 13.4 × 106/m. The axisymmetric cone geometry and the flow conditions of the DNS matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8). The DNS-predicted wall pressure statistics, including the root-mean-square (r.m.s.) fluctuations and the power spectral density (PSD), were compared with those measured in the Sandia HWT-8. A good comparison between the DNS and the experiment was shown for the r.m.s. and PSD of wall-pressure fluctuations after spatial averaging was applied to the DNS data over an area similar to the sensing area of the transducer. The finite size of the PCB132 transducer, with a finite sensing area of d+ ≈ 50, caused significant spectral attenuation at high frequencies in the experimentally measured PSD, and the loss in sensor resolution resulted in an approximately 27% reduction in r.m.s. pressure fluctuations. The attenuation due to finite sensor sizes has only a small influence on wall-pressure coherence, as indicated by the good comparisons between the DNS without spatial filtering and the experiment for transducers with either streamwise or spanwise separations. The characteristics of turbulent pressure fluctuations at the cone surface were also compared with those over a flat plate and at the wind-tunnel nozzle wall to assess the effect of flow configurations on the scaling relations of turbulent pressure fluctuations. The inner scale was found to successfully collapse wall-pressure PSD of the cone with those over a nozzle wall and on a flat plate at a similar freestream Mach number. For all the three flow configurations, the Corcos model was found to deliver good predictions of wall pressure coherence over intermediate and high frequencies, and the Corcos parameters for the streamwise and spanwise coherence at Mach 8 were found to be similar to those reported in the literature at lower supersonic Mach numbers.

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This report documents the initial testing of the Sandia Parallel Aerodynamics and Reentry Code (SPARC) to directly simulate hypersonic, turbulent boundary layer flow over a sharp 7- degree half-angle cone. This type of computation involves a tremendously large range of scales both in time and space, requiring a large number of grid cells and the efficient utilization of a large pool of resources. The goal of the simulation is to mimic and verify a wind tunnel experiment that seeks to measure the turbulent surface pressure fluctuations. These data are necessary for building a model to predict random vibration loading in the reentry flight environment. A low-dissipation flux scheme in SPARC is used on a 2.7 billion cell mesh to capture the turbulent fluctuations in the boundary layer flow. The grid is divided into 115200 partitions and simulated using the Knight's Landings (KNL) partition of the Trinity system. The parallel performance of SPARC is explored on the Trinity system, as well as some of the other new architectures. Extracting data from the simulation shows good agreement with the experiment as well as a colleague's simulation. The data provide a guide for which a new model can be built for better prediction of the reentry random vibration loads.

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The Direct Simulation Monte Carlo (DSMC) method has been used for more than 50 years to simulate rarefied gases. The advent of modern supercomputers has brought higher-density near-continuum flows within range. This in turn has revived the debate as to whether the Boltzmann equation, which assumes molecular chaos, can be used to simulate continuum flows when they become turbulent. In an effort to settle this debate, two canonical turbulent flows are examined, and the results are compared to available continuum theoretical and numerical results for the Navier-Stokes equations.

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We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at Re=500. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.

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We provide the first demonstration that molecular-level methods based on gas kinetic theory and molecular chaos can simulate turbulence and its decay. The direct simulation Monte Carlo (DSMC) method, a molecular-level technique for simulating gas flows that resolves phenomena from molecular to hydrodynamic (continuum) length scales, is applied to simulate the Taylor-Green vortex flow. The DSMC simulations reproduce the Kolmogorov -5/3 law and agree well with the turbulent kinetic energy and energy dissipation rate obtained from direct numerical simulation of the Navier-Stokes equations using a spectral method. This agreement provides strong evidence that molecular-level methods for gases can be used to investigate turbulent flows quantitatively.