Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session GX: Compressible Flows I |
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Chair: Matei I. Radulescu, University of Ottawa Room: Hyatt Regency Long Beach Regency D |
Monday, November 22, 2010 8:00AM - 8:13AM |
GX.00001: ABSTRACT WITHDRAWN |
Monday, November 22, 2010 8:13AM - 8:26AM |
GX.00002: Observable Divergence and Observable Euler Equations for Shocks and Turbulence Kamran Mohseni Both turbulence and shock formation in inviscid flows are prone to high wave number mode generations. This continuous generation of high wavemodes results in an energy cascade to ever smaller scales in turbulence and/or creation of shocks in compressible flows. This high wavenumber problem is often remedied by the addition of a viscous term in both compressible and incompressible flows. A regularization technique for the Burgers equation (Norgard and Mohseni 2008) was recently reported. This inviscid regularization was extended to one-dimensional compressible Euler equations in 2010 (Norgard and Mohseni 2010). This investigation presents a formal derivation of these equations from basic principles. Our previous results are extended to multidimensional compressible and incompressible Euler equations. We define a new {\it observable divergence} based on fluxes calculated from observable quantities at a desired scale. An {\it observable divergence theorem} is then proved and applied in the derivation of the regularized equations. It is shown that the derived equations reduce to inviscid Leray flow model in the limit of incompressibility. It is expected that this technique simultaneously regularizes shocks and turbulence for compressible and incompressible flows. Finally, numerical simulations are presented for the compressible one-dimensional observable Euler equations. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GX.00003: A Numerical Study of the unstart event in a supersonic engine Ik Jang, Rene Pecnik, Parviz Moin The objective of this study is to assess the capability of an unsteady Reynolds averaged Navier-Stokes (URANS) method to predict the unstart phenomenon in a scramjet engine. Both started and unstarted Mach 5 flows in the inlet/isolator part of a scramjet engine were numerically investigated. The unstart event is initiated by raising a mechanical flap located at the downstream of the inlet/isolator, and the motion of the flap was simulated by an immersed boundary method. The simulation results were compared with a series of experiments (Wagner et al., AIAA paper, 2007, 2008, 2009) and a hybrid LES/RANS study (Boles et al., AIAA paper, 2009) performed on the same geometry and flow conditions. The critical angle of the flap to initiate the unstart event as well as the pressure distribution on the wall of the isolator in the started flow are in good agreement with the experiment and the simulation of Boles et al. On the other hand, the upstream moving shock speed is not well predicted and the cause of discrepancy is the subject of the ongoing study. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GX.00004: Compressibility effects in planar wakes Jean-Pierre Hickey, Fazle Hussain, Xiaohua Wu Far-field, temporally evolving planar wakes are studied by DNS to evaluate the effect of compressibility on the flow. A high-order predictor-corrector code was developed and fully validated against canonical compressible test cases. In this study, wake simulations are performed at constant Reynolds number for three different Mach numbers: $Ma=$ 0.2, 0.8 and 1.2. The domain is doubly periodic with a non-reflecting boundary in the cross-flow and is initialized by a randomly perturbed laminar profile. The compressibility of the flow modifies the observed structures which show greater three-dimensionality. A self-similar period develops in which the square of the wake half-width increase linearly with time and the Reynolds stress statistics at various times collapse using proper scaling parameters. The growth-rate increases with increasing compressibility of the flow: an observation which is substantiated by experimental results but is in stark contrast with the high-speed mixing-layer. As the growth-rate is related to the mixing ability of the flow, the impact of compressibility is of fundamental importance. Therefore, we seek an explanation of the modified growth-rate by investigating the turbulent kinetic energy equation. From the analysis, it can be conjectured that the pressure-strain term might play a role in the modified growth-rate. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GX.00005: Energy-Pressure-Velocity Filtered Mass Density Function Mehdi B. Nik, Peyman Givi, Cyrus Madnia, Stephen B. Pope A new methodology termed ``energy-pressure-velocity filtered mass density function'' (EPV-FMDF) is developed for large eddy simulation of high speed turbulent flows. This is an extension of the previously developed ``velocity filtered density function'' (V-FDF) method [1] in low speed flows. To account for the effect of compressibility, the formulation includes 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 EPV-FMDF is obtained by solving its transport equation, in which the effects of convection appear in a closed form. The unclosed terms are modeled in a fashion similar to that in RANS-PDF methods. The modeled EPV-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] Gicquel, L. Y. M., Givi, P., Jaberi, F. A., and Pope, S. B., Velocity Filtered Density Function for Large Eddy Simulation of Turbulent Flows, Phys. Fluids, 14 (3):1196-1213 (2002). [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GX.00006: A PIV Study of Compressibility in a Turbulent Subsonic Axisymmetric Jet Isaac Choutapalli An experimental study has been undertaken to study the effect of nozzle exit Mach number on the flow field characteristics of a turbulent round free jet. Particle Image Velocimetry (PIV) is used as a means of measurement. The Mach numbers considered are 0.30, 0.65 and 0.80. The measurements show that the centerline mean velocity variation, the radial profiles of mean velocity and turbulence quantities within the shear layer can be collapsed on to single curves over the range of Mach numbers considered. The data further shows that it is possible to represent the shear layer mean velocity profile for the turbulent free jet in the subsonic Mach number range with a single analytical expression. [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GX.00007: Shock waves in dense hard disk media: molecular dynamic and continuum descriptions Nick Sirmas, Marian Tudorache, Matei I. Radulescu Mediums composed of a system of colliding hard disks (2D) or hard spheres (3D) serve as good approximations to the molecular structure of gases, liquids and granular media. In the present study, the propagation of piston driven shock waves in a two-dimensional hard-disk medium is studied at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the shock Hugoniot and shock jump conditions were obtained using the approximate Helfand equation of state. The predictions were found in excellent agreement with calculations using the Event Driven Molecular Dynamic method involving 30,000 particles over the entire range of compressibility spanning the dilute ideal gas, liquid and solid phases. In all cases, the energy imparted by the piston motion to the thermalized medium behind the propagating shock is found to be quasi-independent of the medium packing fraction, with a correction vanishing with increasing shock Mach numbers. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GX.00008: Shock wave dynamics in a water-filled log-spiral duct Chuanxi Wang, Veronica Eliasson Both numerical simulations and experiments of converging shock waves in a water-filled log-spiral duct have been performed. A log-spiral shape is considered as one of the ``worst-case scenarios,'' because this particular shape minimizes reflections from the surrounding walls. The simulations were performed using the Overture suite, a package for solving partial differential equations on curvilinear overlapping grids using adaptive mesh refinement. A coupled fluid-solid solver was used to simulate both the water and the surrounding solid domains. Results show that the fluid-structure interaction indeed changes the shock dynamics as compared to using fluid domain with rigid boundary conditions. In the experiments, a projectile from a gas gun impacts the water-filled sample and generates a shock wave, which is then captured by a high-speed schlieren system. Comparison between the experiments and the simulations will be presented, and the results can benefit the design of marine structures with converging sections subjected to dynamic loading events. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GX.00009: Shock Waves in Dense Fluids: An Anisotropic Temperature Theory with Delays Francisco J. Uribe, William G. Hoover, Carol G. Hoover In this work we analyze a recent phenomenological hydrodynamic theory proposed recently by Hoover et al. [arXiv:1005.1525v1] to study shock waves in dense fluids. The theory incorporates anisotropic temperature and relaxation for the fluxes and temperature, following the ideas by Maxwell, Cattaneo, and Krook. For the steady case we analyze the points at which the vector field is infinite (singularities of the field) and obtain conditions for non--existence of a shock profile connecting the two relevant equilibrium points (non--existence of heteroclinic connections). The conditions for non--existence of heteroclinic orbits are then related to the nature of the critical (equilibrium) points and the bifurcations of the system. The results are tested using several numerical methods to solve the hydrodynamic equations for the non--steady and steady problems. [Preview Abstract] |
Monday, November 22, 2010 9:57AM - 10:10AM |
GX.00010: The Structure of Weak Shock Waves in Water Roy Baty, Don Tucker, Carl Hagelberg This talk presents solutions of the Navier-Stokes equations that model weak shock waves in water. One-dimensional jump functions are computed to describe the viscous microstructure of hydrodynamic shocks, which are approximately isentropic. The Tate and Grueneisen equations of state are applied separately with the conservation laws to derive the flow microstructure for shock compressions and pressures up to 1.3 and 20.0 kbars, respectively. The Navier-Stokes equations are integrated along characteristic lines to compute the shock wave thickness. On characteristic lines, the shock wave jump functions reduce to integral equations. The Tate and Grueneisen equations of state yield similar, strictly monotonically increasing, shock wave microstructures. Moreover, the non-dimensional shock wave thicknesses predicted by these equations of state as a function of compression are very similar. [Preview Abstract] |
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