Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M24: Compressible Flows I |
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Chair: Oleg Vasilyev, University of Colorado at Boulder Room: 30E |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M24.00001: A molecular dynamics simulation demonstrating the invalidity of the Navier-Stokes Fourier (NSF) equations for compressible gaseous continua at all Knudsen numbers Howard Brenner, Nishanth Dongari, Jason Reese While it is well known to experimental gas kineticists and other fluid mechanicians that the NSF equations are invalid for noncontinua (rarefied gases) owing to Knudsen number effects, it is nevertheless universally believed that the NSF equations are valid for gaseous continua, namely when the Knudsen number is vanishingly small. This assumption is shown by molecular dynamics simulations to be wrong. This is demonstrated by performing simulations for monatomic gaseous continua undergoing steady-state rigid-body rotation relative to an inertial observer in a rigid circular cylinder that is thermodynamically isolated from its surroundings. The NSF equations, which are universally believed to govern the outcome of this elementary experiment, predict that the temperature will be uniform throughout the gas. In fact, the results of the simulation show that the temperature actually increases radially outward from the center of the cylinder to the wall by a significant amount, the greater the cylinder's angular velocity the greater the amount. Whereas the NSF paradigm fails to predict this nonisothermal radial temperature variation, the temperature distribution is shown to be accurately predicted by the recently proposed bivelocity hydrodynamic paradigm. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M24.00002: A comprehensive theory for the response of gases to localized, transient heat addition David R. Kassoy The response of a gas to localized, transient heat addition depends upon the amount of energy added during the heating period and the ratio of the heating time scale, t(H) to the local acoustic time, t(A). When the ratio is small the process occurs at nearly constant volume conditions, pressure rises with temperature while the density decrease is small. The local expansion Mach number is small. Gas expelled from the boundary of the high-pressure hot spot is the source of mechanical waves in the unheated environmental gas. The range of responses includes acoustic waves, shocks and very strong blast waves. When the amount of energy added exceeds an explicit limit the heating process is fully compressible with a substantial internal Mach number. When the time scale ratio is large energy addition to the volume leads to a nearly constant pressure process with the density inversely proportional to the rising temperature. The local expansion Mach number will range widely, depending on the amount of energy added and the size of the now large time scale ratio. Finally, a systematic formulation for the acoustic response of a gas, confined in a rectangle, to modest spatially distributed transient energy addition on a heating time scale t(H)=O(t(A)) is described. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M24.00003: Delta-Measure Perturbations of a Contact Discontinuity Roy Baty In this presentation, nonstandard analysis is applied to study generalized function perturbations of contact discontinuities in compressible, inviscid fluids. Nonstandard analysis is an area of modern mathematics that studies extensions of the real number system to nonstandard number systems that contain infinitely large and infinitely small numbers. Perturbations of a contact discontinuity are considered that represent one-dimensional analogs of the two-dimensional perturbations observed in the initial evolution of a Richtmyer-Meshkov instability on a density interface. Nonstandard predistributions of the Dirac delta measure and its derivatives are applied as the perturbations of a contact discontinuity. The one-dimensional Euler equations are used to model the flow field of a fluid containing a perturbed density interface and generalized solutions are constructed for the perturbed flow field. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M24.00004: Effect of Large Bulk Viscosity on Two-Dimensional Transonic Flow Mark Cramer We examine steady two-dimensional transonic flows over a thin airfoil or turbine blade. The wing Reynolds number is taken to be large and the fluid is described by the classical Navier-Stokes equations. The bulk viscosity is taken to be large compared to the shear viscosity. We use the Method of Matched Asymptotic Expansions to give the conditions under which the effects of large bulk viscosity are no longer negligible. We show that longitudinal viscous effects must be considered at lowest order when the ratio of bulk to shear viscosity is on the order of the product of the conventional Reynolds number times the two-thirds power of the non-dimensional airfoil thickness. Under these conditions the flow is shown to be frictional, irrotational, and governed by the viscous form of the transonic small disturbance equation. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M24.00005: Effect of Large Bulk Viscosity on High-Speed Separation Fatemeh Bahmani, Mark Cramer We examine the effect of large bulk viscosity on the classical problem of two-dimensional shock boundary layer interaction. The flow is taken to be steady, supersonic and the plate is taken to be flat and adiabatic. The boundary layer is taken to be laminar and the fluid is modeled as a perfect gas with a bulk viscosity which is large compared to its shear viscosity. The flow details are computed using a fifth order weighted essentially non-oscillatory (WENO) finite difference scheme and 3rd order Runge Kutta scheme for the spatial and temporal discretizations. The primary result of interest is the suppression of separation when the fluid has a bulk viscosity which is large compared to the shear viscosity. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M24.00006: Modeling of the subgrid scale viscous/scalar dissipation in compressible turbulence Navid S. Vaghefi, Mehdi B. Nik, Patrick Pisciuneri, Peyman Givi, Cyrus K. Madnia Results are presented of subgrid scale (SGS) viscous/scalar dissipation models using {\it a priori} analysis of compressible turbulent flows. This is done via assessment of DNS of several turbulent flow configurations at varying compressibility levels, Reynolds and Schmidt numbers. These models will be used as sub-closures in the LES via FDF of compressible turbulence. Optimum model parameters are calculated by maximizing the correlation coefficients between the SGS exact and modeled terms, and optimal estimators are used to verify the results. The effects of the filter width are also assessed for sub-closures. Different methods for calculating the model coefficients are evaluated and it is shown that a dynamic procedure based on the global SGS equilibrium between the production and dissipation produces the best results. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M24.00007: A Characteristic-Based Volume Penalization Method for Compressible Viscous Flows in Complex Geometries Eric Brown-Dymkoski, Nurlybek Kasimov, Oleg Vasilyev This is the first of two talks on new volume penalization method for numerical simulations of compressible flows around solid obstacles of complex geometries. This approach overcomes two major limitations of Brinkman penalization -- the inability to model Neumann boundary conditions and shock reflection of solid boundaries. Boundary conditions on the fluxes are achieved through characteristic propagation into the thin layer inside of the obstacles. Inward pointing characteristics ensure nonphysical solution inside the obstacle does not propagate out to the fluid. The Dirichlet boundary conditions are enforced similarly to Brinkman penalization. Parameters defining the penalization terms are chosen so that they act on a much faster timescale than the characteristic time scale of the flow. A principle advantage of this method is the parameters provide a systematic means of controlling the error. The new approach is general and applicable to wide variety of flow regimes. This talk focuses on the application of the method to the Navier-Stokes equations. It is rigorously shown that the solution of the penalized problem converges towards the exact solution with the convergence of the penalization parameters. Examples of application to compressible viscous flows are given and discussed. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M24.00008: A Characteristic-Based Volume Penalization Method for Compressible Inviscid Flows in Complex Geometries Nurlybek Kasimov, Eric Brown-Dymkoski, Oleg Vasilyev This is the second of two talks on new volume penalization method for numerical simulations of compressible flows around solid obstacles of complex geometries. This approach overcomes two major limitations of Brinkman penalization -- inability to model Neumann boundary conditions and shock reflection of solid boundaries. Boundary conditions on the fluxes are achieved through characteristic propagation into the thin layer inside of the obstacles. Inward pointing characteristics ensure nonphysical solution inside the obstacle does not propagate out to the fluid. Dirichlet boundary conditions are enforced similarly to Brinkman penalization. Parameters defining the penalization terms are chosen so they act on a much faster timescale than the characteristic time scale of the flow. A principle advantage of this method is parameters provide a systematic means of controlling the error. New approach is general and applicable to a wide variety of flow regimes. This talk focuses on the application of the method to the Euler equations. The main difference compared to Navier-Stokes formulation is the handling of slip boundary conditions and the effect of the curvature in the momentum equation. Examples of supersonic compressible inviscid complex geometry flows are given and discussed. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M24.00009: Numerical modeling of a compressible multiphase flow through a nozzle Urszula Niedzielska, Jason Rabinovitch, Guillaume Blanquart New thermodynamic cycles developed for more efficient low temperature resource utilization can increase the net power production from geothermal resources and sensible waste heat recovery by 20-40{\%}, compared to the traditional organic Rankine cycle. These improved systems consist of a pump, a liquid heat exchanger, a two-phase turbine, and a condenser. The two-phase turbine is used to extract energy from a high speed multiphase fluid and consists of a nozzle and an axial impulse rotor. In order to model and optimize the fluid flow through this part of the system an analysis of two-phase flow through a specially designed convergent-divergent nozzle has to be conducted. To characterize the flow behavior, a quasi-one-dimensional steady-state model of the multiphase fluid flow through a nozzle has been constructed. A numerical code capturing dense compressible multiphase flow under subsonic and supersonic conditions and the coupling between both liquid and gas phases has been developed. The output of the code delivers data vital for the performance optimization of the two-phase nozzle. [Preview Abstract] |
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