Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

38th Plasmadynamics and Lasers Conference

2007

Self Cite

A multi-species magnetohydrodynamic (MHD) model based on an extended fluid dynamics description for each plasma species is proposed for the prediction of the flow and behavior of fully ionized non-equilibrium anisotropic plasmas. In particular, a two-fluid (ions and electrons) plasma model is described that makes use of a 10-moment or Gaussian anisotropic moment closure to model ion and electron species transport. The ion and electron moment equations are fully coupled to the complete set of Maxwell's equations which govern electromagnetic wave propagation within the plasma and a relaxation time approximation is used to model non-equilibrium Coulomb collisional processes between the ions and electrons. Unlike conventional MHD models, the proposed two-fluid model is capable of taking into account large temperature anisotropies and temperature differences between the electrons and ions, both of which can occur for low-density, high-temperature plasmas and/or strongly magnetized plasmas. A dispersion analysis of the proposed model is undertaken in order to examine further its mathematical properties and explore the nature of its solutions. The dispersive and hyperbolic nature of the equations and the disparate times scales or plasma frequencies of the solutions are revealed. The governing system of partial differential equations would appear to be well suited for solution by Godunov-type finite-volume methods provided that the disparate scales can be dealt with. A higherorder finite-volume method is developed here for the solution of the one-dimensional form of the two-fluid plasma model and dispersion analyses of the discretized equations indicates that a stable and practical scheme is possible if a fully implicit time marching scheme is adopted. The analysis also suggests mechanisms for preconditioning the system of equations to further reduce numerical stiffness, resulting in a plasma model that is more suitable for practical applications. Numerical results for several one-dimensional unsteady plasma flows are described and demonstrate the potential of the proposed multi-species plasma model for predicting non-equilibrium anisotropic plasma flows in engineering applications such as those encountered in electric space propulsion devices. The future extension of the model to partially ionized plasmas in two and three space dimensions is also discussed.

Section: B Damping Of Fundamental Solution Modesmentioning

confidence: 99%

“…Furthermore, it has been recently applied successfully to a range of non-magnetized rarefied gaseous flows. [26][27][28] In the Gaussian closure, the species phase space distribution function is approximated as follows:…”

Section: Multispecies Transport Equationsmentioning

confidence: 99%

Development of Two-Fluid Magnetohydrodynamics Model for Non-Equilibrium Anisotropic Plasma Flows

Miuraand

38th Plasmadynamics and Lasers Conference

2007

Self Cite

“…In previous studies by the authors, 8,35 low-speed flow past a circular cylinder as predicted by the standard Gaussian moment equations has been considered. There is a reasonable amount of data and theory available in the literature regarding this situation.…”

Section: Vc Subsonic Flow Past a Circular Cylindermentioning

confidence: 99%

“…Such an extension has been proposed Hittinger 26 and has been previously studied by the authors. 8 This extension adds an extra transport equation for internal rotational energy, resulting in the following moment equations:…”

Section: Iic the Gaussian Closurementioning

confidence: 99%

Extended Fluid Dynamic Model for Micron-Scale Flows Based on Gaussian Moment Closure

McDonald

46th AIAA Aerospace Sciences Meeting and Exhibit

2008

Self Cite

An extended fluid-dynamic model for micron-scale flows with heat transfer based on the Gaussian moment closure is presented. The standard Gaussian closue moment equations are hyperbolic and closure is achieved by assuming a form for the velocity distribution function which will, by construction, yield zero heat flux; the proposed extension leads to the addition of anisotropic thermal-diffusion terms having an elliptic nature. The extended model can be achieved by taking a Chapman-Enskog-type expansion about either the Gaussian moment equations of the kinetic equation and both methods are presented here. The elliptic nature of the additional generalized heat-flux terms lead to fully dispersed shock wave solutions, unlike the partially dispersed solutions provided by the Gaussian closure as the Mach number increases. Using a Godunov-type finite-volume scheme with block based adaptive-mesh refinement (AMR) on body-fitted multi-block meshes, the proposed equations are applied to several canonical continuum and micron-scale flow situations such as shock structure, Couette flow, and flow past a circular cylinder, as well as for transonic flow past a micro airfoil. Comparisons with analytic, experimental, and direct-simulation Monte Carlo (DSMC) results are made and demonstrate the capabilities of the proposed non-equilibrium model.

“…The proposed AMR approach allows for anisotropic mesh refinement and is well suited to parallel implementation via domain decomposition. Very efficient and highly scalable algorithms have been developed for the predictions of laminar combusting flows, 36 turbulent combusting flows, 37, 38 turbulent multi-phase rocket motor core flows, 51 micro-scale flows, 52 and compressible flows with high-order scheme, 53 all in two space dimensions.…”

Section: Iiib Block-based Adaptive Mesh Refinementmentioning

confidence: 99%

Parallel Adaptive Mesh Refinement Scheme for Three-Dimensional Turbulent Non-Premixed Combustion

Gaoand

46th AIAA Aerospace Sciences Meeting and Exhibit

2008

Self Cite

A parallel adaptive mesh refinement (AMR) algorithm is described for predicting turbulent non-premixed gaseous combusting flows in three space dimensions. The Favreaveraged Navier-Stokes equations governing a reactive mixture of thermally perfect gases, the two transport equations of the k-ω turbulence model, and the time-averaged species transport equations, are all solved using a fully coupled finite-volume formulation on bodyfitted multi-block hexahedral mesh. The numerical algorithm adopts a cell-centred upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solver based flux functions to determine the inviscid (hyperbolic) flux at cell interfaces. The viscous (elliptic) components of the cell face flux are evaluated by employing a hybrid average gradient-diamond path approach. For the treatment of near-wall turbulence, both low-Reynolds-number and wall-function formulations of the k-ω model are used, with a procedure for automatically switching from one to the other, depending on mesh resolution. A flexible block-based hierarchical octree data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. This AMR approach allows for anisotropic mesh refinement and the block-based data structure readily permits efficient and scalable implementations of the algorithm on multi-processor architectures. Numerical results for turbulent non-premixed methane-air diffusion flames are described to demonstrate the validity and potential of the parallel AMR approach for predicting complex combusting flows.