Evaluation of a Hybrid Boltzmann-Continuum Method for High Speed Nonequilibrium Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83556/1/AIAA-2010-1569-683.pd

HIGH TEMPERATURE FLOW SOLVER FOR AEROTHERMODYNAMICS PROBLEMS

A weakly ionized hypersonic flow solver for the simulation of reentry flow is firstly developed at the University of Kentucky. This code is the fluid dynamics module of known as Kentucky Aerothermodynamics and Thermal Response System (KATS). The solver uses a second-order finite volume approach to solve the laminar Navier– Stokes equations, species mass conservation and energy balance equations for flow in chemical and thermal non-equilibrium state, and a fully implicit first-order backward Euler method for the time integration. The hypersonic flow solver is then extended to account for very low Mach number flow using the preconditioning and switch of the convective flux scheme to AUSM family. Additionally, a multi-species preconditioner is developed. The following part of this work involves the coupling of a free flow and a porous medium flow. A new set of equation system for both free flows and porous media flows is constructed, which includes a Darcy–Brinkmann equation for momentum, mass conservation, and energy balance equation. The volume-average technique is used to evaluate the physical properties in the governing equations. Instead of imposing interface boundary conditions, this work aims to couple the free/porous problem through flux balance, therefore, flow behaviors at the interface are satisfied implicitly

DSMC-LBM mapping scheme for rarefied and non-rarefied gas flows

We present the formulation of a kinetic mapping scheme between the Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is at the basis of the hybrid model used to couple the two methods in view of efficiently and accurately simulate isothermal flows characterized by variable rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we propose ensures to accurately couple DSMC and LBM at a larger Kn number than usually done in traditional hybrid DSMC-Navier-Stokes equation models. We show the main steps of the mapping algorithm and illustrate details of the implementation. Good agreement is found between the moments of the single particle distribution function as obtained from the mapping scheme and from independent LBM or DSMC simulations at the grid nodes where the coupling is imposed. We also show results on the application of the hybrid scheme based on a simpler mapping scheme for plane Poiseuille flow at finite Kn number. Potential gains in the computational efficiency assured by the application of the coupling scheme are estimated for the same flow.Comment: Submitted to Journal of Computational Scienc

An open-source hybrid CFD-DSMC solver for high-speed flows

A new open-source hybrid CFD-DSMC solver, called hyperFoam, has been implemented within the OpenFOAM framework. The capabilities of the OpenFOAM computational fluid dynamics (CFD) solver rhoCentralFoam for supersonic simulations were analysed, showing good agreement with state-of-the-art solvers such as DLR-Tau, and then enhanced, by incorporating the local time stepping (LTS) and adaptive mesh refinement (AMR) techniques. These aspects would later be used for the development of the hypersonic CFD code hy2Foam.;hyperFoam relies on hy2Foam and the direct direct simulation Monte Carlo (DSMC) code dsmcFoam to be able to resolve the flow physics while under the slip-transition regime. Using a mixture of Boyd's Gradient-Length-Local Knudsen number and a generalised modified Chapman-Enskog parameter, hyperFoam is capable of identifying the continuum and rarefied zones within the computational domain and solve each with its respective CFD or DSMC solver.;hyperFoam has been used to simulate several Couette flow with heat transfer test cases, each of different complexity. Good agreement was shown between the DSMC and hybrid results for these simulations. The hybrid code was then used to analyse a hypersonic cylinder. Reasonably similar accuracy was found between the DSMC and hybrid results for vibrationless N2 and N2-O2. However, forO2 important discrepancies were found due to an inconsistency between continuum and rarefied vibrational modelling.A new open-source hybrid CFD-DSMC solver, called hyperFoam, has been implemented within the OpenFOAM framework. The capabilities of the OpenFOAM computational fluid dynamics (CFD) solver rhoCentralFoam for supersonic simulations were analysed, showing good agreement with state-of-the-art solvers such as DLR-Tau, and then enhanced, by incorporating the local time stepping (LTS) and adaptive mesh refinement (AMR) techniques. These aspects would later be used for the development of the hypersonic CFD code hy2Foam.;hyperFoam relies on hy2Foam and the direct direct simulation Monte Carlo (DSMC) code dsmcFoam to be able to resolve the flow physics while under the slip-transition regime. Using a mixture of Boyd's Gradient-Length-Local Knudsen number and a generalised modified Chapman-Enskog parameter, hyperFoam is capable of identifying the continuum and rarefied zones within the computational domain and solve each with its respective CFD or DSMC solver.;hyperFoam has been used to simulate several Couette flow with heat transfer test cases, each of different complexity. Good agreement was shown between the DSMC and hybrid results for these simulations. The hybrid code was then used to analyse a hypersonic cylinder. Reasonably similar accuracy was found between the DSMC and hybrid results for vibrationless N2 and N2-O2. However, forO2 important discrepancies were found due to an inconsistency between continuum and rarefied vibrational modelling

Hybrid Particle-Continuum Simulations of Low Knudsen Number Hypersonic Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76429/1/AIAA-2007-3892-932.pd

Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method.

Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a direct result of these improvements. Next, a new parameter for detecting rotational nonequilibrium effects is proposed and shown to offer advantages over other continuum breakdown parameters, achieving further accuracy gains. Lastly, the capabilities of the MPC method are extended to accommodate multiple chemical species in rotational nonequilibrium, each of which is allowed to equilibrate independently, enabling application of the MPC method to more realistic atmospheric flows.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111385/1/averhoff_1.pd

Efficient simulation of internal multiscale gas flows

We develop, validate, and apply an efficient multiscale method for the simulation of a large class of low-speed internal rarefied gas flows, which are critical to a range of future technologies. The method is based on an existing multiscale approach for the simulation of small-scale dense-fluid flows of high-aspect ratio, but has been extended to support fluid compressibility, non-isothermal conditions, three dimensional domains, and transience. Furthermore, the method is able to treat a broader range of flows: periodic, non-periodic, body-force-driven, pressure-driven, thermally-driven, and shear-driven. It also incorporates pseudospectral methods, and so boasts excellent convergence characteristics and accuracy. All verification cases presented herein are designed to be amenable to solution by a full molecular treatment (where scale separation is not exploited). The computationally demanding simulation technique known as direct simulation Monte Carlo (DSMC) is employed to obtain reference solutions, allowing for comparison with those computed by the multiscale method: excellent agreement is observed throughout. The unsteady (time-marching) implementation of the method, which allows for the resolution of transient flows, is validated by comparison with time dependent experimental data. Again, agreement is excellent. The computational efficiency of the multiscale method is exceptional. It provides efficiency gains of multiple orders of magnitude, relative to full molecular simulations (by the DSMC method); in some cases, the multiscale method allows for the solution of otherwise computationally intractable problems. Note, highly scale-separated systems are simulated with even greater efficiency. Following the experimental validation of the method, it is applied to the study of thermal-transpiration compressors (and implicitly Knudsen compressors). We characterise the effectiveness of these devices by considering the maximum pressure difference attainable for various combinations of (realistic) thermodynamic and geometric conditions. The development time required to obtain this pressure difference, which is also considered as a performance indicator, is also computed

Development of a Hybrid Particle Continuum Solver

When simulating complex flows, there are some physical situations that exhibit large fluctuations in particle density such as: planetary reentry, ablation due to arcing, rocket exhaust plumes, etc. When simulating these events, a high level of physical accuracy can be achieved with kinetic methods otherwise known as particle methods. However, this high level of physical accuracy requires large amounts of computation time. If the simulated flow is in collisional equilibrium, then less computationally intensive continuum methods, otherwise known as fluid methods, can be utilized. Hybrid Particle-Continuum (HPC) codes attempt to blend particle and fluid solutions in order to reduce computation time for transitional flows that exhibit both continuum and rarefied flow in a single domain. This thesis details the development of an HPC code in OpenFoam for Cal Poly\u27s Aerospace Engineering department. The primary benchmark for the solver, named hybridFoam, was to simulate a 1D sod-shock simulation. This primary goal was achieved and a collection of test simulations were conducted to map out the solvers current capabilities and identify where future development efforts should focus

Application of a Multiscale Particle Scheme to High Altitude Rocket Exhaust Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76663/1/AIAA-2009-1567-355.pd

Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in the Navier-Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution