Jonathan M. Burt

Novel Cartesian Implementation of the Direct Simulation Monte Carlo Method

A new Cartesian implementation of the direct simulation Monte Carlo (DSMC) method, named the hypersonic aerothermodynamics particle (HAP) code, is presented. This code is intended for rapid setup and simulation of rarefied flow problems, and as a framework for evaluating new physical models and numerical techniques. Unique features include the use of nonuniform Cartesian adaptive subcells, a collision probability modification to reduce errors associated with spatial averaging in collision probabilities, and automatic planar element approximation of analytically defined two or three-dimensional surface geometries. In this work, simulations are performed using both HAP and an established DSMC code for a rarefied hypersonic flow over a flat plate, and excellent overall agreement is found. Additional simulations are employed to demonstrate reduced dependence on cell size through a proposed collision probability modification. Results are also presented for a threedimensional HAP simulation of hypersonic flow over a blunted cone, and reasonably good agreement with experimental data is observed.

Ground and Space-Based Measurement of Rocket Engine Burns in the Ionosphere

On-orbit firings of both liquid and solid rocket motors provide localized disturbances to the plasma in the upper atmosphere. Large amounts of energy are deposited to ionosphere in the form of expanding exhaust vapors which change the composition and flow velocity. Charge exchange between the neutral exhaust molecules and the background ions (mainly O+) yields energetic ion beams. The rapidly moving pickup ions excite plasma instabilities and yield optical emissions after dissociative recombination with ambient electrons. Line-of-sight techniques for remote measurements rocket burn effects include direct observation of plume optical emissions with ground and satellite cameras, and plume scatter with UHF and higher frequency radars. Long range detection with HF radars is possible if the burns occur in the dense part of the ionosphere. The exhaust vapors initiate plasma turbulence in the ionosphere that can scatter HF radar waves launched from ground transmitters. Solid rocket motors provide particulates that become charged in the ionosphere and may excite dusty plasma instabilities. Hypersonic exhaust flow impacting the ionospheric plasma launches a low-frequency, electromagnetic pulse that is detectable using satellites with electric field booms. If the exhaust cloud itself passes over a satellite, in situ detectors measure increased ion-acoustic wave turbulence, enhanced neutral and plasma densities, elevated ion temperatures, and magnetic field perturbations. All of these techniques can be used for long range observations of plumes in the ionosphere. To demonstrate such long range measurements, several experiments were conducted by the Naval Research Laboratory including the Charged Aerosol Release Experiment, the Shuttle Ionospheric Modification with Pulsed Localized Exhaust experiments, and the Shuttle Exhaust Ionospheric Turbulence Experiments.

Evaluation of a Particle Method for the Ellipsoidal Statistical Bhatnagar-Gross-Krook Equation

Abstract : A particle method is presented for the numerical simulation of rarefied gas flows, based on the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) model of the Boltzmann equation. The method includes consideration of rotational nonequilibrium, and enforces exact momentum and energy conservation for a mixture involving monatomic and diatomic species. This method is applied to the simulation of a nozzle flow of the type associated with cold-gas spacecraft thrusters, and flowfield characteristics are compared with experimental data as well as results from direct simulation Monte Carlo (DSMC) and Navier-Stokes simulations of the same flow. The ES-BGK method is shown to allow for a relatively high degree of accuracy in transitional flow regimes, while avoiding the intermolecular collision calculations which typically make the DSMC simulation of low Knudsen number flows prohibitively expensive.

Extension of a Multiscale Particle Scheme to Near-Equilibrium Viscous Flows

A recently proposed low diffusion (LD) equilibrium particle method based on the direct simulation Monte Carlo (DSMC) method is modified for use with near-equilibrium viscous flows. A finite volume discretization of the viscous terms in the compressible Navier-Stokes equations is used to incorporate diffusive transport effects into the LD particle method, and a velocity and temperature slip wall boundary condition is employed for improved accuracy in the slip flow Knudsen number regime. The modified method is compared with both DSMC and theory for a series of unsteady boundary layer problems, and excellent agreement is observed. The computational cost of the modified LD particle method is shown for a representative near-equilibrium case to be roughly four orders of magnitude lower than that of DSMC, due to reduced scatter as well as less stringent cell size and time step requirements in the LD method. Simulation procedures are outlined for a strongly coupled hybrid algorithm, where the LD particle method is used in continuum flowfield regions and DSMC is employed in nonequilibrium regions. The hybrid scheme is evaluated through a comparison with numerical and experimental data for a flow of N2 through a small convergent-divergent nozzle into a near vacuum, and hybrid simulation results are generally found to agree very well with other available data. I. Introduction AS flows involving a wide range of characteristic length scales appear in a number of different engineering applications, including those related to atmospheric flow around reentry or hypersonic vehicles, high-altitude rocket plumes, flows within and around micro-electro-mechanical systems, and any supersonic flow where internal shock structures are of interest. In these types of flows, a near-equilibrium gas velocity distribution may exist through much of the flowfield, as the equilibrating effect of intermolecular collisions dominates over other processes (such as inhomogeneous diffusive transport or gas-surface interaction) which tend to pull the velocity distribution away from equilibrium. However, some flowfield regions may have characteristic length scales comparable to or smaller than the local mean free path, so that the influence of collisions does not dominate and the velocity distribution diverges considerably from the equilibrium limit. While simulation of near-equilibrium flowfield regions may be efficiently performed using computational fluid dynamics (CFD) techniques based on the Navier-Stokes equations, nonequilibrium regions must be simulated using more expensive techniques based on the Boltzmann equation. The Boltzmann equation is the governing equation for dilute gas flows at arbitrary Knudsen numbers, and its derivation follows from assumptions of molecular chaos and binary intermolecular collisions with no approximations regarding the shape of the velocity distribution. The most mature and commonly used simulation method for the Boltzmann equation is the direct simulation Monte Carlo (DSMC) method, first introduced by Bird. 1 In a DSMC simulation, a large number of representative particles are tracked through a computational grid, and move and collide in a manner consistent with physical arguments underlying the Boltzmann equation. While this method may be applied to both nonequilibrium and continuum flowfield regions, cell size and time step limitations often make it prohibitively expensive for simulating continuum flows where global characteristic length scales are far larger than the mean free path. In practice, such multiscale flows are usually simulated using both DSMC and CFD methods, by applying CFD techniques in near-equilibrium regions where the Navier-Stokes equations are valid, and using DSMC elsewhere in the flow. In the simplest type of hybrid CFD-DSMC approach, a CFD simulation is performed on a domain which 1

DEVELOPMENT OF A TWO-WAY COUPLED MODEL FOR TWO PHASE RAREFIED FLOWS

Based on a previously published model for momentum and energy transfer to a spherical solid particle from a locally free molecular gas, a procedure is outlined for the simulation of one-way coupled two phase flows involving a nonequilibrium gas and a dilute solid particle phase. Following a simple analysis of interphase collision dynamics, the procedure is extended for use with a range of nonspherical particles. An extensive modification to this method is proposed to allow the modeling of two-way coupled flows, and a representative test case is used to verify that momentum and energy are conserved. The method described here is thought to be the first to allow for the simulation of two-way coupled two phase rarefied flows, and holds promise as a tool in the analysis of a variety of high altitude plume flows.

High-Altitude Plume Simulations for a Solid Propellant Rocket

A simulation scheme is proposed for flowfield and radiation analysis of solid rocket exhaust plumes at high altitude. Several recently developed numerical procedures are used to determine properties of the gas and condensed phase Al2O3 particles, and spectrally resolved plume radiation calculations are performed using a Monte Carlo ray trace model. Simulations are run for a representative plume flow at 114 km, and a comparison is made with experimental measurements of UV radiance. A series of parametric studies involving simulations of this same flow are used to evaluate the influence of physical processes and input parameters related to gas-particle interaction, particle radiation, and the presence of soot. I. Introduction n of m the flowfield simulation and radiation analysis of solid rocket exhaust plumes at very high altitudes, a number approximations and simplifying assumptions are typically made due to computational cost, a lack of existing odels, or uncertainty over the influence of various physical phenomena. These flows tend to include a large mass fraction of Al2O3 particles, which can significantly influence bulk flow properties and dominate plume radiative emission through much of the IR, visible, and UV range. Some determination of particle phase characteristics is typically required for useful and accurate simulation results, and may be necessary to assess base heating rates, radiation signatures, surface contamination effects, or other flow properties of interest. As a result, important physical processes and phenomena associated with gas-particle interaction must be recognized and incorporated into simulation procedures. Several potentially important effects have received little attention in the literature, and the significance of coupling between many of these effects still remains an open question. In this paper, we attempt to address the uncertainty in the significance of various effects, and describe a general procedure for the simulation of rarefied plume flows from solid propellant rockets. I

Direct Simulation Monte Carlo with Octree Cartesian Mesh

We describe an implementation of a new Direct Simulation Monte Carlo (DSMC) code with adaptive octree Cartesian mesh in the Unified Flow Solver (UFS) framework. UFS combines a variety of coupled Boltzmann and NS solvers, and addition of the DSMC solvers allows one to further expand its capabilities. The UFS-DSMC code utilizes a single mesh for (i) particle collision and (ii) statistics collection/visualization and particle movement. Such a single mesh can be easily built using AMR capabilities based on local properties (mean free path and/or gradients of flow parameters) for flows around complex shapes, and can be used to efficiently perform some of the same functions as transient subcells or other collision partner selection options available in modern DSMC codes. The quad/octree data structure allows straightforward and efficient data management during dynamic grid refinement/coarsening and makes possible seamless parallelization of the code. The capabilities of UFS-DSMC are illustrated for benchmark cases of steady-state flows past blunt objects. Results of UFS-DSMC are compared with solutions of HAP and MONACO DSMC codes and good agreement is found. UFS-DSMC was observed to show similar efficiency compared to the baseline HAP code.

Influence of State-to-State Transport Coefficients on Surface Heat Transfer in Hypersonic Flows

A numerical study is performed to assess the influence of two state-to-state kinetic approaches on the prediction of surface heat transfer of Mach 7 hypersonic external flowfields. One approach consists of a simplified state-to-state kinetic model which utilizes Eucken’s relation for calculating thermal conductivity and a constant Lewis number assumption for calculating self-diffusion in the vibrational quantum levels. The other approach uses a rigorous kinetic theory based model for which collision integrals are used to determine transport coefficients related to thermal diffusion, heat conductivity, self-diffusion, and diffusion of vibrational energy. Inclusion of self-diffusion results in an increase in the surface heat flux of up to 6.5% upstream of a shoulder region. Thermal conductivity is found to be the primary contributor to surface heat flux. The differences in heat flux predictions between the two state kinetic models highlight the sensitivity of surface heat transfer rate to the thermal conductivity models used. As a starting point for future determination of transport coefficient model sensitivities, a probabilistic global sensitivity analysis is performed for a simplified set of hypersonic flow calculations involving the Sutherland viscosity model.

Automated Aerodynamic Optimization for Lifting Hypersonic Vehicles at High Altitude

Automated design optimization procedures are coupled to three-dimensional direct simulation Monte Carlo (DSMC) calculations for deformation of waverider-derived hypersonic vehicle shapes, in order to maximize the lift-to-drag ratio (L/D) under high altitude reentry conditions. For a lifting reentry vehicle, increased L/D under such conditions should permit a reduction in aerothermal heating, body forces and ionization effects, as well as an increase in range and other potential benefits related to mission cost and safety. In the optimization procedure employed in this paper, a new parallel Cartesian adaptive grid implementation of the DSMC method is integrated with surface deformation and threshold accepting algorithms for probabilistic multivariable optimization. Several waverider geometries, created through an inverse design technique, were used as starting points for optimization calculations, and multiple optimization runs were carried out for each starting shape. Including all iterations for each run, optimization calculations performed as part of this work involve 2880 independent three-dimensional DSMC simulations. A maximum increase in L/D of approximately 65% is demonstrated at Mach 14 and 90 km altitude, for a 5 m long vehicle with a global Knudsen number of 0.0033. Additional simulations were performed for this optimized geometry at design conditions, in order to assess the extent of continuum breakdown, flowfield characteristics, surface heat flux and temperatures, and the effect of leading edge bluntness on both heat flux and L/D values. To the authors’ knowledge, this work represents the first integration of DSMC within an automated design optimization scheme, and demonstrates the potential efficacy of DSMC based aerodynamic optimization in reentry vehicle design.

A Monte Carlo Radiation Model for Simulating Rarefied Multiphase Plume Flows

A Monte Carlo ray trace radiation model is presented for the determination of radiative properties of Al2O3 particles in the high altitude plume of a solid propellant rocket. A polydisperse distribution of non-gray particles is modeled as an emitting, absorbing and scattering medium of arbitrary optical thickness. Strong two-way coupling is allowed between radiation and flowfield calculations, where the gas is simulated using the direct simulation Monte Carlo method and particle phase properties are determined using a similar Lagrangian approach. Effects of anisotropic scattering and nozzle searchlight emission are considered, and a procedure is described for the calculation of spectral radiance. The model is applied to the simulation and radiation analysis of the freely expanding plume from a subscale solid rocket motor, and various flowfield properties are presented and discussed.