Iain D. Boyd

Plasma flow and plasma–wall transition in Hall thruster channel

In this paper a model of the quasineutral plasma and the transition between the plasma and the dielectric wall in a Hall thruster channel is developed. The plasma is considered using a two-dimensional hydrodynamic approximation while the sheath in front of the dielectric surface is considered to be one dimensional and collisionless. The dielectric wall effect is taken into account by introducing an effective coefficient of the secondary electron emission (SEE), s. In order to develop a self-consistent model, the boundary parameters at the sheath edge (ion velocity and electric field) are obtained from the two-dimensional plasma bulk model. In the considered condition, i.e., ion temperature much smaller than that of electrons and significant ion acceleration in the axial direction, the presheath scale length becomes comparable to the channel width so that the plasma channel becomes an effective presheath. It is found that the radial ion velocity component at the plasma–sheath interface varies along the thr...

Analysis of rotational nonequilibrium in standing shock waves of nitrogen

The one-dimensional standing shock wave is the simplest flow in which nonequilibrium effects may be considered. The direct-simulation Monte Carlo method (DSMC) has yielded excellent agreement with results reported for the case of nitrogen flow at Mach 1.7. The DSMC technique is presently used in conjunction with a variable energy transfer probability model in which energy is transferred between the translational and rotational modes via the Borgnakke-Larsen (1975) phenomenological model.

Momentum and Heat Transfer in a Laminar Boundary Layer with Slip Flow

Flow in a laminar boundary layer is modeled using a slip boundary condition. The slip condition changes the boundary layer structure from a self-similar profile to a two-dimensional structure. Although the slip condition generally leads to decreased overall drag, two-dimensional effects cause local increases in skin friction. Other effects include thinner boundary layers, delayed transition to turbulence, and changes in the heat transfer at the wall. Without a thermal jump condition, slip will lead to increased heat transfer. When a thermal jump boundary condition is added to simulate real gases, the heat transfer decreases to below the no-slip values.

A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows

A modular particle-continuum (MPC) numerical method for steady-state flows is presented which solves the Navier-Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo (DSMC) method to simulate regions of non-equilibrium gas flow. Existing, state-of-the-art, DSMC and Navier-Stokes solvers are coupled together using a novel modular implementation which requires only a limited number of additional hybrid functions. Hybrid functions are used to adaptively position particle-continuum interfaces and update boundary conditions in each module at appropriate times. The MPC method is validated for 2D flow over a cylinder at various hypersonic Mach numbers where the global Knudsen number is 0.01. For the cases considered, the MPC method is verified to accurately reproduce DSMC flow field results as well as local particle velocity distributions up to 2.2 times faster than full DSMC simulations.

A hybrid particle-continuum method applied to shock waves

A hybrid numerical scheme designed for hypersonic non-equilibrium flows is presented which solves the Navier-Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo method where the flow is in non-equilibrium. Detailed analysis of each stage of the hybrid cycle illustrates the difficulty in defining physically correct DSMC boundary conditions in regards to both macroscopic state and velocity distribution. However, results also show that DSMC boundary conditions have little effect on a previously initialized interior particle domain. A sub-relaxation technique capable of determining macroscopic, hydrodynamic properties in a DSMC simulation is used to determine low-scatter boundary conditions for the NS domain. Particle and continuum domains adapt during the hybrid simulation through application of a continuum breakdown parameter based on the gradient-length Knudsen number. The hybrid code reproduces experimental results and full DSMC simulations in half the time for a large range of 1D shock waves in argon and diatomic nitrogen gas.

Direct simulation methods for low-speed microchannel flows

Large statistical scatter and effective pressure boundary conditions are two critical problems in the computation of microchannel flows with the direct simulation Monte Carlo (DSMC) method. To address these issues, an extension of the DSMC-IP (information preservation) coupled method is developed from the one-dimensional case to the two-dimensional case for microchannel flow. Simulation results in a microchannel flow from DSMC, IP, and numerical and analytical solutions to the Navier-Stokes equations are compared. The DSMC-IP coupled method successfully reduces the large statistical scatter usually obtained with DSMC in such low-speed flow systems. It also provides a suitable implementation of pressure boundary conditions

Experimental and numerical investigations of low-density nozzle and plume flows of nitrogen

Experimental and numerical investigations are performed and compared for the flow of nitrogen in a small nozzle and in the near field of the plume resulting from expansion into near-vacuum conditions. The experimental data obtained were in the form of pressure measurements using a pitot tube, in the nozzle-exit plane and near field of the plume. Since the flow regimes vary from continuum, at the nozzle throat, to rarefied, in the plume, two different numerical studies are undertaken: the first employs a continuum approach in solving the Navier-Stokes equations, and the second employs a stochastic particle approach through the use of the direct simulation Monte Carlo (DSMC) method. Comparison of the experimental data and the numerical results at the nozzle exit reveals that the DSMC technique provides the more accurate description of the expanding flow. It is discovered that the DSMC solutions are quite sensitive to the model employed to simulate the interaction between the gas and the nozzle-wall surface. It is concluded that the simple fully diffuse model is quite satisfactory for the present application. The study provides the strongest evidence to date that the DSMC technique predicts accurately the flow characteristics of low-density expanding flows.

Predicting continuum breakdown in hypersonic viscous flows

This paper presents a study of the breakdown of the Navier–Stokes equations in hypersonic viscous flows over a sharp cone tip and a hollow cylinder/flare geometry. Investigations are performed through detailed comparisons of the numerical results obtained with continuum and particle techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. A modified breakdown parameter is proposed that can predict the failure of the continuum approach accurately for the simple cone flow and fairly well for the more complex cylinder/flare flow. The study of continuum breakdown is the first step toward development of a hybrid numerical code.

Numerical Simulation of Weakly Ionized Hypersonic Flow for Reentry Configurations

Numerical simulations of axisymmetric flows over reentry configurations at hypersonic conditions using a Navier-Stokes solver are presented. The Navier-Stokes equations are modified using Park’s two-temperature model to account for thermochemical nonequilibrium and weak ionization eects. The finite-volume method is used to solve the set of dierential equations. The code has the capability to handle any mixture of hexahedra, tetrahedra, prisms and pyramids in 3D or triangles and quadrilaterals in 2D. The results in this paper only use quadrilaterals. Numerical fluxes between the cells are discretized using a modified Steger-Warming Flux Vector Splitting approach which has low dissipation and is appropriate to calculate boundary layers. A point or line implicit method is used to perform the time integration. Pressure, heat transfer rates and electron number density profiles are compared to available experimental and flight measurements.

Models for direct Monte Carlo simulation of coupled vibration-dissociation

Models are developed to permit direct Monte Carlo techniques to simulate coupled vibration–dissociation (CVD) behavior prevalent in high‐temperature gases. This transient thermochemical phenomenon leads to dissociation incubation, reduced quasisteady dissociation rates, and non‐Boltzmann distributions of vibrational energy during both dissociation and recombination. Essential for simulation of rarefied gas dynamics, Monte Carlo methods employ discrete particles to simulate molecular interactions directly, but have traditionally incorporated simplistic reaction models which failed to capture CVD behavior. To identify thermochemical collisions within the gas, a new dissociation selection probability is developed as a function of the extent by which the collision energy exceeds the gap between the dissociation threshold and the molecular vibrational energy of bounded anharmonic oscillators. A free parameter φ in the probability function controls the extent of vibrational favoring in dissociation selection. T...