Simulations and Measurements of Gas-Droplet Flows in Supersonic Jets Expanding into Vacuum

Simulations and measurements of gas-droplet multiphase flows in application to supersonic expansions into vacuum have been considered and compared with each other. The experiments involved exposing a control surface to a supersonic plume from two different nozzles and measuring the size distribution of droplets at various locations. The simulations are based on the direct simulation Monte Carlo modeling of vapor-phase flow with a one-way coupling of droplet momentum and energy. The droplet trajectories are computed for the experimental conditions for droplets originating at the throat and lip of two different nozzles. The maximum droplet radius reaching the control surface and the variation of droplet size with angle predicted by the trajectory computations agree well with the measurements using Optical Microscopy

Molecular Models for DSMC Simulations of Metal Vapor Deposition

The direct simulation Monte Carlo (DSMC) method is applied here to model the electron‐beam (e‐beam) physical vapor deposition of copper thin films. A suitable molecular model for copper‐copper interactions have been determined based on comparisons with experiments for a 2D slit source. The model for atomic copper vapor is then used in axi‐symmetric DSMC simulations for analysis of a typical e‐beam metal deposition system with a cup crucible. The dimensional and non‐dimensional mass fluxes obtained are compared for two different deposition configurations with non‐uniformity as high as 40% predicted from the simulations

Direct simulation Monte Carlo modeling of e-beam metal deposition

Three-dimensional direct simulation Monte Carlo (DSMC) method is applied here to model the electron-beam physical vapor deposition of copperthin films. Various molecular models for copper-copper interactions have been considered and a suitable molecular model has been determined based on comparisons of dimensional mass fluxes obtained from simulations and previous experiments. The variable hard sphere model that is determined for atomic copper vapor can be used in DSMC simulations for design and analysis of vacuum deposition systems, allowing for accurate prediction of growth rates, uniformity, and microstructure

Scaling law for direct current field emission-driven microscale gas breakdown

The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices

Visualizing Non-Equilibrium Flow Simulations using 3-D Velocity Distribution Functions

Scientific visualization techniques have been used to probe and understand better the physics of non-equilibrium flows. A visualization methodology for nonequilibrium flow simulations using 3-D velocity distribution functions (VDFs) is illustrated in application to various non-equilibrium flow problems. A one-dimensional normal shock wave problem is considered for two different upstream Mach numbers corresponding to weak and strong non-equilibrium flow conditions. The iso-surfaces of 3-D VDFs inside the shock wave obtainedusing various solution techniques including the ES-BGK method, DSMC technique, Mott-Smith solution, and the Navier-Stokes (NS) distribution functions using Chapman-Enskog theory are compared and contrasted. The visualization technique is extended to two-dimensional hypersonic flow at M-19 past a flat plate with sharp leading edge by comparing the isosurfaces of 3-D NS VDFs obtained at three different locations in the flowfield. The visualization of 3-D VDFs is shown to provide valuable information about the degree and direction of non-equilibrium for both 1-D and 2-D flows

Effects of Uncertainty in Gas-Surface Interaction on DSMC Simulations of Hypersonic Flows

This study uses the non-intrusive generalized polynomial chaos method to investigate the effects of uncertainties in the gas-surface interaction model on the hypersonic boundary layer flow over a flat plate. In particular, the polynomial chaos method is applied to assess uncertainties in the surface shea, normal stress, heat flux, flowfield temperature and accomodation coefficient. The polynomial chaos approach allows us to estimate probability density functions from fewer flowfield samples than the traditional random Monte Carlo sampling. The flowfield solutions are computed by the DSMC code SMILE. The analysis shows that surface fluxes and flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient than surface temperature uncertainty

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS model\u27s performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations

Microspike Based Chemical/Electric Thruster Concept for Versatile Nanosat Propulsion

Small spacecraft that can be categorized as microsats, nanosats, and picosats has a strong potential for wide applications in communication, scientific experiments, and space exploration. In order to combine the advantages of both electric and chemical propulsion thrusters, a dual-mode microspike based thruster concept is proposed. For a fixed input power, it can operate in either a high-Isp mode or a high-thrust mode depending on the propulsive maneuver requirements. The hybrid thruster consists of a plug-annular cold or heated gas thruster in the chemical mode and a field emission thruster housed within the plug operating in the electric mode using a metallic propellant. The direct simulation Monte Carlo (DSMC) technique and the particle-in-cell technique are used to model the two different modes to estimate performance parameters of the thruster. The DSMC simulations show that the microspike nozzle can provide an improved specific impulse (Isp) at low Reynolds numbers when compared to a straight orifice or converging-diverging nozzle. The PIC simulations for the field emission thruster are shown to compute the current density, ion beam density, ion beam velocities and, hence, specific impulse and thrust accurately for conditions corresponding to earlier published experiment

Non-Equilibrium Flow Modeling Using High-Order Schemes for the Boltzmann Model Equations

We consider application of higher-order schemes to the Boltzmann model equations with a goal to develop a deterministic computational approach that is accurate and efficient for simulating flows involving a wide range of Knudsen numbers. The kinetic equations are solved for two non-equilibrium flow problems, namely, the structure of a normal shock wave and an unsteady two-dimensional shock tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter as well as a third-order WENO scheme. The normal shock wave solutions using BGK and ES collision models are compared to the DSMC simulations. The solution for unsteady shock tube is compared to the Navier-Stokes simulations at low Knudsen numbers and the rarefaction effects in such flow are also discussed. It is observed that a higher-order flux scheme provides a better convergence rate and, hence, reduces the computational effort. The entropy generation rate is shown to be a very sensitive indicator of the onset of non-equilibrium as well as accuracy of a numerical scheme and consistency of boundary conditions in both flow problems

A comparative study of no-time-counter and majorant collision frequency numerical schemes in DSMC

The direct simulation Monte Carlo (DSMC) method is a stochastic approach to solve the Boltzmann equation and is built on various numerical schemes for transport, collision and sampling. This work aims to compare and contrast two popular O(N) DSMC collision schemes - no-time-counter (NTC) and majorant collision frequency (MCF) - with the goal of identifying the fundamental differences. MCF and NTC schemes are used in DSMC simulations of a spatially homogeneous equilibrium gas to study convergence with respect to various collision parameters. While the MCF scheme forces the reproduction of the exponential distribution of time between collisions, the NTC scheme requires larger number of simulators per cell to reproduce this Poisson process. The two collision schemes are also applied to the spatially homogeneous relaxation from an isotropic non-Maxwellian given by the Bobylev exact solution to the Boltzmann equation. While the two schemes produce identical results at large times, the initial relaxation shows some differences during the first few timesteps