Daniel A. Erwin

Nonequilibrium molecular motion in a hypersonic shock wave

Molecular velocities have been measured inside a hypersonic, normal shock wave, where the gas experiences rapid changes in its macroscopic properties. As first hypothesized by Mott-Smith, but never directly observed, the molecular velocity distribution exhibits a qualitatively bimodal character that is derived from the distribution functions on either side of the shock. Quantitatively correct forms of the molecular velocity distribution function in highly nonequilibrium flows can be calculated, by means of the Direct Simulation Monte Carlo technique.

Nonequilibrium gas flows. I - A detailed validation of Monte Carlo direct simulation for monatomic gases

One‐dimensional shock wave properties in helium and argon are predicted using Monte Carlo direct simulation. The collision model is based directly on the interatomic potential, taking angular scattering into account. The potential is assumed to be of the Maitland–Smith [n(r)−6] form. The detailed validity of the simulation is studied by comparing the predicted macroscopic and microscopic flow properties in shock waves to a wide range of available data.

Testing continuum descriptions of low-Mach-number shock structures

Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDSs) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier—Stokes and the Burnett equations are compared to MCDSs for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater than 1.2, the Burnett predictions are more accurate than the Navier—Stokes results. Temperature—density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.

Two-dimensional hybrid continuum/particle approach for rarefied flows

A hybrid numerical technique previously developed for one-dimensional rarefied gas flows is generalized to two dimensions. The method is based on the fact that the flowfield that develops near a body in a rarefied gas typically contains local regions of continuum, transitional and free-molecular flow. By utilizing the solution technique most appropriate for each region and coupling the techniques in an interface region where both are applicable, more computationally efficient solutions can be obtained, or equivalently, more complex flowfields can be analyzed. The present method combines finite difference solution of the Navier-Stokes equations in the continuum regions, with Direct Simulation Monte Carlo in the more rarefied regions. The two schemes are coupled interactively via a general conservative flux boundary condition. The method is tested by application to the model problem of pressure-driven rarefied flow through a slit. Results show the hybrid scheme offers a speedup of a factor of nearly two for the nominal conditions considered, due to the decrease in the size of the Direct Simulation domain.

Transient motion of a confined rarefied gas due to wall heating or cooling

The transient motion that arises in a confined rarefied gas as a container wall is rapidly heated or cooled is simulated numerically. The Knudsen number based on nominal gas density and characteristic container dimension is varied from nearcontinuum to highly rarefied conditions. Solutions are generated with the direct simulation Monte Carlo method. Comparisons are made with finite-difference solutions of the Navier-Stokes equations, the limiting free-molecular values, and (continuum) results based on a small perturbation analysis. The wall heating and cooling scenarios considered induce relatively large acoustic disturbances in the gas, with characteristic flow speeds on the order of 20 % of the local sound speed. Steadystate conditions are reached after on the order of 5 to 10 acoustic time units, here based on the initial speed of sound in the gas and the container dimension. As rarefaction increases, the initial gas response time is decreased. For the case of a rapid increase in wall temperature, transient rarefaction effects near the wall greatly alter gas response compared to the continuum predictions, even at relatively small nominal Knudsen number. For wall cooling, the continuum solution agrees well with direct simulation at that same Knudsen number. A local Knudsen number, based on the mean free path and the scale length of the temperature gradient, is found to be a more suitable indicator of transient rarefaction effects.

Numerical simulation of rarefied flow through a slit. Part I: Direct simulation Monte Carlo results

The pressure‐driven flow of a rarefied monatomic gas through a two‐dimensional slit is simulated using the direct simulation Monte Carlo technique. Of particular interest is the change in flow field structure as pressure ratio and Knudsen number are varied. Comparisons are made to quantify the limits of validity of free‐molecular theory and approximate, nearly free‐molecular iterative methods. Also addressed is the sensitivity of the numerical solutions to grid structure and boundary conditions. The free‐molecular theory is found to predict quantitative flow field properties (e.g., centerline velocities or downstream flux profiles) reasonably well for large finite Knudsen number with the error dependent on the pressure ratio. The nearly free‐molecular corrections are shown to have limited range of applicability. A previously derived parameter is found to correlate total mass flux well as a function of pressure ratio and Knudsen number over a large portion of the transitional regime.

Laser-induced fluorescence measurements of flow velocity in high-power arcjet thruster plumes

The flow velocity of atomic hydrogen in the plume of an ammonia-propelled arcjet thruster was measured using laser-induced fluorescence (LIF). The velocity was obtained by the Doppler shift of the absorption peak of the Balmer α spectral line. Measurements were made at the nozzle exit, varying the distance from the plume centerline. Results are presented for arcjet operating conditions 13, 20, and 27 kW with a mass flow of 0.31 g/s

Dissociation and ionization of the methane molecule by nonrelativistic electrons including the near threshold region

Several ionization and dissociation channels of electron interaction with the methane molecule are studied using the recently discovered robust scaling law [D. A. Erwin and J. A. Kunc, Phys. Rev. A 72, 052719 (2005)], other experimentally observed relationships between the ionization and dissociation channels, and the most recent information about the processes. The resulting cross sections for the channels are given in the form of analytical expressions valid at all nonrelativistic energies.

Transient energy-release pressure-driven microdevices

A class of transient pressure-driven micromechanical devices that have several advantages over conventional microelectromechanical actuators is described. Although most micromechanical systems developed to date have been involved with electromagnetic or electrostatic forces, in the future micromechanical systems will also involve fluid mechanics, gas dynamics, and thermodynamics at unusually small scales. Generally, the size scaling laws for fluid flows and heat transfer are well understood; however, at the scale of micromachines (say 1-100 mu m), the details of transient behavior become a dominant consideration. The basic principles of transient pressure-driven actuators and some of the factors that must be considered in such designs are discussed. >

Rate Coefficients for Some Collisional Processes in High-Current Hydrogen Discharges

Rate coefficients are presented for a number of collisional processes important in high-current hydrogen discharges. The energy distribution of the plasma electrons has been assumed to be Maxwellian.