Quanhua Sun

Evaluation of Macroscopic Properties in the Direct Simulation Monte Carlo Method

General expressions for evaluating macroscopic properties in the direct simulation Monte Carlo (DSMC) method are examined using numerical examples. DSMC simulations show that the evaluations (both statistically dependent and independent) generally follow Gaussian distributions except that the temperature evaluations follow chi-square distributions, whereas their statistical errors mainly depend on the sample size. To reduce the statistical errors for macroscopic properties required during DSMC simulations, a subrelaxation technique is proposed to build up the sample size by including the previous history using a relaxation factor. It is found that the subrelaxation technique helps reduce the statistical errors as if the sample size were increased by a factor of the reciprocal of the relaxation factor. This property makes use of the technique attractive for many DSMC applications. Nomenclature E = statistical error FN = number of real molecules represented by one simulated particle k = Boltzmann constant m = mass of molecules N = number of particles in a cell or number of time steps n = number density T = temperature V =v elocity Vol =v olume of computational cell � =g amma function θ = relaxation factor ρ = correlation coefficient σ = standard deviation of a distribution Subscripts

Numerical Simulation of Gas Flow over Microscale Airfoils

Flows over microscale airfoils are investigated using both particle and continuum approaches. An implementation of the information preservation technique based on the direct simulation Monte Carlo method is used to simulate flows over a flat plate of zero thickness at low Reynolds number (Re < 1 x 10 2 ). The aerodynamics of a flat plate with thickness ratio of 5% at Re = 4 is quite different from that at Re = 4 x 10 3 that were measured experimentally. A continuum approach with slip boundary conditions predicts a similar basic flow pattern as the information preservation method with differences in details, which may indicate that continuum approaches are not suitable for this kind of flow because of rarefied effects

Flat-plate aerodynamics at very low Reynolds number

Gas flow over a flat-plate airfoil at very-low Reynolds number is investigated in order to understand the aerodynamic issues related to micro air vehicle design and performance. Studies have shown that such low Reynolds number flow exhibits rarefied phenomena and a flat plate having a thickness ratio of 5% has better aerodynamic performance than conventional streamlined airfoils. This paper simulates air flows over a 5% flat plate using a hybrid continuum–particle approach for flows having a Mach number of 0.2 and a Reynolds number varying between 1 and 200. Investigation shows that low Reynolds number flows are viscous and compressible, and rarefied effects increase when the Reynolds number decreases. It is also found that there is a minimum lift slope for the plate airfoil at a Reynolds number near 10 and the drag coefficient monotonically increases with decreasing Reynolds number.

Towards Development of a Hybrid DSMC-CFD Method for Simulating Hypersonic Interacting Flows

A preliminary hybrid particle-continuum computational framework for simulating hypersonic interacting flows is proposed. The framework consists of the direct simulation Monte Carlo-Information Preservation (DSMC-IP) method coupled with a NavierStokes solver. Since the DSMC-IP method provides the macroscopic information in each time step, determination of the continuum fluxes across the interface between the particle and continuum domains becomes straightforward. A hypersonic flow over a two-dimensional wedge is considered as an example and compared with pure particle calculations. The results show that this preliminary hybrid framework is promising but several issues are yet to be resolved.

Gas flows in microchannels and microtubes

This study analyses compressible gas flows through microchannels or microtubes, and develops two complete sets of asymptotic solutions. It is a natural extension of the previous work by Arkilic et al. on compressible flows through microchannels. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for the Reynolds and Mach numbers at the outlets. Second, based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure and temperature distributions of compressible gas flow inside the microchannels and microtubes with a relaxation of the isothermal assumption, which was previously used in many studies. Numerical simulations of compressible flows through a microchannel and a microtube are performed by solving the compressible Navier-Stokes equations, with velocity slip and temperature jump wall boundary conditions. The numerical simulation results validate the analytical results from this study.

Computational Analysis of High-Altitude Ionization Gauge Flight Measurements

The rarefied, three-dimensional flows experienced during the turbulent oxygen mixing experiment (TOMEX) at altitudes between 85 and 143 km are simulated using the direct simulation Monte Carlo (DSMC) method. The present study focuses on ionization gauge measurements obtained by TOMEX. The payload is, thus, modeled in detail, and the simulations employ complex meshes. The simulations show that a bow shock wave is generated in front of the payload at low altitude that becomes diffusive at higher altitudes. When the altitude increases, the pressure in the channels of the ionization gauge and the pressure variation around the payload are both decreased. The DSMC results agree very well with data predicted by compressible flow theory and free molecular theory when applicable. Comparison between the DSMC results and the TOMEX flight data shows generally good agreement.

Theoretical development of the information preservation method for strongly nonequilibrium gas flows

*† The information preservation method is a particle technique for nonequilibrium gas flows with low statistical fluctuations. The foundation of the information preservation method is derived theoretically in this study. First, the evolution of the average information is obtained using Maxwell’s equation of change. Then, the update of individual particle information is assumed to follow the governing equation of the average information. Two approaches are proposed to evaluate the statistical terms appeared in the governing equations. Namely, the local thermodynamic equilibrium approach and the flux splitting approach. It is found that the flux splitting approach is better, and can predict the shock structure of normal shock waves and the temperature distribution of thermal Couette flows for all Knudsen numbers.

Drag on a Flat Plate in Low-Reynolds-Number Gas Flows

Airflow over a flat plate at zero incidence is investigated as a function of the Reynolds number Re and the Mach number M under subsonic, low-Reynolds-number conditions. The flows are simulated using the direct simulation Monte Carlo (DSMC) method and the information preservation (IP) method that is a modified DSMC method developed for low-speed rarefied gas flows. Good agreement is obtained between the DSMC and IP results and between the IP results and available experimental data. The simulations predict that the drag coefficient on the flat plate depends on the Reynolds number and the Mach number, and both the rarefied and compressible effects on the drag coefficient increase when the flow Reynolds number decreases. It is found that the normalized drag CD · M depends on √ (Re)/M 0.8 when this parameter varies between 1 and 100, which suggests a scaling law for engineering analysis.

Free molecular background flow in a vacuum chamber equipped with two-sided pumps

Spacecraft propulsion systems, such as Hall thrusters, are designed and tested in large vacuum chambers. The pumping capacity of modern facilities makes it possible to maintain pressures as low as 10−3–10−4Pa. One fundamental concern for the vacuum chamber is the facility effects on the chamber performance. In this study, several free molecular models are developed to analyze the rarefied background flow inside a vacuum chamber equipped with two-sided vacuum pumps. These models lead to various sets of analytical results including velocity distribution functions for the background flow and formulas to compute the vacuum pump sticking coefficient. These results can be used to evaluate the performance of vacuum chambers and to aid constructing proper background flows for particle simulations of these systems. The results indicate that the background flow conditions can have a significant nonzero mean velocity and cannot be considered to be described by a Maxwellian velocity distribution. The models are appli...

A Hybrid Continuum / Particle Approach for Micro‐Scale Gas Flows

A hybrid continuum/particle approach is proposed for micro scale gas flows in this paper. The approach couples the DSMC‐IP method and a Navier‐Stokes solver with an adaptive interface. The continuum solver uses the particle cells as ghost cells because the IP method preserves the hydrodynamic information that the continuum solver uses. In order to generate particles from the continuum side, two strategies are proposed. The first one uses a condition similar to the Marshak condition in generating particles through the interface. The second strategy adopts buffer cells and reservoir cells, which avoids directly generating particles. The interface is determined by a continuum breakdown parameter that is evaluated in every time step. In order to track the interface, a mapping technique is used in the code. Numerical examples show that the hybrid approach couples the continuum solver and the particle method very smoothly. Simulated results also show the effects of the cutoff value of the continuum breakdown pa...