Chunpei Cai

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

Computation of Rarefied Gas Flows Around a NACA 0012 Airfoil

Raree ed gas e ows around a NACA 0012 airfoil are simulated using both particle and continuum approaches. Three different conditions are considered: supersonic, transonic, and low subsonic. In all three cases, the continuum approach solves the Navier ‐Stokes equations with a slip boundary condition on the airfoil surface. For the supersonic and transonic cases, the particle method employed is the direct simulation Monte Carlo method. Because of problems with this method at the low subsonic condition, caused by excessive statistical e uctuations, a new particle method called the information preservation technique is applied. The computed density and velocity e owe elds are compared with experimental data and found to be in generally good agreement. Some interesting features in the surface pressure distributions along the airfoil are found for these low-Reynolds-number e ows.

Collisionless Gas Expanding into Vacuum

H IGH-SPEED collisionless, or free-molecular, gas flows passing through small circular or annular holes are fundamental problems with many real applications such as neutral gas expansion out of electric propulsion (EP) devices. Usually, the cold plume flow out of an EP device is modeled by assuming freemolecular flows with a nonzero uniform average exit velocity U0. Even when the average bulk velocity of gas near the orifice is zero, the average velocity at the orifice exit plane is not zero, it corresponds to an outflow with a half-Maxwellian distribution. In the past, analytical studies of similar problems were concentrated on true effusion problems with a zero average exit speed. For example, Liepmann [1] reported the efflux of gases through circular apertures, which is an example of a transition from the gas-dynamic to the gaskinetic regime; Narasimha [2] obtained the exact solutions of density and velocity distributions for a free-molecular effusion flow and the results for a nearly free-molecular effusion flow expanding into vacuum through a circular orifice; and Brook [3] reported the density field of free-molecular flow from an annulus, to study the gas leakage effect from a spacecraft hatch. Other researchers reported many approximate methods or numerical simulations to study rarefied flows through a slit; for example, Rotenberg and Weitzner [4], Hasegawa and Sone [5], Cercignani and Sharipov [6], and Sharipov [7]. Recently, Lilly et al. [8] reported their work onmeasurement and computation ofmass flow andmomentum flux through short tubes in rarefied gas. For the case of free-molecular flows with a nonzero average velocity, the problems are usually very complicated and approximations are often made, such as neglecting the details of the exit geometry or assuming that free-molecular flow are emitted from a point source [9]. In our previous study [10,11], we adopted a relation between velocity directions and geometry locations to investigate freemolecular plume flow problems. This treatment is more general than the solid angle treatment [2]. which was widely used in studying true collisionless effusion flows with a zero average exit speed, but is not applicable to collisionless flows with a nonzero average exit speed. In this study, we further investigate collisionless flows out of a circular or an annular exit with a nonzero average speed. These two cases are very important, not only because of their mathematical significance, but also because of their many direct applications, including spacecraft propulsion. This Note is organized as follows: Section II describes the problems, the corresponding complex exact solutions, and also approximate far-field solutions, which are simpler andmore accurate than existing formulas in the literature; Sec. III compares the analytical results with particle simulation results; and Sec. IV summarizes this study.

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.

Vacuum chamber pressure maps of a hall thruster cold-flow expansion

TECHNICAL NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 figures; a page of text may be substituted for a figure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

Highly rarefied two-dimensional jet impingement on a flat plate

In this paper, we investigate highly rarefied jet gas flows out of a two-dimensional slit that impinges on a flat plate which is set vertically to the plume flow direction. The plate is assumed to be completely diffusive and the gaseous plume flow out of the slit is modeled with a Maxwellian distribution function which is characterized with known number density, nonzero exit velocity, and temperature. We present some analytical collisionless flow properties for a free plume and the impingement on the plate. The outcomes include simple results of the largest shear stress on the plate and the corresponding location. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solutions.

Monte Carlo analysis of macroscopic fluctuations in a rarefied hypersonic flow around a cylinder

From consideration of the length scales characteristic of molecular and turbulent phenomena, it is proposed that flow instabilities and structural motions should be generated under certain rarefied, hypersonic flow conditions. This proposal is investigated using the direct simulation Monte Carlo (DSMC) method for hypersonic, rarefied flow over a cylinder. The overall mean flow field contains a number of regions including an undisturbed free stream, a bow shock, a recompression in the wake, and a recirculation zone behind the cylinder. Analysis of the fluctuations in velocity and number density predicted by the DSMC technique for this flow is conducted. An important aspect of this analysis is the clarification of the nature of the observed fluctuations. It is found that different types of fluctuations are found in the bow shock and in the wake. These are attributed to different types of physical phenomena. In the bow shock, large fluctuations are caused by the macroscopic field gradients in the shock front...

Surface properties for rarefied circular jet impingement on a flat plate

In this paper, we investigate rarefied jet gas flows out of a circular exit impinging on a vertical flat plate. We employ a constraint relation about the velocity components of gas particles leaving a nozzle exit point and arriving at a given spatial point outside the nozzle. This relation leads to several analytical expressions for collisionless flow property distributions on the plate surface, including density, slip-velocity, temperature, pressure, shear stress, and heat flux. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solutions. The impingement properties on the plate surface are accurate when the Knudsen number is large.

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.

Nonlinear aeroelastic methodology for a membrane-on-ballute model with hypersonic bow shock

[Abstract] A nonlinear aeroelastic methodology for inflatable/ballute type structures has been successfully developed for, a heuristic case: a 2D membrane-on-wedge model, and an axisymmetric modeled ballute system (MBS), under hypersonic/supersonic shock waves. Specifically, the nonlinear structural ROM methodology ELSTEP/FAT is extended and validated (based on MSC.Nastran FEM model) to the membrane-on-wedge model and the axisymmetric MBS. The time-accurate GasKinetic BGKX methodology has been developed as the key aerodynamic solver. It has great advantages over current continuum CFD solvers with its solution robustness, one-step computation of pressure and heat flux, and broad range of Knudsen number for hypersonic applications. Nonlinear aerodynamic static deformations at various altitudes have been obtained through a tight coupling between the nonlinear structural ROM and the direct BGKX aerodynamic solver. An efficient aerodynamic ROM has been developed for the undeformed/deformed mean 2D/axisymmetric configurations using a system identification technique with staggered modal inputs. The aerodynamic ROM solutions are found to closely match the direct BGK solutions. ROM-ROM time-domain dynamic aeroelastic analyses reveal significant differences between analyses carried out around the undeformed configuration and around the deformed one. In particular, a decrease in altitude will increase the static deformations which lead to a stiffer behavior with respect to additional small perturbations. Accordingly, a decrease in altitude induces an increased stability, in contrary to aeroelastic solutions for the undeformed configuration. This fundamental observation demonstrates the need to perform tightly coupled steady aeroelastic analyses prior to any stability analysis.