Collisionless Gas Flows over a Cylindrical or Spherical Object

Abstract

This paper presents exact density, velocity components, and temperature solutions for collisionless gas flows over a cylinder or a sphere. Possible real applications may include collisionless gas flows over a hot wire inside a vacuum chamber and rarefied gas flows around an aerosol at very high altitude. At any point off the cylinder or the sphere, the local velocity distribution function consists of two pieces of Maxwellian distribution functions: one for the freestream, which is characterized by the freestream density n 0 , temperature T 0 , and velocity U 0 ; the other is characterized by density at the wall n w and wall temperature T w , where n w is not constant at different surface locations. Directly integrating the distribution functions leads to the detailed flowfield solutions; the solutions are complex but exact. We performed numerical simulations with the direct simulation Monte Carlo method to validate these exact solutions. In general, the exact analytical and numerical results are virtually identical.

Collisionless Gas Flow over a Cylinder and a Sphere

“…By following the same principles used in past studies [9], the formulas for collisionless gas flows around a cylinder of diffuse reflections can be solved accurately. In Fig.…”

“…Integrating the two corresponding VDFs for the two integration domains, using 1, u, v, u 2 v 2 w 2 ∕2 as the moments, leads to the macroscopic number density, velocity components, and temperature distributions for the new coordinates: 5 Sphere problem with diffuse reflections [9]. Fig.…”

“…Those past works and results were not well verified due to the difficulties in experiments and numerical simulations. Recently [9], the corresponding detailed flowfield properties for flows over a diffuse cylinder/sphere were derived analytically, evaluated, and verified with the direct simulation Monte Carlo (DSMC) method [10]. Those results were applicable for both the far field and near field.…”

Near continuum flows over a sphere

“…The flowfield properties (i.e., density, velocity, pressure and temperature), were investigated with the gaskinetic methods, and some such analytical methods are documented [3]. However, only recently [4], have the detailed flowfield properties for flows over a diffusive been reflective sphere were evaluated and validated with several DSMC simulations. In the literature, there are some efforts to develop unified solvers (e.g.…”

Slightly rarefied gas flows over a sphere

“…The flowfield properties (i.e., density, velocity, pressure and temperature), were investigated with the gaskinetic methods, and some such analytical methods are documented [3]. However, only recently [4] the detailed flowfield properties for flows over a diffuse reflective sphere were evaluated and validated with DSMC simulations. In this paper, the problem of slightly rarefied gas flows over a sphere will be investigated numerically.…”