Gaskinetic Modeling on Dilute Gaseous Plume Impingement Flows

Abstract

This paper briefly reviews recent work on gaseous plume impingement flows. As the major part of this paper, also included are new comprehensive studies on high-speed, collisionless, gaseous, circular jet impinging on a three-dimensional, inclined, diffuse or specular flat plate. Gaskinetic theories are adopted to study the problems, and several crucial geometry-location and velocity-direction relations are used. The final complete results include impingement surface properties such as pressure, shear stress, and heat flux. From these surface properties, averaged coefficients of pressure, friction, heat flux, moment over the entire flat plate, and the distance from the moment center to the flat plate center are obtained. The final results include accurate integrations involving the geometry and specific speed ratios, inclination angle, and the temperature ratio. Several numerical simulations with the direct simulation Monte Carlo method validate these analytical results, and the results are essentially identical. The gaskinetic method and processes are heuristic and can be used to investigate other external high Knudsen (Kn) number impingement flow problems, including the flow field and surface properties for a high Knudsen number jet from an exit and flat plate of arbitrary shapes. The results are expected to find many engineering applications, especially in aerospace and space engineering.

Rarefication Effects on Jet Impingement Loads

“…For compressible jet and impingement flows from a finite nozzle exit, the corresponding analytical expressions have only recently been studied well . The results include the whole flowfield properties (i.e., density, velocity, pressure, and temperature) and plate surface loads [19,20]. The derivation processes are lengthy, and are well explained with two long papers [20]; they are not the focus of this paper, and to keep this paper concise, only the final expressions for the surface loads are summarized in the two following subsections.…”

“…The exit semi-height is H, the plate semi-length is W, and the center-to-center distance from the exit to the plate is L. The plate surface can be either diffuse or specular. [19,20]. (Reproduced from [19].…”

“…The formulas for coefficients of local surface pressure, shear stress, and heat fluxes over a diffuse plate (i.e., C p,d (s), C f ,d (s), and C q,d (s)) are derived with the gaskinetic theory, and the final expressions are [19]:…”

“…More details about the treatments and results can be found in two recent papers [19,20]. Figure 2 illustrates the problem.…”

“…where A 4 is a complex expression [19]. For a specular reflective surface, the shear stress and heat flux are zero, and the surface pressure coefficient is:…”