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Rarefied Gas Turbulence in the Knudsen Transition Regime

Future hypersonic vehicles may have a flight profile in which the Mach number can range from zero to about 25 and fly in conditions ranging from a conventional continuum at low altitudes to free-molecule flow at high altitudes. Conventional orbital (reentry) vehicles do not spend much time in the transition regime between free-molecule flow and a continuum. However, future vehicles such as the NASP will experience flight in the transition regime for appreciable lengths of time. The nature of the flow in the inlet of an airbreathing propulsion unit greatly impacts the overall design of the hypersonic vehicle. Because of the low to moderate flight Reynolds numbers at high altitude, the boundary layer may be sufficiently thick that it represents a substantial portion of the inlet flow. Furthermore, at moderate Reynolds numbers, this boundary layer may be turbulent.

The object of this research was to determine how, if at all, turbulence in a slightly rarefied gas differs from the relatively well-known phenomena occurring in nonrarefied gases. Because of the difficulty of constructing a physical experiment to determine these differences, a numerical simulation was undertaken.

The turbulent rarefied gas flow in a channel was simulated (see Figure) using Grad's Thirteen Moment Equations (TME). The computational tool with which the TME solution method is obtained is NEAR's TMERC code (Thirteen Moment Equations Research Code). This code is a derivative of NEAR's TMRC (Turbulence Modeling Research Code) in which stresses and heat fluxes are calculated according to Grad's constitutive equations. TMERC is a finite-volume time-explicit solver for the conservation law equations for mass, momentum, and energy, along with any additional number of convection-diffusion equations. A sample result obtained using TMERC for fully turbulent channel flow is shown in the figure, indicating that rarefaction effects occur primarily near the solid walls. In this figure, dark regions (representing a high degree of rarefaction) are seen to coincide with regions in the flow where the Navier-Stokes equations are invalid (light grey surfaces).

Commercial Applications: In addition to the study of turbulence in a rarefied gas and its applications to high altitude hypersonic flight vehicles, the developed Thirteen Moment Equations technology is applicable to microflows, microdiagnostics, and microfabrication, in which the Knudsen number of the working fluid departs from the continuum limit. NEAR consultation using this technology is available. NEAR may also customize the technology for the above mentioned applications and/or for other potential applications.


  1. Reisenthel, P. H. et al, "A Study of Turbulence in Rarefied Gases." AIAA Paper 93-3097.
  2. Reisenthel, P. H. et al, "Turbulence Analysis of a Slightly Rarefied Gas Flowing Through a Channel." AIAA Paper 94-0407.


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