Numerical and Experimental Analysis of Rarefaction Effects on Aerodynamic Coefficients of a Slender Re-entry Vehicle

Abstract

The lift and drag coefficients for a slender re-entry configuration are measured in the near continuum transition regime from continuum to free molecular flow in the 2nd test section of the continuously operating Hypersonic Vacuum Wind Tunnels Göttingen (V2G) of the German Aerospace Center (DLR). In these tests the range of Knudsen numbers based on the wind tunnel model length is 7.2e-4 < Kn < 7.2e-3. Since numerical tools are widely used in the framework of re-entry and hypersonic transport vehicle design they must be capable of correctly accounting for rarefaction effects on the aerodynamic coefficients in case the vehicle will operate in the upper atmosphere. The present unique benchmark data is suitable to validate commonly used numerical design tools. Therefore, a study is conducted using a Direct Simulation Monte Carlo Method (DSMC) as well as a solver for continuum flows. The DSMC computations are performed using the open-source SPARTA code and inviscid and viscous flow solutions are obtained with the DLR TAU code. For the selected wind tunnel free stream conditions, the Euler solver is applied to compute the flow field in the continuum limit. The DSMC method is used to generate the reference solution for the near continuum and rarefied flow conditions as well as the solution for the free molecular limit. The Navier-Stokes solver is applied in two modes. The first refers to the standard setup for viscous flow computations using no-slip wall boundary conditions. In order to account for the slip flow which is expected to develop with increasing rarefaction effects, the second mode of the Navier-Stokes solver includes velocity and temperature slip condition according to Maxwell and Smoluchowski. With this set of numerical tools the experimental data can be used for code validation and to judge in how far the continuum flow solver is applicable for the accurate prediction of the aerodynamic vehicle performance. In general, very good agreement for the lift and drag coefficient and the aerodynamic efficiency, i.e., the lift/drag ratio is obtained between the measurements and the DSMC solutions for the complete range of flow conditions. The Navier-Stokes solver with no-slip boundary conditions can only be applied for the flow condition at the two lowest considered Knudsen numbers. The slip conditions slightly extend the range of applicability, however, for the highest Knudsen number flow, the DSMC method is required for accurate predictions. The simple slip flow conditions utilized here are not sufficient to match the DSMC results. Based on code to code comparisons, a similar result is obtained for the pitching moment coefficient.