On numerical solutions of Burnett equations for hypersonic flow past2-D circular blunt leading edges in continuum transition regime

Using the Burnett equations is one way to advance the continuum approach based on the Navier-Stokes equations into thc continuum transition flow regime for rarefied hypersonic flow. Though two-dimensional flow-field numerical solutions of the Burnett equations have been obtained in our previous studies, it is still uncertain how to formulate boundary conditions for the higher-order Burnett equations. Furthermore, few comparative studies have been performed to validatc the Burnett equations in multidimensional appliclttions. This paper presents a new method to formulate the additional boundary conditions for the Burnett cquations. The new method for the Burnett equations requires the same number of physical surface slip conditions as for the Navier-Stokes equations. We subsequently have obtained numerical solutions of the twodimensional Burnett equations with the new boundarycondition treatment for hypersonic flow past a cylinder where Knudsen numbers range from 0.02 to 0.4. The results show tha t the Burnett solutions with the first order slip conditions agree better with DSMC results than the Navier-Stokes solutions do, bu t the Burnett solutions with the Schamberg second order slip conditions seem to be inaccurate for Knudsen numbers above 0.2. 'v