Modifications have been made to the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) that enable it to compute viscous airflows under the assumption of thermal and chemical equilibrium. Equilibrium thermodynamic and transport property information are input to the code via curve fits. The periodic updating of this information enables the equilibrium algorithm to perform at a computational rate that is only a small percentage larger than the rate associated with the perfect-gas algorithm. Presented in this article are the results of the initial validation of the modified code. Solutions for surface pressure and heating are presented for the flow over slender and blunt cones at realistic re-entry conditions. LAURA solutions are compared with those produced by a viscous shock-layer method, and, for one case considered, with heat transfer data from a flight experiment. For both pressure and heating, the agreement is good. In general, differences in pressures of a few percent were noted, while differences in heating rates were in the 5-10% range.
NomenclatureA = Jacobian matrix of g with respect to q B -Jacobian matrix of h with respect to q E = total energy per unit mass, J/kg e = internal energy per unit mass, J/kg g = inviscid flux vector H = total enthalpy per unit mass, J/kg h = enthalpy per unit mass, J/kg h = viscous flux vector 7 = identity matrix M -right eigenvector matrix of A M~l = left eigenvector matrix of A n = outward unit normal vector of a cell face Pr = total Prandtl number p = pressure, N/m 2 Re = freestream Reynolds number Rn -nose radius, m S = arc length distance along symmetry plane, m t -time, s U = contravariant velocity normal to a cell face u = velocity component in x direction, m/s V = velocity vector, m/s v = velocity component in y direction, m/s w = velocity component in z direction, m/s 7 = h/e \ = eigenvalue matrix of A IJL = viscosity, N-s/m 2 p = density, kg/m 3 a = cell face area, m 2 12= cell volume, m 3