Aerodynamic Heating Prediction Tool for a Supersonic Vehicle for Conceptual Design Phase

Abstract

A computational tool has been developed to compute transient surface temperature utilizing basic flight parameters such as altitude, Mach number and angle of attack. An explicit finite difference technique is used to discretize the governing differential equations that account for convection and radiation heat transfer with non-reactive chemistry. Different approaches are applied to two different surface types; thermally thin and thermally thick. The Biot number criterion between the wall and the surrounding air is considered to determine the surface type. Transport properties of air are calculated at Eckert's reference temperature. Boundary layer transition is taken into account by considering local Mach number and Reynolds number. Heat transfer coefficients are calculated by use of flat plate approaches. Effect of angle of attack is taken into account through modified Newtonian theory. The available X-15 flight data for two different flight trajectories and HIFiRE-5 flight data are used to validate the prediction tool. Vehicles with different geometries are modeled using CFD simulations and results of different configurations are compared with the computed temperatures. Predicted results for surface temperatures are found to be in good agreement with measured flight data and simulation results. The validation shows that the methodology developed in the present study could be useful in predicting aerodynamic heating loads during conceptual and preliminary design phases. NomenclatureA = area Bi = Biot number c p = specific heat of the structural material c p_flow = specific heat of fluid C p = pressure coefficient C p_max = maximum pressure coefficient on the body surface C m = transition Mach number coefficient E = Energy ̇ = energy inflow to the structure ̇ = energy outflow from the structure ̇ = the rate change of thermal energy stored by the structure h = heat transfer coefficient k = thermal conductivity k* = thermal conductivity evaluated at the reference temperature m = mass M = Mach number 1 Senior Thermal Design Engineer, Roketsan Missiles Industries Inc., bsimsek@roketsan.com.tr 2 2 M L = local Mach number M ∞ = free stream Mach number N = number of nodes Nu = Nusselt number Nu x = Nusselt number at a position x. Re = Reynolds number Re L = local Reynolds number Re t = local transition Reynolds number Re x = Reynolds number at a position x q = dynamic pressure Q = rate of heat flow due to aerodynamic heating P = pressure P L = local pressure P 0L = local stagnation pressure P ∞ = free stream pressure r = recovery factor t = time T = temperature T L = local temperature T r = recovery temperature T ref = reference temperature for radiation T w = wall temperature T* = Eckert's reference temperature U = velocity x = distance to point of interest from the leading edge/nose tip α = thermal diffusivity γ = specific heat ratio of flow δ = thickness of the structure ε = emissivity σ = Stefan-Boltzmann constant ρ = density θ = angle normal to freestream µ = viscosity Δy = distance between the nodes Δt = time step...