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This report details a computational fluid dynamics study conducted in support of the phase II development of the X-33 vehicle. Aerodynamic and aeroheating predictions were generated for the X-33 vehicle at both flight and wind-tunnel test conditions using two finite-volume, Navier-Stokes solvers. Aerodynamic computations were performed at Mach 6 and Mach 10 wind-tunnel conditions for angles of attack from 10 to 50 with body-flap deflections of 0 to 20. Additional aerodynamic computations were performed over a parametric range of free-stream conditions at Mach numbers of 4 to 10 and angles of attack from 10 to 50. Laminar and turbulent wind-tunnel aeroheating computations were performed at Mach 6 for angles of attack of 20 to 40 with body-flap deflections of 0 to 20. Aeroheating computations were performed at four flight conditions with Mach numbers of 6.6 to 8.9 and angles of attack of 10 to 40. Surface heating and pressure distributions, surface streamlines, flow field information, and aerodynamic coefficients from these computations are presented, and comparisons are made with wind-tunnel data.Hollis, Brian R. and Thompson, Richard A. and Berry, Scott A. and Horvath, Thomas J. and Murphy, Kelly J. and Nowak, Robert J. and Alter, Stephen J.Langley Research CenterAERODYNAMIC HEATING; COMPUTATIONAL FLUID DYNAMICS; FLOW DISTRIBUTION; NAVIER-STOKES EQUATION; PRESSURE DISTRIBUTION; AERODYNAMIC COEFFICIENTS; ANGLE OF ATTACK; FINITE VOLUME METHOD; FLIGHT CONDITIONS; HYPERSONIC SPEED; WIND TUNNEL TESTS; X-33 REUSABLE LAUNCH VEHICLE