Multiobjective Optimization of Earth-Entry Vehicle Heat Shields

Abstract

A differential evolutionary algorithm has been executed to optimize the hypersonic aerodynamic and stagnationpoint heat transfer performance of Earth-entry heat shields for manned and unmanned missions. Objective functions comprise maximizing cross range, minimizing heat flux, and minimizing heat load. Each considered heatshield geometry is composed of an axial profile tailored to fit a base cross section. Axial profiles consist of spherical segments, spherically blunted cones, and power law geometries. Heat-shield cross sections include oblate and prolate ellipses, rounded-edge parallelograms, and blendings of the two. Aerothermodynamic models are based on modified Newtonian impact theory with semiempirical correlations for convection and radiation. Entry velocities of 11 and 15 km=s are used to simulate atmospheric entry conditions at lunar and Mars return conditions, respectively. Results indicate that skip trajectories allow for vehicles with a low lift-to-drag ratio of 0.25 to achieve 1000 km cross range, a factor of 4 increase in capability over direct entry. For 11 km=s entry with a 6g deceleration limit, the spherical segment provides optimal performance. For 15 km=s entry with a 12g deceleration limit, the spherically blunted cone produces an 8% lower heat flux when compared with spherical segments with similar aerodynamic characteristics. This result is attributed to the blunted cone's smaller shock standoff, which reduces the heat load generated by thermal radiation, the dominant heat transfer mode.= total emitted power density, J=m 3 s e = eccentricity g w = ratio of wall enthalpy to total enthalpy g 1 , g 2 , g 3 = coefficients and exponents [Eq. (6)] H = exponent [Eq. (7)] h = length along y direction, m h t = altitude, km j = semimajor axis length of a blunt body, m j max = maximum mesh points in x direction k = semiminor axis length of a blunt body, m k max = maximum mesh points in direction L = lift, N l = length along x direction, m M 1 = freestream Mach number m = mass, kg m 1 = number of sides of the superellipsê n = normal unit vector, away from surface n crew = crew number, person n max = peak deceleration load, Earth g n 1 , n 2 , n 3 = superelliptic parameters p xrs = cross range, km Q = heat load, kJ=cm 2 q = heat flux, W=cm 2 q 1 = freestream dynamic pressure, Pa r = base radius, m r n = nose radius of blunted cone, m r s = radius of curvature of spherical segment, m S = area of base cross section, m 2 t = time, s t d = total mission duration, days V PR = pressurized volume, m 3 v 1 , v 2 = superellipse parameters V 1 = freestream velocity, m=s x, y, z = coordinate values, m = angle of attack, = sideslip angle, = trajectory flight-path angle; positive pointing away from planet, so = shock-standoff distance, m "= edge tangency angle, v = volumetric efficiency c = half-cone angle, s = half-spherical segment angle, = density, kg=m 3 2 = 1 = normal-shock density ratio = sweep angle, rad b = bank angle,axial force, N b = base cg = center of gravity conv = convective D = drag, N EI = entry int...

Hypersonic lifting body aerodynamic shape optimization based on the multiobjective evolutionary algorithm based on decomposition

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Contemporary Impact Analysis Methodology for Planetary Sample Return Missions

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