Optimization of steady-state thermal design of space radiators

Abstract

Equations are derived for use in optimization of fin width and tube diameter to minimize system weight of single-and double-surf ace space radiators. Pumping power weight penalty is included in the optimization. Incident radiation from external sources is accounted for, and calculation of required armor thickness for protection against meteoroids is included. Adaptation of the equations to numerical solution by digital computer is discussed. An illustrative problem solution is discussed in which a single-surf ace radiator is optimally designed for typical baseline constraints. Parametric curves are presented which illustrate the effects of off-design incident radiation levels and spacecraft internal heat loads on required fluid flow rate through the optimally designed radiator. The analysis demonstrates that required fin width and tube length are very sensitive to the level of incident radiation. Nomenclature A -sensitive area for meteoroid protection, ft 2 B = fin width, ft CP = average specific heat of radiator fluid, Btu/lb-°R D = outside diameter of armor around tubes, ft Di = inside diameter of radiator tube, ft Ffft -average configuration factors, fin to space and tube to space, respectively h = forced convection heat-transfer coefficient, Btu/hrft 2 -°R K r = constant: 1.09 for Al projectiles impinging on Al targets; 0.606 for iron particles impinging on iron targets k/,kt = thermal conductivities of fin and tube materials, respectively, Btu/hr-ft-°R L = radiator tube length, ft N = number of tubes p(n) -probability that n punctures will occur in time r over sensitive area A Q s = average absorbed irradiation flux from all external sources (for double-surface radiators Q 8 is the sum of the average values on both sides), Btu/hr-ft 2 Rd,R s = equivalent thermal resistances between working fluid and base of fin for double-and single-surface radiators, respectively, hr-ft 2 -°F/Btu T -radiator surface temperature, °R; Ti m , T% m = mean values at z = 0, x = (B + D)/2, respectively (and AT m = Ti m -T 2m )', T ly , T 2y = local values at x = 0, x = (B + D)/2, respectively T b = bulk fluid temperature, °R; T bi and T bo = inlet and outlet values, respectively t,t a ,t w = fin, armor, and tube wall thicknesses, respectively, ft v -meteoroid velocity, miles/sec, Eq. (31) W eq = radiator equivalent weight = W r + W/ + W m + W p p, where W r = basic radiator weight, Wf = fluid weight, W m = meteoroid protection penalty, and Wpp = pumping power penalty, Ib WT = radiator fluid flow rate per tube, Ib/hr-tube x, y -rectangular coordinates of radiator surface, ft e = emissivity of radiator coating tif^f' = fin effectiveness over elemental strip dy of single-and double-surface radiators, respectively: T?/,*// = mean values £ = fin temperature gradient in x direction, Eq. (10), deg/ft o-= Stephan-Boltzmann constant, 0.1714(10~8), Btu/hrft 2 -°R 4 T -duration of exposure to meteoroids, days

Detailed Thermal Design and Control of an Observation Satellite in Low Earth Orbit

“…Garzon [8] presented a Master's thesis on OSIRICI-3U CubeSat. Thurman [9] proposed an analytical approach to the optimum thermal design of space radiators. Similarly, Aslanturk [10] studied the optimisation of a central-heating radiator.…”