Some Radiator Design Criteria for Space Vehicles

Callinan, Joseph P.; Berggren, W. P.

doi:10.1115/1.4008193

Cited by 19 publications

(6 citation statements)

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“…Thus, for hydrogen at 2000 °R, the paiameter D^h/m 08 = 5 77 A reduction in the hydrogen temperature to 1500°R, hich may correspond to the exit condition, will lower the value of D l 8 h/m° 8 The two parameters of the system which may be used to optimize the radiator configuration are the fin thickness and length Specifically, at each point along the tube, there is one value of fin thickness and one corresponding value of fin length that will result in a maximum value of dtt/d\I/ As was pointed out previously, Eqs (10, 15, and 16) define the optimum values of the fin dimensions and relate them to the 77 coordinate along the tube Specifically, Eqs (15) Aside from the shape of the curves, a significant result borne out by Fig 5 is the fact that the magnitude of the optimum fin thickness required for maximizing dQ/d\l/ is relatively small and, therefore, may not be structural^ feasible This would indicate that a space-radiator system of the type considered here would have to be designed on the basis of an optimum fin length that would vary along the tube axis The fin thickness, however, now taken as a constant, would have to be selected on the basis of minimum thickness required to provide structural integrity A configuration using a constant thickness fin would, in addition, be desirable because of its relative simplicity in fabrication Only Eqs (10) and (15) are therefore required for an optimization study because the value of A/ is now specified Thus, Eq (15) may be solved to yield the variation of £2(77) opt with 0(0, 77) for several values of A/ These parameters are then related to 77 through Eq (10) in the same manner as was done previously for Fig 5 The results of such a study using three values of A/ are shown in Fig 6 As may be seen for the range of fin thicknesses considered, an increase in A/ is accompanied by a decrease in the optimum fin length £2(77) and only a relatively slight change in 0(0, 77)…”

Section: Application Of Analysismentioning

confidence: 98%

Optimization study of space radiators

Imber¹,

Rubin²

1964

AIAA Journal

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A method has been developed for optimizing a rectangular fin with a variable root temperature along the tube length Calculations have been performed for a typical set of system conditions The results indicate that the magnitude of the optimum fin thickness is, for the representative case considered, too small to be structuially feasible Hence, the fin thickness, now taken as a constant, should be selected on a minimum thickness basis requii ed to provide structural integrity Thus, only the fin length would be optimized A comparison was made between the method that treats an optimum constant-length fin and the present analysis for the variable-length fin The results show that the radiator system with the constant-length fin is 1 5% heaviei than the sjstem that uses the vai iable-length fin Although this represents a small weight increase and therefore justifies the use of a constant-length fin, it has been shown that, in general, large deviations from the optimum design condition would introduce relatively small weight penalties As a result, the 1 5% diffeience between the two methods may, in fact, i epresent a large deviation from the optimum This indicates that strict adherence to optimum design conditions is not geneially necessaiy

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Section: Application Of Analysismentioning

confidence: 98%

Optimization study of space radiators

Imber¹,

Rubin²

1964

AIAA Journal

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“…If the radiator is constructed of a thin material of high thermal conductivity and if the fluid heat-transfer coefficient is large, it may be assumed that (4) (5) (6) Employing the method of partial fractions and integrating Eq. (16) in the y direction from y = 0, T iy = T u to y = L, Ti y = TI O , yields the following equation for required tube length L:…”

Section: Single-surf Ace Radiatorsmentioning

confidence: 99%

“…(14); assign several specific values to T 2m and perform the following steps (3)(4)(5) 5) Calculate L from Eq. (7a) or (7b).…”

Section: Single-surf Ace Radiatorsmentioning

confidence: 99%

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Optimization of steady-state thermal design of space radiators

Thurman

1969

Journal of Spacecraft and Rockets

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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

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“…(8) The reactor should be compact, have a high reliability factor, and have a control system which is compatible with the generator characteristics. (9) If the rejection of cycle heat is to space by radiation, the temperature of the working fluid should be as high as possible, and a compromise must be made between cycle efficiency, radiation weight, and radiator reliability.…”

Section: Legal Noticementioning

confidence: 99%