F (23) Thus, for simple cooling the fractional increase in radiator
5) Adequacy of ideal fluid assumption
Solution: F r o m information given in the statement of the problem, the basic input is:
Τι = 2000*R
Since β < , compression of the secondary coolantprior to entering the radiator is the optimum mode for removal of
secondary waste heat.
# Rubidium is considered as a possible working fluid for space power plants in Réf. 1.
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than that for simple cooling.
5. F r o m Fig. 3 of Ref. 2, Ρχ is about 2 and P 4 is about 3.6.
If it is assumed that both Ρχ and P 4 are equal to 2, the maxi
mum deviation of the ideal fluid analysis from that of real fluids will be obtained, since the deviation increases as Ρ de
creases. F r o m Fig. 11, < £m/φτ η = 1.05. Thus, the radiator area for the real working fluid is at most 5% greater than that for the ideal fluid.
Conclusions
The production of secondary waste heat aboard spacecraft (waste heat from processes other than the inefficient conver
sion of thermal energy to some other form) can result in a significant increase in radiator area when (1) the secondary waste heat production rate is a significant fraction of gener
ated power, and (2) the temperature of the component in which secondary waste heat appears is small compared to the maxi
mum power cycle temperature.
Secondary waste heat may be rejected by simple cooling followed by direct transfer of the coolant to a secondary radi
ator, or by expansion or compression of the coolant prior to entering the radiator. The optimum cooling mode is deter
mined primarily by β, the ratio of the secondary heat source temperature to the maximum power cycle temperature. When
β exceeds 0.5, simple cooling is preferred. When β is less than 0.5, either simple cooling or prior compression of the coolant is preferred, depending on the magnitude of rj , the compressor or turbine efficiency, and a , the ratio of second
ary waste heat production to generated power.
Within the range of operating conditions for which sec
ondary waste heat significantly influences radiator area, an increase in the permissible temperature of components in which secondary heat is produced and/or a reduction of the secondary heat production rate may be more effective in r e ducing radiator area than an increase in the maximum power cycle temperature.
Within the range of operating conditions for which most of the radiator area is determined principally by the rejection of
secondary heat, optimization of the p r i m a r y radiator area has 166
relatively little effect on total radiator area. F o r these con
ditions, other considerations may become dominant, such as efficiency of thermal energy conversion or design of the ther
mal energy source.
Use of an ideal fluid rather than a real cycle working fluid results in an underestimate of radiator area. When β^
0.3, the ideal fluid analysis results in a radiator area which is 20% or less below that required for liquid metal fluids.
When β > 0.4, the er ror resulting from use of the ideal fluid analysis is 10% or less.
Nomenclatur e
= maximum absolute temperature of power cycle
= absolute temperature of p r i m a r y radiator = min
imum absolute temperature of power cycle
= absolute temperature of secondary waste heat source
= absolute temperature of secondary radiator W = power generated in power cycle
A = p r i m a r y radiator area needed to generate W units of power
w = power to compress secondary coolant or power produced by secondary coolant
a = secondary radiator area needed to generate W units of power
a = secondary heat ratio = ratio of secondary waste heat production rate to generated power W S = entropy
7f^ = expansion efficiency in power cycle
r) = expansion or compression efficiency in second
ary coolant cycle
7} = component efficiency = rj^ = rj^
(T = Stefan-Boltzmann constant
€ = radiator emissivity C = specific heat of liquid h^g = heat of vaporization
Ρ = fluid parameter = hf r Y/ CT
167
τ = ratio of heat rejected to heat added in ideal power cycle
δ = ratio of heat rejected to heat added in ideal sec
ondary coolant cycle
φ = dimensionless specific radiator area for ideal fluid
φ^ = φ when secondary waste heat is negligible R = for ideal fluid, ratio of radiator areas with and
without secondary waste heat = φ/φ^ or φ / Φο τ η F = for ideal fluid, ratio of increase in radiator area
with secondary waste heat and simple cooling to radiator area without waste heat
ρ = τ / τ ' = ratio of heat rejection rates in Rankine and Carnot cycles
η = δ * / δ = ratio of heat rejection rates in reversed Rankine and reversed Carnot cycles
Subscript "m" — denotes minimum value or optimum value Subscript "1" — denotes secondary waste heat removal by
simple cooling Superscript "1" — denotes real fluid
Superscript "*" — denotes real fluid or Rankine cycle References
1. Mackey, D. Β. , "Powerplant Heat Cycles for Space Vehi
cles," IAS Paper No. 59-104. Presented at IAS National Summer Meeting, June 16-19, 1959, Los Angeles, Calif.
2. Mackey, D. Β. , "Secondary Power Systems for Space Vehi
cles," for presentation at the Society of Automotive Engi
neers, National Aeronautic Meeting, October 10-14, I960, Los Angeles, Calif.
3. English, R. Ε. , jet al, " A 20,000 Kilowatt Nuclear Turbo-electric Power Supply for Manned Space Vehicles," Memo 2-20-59E, National Aeronautics and Space Administration, Washington, March 1959.
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Moffitt, T . P . , and Klag, F. W . , "Analytical Investigation of Cycle Characteristics for Advanced Turboelectric Space Power Systems," N A S A T N D-472, National Aeronautics and Space Administration, Washington, October I960.
Fisher, J . H . , and Stéphane, C. W . , "Basic Energy Con
version in Space Vehicles," presented at American Rocket Society 14th Annual Meeting, November 16-20, 1959, Washington, D. C.
Macklin, Μ . , "Space Cooling P r o c e d u r e s , " IAS Paper 61-18, presented at the IAS 29th Annual Meeting, New York, January 23, 1961.