Space Grant Consortium - University of Wisconsin - Green Bay

load total load
( nd ) ( 1 nd 8 nd )
Q� v� = Q� m� v� m� + v� m�
(25)
2 2 2
Optimization Algorithm. The optimization process for the results presented in this paper
identify the optimal mixture composition in the 2 nd stage ( y nd , the vector of compositions of
2
each mixture component) for a particular set of operating conditions. The total heat exchanger
compactness figure of merit ( QUA �
total ) calculated by the thermodynamic model varies
significantly as the mixture mole fraction vector ( y nd ) changes, so it is necessary to evaluate a
2
wide range of mole fraction combinations. It is not computationally efficient to parametrically
evaluate the mole fractions for all possible y nd combinations. Therefore, an optimization
2
algorithm that is able to select the optimal mixture using significantly less computations than a
parametric study is utilized here.
The optimization routine selected is the PIKAIA 1.2 [9] genetic algorithm that finds the
maximum of the objective function using an algorithm that mimics biological evolution. A
detailed description and demonstration of the routine as it is used to select a best mixture is
found in [0]. As shown by [0], other optimization techniques such as the direct search and
variable metric strategies do not reliably converge because of the sharp discontinuities in mixture
properties near phase boundaries as well as other constraints that are placed on the mixture.
Note that the reliability of the genetic optimization routine comes at the expense of computation
speed; the genetic algorithm should only be used when other, faster, routines have failed.
The optimization routine excludes mixtures based on two practical considerations: 1) A mixture
is excluded from further consideration if the temperature at the exit of the 2 nd stage expansion
valve is below the freezing point temperature. 2) Mixtures in a saturated or liquid state leaving
the recuperator (state 1) are excluded to avoid the introduction of liquid into the 2 nd stage
compressor. The freezing point is calculated as the weighted average of the triple point of the
mixture constituents, as described in [0]
Optimization Results
The results of the optimization model using a pure refrigerant in the 1 st stage and a hydrocarbon
based mixture in the 2 nd stage are presented in this section. The refrigerant used for analysis in
the 1 st stage is R22. The Q� load UAtotal
figure of merit is optimized in order to yield the MGJT
system that provides the most cooling for a given geometric size for load temperatures spanning
100 K to 180 K. The effect of the precooling temperature (T4) on Q� load UAtotal
is studied in
order to show the optimal balance between the precooler and the recuperator. The other figure of
merit, the load specific compressor volumetric flow rate is not explicitly optimized but is
reported as it is important in the design of a practical system. The performance of the two stage
system is normalized against the performance of a single stage system in order to show the
relative benefit and penalty associated with the addition of precooling.
The Q� load UAtotal
for a two stage system in which an optimal mixture has been selected for each
precooling and load temperature is shown in FIGURE 3(a). As the precooling temperature is
35