Optimization and Thermodynamic Performance Measures of a Class of Finite Time Thermodynamic Cycles

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Modifications to the quasistatic Carnot cycle are developed in order to formulate improved theoretical bounds on the thermal efficiency of certain refrigeration cycles that produce finite cooling power. The modified refrigeration cycle is based on the idealized endoreversible finite time cycle. Two of the four cycle branches are reversible adiabats, and the other two are the high and low temperature branches along which finite heat fluxes couple the refrigeration cycle with external heat reservoirs. This finite time model has been used to obtain the following results: First, the performance of a finite time Carnot refrigeration cycle (FTCRC) is examined. In the special case of equal heat transfer coefficients along heat transfer branches, it is found that by optimizing the FTCRC to maximize thermal efficiency and then evaluating the efficiency at peak cooling power, a new bound on the thermal efficiency of certain refrigeration cycles is given by $\epsilon\sb{m} = (\tilde\tau\sp2\sb{m}\ (T\sb{H}/T\sb{L}) - 1)\sp{-1},$ where $T\sb{H}$ and $T\sb{L}$ are the absolute high and low temperatures of the heat reservoirs, respectively, and $\tilde\tau\sb{m}=\sqrt{2}$ + 1 $\simeq$ 2.41 is the dimensionless cycle period at maximum cooling power. Second, a finite time refrigeration cycle (FTRC) is optimized to obtain four distinct optimal cycling modes that maximize efficiency and cooling power, and minimize power consumption and irreversible entropy production. It is found that to first order in cycling frequency and in the special symmetric case, the maximum efficiency and minimum irreversible entropy production modes are equally efficient. Additionally, simple analytic expressions are obtained for efficiencies at maximum cooling power within each optimal mode. Under certain limiting conditions the bounding efficiency at maximum cooling power shown above is obtained. Third, the problem of imperfect heat switches linking the working fluid of an FTRC to external heat reservoirs is studied. The maximum efficiency cycling mode is obtained by numerically optimizing the FTRC. Two distinct optimum cycling conditions exist: (1) operation at the global maximum in efficiency, and (2) operation at the frequency of maximum cooling power. The efficiency evaluated at maximum cooling power, and the global maximum efficiency may provide improved bench-mark bounds on thermal efficiencies of certain real irreversible refrigeration cycles.