Thermodynamic analysis of the basic pulse-tube refrigerator

Abstract

The basic pulse-tube refrigerator is modelled as a tube with one end closed and with a movable piston at the other end. Both ends contain heat exchangers. The piston is capable of moving through the heat exchanger at its end. The thermodynamic model consists of four steps: adiabatic compression of the gas in the pulse tube; isobaric heat transfer from the gas to the wall of the pulse tube; adiabatic expansion of the gas in the pulse tube; and isobaric heat transfer from the wall of the pulse tube to the gas. During the entire cycle the pressure is taken to be uniform, and the gas inside either heat exchanger is assumed to be at the temperature of that exchanger. Upon neglecting gas motion during the isobaric heat transfer steps, complete analytical results are obtained for the temperature profiles of the wall, of the gas after compression, and of the gas after expansion. Each of these profiles is piecewise adiabatic. The profiles are used in finding the coefficient of performance and the net work done per cycle. The coefficient of performance is derived by noting that the basic heat transfer process consists of several reverse Brayton cycles, staged in series. The net work done per cycle is found by constructing the p-V diagram for the piston. This diagram represents a modified reverse Brayton cycle, with each of the compression and expansion steps consisting of two hyperbolic segments. The parameters determining these segments depend on the temperature at which gas enters the heat exchangers. Results are presented for the coefficient of performance and the heat removed per cycle as a function of the temperature ratio of the heat exchangers, for various values of the pressure ratio π and the non-dimensional length L h of the heat exchanger at the closed end. The model is non-linear and permits study of the effect of large values of π and L h.