Introduction In this paper, we first review our recent experimental and computational studies on the orificetype [1] and inertance-type [2] pulse tube refrigerators along with related optimization studies. The experimental studies are done at various values of mean pressure of helium (~ 0.35 MPa to 2.2 MPa), different amplitudes of pressure oscillations, and frequency of operation and size of inertance length and orifice opening. Time-dependent axisymmetric CFD simulations of the inertance-type and orifice-type pulse tube refrigerators are reported where the transient as well as the cycle-averaged operation of the in-line pulse tube refrigerator is studied for the processes occurring in the system. Phase relation between mass flow and pressure waves are also reported for both systems. These relations play important roles in the performance of thermoacoustic devices. While passive forms of phase shifting is considered in [1, 2], we also present numerical results for a thermoacoustic refrigerator where active mechanical phase shifting is achieved via a spring-mass system that replaces the inertance tube and the orifice opening traditionally used in passive phase shifting systems. In an active phase shifting system (see figure below), greater control of phase shifting is achieved which would produce lower temperatures at the cold spot.