The Temperature Profile within Pulse Tubes

Abstract

A simple model is developed of the temperature profile within the pulse tube section of Pulse Tube Refrigerators. Using the Lagrangian reference frame, this simplified model directly gives the temperature overshoot at the hot and cold ends. The overshoots are the result of the interaction of the gas flow and the heat exchangers. They result from the work flow in the gas being converted to heat flow prior to reaching the heat exchangers. The mean temperature overshoot at the hot end is ΔT ≈ π/₂ T₁, where T₁ is the amplitude of the temperature oscillation within the pulse tube. At the cold end, the mean temperature overshoot is ΔT ≈ -(π/₂) (Q̇_net/Q̇_gross) T₁, where Q̇_net and Q̇_gross refer to the net and gross cooling powers respectively. Away from the ends, the temperature gradient is primarily due to thermal conductivity. The temperature overshoot effects are excluded in many models developed in the Eulerian reference frame because these models often explicitly exclude the changes in mean gas temperature that occur at the entrance to the heat exchangers.