Modeling Orifice Pulse Tube Coolers

We have developed a calculational model that treats all the components of an orifice pulse tube cooler. We base our analysis on 1-dimensional thermodynamic equations for the regenerator and we assume that all mass flows, pressure oscillations and temperature oscillations are small and sinusoidal. Non-linear pressure drop effects are included in the regenerator to account for finite pressure amplitude effects. The resulting mass flows and pressures are matched at the boundaries with the other components of the cooler: compressor, aftercooler, cold heat exchanger, pulse tube, hot heat exchanger, orifice and reservoir. The results of the calculation are oscillating pressures, mass flows and enthalpy flows in the main components of the cooler. By comparing with the calculations of other available models, we show that our model is very similar to REGEN 3 from NIST and DeltaE from Los Alamos National Lab. Our model is much easier to use than other available models because of its simple graphical interface and the fact that no guesses are required for the operating pressures or mass flows. In addition, the model only requires a few minutes of running time allowing many parameters to be optimized in a reasonable time. A version of the model is available for use over the World Wide Web at http://irtek.arc.nasa.gov. Future enhancements include adding a bypass orifice and including second order terms in steady mass streaming and steady heat transfer. A two-dimensional anelastic approximation of the fluid equations will be used as the basis for the latter analysis. Preliminary results are given in dimensionless numbers appropriate for oscillating compressible flows. The model shows how transverse heat transfer reduces enthalpy flow, particularly for small pulse tubes. The model also clearly shows mass recirculation in the open tube on the order of the tube length. They result from the higher order Reynolds stresses. An interesting result of the linearized approach is that the steady mass streaming does not affect the enthalpy flow at second order. The major effect of recirculating mass streaming is to increase transverse temperature gradients, which leads to higher entropy production and reduced efficiency.