The effect of `flushing ratio´ on the performance of counterflow fixed-bed thermal regenerators [for Stirling cycle machines]

A closed form-expression for the effectiveness of a counterflow thermal regenerator is given. It takes account for the flushing phase, i.e. for that part of the blow involved in removing the residue of fluid from a previous blow. The proposed analytical approach is based on a Lagrange viewpoint for evaluating the fluid temperature and involves some mathematical difficulties for calculating the matrix temperature, as the solution of a linear integral equation, whose overcoming is discussed in the text. The developed method allows, indeed, the matrix and gas temperature profiles within the regenerator to be obtained also. The obtained results are very useful for the heat regenerators adopted in Stirling cycle machines, where the time required for an element of gas to pass through the regenerator is approximately equal to the blow time. In addition, the availability of a closed-form expression for the regenerator effectiveness is useful especially for those engines, like the free-piston Stirling engine, whose design requires the application of analytically based optimization criteria