A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones

There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as a refrigerator, which is much easier to operate. For this purpose, an improved Simple model for both the positive and the reverse Stirling cycles, considering the various loss mechanisms and actual operating conditions, is proposed and verified by a self-designed Stirling engine. As to the positive cycle with helium and nitrogen at 2.8 MPa, the model errors range from 5.4–11.3% for the indicated power, and 1–10.2% for the cycle efficiency. As to the reverse cycle with helium and nitrogen, the errors of the predicted input power range from 7.9–15.3% and from 2.5–10.9%, respectively. The experimental cooling temperatures can reach −92.2 and −53.6 °C, respectively, for the reverse cycle with the helium and nitrogen at 2.8 MPa. This Stirling-cycle analysis model shows a good adaptability for both the positive and the reverse cycles. In addition, the p-V maps of the positive and reverse cycles are compared in terms of “pressure ratio” and “curve shape”. The pressure ratio of the reverse cycle is significantly higher than that of the positive one at the same mean pressure. A method is proposed to predict the indicated work of the positive Stirling cycles using the reverse ones. A mathematical model to predict the indicated power of the positive Stirling cycles based on the reverse ones is proposed: W h e a t 2 − W c o o l 1 = A · ( T g e 2 − T g c 2 T g c 1 − T g e 1 ) B . The most critical issue with this method is to establish an associated model of the temperatures of the expansion and the compression space. This model shows a good adaptability for both the positive and the reverse cycles and can provide detailed information for deep discussion between the positive and the reverse cycles.