Validation of Multi-Dimensional Stirling Engine Codes: Modeling of the Heater Head

In this paper we describe both CFD (at CSU) and experimental (at UMN) activities related to Stirling engine Multi-D code development. On the CFD side we investigated two novel approaches in engine modeling. In one approach we eliminated the solid in both the heater and cooler fins (Engine-4). The other approach (Engine-5) starts by modeling each component of the engine (Expansion Space, Heater, Regenerator, Cooler and Compression Space) separately and reaching steady state results with good energy balance. We started integrating the whole engine and tried to reach an energy balance for the whole engine (Sage model results were used to provide the appropriate boundary conditions for each component). The two approaches proved successful in cutting down the number of iterations as well as the number of cycles to reach a steady oscillatory solution. CFD-ACE+ was used for this modeling exercise. The second approach proved to be particularly successful and will be of great value for the following reasons, we will be able to: a) import any regenerator model that could be developed under other programs, b) to examine engines (in a shorter time frame) that have some changes in one component (say a new heater head design) and all other components are the same, and c) overcome some of the difficulties in parallel processing that we are encountering today. The comparison among Sage, Engine-4 and 5 showed thermal efficiencies of 42.27%, 45.6% and 45.06% respectively. These efficiency differences are attributed to the lack of an overall energy balance in the 2-D analysis: 1.7% imbalance for Engine-4 and 5.77% for Engine-5. Improving the grid structure should eliminate this energy imbalance. Separate component energy balance (for Engine-4) showed that the compression space and regenerator have the two worst energy balances. The heater is the best, while the cooler and the expansion space are in the middle. These component analyses suggest where future grid refinement or CFD improvement should be made. Further attention was given to the expansion space of the engine (Engine-4). Upon examining the displacer dome separately we found that there is a difference of more than 5 degrees from the top of the dome (near the heater) and the center line. On the other hand the expansion space dome has a difference of more than 10 degrees from the top of the dome (near the heater) to the center line. Moreover our computations indicate an average temperature difference between the displacer dome and the expansion space dome of about 30 K which might suggest including radiation heat transfer in the CFD analysis. The flow and thermal fields in the expansion space indicate temperature differences as high as 70 K due to less effective mixing. Also the fluid layers near the expansion space dome behave differently than in the core of the fluid due to oscillations, as expected.