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

Document Type

Conference Proceeding

Publication Date


Publication Title

Proceedings of the 3rd International Energy Conversion Engineering Conference


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. Near the heater-regenerator interface, fluid non-uniformity (in the radial direction) is noticed, which is attributed to jetting effect of flow from the heater fins. This can result in lower effectiveness values for the regenerator. The model used for the regenerator is the porous media model available today in CFD-ACE code. Work is underway to improve this model and therefore no detailed evaluations can be made at this point, for the regenerator thermal performance. A separate experimental effort has begun at UMN to provide detailed flow and thermal fields measurements. Thus we can validate the CFD models developed for jetting and flow mixing effects, among others. A new 180 degree test section has been fabricated at the UMN to more accurately experimentally simulate the flow in the Stirling engine expansion space. Flow visualization shows a vortex in the flow at the knuckle region. Measurements of flow and local heat transfer coefficients are in progress. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


Paper AIAA 2005-5654 presented at the 3rd International Energy Conversion Engineering Conference, San Francisco, CA, August 15 - 18, 2005.