Effect of Heat Exchanger Volume and Geometry on Power Output of a Low Temperature Difference Stirling Engine
Creators: Hasanovich, Linda
Publisher: name: University of Alberta Library
Year: 2022

<p>This work presents the results of an investigation into heat exchanger design for low temperature difference Stirling engines (LTDSEs). The aim of this study was to determine if there is an optimum heat exchanger geometry for producing maximum power output for a LTDSE. There are multiple factors that affect the optimum heat exchanger geometry: the gas temperature achieved by the heat exchangers, the pressure drop through the heat exchangers, and the effect of dead volume on the pressure achieved by the Stirling cycle. This study was undertaken using several models based on an experimental LTDSE.</p>

<p>A fundamental analysis using analytical and empirical relations for steady state heat transfer through a heat exchanger with isothermal walls showed that the output temperature of the gas is dependent on heat exchanger surface area regardless of aspect ratio. Additionally, long heat exchangers and heat exchangers with small cross-sectional area led to large pressure drops through the heat exchanger. To evaluate the effect of dead volume on output power, the Schmidt model was used. The results confirmed that the engine power output decreased with increasing dead volume ratio. The Schmidt model was used to determine a maximum optimal dead volume ratio, below which the peak power output with an optimal heat exchanger volume must be located.</p>

<p>To determine the optimum heat exchanger volume and geometry the 3rd order commercial Stirling engine model, Sage, was used. Sage is able to model the heat transfer in the heat exchangers and the effect on the engine gas during the cycle. A model was created in Sage based on the experimental LTDSE. This model needed to connect the liquid source and sink of the heat exchangers to the gas within the engine. This was done using a temperature drop determined by a convective heat transfer resistance of the liquid. To determine this resistance, a multi-fluid steady state CFD study was done in the absence of experimental data in order to capture the interaction between the air and liquid in the heat exchanger. From this study, an average convective heat transfer resistance was able to be determined. </p>

<p>With the convective heat transfer resistance obtained the Sage model was validated against the experimental LTDSE results. Sage was found to generally agree with the experimental results, but showed overprediction and an increased dependence on speed that was not present in the experimental results. Some model tuning was done to improve the model results. The overprediction was able to be reduced by tuning the convective heat transfer to match the model gas temperatures to the experiment. The dependence of the model output power on engine speed was reduced by reducing the flow friction multiplier, which changed the phase of the pressure curve. However, this led to increased overprediction, so it was not included in the final version of the Sage model.</p>

<p>Using the model with tuned convective heat transfer resistance, the heat exchanger geometry was varied by changing the heat exchanger length and cross-sectional area. An optimum heat exchanger geometry was determined. This optimum geometry was at the shortest heat exchanger length with a large cross-sectional area. To maximize the power output, the surface area of the heat exchanger needs to be maximized while keeping pressure drop through the heat exchanger low and not contributing excess dead volume to the engine.</p>

<p>Some sensitivities were considered to better understand this result. When the engine pressure and speed were varied, it was found that the optimum heat exchanger geometry was larger for high speed and high pressure cases, as the heat transfer requirement increased. Additional dead volume that scaled with the heat exchanger volume was added to represent a plenum volume that connects the heat exchangers to the main engine volume. The optimum heat exchanger geometry in this case had a longer heat exchanger with smaller cross-sectional area. This results from the excess dead volume associated with a large cross-sectional area having a more significant penalty than the benefit of low pressure drop through the heat exchanger. Finally, the compression ratio of the engine was held constant, and it was found that a larger heat exchanger was required, and the effect of excess dead volume on engine output power was reduced.</p>