Validation and Testing of a Numerical Model for the Design and Up-Scaling of Low Temperature Difference Stirling Engines

• Author / Creator

  Lottmann, Matthias

• This thesis presents the experimental validation, testing and review of a numerical model for low temperature difference Stirling engines (LTDSEs). The research of LTDSEs is motivated by the potential use of low temperature heat as an unconventional sustainable energy source.
  An experimental setup was designed with a gamma-type LTDSE that has a working space volume of 4.6 liters, source and sink temperatures of 150 °C and 5 °C, charge pressure between 200 kPa and 450 kPa (gauge), and a maximum shaft power of 15 W. The system allowed automated control of the setpoint through source and sink temperatures, pressure, and torque load; and automated acquisition of data consisting of temperatures, average and instantaneous pressures, crankshaft angle and shaft torque.
  The engine was modeled as a simplified axisymmetric geometry with the numerical model, MSPM. It was found that two model input parameters have a significant influence on the model predictions and are at the same time difficult to measure experimentally. One is the heat transfer between the heat source/sink medium and the heat exchanger, which was not accounted for by MSPM and was then implemented as a custom heat transfer coefficient. Two different estimates for these coefficients, one analytical and one from CFD analysis, were tested in the subsequent model validation. The other parameter is the leakage of piston seals. The power piston was modeled with a leak-free seal and the displacer piston was tested with both a leak-free seal and no seal.
  The experimental validation of this model focused on the thermodynamic model at constant engine speed, so that the modeling of the gas processes could be assessed without influences of mechanical friction from the mechanism model. The model variants with the different heat transfer coefficients and displacer piston seals differed substantially from each other in their agreement with the experimental data. Consistent predictions of the heat input and rejection rates within 20 % and the gas temperatures within 3 % or 10 °C were achieved by one model variant. However, no model predicted the indicated cycle work consistently. The observed model deviations suggest that if the sensitive coefficients of source/sink heat transfer and seal leakage for both seals would be determined more rigorously through experiments or other analyses, the model agreement could be improved to a reliable level. Therefore, the key outcome of this validation is that overall, MSPM predicted the performance of the given LTDSE well, and it shows promising potential to model future LTDSE designs, but its accuracy relies sensitively on the heat transfer resistances and seal leakages to be well defined.
  MSPM was used to scale up a similar LTDSE model to an output power of kilowatts, and to model an existing commercial LTDSE. The model gave a reasonable estimate of this engine’s performance, but the accuracy could not be assessed conclusively due to lack of detailed engine specifications and experimental data. This analysis showed that the regenerator plays an important role for engines even with low source temperatures, and MSPM demonstrated its ability to optimize the regenerator properties. The study also indicated that the heat exchangers for an LTDSE should be chosen to minimize flow friction and heat transfer resistances. This favours geometries with large surface areas and short conduction distances such as shell-and-tube heat exchangers.
  The presented studies are limited in scope because mechanical friction and seal leakage were not investigated in detail, and they were based on a small variety of engine and heat exchanger geometries, and only laminar heat exchanger flow conditions. The experimental setup was unsuccessful in measuring the heat exchanger pressure drop, so the effects of flow friction could not be validated. Furthermore, the use of steady state flow correlations out of scope in an oscillating flow system was identified as a weakness of MSPM. The model was also found to produce questionable results with working gases other than air and at high pressures above 120 bar, which limits the scope of the model in its current state. On this basis, future work should validate the pressure drop, investigate and model seal leakage, expand the variety of validation data, implement and validate mechanism models with friction, and review the implementation of working gases and the steady-state assumption in MSPM.

• Subjects / Keywords

  • Stirling engine
  • Low temperature
  • Numerical model
  • Validation
  • Thermodynamics
  • Heat transfer
  • Scaling
  • Experimental

• Graduation date

  Spring 2023

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-45ek-8f98

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.