A Modular Numerical Model for Stirling Engines and Single-Phase Thermodynamic Machines

• Author / Creator

  Middleton, Steven Mark William

• A numerical model and software interface for the design and modelling of Stirling engines was
  presented. This model was developed to suit low-temperature Stirling engines, those that run at
  source temperature of less than 150 °C and run at speeds where temporarily developed losses
  become significant. The work had three objectives. The first was to create a combined mechanical
  and thermodynamic model to solve dynamic problems. The second objective was to provide
  graphical feedback during creation of the geometry and reviewing of a solution. The third objective
  was to test the model against experimental data taken from a low-temperature gamma-type engine
  and compare the model against another numerical code.
  The resulting model, called the modular single-phase model or MSPM, incorporated a uniform
  pressure assumption which was used to solve the instantaneous flow rates in a one-dimensional
  network of pipes. The flow network is generated automatically from arbitrary arrangements of
  cylindrical or annular extrusions created by the user, within which the solid heat conduction is
  solved in 2-dimensions. Angular position dependent deformations are driven by the mechanical
  system, which responded to the forces generated by the gas system. This scheme transferred
  impulses from the gas network after short increments, which then defined the dynamics next
  increment. To capture flow losses pressure drops are approximated from gas velocities and the
  modified pressures are used to calculate the mechanism response.
  The software itself presents the user with graphical feedback like that found in CAD software.
  This makes it possible to generate informative animations of the moving boundaries of an engine.
  These animations carry forward into the output of the code, presenting temperature, pressure,
  turbulence, heat flow, flow direction and pressure drop in spatially relevant positions on the virtual
  engine cross-section. The user can also place sensors, reuse previous simulation data, and run batch
  tests and optimize engine geometry using the software.
  When the uncalibrated model was compared against experimental results featuring an in-lab
  engine running at 0.56 to 2.26 Hz, this numerical code developed a maximum discrepancy of
  43.1% with an average deviation from the experimental results of 30.6%. An exploratory
  calibration of the effects of compression was conducted drawing on conclusions from the initial tests, resulting in an overall improvement of the accuracy to an average of 21.9%. The final
  discrepancy is largely systematic, possibly correctable with reasonable adjustments to the
  automatically generated convection and friction terms. A sensitivity study of the properties related
  to heat transfer and friction was presented at two different speeds, the results indicated that the
  most substantial and predictable effector of power was the convection coefficient. Flow friction
  became a larger contributed at higher speeds. The code was then compared against SAGE, the
  numerical code of choice, with 5 tests at 16.7 Hz and 50 bar and with source temperatures ranging
  from 150 °C to 750 °C. Over these tests MSPM produced a maximum error of 59.1% and an
  average deviation of 33.5%. When compared against a second patch of in-lab produced SAGE
  results at slow speeds the two models diverged, it was concluded that the two models featured very
  different flow loss characteristics at low speeds among a variety of other differences. In a final
  experiment the optimal design of a beta type Stirling engine was obtained using the geometrical
  optimization tool within MSPM the results and design process of the beta type engine was
  presented.

• Subjects / Keywords

  • Stirling Engine
  • Thermodynamics
  • Numerical Modelling
  • Dynamic Modelling
  • 3rd Order Model

• Graduation date

  Fall 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-x8qd-p159

• 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.