Stirling Cycle and Engines Bryan Tibbetts California State University, Sacramento Fall 2012

Reverend Dr. Robert Stirling Born: October 25, 1790 Died: June 6, 1878 Studied divinity at the University of Glasgow and the University of Edinburgh. Became a minister of the Church of Scotland. Obtained a patent for his “Heat Economiser” in 1816. “Heat Economiser” now called the regenerator. Built first practical engine in 1818 used to pump water out of a quarry. The thermodynamic cycle driving Stirling’s engine was not completely understood until the work of Sadi Carnot (1796 - 1832) and was named the Stirling Cycle.

Ideal Stirling Cycle 1  2: Isometric heat addition 2 Stirling Cycle P-V Diagram 1  2: Isometric heat addition P 2 2  3: Isothermal expansion T = const QR Qin 3  4: Isometric heat rejection 3 4  1: Isothermal compression 1 QR Qout T = const 4 Cycle is reversible, and so can be mechanically powered to operate as a heat pump for cooling. V

Ideal Stirling Cycle 2 3 1 4 Stirling Cycle P-V Diagram P T = const QR Qin 3 1 QR Qout T = const 4 V

Ideal Stirling Cycle 2 3 1 4 Stirling Cycle P-V Diagram P T = const QR Qin 3 1 QR Qout T = const 4 V

Ideal Stirling Cycle 2 3 1 4 Stirling Cycle P-V Diagram P T = const QR Qin 3 1 QR Qout T = const 4 V

Regenerator 2 3 1 4 Stirling Cycle P-V Diagram P T = const QR Qin QR Qout T = const 4 V

Thermodynamic Optimization of a Stirling Engine Authors: M.C. Campos, J.V.C. Vargas, J.C. Ordonez Model based on Ford-Philips 4-215 engine

Thermodynamic Optimization of a Stirling Engine Authors: M.C. Campos, J.V.C. Vargas, J.C. Ordonez Dimensionless Equations Describing System Solved numerically using an adaptive time step fourth-fifth order Runge-Kutta method

Thermodynamic Optimization of a Stirling Engine Authors: M.C. Campos, J.V.C. Vargas, J.C. Ordonez Optimized Efficiency and Work Plot Two-way maximized system efficiency (ηmax,max) based on optimization of two system characteristic parameters, φ and y. φ is the ratio of the swept expansion volume over the total swept volume. y is the ratio of the hot side heat transfer area over the total heat transfer area.

Finite Time Thermodynamic Evaluation of Endoreversible Stirling Heat Engine at Maximum Power Conditions Author: Iskander Tlili Finite Time Thermodynamic analysis accounts for a finite temperature difference between the hot and cold sources and the working fluid of the engine (required for heat transfer to occur) and the finite amount of heat transferred in a finite time period per process.

Finite Time Thermodynamic Evaluation of Endoreversible Stirling Heat Engine at Maximum Power Conditions Author: Iskander Tlili Regenerator effectiveness only effects Thermal Efficiency Hot and cold side heat exchanger effectiveness only effects maximum power output

Finite Time Thermodynamic Evaluation of Endoreversible Stirling Heat Engine at Maximum Power Conditions Author: Iskander Tlili Temperatures of the external hot and cold source fluids effect both the thermal efficiency and maximum power output

Model based on General Motors GPU-3 engine Thermodynamic Study on Optimal Solar Stirling Engine Cycle Taking Into Account the Irreversibilities Effects Author: Iskander Tlili Model based on General Motors GPU-3 engine

Equations Describing System Thermodynamic Study on Optimal Solar Stirling Engine Cycle Taking Into Account the Irreversibilities Effects Author: Iskander Tlili Equations Describing System

Thermodynamic Study on Optimal Solar Stirling Engine Cycle Taking Into Account the Irreversibilities Effects Author: Iskander Tlili Results

Oscillating Flow in a Stirling Engine Heat Exchanger Authors: M. Kuosa, K. Saari, A. Kankkunen, T.-M. Tveit Problem Approached No correlations existed for calculating heat transfer coefficient and friction factor in oscillating flow Annular Effect occurs in oscillating flow in a pipe, which is the maximum flow velocity occurs near the wall instead of the center of the pipe Fluid flow in a Stirling engine is comprised of laminar, transitional, and turbulent flows during every cycle Pressure losses for various geometries were also analyzed:

Oscillating Flow in a Stirling Engine Heat Exchanger Authors: M. Kuosa, K. Saari, A. Kankkunen, T.-M. Tveit Equations

Oscillating Flow in a Stirling Engine Heat Exchanger Authors: M. Kuosa, K. Saari, A. Kankkunen, T.-M. Tveit Nu vs. Re plot

Oscillating Flow in a Stirling Engine Heat Exchanger Authors: M. Kuosa, K. Saari, A. Kankkunen, T.-M. Tveit Results The pressure losses and Nusselt numbers were examined to determine that designs which form thinner boundary layers along the length of heat exchanger tubes but do not significantly increase the dead volume space or pressure losses are recommended

Analytical Model for Predicting the Effect of Operating Speed on Shaft Power Output of Stirling Engines Authors: Chin-Hsiang Cheng, Hang-Suin Yang

Analytical Model for Predicting the Effect of Operating Speed on Shaft Power Output of Stirling Engines Authors: Chin-Hsiang Cheng, Hang-Suin Yang

Analytical Model for Predicting the Effect of Operating Speed on Shaft Power Output of Stirling Engines Authors: Chin-Hsiang Cheng, Hang-Suin Yang

Analytical Model for Predicting the Effect of Operating Speed on Shaft Power Output of Stirling Engines Authors: Chin-Hsiang Cheng, Hang-Suin Yang

Questions? References: M.C. Campos, J.V.C. Vargas, J.C. Ordonez, Thermodynamic optimization of a Stirling engine, Energy, Volume 44, Issue 1, August 2012, Pages 902-910, ISSN 0360-5442, 10.1016/j.energy.2012.04.060. Iskander Tlili, Finite time thermodynamic evaluation of endoreversible Stirling heat engine at maximum power conditions, Renewable and Sustainable Energy Reviews, Volume 16, Issue 4, May 2012, Pages 2234-2241, ISSN 1364-0321, 10.1016/j.rser.2012.01.022. Iskander Tlili, Thermodynamic Study on Optimal Solar Stirling Engine Cycle Taking Into Account the Irreversibilities Effects, Energy Procedia, Volume 14, 2012, Pages 584-591, ISSN 1876-6102, 10.1016/j.egypro.2011.12.979. M. Kuosa, K. Saari, A. Kankkunen, T.-M. Tveit, Oscillating flow in a stirling engine heat exchanger, Applied Thermal Engineering, Volumes 45–46, December 2012, Pages 15-23, ISSN 1359-4311, 10.1016/j.applthermaleng.2012.03.023. Chin-Hsiang Cheng, Hang-Suin Yang, Analytical model for predicting the effect of operating speed on shaft power output of Stirling engines, Energy, Volume 36, Issue 10, October 2011, Pages 5899-5908, ISSN 0360-5442, 10.1016/j.energy.2011.08.033.