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TECHNICAL PAPERS: Gas Turbines: Cycle Innovations

Basic Limitations on the Performance of Stirling Engines

[+] Author and Article Information
P. C. T. de Boer

Cornell University, Upson Hall, Ithaca, NY 14853

In (24), the amplitude of the pressure on the expansion side was taken to be given. The efficiency corresponding to maximum nondimensional power output then was shown to be half of the Carnot efficiency. If, instead, the amplitude of the pressure on the compression side is taken to be given, the efficiency corresponding to maximum nondimensional power output is considerably higher. This is analogous to the present situation with respect to taking either $Δxh$ or $Δxc$ to be given.

J. Eng. Gas Turbines Power 129(1), 104-113 (Jan 31, 2006) (10 pages) doi:10.1115/1.2204629 History: Received January 26, 2006; Revised January 31, 2006

Abstract

The performance of Stirling engines is subject to limitations resulting from power dissipation in the regenerator. The dissipation is caused by pressure gradients in the regenerator required to generate flow. Without this flow the power output would be zero. Hence the dissipation is an essential element of the operation of the engine. Using linearized theory, the pressure in the compression and expansion spaces is found as a function of the ratio of piston amplitudes and piston phase difference. The regenerator is taken to be thermally perfect. All variations are taken to be sinusoidal in time. Expressions are derived for the dimensionless power output and the thermal efficiency at a given amplitude of the compression piston. Upper bounds on the power output and the efficiency are found as function of frequency and of regenerator void volume. Special attention is given to the case of piston amplitude ratio equal to 1.

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Figures

Figure 1

Sketch of model used for Stirling engine. The high-temperature space is the expansion space, the low-temperature one is the compression space. Lr is the effective length of the void volume of the regenerator.

Figure 2

Nondimensional power outputs P, P∕χ2 and thermal efficiency η∕ηC as function of piston amplitude ratio χ≡δxh∕δxc for the case Th∕Tc=4, F=1, Kcr=1. ϕ was chosen to optimize P.

Figure 3

Nondimensional power output P and thermal efficiency η∕ηC as function of piston amplitude ratio χ≡δxh∕δxc for the case Th∕Tc=4, F=1, Kcr=1. ϕ was chosen to optimize η∕ηC.

Figure 4

Nondimensional power output Pmax and corresponding thermal efficiency η*∕ηC as function of frequency F, at several values of regenerator void volume Kcr

Figure 5

Upper bounds for power output Pmax and corresponding thermal efficiency η*∕ηC as function of regenerator void volume parameter Kcr

Figure 6

Piston amplitude ratio χ* and phase difference ϕ* as function of frequency F, at P=Pmax

Figure 7

Thermal efficiency ηmax∕ηC and corresponding power output P+ as function of frequency F, at several values of relative regenerator void volume Kcr

Figure 8

Thermal efficiency η∕ηC and power output P as function of frequency F, at piston amplitude ratio χ=1, for several values of relative regenerator void volume Kcr

Figure 9

Power output P∞ and thermal efficiency η∕ηC as function of Kcr, at infinite regenerator conductivity Cxr∕Lr and piston amplitude ratio χ=1

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