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Research Papers

# An Axisymmetric Computational Fluid Dynamics Approach to the Analysis of the Working Process of a Solar Stirling Engine

[+] Author and Article Information
K. Mahkamov

School of Engineering, Durham University, South Road, Durham, DH1 3LE UK

J. Sol. Energy Eng 128(1), 45-53 (Feb 25, 2005) (9 pages) doi:10.1115/1.2148979 History: Received July 20, 2004; Revised February 25, 2005

## Abstract

The use of computational fluid dynamics (CFD) models significantly extends the capabilities for the detailed analysis of the complex heat transfer and gas dynamic processes that occur in the internal gas circuit of a Stirling engine by more accurately predicting the engine’s performance. This accurate data on operational characteristics of the engine can then contribute to more precise calculations of the dimensions of a parabolic concentrator in a dish/Stirling engine installation. In this paper a successful axisymmetric CFD simulation of a solar “V”-type Stirling engine is described for the first time. The standard $κ-ε$ turbulence model, with a moving mesh to reflect the reciprocating motion of the pistons, has been employed for the analysis of the engine’s working process. The gas temperature and pressure distributions and velocity fields in the internal gas circuit of the machine have been obtained and the pressure-volume diagrams have been calculated. Comparison of the numerical results produced from the axisymmetric CFD simulation of the engine’s working process with those computed with the use of second-order mathematical analysis shows that there are considerable differences. In particular, analysis of the data obtained indicates that the gas temperature in the compression space depends on the location in the cylinder for the given moment in the cycle and it may differ substantially from being harmonic in time.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 3

Five-chamber calculation scheme of the Stirling engine

Figure 4

Temperature as a function of the crank angle. Te, TH, TR, TC, and Tc are the temperatures of the gas in the expansion space, the heater, the regenerator, the cooler, and in the compression space, respectively; Twe, TwH, TwC, and Twc are the temperatures of the walls of the expansion space, the heater, the cooler, and of the compression space, respectively; TMR is the temperature of the regenerator matrix.

Figure 6

Axisymmetric calculation scheme of the Stirling engine

Figure 7

Computational mesh

Figure 8

(a) Velocity field in the expansion space (left), the regenerator (center), and the compression space (right) for the instant φ=0° and 90°, (b) Velocity field in the expansion space (left), the regenerator (center), and the compression space (right) for the instant φ=180° and 270°

Figure 9

(a) Temperature (K) distribution in the expansion space of the engine for the instant φ=0°, (b) temperature (K) distribution in one of the sections of the heater of the engine for the instant φ=0°, (c) temperature (K) distribution in the compression space of the engine for the instant φ=0°, and (d) temperature (K) distribution in the compression space of the engine for the instant φ=0°

Figure 10

(a) Temperature as a function of the crank angle φ along the radius of the regenerator in its middle plane: Tcenter−r=0m; Tmiddle−r=0.02m; Tedge−r=0.04m. (b) Temperature as a function of the crank angle φ in the compression space: Thc—in the cells next to the head of the cylinder; Tm—in the middle plane of the compression space; Tp—in the cells next to the piston.

Figure 11

Pressure (MPa) distribution (a) in the compression space of the engine for the instant φ=0°; (b) on the surface of the “cold” piston along its radius for the instant φ=0°

Figure 12

Engine’s pressure-volume diagrams computed with the use of the CFD model

Figure 1

Schematic diagram of a 1-kWe Dish/Stirling engine unit

Figure 2

Sketch of a 1-kWe “V”-type Stirling engine. (a) expansion space; (b) compression space; (c) engine’s crankcase; (d) cavity type heater (heat receiver); (e) external surface of the heat receiver; (f) regenerator; (g) cooler; (h) thermoinsulation; (i) piston in the expansion space; (j) piston in the compression space

Figure 5

Engine’s pressure-volume diagrams computed with the use of the second-order model. Pe, Pc are the pressure of the gas in the expansion and compression space, respectively. Li, Ni are the indicated cyclic work and indicated power, respectively.

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