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RESEARCH PAPERS

Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling

[+] Author and Article Information
K. Mahkamov

School of Engineering, Durham University, Durham, DH1 3LE, UKkhamid.mahkamov@durham.ac.uk

J. Energy Resour. Technol 128(3), 203-215 (Sep 16, 2005) (13 pages) doi:10.1115/1.2213273 History: Received April 26, 2005; Revised September 16, 2005

A prototype of a biomass Stirling engine was developed and manufactured by an industrial company prior to the numerical investigations described in this paper. Dimensions and performance of the prototype had originally been estimated using the company’s own simplified “first-order” mathematical model of the engine’s working cycle. The manufactured engine was experimentally tested, and the results demonstrated that the power output from the machine was far less than expected. To understand what caused the engine’s low operational characteristics and to predict how to refine the design, more advanced numerical investigations of the working process of the engine were performed. This utilized a “second-order” type 5 control volumes model, together with three-dimensional computational fluid dynamics modeling. As an outcome of this study, several recommendations on to how alter the prototype’s design were forthcoming, which, in practice, allow significant improvements in the engine’s performance.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 8

A CFD grid for the γ engine for the instance when the power piston is in its bottom dead center and the displacer is in its middle position and moving upwards. (1) the heater; (2) the heater’s manifold; (3) the regenerator; (4) the coolers; (5) the expansion space; (6,7) the first and second parts of the compression space, respectively; (8) the connecting pipe.

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Figure 1

A general scheme of the original “gamma” biomass Stirling engine. 1-a “hot” cylinder; 2-a “cold” cylinder; 3-a displacer; 4-a power piston; 5,6-the first and second parts of the compression space, respectively; 7-a connecting pipe; 8-an expansion space; 9-a heater; 10,11-heater’s manifolds; 12-a regenerator; 13-a cooler.

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Figure 2

A 5 control volumes calculation scheme of the engine in the second-order mathematical model

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Figure 3

The variation of the volumes in the expansion (Ve) and compression (Vc) spaces of the original γ engine over the cycle

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Figure 4

The variation of the gas temperature in the five control volumes of the original γ engine. Results of the second-order mathematical model simulation for the cycle with the maximum pressure of ∼2MPa at the speed 240rpm(4Hz), the regenerator’s porosity is 31%. Te, TH, TR, TC, and Tc are the temperature of the gas in the expansion space, the heater, the regenerator, the cooler, and in the compression space, respectively.

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Figure 5

The variation of the pressure losses across the heat exchangers of the original γ engine. Results of the second-order mathematical model simulation for the cycle with the maximum pressure of ∼2MPa at the speed 240rpm(4Hz), the regenerator’s porosity is 31%. ΔPC, ΔPR, ΔPH-pressure losses in the channels of the cooler, regenerator, and heater, respectively; ΔPsum-total pressure losses in the heat exchangers.

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Figure 6

Pressure-volume diagrams of the original γ engine. Results of the second-order mathematical model simulation for the cycle with the maximum pressure of ∼2MPa at the speed 240rpm(4Hz), the regenerator’s porosity is 31%. PeVe and PcVc are the pressure-volume diagrams in the expansion and compression space, respectively; Ni and n are the indicated power and speed of the engine, respectively.

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Figure 7

The indicated power of the original γ Stirling engine as a function of the crankshaft speed. Results of the second-order mathematical model simulation for the cycles with the maximum pressure of ∼2MPa, the regenerator’s porosity is 31%.

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Figure 9

The velocity distribution in the first (a) and second (b) parts of the compression space of the original γ engine for the instance when the power piston is in its bottom dead centre and the displacer is in its middle position and moving upward. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa at the speed of 200rpm(3.33Hz).

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Figure 10

The temperature (K) distribution in the internal gas circuit of the original γ engine for different positions in the cycle. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa at the speed of 200rpm(3.33Hz). (a) The power piston is in its bottom dead center, the displacer is in its middle position and moving upwards; (b) the power piston is in its middle position and moving upwards, the displacer is in its top dead center; (c) the power piston is in its top dead center, the displacer is in its middle position and moving downward; and (d) the power piston is in its middle position and moving downwards, the displacer is in its bottom dead center.

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Figure 11

The variation of the gas temperature over the cycle in different locations in the internal gas circuit of the original γ engine. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa at the speed of 200rpm(3.33Hz). T1-the center of the entrance to the expansion space, T2-in the middle of the outer heater tube in the first row from the expansion space, T3-in the middle of the regenerator along its length, T4-in the middle of the cooler along its length; T5-in the centre at the top of the compression space in the cold cylinder, T6-in the middle of the connecting pipe, and T7-in the centre of the bottom of the compression space under the displacer.

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Figure 12

The pressure (Pa) distribution in the internal gas circuit of the original γ engine for the instance when the power piston is in its bottom dead centre and the displacer is in its middle position and moving upward. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa at the speed of 200rpm(3.33Hz).

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Figure 13

The variation of the gas pressure over the cycle in different locations in the internal gas circuit of the original γ engine. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa at the speed of 200rpm(3.33Hz).

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Figure 14

The pressure-volume diagrams of the original γ engine. The CFD simulation results for the cycle with the maximum pressure of ∼2.2MPa and at the speed of 200rpm(3.33Hz). P1V1-The pressure-volume diagram for the expansion space; P2V2-The pressure-volume diagram for the first part of the compression space; P3V3-The pressure-volume diagram for the second part of the compression space.

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Figure 15

The indicated power of the α Stirling engine as a function of the crankshaft speed. The second-order mathematical simulation results of cycles with the maximum pressure of ∼2.1MPa, the regenerator’s porosity is 40%.

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Figure 16

A CFD grid for the α engine for the instance when the power piston is in its bottom dead centre and the displacer is in its middle position and moving upward.

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Figure 17

The pressure-volume diagrams of the α engine. The CFD simulation results for the cycle with the maximum pressure of ∼2MPa and at the speed of 300rpm(5Hz), the regenerator’s porosity is 40%. PeVe and PcVc are the pressure-volume diagrams in the expansion and compression space, respectively; Ni and n are the indicated power and speed of the engine, respectively.

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