Working Fluids
The working fluid of the Stirling engine should possess high specific heat capacity low viscosity and high thermal conductivity.
Clarke et al in [98] defined the capability factor for working fluid in relation to the specific heat capacity, density and thermal conductivity. This capability is defined as:
Capability factor = thermal conductivity/ specific heat capacity × density of the working fluid
Tables 3.1 and 3.2 shows the relative heat transfer capability of various gases and the relative performance of selected working fluids.
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The Stirling engines require a mechanism to control and regulate the power output, their speed and torque. The basic methods which can be used for power control are: (i) Mean pressure variation, (ii) Variation in temperature of the working fluid, (iii) Variation in the phase angle, (iv) Variation of the dead volume and (v) Variation of the piston strokes.
Table 3.1: Relative heat transfer characteristics of various gases [99].
Working fluid Heat transfer Capability factor
Air 1.0 1.0
Helium 1.42 0.83
Hydrogen 3.42 0.68
Water 1.95 0.39
Table 3.2: Relative performance of selected working fluid [99].
Gas Nominal molar mass M (kg/kmol) Gas constant R ( kJ/kg K) Specific heat Cp (kJ/kg K) Specific heat Cv (kJ/kg K) Specific heat ratio (Cp/Cv) H2 1 4.12 14.20 10.08 1.41 He 4 2.08 5.19 3.11 1.67 Ne 20 0.415 1.03 0.62 1.66 N2 28 0.297 1.04 0.74 1.4 CO 28 0.297 1.04 0.75 1.4 Air 29 0.287 1.01 0.72 1.4 O2 32 0.260 0.92 0.66 1.4 Ar 40 0.208 0.52 0.31 1.67 CO2 44 0.189 0.85 0.66 1.28
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Mean pressure variation
The output power of the Stirling engine is directly proportional to the cyclic mean pressure of the working fluid. The variation in mean cyclic pressure is not easy to achieve in reality. To achieve this, a gas compressor or gas storage compartment is required in the engine system. To increase power output the working fluid will be supplied to the engine from the storage compartment of from the compressor and to minimize power, the working fluid will be transferred to a reservoir. Such control of the engine is difficult to implement in real life practice due to complexity of the timing of controlling valves opening and closing.
Variation in the temperature of working fluid
The maximum temperature of the working fluid which depends on the heater’s temperature can be used to control the output power of the engine. For example, this can be controlled by adjusting the fuel flow, but temperature change results in prolonged time reaction time.
Variation of the dead volume
The output power of the Stirling engine can be changed if the dead volume is increased or decreased, thereby reducing or increasing the pressure’s amplitude during operation. The effects of the dead volume variation on the performance of Stirling engine was analysed by Erbay [16] using polytrophic processes. The increase in the dead volume within a Stirling engine system results in reduction in output power but does not necessarily reduce the efficiency of the system. However the efficiency can be reduced when there is a considerable amount of dead volume variation. This was observed in the investigation carried out on the DVV (dead volume variation) system developed by United Stirling engine (Alm et al cited [100]). A significant number of gas spaces were incorporated into the main engine block and coupled to the internal working space using ducts with valves in
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the engine. The capacity of the dead volume was controlled with the extra spaces to give the required amount of dead spaces possible. The system was employed to control one of the first developed United Stirling engines used in a Ford Pinto automobile.
Variation of Stroke
The stroke of the reciprocating piston and displacer can be controlled so as to regulate the output power of the engine. It is suitable for all Stirling engines (single, double acting and free piston Stirling engines). Such method of controlling power output of the engine is widespread in existing engines.
Variation in phase angle
One of the most effective ways of controlling the output power of Stirling engines is the variation of the phase angle. The phase angle is the angle between the oscillations or displacements of the displacer and power piston. The total engine volume variation depens on the phase angle and can be reduced if the phase angle is different from the optimal one. This method can be applied to a single acting machines though requires complex modifications in the kinematical mechanism. However, for double acting engines the variation of phase angle is not applicable.
Effectiveness of the regenerator
The regenerator of the Stirling engines must be designed so that area of the regenerator matrix should have an optimal porosity to balance heat accumulating capacity and minimize gas flow losses. Usually not all the working fluid pass through the regenerator matrix, while some remaining and oscillating inside the regenerator.
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Material of the regenerator
The performance of the Stirling engine is influenced by the material used for the regenerator matrix. Usually ceramic and metallic materials are used in the regenerator. Ceramics have a lower rate of permeation than metals. Hence, the efficiency of engines with regenerator made of ceramic coated materials are higher than that with metallic regenerators.
Leakage of the working fluid
In reality the leakage of working fluid in an engine cannot be avoided. Pertescu [32] analysed the effect of pressure loss due to the working fluid leakage during engine operation.
Fluid friction
The regenerator of Stirling engines is very often the source of the highest fluid friction. Isshiki [101] and Muralidhar [102] derived equations to calculate the friction factor of a stacked wire mesh as a function of Reynolds number. The investigation carried out showed that there is a substantial increase in the heat transfer and flow resistance in oscillatory flow in wire meshes of regenerator in Stirling engines.
Engine dynamics
Heat engines analysis requires simultaneous consideration of heat transfer processes and dynamics. The slider-crank mechanism is mostly used in conventional engines, while the Stirling engines employ different forms of drive mechanisms. A general method for Stirling engine optimisation for different engine configurations and operating conditions was presented by Shoureshi in [103]. Gary et al in [104] demonstrated that the engine configuration suitability depends mainly on some certain factors such as output power,
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type of fuel, engine speed etc. The relationships for calculation of mechanical efficiency of Stirling engines were investigated by Senft in [105]. Results can be employed for selection of engine mechanism to suit the required application and output.