West number

The West number is an emperical parameter used to characterize the performance of Stirling engines, and other Stirling systems. It is very similar to the Beale number where a larger number indicates higher performance; however, the West number includes temperature compensation. The West number is often used to approximate of the power output of a Stirling engine. The average value is (0.25) [1] for a wide variety of engines, although it may range up to (0.35) [2], particularly for engines operating with a high temperature differential.

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The West number may be defined as:

where:

• W_n is the West number
• W_o is the power output of the engine (watts)
• P is the mean average gas pressure (Pa) or (MPa, if volume is in cm³)
• V is swept volume of the expansion space (m³) or (cm³, if pressure is in MPa)
• f is the engine cycle frequency (Hz)
• T_H is the absolute temperature of the expansion space or heater (kelvin)
• T_K is the absolute temperature of the compression space or cooler (kelvin)

To estimate the power output of a new engine design, nominal values are assumed for the West number, pressure, swept volume and frequency, and the power is calculated as follows:

[3]

For example, with an absolute temperature ratio of 2, the portion of the equation representing temperature correction equals 1/3. With a temperature ratio of 3, the temperature term is 1/2. This factor accounts for the difference between the West equation, and the Beale equation in which this temperature term is taken as a constant. Thus, the Beale number is typically in the range of 0.10 to 0.15, which is about 1/3 to 1/2 the value of the West number.

See also

• Beale Number