West number

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The West number is a 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], but may range up to (0.35) [2], particularly for engines operating with a high temperature differential.

The West number may be defined as:

$W_n = \frac{Wo}{P V N} \frac{(T_H + T_K)}{(T_H - T_K)}$

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)
N 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: