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: