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The '''West number''' is an empirical parameter used to characterize the performance of '''[[Stirling engine]]s''' 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 (physics)|power]] output of a Stirling engine. The average value is (0.25) [http://www.ornl.gov/~webworks/cppr/y2001/rpt/27113.pdf] for a wide variety of engines, although it may range up to (0.35) [http://www.bekkoame.ne.jp/~khirata/academic/simple/simplee.htm], particularly for engines operating with a high [[temperature]] differential.
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The West number may be defined as:
 
:<math>W_n = \frac{Wo}{P V f} \frac{(T_H + T_K)}{(T_H - T_K)} = B_n \frac{(T_H + T_K)}{(T_H - T_K)}</math>
 
where:
*'''W<sub>n</sub>''' is the West number
*'''W<sub>o</sub>''' is the power output of the engine ([[watt]]s)
*'''P''' is the [[Arithmetic_mean|mean average]] gas [[pressure]] ([[Pascal (unit)|Pa]]) or ([[MPa]], if volume is in cm<sup>3</sup>)
*'''V''' is swept [[volume]] of the expansion space (m<sup>3</sup>) or (cm³, if pressure is in MPa)
*'''f''' is the engine cycle [[frequency]] ([[Hertz|Hz]])
*'''T<sub>H</sub>''' is the absolute [[temperature]] of the expansion space or [[heater]] ([[kelvin]]s)
*'''T<sub>K</sub>''' is the absolute temperature of the compression space or cooler (kelvins)
*'''B<sub>n</sub>''' is the [[Beale number]] for an engine operating between temperatures ''T''<sub>''H''</sub> and ''T''<sub>''K''</sub> 
 
When the Beale number is known, but the West number is not known, it is possible to calculate it. First calculate the West number at the temperatures ''T''<sub>''H''</sub> and ''T''<sub>''K''</sub> for which the Beale number is known, and then use the resulting West number to calculate output power for other temperatures.
 
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:
 
:<math>W_o = W_n P V f \frac{(T_H - T_K)}{(T_H + T_K)} </math> <ref>[http://www.ornl.gov/~webworks/cppr/y2001/rpt/27113.pdf ornl-tm-10475<!-- Bot generated title -->]</ref>
 
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.
 
== References ==
<references/>
 
==External links==
* [http://www.bekkoame.ne.jp/~khirata/academic/simple/simplee.htm Stirling Engine Performance Calculator]
 
{{heat engines}}
 
[[Category:Dimensionless numbers]]
[[Category:Piston engines]]
[[Category:Mechanical engineering]]

Latest revision as of 23:32, 24 November 2014

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