The West number is an empirical parameter used to characterize the performance of
Stirling engine
A Stirling engine is a heat engine that is operated by the cyclic compression and expansion of air or other gas (the ''working fluid'') between different temperatures, resulting in a net conversion of heat energy to mechanical work.
More specif ...
s and other Stirling systems. It is very similar to the
Beale number
In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power output of a Stirling engine design. For engines operating with a high temperature differenti ...
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
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
output of a Stirling engine. The average value is (0.25) for a wide variety of engines, although it may range up to (0.35), particularly for engines operating with a high
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
differential.
The West number may be defined as:
:
where:
* ''W
n'' is the West number
* ''W
o'' is the power output of the engine (
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
s)
* ''P'' is the
mean average gas
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
(
Pa) or (
MPa, if volume is in cm
3)
* ''V'' is swept
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
of the expansion space (m
3, or cm³, if pressure is in MPa)
* ''f'' is the engine cycle
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
(
Hz)
* ''T''
H is the absolute
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
of the expansion space or
heater
Heating, ventilation, and air conditioning (HVAC) is the use of various technologies to control the temperature, humidity, and purity of the air in an enclosed space. Its goal is to provide thermal comfort and acceptable indoor air quality. ...
(
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
s)
* ''T''
K is the absolute temperature of the compression space or cooler (kelvins)
* ''B
n'' is the
Beale number
In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power output of a Stirling engine design. For engines operating with a high temperature differenti ...
for an engine operating between temperatures ''T''
H and ''T''
K
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''
H and ''T''
K 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:
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:
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
External links
{{heat engines
Dimensionless numbers
Piston engines
Mechanical engineering