West number

Last updated

The West number is an empirical 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) for a wide variety of engines, although it may range up to (0.35), [1] particularly for engines operating with a high temperature differential.

The West number may be defined as:

where:

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 TH and TK 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: [2]

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.

Related Research Articles

Carnot heat engine Theoretical engine

A Carnot heat engine is a heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.

Equation of state An equation describing the state of matter under a given set of physical conditions

In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars.

Horsepower Unit of power with different values

Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the mechanical horsepower, which is about 745.7 watts and the metric horsepower, which is approximately 735.5 watts.

In thermodynamics, the specific heat capacity(symbol cp) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample. Specific heat is also sometimes referred to as massic heat capacity. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

Thermodynamic temperature Measure of absolute temperature

Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. A thermodynamic temperature reading of zero is of particular importance for the third law of thermodynamics. By convention, it is reported on the Kelvin scale of temperature in which the unit of measurement is the kelvin. For comparison, a temperature of 295 K is equal to 21.85 °C and 71.33 °F.

The molar gas constant is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.

Ideal gas law Equation of the state of a hypothetical ideal gas

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:

Otto cycle Thermodynamic cycle for spark ignition piston engines

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 15 °C, air has a density of approximately 1.225 kg/m3, about 1/800 that of water according to ISA.

Compressor Machine to increase pressure of gas by reducing its volume

A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor.

Rankine cycle

The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat source and heat sink. The Rankine cycle is named after William John Macquorn Rankine, a Scottish polymath professor at Glasgow University.

Density altitude

The density altitude is the altitude relative to standard atmospheric conditions at which the air density would be equal to the indicated air density at the place of observation. In other words, the density altitude is the air density given as a height above mean sea level. The density altitude can also be considered to be the pressure altitude adjusted for a non-standard temperature.

The mean effective pressure (MEP) is a quantity relating to the operation of a reciprocating engine and is a measure of an engine's capacity to do work that is independent of engine displacement. When quoted as an indicated mean effective pressure (IMEP), it may be thought of as the average pressure acting on a piston during the different portions of its cycle.

Thermodynamic cycle Linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state

A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. At every point in the cycle, the system is in thermodynamic equilibrium, so the cycle is reversible.

Thermal efficiency Performance measure of a device that uses thermal energy

In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace,refrigerator, ACs etc.

Rocket engine nozzle Type of propelling nozzle

A rocket engine nozzle is a propelling nozzle used in a rocket engine to expand and accelerate combustion products to high supersonic velocities.

In aircraft and rocket design, overall propulsion system efficiency is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. Mathematically, it is represented as , where is the cycle efficiency and is the propulsive efficiency.

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 differential, typical values for the Beale number are in the range 0.11−0.15; where a larger number indicates higher performance.

Heat pump and refrigeration cycle Mathematical models of heat pumps and refrigeration

Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pump, air conditioning and refrigeration systems. A heat pump is a mechanical system that allows for the transmission of heat from one location at a lower temperature to another location at a higher temperature. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink, or a "refrigerator" or “cooler” if the objective is to cool the heat source. In either case, the operating principles are similar. Heat is moved from a cold place to a warm place.

Temperature Physical quantity that expresses hot and cold

Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder or hotter. Temperature should not be confused with heat.

References

  1. "Simple Performance Prediction Method -English-".
  2. ornl-tm-10475