C.O.P. of simple air cycle Calculator

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Air Refrigeration Systems

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Reduced Ambient Air Cooling System

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✖Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments.ⓘ Inside temperature of cabin [T₆]			+10% -10%
✖Actual temperature at end of isentropic expansion is the exit temperature of the cooling turbine and is the temperature at which the refrigeration process starts.ⓘ Actual temperature at end of isentropic expansion [T5^']			+10% -10%
✖Actual End Temp of Isentropic Compression is greater than the ideal temperature.ⓘ Actual End Temp of Isentropic Compression [Tt^']			+10% -10%
✖Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.ⓘ Actual temperature of Rammed Air [T2^']			+10% -10%

✖The actual coefficient of Performance is the ratio of the actual cooling effect produced to the actual power consumption.ⓘ C.O.P. of simple air cycle [COP_actual]

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Formula

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C.O.P. of simple air cycle

Formula

`"COP"_{"actual"} = ("T"_{"6"}-"T5"^{"'"})/("Tt"^{"'"}-"T2"^{"'"})`

Example

`"0.064935"=("270K"-"265K")/("350K"-"273K")`

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C.O.P. of simple air cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)
COP_actual = (T₆-T5^')/(Tt^'-T2^')
This formula uses 5 Variables

Variables Used

Actual Coefficient of Performance - The actual coefficient of Performance is the ratio of the actual cooling effect produced to the actual power consumption.
Inside temperature of cabin - (Measured in Kelvin) - Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments.
Actual temperature at end of isentropic expansion - (Measured in Kelvin) - Actual temperature at end of isentropic expansion is the exit temperature of the cooling turbine and is the temperature at which the refrigeration process starts.
Actual End Temp of Isentropic Compression - (Measured in Kelvin) - Actual End Temp of Isentropic Compression is greater than the ideal temperature.
Actual temperature of Rammed Air - (Measured in Kelvin) - Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.

STEP 1: Convert Input(s) to Base Unit

Inside temperature of cabin: 270 Kelvin --> 270 Kelvin No Conversion Required
Actual temperature at end of isentropic expansion: 265 Kelvin --> 265 Kelvin No Conversion Required
Actual End Temp of Isentropic Compression: 350 Kelvin --> 350 Kelvin No Conversion Required
Actual temperature of Rammed Air: 273 Kelvin --> 273 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

COP_actual = (T₆-T5^')/(Tt^'-T2^') --> (270-265)/(350-273)

Evaluating ... ...

COP_actual = 0.0649350649350649

STEP 3: Convert Result to Output's Unit

0.0649350649350649 --> No Conversion Required

FINAL ANSWER

0.0649350649350649 ≈ 0.064935 <-- Actual Coefficient of Performance

(Calculation completed in 00.020 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Air Refrigeration Systems » C.O.P. of simple air cycle

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Created by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

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National Institute Of Technology (NIT), Hamirpur

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< 17 Air Refrigeration Systems Calculators

Power required to maintain pressure inside cabin excluding ram work

Go Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Actual temperature of Rammed Air)/(Compressor Efficiency))*((Cabin Pressure/Pressure of Rammed Air)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

Power Required to Maintain Pressure inside Cabin including Ram Work

Go Input Power = ((Mass of Air*Specific Heat Capacity at Constant Pressure*Ambient Air Temperature)/(Compressor Efficiency))*((Cabin Pressure/Atmospheric Pressure)^((Heat Capacity Ratio-1)/Heat Capacity Ratio)-1)

C.O.P. of simple air evaporative cycle

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))

C.O.P. of simple air cycle

Go Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)

Mass of air to produce Q tonnes of refrigeration given exit temperature of cooling turbine

Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Temperature at End of Isentropic Expansion-Actual exit Temperature of cooling turbine))

Mass of air to produce Q tonnes of refrigeration

Go Mass of Air = (210*Tonnage of Refrigeration in TR)/(Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion))

Expansion Work

Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Temperature at the end of cooling process-Actual temperature at end of isentropic expansion)

Refrigeration Effect Produced

Go Refrigeration Effect Produced = Mass of Air*Specific Heat Capacity at Constant Pressure*(Inside temperature of cabin-Actual temperature at end of isentropic expansion)

Heat rejected during cooling process

Go Heat Rejected = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Temperature at the end of cooling process)

Compression Work

Go Work Done per min = Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air)

Power Required for Refrigeration System

Go Input Power = (Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))/60

Temperature Ratio at Start and End of Ramming Process

Go Temperature Ratio = 1+(Velocity^2*(Heat Capacity Ratio-1))/(2*Heat Capacity Ratio*[R]*Initial Temperature)

Ram Efficiency

Go Ram Efficiency = (Stagnation Pressure of System-Initial Pressure of System)/(Final Pressure of System-Initial Pressure of System)

Local Sonic or Acoustic Velocity at Ambient Air Conditions

Go Sonic Velocity = (Heat Capacity Ratio*[R]*Initial Temperature/Molecular Weight)^0.5

Initial Mass of Evaporant Required to be Carried for given Flight Time

Go Mass = (Rate of Heat Removal*Time in Minutes)/Latent Heat of Vaporization

COP of Air Cycle for given Input Power and Tonnage of Refrigeration

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

COP of Air Cycle given Input Power

Go Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)

C.O.P. of simple air cycle Formula

How do you calculate coefficient of performance?

You can calculate the coefficient of performance by dividing how much energy a system produces by the amount of energy you input into the system. This coefficient of performance formula applies across fields.

How to Calculate C.O.P. of simple air cycle?

C.O.P. of simple air cycle calculator uses Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air) to calculate the Actual Coefficient of Performance, The C.O.P. of simple air cycle formula is the simplified form of the ratio of refrigeration effect produced to the work done. Actual Coefficient of Performance is denoted by COP_actual symbol.

How to calculate C.O.P. of simple air cycle using this online calculator? To use this online calculator for C.O.P. of simple air cycle, enter Inside temperature of cabin (T₆), Actual temperature at end of isentropic expansion (T5^'), Actual End Temp of Isentropic Compression (Tt^') & Actual temperature of Rammed Air (T2^') and hit the calculate button. Here is how the C.O.P. of simple air cycle calculation can be explained with given input values -> 0.064935 = (270-265)/(350-273).

FAQ

What is C.O.P. of simple air cycle?

The C.O.P. of simple air cycle formula is the simplified form of the ratio of refrigeration effect produced to the work done and is represented as COP_actual = (T₆-T5^')/(Tt^'-T2^') or Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air). Inside temperature of cabin is the temperature inside the aircraft due to the occupancy and heating equipments, Actual temperature at end of isentropic expansion is the exit temperature of the cooling turbine and is the temperature at which the refrigeration process starts, Actual End Temp of Isentropic Compression is greater than the ideal temperature & Actual temperature of Rammed Air is equal to the ideal temperature of Rammed Air.

How to calculate C.O.P. of simple air cycle?

The C.O.P. of simple air cycle formula is the simplified form of the ratio of refrigeration effect produced to the work done is calculated using Actual Coefficient of Performance = (Inside temperature of cabin-Actual temperature at end of isentropic expansion)/(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air). To calculate C.O.P. of simple air cycle, you need Inside temperature of cabin (T₆), Actual temperature at end of isentropic expansion (T5^'), Actual End Temp of Isentropic Compression (Tt^') & Actual temperature of Rammed Air (T2^'). With our tool, you need to enter the respective value for Inside temperature of cabin, Actual temperature at end of isentropic expansion, Actual End Temp of Isentropic Compression & Actual temperature of Rammed Air and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Actual Coefficient of Performance?

In this formula, Actual Coefficient of Performance uses Inside temperature of cabin, Actual temperature at end of isentropic expansion, Actual End Temp of Isentropic Compression & Actual temperature of Rammed Air. We can use 3 other way(s) to calculate the same, which is/are as follows -

Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)
Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Input Power*60)
Actual Coefficient of Performance = (210*Tonnage of Refrigeration in TR)/(Mass of Air*Specific Heat Capacity at Constant Pressure*(Actual End Temp of Isentropic Compression-Actual temperature of Rammed Air))

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