Thermal Efficiency of Atkinson Cycle Calculator

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✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Expansion ratio is the ratio of larger volume to lesser volume during an expansion process, i.e. ratio of volume after expansion to the volume before expansion.ⓘ Expansion Ratio [e]			+10% -10%
✖Compression ratio is ratio of volume of cylinder to volume combustion chamber.ⓘ Compression Ratio [r]			+10% -10%

✖Thermal Efficiency of Atkinson Cycle (in %) represents the fraction of heat converted into useful work in an engine following the Atkinson cycle.ⓘ Thermal Efficiency of Atkinson Cycle [η_atkinson]

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Thermal Efficiency of Atkinson Cycle

Formula

`"η"_{"atkinson"} = 100*(1-"γ"*(("e"-"r")/("e"^("γ")-"r"^("γ"))))`

Example

`"62.24168"=100*(1-"1.4"*(("4"-"20")/(("4")^("1.4")-("20")^("1.4"))))`

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Thermal Efficiency of Atkinson Cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio))))
η_atkinson = 100*(1-γ*((e-r)/(e^(γ)-r^(γ))))
This formula uses 4 Variables

Variables Used

Thermal Efficiency of Atkinson Cycle - Thermal Efficiency of Atkinson Cycle (in %) represents the fraction of heat converted into useful work in an engine following the Atkinson cycle.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air.
Expansion Ratio - Expansion ratio is the ratio of larger volume to lesser volume during an expansion process, i.e. ratio of volume after expansion to the volume before expansion.
Compression Ratio - Compression ratio is ratio of volume of cylinder to volume combustion chamber.

STEP 1: Convert Input(s) to Base Unit

Heat Capacity Ratio: 1.4 --> No Conversion Required
Expansion Ratio: 4 --> No Conversion Required
Compression Ratio: 20 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_atkinson = 100*(1-γ*((e-r)/(e^(γ)-r^(γ)))) --> 100*(1-1.4*((4-20)/(4^(1.4)-20^(1.4))))

Evaluating ... ...

η_atkinson = 62.2416815892081

STEP 3: Convert Result to Output's Unit

62.2416815892081 --> No Conversion Required

FINAL ANSWER

62.2416815892081 ≈ 62.24168 <-- Thermal Efficiency of Atkinson Cycle

(Calculation completed in 00.004 seconds)

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Created by Aditya Prakash Gautam

Indian Institute of Technology (IIT (ISM) ), Dhanbad, Jharkhand

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AISSMS College of Engineering, Pune (AISSMSCOE, Pune), Pune

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< 18 Air-Standard Cycles Calculators

Mean Effective Pressure in Dual Cycle

Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Pressure Ratio in Dual Cycle-1)+Heat Capacity Ratio*Pressure Ratio in Dual Cycle*(Cut-off Ratio-1))-Compression Ratio*(Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness

Go Thermal Efficiency of Stirling Cycle = 100*(([R]*ln(Compression Ratio)*(Final Temperature-Initial Temperature))/(Universal Gas Constant*Final Temperature*ln(Compression Ratio)+Molar Specific Heat Capacity at Constant Volume*(1-Effectiveness of Heat Exchanger)*(Final Temperature-Initial Temperature)))

Work Output for Dual Cycle

Go Work Output of Dual Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cut-off Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cut-off Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1)

Work Output for Diesel Cycle

Go Work Output of Diesel Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cut-off Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1)

Mean Effective Pressure in Diesel Cycle

Go Mean Effective Pressure of Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cut-off Ratio-1)-Compression Ratio*(Cut-off Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))

Thermal Efficiency of Dual Cycle

Go Thermal Efficiency of Dual Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*((Pressure Ratio in Dual Cycle*Cut-off Ratio^Heat Capacity Ratio-1)/(Pressure Ratio in Dual Cycle-1+Pressure Ratio in Dual Cycle*Heat Capacity Ratio*(Cut-off Ratio-1))))

Mean Effective Pressure in Otto Cycle

Go Mean Effective Pressure of Otto Cycle = Pressure at Start of Isentropic Compression*Compression Ratio*(((Compression Ratio^(Heat Capacity Ratio-1)-1)*(Pressure Ratio-1))/((Compression Ratio-1)*(Heat Capacity Ratio-1)))

Thermal Efficiency of Atkinson Cycle

Go Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio))))

Work Output for Otto Cycle

Go Work Output of Otto Cycle = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*((Pressure Ratio-1)*(Compression Ratio^(Heat Capacity Ratio-1)-1))/(Heat Capacity Ratio-1)

Air Standard Efficiency for Diesel Engines

Go Air Standard Efficiency of Diesel Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cut-off Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))

Thermal Efficiency of Diesel Cycle

Go Thermal Efficiency of Diesel Cycle = 100*(1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cut-off Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cut-off Ratio-1)))

Thermal Efficiency of Lenoir Cycle

Go Thermal Efficiency of Lenoir Cycle = 100*(1-Heat Capacity Ratio*((Pressure Ratio^(1/Heat Capacity Ratio)-1)/(Pressure Ratio-1)))

Thermal Efficiency of Ericsson Cycle

Go Thermal Efficiency of Ericsson Cycle = (Higher Temperature-Lower Temperature)/(Higher Temperature)

Air Standard Efficiency for Petrol engines

Go Air Standard Efficiency of Otto Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1)))

Relative Air-Fuel Ratio

Go Relative Air Fuel Ratio = Actual Air Fuel Ratio/Stoichiometric Air Fuel Ratio

Air Standard Efficiency given Relative Efficiency

Go Air Standard Efficiency = Indicated Thermal Efficiency/Relative Efficiency

Thermal Efficiency of Otto Cycle

Go OTE = 1-1/Compression Ratio^(Heat Capacity Ratio-1)

Actual Air Fuel Ratio

Go Actual Air Fuel Ratio = Mass of Air/Mass of Fuel

Thermal Efficiency of Atkinson Cycle Formula

Atkinson Cycle

The Atkinson cycle delays the intake valve’s closing until the piston has completed 20 to 30 percent of its upward travel on the compression stroke. As a result, some of the fresh charge is driven back into the intake manifold by the rising piston so the cylinder is never completely filled (hence the low-speed power reduction). The payoff comes after ignition when the piston begins descending on the expansion (also called power) stroke. Consistent with Atkinson’s original thinking, the shortened intake stroke combined with a full-length expansion stroke squeezes more work out of every increment of fuel.

Why do we need to reduce the compression ratio for the Atkinson cycle?

In the Otto cycle, after the combustion process, the force exerted on the piston during the power stroke increases so that when the piston reaches BDC, the exhaust valve opens, and useless heat discharges from the combustion chamber.

Therefore, this cycle uses to reduce the compression ratio for more expansion during the expansion stroke so that the entire force generated due to the combustion process can be used on the piston before the piston reaches BDC.

This means that the Atkinson cycle always has a lower/equivalent performance than the Otto cycle. However, the Otto cycle has lower thermal efficiency than the Atkinson cycle.

How to Calculate Thermal Efficiency of Atkinson Cycle?

Thermal Efficiency of Atkinson Cycle calculator uses Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))) to calculate the Thermal Efficiency of Atkinson Cycle, The Thermal Efficiency of Atkinson Cycle formula is defined as the fraction of heat converted into useful work in an Otto engine following Atkinson cycle. It considers both compression ratio and expansion ratio with the adiabatic index as well. Thermal Efficiency of Atkinson Cycle is denoted by η_atkinson symbol.

How to calculate Thermal Efficiency of Atkinson Cycle using this online calculator? To use this online calculator for Thermal Efficiency of Atkinson Cycle, enter Heat Capacity Ratio (γ), Expansion Ratio (e) & Compression Ratio (r) and hit the calculate button. Here is how the Thermal Efficiency of Atkinson Cycle calculation can be explained with given input values -> 62.24168 = 100*(1-1.4*((4-20)/(4^(1.4)-20^(1.4)))).

FAQ

What is Thermal Efficiency of Atkinson Cycle?

The Thermal Efficiency of Atkinson Cycle formula is defined as the fraction of heat converted into useful work in an Otto engine following Atkinson cycle. It considers both compression ratio and expansion ratio with the adiabatic index as well and is represented as η_atkinson = 100*(1-γ*((e-r)/(e^(γ)-r^(γ)))) or Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))). The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heat at constant pressure to specific heat at constant volume of air, Expansion ratio is the ratio of larger volume to lesser volume during an expansion process, i.e. ratio of volume after expansion to the volume before expansion & Compression ratio is ratio of volume of cylinder to volume combustion chamber.

How to calculate Thermal Efficiency of Atkinson Cycle?

The Thermal Efficiency of Atkinson Cycle formula is defined as the fraction of heat converted into useful work in an Otto engine following Atkinson cycle. It considers both compression ratio and expansion ratio with the adiabatic index as well is calculated using Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio)))). To calculate Thermal Efficiency of Atkinson Cycle, you need Heat Capacity Ratio (γ), Expansion Ratio (e) & Compression Ratio (r). With our tool, you need to enter the respective value for Heat Capacity Ratio, Expansion Ratio & Compression Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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