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))))
ηatk = 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 Otto engine following the Atkinson cycle.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
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 between volume of cylinder and 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: 1.75 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηatk = 100*(1-γ*((e-r)/(e^(γ)-r^(γ)))) --> 100*(1-1.4*((4-1.75)/(4^(1.4)-1.75^(1.4))))
Evaluating ... ...
ηatk = 34.0364789219349
STEP 3: Convert Result to Output's Unit
34.0364789219349 --> No Conversion Required
FINAL ANSWER
34.0364789219349 34.03648 <-- Thermal Efficiency of Atkinson Cycle
(Calculation completed in 00.004 seconds)

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18 Air-Standard Cycles Calculators

Thermal Efficiency of Stirling Cycle given Heat Exchanger Effectiveness
Go Thermal Efficiency of Stirling Cycle = 100*((Universal Gas Constant*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)))
Mean Effective Pressure in Dual Cycle
Go Mean Effective Pressure of Dual Cycle = Pressure at Start of Isentropic Compression*(Compression Ratio^Heat Capacity Ratio*((Explosion Ratio-1)+Heat Capacity Ratio*Explosion Ratio*(Cutoff Ratio-1))-Compression Ratio*(Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1))/((Heat Capacity Ratio-1)*(Compression Ratio-1))
Work Output for Dual Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*Pressure Ratio*(Cutoff Ratio-1)+(Pressure Ratio-1))-(Pressure Ratio*Cutoff Ratio^(Heat Capacity Ratio)-1))/(Heat Capacity Ratio-1)
Work Output for Diesel Cycle
Go Work Output of Engine = Pressure at Start of Isentropic Compression*Volume at Start of Isentropic Compression*(Compression Ratio^(Heat Capacity Ratio-1)*(Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio^(1-Heat Capacity Ratio)*(Cutoff Ratio^(Heat Capacity Ratio)-1)))/(Heat Capacity Ratio-1)
Mean Effective Pressure in Diesel Cycle
Go Mean Effective Pressure in Diesel Cycle = Pressure at Start of Isentropic Compression*(Heat Capacity Ratio*Compression Ratio^Heat Capacity Ratio*(Cutoff Ratio-1)-Compression Ratio*(Cutoff 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))*((Explosion Ratio*Cutoff Ratio^Heat Capacity Ratio-1)/(Explosion Ratio-1+Explosion Ratio*Heat Capacity Ratio*(Cutoff Ratio-1))))
Mean Effective Pressure in Otto Cycle
Go Mean Effective Pressure = 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 Engine = 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)
Thermal Efficiency of Diesel Cycle
Go Thermal Efficiency of Diesel Cycle = 100*(1-1/Compression Ratio^(Heat Capacity Ratio-1)*(Cutoff Ratio^Heat Capacity Ratio-1)/(Heat Capacity Ratio*(Cutoff Ratio-1)))
Air Standard Efficiency for Diesel Engines
Go Air Standard Efficiency = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1))*(Cutoff Ratio^(Heat Capacity Ratio)-1)/(Heat Capacity Ratio*(Cutoff 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 = 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

Thermal Efficiency of Atkinson Cycle = 100*(1-Heat Capacity Ratio*((Expansion Ratio-Compression Ratio)/(Expansion Ratio^(Heat Capacity Ratio)-Compression Ratio^(Heat Capacity Ratio))))
ηatk = 100*(1-γ*((e-r)/(e^(γ)-r^(γ))))

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 ηatk 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 -> 34.03648 = 100*(1-1.4*((4-1.75)/(4^(1.4)-1.75^(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 ηatk = 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 heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume, 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 between volume of cylinder and 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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