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))))
ηa = 100*(1-γ*((e-r)/(e^(γ)-r^(γ))))
This formula uses 4 Variables
Variables Used
Thermal Efficiency of Atkinson Cycle - The Thermal Efficiency of Atkinson Cycle represents the effectiveness of Atkinson engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.
Heat Capacity Ratio - The Heat Capacity Ratio or, adiabatic index quantifies the relationship between heat added at constant pressure and the resulting temperature increase compared to heat added at constant volume.
Expansion Ratio - Expansion ratio is the ratio of cylinder volume after compression (highest pressure) to volume at exhaust (lowest pressure).
Compression Ratio - Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC.
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
ηa = 100*(1-γ*((e-r)/(e^(γ)-r^(γ)))) --> 100*(1-1.4*((4-20)/(4^(1.4)-20^(1.4))))
Evaluating ... ...
ηa = 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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Air Standard Cycles Calculators

Mean Effective Pressure in Dual Cycle
​ LaTeX ​ 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))
Mean Effective Pressure in Diesel Cycle
​ LaTeX ​ 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))
Mean Effective Pressure in Otto Cycle
​ LaTeX ​ 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)))
Work Output for Otto Cycle
​ LaTeX ​ 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)

Thermal Efficiency of Atkinson Cycle Formula

​LaTeX ​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))))
ηa = 100*(1-γ*((e-r)/(e^(γ)-r^(γ))))

What are the theoretical processes involved in the Atkinson cycle?

The Atkinson cycle, like the Otto cycle used in many gasoline engines, involves four theoretical processes:
1. Isentropic Compression(1-2): Air is compressed in the cylinder without heat transfer, raising its pressure and temperature. This process is similar in both Atkinson and Otto cycles.

2. Constant Pressure Heat Addition(2-3): Fuel is injected and combusts at a nearly constant pressure, further increasing the temperature. This process is also largely similar between the cycles.

3. Isentropic Expansion(3-4-4'): In the Atkinson cycle, this is where it diverges from the Otto cycle. The Atkinson cycle employs a longer isentropic expansion stroke compared to compression. This allows the hot, high-pressure gas to expand further, extracting more thermal energy and potentially leading to higher efficiency.

4. Constant Volume Heat Rejection(4'-1): Heat is removed from the cylinder at a constant volume, lowering the temperature and pressure back to its starting point.

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, Thermal Efficiency of Atkinson Cycle refers to the effectiveness of Atkinson engine to convert heat energy from burning fuel into usable work output. Atkinson cycle engines prioritize a longer expansion stroke compared to a traditional Otto cycle. This theoretically allows for more complete extraction of thermal energy, potentially leading to higher efficiency. However, achieving this theoretical advantage in real-world engines requires balancing efficiency gains with power output. Thermal Efficiency of Atkinson Cycle is denoted by ηa 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?
Thermal Efficiency of Atkinson Cycle refers to the effectiveness of Atkinson engine to convert heat energy from burning fuel into usable work output. Atkinson cycle engines prioritize a longer expansion stroke compared to a traditional Otto cycle. This theoretically allows for more complete extraction of thermal energy, potentially leading to higher efficiency. However, achieving this theoretical advantage in real-world engines requires balancing efficiency gains with power output and is represented as ηa = 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 or, adiabatic index quantifies the relationship between heat added at constant pressure and the resulting temperature increase compared to heat added at constant volume, Expansion ratio is the ratio of cylinder volume after compression (highest pressure) to volume at exhaust (lowest pressure) & Compression ratio refers to how much the air-fuel mixture is squeezed in the cylinder before ignition. It's essentially the ratio between the volume of the cylinder at BDC to TDC.
How to calculate Thermal Efficiency of Atkinson Cycle?
Thermal Efficiency of Atkinson Cycle refers to the effectiveness of Atkinson engine to convert heat energy from burning fuel into usable work output. Atkinson cycle engines prioritize a longer expansion stroke compared to a traditional Otto cycle. This theoretically allows for more complete extraction of thermal energy, potentially leading to higher efficiency. However, achieving this theoretical advantage in real-world engines requires balancing efficiency gains with power output 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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