Thermal Efficiency of Dual Cycle Calculator

✖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.ⓘ Compression Ratio [r]			+10% -10%
✖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.ⓘ Heat Capacity Ratio [γ]			+10% -10%
✖Pressure ratio in dual cycle is the ratio of the maximum pressure during combustion to the minimum pressure at the end of exhaust, reflecting compression and expansion characteristics of the cycle.ⓘ Pressure Ratio in Dual Cycle [R_p]			+10% -10%
✖Cut-off ratio is the ratio of the cylinder volume at the start of compression stroke to the volume at the end of expansion stroke. It's a measure of piston's compression of the charge before ignition.ⓘ Cut-off Ratio [r_c]			+10% -10%

✖The Thermal Efficiency of Dual Cycle represents the effectiveness of dual engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.ⓘ Thermal Efficiency of Dual Cycle [ε_d]

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Formula

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Thermal Efficiency of Dual Cycle

Formula

`"ε"_{"d"} = 100*(1-1/("r"^("γ"-1))*(("R"_{"p"}*"r"_{"c"}^"γ"-1)/("R"_{"p"}-1+"R"_{"p"}*"γ"*("r"_{"c"}-1))))`

Example

`"66.60463"=100*(1-1/(("20")^("1.4"-1))*(("3.35"*("1.95")^"1.4"-1)/("3.35"-1+"3.35"*"1.4"*("1.95"-1))))`

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Thermal Efficiency of Dual Cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
ε_d = 100*(1-1/(r^(γ-1))*((R_p*r_c^γ-1)/(R_p-1+R_p*γ*(r_c-1))))
This formula uses 5 Variables

Variables Used

Thermal Efficiency of Dual Cycle - The Thermal Efficiency of Dual Cycle represents the effectiveness of dual engine. It is measured by comparing how much work is done through out the system to the heat supplied to the system.
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.
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.
Pressure Ratio in Dual Cycle - Pressure ratio in dual cycle is the ratio of the maximum pressure during combustion to the minimum pressure at the end of exhaust, reflecting compression and expansion characteristics of the cycle.
Cut-off Ratio - Cut-off ratio is the ratio of the cylinder volume at the start of compression stroke to the volume at the end of expansion stroke. It's a measure of piston's compression of the charge before ignition.

STEP 1: Convert Input(s) to Base Unit

Compression Ratio: 20 --> No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
Pressure Ratio in Dual Cycle: 3.35 --> No Conversion Required
Cut-off Ratio: 1.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_d = 100*(1-1/(r^(γ-1))*((R_p*r_c^γ-1)/(R_p-1+R_p*γ*(r_c-1)))) --> 100*(1-1/(20^(1.4-1))*((3.35*1.95^1.4-1)/(3.35-1+3.35*1.4*(1.95-1))))

Evaluating ... ...

ε_d = 66.6046251914744

STEP 3: Convert Result to Output's Unit

66.6046251914744 --> No Conversion Required

FINAL ANSWER

66.6046251914744 ≈ 66.60463 <-- Thermal Efficiency of Dual Cycle

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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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))/([R]*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 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 = 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 Efficiency of Otto Cycle = 100*(1-1/(Compression Ratio^(Heat Capacity Ratio-1)))

Thermal Efficiency of Otto Cycle

Go Thermal Efficiency of Otto Cycle = 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 Efficiency = Indicated Thermal Efficiency/Relative Efficiency

Actual Air Fuel Ratio

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

Thermal Efficiency of Dual Cycle Formula

What is a Dual cycle?

Dual cycle, or limited pressure cycle, is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In the dual cycle, combustion occurs partly at constant volume and partly at constant pressure.

What are the thermodynamic process involved in Dual Cycle?

The dual combustion cycle consists of following operations:
(1-2) Adiabatic Compression => (2-3) Isochoric Heat Addition => (3-4) Isobaric Heat Addition => (4-5) Adiabatic Expansion => (5-1) Isochoric Heat Rejection.

How to Calculate Thermal Efficiency of Dual Cycle?

Thermal Efficiency of Dual Cycle calculator uses 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)))) to calculate the Thermal Efficiency of Dual Cycle, Thermal Efficiency of Dual Cycle refers to the ability to efficiently convert heat energy from burning fuel into usable work output of dual cycle engine. It aims to combine the benefits of both Diesel and Otto cycles, potentially achieving improved overall efficiency in certain operating conditions. Thermal Efficiency of Dual Cycle is denoted by ε_d symbol.

How to calculate Thermal Efficiency of Dual Cycle using this online calculator? To use this online calculator for Thermal Efficiency of Dual Cycle, enter Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio in Dual Cycle (R_p) & Cut-off Ratio (r_c) and hit the calculate button. Here is how the Thermal Efficiency of Dual Cycle calculation can be explained with given input values -> 66.60463 = 100*(1-1/(20^(1.4-1))*((3.35*1.95^1.4-1)/(3.35-1+3.35*1.4*(1.95-1)))).

FAQ

What is Thermal Efficiency of Dual Cycle?

Thermal Efficiency of Dual Cycle refers to the ability to efficiently convert heat energy from burning fuel into usable work output of dual cycle engine. It aims to combine the benefits of both Diesel and Otto cycles, potentially achieving improved overall efficiency in certain operating conditions and is represented as ε_d = 100*(1-1/(r^(γ-1))*((R_p*r_c^γ-1)/(R_p-1+R_p*γ*(r_c-1)))) or 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)))). 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, 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, Pressure ratio in dual cycle is the ratio of the maximum pressure during combustion to the minimum pressure at the end of exhaust, reflecting compression and expansion characteristics of the cycle & Cut-off ratio is the ratio of the cylinder volume at the start of compression stroke to the volume at the end of expansion stroke. It's a measure of piston's compression of the charge before ignition.

How to calculate Thermal Efficiency of Dual Cycle?

Thermal Efficiency of Dual Cycle refers to the ability to efficiently convert heat energy from burning fuel into usable work output of dual cycle engine. It aims to combine the benefits of both Diesel and Otto cycles, potentially achieving improved overall efficiency in certain operating conditions is calculated using 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)))). To calculate Thermal Efficiency of Dual Cycle, you need Compression Ratio (r), Heat Capacity Ratio (γ), Pressure Ratio in Dual Cycle (R_p) & Cut-off Ratio (r_c). With our tool, you need to enter the respective value for Compression Ratio, Heat Capacity Ratio, Pressure Ratio in Dual Cycle & Cut-off 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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