Thermal Efficiency of Diesel Cycle Calculator

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✖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%
✖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 Diesel Cycle represents the effectiveness of Diesel 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 Diesel Cycle [η_th]

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Formula

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Thermal Efficiency of Diesel Cycle

Formula

`"η"_{"th"} = 1-1/"r"^("γ"-1)*("r"_{"c"}^"γ"-1)/("γ"*("r"_{"c"}-1))`

Example

`"0.649039"=1-1/("20")^("1.4"-1)*(("1.95")^"1.4"-1)/("1.4"*("1.95"-1))`

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Thermal Efficiency of Diesel Cycle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
η_th = 1-1/r^(γ-1)*(r_c^γ-1)/(γ*(r_c-1))
This formula uses 4 Variables

Variables Used

Thermal Efficiency of Diesel Cycle - The Thermal Efficiency of Diesel Cycle represents the effectiveness of Diesel 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.
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
Cut-off Ratio: 1.95 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_th = 1-1/r^(γ-1)*(r_c^γ-1)/(γ*(r_c-1)) --> 1-1/20^(1.4-1)*(1.95^1.4-1)/(1.4*(1.95-1))

Evaluating ... ...

η_th = 0.649039049927023

STEP 3: Convert Result to Output's Unit

0.649039049927023 --> No Conversion Required

FINAL ANSWER

0.649039049927023 ≈ 0.649039 <-- Thermal Efficiency of Diesel 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 Diesel Cycle Formula

What are the processes involved in the diesel cycle?

Isentropic Compression(1-2): Air is compressed in the cylinder without heat transfer, raising its pressure and temperature.
Constant Pressure Heat Addition(2-3): Fuel is injected and combusts at a constant pressure, increasing the temperature further.
Isentropic Expansion(3-4): The hot, high-pressure gas expands in the cylinder, performing work on the piston.
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.

What terms do the maximum thermal efficiency of Diesel cycle depends on?

The maximum thermal efficiency of a Diesel cycle depends on three key terms:

Compression Ratio (r): This is the ratio of the cylinder's maximum volume to its minimum volume. A higher compression ratio in the Diesel cycle leads to higher theoretical efficiency because it allows for more complete combustion and extraction of energy from the fuel.

Cut-off Ratio (rc): This represents the ratio of the cylinder's volume at the end of the compression stroke to its volume at the point where combustion ends. In simpler terms, it defines how much of the compressed fuel-air mixture is burned at constant pressure. An optimal cut-off ratio balances efficiency and power output.

Specific Heat Ratio (γ): This is a property of the working fluid (usually air) and represents the ratio of its specific heat capacity at constant pressure to its specific heat capacity at constant volume. A higher specific heat ratio for the working fluid can contribute to a slightly higher theoretical efficiency in the Diesel cycle.

How to Calculate Thermal Efficiency of Diesel Cycle?

Thermal Efficiency of Diesel Cycle calculator uses 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)) to calculate the Thermal Efficiency of Diesel Cycle, The thermal efficiency of Diesel cycle measures how efficiently a diesel engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. Diesel engines achieve ignition through high compression, eliminating the need for spark plugs, but this high compression results in some theoretical efficiency loss compared to gasoline engines using the Otto cycle. Thermal Efficiency of Diesel Cycle is denoted by η_th symbol.

How to calculate Thermal Efficiency of Diesel Cycle using this online calculator? To use this online calculator for Thermal Efficiency of Diesel Cycle, enter Compression Ratio (r), Heat Capacity Ratio (γ) & Cut-off Ratio (r_c) and hit the calculate button. Here is how the Thermal Efficiency of Diesel Cycle calculation can be explained with given input values -> 0.649039 = 1-1/20^(1.4-1)*(1.95^1.4-1)/(1.4*(1.95-1)).

FAQ

What is Thermal Efficiency of Diesel Cycle?

The thermal efficiency of Diesel cycle measures how efficiently a diesel engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. Diesel engines achieve ignition through high compression, eliminating the need for spark plugs, but this high compression results in some theoretical efficiency loss compared to gasoline engines using the Otto cycle and is represented as η_th = 1-1/r^(γ-1)*(r_c^γ-1)/(γ*(r_c-1)) or 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)). 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 & 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 Diesel Cycle?

The thermal efficiency of Diesel cycle measures how efficiently a diesel engine converts heat energy from fuel into mechanical work. It reflects the effectiveness of converting heat from burning fuel into usable work output at crankshaft. Diesel engines achieve ignition through high compression, eliminating the need for spark plugs, but this high compression results in some theoretical efficiency loss compared to gasoline engines using the Otto cycle is calculated using 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)). To calculate Thermal Efficiency of Diesel Cycle, you need Compression Ratio (r), Heat Capacity Ratio (γ) & Cut-off Ratio (r_c). With our tool, you need to enter the respective value for Compression Ratio, Heat Capacity Ratio & 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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