Power Cycle Analysis Online Calculator

***Carnot Cycle***
*Input Values:*
*Q-Supply Temperature [K]*	*Q-Reject Temperature [K]*
*Output Values:*
*Thermal Efficiency [%]*	*Heat Rate [Btu/kWhr]*

***Brayton Cycle (Power)***
*Input Values:*
Compressor Inlet Temperature [K]	Compressor Inlet Pressure [atm]
Turbine Inlet Temperature [K]	Turbine Inlet Pressure [atm]
Working Fluid Mass Flow Rate [kg/s]	*Fuel HHV [Btu/lbm]*
**Specific Heat [J/kgK]***	*Kappa [/]*
*Output Values:*
*Power Output [kW]*	*Cycle Efficiency [%]*
*Fuel Mass Flow Rate [kg/s]*	*Heat Rate [Btu/kWhr]*

***Brayton Cycle (Propulsion)***
*Input Values:*
Compressor Inlet Temperature [K]	Compressor Inlet Pressure [atm]
Turbine Inlet Temperature [K]	Turbine Inlet Pressure [atm]
Working Fluid Mass Flow Rate [kg/s]	*Fuel HHV [Btu/lbm]*
**Specific Heat [J/kgK]***	*Kappa [/]*
*Output Values:*
*Fuel Mass Flow Rate [kg/s]*	*Thrust [N]*

***Otto Cycle***
*Input Values:*
*Ambient Temperature [K]*	*Ambient Pressure [atm]*
*Compression Ratio [/]*	*Combustion Temperature [K]*
**Gas Constant [J/kgK]***	**Specific Heat [J/kgK]***
*Kappa [/]*
*Output Values:*
*Compression Temperature [K]*	*Compression Pressure [atm]*
	*Combustion Pressure [atm]*
*Exhaust Temperature [K]*	*Exhaust Pressure [atm]*
*Cycle Efficiency [%]*	*Heat Rate [Btu/kWhr]*

***Diesel Cycle***
*Input Values:*
*Ambient Temperature [K]*	*Ambient Pressure [atm]*
*Compression Ratio [/]*	*Cut-Off Ratio [/]*
**Gas Constant [J/kgK]***	**Specific Heat [J/kgK]***
*Kappa [/]*
*Output Values:*
*Compression Temperature [K]*	*Compression Pressure [atm]*
*Combustion Temperature [K]*	*Combustion Pressure [atm]*
*Exhaust Temperature [K]*	*Exhaust Pressure [atm]*
*Cycle Efficiency [%]*	*Heat Rate [Btu/kWhr]*

***Magnetohydrodynamics (MHD)***
*Input Values:*
Inlet Stagnation Temperature [K]	Inlet Stagnation Pressure [atm]
*Inlet Velocity [m/s]*	*Conductivity [mho/m]*
*Magnetic Field Strength [T]*	*Loading Parameter [/]*
*Channel Length [m]*	*Kappa [/]*
**Specific Heat [J/kgK]***	**Gas Constant [J/kgK]***
*Output Values:*
*Inlet Static Temperature [K]*	*Inlet Static Pressure [atm]*
*Inlet Mach Number [/]*	*Induced Voltage Field [V/m]*
*Current Density [A/m^2]*
Outlet Stagnation Temperature [K]	Outlet Stagnation Pressure [atm]
*Outlet Static Temperature [K]*	*Outlet Static Pressure [atm]*
*Outlet Velocity [m/s]*	*Outlet Mach Number [/]*
*Specific Work Output [kJ/kg]*	*Enthalpy Extraction [%]*

Kappa, Gas Constant and Specific Heat Values

Gas

Gas

Kappa
[/]

Gas Constant
[J/kg*K]

Specific Heat
[J/kg*K]

Air

1.4

286.7

1,004

Ammonia

NH₃

1.3

488.2

2,092

Argon

Ar

1.67

208.1

519

Carbon Dioxide

CO₂

1.28

188.9

845

Carbon Monoxide

CO

1.4

296.8

1,042

Helium

He

1.66

2,078.5

5,200

Hydrogen

H₂

1.4

4,124

14,350

Methane

CH₄

1.32

518.2

2,223

Nitrogen

N₂

1.4

296.9

1,038

Oxygen

O₂

1.4

259.8

916

Water Vapor

H₂O

1.33

188.5

1,690

***Kappa, Gas Constant and Specific Heat Values***
*Gas*	*Gas*	Kappa [/]	Gas Constant [J/kg*K]	Specific Heat [J/kg*K]
*Air*		*1.4*	*286.7*	*1,004*
*Ammonia*	*NH₃*	*1.3*	*488.2*	*2,092*
*Argon*	Ar	*1.67*	*208.1*	*519*
*Carbon Dioxide*	*CO₂*	*1.28*	*188.9*	*845*
*Carbon Monoxide*	CO	*1.4*	*296.8*	*1,042*
*Helium*	He	*1.66*	*2,078.5*	*5,200*
*Hydrogen*	H₂	*1.4*	*4,124*	*14,350*
*Methane*	*CH₄*	*1.32*	*518.2*	*2,223*
*Nitrogen*	N₂	*1.4*	*296.9*	*1,038*
*Oxygen*	O₂	*1.4*	*259.8*	*916*
*Water Vapor*	*H₂O*	*1.33*	*188.5*	*1,690*

***Fuel HHV Values***
*Fuel*	*HHV [Btu/lbm]*
*Hydrogen*	*60,000*
*Natural Gas*	*24,000*
*Oil*	*18,000*
*Carbon*	*14,000*
*Coal*	*8,000 through 12,000*
*Wood*	*6,000*

Here are some of the basic engineering formulas/equations related to energy conversion systems which are built into the Engineering Software product line:

Continuity Equation

m = vA

Momentum Equation

F = (vm + pA)_{out
-
in}

Energy Equation

Q - W = ((h + v²/2 + gh)m)_{out -
in}

State Equation for Ideal Gas

pv = RT/MW

Perfect Gas

c_p = constant

k = c_p / c_v

Isentropic Compression

T₂ / T₁ = (p₂/ p₁)^(k-1)/k

T₂ / T₁ = (V₁/ V₂)^(k-1)

p₂ / p₁ = (V₁/ V₂)^k

Combustion

h_reactants = h_products

Isentropic Expansion

T₁ / T₂ = (p₁ / p₂)^(k-1)/k

T₁ / T₂ = (V₂/ V₁)^(k-1)

p₁ / p₂ = (V₂/ V₁)^k

Sonic Velocity

vs = (kRT/MW)^1/2

Mach Number

M = v/vs

Isentropic Flow

T_t/ T = (1 + M²(k - 1)/2)

p_t/ p = (1 + M²(k - 1)/2)^k/(k-1)

h_t = (h + v²/2)

T_t = (T + v²/(2c_p))

Thrust

Thrust = vm + (p- p_a)A

Cycle Efficiency

Cycle Efficiency = Net Work/Heat

Carnot Cycle Efficiency

Carnot Cycle Efficiency = 1 - T_{heat rejection}/ T_{heat addition}

Brayton Cycle Efficiency

Brayton Cycle Efficiency = 1 - 1/(p₂ / p₁)^(k-1)/k

Otto Cycle Efficiency

Compression Ratio = V₁/ V₂

Otto Cycle Efficiency = 1 - 1/Compression Ratio^(k-1)

Diesel Cycle Efficiency

Compression Ratio (CR) = V₁/ V₂

Cut-Off Ratio (COR) = V₃/ V₂

Diesel Cycle Efficiency = 1 - (COR^k - 1)/(k*CR^(k-1)*(COR - 1))

Fuel Cell

Fuel Cell Efficiency = - (G_out - G_in)/HHV

Heat Rate

Heat Rate = (1/Cycle Efficiency)*3,412

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