Energy Conversion Analysis Webinar

Engineering Software
P.O. Box 2134
Kensington, MD 20891
Phone: (301) 919-9670
E-Mail: info@engineering-4e.com
http://www.engineering-4e.com
Copyright © 1996

Energy Conversion Analysis Webinar
Objectives
In this webinar, the engineering students and professionals get familiar with the ideal
simple and basic power cycles, power cycle components/processes and compressible
flow and their T - s, p - V and h - T diagrams, operation and major performance trends
when air is considered as the working fluid.
Performance Objectives:
Introduce basic energy conversion engineering assumptions and equations
Know basic elements of Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle,
compression, combustion and expansion processes and compressible flow (nozzle,
diffuser and thrust) and their T - s, p - V and h - T diagrams
Be familiar with Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle, compression,
combustion, expansion and compressible flow (nozzle, diffuser and thrust) operation
Understand general Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle,
compression, combustion, expansion and compressible flow (nozzle, diffuser and
thrust) performance trends

This webinar consists of the following three major sections:
• Power Cycles (Carnot, Brayton, Otto and Diesel)
• Power Cycle Components/Processes (compression,
combustion and expansion)
• Compressible Flow (nozzle, diffuser and thrust)
In this webinar, first overall engineering assumptions and basic engineering
equations are provided. Furthermore, for each major section, basic
engineering equations, section material and conclusions are provided.
Energy Conversion Analysis Webinar

The energy conversion analysis presented in this webinar considers ideal (isentropic) operation and the
working fluid is air. Furthermore, the following assumptions are valid:
Power Cycles
Single species consideration -- fuel mass flow rate is ignored and its impact on the properties of the working
fluid
Basic equations hold (continuity, momentum and energy equations)
Specific heat is constant
Power Cycle Components/Processes
Single species consideration
Compressible Flow
Thermodynamic and Transport Properties
Ideal gas approach is used (pv=RT)
Specific heat is not constant
Coefficients describing thermodynamic and transport properties were obtained from the NASA Glenn Research
Center at Lewis Field in Cleveland, OH -- such coefficients conform with the standard reference temperature of
298.15 K (77 F) and the JANAF Tables
Engineering Assumptions

Basic Conservation Equations
Continuity Equation
m = ρvA [kg/s]
Momentum Equation
F = (vm + pA)out - in [N]
Energy Equation
Q - W = ((h + v2/2 + gh)m)out - in [kW]
Basic Engineering Equations

Ideal Gas State Equation
pv = RT [kJ/kg]
Perfect Gas
cp = constant [kJ/kg*K]
Kappa
χ = cp/cv [/]
For air: χ = 1.4 [/], R = 0.2867 [kJ/kg*K] and
cp = 1.004 [kJ/kg*K]
Basic Engineering Equations

Power Cycles Engineering Equations
Carnot Cycle Efficiency
 = 1 - TR/TA
Otto Cycle Efficiency
 = 1 - 1/ε(χ-1)
Brayton Cycle Efficiency
 = 1 - 1/rp
(χ-1)/χ
Diesel Cycle Efficiency
 = 1 - (φχ-1)/ (χε(χ-1)(φ-1))
Cycle Efficiency
 = Wnet/Q [/]
Heat Rate
HR = (1/)3,412 [Btu/kWh]
rp = p2/p1 [/]; ε = V1/V2 [/]; φ = V3/V2 [/]

Power Cycles Engineering Equations
Otto Cycle
wnet = qh - ql = cv(T3 - T2) - cv(T4 - T1) [kJ/kg]
Wnet = wnetm [kW]
Brayton Cycle
wnet = qh - ql = cp(T3 - T2) - cp(T4 - T1) [kJ/kg]
Wnet = wnetm [kW]
Diesel Cycle
wnet = qh - ql = cp(T3 - T2) - cv(T4 - T1) [kJ/kg]
Wnet = wnetm [kW]

Carnot Cycle Schematic Layout
Compressor
Heat Exchanger
Gas Turbine
1
32
4
Heat Addition
Heat Exchanger
Heat Rejection
Carnot Cycle

Carnot Cycle T - s Diagram
1
32
4
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Carnot Cycle

0
20
40
60
80
500 600 700 800 900 1,000
CarnotCycleEfficiency[%]
Heat Addition Temperature [K]
Compressor Inlet Temperature: 298 [K]
Carnot Cycle

0
20
40
60
80
278 288 298 308 318 328
CarnotCycleEfficiency[%]
Heat Rejection Temperature [K]
Turbine Inlet Temperature: 800 [K]
Carnot Cycle

Brayton Cycle (Gas Turbine) Schematic Layout -- Open Cycle
Compressor
Combustor
Gas Turbine
1
32
4
Fuel
Brayton Cycle (Gas Turbine)
Heat Addition
Working Fluid In Working Fluid Out

Brayton Cycle Schematic Layout -- Closed Cycle
Compressor
Heat Exchanger
Gas Turbine
1
32
4
Heat Addition
Heat Exchanger
Heat Rejection

Brayton Cycle (Gas Turbine) T - s Diagram
1
3
2
4
Temperature--T[K]

Brayton Cycle (Gas Turbine) Efficiency
0
20
40
60
80
5 10 15 20 25
Compression Ratio (P2/P1) [/]
P2/P1 [/]
Working Fluid: Air
BraytonCycle(GasTurbine)Efficiency[%]

Brayton Cycle (Gas Turbine) Specific Power
Output
100
200
300
400
500
900 1,200 1,500
Gas Turbine Inlet Temperature [K]
BraytonCycle(GasTurbine)SpecificPowerOutput
[kJ/kg]
5 15
Working Fluid: Air

Brayton Cycle (Gas Turbine) Power Output
0
25
50
75
100
50 100 150
Working Fluid Mass Flow Rate [kg/s]
BraytonCycle(GasTurbine)PowerOutput[MW]
5 15
Working Fluid: Air
Compressor Inlet Temperature: 298 [K] -- Gas Turbine Inlet Temperature: 1,500 [K]

Otto Cycle p - V Diagram
1
3
2
4
Pressure--p[atm]
Volume -- V [m^3]
Otto Cycle

Otto Cycle T - s Diagram
1
3
2
4
Temperature--T[K]
Otto Cycle

Otto Cycle Efficiency
0
20
40
60
80
2.5 5 7.5 10 12.5
Compression Ratio (V1/V2) [/]
V1/V2 [/]
Working Fluid: Air
Otto Cycle
OttoCycleEfficiency[%]

Otto Cycle Power Output
100
200
300
400
1,200 1,500 1,800
Combustion Temperature [K]
OttoCyclePowerOutput[kW]
5 10
Working Fluid: Air
Ambient Temperature: 298 [K] -- Number of Revolutions: 60 [1/s]
For Given Geometry of the Four Cylinder and Four Stroke Otto Engine
Otto Cycle

Diesel Cycle p - V Diagram
1
32
4
Pressure--p[atm]
Volume -- V [m^3]
Diesel Cycle

Diesel Cycle T - s Diagram
1
3
2
4
Temperature--T[K]
Diesel Cycle

0
20
40
60
80
7.5 10 12.5 15 17.5
DieselCycleEfficiency[%]
3 4
Working Fluid: Air
Cut Off Ratio V3/V2 [/]
Diesel Cycle

20
40
60
80
1,500 1,800 2,100
DieselCycleEfficiency[%]
10 15
Diesel Cycle
Ambient Temperature: 298 [K]

Diesel Cycle Cut Off Ratio
0
1
2
3
4
1,500 1,800 2,100
DieselCycleCutOffRatio[/]
10 15
Diesel Cycle
Ambient Temperature: 298 [K]

Diesel Cycle Power Output
200
300
400
500
600
1,500 1,800 2,100
DieselCyclePowerOutput[kW]
10 15
Working Fluid: Air
Diesel Cycle
Ambient Temperature: 298 [K] -- Number of Revolutions: 60 [1/s]
For Given Geometry of the Four Cylinder and Four Stroke Diesel Engine

Power Cycles Conclusions
The Carnot Cycle efficiency increases with an increase in the heat addition temperature when the heat rejection
temperature does not change at all. Furthermore, the Carnot Cycle efficiency decreases with an increase in the
heat rejection temperature when the heat addition temperature does not change at all. The Carnot Cycle
efficiency is not dependent on the working fluid properties.
The Brayton Cycle efficiency depends on the compression ratio and working fluid properties. The efficiency
increases with an increase in the compression ratio values. Also, the efficiency increases with the higher value
for ϰ, which is a ratio of gas specific heat values (cp/cv).
The Brayton Cycle specific power output increases with an increase in the gas turbine inlet temperature.
Furthermore, the increase is greater for the higher compression ratio values. The Brayton Cycle power output
increases with an increase in the working fluid mass flow rate for a fixed gas turbine inlet temperature. The
increase is greater for the higher compression ratio values.
The Otto Cycle efficiency increases with an increase in the compression ratio values. Also, the Otto Cycle
power output increases with an increase in the combustion temperature. The Otto Cycle power output is greater
for the higher compression ratio values for the given combustion temperature values and geometry of the four
cylinder and four stroke Otto engine.
The Diesel Cycle efficiency increases with an increase in the compression ratio and with a decrease in the cut
off ratio values. Also, the Diesel Cycle power output increases with an increase in the compression ratio values
for the given combustion temperature values and geometry of the four cylinder and four stroke Diesel engine.

Isentropic Compression
T2/T1 = (p2/p1)(χ-1)/χ [/]
T2/T1 = (V1/V2)(χ-1) [/]
p2/p1 = (V1/V2)χ [/]
wc = cp(T2 - T1) [kJ/kg]
Wc = cp(T2 - T1)m [kW]
Engineering Equations

Combustion is ideal, complete with no heat loss and at
stoichiometric conditions.
Also,
Flame Temperature [K]
hreactants = hproducts [kJ/kg]

Isentropic Expansion
T1/T2 = (p1/p2)(χ-1)/χ [/]
T1/T2 = (V2/V1)(χ-1) [/]
p1/p2 = (V2/V1)χ [/]
we = cp(T1 - T2) [kJ/kg]
We = cp(T1 - T2)m [kW]

Compression Schematic Layout
Working Fluid In
Working Fluid Out
Compressor
1
2
Compression

Compression T - s Diagram
2
1
Temperature--T[K]
Compression

Compression Specific Power Input
100
200
300
400
500
5 10 15
CompressionSpecificPowerInput[kJ/kg]
Working Fluid: Air
Compression

Compression Power Input
0
25
50
75
100
50 100 150
CompressionPowerInput[MW]
5 15
Compression
Working Fluid: Air

Combustion Schematic Layout
Fuel
Oxidant -- Air
Combustion Products
Combustion

Specific Enthalpy vs Temperature
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
500 800 1,100 1,400 1,700 2,000 2,300 2,600 2,900 3,200 3,500 3,800 4,100 4,400 4,700 5,000
C(S) H2 S(S) N2 O2 H2O(L) CH4 CO2 H2O SO2
Combustion
SpecificEnthalpy[kJ/kg]
Temperature [K]

Combustion h – T Diagram
SpecificEnthalpy--h[kJ/kg]
Temperature -- T [K]
Reactants
Products
TflameTreference
Combustion

Combustion
Oxidant Composition
Fuel Composition
C
[kg/kg]
1.000
0.000
0.000
0.780
0.860
-
H
[kg/kg]
0.000
1.000
0.000
0.050
0.140
-
S
[kg/kg]
0.000
0.000
1.000
0.030
0.000
-
N
[kg/kg]
0.000
0.000
0.000
0.040
0.000
-
O
[kg/kg]
0.000
0.000
0.000
0.080
0.000
-
H2O
[kg/kg]
0.000
0.000
0.000
0.020
0.000
-
CH4
[kg/kg]
-
-
-
-
-
1.000
Fuel
Carbon
Hydrogen
Sulfur
Coal
Oil
Gas
N
[kmol/kmol]
0.790
O
[kmol/kmol]
0.210
N
[kg/kg]
0.767
O
[kg/kg]
0.233
Oxidant
Air

Combustion
CO2
[kg/kg]
0.295
0.000
0.000
0.249
0.202
0.151
H2O
[kg/kg]
0.000
0.255
0.000
0.041
0.080
0.124
SO2
[kg/kg]
0.000
0.000
0.378
0.005
0.000
0.000
N2
[kg/kg]
0.705
0.745
0.622
0.705
0.718
0.725
O2
[kg/kg]
0.000
0.000
0.000
0.000
0.000
0.000
CO2
[kmol/kmol]
0.210
0.000
0.000
0.170
0.132
0.095
Fuel
Carbon
Hydrogen
Sulfur
Coal
Oil
Gas
SO2
[kmol/kmol]
0.000
0.000
0.210
0.002
0.000
0.000
N2
[kmol/kmol]
0.790
0.653
0.790
0.759
0.739
0.715
Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and HHV
Flame Temperature
[K]
2,460
2,525
1,972
2,484
2,484
2,327
Stoichiometric
Oxidant to Fuel Ratio
[/]
11.444
34.333
4.292
10.487
14.649
17.167
HHV
[Btu/lbm]
14,094
60,997
3,982
14,162
20,660
21,563
Fuel
Carbon
Hydrogen
Sulfur
Coal
Oil
Gas
H2O
[kmol/kmol]
0.000
0.347
0.000
0.068
0.129
0.190
O2
[kmol/kmol]
0.000
0.000
0.000
0.000
0.000
0.000
Stoichiometric Combustion
Combustion Products Composition on Weight and Mole Basis

Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg]
Carbon Hydrogen Sulfur Coal Oil Gas
Combustion
Fuel and Oxidant Inlet Temperature: 298 [K]

Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/kmol]
Combustion

Combustion Products Flame Temperature
1,900
2,000
2,100
2,200
2,300
2,400
2,500
2,600
Flame Temperature [K]
Combustion
FlameTemperature[K]

Combustion Stoichiometric Oxidant to Fuel Ratio
0
5
10
15
20
25
30
35
40
Stoichiometric Oxidant to Fuel Ratio [/]
Combustion
StoichiometricOxidanttoFuelRatio[/]

Higher Heating Value (HHV)
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
HHV [Btu/lbm]
Combustion
HHV[Btu/lbm]

Expansion Schematic Layout
Working Fluid In
Working Fluid Out
Turbine
1
2
Expansion

Expansion T - s Diagram
1
2
Temperature--T[K]
Expansion

Expansion Specific Power Output
500
600
700
800
900
1,000
5 10 15
ExpansionSpecificPowerOutput[kJ/kg]
Expansion Ratio (P1/P2) [/]
Working Fluid: Air
Turbine Inlet Temperature: 1,500 [K]
Expansion

Expansion Power Output
0
40
80
120
160
50 100 150
ExpansionPowerOutput[MW]
5 15
Expansion Ratio (P1/P2) [/]
Expansion
Working Fluid: Air
Turbine Inlet Temperature: 1,500 [K]

Conclusions
Both compression specific power input and power input increase with an increase in
the compression ratio values. As the working fluid mass flow rate increases for a fixed
compression inlet temperature value, the compression power input requirements
increase too. The compression power input requirements are greater for the higher
compression ratio values.
Hydrogen as the fuel has the highest flame temperature, requires the most mass
amount of oxidant/air in order to have complete combustion per unit mass amount of
fuel and has the largest fuel higher heating value.
When hydrogen reacts with oxidant/air, there is no CO2 present in the combustion
products.
Both expansion specific power output and power output increase with an increase in
the expansion ratio values. As the working fluid mass flow rate increases for a fixed
expansion inlet temperature value, the expansion power output values increase too.
The expansion power output is greater for the higher expansion ratio values.

Sonic Velocity
vs = (χ RT)1/2 [m/s]
Mach Number
M = v/vs [/]
Compressible Flow Engineering Equations

Isentropic Flow
Tt/T = (1 + M2(χ - 1)/2) [/]
pt/p = (1 + M2(χ - 1)/2)χ/(χ-1) [/]
ht = (h + v2/2) [kJ/kg]
Tt = (T + v2/(2cp)) [K]
Thrust = vm + (p - pa)A [N]
Compressible Flow Engineering Equations

Nozzle Schematic Layout
Nozzle
1 2
Nozzle

Nozzle T - s Diagram
1
2
Temperature--T[K]
Nozzle

Nozzle Performance
1.00
1.05
1.10
1.15
1.20
0.39 0.67 1
Mach Number [/]
1.0
1.2
1.4
1.6
1.8
2.0
Tstagnation/Tstatic [/] Pstagnation/Pstatic [/]
Working Fluid: Air
Nozzle Inlet Stagnation Conditions -- Temperature: 1,500 [K] and Pressure: 10 [atm]
Nozzle
Tstagnation/Tstatic[/]
Pstagnation/Pstatic[/]

Diffuser Schematic Layout
Diffuser
1 2
Diffuser

Diffuser T - s Diagram
2
1
Temperature--T[K]
Diffuser

Diffuser Performance
1.00
1.05
1.10
1.15
1.20
0.29 0.58 0.95
Mach Number [/]
1.00
1.25
1.50
1.75
2.00
Working Fluid: Air
Diffuser Inlet Static Conditions -- Temperature: 298 [K] and Pressure: 1 [atm]
Diffuser

Thrust Schematic Layout
Working Fluid Out
Nozzle
21
Working Fluid at Still
Thrust

Thrust T - s Diagram
1
2
Temperature--T[K]
Thrust

Working Fluid: Air
Thrust
700
800
900
1,000
1,100
1,200
900 1,200 1,500
Nozzle Inlet Stagnation Temperature [K]
Thrust[N]
5 10 15
Nozzle Outlet Static Conditions -- Mach Number: 0.85 [/]
Ambient Conditions – Pressure: 1 [atm]
Nozzle Inlet Stagnation Pressure [atm]
Working Fluid Mass Flow Rate: 1 [kg/s]
Thrust

Nozzle -- Thrust Performance
1.140
1.142
1.144
1.146
1.148
1.150
900 1,200 1,500
Nozzle Inlet Stagnation Temperature [K]
1.58
1.59
1.60
1.61
1.62
Working Fluid: Air
Nozzle Inlet Stagnation Conditions -- Pressure : 10 [atm]
Ambient Conditions -- Pressure: 1 [atm]
Nozzle Outlet Static Conditions -- Mach Number: 0.85 [/]
Thrust

Compressible Flow Conclusions
Nozzle stagnation over static temperature and pressure ratio values increase with an
increase in the Mach Number.
Diffuser stagnation over static temperature and pressure ratio values increase with an
increase in the Mach Number.
Thrust increases with an increase in the inlet stagnation temperature and pressure
values.

Energy Conversion Analysis Webinar

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