This document outlines engineering assumptions and equations for analyzing energy conversion cycles that use air as the working fluid. Key assumptions include treating air as a single species with constant specific heat, and using the ideal gas law. Equations presented include the continuity, momentum and energy conservation equations, as well as equations of state and equations specific to analyzing cycles like Otto, Brayton, and Diesel cycles. Thermodynamic property data for air is also referenced.

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2. When dealing with energy conversion and considering ideal (isentropic) operation and the working fluid is air,
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
Basic equations hold (continuity, momentum and energy equations)
Specific heat is constant
Compressible Flow
Single species consideration
Basic equations hold (continuity, momentum and energy equations)
Specific heat is constant
Thermodynamic and Transport Properties
Single species consideration
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

3. 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

4. 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

5. 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 [/]

6. 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]

7. 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]
Power Cycle Components/Processes
Engineering Equations

8. Combustion is ideal, complete with no heat loss and at
stoichiometric conditions.
Also,
Flame Temperature [K]
hreactants = hproducts [kJ/kg]
Power Cycle Components/Processes
Engineering Equations

9. Combustion Schematic Layout
Fuel
Oxidant -- Air
Combustion Products
Power Cycle Components/Processes
Engineering Equations

10. 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
SpecificEnthalpy[kJ/kg]
Temperature [K]
Power Cycle Components/Processes
Engineering Equations

11. Combustion h – T Diagram
SpecificEnthalpy--h[kJ/kg]
Temperature -- T [K]
Reactants
Products
TflameTreference
Power Cycle Components/Processes
Engineering Equations

12. 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]
Power Cycle Components/Processes
Engineering Equations

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

14. 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