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# Engineering Energy Conversion Assumptions and Equations

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Coursework material provides engineering energy conversion assumptions and equations.

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### Engineering Energy Conversion Assumptions and Equations

1. 1. 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
2. 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. 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. 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. 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. 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. 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. 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. 9. Combustion Schematic Layout Fuel Oxidant -- Air Combustion Products Power Cycle Components/Processes Engineering Equations
10. 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 O2 N2 C(S) S(S) H2 CO2 SO2 H2O H2O(L) CH4 SpecificEnthalpy[kJ/kg] Temperature [K] Power Cycle Components/Processes Engineering Equations
11. 11. Combustion h – T Diagram SpecificEnthalpy--h[kJ/kg] Temperature -- T [K] Reactants Products TflameTreference Power Cycle Components/Processes Engineering Equations
12. 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. 13. Sonic Velocity vs = (χ RT)1/2 [m/s] Mach Number M = v/vs [/] Compressible Flow Engineering Equations
14. 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