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Gas Cycles Carnot Cycle Heat Q 2 3 T2 Work W 1 T1 4 s1 s2
ADIABATIC COMPRESSION (ISENTROPIC) HEAT ADDITION (ISOTHERMAL) ADIABATIC EXPANSION WORK Heat Q 2 3 T2 Work W 1 T1 4 s1 s2
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Carnot Cycle Carnot cycle is the most efficient cycle that can be executed between a heat source and a heat sink. However, isothermal heat transfer is difficult to obtain in reality--requires large heat exchangers and a lot of time.
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Carnot Cycle Therefore, the very important (reversible) Carnot cycle, composed of two reversible isothermal processes and two reversible adiabatic processes, is never realized as a practical matter. Its real value is as a standard of comparison for all other cycles.
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Gas cycles have many engineering applications
Internal combustion engine Otto cycle Diesel cycle Gas turbines Brayton cycle Refrigeration Reversed Brayton cycle
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Some nomenclature before starting internal combustion engine cycles
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More terminology
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Terminology Bore = d Stroke = s Displacement volume =DV =
Clearance volume = CV Compression ratio = r
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Mean Effective Pressure
Mean Effective Pressure (MEP) is a fictitious pressure, such that if it acted on the piston during the entire power stroke, it would produce the same amount of net work.
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The net work output of a cycle is equivalent to the product of the mean effect pressure and the displacement volume
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Real Otto cycle
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Real and Idealized Cycle
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Otto Cycle P-V & T-s Diagrams
Pressure-Volume Temperature-Entropy
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Otto Cycle Derivation Thermal Efficiency:
For a constant volume heat addition (and rejection) process; Assuming constant specific heat:
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Otto Cycle Derivation For an isentropic compression (and expansion) process: where: γ = Cp/Cv Then, by transposing, Leading to
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Differences between Otto and Carnot cycles
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Otto Cycle Derivation The compression ratio (rv) is a volume ratio and is equal to the expansion ratio in an otto cycle engine. Compression Ratio where Compression ratio is defined as
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Otto Cycle Derivation Then by substitution,
The air standard thermal efficiency of the Otto cycle then becomes:
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Otto Cycle Derivation Summarizing where and then Isentropic behavior
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Otto Cycle Derivation Heat addition (Q) is accomplished through fuel combustion Q = Lower Heat Value (LHV) BTU/lb, kJ/kg also
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Effect of compression ratio on Otto cycle efficiency
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Sample Problem – 1 The air at the beginning of the compression stroke of an air-standard Otto cycle is at 95 kPa and 22C and the cylinder volume is 5600 cm3. The compression ratio is 9 and 8.6 kJ are added during the heat addition process. Calculate: (a) the temperature and pressure after the compression and heat addition process (b) the thermal efficiency of the cycle Use cold air cycle assumptions.
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Draw cycle and label points
r = V1 /V2 = V4 /V3 = 9 Q23 = 8.6 kJ T1 = 295 K P1 = 95 kPa
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Carry through with solution
Calculate mass of air: Compression occurs from 1 to 2: But we need T3!
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Get T3 with first law: Solve for T3:
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Thermal Efficiency
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Sample Problem – 2
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Solution
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Diesel Cycle P-V & T-s Diagrams
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Sample Problem – 3
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Gasoline vs. Diesel Engine
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