Gas Cycles Carnot Cycle Heat Q 2 3 T2 Work W 1 T1 4 s1 s2

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Presentation transcript:

Gas Cycles Carnot Cycle Heat Q 2 3 T2 Work W 1 T1 4 s1 s2 1-2 - ADIABATIC COMPRESSION (ISENTROPIC) 2-3 - HEAT ADDITION (ISOTHERMAL) 3-4 - ADIABATIC EXPANSION 4-1 - WORK Heat Q 2 3 T2 Work W 1 T1 4 s1 s2

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.

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.

Gas cycles have many engineering applications Internal combustion engine Otto cycle Diesel cycle Gas turbines Brayton cycle Refrigeration Reversed Brayton cycle

Some nomenclature before starting internal combustion engine cycles

More terminology

Terminology Bore = d Stroke = s Displacement volume =DV = Clearance volume = CV Compression ratio = r

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.

The net work output of a cycle is equivalent to the product of the mean effect pressure and the displacement volume

Real Otto cycle

Real and Idealized Cycle

Otto Cycle P-V & T-s Diagrams Pressure-Volume Temperature-Entropy

Otto Cycle Derivation Thermal Efficiency: For a constant volume heat addition (and rejection) process; Assuming constant specific heat:

Otto Cycle Derivation For an isentropic compression (and expansion) process: where: γ = Cp/Cv Then, by transposing, Leading to

Differences between Otto and Carnot cycles

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

Otto Cycle Derivation Then by substitution, The air standard thermal efficiency of the Otto cycle then becomes:

Otto Cycle Derivation Summarizing where and then Isentropic behavior

Otto Cycle Derivation Heat addition (Q) is accomplished through fuel combustion Q = Lower Heat Value (LHV) BTU/lb, kJ/kg also

Effect of compression ratio on Otto cycle efficiency

Sample Problem – 1 The air at the beginning of the compression stroke of an air-standard Otto cycle is at 95 kPa and 22C 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.

Draw cycle and label points r = V1 /V2 = V4 /V3 = 9 Q23 = 8.6 kJ T1 = 295 K P1 = 95 kPa

Carry through with solution Calculate mass of air: Compression occurs from 1 to 2: But we need T3!

Get T3 with first law: Solve for T3:

Thermal Efficiency

Sample Problem – 2

Solution

Diesel Cycle P-V & T-s Diagrams

Sample Problem – 3

Gasoline vs. Diesel Engine