Gas Cycles

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

3. 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.

4. 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.

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

6. Some nomenclature before starting internal combustion engine cycles

7. More terminology

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

9. 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.

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

11. Real Otto cycle

12. Real and Idealized Cycle

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

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

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

16. Differences between Otto and Carnot cycles

17. 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

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

19. Otto Cycle Derivation • Summarizing where and then Isentropic behavior

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

21. Effect of compression ratio on Otto cycle efficiency

22. 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.

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

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

25. Get T3 with first law: Solve for T3:

26. Thermal Efficiency

27. Sample Problem– 2

28. Solution

31. Diesel Cycle P-V & T-s Diagrams

34. Sample Problem– 3

37. Gasoline vs. Diesel Engine