Compressible Flow

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Coursework material provides the technical performance analysis of nozzle, diffuser and thrust for subsonic compressible flow conditions.

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Compressible Flow

  1. 1. Compressible Flow -- i -- Engineering Software P.O. Box 1180, Germantown, MD 20875 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Compressible Flow By Engineering Software Copyright @ 1996
  2. 2. Compressible Flow -- 1 -- Table of Contents Nozzle............................................................................................................................................................................2 Analysis .....................................................................................................................................................................2 Assumptions...............................................................................................................................................................5 Governing Equations .................................................................................................................................................6 Input Data ..................................................................................................................................................................6 Results .......................................................................................................................................................................7 Conclusions................................................................................................................................................................8 Diffuser..........................................................................................................................................................................9 Analysis .....................................................................................................................................................................9 Assumptions.............................................................................................................................................................12 Governing Equations ...............................................................................................................................................13 Input Data ................................................................................................................................................................13 Results .....................................................................................................................................................................14 Conclusions..............................................................................................................................................................15 Thrust...........................................................................................................................................................................16 Analysis ...................................................................................................................................................................16 Assumptions.............................................................................................................................................................19 Governing Equations ...............................................................................................................................................20 Input Data ................................................................................................................................................................20 Results .....................................................................................................................................................................21 Conclusions..............................................................................................................................................................22
  3. 3. Compressible Flow -- 2 -- Nozzle This section provides an isentropic nozzle analysis when the working fluid is air. Analysis In the presented nozzle analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a nozzle at point 1 and it exits the nozzle at point 2. Isentropic expansion is considered with no entropy change. Figure 1 presents a nozzle schematic layout.
  4. 4. Compressible Flow -- 3 -- Figure 1 - Nozzle Schematic Layout Figure 2 presents a nozzle temperature vs entropy diagram.
  5. 5. Compressible Flow -- 4 -- Figure 2 - Nozzle Temperature vs Entropy Diagram Figure 3 presents nozzle performance -- stagnation over static temperature and pressure ratio values-are provided as a function of the Mach Number. Only subsonic nozzle operation is considered. It should be noted that air enters the nozzle at the stagnation conditions of 1,500 [K] and 10 [atm] of absolute pressure.
  6. 6. Compressible Flow -- 5 -- Figure 3 - Nozzle Performance vs Mach Number One can notice that nozzle stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. Assumptions Working fluid is air. There is no friction and heat transfer. Expansion is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
  7. 7. Compressible Flow -- 6 -- Governing Equations Tt /T = (1 + M2(ϰ - 1)/2) pt/p = (1 + M2(ϰ - 1)/2)ϰ/(ϰ-1) Tt/T = (pt/p)(ϰ-1)/ϰ v = (2cp(Tt - T))1/2 vs = (ϰRT)1/2 M = v/vs ϰ = cp/cv cp - cv = R pv = RT Input Data T1 = 1,500 [K] p1 = 10 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = 1.4 [/] M = 0.39, 0.67 and 1 [/]
  8. 8. Compressible Flow -- 7 -- Results Nozzle Performance vs Outlet Mach Number Nozzle Inlet Stagnation Temperature = 1,500 [K] and Pressure = 10 [atm] Outlet Mach Number [/] Stagnation/Static Temperature Ratio [/] Stagnation/Static Pressure Ratio [/] 0.39 1.03 1.11 0.67 1.09 1.35 1.00 1.19 1.86
  9. 9. Compressible Flow -- 8 -- Conclusions Nozzle stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
  10. 10. Compressible Flow -- 9 -- Diffuser This section provides an isentropic diffuser analysis when the working fluid is air. Analysis In the presented diffuser analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a diffuser at point 1 and it exits the diffuser at point 2. Working fluid inlet velocity gets reduced to zero resulting in the stagnation temperature and pressure increase. Isentropic process is considered with no entropy change. Figure 1 presents a diffuser schematic layout.
  11. 11. Compressible Flow -- 10 -- Figure 1 - Diffuser Schematic Layout Figure 2 presents a diffuser temperature vs entropy diagram.
  12. 12. Compressible Flow -- 11 -- Figure 2 - Diffuser Temperature vs Entropy Diagram Figure 3 presents diffuser performance -- stagnation over static temperature and pressure ratio values are provided as a function of the Mach Number. Only subsonic diffuser operation is considered. It should be noted that the air enters the diffuser at the static conditions of 298 [K] and 1 [atm] of absolute pressure.
  13. 13. Compressible Flow -- 12 -- Figure 3 - Diffuser Performance vs Mach Number One can notice that diffuser stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. Assumptions Working fluid is air. There is no friction and heat transfer. Isentropic process -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
  14. 14. Compressible Flow -- 13 -- Governing Equations Tt /T = (1 + M2(ϰ - 1)/2) pt/p = (1 + M2(ϰ - 1)/2)ϰ/(ϰ-1) Tt/T = (pt/p)(ϰ-1)/ϰ Tt = T + v2/(2cp) vs = (ϰRT)1/2 M = v/vs ϰ = cp/cv cp - cv = R pv = RT Input Data T1 = 298 [K] p1 = 1 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = 1.4 [/] M = 0.29, 0.58 and 0.95 [/]
  15. 15. Compressible Flow -- 14 -- Results Diffuser Performance vs Inlet Mach Number Diffuser Inlet Static Temperature = 298 [K] and Pressure = 1 [atm] Inlet Mach Number [/] Stagnation/Static Temperature Ratio [/] Stagnation/Static Pressure Ratio [/] 0.29 1.017 1.06 0.58 1.067 1.25 0.95 1.182 1.80
  16. 16. Compressible Flow -- 15 -- Conclusions Diffuser stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
  17. 17. Compressible Flow -- 16 -- Thrust This section provides an isentropic thrust analysis when the working fluid is air. Analysis In the presented thrust analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a nozzle at point 1 and it exits the nozzle at point 2. Isentropic expansion is considered with no entropy change. Figure 1 presents a thrust schematic layout.
  18. 18. Compressible Flow -- 17 -- Figure 1 - Thrust Schematic Layout Figure 2 presents a thrust temperature vs entropy diagram.
  19. 19. Compressible Flow -- 18 -- Figure 2 - Thrust Temperature vs Entropy Diagram Figure 3 presents thrust performance as a function of the nozzle inlet stagnation temperature and pressure values for a few fixed values such as: working fluid mass flow rate, nozzle outlet Mach Number and ambient pressure. Only subsonic nozzle operation is considered.
  20. 20. Compressible Flow -- 19 -- Figure 3 - Thrust Performance One can notice that thrust increases with an increase in the inlet stagnation temperature and pressure values. Assumptions Working fluid is air. There is no friction and heat transfer. Expansion is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
  21. 21. Compressible Flow -- 20 -- Governing Equations Tt /T = (1 + M2(ϰ - 1)/2) pt/p = (1 + M2(ϰ - 1)/2)ϰ/(ϰ-1) Tt/T = (pt/p)(ϰ -1)/k v = (2cp(Tt - T))1/2 vs = (ϰRT)1/2 M = v/vs ϰ = cp/cv cp - cv = R pv = RT Thrust = vm + (p - pa)A Input Data T1 = 900, 1,200 and 1,500 [K] p1 = 5, 10 and 15 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = 1.4 [/] m = 1 [kg/s] M = 0.85 [/] pa = 1 [atm]
  22. 22. Compressible Flow -- 21 -- Results Thrust Performance vs Nozzle Inlet Stagnation Temperature and Pressure Outlet Mach Number = 0.85 [/] and Ambient Pressure = 1 [atm] Working Fluid Mass Flow rate = 1 [kg/s] Thrust [N] Inlet Stagnation Temperature [K] Inlet Stagnation Pressure [atm] 900 1,200 1,500 5 797.7 922.3 1,031.1 10 873.5 1,009.5 1,128.6 15 898.7 1,038.7 1,161.3
  23. 23. Compressible Flow -- 22 -- Conclusions Thrust increases with an increase in the inlet stagnation temperature and pressure values. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.

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