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One Dimensional Flow with Heat Addition

One Dimensional Flow with Heat Addition. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. A Gas Dynamic Model for Combustors…. Conservation Laws for a Real Fluid. One Dimensional Stead Flow. A+dA, V+dV r+ d r. A, V r. dl.

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One Dimensional Flow with Heat Addition

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  1. One Dimensional Flow with Heat Addition P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Gas Dynamic Model for Combustors…..

  2. Conservation Laws for a Real Fluid

  3. One Dimensional Stead Flow A+dA, V+dV r+dr A, V r dl

  4. Conservation of Momentum For A Real Fluid Flow No body forces One Dimensional Steady flow A+dA, V+dV r+dr A, V r dl

  5. Conservation of Energy Applied to 1 D Steady Flow Steady flow with negligible Body Forces For a real fluid the rate of work transfer is due to viscous stress and pressure. The effect of viscous dissipation can be modified as flow with some extra heat addition.

  6. For steady and perfect gas flow :

  7. Summary of Real Fluid with Heat Transfer Ideal Gas law:

  8. Flow in A Constant Area Duct with heat Transfer

  9. Ideal Flow in A Constant Area Duct with heat Transfer

  10. Using continuity and gas equations: We get Momentum equation gives Substitute gas equation in momentum equation to get:

  11. Using energy equation

  12. Mach number equation: This shows that dV has same sign as dM.

  13. is positive Subsonic Flows At low velocities, adding heat increases the velocity. Removing heat decreases the velocity.

  14. is negative Supersonic Flows At high velocities, adding heat decreases the velocity. Removing heat increases the velocity.

  15. Entropy Change : Heat Addition or Removal

  16. gas equation in momentum equation gives:

  17. Change over A Finite Length 2 1 Momentum equation gives

  18. Integrating from point 1 to point 2:

  19. Integrating from point 1 to point 2: At low velocities, adding heat increases the velocity. At low velocities, removal of heat dereases the velocity. Addition of heat leads to leads the flow to move towards M=1. Removal of heat leads to leads the flow to move away from M=1. Therefore T0 will be maximum when M=1.

  20. Change In Static Temperature On Integration :

  21. Variation of Stagnation Temperature with Mach Number Heat Removal Heat Removal T0 Heat Addition Heat Addition M

  22. Entropy Change : Heat Addition or Removal Integration from 1 to 2:

  23. Total heat transfer per unit mass flow rate

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