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Gas Dynamics for Study of Nozzles@ Critically Off-Design Conditions

Gas Dynamics for Study of Nozzles@ Critically Off-Design Conditions. P M V Subbarao Professor Mechanical Engineering Department. Recognize the Surprises, if Any …. Convergent-Divergent Nozzle : p b,design <p bt < p b,critical. Standing Normal Shock in Diverging Section of CD Nozzle.

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Gas Dynamics for Study of Nozzles@ Critically Off-Design Conditions

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  1. Gas Dynamics for Study of Nozzles@ Critically Off-Design Conditions P M V Subbarao Professor Mechanical Engineering Department Recognize the Surprises, if Any…..

  2. Convergent-Divergent Nozzle : pb,design <pbt < pb,critical

  3. Standing Normal Shock in Diverging Section of CD Nozzle Normal Shock : A large discontinuity M<1 M<1 M>1

  4. Movement of Normal Shock Towards Exit pb,design <pbt < pb,critical

  5. Back Pressure Responsible for NS at Nozzle Exit

  6. Occurrence of Attached Oblique Shock

  7. Flow Visualization Studies

  8. Approaching to Design Back Pressure

  9. Steady Cruising Design Conditions

  10. Local Turbulence leading to Back Pressure Lower than the design conditions

  11. Back Pressure Lower than the design conditions

  12. Back Pressure Lower than the design conditions

  13. Temperature Entropy Diagram for A Real Nozzle p0jet,s = p0in P0jet,a T0in T p = pjet Tjet,s Tjet,a s Main Irreversibility : Friction

  14. Comprehensive Design Methods for Efficient Nozzles

  15. Design of Nozzle : First Step • The nozzle deals with expansion of turbine exit gas from a low subsonic flow to supersonic outlet condition and hence this is a convergent-divergent (CD) nozzle. • The first step in the design of a nozzle is to determine the dimensions of inlet area:

  16. One dimensional Gas Dynamics Equations Non reaction, no body forces, viscous work negligible Conservation of mass for steady flow: Conservation of momentum for frictional steady flow: Conservation of energy for ideal steady flow:

  17. Other Equations Ideal Gas law : Mach number equation :

  18. Theory of Nozzle Design Momentum equations for Adiabatic steady one dimensional frictional flow : • The conventional design practices are based on dictating the variation of cross-sectional area (geometric theory)of the ejector. • It is well known fact that the nozzle establishes continuous momentum and energy changes in the flow of gas from inlet to exit. • Final flow outlet conditions are achieved for a given inlet conditions of flow. • A physics based design theory is essential.

  19. Physics based Design Theories • Constant Rate of Momentum Change (CRMC) • Constant Rate of Kinetic Energy Change (CRKEC) • CRMC theory: • Define M as rate Momentum of gas flow. • The change in rate of momentum of gas flow is defined as: • The basis for the CRMC theory is to keep the value of dM/dx constant. • Select an appropriate value for this constant.

  20. Design Equations for CRMC Nozzle Base equation for CRMC nozzle: Momentum equation: Contd…

  21. Estimation of Friction Term

  22. Flow Chart for Geometry generation

  23. Model Nozzle λ = 45658 Inlet temperature = 298K Inlet Pressure= 400kPa Inlet Area = 0.000176625 m2 Mass flow rate = 0.03767 kg/s Thickness of the pipe = 0.0125 m Coeffecient of condcution of the material = 54 W/m2K (Mild steel) Tamb = 298 K

  24. Shape of CRMC Nozzle

  25. Pressure variation in CRMC Nozzle

  26. Design Equations for CRKEC Nozzle Base equation for CRKEC nozzle: Incremental change in local cross sectional area :

  27. Road Map to Test Novel Ideas

  28. Computerized Gas Dynamic Analysis of Nozzle

  29. Continuity equation R- momentum equation Equation of state Turbulence equations Energy equation COMPUTATIONAL STUDIES - Governing Equations Z- momentum equation

  30. Boundary Conditions

  31. Grid Size independence check We have selected grid size of 0.1mm Comparison of Friction vs. frictionless model Lambda 200 Lambda 500

  32. Optimization of CRMC nozzle length

  33. Simulation Results

  34. Analysis of Simulation data

  35. Optimal design of CRMC Design Total

  36. Experimental Set-up

  37. IIT DELHI

  38. Comparison of Experimental and Fluent data Inlet Pressure=300kPa

  39. Comparison of Experimental and Fluent data

  40. F-14 Engine TF-30-P-414 engine manufactured by Pratt and Whitney Aircraft

  41. F-14 Engine Performance Rating Performance ratings at standard altitude conditions

  42. Simulation at Design Condition (CRMC) Static Temperature variation along nozzle length Static Pressure variation along nozzle length Mach number variation along nozzle length

  43. Simulation at Intermediate at Sea Level Conditions (CRKC) Static Pressure variation along nozzle length Static Temperature variation along nozzle length Mach number variation along nozzle length

  44. Comparison of Normalized total Pressure

  45. Comparison of Normalized total Pressure

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