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Comprehensive Design Methods for Steady Flow Control Volumes

This design guide provides a thorough approach to optimizing fuel savings in mechanical engineering by focusing on conservation laws and geometric design principles for steady flow. It covers equations for mass, momentum, energy conservation, and additional ideal gas laws, with special emphasis on controlling Mach numbers in subsonic and supersonic flows. By incorporating considerations like area changes, friction, and heat transfer, the guide equips designers with tools to enhance flow performance effectively.

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Comprehensive Design Methods for Steady Flow Control Volumes

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  1. Design of Passive (Adiabatic) Control Volumes P M V Subbarao Professor Mechanical Engineering Department A Comprehensive Design Method for Overall Fuel Savings…..

  2. Geometric Design of Intakes & Nozzles

  3. One–Dimensional Frictional Flow through Variable Area

  4. Conservation Laws for a Real Fluid

  5. Conservation of Mass Applied to 1 D Steady Flow Conservation of Mass: Conservation of Mass for Steady Flow: Integrate from inlet to exit :

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

  7. Governing Equations for 1D Steady flow 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:

  8. Additional Equations Ideal Gas law : Mach number equation :

  9. Wall Shear Stress & Friction Factor Convenient to write the friction induced shear force, x, in terms of a friction factor Darcy Friction Factor Hydraulic Diameter

  10. Design Model thru momentum equation

  11. Design Equations for 1D Steady flow 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:

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

  13. Design Equation for Variable Area Conduit Combine conservation, state equations– to get design equations for steady one dimensional frictional flow : So we have three ways to change the Mach number of a flow – area change (dA): – friction: f > 0, same effect as –dA – heat transfer: heating, q’’’ > 0, like –dA cooling, q’’’ < 0, like +dA

  14. Effect of Shape of duct on Flow Consider an isentropic flow through a variable area duct: Pure shape effects :

  15. Pure Shape Effects ….. A truth Beyond Common Sense

  16. Control of Mach Number in Subsonic Flows Subsonic Diffuser : M <1 Subsonic Nozzle: M <1 dA < 0 dA > 0 So, dV > 0 & dp <0 So, dV < 0 & dp>0

  17. Control of Mach Number in Supersonic Flows Supersonic Nozzle Supersonic Diffuser dA < 0 & M >1 So, dV < 0 & dp >0 dA > 0 & M >1 So, dV >0 & dp<0

  18. Generation of High Pressure from Supersonic velocity : Isentropic Devices

  19. Occurrence of Maximum Allowable Velocity Section At M =1 Minimum Area = A* : Also called throat For a given mass flow rate:

  20. Geometry of Isentropic Diffuser

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