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 for Steady Flow:
Integrate from inlet to exit :

6. One Dimensional Stead FlowV 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 Nozzle: M <1
Subsonic Diffuser : 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 Diffuser
Supersonic Nozzle
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