2. Model to Schedule A Flow Path through A Turbo-machine P M V Subbarao Professor Mechanical Engineering Department Description of the Journey is More Important than the Outcome ….

3. Complete Fluid Dynamics of Turbo-machinery Intake Delivery

4. Conservation Laws for a Fluid

5. Conservation of Mass : A Law for Sizing Conservation of Mass: Conservation of Mass for SSSF: Integrate from intake to delivery over entire volume :

6. Gauss Divergence Theorem The entire flow is only due to normal component of the velocity to the flow area : Specific Speed of the machine dictates the variation of Flow area along the fluid path!

7. Flow Area through A Turbo Machine Along the flow path, define area averaged mean velocity as:

8. Define area averaged mean density as:

9. Order of Velocity Vectors The real flow through any turbomachine is three dimensional. Axial, Radial and Circumferential. Axi-symmetry: Inter blade row space. Axi-symmetry assumes an average value to represent the state of working fluid in the blade-to-blade plane.

10. Meridional Plane The momentum balance is considered in a plane constructed through axis of rotation and radial axis. This Plane is called Meridional Plane. Euler Turbo-machinery Equation.

11. Axial Momentum Equations Axial Momentum Equation: A turbomachine cannot tolerate this force doing any work. The axial force should be completely absorbed by a thrust bearing. Any remaining traces of this force can cause mechanical or aerodynamic damages.

12. Concurrent Designs for Minimum Axial Thrust

13. Euler Turbo-machinery Power Equation. Conservation of Energy for Turbo-machines

14. For a Turbomachine: Combination of Euler and SFEE Over an ideal turbomachine blade along flow direction rothalpy remains constant

15. Conservation of Rothalpy A cornerstone of the analysis of steady, relative flows in rotating systems has, for many years, been the immutable nature of the fluid mechanical property rothalpy. "In a moving passage the rothalpy is therefore constant provided: – the flow is steady in the rotating frame; –no friction from the casing; –there is no heat flow to or from the flow. or