1. Frames of Reference 1

2. 2 Axial Compressor Velocity Diagram: 1 2 3 N

3. Frames of Reference 3

4. 4 Compressor Stage Thermodynamic and Kinematic View Across rotor, power input is Across stator, power input is From mass conservation, and if c x = constant, then Euler’s equation

5. 5 Analysis of Stage Performance Geometry = velocity triangles Flow = isentropic relations [CD] Thermodynamics =Euler eqn., etc. –All static properties independent of frame of reference –All stagnation properties not constant in relative frame

6. 6 Compressor Stage Thermodynamic and Kinematic View Euler’s equation continued Large turning (  1 -  2 ) within rotor leads to high work per stage, but this is in reality limited by boundary layer effects for constant U, the work per pound of air decreases linearly with increasing mass flow rate. Thus slight increases in m leads to decreased W, decreased pressure ratio leading to lower m

7. 7 Work Coefficient Define Work Coefficient: Applying Euler's Equation to E

8. 8 Work Coefficient

9. 9 This equation relates 2  terms to velocity diagrams and applies to both compressors & turbines. The physics, represented by Euler’s Equation, matches the implications of Dimensional Analysis.

10. 10 Work and Flow Coefficients Solution continued : W1 C1 U Cx1 11 11