1. Turbomachinery
Lecture 4b
Compressor / Engine Maps
Radial Turbine

2. Total Pressure Mass Flow Parameter
Defines common flow parameters.
Valid for flow with one gas.
Corrected flow to standard day [eliminate effect of outside ambient conditions].

3. Total Pressure Mass Flow Parameter
Altitude
Altitude
Stratosphere
>65,000 ft
36,089 ft
36,089 ft
3.202 psia
psia
59 F
Pressure
Temperature
Std.
Ambient Temperature
Ambient Pressure B A
How to compare performance
of engines A & B, each at own
ambient conditions?
- Use corrected flow variables

4. Compressor Performance Map

5. Turbomachine Map
Functional behavior of map [mc, Nc, PR] is solely dependent on machine
Behavior is applicable to
Compressors: axial, centrifugal
Turbines: axial, centrifugal
Multi-stage machines
Choke limit: cannot pass more massflow
Sonic flow occurs at minimum area location
Surge limit: onset of instability
Stall: too low mass flow, flow separates

6. Example: Compressor Test Assessment

7. Example: Compressor Test Assessment

8. Example: Compressor Test Assessment

9. Example: Compressor Test Assessment
Test 1: Baseline
Test 2: After modifications

10. Ex: Compressor Test Assessment2 1

11. Flow Coefficient-Compressible

12. Specific Speed
Ns is a non-dimensional combination of so that diameter does not appear.

13. Specific Speed
Ns is non-dimensional when consistant units are used for N, Q & H.
Inconsistent units are often used making Ns a garble of funny units. Typical:
N RPM
Q CFS
H "Ft" Bad!
Efficiency Correlated with Specific speed for many different machines…e.g. Pumps and Compressors

14. Specific Speed U.S. Customary Units: H [ft], Q [gal/min], N [rpm]
Europe Customary Units: H [m], Q [m3/s], N [rot/sec – Hz]
Conversion ratios

15. Specific Speed Used to Determine Turbomachine Type

16. Specific Speed Used to Determine Turbomachine Type
Here H (head) is in ft
Q (volume flow) is in gallons per minute
N (shaft speed) is in RPM
Ns is dimensional  (rpm)(gpm)0.5/(ft0.75)
Be careful with these strange units
Low Ns
High Ns

17. Variation of Efficiency with Ns for Various Pump SizesQ
Low Ns
High Ns

18. Specific Speed - Compressors

19. Specific Speed - Turbines

20. Example
A pump is designed to deliver 320 gpm of gasolene. The required net head is 23.5 ft. The pump shaft rotates at 1170 rpm. Pick the best type of pump.
Centrifugal pump is the most apt choice [see chart 18]

21. Specific Speed Consider Range of Impellers If We Set:
Inducer (Inlet) Diameters
Inducer (Inlet) Axial Velocity, Flow
Work Coefficient
Backsweep (Impeller Exit Angle)
RPM
Pressure Rise, Inlet P & T
Then:
Exit Velocity Diagram, Angles & Speeds are Set

22. Specific Diameter
Specific Diameter is another combination of the non-dimensional P’s so that N does not appear:

23. Specific Speed and Diameter Indicates Flowpath Shape

24. Specific Speed Indicates Flowpath Shape (Cordier Diagram)
From Logan
Ns is dimensionless
From Wright and Balje

25. Specific Speed Indicates Flowpath Shape (Cordier Diagram)
Ns is in consistent units for this plot
Note that axes are switched from previous figure
From Wright

26. Intro to Turbomachinery Analysis

27. Hydraulic Turbines Low flow, high head: impulse, Pelton turbine
Medium flow, medium head: Francis, pump turbine
High flow, low head: Kaplan, bulb turbine

28. Impulse Type

29. Francis Type

30. Francis Turbine

31. Francis Turbine Runner
Velocity Triangles for Inward
Flow Reaction Turbine

34. Blade Design Intro - Centrifugal Turbomachines Radial Turbines
If no viscosity: flow off blade surface tangent to metal surface

35. Centrifugal Turbomachines Radial Turbines

36. Radial Turbine Example
T0=1500 R
P0=200 psia
N=50,000 rpm
=90%
Cu1=U1, 1=0
Cu2=0 [no swirl]
M2=0.25
C is absolute frame velocity vector [Cu, Cr]
Cu is tangential or circumferential component

37. Radial Turbine Example
Tip Speed
Entrance Velocity Diagram [W is relative frame velocity vector]

38. Radial Turbine Example

39. Intro to Turbomachinery Analysis
Uses Euler’s Equation Which Works for Axial, Radial, and Mixed Flow Turbomachinery
Work done by turning Cu and by change in radius U
Temperature Drops Across Turbine Rotor

40. Radial Turbine Example
Temperature Ratio:
Tr = = (1500)/( )=TT1/TT2
Rearranging the Turbine Efficiency Equation:
Mass Flow:
Tt2 abs = R =
Pt2 abs = psia = 200/1.4123
M2 abs = .25 = given
A2 = 2.7 sq. in. =

41. Radial Turbine Example
FP0 Equation:
Power Output:

42. Radial Turbine Example
Exit Velocity Diagram:

43. Radial Turbine Ex. – Dmean Velocity Triangle
Circumferential Direction