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

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].

0

0 cos

m RT

P A

0

0

m T

P

0

0

519

14.7

Tm

mP

0 0

0 0STD STD

T p

T p

3

Total Pressure Mass Flow Parameter

Std.

Std.

Ambient Temperature

Am

bie

nt P

ress

ure

B

A

Stratosphere >65,000 ft

59 FTemperature

Altitude

3.202 psia

14.696 psiaPressure

36,089 ft

Altitude

36,089 ft

How to compare performanceof engines A & B, each at ownambient 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

0 02

0.4911628.73 . 14.11

1 .

56 515.67 47.4 61.51

39.3 /

29

a

a

a

psip in Hg psi

in Hg

T F R p psig psia

m lbm s

p

1 2

Consider the test of a compressor operating at the following conditions

Rig modificationat same indicated speed N = N

0 02

1

.88 . 14.68

29 488.67 49.6 64.28

41.1 /

. 2 ,

a

2

in Hg psi

T F R p psig psia

m lbm s

Consider Pr = p /p Since the tests were run at different conditions

they mus

Discuss value of rig modification as it relates to the compressors performance

.t be corrected to be compared

7

Example: Compressor Test Assessment

1 0

1 0

2 2

1

1

1:

/ 14.11 /14.7 0.960

/ 515.67 / 520 0.992

/ 61.51/ 0.960 64.073

/ 39.3 0.992 / 0.96 40.773 /

Pr 4.359

/ / 0.992 1.0040

a

a

C

C

Test

c

Test

p p

T T

p p psia

m m lbm s

N N N N

8

Example: Compressor Test Assessment

2 0

2 0

2 2

2

2

2 :

/ 14.68 /14.7 0.999

/ 488.67 / 520 0.940

/ 64.28 / 0.999 64.344

/ 41.1 0.940 / 0.999 39.888 /

Pr 4.377

/ / 0.940 1.0314

a

a

C

C

Test

c

Test

p p

T T

p p psia

m m lbm s

N N N N

Pr (4.377 4.359 / 0 / 4.359 100% 0.41%

( 40.773 39.888) / 40.773 100% 2.17%

(1.0314 1.0040 ) /1.0040 100% 2.73%c

test equipment may not be this accurate

m

N N N N

9

Example: Compressor Test Assessment

• Test 1: Baseline

• Test 2: After modifications

Pr

/

/

m

N

Pr

/

/

m

N

, .

.

Pr ,

.

Since N changed we are on a different speed line

We cannot really tell if efficiency increased or decreased

We can only say that and flow increased by the mods

which may improve performance

10

1

2

Ex: Compressor Test Assessment

11

Flow Coefficient-Compressible

1 2

1

1 1

1 1 1 1

QND D

m RTm

U A P U A

1

1 / 1m T mU UPA AT

12

Specific Speed

• Ns is a non-dimensional combination of so that diameter does not appear.

1/2 1/2 3/21/21

3/43/4 3/2 3/22

/

/s

Q N DN

gH N D

1/2

3/4s

N QN

gH

21 &

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 RPMQ CFSH "Ft".......Bad!

• Efficiency Correlated with Specific speed for many different machines…e.g. Pumps and Compressors

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

14

4/ 3.568 10

/ 2

/ 17,180

s s US

s s Eur

s US s Eur

N N

N N

N N

15

Specific Speed Used to Determine Turbomachine Type

1/2

3/4s

N QN

gH

16

Specific Speed Used to Determine Turbomachine Type

Low Ns High Ns

Be careful with these strange units

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)

1/2

3/4s

N QN

gH

17

Variation of Efficiency with Ns for Various Pump Sizes

Low Ns High Ns

Q

18

Specific Speed - Compressors

19

Specific Speed - Turbines

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]

1/21/2

3/4 3/4

4

1170 3201960

23.5

[ ] 3.658 10 0.717

s US

s s US

rpm gpmN QN

gH ft

N nondim N

21

Specific Speed• Consider Range of Impellers

• If We Set:Inducer (Inlet) DiametersInducer (Inlet) Axial Velocity, FlowWork CoefficientBacksweep (Impeller Exit Angle)RPMPressure Rise, Inlet P & T

• Then:– Exit Velocity Diagram, Angles & Speeds are Set

22

Specific Diameter• Specific Diameter is another combination of the

non-dimensional ’s so that N does not appear:

14

dim 12

14

dim 12

s

s non

DHD

Q

D gHD

Q

23

Specific Speed and Diameter Indicates Flowpath Shape

24

Specific Speed Indicates Flowpath Shape(Cordier Diagram)

From Wright and Balje

From Logan

Ns is dimensionless

25

Specific Speed Indicates Flowpath Shape (Cordier Diagram)

Note that axes are switched from previous figure

From Wright

Ns is in consistent units for this plot

26

Intro to Turbomachinery Analysis

[ , ]

[ , ]

[ ]

1

2

x U

x U

R

C absolute frame velocity C C C

also V

W relative frame velocity W W W

also V

absolute frame angle of velocity to axial

relative frame angle of velocity to axial

Subscripts normally

inlet to blade or stator

exit to blade

or stator

Hydraulic Turbines

• Low flow, high head: impulse, Pelton turbine

• Medium flow, medium head: Francis, pump turbine

• High flow, low head: Kaplan, bulb turbine

Impulse Type

Francis Type

Francis Turbine

Francis Turbine Runner Velocity Triangles for InwardFlow Reaction Turbine

33

0.5 0.75 0.5 0.75

: 250 [ ]

18 [ ] 1500 [ ]

. . .

/ 1500 250 /18 2714

[16,17]s

Ex Select type of pump to pump water of gpm Q to

overcome resistance of ft H if a motor of rpm N

is available Also estimate approx size and efficiency

N NQ H

From charts Franc

0.75

dim

dim

0.250.5

, 74%

1500, 250 0.5575 / 32.2 18 0.992

30

, 3.1

/ 0.472 5.7

s non

s non

s

is type

For size N

From Cordier D

D D Q gH ft in

34

Blade Design Intro - Centrifugal TurbomachinesRadial Turbines

If no viscosity: flow off blade surface tangent to metal surface

35

Centrifugal TurbomachinesRadial 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]

( )2 872.7

60 2 12 720

N D in NDU fps

1C��������������

1U��������������

1 1xW C����������������������������

38

Radial Turbine Example

22

1

2 22 2 1 1 2 1 1

0

0 0

2 300 / sec2 720 720

872.67 / sec720

030.4 /

/ 30.4 / 0.24 126.8

id od m

u um

r r D NNU ft

DNU ft

Euler equation

U C U C U U Uh BTU lb

gJ gJ gJ

T h Cp R

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

2 2 1 10

1 1 2

21

0

0 0

Since & 0

30.4 /

/ 30.4 / 0.24 126.8

u u

u u

p

U C U Ch

gJ

C U C

Uh BTU lbm

gJ

T h c R

40

Radial Turbine Example• Temperature Ratio:

Tr = 1.0923 = (1500)/(1500-126.8)=TT1/TT2

• Rearranging the Turbine Efficiency Equation:

• Mass Flow:

Tt2 abs = 1373.2 R = 1500 - 126.8

Pt2 abs = 141.61 psia = 200/1.4123

M2 abs = .25 = given

A2 = 2.7 sq. in. =

/ 1

01

02

1 1/1 1.4123r

r

pTP

p

2 22 14

D D

41

Radial Turbine Example

• FP0 Equation:

• Power Output:

1

2 10 2

0

11.0883 1

cos 2

2.28 / secm

m TM M

P A

m lb

.2.28 30.41 778.16

sec 98.1.

550sec

lbm BTU ft lbflbm BTU HPft lbfHP

42

Radial Turbine Example

• Exit Velocity Diagram:

0

2

1356.21

12

. 451.3 / sec

TT

M

Total Abs Velocity C M gRT ft

2 2. 541.92 / secTotal Rel Velocity W C U ft

2. . 300 / sec720

mU

D NRel Circ Velocity U W ft

43

Radial Turbine Ex. – Dmean Velocity Triangle

Circumferential Direction

1 1 0451.3cos cos 33.61

541.92exit

C

W