5BB49ECBd01

8/8/2019 5BB49ECBd01

1/48

Copyright 2003

Nara anan Komerath

1

AE6450 Fall 2004

Lecture # 8Turbomachinery for Liquid Rocket Engines

8/8/2019 5BB49ECBd01

2/48

Copyright 2003

Nara anan Komerath

2

Demands on Rocket Turbomachinery

Huge propellant flow rates.F1 (Apollo Saturn II first stage, LOX-RP1) 2600 kg/s

J2 (Apollo Saturn II 2nd & 3rd stages: LOX-LH2: 250 kg/s

SSME: LOX/LH2 468 kg/s

(Compare to 100 kg/s for typical 20,000 lbf thrust fighter engine)

Huge pressures: 55MPa for SSME LOX pump; 45 MPa for LH2

Very high Power per unit mass. SSME LH2 pump: 100HP per lb.

8/8/2019 5BB49ECBd01

3/48

Copyright 2003

Nara anan Komerath

3

Where we need turbopumps

PayloadRatio

u

Turbopump System

Gas PressurizedSystem

At high values ofu, the turbopump makes a big difference to thepayload ratio of the vehicle

8/8/2019 5BB49ECBd01

4/48

Copyright 2003

Nara anan Komerath

4

Successful DesignsRocketDyne Mark 3 (2500+ produced) or H-1 pump (below)

Both fuel and LOX pumps on the same shaft. Each has:

- Axial inducer single centrifugal stage pump on the same

shaft.

Two-stage axial turbine running at 4.9 times the pump speed.

Large gear reduction unit.

This cutaway drawing of the turbopump

for the H-1 engine shows the back-to-back arrangement of oxidizer pump (at

left end) and fuel pump (at right end)

operating off a common turbine and

gear box (center). The propeller-likeinducer blades can be seen on the left

end of the shaft.

history.nasa.gov/ SP-4206/p94.jpg

8/8/2019 5BB49ECBd01

5/48

Copyright 2003

Nara anan Komerath

5

A cutaway drawing of

the Mark 10

turbopump for the F-1engine

http://history.nasa.gov/ SP-4206/ch4.htm

8/8/2019 5BB49ECBd01

6/48

Copyright 2003

Nara anan Komerath

6

SSME Turbopumps

LOX and LH2 inducers separated from respective pumps and driven by different

turbines at very different speeds. One centrifugal stage for LOX (highest

pressure); Three centrifugal stages for LH2. No gear reduction unit.

http://elifritz.members.atlantic.net/photos/ssme3.gif

8/8/2019 5BB49ECBd01

7/48

Copyright 2003

Nara anan Komerath

7

Some Preliminary Design Considerations

Engine thrust requirement generates requirements for mass flow rate andchamber pressure.

This leads to the requirement for the pump system mass flow rate and

exit pressure.

Centrifugal pumps allow much larger pressure rise per stage than axial pumps.

Also, easier to deal with fluid vaporization / multiphase flows in centrifugal

pumps than in axial pumps.

A centrifugal pump stage takes fluid in near the hub and sends it out near

the tip of the Impeller.

1tD 2tD

8/8/2019 5BB49ECBd01

8/48

Copyright 2003

Nara anan Komerath

8

At the first stage inlet of a centrifugal impeller, there is suction.

An Inducer is a pump which pressurizes fluid whose static pressure isnot much higher than its vapor pressure. This allows the propellant tank

pressure to be kept low, minimizing tank weight.

Without an inducer, the suction at the impeller inlet would boil the liquid

and cause cavitation. Cavitation has two terrible effects:

Extended operation under cavitation (bubble form and burst, with very

large pressure fluctuations) erode and eventually destroy blade surfaces.

This is not a big deal for rocket pumps whose entire operation lifetimes are

measured in a few minutes.

Formation of vapor blocks the flow passages and cuts down the mass

flow rate. Big problem.

An inducer pressure rise of 10%-20% prevents cavitation

Inducer

8/8/2019 5BB49ECBd01

9/48

Copyright 2003

Nara anan Komerath

9

=

=g

PPNPSH

vapori

Net Positive Suction Head

How far the inlet pressure is above the vapor pressure. About 10 20% is

considered adequate to prevent significant cavitation problems.

net positive suction head (m, ft)

(Table B.1 pp 696 Humble)

8/8/2019 5BB49ECBd01

10/48

Copyright 2003

Nara anan Komerath

10

Humble recommends (Pg. 212) 80% for LOX,

RP and other dense liquids; 75% for LH2This power comes from the turbine

=

1

11turbine avail t t P i

t ratio

P m C T

P

=(turbine efficiency) (mass flow through the turbine)(function of turbine

inlet temp. & turbine pressure ratio)

ratiot

turbineout

in PP

P=

hp

Specific Speed

turbine gas

where

Pump efficiencies vary with speed, size, propellant types.

8/8/2019 5BB49ECBd01

11/48

Copyright 2003

Nara anan Komerath

11

mass flow rate depends on cycle choice, GG vs SC etc.

For GG or SC engines,

70T

KTi 1100=

This is often an iterative solution as speeds, efficiencies, mass flows,

and other parameters change.

availturbinereqpump =

% per Humble (varies)

which is the highest obtainable for

typical construction materials

(titanium).

For expander cycle, Ti is lower depending on how much heat isabsorbed through nozzle cooling (650K down to 225K).

In balance,

8/8/2019 5BB49ECBd01

12/48

Copyright 2003

Nara anan Komerath

12

Example:

= 65.8%P

[ ] [ ][ ]

658.

4790/8922.32

1/2.32 2 ftslbm

lbm

kgsft

P reqpump

=

HPlbft 800,1110493.6

6

==

Fuel side892lbm/s

H=4790ft

8/8/2019 5BB49ECBd01

13/48

Copyright 2003

Nara anan Komerath

13

Turbine

(1BTU/s=1.41455HP )

0

0

.

.415 /

1.124

.653

1400 1860

58.2%23.7

92

P

i

T

tmt

OforLOX RP

F

BTUC

lbm R

T F R

P

lbmm

s

=

=

= =

=

=

=

Pi, Ti

Pe

8/8/2019 5BB49ECBd01

14/48

Copyright 2003

Nara anan Komerath

14

[ ] [ ]

=

124.1

124.

0

7.23

11

1860653./92582. RRlbm

BTUslbmP availturbine

== sBTU

HP

s

BTU

/1

415.12.19169

HPavailturbine 27124=

8/8/2019 5BB49ECBd01

15/48

8/8/2019 5BB49ECBd01

16/48

Copyright 2003

Nara anan Komerath

16

This characterizes suction performance, and indicates the minimum netpositive suction head at which a pump operating at a given rotation speed and

volume flow rate, can operate without cavitation affecting performance. A given

pump inlet geometry gives close to the same suction specific speed no matter

what its absolute values of size, rotation speed or volume flow rate.

Large values indicate ability to operate at low inlet pressure

- large pump inlet tip diameter and small inlet hub diameter to minimize inletaxial velocity head (which is a big part of the NPSH) .

- thin, gradually curving blades with sharp leading edges to get minimal static

pressure gradients on blade surfaces.

Suction-specific speed Uss

8/8/2019 5BB49ECBd01

17/48

Copyright 2003

Nara anan Komerath

17

( ) =

.75

ss

u NPSH

Q

(Humble eq. 5.63)

ssuwhere = suction-specific speed depending on type of propellantbeing pumped

= 130 LH2

90 cryogenics other than LH2

70 non-cryogenic liquids

(this limits how fast the pump rotates)

8/8/2019 5BB49ECBd01

18/48

Copyright 2003

Nara anan Komerath

18

Turbo-machinery design variables

==

pumpm

Q

.

Pumps

Types of pumps

Radial

Mixed Flow

Axial

good for higher specific speeds provides higher suction parameter

Define

volumetric flow rate (m3/s or gpm)

=

=g

H PPpump head pressure rise (m, ft)

==g

PPNPSH

vaporinet positive suction head (m, ft)

(amount of excess pressure at pump inlet above vapor pressure to avoid

cavitation)

(Table B.1 pp 696 Humble)

8/8/2019 5BB49ECBd01

19/48

Copyright 2003

Nara anan Komerath

19

Assuming we have a boost pump in the line

Then

= =

.75s

P

QN

H

n

pump stage specific speed (units =

2/1

75.

75.

3 /

s

m

m

sm=

n = number of stages to get head rise required by each stage

In SI units, Humble recommends sizing Ns to be ~ 2 for LH2 and 3 for other liquids

as a reasonable compromise between pumping efficiency and high rad/s.

Humble Eq. 5.61

8/8/2019 5BB49ECBd01

20/48

Copyright 2003

Nara anan Komerath

20

=

30N RPM (revolutions per minute)

Note 1: in English units, Q is often gallons/minuts and H is in ft. As a

result, Ns in English units is typically 500-3000 meets higher numbers.

Note 2: At higher Ns values, axial pumps are more competitive (often

used for LH2) where is low.

If we dont have a boost pump, then we need to worry about cavitation

(i.e., NPSH)

Alternatively,

8/8/2019 5BB49ECBd01

21/48

Copyright 2003

Nara anan Komerath

21

= =

Pt

gHu

n

=

r

t

t N

u

D

2

2 =

( )

=

31

2

4

1t

r

Q

DN L

Humble recommends taking the lower allowable from the two expressions(based on uss or Ns) if there is no boost pump, else just use the first formula (5.61)

Once we have , we can estimate the pump size ( for a typical centrifugal pumpwith an inducer) (empirical)

impeller tip speed (m/s)

pump head coefficient

Use .60 for LH2

.55 for others

1tD 2tD

Pump Size

8/8/2019 5BB49ECBd01

22/48

Copyright 2003

Nara anan Komerath

22

= inducer flow coefficient; Use 0.10

inducertip

hub

D

D

L = inducer ; Use 0.3

P

Preq

HmgP

.

=Recall, required shaft power (numerator is fluid power)

(pump efficiency ~ 80% - changes with Ns)

8/8/2019 5BB49ECBd01

23/48

Copyright 2003

Nara anan Komerath

23

B

r

req

tp N

P

Am

=

reqP tpmrNtpm

Thinking ahead to system weight (empirical relationship)

Mass of turbo-pump assembly

in kg (Humble 5.70)

A = 1.3- 2.6 (say 1.5)

B = 0.6- 0.667 (say 0.6)

Nr in rad/s, Preq in watts or Nm/s

As as

8/8/2019 5BB49ECBd01

24/48

Copyright 2003

Nara anan Komerath

24

Compressor Basics

Compressors usually operate in two steps (though in some designs

it may not be possible to distinguish between these steps):

1. Increase the momentum of the fluid by doing work on it (using

rotor blades, for example)2. Decelerate the air to increase static pressure (using stator stages).

Often, the compression takes place through several compressor

stages, with each stage increasing the pressure by a factor of, say,1.8 or 2. Modern jet engines may have as many as 15 compressor

stages, rotating on as many as three independent concentric shafts.

Both "Centrifugal" and "Axial" compressors are used.

Objective: To increase the pressure of a propellant/working fluid before heataddition. The thermodynamic cycle efficiency of a gas turbine engine is

strongly dependent on the ratio of the highest to the lowest pressure in the

engine.

8/8/2019 5BB49ECBd01

25/48

Copyright 2003

Nara anan Komerath

25

CENTRIFUGAL COMPRESSOR

The tuboprop engine shown above uses

two stages of centrifugal compression.

Here the air enters the compressor close

to the hub, and is then impelled outwards

by the blades. It is then passed through an

expanding duct at the periphery beforebeing led back towards the hub for the

next compression stage. The blades that

push the air towards the periphery and

increase its momentum are the rotorblades, while the expanding duct is the

stator or diffuser passage.

Features of centrifugal compressors

8/8/2019 5BB49ECBd01

26/48

Copyright 2003

Nara anan Komerath

26

1. Large pressure ratio perstage: stage pressure ratios

can be as high as 3 or 4.

2. Few moving parts.

Such compressor stages are

used on the low-pressure

shaft of helicopter engines

and turboprop engines. Onefamous application is in the

Space Shuttle Main Engine

turbopumps.

Features of centrifugal compressors

142.26.194.131/systems1/Engines/ gas_turbine_engines.htm

8/8/2019 5BB49ECBd01

27/48

Copyright 2003

Nara anan Komerath

27

AXIAL COMPRESSOR

The compressor of the turbofan engine

shown above is axial: the air moves

primarily in a direction parallel to the axis

of the engine.

Each stage of the axial compressor consists of a rotor and a stator. Bothrotor and stator are made up of a large number of individual blades, which

are twisted airfoils, usually with a high degree of camber.

The rotor blades add work to the air, so that the stagnation enthalpy rises,

along with the stagnation temperature and stagnation pressure. This is

usually accompanied by an increase in the velocity.

The stator blade passages straighten out the flow and act as diffusers,

slowing down the flow and thus increasing the static pressure and static

temperature.

8/8/2019 5BB49ECBd01

28/48

Copyright 2003

Nara anan Komerath

28

1. Axisymmetric flow with work addition through an annular duct:

Cz1

A1

A2

Cz 2

The flow through an axial compressor can be considered to

consist of three types of flows:

1 1 1 2 2 2z zc A c =

8/8/2019 5BB49ECBd01

29/48

Copyright 2003

Nara anan Komerath

29

ROTOR STATOR

Streamline

2. Flow over blade rows (cascades)

8/8/2019 5BB49ECBd01

30/48

Copyright 2003

Nara anan Komerath

30

3. Secondary flows (recirculating flows, tip vortices, hub vortices,

rotor/stator interactions, etc.)

Horseshoe Vortex

Root Vortex

Stator

Interaction

Blade Wake

Wall Boundary Layer

Secondary-flow features in theinboard region of an axial compressorstage

Boundary layer

Separation

Leakage Flow

Shock/Boundary layer

Interaction

Secondary-flow features in theoutboard region of an axial compressorstage

Centrifugal

Effects

Inboard

Wake

8/8/2019 5BB49ECBd01

31/48

8/8/2019 5BB49ECBd01

32/48

Copyright 2003

Nara anan Komerath

32

Velocity Diagrams for a Single Axial Stage

U

c1

c2

w1

w2

Ua

Note: Values in

diagram, such as U, changefrom section to section

along same blade.

If a given streamline stays neara given radial location, U

remains almost the same going

from rotor inlet through stator exit

- true in axial compressor.

8/8/2019 5BB49ECBd01

33/48

Copyright 2003

Nara anan Komerath

33

Relation Between Work and Turning Angles

c1

c2

w1

w2

Ua

( ) ( )2 1

rc rcm

=

1 2

1 2

r r

U U

=

=

2 1( )U

U c cr

=

Conservation of Angular Momentum gives:

Torque per unit mass flow rate = rate of change of angular momentum

Assuming that radial movement of the air is negligible within each stage.

Thus, air entering the stage at radius r will leave at the same radius r.

Work done on the fluid per unit time per unit mass flow rate by the rotor is:

8/8/2019 5BB49ECBd01

34/48

Copyright 2003

Nara anan Komerath

34

( ) ( )3 2

m rc rc

02 01 ( )h h U c = 001 01

( )

p

T U c

T c T

=

Torque on the stator =

Work done by the stator is zero, because the stator blades do not move

with respect to the engine walls. Thus, there is no rise in stagnation

enthalpy in the stator.

Assuming

a) uniform stagnation enthalpy per unit mass along the radius of

the blades, and

b) Adiabatic conditions (heat transfer effects are negligible),

from which we get:

Relation Between Stagnation Temperature and

Flow Turning Angle

For the stator, since no work is done, 03 02T T=

Thus, the changes in air properties through a compressor stage are relatedto the velocity vectors through the rotor and stator.

8/8/2019 5BB49ECBd01

35/48

Copyright 2003

Nara anan Komerath

35

03 01

03 01

sst

h h

h h

Stage Efficiency

Stage efficiency is defined as the ratio of the ideal work to the actual work.

Thus, the pressure stage pressure ratio is related to the stage

temperature rise using the isentropic relations:

103 0

01 01

1 stP TP T

= +

8/8/2019 5BB49ECBd01

36/48

Copyright 2003

Nara anan Komerath

36

Limits on Stage Pressure Ratio

1. Compressibility:As the relative Mach number becomes supersonic, shock losses can

become substantial. In earlier compressors, the blade tip Mach number was

kept below 1.0 to avoid the transonic drag rise. This imposed a severe limit on

compressor shaft rpm, blade radius, and stage pressure ratio. In moderncompressors, the rotor operates in the transonic regime, with shocks present in

the rotor. While this causes some loss in stagnation pressure, much more work

can be done by each rotor stage, and the shock provides a convenient way of

increasing static pressure. As a result, stage pressure ratio is higher, and the

overall weight of the compressor is reduced.

2

8/8/2019 5BB49ECBd01

37/48

8/8/2019 5BB49ECBd01

38/48

Copyright 2003

Nara anan Komerath

38

22

11

1 0.5 p rel p

C Mp = +

This shows why the stage pressure ratio is usually limited to about 1.4

for subsonic rotors. Under extreme conditions, transonic stages canreach stage pressure ratios as high as 2.2.

The effect of limiting stage pressure ratio on the number of stages in a

compressor can be seen from the following:

c stGiven a compressor pressure ratio of , and a stage pressure ratio of ,the number of stages is:

( )( )

10

10

loglog

c

st

n

Efficiency of Multistage Compressors

8/8/2019 5BB49ECBd01

39/48

Copyright 2003

Nara anan Komerath

39

Usually, axial compressors have several stages. The efficiency of a

compressor depends not only on the design of each stage, but also on the

overall pressure ratio. In other words, given the same level of technology, acompressor with a higher pressure ratio will have a lower efficiency. This

can be seen by relating the stage efficiency to the overall compressor

efficiency.

Polytropic efficiency:

This is a useful concept to define the level of technology of the

compressor. It is defined as the ratio of the ideal work required for a given

differential pressure change to the actual work required.

0

0

sc

dhe

dh

Efficiency of Multistage Compressors

8/8/2019 5BB49ECBd01

40/48

Copyright 2003

Nara anan Komerath

40

Using this definition, simple thermodynamics can be used to show that the

compressor efficiency and stage efficiency become

( )

( )

1

1

1

1

=

cc

ecc

( )

( )

1

1

1

1

st

stecst

=

The stagnation temperature ratio across a compressor with 'n' stagescan be calculated as

and

( )

1

03

102

1 1n

st cjj

T

T

=

= +

where 2 and 3 refer to stations

upstream and downstream of the

compressor

8/8/2019 5BB49ECBd01

41/48

Copyright 2003

Nara anan Komerath

41

Illustration

An axial compressor has 16 stages, with an overall pressure ratio of 25.

The stage efficiency is 0.93, and the pressure ratio is the same across

each of the stages. Calculate the compressor efficiency.

Using the above expressions, the stage pressure ratio is 1.22284. Thepolytropic efficiency is 0.932, slightly higher than the stage pressure

ratio as expected, and the compressor efficiency is obtained as 0.8965.

8/8/2019 5BB49ECBd01

42/48

Copyright 2003

Nara anan Komerath

42

Degree of Reaction

The Degree of Reaction of a turbomachine stage is defined as the ratio of

the static pressure change in the rotor to the static pressure change

through the whole stage. Thus, for example, a compressor stage with a

degree of reaction of 0.5 would share the pressure rise about equally

between the rotor and stator. This is desirable in the case of a

compressor, where the pressure gradient is the major concern. However,

turbine stages can be designed with extreme degrees of reaction

8/8/2019 5BB49ECBd01

43/48

Copyright 2003

Nara anan Komerath

43

Solidity

The solidity of a stage is defined as the ratio of the blade chord to the

blade spacing. If the solidity is low, there is less friction in the flow,

but the blades have to work harder, and thus the pressure gradient is

worse. If the solidity is high, the frictional losses are greater, but themachine can operate over a wider range of inlet conditions.

Generally, the solidity is around 1.

AXIAL TURBINES

8/8/2019 5BB49ECBd01

44/48

Copyright 2003

Nara anan Komerath

44

Differences between flow field characteristics of turbines and compressors

Compressor TurbineAdverse pressure gradient Favorable pressure gradient

Low stage pressure ratio (1.2 to 2) High stage pressure ratio (> 4)

Limited by stall Limited by choking and blade stress

Moderate temperature High temperature, requiring cooling

The engine shown has 10 fan and compressorstages, but only four turbine stages (2 on each

spool) to provide enough work to run them. A

turbine stage consists of a "nozzle", which is

static with respect to the engine walls, and a

"rotor". The nozzle is in fact a series of

passages between aerodynamically-shaped

surfaces (essentially airfoils). The rotor blades

may be highly cambered, since flow separation

is not as big a concern as in compressors.

A i l T bi

8/8/2019 5BB49ECBd01

45/48

Copyright 2003

Nara anan Komerath

45

Axial Turbine

Nozzle

Rotor Blade

Rotor Disc

Exhaust

Nozzle

Streamline

Rotor

1 2 3

Directionof Blade Motion

8/8/2019 5BB49ECBd01

46/48

Copyright 2003

Nara anan Komerath

46

2 3( )W U c c =

01 03W h h=

0

01 01

( )

p

T U cT c T

=

Using the same nomenclature as for the axial compressor stage

velocity diagram,

Work Output per unit mass flow rate

Also,

thus,

Note that here, T01 = T02 (no work in the nozzle).

Again, the work done per unit mass flow rate is proportional to the bladespeed achieved, and the turning of the flow.

Impulse Stage

8/8/2019 5BB49ECBd01

47/48

Copyright 2003

Nara anan Komerath

47

In an impulse turbine stage, the entire pressure drop occurs in the

nozzle. The velocity diagram is shown below:

p g

Note that for a turbine stage to operate, the C vector must be

considerably longer than the U vector. In the case of an impulse stage,the flow gets turned by the impulse rotor, so that the static

termperatures and the relative flow angles are:

2 3

2 3

T T

=

=

0% S

8/8/2019 5BB49ECBd01

48/48

50% Reaction Stage

In a 50% Reaction Stage, the static pressure drop is split between the

rotor and the nozzle. Here, the velocity diagram is as shown below:

2 3

2 3

| | | |

| | | |

w c

c w

=

=

Nozzle

Streamline

Rotor

1 2 3

Directionof Blade Motion

The velocity triangles become symmetric

w3

c2

Uc3