Ch. 31 - 1

The World of Energy

31.1. Gas Turbine Fundamentals

Chapter 31 LNG Gas Turbine

Ch. 31 - 2

First gas turbine was developed in 1872 by Dr. F. Stolze

Generates thrust by mixing compressed ambient air with fuel and combusting the mixture through a nozzle to propel an object forward or to produce shaft work.

Gas Turbine History

Ch. 31 - 3

What is a gas turbine ?

A Heavy Duty GT is a single shaft turbo-machine with:

1 compressor, 1 combustion system, 1 expansion

turbine

Ch. 31 - 4

Turbine and Compressor Design

Ch. 31 - 5

Gas Turbine Issues

Compressor and Turbine Design

Cooling

Dynamic Surge

Stall Propagation

Ch. 31 - 6

How Does it Work?

As the working fluid is exhausted out the nozzle of the gas turbine engine, the object that the engine is attached to is pushed forward

In the case of generating shaft work, the shaft turns a generator which produces electrical power.

Ch. 31 - 7

How Does it Work?

Shaft

Exhaust Gas

Ambient Air In

Ch. 31 - 8

Gas Turbine Components

Ch. 31 - 9

Gas Turbine Components

Ch. 31 - 10

heatexchanger

Closed Brayton cycle

turbinecompressorWnet

QH

QL

heatexchanger

Ch. 31 - 11

Open Brayton cycle

turbine

exhaust

compressor

air intake

combustion

chamber

Gas turbine cycle

fuel

Wnet

Ch. 31 - 12

turbine

exhaust

compressor

Air intake

combustion

chamber

fuel

Wnet

regenerator

Brayton cycle with regeneration

Ch. 31 - 13

Brayton Cycle: The Ideal Cycle for Gas Turbine Engines

Ideal Brayton Cycle

In reality, gas turbines operate on an open cycle

Fresh air is continuously drawn into the compressor and exhaust gases are thrown out

Ch. 31 - 14

Brayton Cycle: The Ideal Cycle for Gas Turbine Engines

Ideal Brayton Cycle (cont.)

The open gas-turbine cycle can be modeled as a closed cycleThe combustion process is replaced by a constant-pressure heat-addition process and the exhaust process is replaced by a constant-pressure heat-rejection process

Ch. 31 - 15

Gas Turbine Schematic

Ch. 31 - 16

Land Base Gas Turbine Cutaway

1. Air Intake Section2. Compression Section3. Combustion Section4. Turbine Section5. Exhaust Section6. Exhaust Diffuser

Ch. 31 - 17

Gas Turbine Operation

Compressor is connected to the turbine via a shaft. The turbine provides the turning moment to turn the compressor.

The turning turbine rotates the compressor fan blades which compresses the incoming air.

Compression occurs through rotors and stators within the compression region.

Rotors (Rotate with shaft)

Stators (Stationary to shaft)

Ch. 31 - 18

Types of Gas Turbines

Centrifugal

Compressed air output is around the outer perimeter of engine

Axial

Compressed air output is directed along the centerline of the engine

Combination of Both

Compressed air output is initially directed along center shaft of engine and then is compressed against the perimeter of engine by a later stage.

Ch. 31 - 19

Example of Centrifugal Flow

Intake airflow is being forced around the outside perimeter of the engine.

Centrifugal Compressor

Airflow being forced around body of engine

Ch. 31 - 20

Example of Axial Flow

Intake airflow is forced down the center shaft of the engine.

Multistage Axial Compressor

Center Shaft

Ch. 31 - 21

Example of Combination Flow

Intake Air Flow

Axial Compressor

Centrifugal Compressor

Intake air flow is forced down the center shaft initially by axially compressor stages, and then forced against engine perimeter by the centrifugal compressor.

Ch. 31 - 22

Major Components of Interest

Compressor

Axial

Centrifugal

Turbine

Axial

Radial

Axial Compressor

Centrifugal Compressor

Ch. 31 - 23

Axial Compressor Operation

A&P Technician Powerplant Textbook published by Jeppesen Sanderson Inc., 1997

Axial compressors are designed in a divergent shape which allows the air velocity to remain almost constant, while pressure gradually increases.

Average Velocity

Ch. 31 - 24

The airflow comes in through the inlet and first comes to the compressor rotor.

Rotor is rotating and is what draws the airflow into the engine.

After the rotor is the stator which does not move and it redirects the flow into the next stage of the compressor

Air flows into second stage.

Process continues and each stage gradually increases the pressure throughout the compressor.

Axial Compressor Operation

Ch. 31 - 25

An axial compressor stage consists of a rotor and a stator.

The rotor is installed in front of the stator and air flows through accordingly. (See Fig.)

www.stanford.edu/ group/cits/simulation/

Axial Compressor Staging

Ch. 31 - 26

Centrifugal compressors rotate ambient air about an impeller. The impeller blades guide the airflow toward the outer perimeter of the compressor assembly. The air velocity is then increased as the rotational speed of the impeller increases.

Centrifugal Compressor Operation

Ch. 31 - 27

Axial Turbine Operation

Hot combustion gases expand, airflow pressure and temperature drops.

This drop over the turbine blades creates shaft work which rotates the compressor assembly.

Axial Turbine with airflowAirflow around rotor

Airflow through stator

Ch. 31 - 28

Radial Turbine Operation

Same operation characteristics as axial flow turbine.

Radial turbines are simpler in design and less expensive to manufacture.

They are designed much like centrifugal compressors.

Airflow is essentially expanded outward from the center of the turbine.

Radial Flow Turbine

Ch. 31 - 29

Gas Turbine Issues

Gas Turbine Engines Suffer from a number of problematic issues:

Thermal Issues

Blade (airfoil) Stalls

Dynamic Surge

http://www.turbosolve.com/index.html

Ch. 31 - 30

Thermal Issues

Gas Turbines are limited to lower operating temperatures due to the materials available for the engine itself.

Operating at the lower temperature will decrease the efficiency of the gas turbine so a means of cooling the components is necessary to increase temperatures at which engine is run.

Ch. 31 - 31

Cooling Methods

Spray (Liquid)Passage Transpiration

Ch. 31 - 32

Spray Cooling

The method of spraying a liquid coolant onto the turbine rotor blades and nozzle

Prevents extreme turbine inlet temperatures from melting turbine blades by direct convection between the coolant and the blades.

Ch. 31 - 33

Passage Cooling

Hollow turbine blades such that a passage is formed for the movement of a cooling fluid.

DOE has relatively new process in which excess high-pressure compressor airflow is directed into turbine passages.

http://www.eere.energy.gov/inventions/pdfs/fluidtherm.pdf

Ch. 31 - 34

Transpiration Cooling

Method of forcing air through a porous turbine blade.

Ability to remove heat at a more uniform rate.

Result is an effusing layer of air is produced around the turbine blade.

Thus there is a reduction in the rate of heat transfer to the turbine blade.

Ch. 31 - 35

Blade (airflow) Stalls

When airflow begins separating from the compressor blades over which it is passing as the angle of attack the blades exceeds the design parameters

The result of a blade stall is that the blade(s) no longer produce lift and thus no longer produces a pressure rise through the compressor.

Separation Regions

Ch. 31 - 36

Occurs when the static (inlet) air pressure rises past the design characteristics of the compressor.

When there is a reversal of airflow from the compressor causing a surge to propagate in the engine.

Essentially, the flow is exhausted out of the compressor, or front, of the engine.

Result, is the compressor no longer able to exhaust as quickly as air is being drawn

http://www.turbosolve.com/index.html

Compressor Inlet

Turbine Exit

Dynamic Surge

Ch. 31 - 37

Dynamic Surge Effects

Cause: Inlet flow is reversed

Effect: Mass flow rate is reduced into engine.

Effect: Compressor stages lose pressure.

Result: Pressure drop allows flow to reverse back into engine.

Result: Mass flow rate increases

Cause: Increased mass flow causes high pressure again.

Effect: Surge occurs again and process continues.

Result: Engine surges until corrective actions are taken.

Ch. 31 - 38

outm

P

V

Surge Point, Flow Reverses

No Surge Condition

Compressor Pressure Loss Occurs

Flow reverses back into engine

Corrective Action Taken

inm

outm

Dynamic Surge Process

Ch. 31 - 39

Axial Compressor Design

Assumption of Needs

Determination of Rotational Speed

Estimation of number of stages

General Stage Design

Variation of air angles

Ch. 31 - 40

Assumption of Needs

The first step in compressor design in the determination of the needs of the system

Assumptions:Standard Atmospheric Conditions

Engine Thrust Required

Pressure Ratio Required

Air Mass Flow

Turbine inlet temperature

Ch. 31 - 41

Rotational Speed Determination

First Step in Axial Compressor Design

Process for this determination is based on assumptions of the system as a whole

Assumed: Blade tip speed, axial velocity, and hub-tip ratio at inlet to first stage.

Rotational Speed Equation

Ch. 31 - 42

Derivation of Rotational Speed

First Make Assumptions:

Standard atmospheric conditions

Axial Velocity:

Tip Speed:

No Intake Losses

Hub-tip ratio 0.4 to 0.6

U t 350m

s

C a 150 200m

s

Ch. 31 - 43

Compressor Rotational Speed

Somewhat of an iterative process in conjunction with the turbine design.

Derivation Process:First Define the mass flow into the system

is the axial velocity range from the root of the compressor blades to the tips of the blades.

AUmdot where U =1aC

1aC

Ch. 31 - 44

Axial Velocity Relationship

a

t

ra C

r

rC *1

2

1

Radius to root of blade

rr

tr Radius to tip of blade

Ch. 31 - 45

Tip Radius Determination

2

11

2

1t

ra

dott

r

rC

mr

By rearranging the mass flow rate equation we can obtain an iterative equation to determine the blade tip radius required for the design.

Now Looking at the energy equation, we can determine the entry temperature of the flow.

p

a

c

CTT

2

2

101

22

2

11

2

00

UTc

UTc pp

Ch. 31 - 46

Isentropic Relationships

Now employing the isentropic relation between the temperatures and pressures, then the pressure at the inlet may be obtained.

Now employ the ideal gas law to obtain the density of the inlet air.

1

0

101T

TPP

1

11

RT

P

Ch. 31 - 47

Using the equation for tip speed

Rearranging to obtain rotational speed.

Finally an iterative process is utilized to obtain the table seen here.

NrU tt 2

t

t

r

UN

2

Finally Obtaining Rotational Speed

Ch. 31 - 48

Make keen assumptions

Polytropic efficiency of approximately 90%.

Mean Radius of annulus is constant through all stages.

Use polytropic relation to determine the exit temperature of compressor.

n

n

P

PTT

1

01

020102

n = 1.4, Ratio of Specific Heats, Cp/Cv

is the pressure that the compressor outputs

To1 is ambient temperature

02P

Determining Number of Stages

Ch. 31 - 49

Assuming that Ca1 = Ca

is the work done factor

Work done factor is estimate of stage efficiency

Determine the mean blade speed.

Geometry allows for determining the rotor blade angle at the inlet of the compressor.

NrU meanm 2

a

m

C

U1tan

Determine Temperature Change

Ch. 31 - 50

Temperature Rise in a Stage

p

ams

c

CUT 210

tantan

1

1cos

aCV

This will give an estimate of the maximum possible rotor deflection.

Finally obtain the temperature rise through the stage.

2

2cosV

Ca

Determine the speed of the flow over the blade profile.

Velocity flow over blade V1.

DeflectionBlade_12

Ch. 31 - 51

Number of Stages Required

The number of stages required is dependent upon the ratio of temperature changes throughout the compressor.

sT

TStages

0

ambTTT 2

is the temperature change within a stage

is the average temperature change over all the stagessT

T

0

Ch. 31 - 52

Make assumptions

Assume initial temperature change through first stage.

Assume the work-done factors through each stage.

Ideal Gas at standard conditions

Determine the air angles in each stage.

Designing a Stage

Ch. 31 - 53

Stages 1 to 2

Determine the change in the whirl velocity.

Whirl Velocity is the tangential component of the flow velocity around the rotor.

Ch. 31 - 54

Change in whirl velocity through stage.

12 www CCC

m

p

wU

TcC

11 tanaw CC

Alpha 1 is zero at the first stage.

a

w

a

wm

C

C

C

CU

22

22

tan

tan

Stage 1 to 2

Ch. 31 - 55

Compressor Velocity Triangles

Ch. 31 - 56

Pressure ratio of the Stage

10

01

03 1amb

sss

T

T

P

PR

9.0s

The pressure ratio in the stage can be determined through the isentropic temperature relationship and the polytropic efficiency assumed at 90%.

Ch. 31 - 57

The analysis shows that the stage can be outlined by the following attributes:

1.) Pressure at the onset of the stage.

2.) Temperature at the onset of the stage.

3.) The pressure ratio of the stage.

4.) Pressure at the end of the stage.

5.) Temperature at the end of the stage.

6.) Change in pressure through the stage.

Example of a single stage

Stage Attributes

Ch. 31 - 58

Assume the free vortex condition.

Determine stator exit angle.

Then determine the flow velocity.

constrCw2

13 tantana

m

C

U

3

3cos

mUC

Variation in Air Angles of Blade

Ch. 31 - 59

Alpha 1 is 0 at the inlet stage because there

Thus, Ca1=C1, and Cw1 is 0

Note: This is the whirl velocity component and not a blade spacing!

Air Angle Triangle

Ch. 31 - 60

Red is

Green is

Blue is

Velocity Triangle

aC

aC

aC

Ch. 31 - 61

Variation in Air Angles of Blade

Determine the exit temp., pressure, and density of stage 1

Determine the blade height at exit

Finally determine the radii of the blade at stator exit.

p

a

c

CTT

2

2

03

1

03

3033T

TPP

3

33RT

P

meanr

Ah

2

3

2

hrr meants 2

hrr meanrs

a

dot

C

mA

3

3

Ch. 31 - 62

Variation in Air Angles of Blade

Determine the radii at the rotor exit.

Determine the whirl velocities at the blade root and tip.

2

tstritr

rrr

2

rsrrirr

rrr

Note: That is the radius of the blade at the tip at rotor inlet.

trir

Note: That is the radius of the blade at the root at rotor inlet.

rrir

rr

meanmwrwr

rCC 22

tr

meanmwtwr

rCC 22

Note: because there is no other whirl velocity component in the first stage.

22 wmw CC

Ch. 31 - 63

a

twtrt

a

mwmm

a

rwrrr

a

twt

a

mwm

a

rwr

C

CU

C

CU

C

CU

C

C

C

C

C

C

22

22

22

22

22

22

tan

tan

tan

tan

tan

tan Stator air angle at root of blade

Stator air angle at middle of blade

Stator air angle at tip of blade

Deflection air angle at root of blade

Deflection air angle at middle of blade

Deflection air angle at tip of blade

Finally determine the Air Angles

Ch. 31 - 64

Compressor Design Example

Design of a 5 stage axial compressor:

98.0

150

5.452

288

2262.0

2

sm

a

a

t

C

KT

KT

mrGivens:

Use this and chart to get Rotational speed of engine.

Once rotational speed is found, determine mean blade tip speed.

Ch. 31 - 65

Example

s

mNrU

mrr

r

meanm

rtmean

6.2662

1697.02

KTTT amb 5.1642

Determine the total temperature rise through the first stage.

We are designing for more than just one stage, so we need to define an average temperature rise per stage:

KStages

TT s 9.32

#0

Ch. 31 - 66

2

0

1

12

1

1

55.126

0

64.60tan

w

m

sp

w

w

www

a

m

Cs

m

U

TcC

s

mC

CCC

C

U

Example (Air Angle Determination)

Ch. 31 - 67

s

mCV

C

CU

a

a

wm

21.205cos

03.43tan

2

2

21

2

15.40tan 21

2

a

w

C

C

Example (Air Angle Determination)