principle of turbomachinery mechanical engineering

8/13/2019 Principle of Turbomachinery mechanical engineering

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Internal CombustionEngine and

TurbomachineryMCHE 562

Dr. Gongtao Wang


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Lecture Outline1. Introduction to Internal Combustion Engine

2. Introduction to Gas Turbine Engine

Definition and Applications

Thermal Cycles

Applications

Illustrations

3. Introduction to Turbomachinery Terms

Definition and classifications

Coordination systems and velocity diagrams

Variables and geometry


4/159

Lecture Outline4. Review of Aerodynamics and Fluidics

Conservation: Mass, energy and Momentum

Gas Dynamics: Compressible flow

5. Dimensionless Analysis

Off Design Performance and specific speed

Buckingham -Theorem

Application in Turbomachinery


5/159

Lecture Outline6. Energy transfer between fluid and a rotor

Eulers Equation

Energy Transfer and velocity diagram

ReactionDefinition

Definition of total relative properties

7. Radial Equilibrium Theory

Derivation of Radial Equilibrium Equation

Free vertex

Problem


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Lecture Outline8. Axial flow turbine

Preliminary design of axial flow turbines

Detailed design Final project

9. Axial flow compressor

10. Polytropic (small stage) efficiency


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Introduction to Internal

Combustion Engine Classification

Otto CycleFour stroke

Clark CycleTwo Stroke Diesel CycleCompression Ignition

Wankel cycleRotary Engine


8/159

Latest 2-Stroke Engine


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Wankel Engine


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Clerk/Otto/Diesel Cycle Mechanism

Thermal Cycle

Design Issues


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Piston Dynamics

Exact piston acceleration


13/159

Piston Dynamics

Approximate piston acceleration


14/159

Gas Force and Torque

Gas force

Gas torque


15/159

Inertia and Shaking force

Shaking = - inertia forces


16/159

Inertia and Shaking


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Inertia and Shaking


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Inertia and Shaking


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Otto Cycle P-V & T-s Diagrams


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Otto Cycle Derivation

Thermal Efficiency:

Air standard assumption (constant v + q)

Cold-air standard assumption (constant c)

Q

Q-1=

Q

Q-Q=

H

L

H

LHth

TCm=Q vin

1-T

TT

1-TTT

-1=)T-T(Cm

)T-T(Cm-1=

2

32

1

41

23v

14v

th

TCm=Q vRej


23/159

For an isentropic compression (and expansion)

process:

where: = Cp/Cv Then, by transposing,

T

T

=V

V

=V

V

=T

T

4

3

3

4

1-

2

1

1-

1

2

T

T=

T

T

1

4

2

3


T

T-1=

2

1

thLeading to


24/159

The compression ratio (rv) is a volume ratio and

is equal to the expansion ratio in an otto cycle

engine.

Compression Ratio

V

V=

V

V=r

3

4

2

1v

1+v

v=r

v

v+v=

volumeClearance

volumeTotal=r

cc

sv

cc

ccsv

where Compression ratio is defined as



25/159

Then by substitution,

)r(

1-1=)r(-1= 1-

v

-1

vth

)r(=

V

V=

T

Tv

1

2

2

1 1

1

The air standard thermal efficiency of the Otto cycle

then becomes:



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Summarizing

Q

Q-1=

Q

Q-Q=

H

L

H

LHth

TCm=Q v

1-T

TT

1-T

TT

-1=

2

32

1

41

th

)r(=V

V=

T

T -1v

1

2

-1

2

1

)r(

1-1=)r(-1= 1-

v

-1

vth

T

T=

T

T

1

4

2

3

2

11T

T

th

where

and then

Isentropic

behavior



27/159

Determine the temperatures and pressures at each point in

the Otto cycle. k=1.4

Compression ratio = 9:1T1temperature = 25

oc = 298ok

Qinheat add in = 850 kj/kg

P1pressure = 101 kPa

T2 = 717 p2 = 2189kpa

T3 = 1690k p3 = 5160kpa cv=1.205

T4 = 701k p4 =238kpa

Otto Cycle P & T Prediction


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Diesel Cycle P-V & T-s Diagrams


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Diesel Cycle Derivation

Thermal Efficiency (Diesel):

Q

Q-1=

Q

Q-Q=

H

L

H

LH

th

TCm=Q p

For a constant pressure heat

addition process;For a constant volume heat

rejection process;

TCm=Q v

Assuming constant specific heat:

1-

T

TT

1-T

TT

-1=)T-T(Cm

)T-T(Cm-1=

2

32

1

41

23p

14v

th

where: = Cp/Cv


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Otto-Diesel Cycle Comparison


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Dual Cycle Thermal Efficiency

5.2

3

V

V

P

P=

2

3

)T-T(Cm+)T-T(Cm=Q 2.53p22.5vin

1)-(+1)-(

1-

CR

1-1=

1)-(

Dual Cyc le Eff ic iency

where: = Cp/Cv

14Rej TTCm=Q v


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Critical Relationships in the process include

)r(=V

V=

T

T -1v

1

2

-1

2

1

QA

Fm=

cycle

Qfuela

r=V

V=

P

Pv

2

1

1

2

Diesel Cycle Derivation

TCm=Q p TCm=Q v

1)-r(

1-r

)r(

1-1=

cp

cp

1-

v

th


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Design Issue

Improve efficiency

Higher compression ratio

Combustion control

Ignition timing Exhaust recuperate

Minimize shaking force/torque

Lubrication

Pollution control

Cost deductionshort stroke engine


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MCHE 569 Project 1Given a single cylinder internal combustion engine,

r=2.6, l=10.4, m2=0.060 blob,

rG2=0.4r, m3=0.12, rG3=0.36l,

m4=0.16blob. Piston dia. is 5.18.

The crank rotates at 1850 rpm.

Compression ratio is 8:1.

Thermal condition: T1 = 20 deg. C, P1 = 101kpa, Qin = 810 kJ/kg

Calculate in Excel:

Thermal condition of all 4 stroke

Thermal efficiency

Gas force

Gas torque

When theta = 0, 90, 180, 270, 720 calculate shaking force and torque Gas-fuel mixture mass flow rate

If mass ratio of the mixture is 4 part air vs. 1 part fuel, calculate fuel consumption rate, and volumetric airflow rate.


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Gas Turbines - Definition

Definitions

Thermal energy conversion device

Fuel -> mechanical/electrical power Fuel -> Propulsion

Difference from ICE

Absence of Reciprocating and RubbingMembers

Power/Weight ration


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41/159

Gas Turbine / ICE

Higher Efficiency,

High power/weight

Robust Combustion/Insensitive to fuelcondition

Minimum Power output

Complexity/Maintenance

Higher Cost


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Turbine Configuration

Shaft arrangement

Single: Fix speed and load

Twin/Triple shafting HPT drives compressor and LPT not need for gear

reducer

High efficiency at variable speed

High reliability at variable power

Multiple coaxial shaftes

Complex control, high efficiency with more flexibility


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Classification of Turbomachine

By function

Work absorber - Compressors, fans and pumps

Worker - Turbines

By fluid

Compressible

Incompressible

By meridional flow path

Axial

Radial


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Stage

Definition -- Stator and rotor pair

Stator

Convert fluid thermal to fluid kinetic energy No energy transfer to or from blade

Rotor

Energy transfer from or to the fluid -- fluid totalenergy change


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Coordinate System and Velocity Diagram

Coordination system

Polar cylindrical system

Radialr, tangential , axialz

Velocity diagram

Total (absolute) velocity -- V

Relative (fluid flow vs. blade) -- W

Blade velocity due to rotationU

1inlet, 2 -- exit

V=W+U


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Blade VD

Stator

U = 0

V = W

Rotor

V=W+U

Impeller

Compressor and turbine VD are reversed

Subscription convention Vr1 ,


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Axial Flow Turbine

Sign convention

Positive if along the rotation

How to determine fluid acting surface TurbineFluid acting on the convex side of

blade airfoil

CompressorConcave side


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Comparison Between Axial and Radial

Flow Turbine

Signal stage efficiency

Radial is higher

Loss between stages Radial is higher

Way to improve efficiency

Radialmake the diameter of the rotor larger Axialadd stages


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Compressor Stall, Surge

Stall

In axial compressors, gas density/pressure, sometime eventemperature, may change sharply in certain stage

Low-speed, low-flow, high stagger, stall is imperceptible,and recoverable

Surge

Domino stalls occur from last stage in high speed

compressor Non-recoverable, cause temperature rise, significantly

reduce the performance of the compressor, and often endup with blade damage


52/159

Turbine Choke / Blade Cooling

Choke / shock

Relative velocity become supersonic

Blade High temperature alloy

Intensive cooling

Current technologyturbine temperature can be25% high than the melting point of the blade


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Variable Geometry in Compressor

and Turbine

Power = pressure * volume flow rate

Recover from surge in compressor

Startupignitionsurge

Squeeze stall out

Different turbine work at different design point

Keep pressure the same, reduce flow channel cross-

section area reduces volume flow rate reduce powerand mass flow rate to maintain the pressure and less

mass flow burn less fuel


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Ch3. Aerodynamics of Flow Processes

General flow governing equation

Total properties

Ideal gas isentropic properties Sonic speed and mach numbers

Mach number expressed relations

Isentropic relation in term of local mach Critical velocity and critical properties

Isentropic relation in term of critical mach


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Continue

Compressible flow in isentropic nozzle

Varying-area equation

DeLaval nozzle - CD nozzle Unfavorable back pressure gradient

Other important relations for nozzle

Choking flow Shock equations


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Continue Outline

Definition of turbomachinery isentropic

efficiency

Total-total efficiency Compressor

Turbine

Total-static efficiency

Total condition of an incompressible flow

Limitation of Bernoulli's equation


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General Flow Governing Equation

Continuity equation

Linear momentum equation

Energy equation

)]()()[()()()(

12

2

1

2

221

12

12

2

1

2

22

1

12

ZZgVVhhmWQZZgVVhhwq

Shaft

shaft

)()( 1212 yyyxxx VVmFVVmF

constAVAVm 222111


58/159

Total Properties

Isentropically convert all energy into enthalpy

Total/Stagnational, local/static

tt

ptpt

t

PP

TchTch

gZVhh

2

21

)(


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Ideal gas isentropic relations

Stateequation andConstants

Entropychange of a

process

Isentropicprocess

turbinefor

compressorfor

RRTpKkg

J

33.1

4.1

287

)ln()ln(1

2

1

2

11

1

P

P

T

T

P

vP

Rcs

RcRc

1

1

2

1

2

1

2

T

T

P

P


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61/159

Sonic Speed and Mach Number

Sonic speed

Mach Number

RT

d

dpa

a

VM


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Isentropic Relations in Term of Mach

Total to local

1

1

2

12

2

2

11

2

11

2

11

M

MP

P

MT

T

t

t

t


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Critical Property

The local condition at

unity mach

Critical mach

tcrcrtcr T

R

aVTT

1

2

1

2

)2

11(

1

2

1

2 2M

M

TR

V

Mt

cr


64/159

Isentropic Flow in Critical Mach

1

1

2

12

2

1

11

1

11

1

11

crt

crt

crt

M

MPP

MTT


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Isentropic Flow in Varying Nozzle

To increase the speed of fluid

Converging the subsonic flow

Diverging the supersonic flow

)1(2

1

2

`1

2

2

1

* 11

MMA

A


66/159

Nozzles in turbomachinery

The most important feature

Diffuser must be carefully designed so that

the flow remains attached to the wall Unfavorable pressure gradient makes the

design curve of diffuser


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Other Important Features

Choking flow


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Normal Shocks-1

Control Volume


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Normal Shocks-2 Basic Equations for a Normal Shock


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Normal Shocks-3

Intersection of Fanno & Rayleigh Lines


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Normal Shocks-4

Normal Shock Relations


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Normal Shocks-5

Normal Shock Relations (Continued)

Supersonic Channel Flow


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Supersonic Channel Flow

with Shocks

Flow in a Converging-Diverging Nozzle

Isentropic Flow of an Ideal Gas


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Isentropic Flow of an Ideal Gas

Area Variation

Isentropic flow in aconverging-diverging nozzle


75/159

Example 3-1


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Example 3-2


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Example 3-3


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Definition of Turbomachinery Efficiency

Total-to-total

efficiency

Compressor

Turbine

1

1

)(

)(

1

2

1

1

2

t

t

t

t

actualt

idealttt

TT

PP

h

h

1

1

)()(

1

1

2

1

2

t

t

t

t

idealt

actualttt

PP

T

T

hh


79/159

Turbine Efficiency

Total-to-static

Efficiency

use in

applicationswhere exhaust

is counted as

waste, such as

power plant

12 211

22

22

1

22

1

1

2

1

,

1)1(

1

)(

1

crtt

ttP

actualtturbinest

MPM

PP

P

PTc

h

C ibilit d B lli


80/159

Compressibility and Bernoulli

Equation

Error of Bernoulli when used in compressible flow

M


81/159

Chapter 4

Dimensional analysis

Buckingham -Theorem

Off-design performance of gas turbine Dimensional analysis in turbomachinery

Specific speed


82/159

Dimensional Analysis

Buckingham -theorem

Select all related as a set of n variables

Determine k (either MLT 3, or MLTt 4)

Select k most important variables as the centralgroup

Multiply each of the rest n-k variables to solve forn-k s

Set up the system of equation

Arbitrarily set one variables exponential as unity

Solve the rest exponentials


83/159

Application to Turbomachinery

Geometric similarity

Dimensional proportional

Dynamical similarity Geometrical similar machines with each velocity

vector parallel

Similarity principle

Geometrically similar

Non-dimensional term/number identical


84/159

Performance Characteristic

Head coefficient

Head efficiency

Power coefficient

2

3

2

3

2

32

,

,

,

ND

ND

QfP

PP

ND

ND

Qf

gH

gH

ND

ND

Qf

U

gH

i

oP

ideal

actH


85/159

Compressible-flow Turbomachine

1.33Turbine

1.4Compressor

mixturegastheofheatspecificofratio:

constantGas:R

retemperatulinlet totavs.changeretemperatuTotal:

efficiencytotalto-Total:

ratioPressureTotal-to-Total:Pr

Re,,,,Pr,

,

,,

2

,

,

int

t

tt

intint

int

int

ttt

T

T

RT

ND

PD

RTmf

T

T


86/159


87/159

Map and Characteristics

Turbine or compressor mapthe plot

Characteristicthe curves in the plot

Design point of compressor is close to surge Design point for turbine is close to choke


88/159


89/159


90/159

Ch5. Eulers Equation

Energy transfer between fluid and rotors

Force/torque generated through momentum

change

Energy transfer happens while these force/torque

do works


91/159

Momentum Change at All Directions

Axial velocity change

Axial load on to the shaftno works

Radial velocity change Radial load bending moment vibration

Destructive works

Both of above should be minimized Tangential directioneffective works


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Eulers Equation

Torque

Power

Specific work

1122

1122

1122

)(

)(

VUVUp

VUVUmP

VrVrm


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94/159

Heads

Dynamic Head (Absolute V)

Total kinetic energy lost/gain in fluid flow

Effective shaft works

Convective Head (U)

Annual expansion/shrinkage

Small

Static Head (relative W) Action of fluid flow to stages


95/159

Enthalpy Across A Stage

Absolute

Relative

Rothalpy

RothalpyUVhI

totalrelativeTch

totalabsoluteTch

etemperaturStaticLocalTs

MMTT

MMTT

t

rtprt

tpt

aW

rsrt

aV

st

r

,,

2

2

1

,

2

2

1

)(:

)1(

)1(


96/159

Reaction

Definition

)()()(

)()(

)()()(

)()(

2

2

2

1

2

1

2

2

2

1

2

2

2

2

2

1

2

1

2

2

2

1

2

2

2

2

2

1

2

2

2

1

2

1

2

2

2

2

2

1

WWUUVV

WWUUR

WWUUVV

WWUUR

Compressor

Turbine


97/159

Stage Blade Design vs. Reaction

Inlet and exit angles for stator

0, 1

Inlet and exit angles for rotor

0, 1

Deviation angle

difference of flow and metal

Swirl angle local absolute angles


98/159

Axial Turbomachine

Zero-reaction stageImpulse stage

W1=W2, 1= -2

50% reaction (symmetric) turbine stage

V1=W2, V2=W1

1= -2, 2 = - 1

50% reaction (symmetric) compressor stage

V1=W2, V2=W1 1= -2, 2 = - 1


99/159

Incidence and Deviation Angles

Incidence angle

Flow angle to leading edge metal angle

Always exists like attacking angle

Positive or negative

Deviation angle

Insufficient flow momentum change

A very important controlled feature in compressor

A measure to adverse/unfavorable pressure gradient


100/159

Real-life Flow path in Axial Turbo Explain with isentropic and / (-1)>>1

Total pressure drop much faster than temperature

Total density decrease across rotor

If Mach change over rotor is neglected, Static density decreases across the rotor

To keep Vz constant, the annular cross area

Decreasing for compressor

Increasing for turbine Flow passage over stator, due to significant M increase

Converging for compressor

Diverging for Turbine

Definition of Total Relative Properties in


101/159

Definition of Total Relative Properties in

the Rotor Sub-domain

Relative properties can be modeled as flow through nozzleat speed W across

11

11

,

11

,

,

1

2

)1()1(

)1()1(

)1()1(

2

2

1

12

1

1

2

1

12

1

1

2

1

12

1

1

,

,

2

MM

MPMPP

MTMTT

M

rotoracrossconstTc

WTT

ttr

ttr

ttr

RT

WWW

crr

rt

p

str

crr

crr

crr

trcr


102/159

Continue

General term

IsentropicTotal

relative pressure is

constant across rotor

Other process totalrelative pressure

decrease

1

1

2

1

2

1

2

21

t

t

t

t

T

T

P

P

tr

tr

trtr

P

P

TT


103/159

Graphic Shown

For Turbine

P2 < Pt2


104/159

Ch6 Radial Equilibrium Theory

Background

Study for thermal properties as traverses a stage

Pitch line analysis

How properties (except U) vary at a given axial location

Assumptionaxi-symmetric flow

NoteWake at gap is negligible

The Problem Find the relationship among fluid properties, annual

geometry, and velocity


105/159

Derivation

Pressure force, andmass of the differentialcontrol elements

rdrdd

rdrrm

ddprFFFF

rpF

prdF

ddrrdppF

sideundertopp

ddrdp

side

under

top

2)(

)sin())((2

))((

22

222


106/159

Acceleration

Centrifigal

Meridional curvature

Convective )sin(

)cos(2

2

mmconvective

m

m

mlcentrifigameridional

lCentrifiga

Va

r

Va

r

Va


107/159

Radial Equilibrium Theory

F=ma

)()sin()cos(1

)()sin()cos(1

)sin()cos(

22

22

22

ConvergingVr

V

r

V

dr

dp

divergingVr

V

r

V

dr

dp

Vr

V

r

V

rdrd

ddpr

aaadm

F

mmm

m

m

mmmm

m

mmm

m

m

convectivelcentrifigameridionallCentrifiga


108/159

Simplified cases

Vm = const

Vr=0

Invoke total

enthalpy

r

V

dr

dp 21

r

V

dr

dV

dr

dV

zdr

dh

dr

dp

p

p

dr

dp

dr

dV

dr

dV

zdr

dh

dr

dp

pdr

d

dr

d

dr

dpp

dr

dp

dr

dp

dr

dV

dr

dV

zdr

dh

convectivelcentrifigameridional

p

zzpV

t

VV

VV

const

VV

a

VVVVTchh

zt

zt

zt

2

2

2

2

)(

0

)(

)()(

11

1

11

1

22

2122

21

2


109/159

Continue Simplification

dVz / dr = 0 dht / dr = 0

Free Vertex

Nature fluid flow

Flow vorticityflow particles spinning around

its own axis

Least vorticity in free vortex flow

Free vortex blade design is most desired in

aerodynamics, but unrealistic

Disadvantage in structural design andmanufacturing

Boundary layer and tip leakage cancel the idea

effect of free-vortex

constrV

V

r

V

dr

dV

r

V

dr

dV

2

00


110/159

Chapter 7 Axial Flow Turbine

Steam Turbine

Superheated Region

Wet Mixture Region

Gas Turbine

Similar to superheat steam turbine

High temperature alloy

Basic gas turbine design process


111/159

Stage Definition Stator followed by rotor

Stator airfoil cascadesvanes

Rotor airfoil cascadesblades

Design process

Preliminary phases Compressor/combustor exit, inlet path/nozzle,

Stage 1,2,3,4, Casing, pitch line, interstage axial gap

Detailed phases Blade geometry design

Real flow effects

Empirical equation Stacking vanes and blade sections

CAD Approach to axial turbine


112/159

Preliminary Design of Axial-Flow Turbines

Given conditions

Turbine inlet conditions (p, t,,)

Rotary speed

min. tip clearance,

max tip Mach

Envelope radial constrains (casing), max axiallength, max diverging angle

Interstage Tt, max exit flow rate (A*N^2), Mach

Other, (such as overall efficiency, etc.)


113/159

Preliminary Design -- Find

Meridional flow path

Flow condition along pitch line

Hub and tip velocity diagram (assuming free-vortex stages)


114/159

Design Processes Step 1 -- Justify axial turbine type

Ns = N*Q^0.5/(ht)^0.75 > = 0.775

ht is enthalpy change over a single stage, you change the number of stagesto make the Ns to be optimum (usually 1)

Step 2Split work across turbine individual stages (ht1, ht2),according to experience Efficiency

Off-design, and operation conditions usually 60:40, 55:45,50:50

Step 3 According to the experienced work split, and efficiency, determineinterstage total condition Too small axial gap triggers strong and dangerous flow interaction

Too large axial gap increases end-wall friction loss Stator/rotor gap is more critical that interstage because large swirl velocity


115/159

Formulating an Simplified Approach

Calculate specific speed

Find optimum number of stage

Estimate turbine efficiency

Define a stage work coefficient

Define Flow coefficient

)tan(tan 21

))( 21212

21

22

U

V

U

WW

U

VV

U

VVU

U

Tc

U

W

z

tps

)tan(tan 21

U

Vz


116/159

Coefficient Design-1

)tan(tan2

)tan(tan2

tantan

2)(2)(2

2121

2

2

1

1

21

21

2

1

2

2

21

2

1

2

2

2

1

2

2

22

1

22

2

2

1

2

2

2121

U

VR

VWWW

UWW

WWUWW

VVUWWR

WWWWWWWW

UWWVV

z

zz

ZZ


117/159

Coefficient Design-2

1tantan

1tantan

)2(

2

1tan

)2(2

1tan

)tan(tan

)tan(tan2

11

22

2

1

21

21

R

RR


118/159

Example 7-1

turbinestageoneFind

KkgkJ

sm

:

/287R1.333,Assume

5.1)U

h

(tcoefficienworkStage

/340speedbladeMean

rpm15000speedRotational

1.873rationPressureTotal

bars4pressurelInlet tota

K1100retemperatulInlet tota

90%efficiencyStage

20kg/smrateflowMass

0angleinletFlow

:Given

gas

2

t

0


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Solution

Calculate specific speed

As a rule of thumb, you may assume the density

of the fluid is 1kg/m^3

It may invoke too much error if calculate

isentropic process, why? -- rotor

This is just an initial calculation, so it is not wise

to spend too much time and effort to make yourresult very accurate


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Step 1.

From density; mass flow rate volumetric flow rate

From inlet total temperature; inlet/exit total pressure

ratio outlet temperature assuming isentropic

process Inlet/exit temperature and Cp total enthalpy

change over the turbine stages

Calculate Ns using N*Qex^1/2 / (ht)^0.75 Increase number of stages to make Ns per each stage

to be > 0.775


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Other parameters

U=340 m/s and N1500rpm

rm = 0.216m

1= atan (tan1+1/)=?

Sketch the velocity diagram

Calculate V1, W1, V2, W2

Check Mcr

None of the Mach can be greater than 1


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Stage Configuration

Symmetric design (Config 1.)

Simplest for design calculation

Rotor rubbing

Descendent (Configuration 2) No rotor and simple enough

Hub weakening

Optimized (Config. 3) Theoretically optimum


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Design for blade shape

Aspect ratio

Chord (the axial projective length of blade)

Cz_vane, Cz_blade

Gap between rotor and stator

Gap = 0.25*(Cz_vane+Cz_blade)/2

1/8 of the stage solidity length


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Detail turbine airfoil cascades

Select an airfoil

Camber the center line to achieve the inlet and

exit flow

Consider other factors that affects the

efficiency of the flow

The detailed design procedure


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Detail Design Procedure

With the velocity diagram

Design for the efficiency of flow deflection

Blade geometry parameters

Iterative process

Given inlet/exit condition

Find the most efficient shape of blade

Real flow considerations Some CAD packages


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l l id ff


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Real Fluid Effects

Pitch/axial chord ratio s/c

Aspect ratio h/c

Incidence Tip clearance

Viscosity and friction

Pi h/ i l h d i /


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Pitch/axial chord ratio s/c

Definition of s and c

s: circular pitch of at given radius, usually the

meridional

c: tip to trail linear distance, not counting the

curvature of the blade

Figure 7.14 on Page 124

Conclusion: larger deflection smaller s/c

A R i h/


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Aspect Ratio h/c

Definition

h: tip-hub distance (delta-R)

c: tip to hub distance of blade

Design perference - smaller the better


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Incidence

Gas (attacking) angle and metal angle

Profile (pressure) loss coefficient Yp

Yp = ( Total pressure loss )

(exit total to local pressure Difference)

Reaction blade (momentum absorberbothvelocity magnitude and direction change counts)has lower Yp than Impulse blade (direction only)

Lead edge thickness reduces sensitivity ofincidence effect on Yp

Ti Cl


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Tip Clearance

Tip leakage

Direct leakage axial leakage

Indirect leakage tangential from pressure side

to suction side

Leakage prevention

Direct leakage prevention slot in casing

Indirect leakage prevention Full or partial

shroud

R ld N b Vi i


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Reynolds Number - Viscosity

Similar to a plate

Re > 10^5 Ypconstant

Re > 10^5 Yp

change rapidly

G id li F Bl d D i


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Guideline For Blade Design

Criterion for Acceptable Diffusion

Downstream turning angle of cambered airfoil

Location of front stagnation point

Trailing edge thickness

Effect of Endwall contouring


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L ti f F t St ti P i t


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Location of Front Stagnation Point

Front Stagnation Point the point where

flow hit metal surface at 90deg

Actual stagnation point s can be far from the

theoretically point a

With high flow velocity separation

Correction

Negative incidence angle

leading edge radius, arc length

T ili Ed Thi k


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Trailing Edge Thickness

Trailing edge of airfoil

Flow from different blades mixed after

trailing edge sudden expansion duct flow

Thinner the better, but

Strength consideration

Coolant pass


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U f l E ti


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Useful Equations

Choice of stagger angle

Stagger angle between the connecting line airfoil front

tip to trailing edge and the axial direction

Note:

Stator design use instead of One of the two angle is negative

52

tantantan95.0 111

O ti S i d Ch d R ti


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Optimum Spacing and Chord Ratio

Definition of Zweifels loading coefficient

Zweifels law

Optimum Zweifels coefficient is 0.8

)tan(tancos28.0

:

)tan(tancos2

212

2

212

2

s

cRatioSolidity

c

s

z

z

T

St ki f 2D Se ti


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Staking of 2D Sections

Blade design is first done by design sections at each

radius

Staking these 2d Sections to form a 3D blade

Experiment and and reworking Problems: secondary flowflow crossed original design

path into other plane

Method of staking

Fix a staking axis

Rotate each design 2d airfoil to optimize


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Axial compressor vs turbine


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Axial compressor vs turbine

Turbine

Fluid flow from high pressure to low pressure

naturally

Accelerating though passage

Compressor

Fluid flow from low pressure to high pressure

Convert kinetic energy to pressure potential

Compression must be a slow decelerating flow

Multi-stage Compressors and Stage

D fi iti


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Definition

Multi-staging is necessary

Pressure ratio vs performance

Compressor stages

Inlet Guide vanenozzle axial flow totangential flow

Rotor-stator for each stage

Subscription 1rotor inlet; 2rotoroutlet/stator inlet; 3vane outlet

V3=V1; 3=1


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Real Flow Effect


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Real Flow Effect

Incident and deviation

Total pressure loss coefficient (PLC)

Pt/(V^2/2)

Deflection angle

Stalling

PLC is twice as minimum

Nominal e* is 0.8 of stalling es

Positive incident angle cause high loss

Reynolds Number


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Reynolds Number

Lower than 2x10^5 leads to high profile loss

Higher than 3x10^5 does not change much

Critical Re is 3x10^5 This effect is partially affected by the

turbulence.

Effect of Mach


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Effect of Mach


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principle of turbomachinery mechanical engineering

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