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MEEN-4350/5350

Axial-Flow Turbines

Xianchang Li

Department of Mechanical Engineering

Lamar University

Spring 2015

Lamar University The Map Where are we now?

Fan; Pump;

Compressor Turbines

Turbomachinery Efficiency

Energy Transfer Rate

Pressure Rise

Blade

Design Performance

Analysis Efficiency

Prediction

Simplified Blade Model

Cascade Test/Analysis

Correlations

STAGE Model

Fluid/Thermo Analysis

Correlations

3D Model;

System Level Analysis

Efficiency Calculation

Objectives: 1. Introduce 2D axial turbine STAGE efficiency and analysis

2. Study the correlations for 2D axial turbine stages

Mean-Line Analysis on Axial Turbines

Assignments/Notice:

Reading: Chapter 4

Axial-Flow Turbines

Humpback Whale – Wavy Blade – Better for Stall or Noise

Axial-Flow Turbine Stage

Where are the stators?

How many stages in total?

Turbine Stage Velocity Vector

Stator

Nozzle

Vane

Rotor

Blade

Bucket

Turbine stage:

Stator Rotor

Compressor stage:

Rotor Stator

For rotors –

Relative flow (w2, b2, w3, b3)

Absolute flow(c2, a2, c3, a3)

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Basic Relationship in Turbine Stage

For Stator

For Rotor

Basic Relationship in Turbine Stage (2)

Turbine Stage Design Parameters

Flow coefficient Higher flow coefficient Relative

velocity closer to the axial direction

Stage loading coefficient

Higher stage loading larger flow

turning more work extraction

Stage reaction R value is important to the shape

of the velocity triangle and thus

the shape of the rotor and stator

Turbine Stage Design Parameters (2)

a1= a3

Repeating or normal stage

For a repeating or normal stage

For Stator

Turbine Stage Design Parameters (3)

More relationships among the design parameters

a1= a3

Turbine Stage Design Parameters (4)

For the velocity triangle of a normal stage, how many

parameters do we have?

Relative flow (w2, b2, w3, b3)

Absolute flow(c2, a2, c3, a3)

Rotation speed (U)

How many parameters do we need to fix the velocity triangle of a

normal stage? 4

How many parameters do we need to fix the shape of the normal-

stage velocity triangle? 3 Only velocity ratio is needed

The design parameters (R, j, y) can be used to fix the velocity triangle.

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Turbine Stage Design Parameters (5)

Example #1:

Given: c2= 160 m/s, U=100 m/s , a2=60o and a3 =30o

Find: c3, w2, b2, w3, b3, R, j, and y

Example #2:

Given: R= 0.6, j =0.5 , y= 1.5

Find: c2/U, a2, a3,

and then c3 /U, w2 /U, b2, w3 /U, b 3

Turbine Stage Design Parameters (6)

Example #1 solution: c3cosa3 =c2cosa2 =cx c3= 92.4 cx=80

U=c2sina2-cxtanb2 b2 = 25.7o w2 =cx/cosb2=88.8

U=-c3sina3+cxtanb3 b3 = 61.3o w3 =cx/cosb3=166.6

j = cx/U = 80/100 =0.8

R= 1+ j /2(tana1 - tana2) = 0.54

y = 2(1-R+ j tana1) =1.85

Example #2 solution:

y = 2(1-R+ j tana1) a1 = a3 = 35.0o

R= 1+ j /2(tana1 - tana2) a2 =66.5o

j = cx/U = c2cosa2/U c2/U = 1.25

Stage Efficiency

Normal Stage: a1= a3

Assume:

Why this?

Try to relate the efficiency to the loss of individual blade

(supported by cascade test)

Repeating stage

Stage Efficiency (2)

Note the definition of loss coefficient

is different from that in Chapter 3.

Use Soderberg’s correlation

for approximation

Use b2, b3 for the rotor

Stage Efficiency (3)

Given by STAGE inlet and outlet parameters as well as

the loss coefficient for both stator and rotor.

Assuming T3/T2=1.

h1-h3=DW= yU2.

Stage Efficiency (4)

Example #3: (Continued from Example #2)

Given: R= 0.6, j =0.5 , y= 1.5

Find: htt and hts

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Stage Efficiency (5)

Example #3: (Solution)

R= 0.6, j =0.5 , y= 1.5 a1 = a3 = 35.0o, a2 =66.5o , c2/U = 1.25

c3cosa3 =c2cosa2 =cx c3 /U =0.61 cx /U = j = 0.5

U=c2sina2-cxtanb2 b2 = 16.3o w2 /U =cx/U/cosb2=0.52

U=-c3sina3+cxtanb3 b3 = 69.7o w3 /U =cx/U/cosb3=1.44

zN = 0.04+0.06[(66.5+35.0)/100]^2 = 0.102

zR = 0.04+0.06[(16.3+69.7)/100]^2 = 0.084

h1-h3=DW= yU2.

htt = [1+(0.084*1.44^2+0.102*1.25^2)/2/1.5]^(-1) = 90.0%

hts = [1+(0.084*1.44^2+0.102*1.25^2+0.61^2)/2/1.5]^(-1) = 81.0%

Stage Efficiency (6)

Sample calculation

with the parameters

shown in the figure

Given:

DW/U2

cy2/U

and cx/U

Axial Turbine Design

Material Stress Limit U (Rotation speed) and d

DW (Power) H A cx

After selecting the angles and other geometry, we can

estimate the efficiency

The process needs many iterations to achieve the best

performance

The End

Questions and comments ?