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3 1293 016914

                                   

This is to certify that the

thesis entitled

AN EXPERIMENTAL RESEARCH AND ANALYSIS OF USING STEAM FOR

COOLING TURBINE BLADES
presented by

Patrick Douglas Henderson

has been accepted towards fulfillment
of the requirements for

 

M.S. degree in Mechanigl Engineering

-

 

Major p essor

Date 03-13" (5}

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

LIBRARY

Michigan State
Universlty

 

 

 

PLACE IN RETURN BOX
to remove this checkout from your record.
TO AVOID FINES return on or before'date due.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/98 WM“

 

AN EXPERIMENTAL RESEARCH AND ANALYSIS OF USING STEAM FOR

COOLING TURBINE BLADES

By

Patrick Douglas Henderson

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1 997

ABSTRACT
AN EXPERIMENTAL RESEARCH AND ANALYSIS OF USING

STEAM FOR COOLING TURBINE BLADES
By

Patrick Douglas Henderson

Using steam as a possible coolant for gas turbine blades was investigated as early
as 1962 by V. A. Zyzin. Steam has a lower viscosity and relatively higher thermal
conductivity compared to air, the most common turbine blade coolant. Successful use of
steam as a blade coolant would allow even higher gas turbine operating temperatures,
which mean higher operating efficiency. Thus to obtain specific steam heat transfer rate
data, Michigan State University’s Turbomachinery Lab has built a wind tunnel test stand.
This fully instrumented set up has a test cell where turbine blade models can be analyzed.
Using this set up and a simple turbine blade model, a series of tests were run which
measuredthemassflowrate ofairandcompareditto themassflowrate ofsteam.

A theoretical model of a cooled turbine blade is reviewed from which a differential
equation of the blade cooling process is derived. This theoretical model and the test
results will help predict and aid in the design of further experiments. This data will be
available for gas turbine blade designers to utilize steam as a blade coolant.

Using published data for air and steam, a series of plots are presented which
compare the fluid properties of air and steam. From these the relative merits of air and
steam as blade coolants are discussed. The test data is also plotted and a complete

discussion of the results follows.

Acknowledgment

I must express my gratitude to Professor Abraham Engeda for his total support
and patience while completing my thesis here at Michigan State University. I must also
thank Professor John Lloyd and Professor Craig Somerton for their generous support in
getting me started in the masters program, their assistance while in the program, and
finally for serving with Professor Engeda as my thesis defense committee.

To the fellow students at the MSU Turbomachinery Lab I am grateful for their
generous assistance and friendship while working at the hb.

To complete this thesis took the patience of my wife, so I wish to give her credit
for her support and understanding during my work here.

Finally, I want to thank General Motors Corporation for their generous support
through the Tuition Assistance Program in funding my studies here at Michigan State

University.

iii

Table of Contents

List of Tables ..................................................................... vi
List of Figures ................................................................. vii, x
Nomenclature ............................................................... xi,xiv
Chapter 1 ........................................................................... 1
1.0 Introduction ...................................................... 1
Chapter 2 Blade Cooling Methods ........................................ 10
2.0 Classification of Blade Cooling Methods ..................... 10
2.1 Cooling by Gaseous Fluids .................................... 13
2.2 Cooling by Internal Forced Convection ........................ 13
2.3 Impingement Cooling ............................................ 14
2.4 Film Cooling ....................................................... 15
2.5 Transpiration Cooling ........................................... 15
2.6 Liquid Cooling ................................................ 18
2.7 Advantages of Liquid Cooling .................................... 18
2.8 Principal Disadvantages of Liquid Cooling ................. 19
2.9 Cooling by Internal Forced Convection ..................... 19
2.10 Thermosyphon Cooling ......... . .......................... 20
2.11 Closed Thermosyphon Cooling .............................. 21
2.12 Open Thermosyphon Cooling .............................. 23
2.13 Closed Loop Thermosyphon Cooling ..................... 25
2.14 Spray Cooling ................................................... 26
2.15 Sweat Cooling ................................................... 27

iv

2.16 Rim Cooling ................................................... 28
2.17 Equations, parameters, and coolant properties for

blade cooling ................................................... 31
Chapter 3 Properties of steam ............... . ............................ 35
3.1 Physical Properties ............................................... 35
Chapter 4 The Test Stand .................................................. 42
4.0 Introduction ........................................................... 42
4.1 The Steam Circuit .................................................. 45
4.2 The Air Circuit ................................. . .................... 45
4.3 Measurement Technique ............................................ 47
4.4 Test Stand Operating Procedures ............................... 53
4.4.1 Steps to Starting up the Test Stand ..................... 53
4.4.2 Turning on the Temperature and Pressure
Measuring Devices ............................................ 54
4.4.3 Blow Down Procedures for Shutting Off the
Equipment ..................................................... 54
Chapter 5 Analysis and Expected Results .................................. 62
5.0 Theoretical Analysis ................................................ 62
5.1 Expected Results and Calculation of Heat Transfer ...... 69
Chapter 6 Discussion of the Results and Conclusions ................... 90
6.0 Discussion of Results ............................................ 90
6.1 Conclusions ...................................................... 91
6.2 Suggestions for further work ................................. 92
Chapter 7 References ......................................................... 93
Chapter 8 Appendix ......................................................... 95

List of Tables

Table 3.1 A Comparison of Steam Properties to Air Properties ........................... 35
Table 8.1 Calibration of the transducer ....................................................... 95

List of Figures

Figure 1.1 T-s dhgram showing the transfer of energy cycle for a gas turbine ............ 1
Figure 1.2 An h-s-diagram of the thermodynamic process of a gas turbine ............... 2
Figure 1.3 Efi‘ective work and efficiency of the simple open cycle gas turbine /1/ ...... 4

Figure 1.4 Thermodynamic illustration of a combined cycle gas/steam turbine process .. 7

Figure 1.5 Development of the gas turbine inlet temperature with the improvement of

material properties and cooling methods /3/ .................................... 8
Figure 2.1 Existing Blade Cooling Methods ................................................ 11
Figure 2.2 Internal Convection Cooling with Air ........................................... 12
Figure 2.3 Internal Water Cooled Turbine Blades .......................................... 12
Figure 2.4 Convection-cooled turbine rotor blade with cast fins /3/ ...................... 14
Figure 2.5 Turbine nozzle vane with impingement and film cooling /3/ ................. 17
Figure 2.6 Water-cooled blades /3/ ........................................................... 20
Figure 2.7 Closed thermosyphon system /5/ ................................................. 23
Figure 2.8 Open thermosyphon system /5/ ................................................... 24
Figure 2.9 Closed-loop thermosyphon system /5/ .......................................... 26
Figure 2.10. Spray cooling configuration /5/ ................................................. 27
Figure 2.11. Rim cooling ........................................................................ 28

Figure 2.12 Cooling efficiency /1/ ............................................................. 30

Figure 2.13 Internal thermal efficiency /1/ .................................................... 30
Figure 2.14. Blade Cooling Eflectiveness ...................................................... 34

Figure 3.1 A broad illustration of the equation of state properties for steam,

as the gas phase of water. Here a 3-D plot of temperature, pressure and specific

volume results in an equation of state surface on which the state properties

of steam, water, and ice must lie. /12/ .......................................................... 36

Figure 3.2 Shows the specific volume versus pressure for steam near the critical

point for various temperatures above the critical temperature. / 7/ ....................... 36
Figure 3.3 Plot of Compressibility Factor versus Temperature. /7/ ...................... 37
Figure 3.4 Specific heat capacity of water and steam/8/ ..................................... 38
Figure 3.5 Dynamic viscosity of water and steam/8/ ....................................... 39
Figure 3.6 Thermal conductivity of water and steam/8/ .................................... 40
Figure 3.7 Prandtl number of water and steam/8/ ........................................... 41
Figure 4.1 Actual configuration of the test stand ............................................ 43
Figure 4.2 ....................................................................................... 44

Figure 4.3 The test stand showing the position of the temperature and pressure sensors 46

Figure 4.4 .......................................................................................... 49
Figure 4.5 .......................................................................................... 55
Figure 4.6 ......................................................................................... 56
Figure 4.7 .......................................................................................... 57
Figure 4.8 .......................................................................................... 58
Figure 4.9 .......................................................................................... 59
Figure 4.10 ........................................................................................ 60

Figure 4.11 ........................................................................................ 61

Figure 5.1. Heat flows using a thin wall tube as a simplified blade model ................. 62
Figure 5.2 Typical temperature profile of a cross section of the tube ................... 65

Figure 5.3. Circumferential variation of the Nusselt number at low Reynolds
number for a circular cylinder in a cross flow /9/ ............................................. 73
Figure 5.4. Circumferential variation of the Nusselt number at high Reynolds
number for a circular cylinder in a cross flow/9/ .............................................. 73

Figure 5.5. Distribution of heat transfer coefficient and adiabatic wall temperature

around a typical turbine blade /10/ ......................................................... 74
Figure 5.6. Characteristic of a cross flow heat exchanger /7/ .............................. 76
Figure 5.7. Specific heat transfer coefficients of steam and air ........................... 78
Figm'e 5.8. Prandtl numbers of steam and air ............................................... 79
Figure 5.9. Thermal conductivities for steam and air ....................................... 79
Figure 5.10. Dynamic viscosities for steam and air .......................................... 80
Figure 5.11. Blade temperature of steam and air cooled blade ............................ 80
Figure 5.12. Cooling effectiveness for a steam and an air cooled blade .................. 81

Figure 5.13 Pressure drop in a steam and an air cooled blade against blade temperature 82
Figure 5.14. Pressure drop in a steam and an air cooled blade against mass

flow ratio. Their viscosity’s shown in Figure (5.9) and Figure (5.10)

are about the same ............................................................................... 83
Figure 8.1. Calibration curves for transducer 1 .............................................. 95
Figure 8.2. Cah'bration curves for transducer 2 .............................................. 96

Figure 8.3. Calibration curves for transducer 3 .............................................. 96

Figure 8.4a ........................................................................................ 97
Figure 8.4b ........................................................................................ 98
Figure 8.5a ........................................................................................ 99
Figure 8.5b .................................................................................... 100
Figure 8.63 .................................................................................... 101
Figure 8.6b .................................................................................... 102
Figure 8.7a .................................................................................... 103
Figure 8.7b .................................................................................... 104
Figure 8.8a .................................................................................... 105
Figure 8.8b .................................................................................... 106
Figure 8.9a .................................................................................... 107
Figure 8.9b .................................................................................... 108
Figure 8.10a ................................................................................ 109
Figure 8.1% ................................................................................ 110
Figure 8.11a ................................................................................ l 1 1
Figure 8.11b ................................................................................ 112
Figure 8.12a ................................................................................ 113
Figure 8.12b ................................................................................ 114

3.3rwmugq.>

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Nomenclature

area

heat flow capacity
specific heat capacity
diameter

gravitation constant
passage heat coefficient
length of the test section
area ratio

mass flow rate
constant

Nusselt number
pressure

Prandtl number
gas constant
Reynolds number

heat flow rate

specific heat flow
entropy

time

temperature
voltage
circumference
specific volume
velocity

volume flow

correction factor
compressibility factor

flow coefficient

convective heat transfer coeficient
thickness of the wall or tube
expansion correction coefficient
efficiency

dynamic viscosity

thermal conductivity coefficient
friction factor

kinematics viscosity

density

Subscripts

8
20

"""‘:]::130 0‘81 hWN—t

compressor inlet
compressor outlet
turbine inlet
turbine outlet
air

blade

coolant

mercury

water

inlet

inner

ian inch mercury
in H20 inch water

1th

g—amoogggw

inner thermodynamic
convective

mean

maximum

minimum

outlet

outer

steam

triple point

wall

Graphic symbols

Symbols for Matter
steam

 

cycle water

 

air

 

combustible gases

 

non combustible gases

 

 

Surface Heat Exchanger

 

 

 

 

 

l heatuchnpm’thmuingairflm

 

 

(condenser)

 

 

 

 

heat mhangerwithout cussing 11m

Machines

turbine

 

compressor (blower)

pump

 

electric motor

generator

0 0 @OF\

Various Things

® combustion chamber

N Shut off fittings

xiv

 

Chapter 1

1. Introduction

The primary goal of all gas turbine manufactures is to construct gas turbines that

produce more power at a higher efiiciency. One of the most powerful parameters

controlling the gas turbine efficiency is the turbine inlet temperature. In fact much of the

rapid development of gas turbines has been possible due to the increase in the turbine inlet

temperatures. Thermodynamically, by increasing the turbine inlet temperature you

increase the efficiency. The ideal efficiency of a gas turbine is similar to the efiiciency of

an ideal gas process given by Joule-Brayton /1/.

 

Tm _T4 +1311: -T2
Tm —T2

 

nub = where

 

 

 

Tm is the temperature of the gas coming out of the combustor, T2 is the temperature of

the gas leaving the compressor and entering the combustor, T4 is the gas temperature

leaving the turbine, and Tm is the atmospheric air temperature entering the compressor.

 

 

 

 

 

 

 

‘ 1

External .

Heat Addition Expansron Work
r— i‘“*‘ ‘ “ 5 l
0' Heat-Exchanger I
‘3 Heat Adilition Heat-Exchanger
0 F _ 1 Heat Rejection
O. 2 ‘
5 Compression 6 _
[d Work

__L-_I 1
Entropy, S

Figure 1.1 T-s diagram showing the transfer of energy cycle for a gas turbine

2
Even though a higher turbine inlet temperature increases its efficiency, the
turbine’s efficiency will always be lower than that of the ideal J oule-Brayton process.

Figure 1.2 shows the process of a gas turbine schematically in an h-s diagram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.2 An h-s-diagram of the thermodynamic process of a gas turbine

Also, there is a limit to higher turbine inlet temperatures. If the blades physical property
limits are exceeded the blade will fail. The most critical physical property is temperature
because it affects all the others. The stators, which represent the first stage of the turbine,

are subjected directly to the highest temperature and pressure of the gas flow coming

3
from the combustion chamber. In the early fifiies the only blade material available was

steel which could then withstand temperatures up to 1000 K But the development of high
temperature steels and new casting methods made the higher temperatures mentioned
below possible. In the present state of the art, the highest temperature allowed for
refiactory steel does not exceed to 1300 K. Exceeding this temperature by about 40
degrees Kelvin shortens the life span of the blade by half. Presently the limits for blades
cooled by advanced convection cooling techniques alone are approximately 1600 K

degrees at 20 bars pressure.

Because the temperature is not constant around the circumference of the blade and varies
radially from hub to tip, thermal stresses result. Due to the rotation through the hot gas,
the rotor blades have a cooler overall temperature distribution hub to tip than the fixed
stators, and a lower average temperature around the circumference. The temperature
conditions for the stator blades on the other hand are higher and less uniform, but because

they are fixed, don’t have the high centrifugal stresses experienced by the rotors.

Two main factors determine the life of turbine blades: One is plastic deformation at high
temperatures, known as creep. Another is thermal fatigue, caused by non uniform
expansion and contraction of a material subjected to non uniform thermal loads. The stress
rupture behavior of even super alloys is reduced by as much as eight times when the
temperature is raised from 650 C to 1100 C. A third effect is oxidation and corrosion

which are accelerated at higher temperatures leading to the onset of failure.

If the turbine blades are kept cool enough so they don’t fail prematurely, the possible gains

to be made are significant. For example by increasing the turbine inlet temperatures from

4
900°C to 1200°C, the efliciency can be increased by five percent for a pressure ratio of 15.

There is also an efficiency and effective work dependency shown in Figin'e 1.3 related to
the pressure ratio. While higher pressure ratios can raise the efliciency of gas turbines and
an optimum pressure ratio can be found for every turbine, still cycle efficiency is measured
by inlet versus outlet temperature ratios. For aircraft turbines much work is done to
increase pressure ratios. This is because of the difliculty of incorporating heat exchangers
into an aircraft turbine design. Therefore, it is the heat exchanger and pressure ratio
together which determine the actual specific work possible for a turbine. For example, by
increasing of the pressure ratio from 15 to 30 by a modification of the compressor, the

eficiency canbe increased by 8 percent.

 

 

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,a "' " Pro Ratio
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---- was“: Cooling
Specific Won-k

 

 

 

Figure 1.3 Effective work and efficiency of the simple open cycle gas turbine /1/

5
Other efficiencies are possible in turbines related to component design.
However, thermal efficiencies still will increase with increasing inlet temperature.
Limited by the blade material thermal property limits that exist, to get even higher turbine
entry temperatures the blades have to be cooled. There are several different methods
which have been developed to cool the blades. However, they must all fulfill realistic

basic requirements to be applied as a blade cooling system for general use:

0 The level and distribution of blade metal temperatures should be such that a

satisfactory blade life is achieved.

0 The reduction in turbine efficiency and overall cycle efficiency compared to an
uncooled turbine with the same turbine inlet temperature should be kept as small

as possible.

0 The performance level of the cooling system should not deteriorate during

operation.

0 The system should be mechanically simple and relatively easy to manufacture and

to service.

0 The application of the cooling system has to be justified on the basis of the overall

economics of the installation.

Presently air is the most common coolant used for gas turbine blade cooling. This
is because it is readily available. However, air has a low specific heat so its capacity to
cool depends on moving large volumes of air rapidly. It also has the disadvantage that is

taken from the compressor which means the efficiency of the compressor will decrease.

6
From the compressor cooling air is usually blown through cooling channels out into the
turbine flow. The pressure losses in the cooling channels are so high that this pressure
energy of the compressor in the cooling air cannot be used in the turbine. This limits the
amount of cooling air that can be used and still realize the thermal efficiency gains to be
made by having a higher inlet temperature. To maximize the overall efficiency an
optimum proportion can be found. Usually the proportion of compressor air diverted to

blade cooling does not exceed 15% of the compressor air mass flow.

The possibility of using liquids for cooling turbine inlets makes good sense
because of their high specific heat. However, they also have a high viscosity which
would tend to slow them down in coolant passage design. This wouldn’t be as big a
problem in stator applications as in rotor applications. Because the rotor is moving at very
high velocity, designing coolant flow passages within the blade, so that hopefully a
uniform blade temperature results, is one problem. If the liquid could be run through the
blade while undergoing the constant temperature associated with phase change, that
would help maintain uniform blade temperature. Unfortunately, to predict whether the
two phase mixture will flow where it is needed or will it separate out under high
centrifugal accelerations is a problem no one has solved. If it separated suddenly the
possibility of the blade imbalance exits. There is another technical difficulty with liquid
cooling. If the liquid changed phase to a gas suddenly, there would be a rapid increase of
pressure if the liquid . To accommodate all the difficulties of a liquid cooled design into

a reliable, efficient, and economic design hasn’t been done.

7
Looking at steam as another possible candidate for blade cooling began in the early

sixties(Zysin 1962)/2/. It has the advantage of the good thermal properties of liquid and
the low viscosity of air. Like air it is easily available. It can be generated by the high
temperature heat of the exhaust gas of the gas turbine. The pressure necessary to force it
through a cooling passage can be generated by a small efficient pump, pushing water into
a steam generator, heated by the turbine exhaust. For example, in the combined cycle
turbine where the hot exhaust of the gas turbine stage is used to generate steam for a
second steam turbine stage, the steam is readily available. Presently the combined cycle
turbine has achieved an overall efficiency of up to 58%, which is higher than all the fossil
fired engines. To employ steam to cool the gas turbine stage would allow even higher

efficiencies as schematically shown in Figure 1.4.

 

 

 

 

 

Figure 1.4 Thermodynamic illustration of a combined cycle gas/steam turbine process

 

 

 

      
 
 

 

 

 

 

 

c F . l T'
2200 '1 ' .
1,. Tums-mm TEMPERATURE. To, .. a0
a COMPRESSOR-MET TEMPERATURE. To. ‘ W
FOR ‘I’ofBOOKaZ'IC'MORIBOF cm"
- m“
2000-1 3500 COATED
. ercomn
‘ - - 7.0
m -:
a: 1’
a *3000 ’
g, 1600* I’
E. JT9 SINGLE CRYSTAL ’ - so
i3 TYPE 11 CERAMICS”
‘ E ”00' 2500
i, TYPEI CERAMICS
_ T ‘
‘i’
a 1200~ — 5.0
a:
2
'1-2000
1000‘
TEMPERATURE PLATEAU FOR __ 4 o
_ UNCOATED METALS? '
UPPER TEMPERATURE um ,
3005—1500 FOR CLOSED-CYCLE
GAS-TURBINE
I I I I I
1950 1960 1970 . 1980 1990
YEAR

 

 

Figure 1.5 Development of the gas turbine inlet temperature with the improvement of
Medal properties and cooling methods /3/

The chart as shown in Figure 1.5 above shows that the inlet temperatures of gas turbines
have steadily increased from about 1950. Higher temperature materials accounted for
most improvements until early 1960. Then blade cooling was introduced and even higher
inlet temperatures became possible. The stoichiometric limit for gas turbines is about

2200 degrees °C, so there is room for much improvement in better cooling methods.

9

Although steam seems like an ideal candidate for use as a blade coolant in high
temperature gas turbines, there is, however, very little experimental data. To remedy this
situation is the goal of this research. To collect useful data an experimental setup was
designed using a steam generator and a high volume compressor to simulate air flow
across turbine blades modeled in the test cell. Before starting a theoretical model was
generated and the test data will be used to verify this model The model can then be used

in an initial analysis to compare the coolant properties of steam and air.

Chapter 2 Blade Cooling Methods

2.0 Classification of Blade Cooling Methods

In gas turbines it can be shown that the higher the inlet temperature the greater net
output and the higher the cycle efficiency. Since the designer has material temperature
limits which constrain the inlet operating temperature, blade cooling allows higher inlet
temperatures and a wider range of materials to choose for blades. There is a penalty in
cooling the blades, however, and that lies in the energy cost to cool the blades. To
minimize this energy cost means using a blade cooling process that seeks to maximize the
heat transfer coefficient of the cooling passages. Also it means that the mass flow rate of
the coolant should be minimized as well as the pumping power to move the coolant.
Therefore, much ingenuity has been applied to the design of cooling techniques that
attempt to achieve a maximum cooling effectiveness at a minimum thermodynamic loss.
The cooling methods can be separated into liquid cooling and gaseous cooling techniques.
Figure 2.1 gives an overview of the existing blade cooling methods. Generally the
internal and external construction of the blade, determines how the coolant is applied and

how effective it will be.

10

11

.533 s.

3.22::

ease: usueeo eesm masses 2 same

5.3.3.2.:
e333

.538 is

 

 

 

 

 

 

 

 

 

 

 

 

 

see 2:20 as

 

 

 

12

Figure 2.2 shows the cooling air flow in high pressure jet propulsion engine turbine
utilizing internal convection cooling while Figure 2.3 is an example of internal liquid

cooling.

 

 

 

 

 

Hiii

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.2 Internal Convection Cooling with Air

 

WATER - COOLEO BLADES

 

  
 
  
 
 

 

 

DESIGN WATER LEVEL

WATER ~FEEO
CONTROL

STEAM CHANNEL

\ Ar
-/ a) WATER-FEEDIMPELLER 63:? ZMAIN STEAM FLOW
WATER-FEED THROUGH

BRAKE SHAFT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.3 Internal Water Cooled Turbine Blades

13
2.1 Cooling by Gaseous Fluids

Blade cooling may be accomplished using either a gas such as air or steam, or a
liquid 'such as water. Air cooling is common because of the fact that many gas turbines
either operate on air or air in combination with some other gas. The air is generally taken
from the compressor outlet and lead directly to the turbine blades and vanes by-passing
the combustion chamber. The temperature difference between the air coolant and hot gas
from the combustor of about 700° C /4/ makes it possible to keep the blades and the
vanes at relatively lower temperature. The cooling air is generally reinjected into the main
gas stream in order to utilize its energy and thereby reduce the performance losses of the

cycle.

2.2 Cooling by Internal Forced Convection

For internal forced convection, cooling air is pushed through the blade, circulating
inside, and picking up heat by convection. Then in general, the heated air is blown out at
the blade tip and/or at the blade’s trailing edge, mixing with the gas flow. By this method
a gas temperature of some 1400 to 1500 K is possible, depending upon the blade’s
interior design. To increase the effectiveness of this convection cooling, the inner surface
of the cavity is increased by means of inserting a series of blade passages with large
numbers of fins to absorb the heat conducted through the blade. The heated air leaves the
cavity through the holes or slots near or in the trailing edge. By exiting through the tip or
the trailing edge , any disruption of the aerodynamic air flow is minimized. Figure (2.4)

shows an example for a convection-cooled blade.

14

 

 

 

 

 

Figure 2.4 Convection-cooled turbine rotor blade with cast fins /3/

2.3 Impingement Cooling

Because the leading edge of a blade represents the region of highest temperatures,
an improvement on internal cooling is impingement cooling. Here the airflow entering the
blade is blown directly on the inside of the leading edge in such manner that it impinges

perpendicularly in a distributed single jet on the edge. This produces a stagnation region

15

inside the blade opposite a corresponding stagnation region outside the blade. Because
stagnation regions have a high heat transfer coefficient, convection heat transfer is

enhanced.

2.4 Film Cooling

To further increase turbine inlet temperatures film cooling can be used. A protective
cooling film between the hot gas and blade wall is created by venting the air coolant,
forced into the blade cavity, out through a series of holes or slots at or near the leading
edge of the blade. This coolant air is swept along the surface of the blade forming a
cooler boundary layer which reduces heat transfer to the blade from the hotter free stream
gas. As heat is conducted and mixed with this film is its effect is diminished. Therefore,
other series of similar slots or holes may be added downstream from the original set to
maintain continual blade cooling. Because the coolant is forced through the blade cavity
to the film cooling slots or holes, a combination of internal convection and film cooling is
possible. This is actually employed in the highly stressed turbine blades of today. If
enough coolant is vented its low velocity may have the effect of causing an aerodynamic

drag on the airfoil and decrease its performance.

2.5 Transpiration Cooling

Transpiration or effusion cooling is similar to film cooling in that the coolant is
vented into the boundary layer flowing over the blade. But because the holes venting the
coolant are actually a continuous distribution of small porous holes in the surface of the

blade a more uniform protective boundary layer is created with a more uniform

16

convection coefficient. The porous blade wall is usually supported by load-bearing core.
This continual renewal of the cooling film on the hot gas side makes possible a higher
cooling effect over the entire blade. surface than with conventional film cooling. This
higher cooling effect combined with reduced aerodynamic penalties due to a more
uniform boundary layer by this method, are reasons why it is acknowledged as the most
efficient turbine cooling technique. There are problems, however, with reliability because,
should the porous wall of the blade become clogged with debris, the blade could fail
catastrophically. Also, although the cooling effectiveness of film cooling is lower than the
effectiveness of the transpiration cooling, a number of important advantages make film
cooled blades a better option. One is where the attachment of the porous blade wall to the
supporting cores is difficult to achieve. Film cooled blades, however, can be fabricated by
the same methods as convection cooled blades with internal passages, by casting or
forging and diffusion bonding. The vent holes or slots can then be machined later by a

ram type electrical discharge machine or by electronic bombardment.

17

 

 

 

 

Figure 2.5 Turbine nozzle vane with impingement and film cooling /3/

 

18

2.6 Liquid Cooling

Frequently air is thought of more for its insulating preperties than for its heat
transfer capabilities. This was evident in the discussion of air film cooling above where
the film coolant, while providing a cooling effect, also provided an insulating layer
between the hot free stream gas and the blade. Liquids, however, have superior thermal
conductivity, superior specific heat and greater density, compared to gases such as air.
The viscosity of liquids, however, is much higher as an alternative to cooling fluids such
as air. Despite this air still enjoys the tremendous advantage of being readily available
from the compressor discharge air and being compatible with all elements of the gas
turbine system. Thus it’s advantages over various alternative systems has given it

preeminence.
2.7 Advantages of liquid cooling systems

1. Attainment of very high convective heat transfer coefficients without the necessity

of additional pumping equipment(liquid is moved by natural convection)

2. A broad selection of potential coolants (particularly for closed systems where

even liquid metals are a possibility)

3. Independent control of the thermodynamic state of the cooling medium(a liquid

may be allowed to vaporize to take advantage of the heat of vaporization)

4. Free stream flow of the turbine inlet gas) no aerodynamic penalties for dumping
air into the gas path(liquid is in some cases allowed to exit through the blade tips

where it won’t interfere with the

19
2.8 Principal disadvantages of liquid cooling

1. High pressure corresponding to high temperature to maintain coolant in liquid

form(a liquid-could reach it’s critical temperature and pressure)

2. Possible large thermal stresses resulting from large temperature differences
necessary to conduct resultant large heat fluxes across a blade wall, characteristic

of the next-generation, maximum-temperature blades.

3. The necessity to transfer heat from blade passages to a secondary heat exchanger

(for certain closed systems)

4. Limited research background to support meaningful applications(lack of
knowledge of flow instabilities, pressure drop problems, and long term reliability

of proposed systems)

2.9 Cooling by Internal Forced Convection

Liquid cooling by internal forced convection works in a similar way to gaseous
cooling by internal forced convection. The coolant, however, is generally not discharged
at the at the trailing edge of the blade because of possible erosion and corrosion on
following blades. To get around this the coolant has been discharged at the blade tip and
collected, thus not interfering with other rows of blades further down the free stream

flow.

Figure 2.6 shows a water-cooled rotor blade where the coolant is collected after being

discharged at the blade tip.

20

 

 

  

'

 

      

\\\\\\\\\. g

I
u

   

I

Supptyresorvoir
Waterbedhob

 

 

Figure 2.6 Water-cooled blades /3/

2.10 Thermosyphon Cooling

In a thermosyphon, heat is transported by moving a fluid; the fluid is set in motion
by a temperature gradient in the fluid which gives rise to density gradient. This density
gradient creates a body force on the fluid proportional to its density. As the fluid warms
its density decreases and it is displaced by denser cooler fluid in a body force field created
by the centrifugal force of the rotating blade. The centrifugal force field caused by
rotation is proportional to the product of radius and the square of the rotational speed. For
a typical turbine this can be as high as 20000 g’s. Thus no pump is required to force the

fluid through the blade and the heat transfer drives the whole process. There are three

21

basic types of thermosyphon: the closed thermosyphon, the open thermosyphon, and the

closed loop thermosyphon.

2.11 Closed thermosyphon

The closed thermosyphon system is illustrated for a possible turbine application in
Figure 2.7(a). The thermosyphons form the cooling passages in the blade; each cooling
passage is a closed tube with the primary heat-transfer media (liquid or gas or both)
sealed inside. The primary coolant near the tube wall is heated in the blade cooling
passage; this hot, less dense, coolant flows inward toward the cool end and is displaced
by cold more dense fluid from the heat exchanger. This process is illustrated in Figure
2.7(b). In the heat exchanger section of the tube, heat is removed from hot primary fluid
and cooled. Once cooled, it is denser and moves back again toward the warmer end of the
blade nearer the tip following the cooler inner region of the coolant . The heat exchanger
is kept cooler than the primary coolant by a secondary coolant which removes heat from
the heat exchanger and carries it away. The secondary coolant could be externally
supplied water. It could also be fuel which becomes preheated before entering the
combustor. Also, because air is part of the combustion process, as it comes from the
compressor on its way to the combustor, it could be used to cool the heat exchanger.
Using fuel or compressor air would be applicable to aircraft systems, while water cooling

would be appropriate for ground-based machines.

Another type of closed thermosyphon is the two-phase thermosyphon or vapor
chamber. This type has a similar construction, but the chamber is only partially filled with

the working fluid. At the design condition, the working fluid is vaporized in the blade

22

cooling passage and recondenses at the cooled heat exchanger end. Condensed vapor runs
outward in a film from the condenser end to the heated end, thus the cooling the blade.
This method takes advantage of the heat of vaporization as the coolant changes phase

from liquid to gas.

Since the closed thermosyphon is completely sealed, clogging by debris is not a problem;
Because it is a sealed system the maximum coolant pressure within the blades can be
controlled by how much coolant is added before the blade is sealed. This means that
maximum pressure can be lower than that for some other systems. This also means that
the choice of primary working fluid is not limited as with open systems; thus liquid
metals or special fluids with specific heat transfer characteristics which allow the fluid to
vaporize and then condense can be considered. There is a negative side to the closed
thermosyphon. Should a crack in the blade material develop, the primary coolant may be
lost and cooling will no longer take place. Also, because the closed thermosyphon system
requires a primary to secondary coolant heat exchanger it may be difficult to find
adequate space on the turbine wheel to place it and it may also be costly compared to
other methods. While clogging should not be a problem, if the working fluid and the
thermosyphon wall material are not compatible, corrosion could cause clogging or reduce

efficiency for long-term operation.

23

 

 

 

 

 

 

 

 

 

mm“ z-Coollng ‘—
pesseges :
Primarylsecondary (closed Blade .—
000an hot thermosyphons) ”cum ; t ‘_ Hm
archangerx“ Egg; - passages ._ added
l I i “'—
9
I m
Heat
exchanger 1 l r I removed
(a)Possible gas turbine application (b)Closed thermosyphon tube

 

Figure 2.7 Closed thermosyphon system /5/

2.12 Open thermosyphon

Figure 2.8(a) shows the open thermosyphon system, and Figure 2.8(b) shows the
cross section of a single cooling passage. The coolant enters a cavity or reservoir at the
base of the blade. Cooling passages in the blade are open to this reservoir so no heat
exchanger is needed. The fresh, denser, coolant in the reservoir displaces the hot fluid in
the cooling passages. The hot fluid from the blade mixes with the fluid in the reservoir,
which is continually being replenished with cool fluid from the inlet. Advantages of this
system are its simplicity in that no heat exchanger is required. Fluid pressure at the blade

tip is a function of the location of the free stream in the reservoir. The heated fluid

 

24

returning from the blade is swept directly into the free stream and carried away. Thus the
temperature can be controlled easier which allows better control of the pressure than that
for closed systems. A disadvantage of the open thermosyphon system is that foreign
matter in the coolant can collect at the blade tips because the cooling passages are blind
holes. If the length to diameter ratio of the thermosyphon is too large, performance will
suffer because of the growth and mixing of the boundary layers of hot and cold fluids
flowing in opposite directions. Water is the only practical coolant for the open
thermosyphon system. Water, however, can be chemically active so corrosion could be a

problem.

 

 

Cooling
F8998
IbIInd hoIesI-E’

 

 

 

 

 

s
~“
‘
~§

(a) Possible turbine cooling configuration (b) Single cooling passage

 

Figure 2.8 Open thermosyphon system /5/

 

25

2.13 Closed-Loop Thermosyphon

The third type of thermosyphons the closed-loop shown in Figure 2.9(a) in a
possible turbine blade cooling configuration. Details of the blade cooling passage and the
heat exchanger are depicted in Figure 2.9(b). Instead of the coolant flowing in two
directions simultaneously in the cooling passages as in the closed an open
thermosyphons, it flows in one direction each passage. Cool, more dense fluid moves
radially outward through the centrifugal feed passages and is then manifolded at the tip to
flow radially inward through the small cooling passages around the perimeter of the
blade. Heated fluid in the cooling passages the moves inward to a heat exchanger where it

is cooled by a secondary coolant.

The closed-loop thermosyphon has the same advantages and disadvantages as the
closed thermosyphon. However, because flow is unidirectional in all passages much
longer passages can be utilized. Long, thin passages may be necessary in the turbine

application to minimize thermal gradients.

26

 

 

 

mma Cooling
‘ Passages
m8 ‘ \- Manifold
coolant
hat
caching» «‘

 

\
\

 

 

 

 

 

 

 

  
   

 

 

 

I l ‘~Disk
Sanctuary
coolant
Inlet
{2.3, I.
~- a???" T'
I- 1 ‘ u i j
\ T “h-‘nm fit: /
Outlet manifold-I ,’ “TN-\n...” .‘i’ r
L
\‘000019 Sfll "1M 111311110111 \ \ \
outlet exchanger -I \
(a) Possible turbine cooling configuration (b) Details of blade cooling passages

and heat exchanger

 

Figure 2.9 Closed-loop thermosyphon system /5/

2.14 Spray Cooling

Spray cooling is illustrated in Figure 2.10. Water is sprayed from stationary
nozzles or nozzles located in the rotating blade bases onto the exterior of the rotating
blades. The evaporating water cools the blade surface. The large quantities of water

required make the system practical for steady-state use.

 

 

Water ,3 ,
scrim"

 

Water
Inlet "

 

 

 

 

Figure 2.10. Spray cooling configuration /5/

2.15 Sweat Cooling

Sweat cooling, as the name implies, uses a liquid coolant that seeps through pores
in the blade wall and evaporates fiom the blade surface. The air-cooled counterpart of
sweat cooling is transpiration cooling. In order to control coolant flow distribution and
flow rates, very fine pores would be required in the blade. These would be subjected to
clogging fiom foreign matter in the coolant as well as plugging from corrosion. Sweat

cooling has not been tried in a turbine application.

28

2.16 Rim Cooling

Rim cooling, where the heat is extracted only at the blade root, allows only very

moderate temperature differences between gas and blade and is therefore not efficient

enough for higher temperature applications.

 

 

blade

 

 

 

-____-‘---II

 

 

 

\

 

 

 

Figure 2.11. Rim cooling
Figure 2.12 and Figure 2.13 show a comparison of different cooling methods for air with

respect to their relative effectiveness and efliciency. Effectiveness is defined as:

 

_(T.-T.)

”(:— T's—T;

 

 

 

Tb is the blade temperature, To is the coolant temperature, and Tg is the temperature of
the turbine gas. In words, the most effective blade cooling method is the one with the

lowest blade temperature resulting, Tb.

29

 

A mcxcp
-Ez_xeI

 

 

The effectiveness is plotted against efficiency, A :

 

where the mass flow rate times the specific heat represents the energy diverted to blade
cooling in Joules/sec. This is divided by the heat transfer coeflicient times the blade
area(blade perimeter, U, times the blade length, l), the actual Joules of heat dissipated by

blade cooling.

Looking at the effectiveness the four different methods in Figure 2.12 shows that
transpiration cooling provides the best effectiveness, followed by in descending order,

film cooling, impingement cooling, and free convection cooling.

Figure 2.13 shows the emciency of a gas turbine for the same four cooling
methods in Figure 2.12 and also for a blade with no cooling. These eficiencies are plotted
against the turbine inlet temperature. Curve 1 stands for a blade without cooling. It has the
highest efficiency because no energy is expended in cooling the blade. This is the ideal
case where the higher the inlet temperature the higher the efficiency. However, without
cooling a blade will not survive the high temperatures where increased efliciency is
possible. The other four curves illustrate that past a certain temperature their efiiciency
decreases because of the extra energy expended to cool the blade. This energy comes fi'om
the compressor. Thus the compressor’s pressure ratio is lowered and as mentioned earlier

the pressure ratio effects the overall efficiency of the turbine.

30

 

 

 

1 Convection
‘m
\ .
o ‘n o
3 Irwin-3mm I
AW“ I " 1,4
M a
. /
. 5'2
- C

At? "/“

 

 

ll\

 

 

 

0.2‘

 

 

 

 

 

 

o «:4 011.2152»
Afi

 

 

Figure 2.12 Cooling efficiency /1/

 

 

 

 

 

 

 

 

 

 

 

1
ll
.5
.3 1 -
s M 2 1’
§ /""'— 3 1
fi >5- 4
m as —-
E 5
1
g
u _
DJ 3
750 I. "a I”
Turbine Inlet Temperahrrc '1: [‘CI

 

 

Figure 2.13 lntemal thermal efficiency /1/

 

 

31

For higher the turbine inlet temperatures, the more coolant is needed. New
manufacturing techniques such as thermal barrier coatings and diffusion bonding have
reduced the amount of coolant needed by a factor of about 8. By increasing coolant flow,
the adverse aerodynamic effects on flow around the blade are increased when film and
transpiration cooling methods are used. Therefore, by optimizing these blade
cooling methods the overall efficiency of the process can be increased. A combination of
internal and external cooling methods will provide a better effectiveness than a single
cooling method. The application of impingement and film cooling together in large gas
turbines (see Figure 2.5) is very common.

Lowest in efiiciency and yet the simplest to analyze is internal convection cooling where a
coolant is forced through cooling passages in the blade. It is this type of cooling for a

typical blade which is describe below.

2.17 Equations, parameters, and coolant properties for blade cooling

A basic concept used in blade cooling analysis is the Reynolds analogy which
relates the velocity profile in the boundary layers of a fluid to the temperature profile

through the same boundary layers. The analogy may be written:

 

C
——f=sr
2

 

 

 

Where Cf is the fiiction coefficient and St is the Station number. The fiiction coeflicient,

 

 

Cf, itself is defined as: C f =

 

 

 

32

In the formula, p is the density and u infinity infinity is the velocity in the free stream of

the flow. This equation is valid for what is called a "Newtonian" fluid. That is, where
the surface shear stress is a function of the velocity gradient at the surface. This is

reflected in the numerator of the expression as Is, the surface shear stress, a function of

the dynamic viscosity, u . This may be written as:

 

 

 

 

I Site? |y=0 where :3 of the coolant is evaluated at the surface, y=0.
Y Y
25'
Rewriting this in terms of u: 'u — a“

defining viscosity as the ratio of the shear stress at the surface to the velocity profile there.

The fluid conductivity, k, is also defined at the surface. It is defined in terms of

the heat transferred per unit area and the temperature gradient at the surface:

Q rate

k J— where 0 = T-Ts , Ts being the surface temperature.

as
3y y=0

 

Combining the two expressions: where k/u is the proportionality that relates 89 and au

 

Q rate

at the surface. , A Bkfii

‘5 Iran

 

 

 

 

 

33

If the point of interest is not at the surface, but above it in an area of turbulence

then the expression becomes, because of the mass heat transfer in the turbulent layers:

 

 

 

 

QraE
I 5 3" (y=0)

When Cp=—ls then the expressions are identical. This defines a new property called the
u

Prandtl number, Pr=Cp x u/k =1 when the expressions are identical. For air Pr = l. Pris

Q rate

dimensionless. Grouping terms from the expression above such as: :53

Q rate

defines the heat transfer coefficient hFTB—e

This generates another dimensionless number Nu=ht x l/k, the Nusselt number.

A third dimensionless number is defined as Re=p*L*U/u , is known as the Reynolds
number which if greater than 2300 implies turbulence exists in tubular flow. For flow
over a flat plate Re>5x10"5 denotes turbulence in the flow. Finally all these are all
related by the original expression: St = Nu x 1/Re x l/Pr = Cf . From this properties

such as the heat transfer coefficient may be defined: ht=p *U*Cp*Nu* l/Re* l/Pr.

Typical blade coolants air, water, and steam and Prandtl numbers for these and many
others can be found in tables( See Chapter 3 for properties of steam). For air Pr = .7 and

for steam at atmospheric pressure, he].

34

For liquids such as water Pr numbers rise above zero reaching almost 14 at room
temperature and pressure. Performance of blade cooling can be measured in terms of its
effectiveness which is a measure of the ratio of actual heat transferred to the maximum

amount of heat that could be transferred. This may be written:

ex =NTU x (Om/00)where NTU is the dimensionless heat exchanger size and (Gm/00) is

the ratio of the mean temperature difference to the inlet temperature. See Figure 2.14

below.

 

 

TEMPERATURE

 

 

 

 

 

 

 

~
’—

HEAT- EXCHANGER LENGTH

Figure 2.14. Blade Cooling Effectiveness

Chapter 3 Properties of Steam

3.1 Physical properties

Steam at one atmosphere of pressure and at 100°C occupies a volume of almost

1700 times that of its liquid form, water. It has been used to establish the upper end of

the Fahrenheit and Celsius temperature scales by which the temperatures of other

substances are measured. Its thermodynamic properties are well known and documented

in steam temperature and pressure tables. Below is a table comparing the properties of

steam and air.

Table 3.1 A ComJLarison of Steam Properties to Air Properties

 

 

 

 

 

 

Material Steam Air
Chemical formula H20 Mixture of 02, N2, & small
amounts of other gses
Mlolecular Weight 18.016 28.964 approx.
Triple Point 001°C at
0.0006112 bar pressure
Critical Point 647.3° K at 133° K at
221.20 bar pressure 113.5 bar pressure
Gas Constant R=0.46l.5 kJ/kgK R=0.2870 kJ/kgK

 

Specific heat @ 300 K

Cpo=l.8723 kJ/kgK
Cvo=1.4108 kJ/kgK

Cpo=1.005 kJ/kgK
Cvo=0.718 kJ/kgK

 

Specific heat ratio, k
@ 300 K

1.327

1 .400

 

Thermal conductivity, k, @
20 ° C, 1 bar pressure

0.0248 W/m°C

0.02624 W/m°C

 

 

Prandtl # @ 20 ° C, 1 bar 0.98 0.72
pressure
Viscosity, u, @ 20 ° C, 1 1.20 x 10"-5 kg m 1.81 x 10‘-5 kg m
bar pressure

 

 

Kinematic viscosity
v x 10"6 m"2/s @ 600°K
at atmospheric pressure

 

56.60

 

51.50

 

35

 

 

Pressure

 

 

 

 

Figure 3.1 A broad illustration of the equation of state properties for steam, as the gas
phase of water. Here a 3-D plot of temperature, pressure and specific volume results in an

equation of state surface on which the state properties of steam, water, and ice must lie.
/12/

 

Super heated Steam

P‘P,‘
Fluid ‘

Wet Stean

 

0 4 d 12 16 20 24 20
V

 

 

 

Figure 3.2 Shows the specific volume versus pressure for steam near the critical point for
various temperatures above the critical temperature. /7/

37
Steam for most calculations can be treated as an ideal gas where:

 

 

 

P*v=R*T

 

For more exacting work the compressibility factor Z must be taken into account:

 

_ P*v
_R*T

 

Z

 

 

 

The compressibility factor, Z is assumed to be a function of entropy. From empirical data

the plot of Z versus temperature for various pressures is shown below in Figure 3.3.

 

P. 0.1"”

+, /

 

 

C/
////
.7
F
/ /
l~ /

100 200 300. 400 500 6%. mo 8W?

/
/‘

 

\\

 

9 .9
V Q
\15

 

\‘o

 

‘8
/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.3 Plot of Compressibility Factor versus Temperature. /7/

The thermodynamic pr0perties of steam are well known and published in tables
which describe steam with great accuracy. However, the graphs that follow give a more

visual description of steam properties as a function of temperature and pressure.

 

 

 

 

 

 

Ill/lg gdi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-—>

 

D
Figure 3.4 Specific heat capacity of water and steam/Bl

39

 

—.

Figure 3.5 Dynamic viscosity of water and steam/8l

40

M M W ow

t———> ’0

 

Figure 3.6 Thermal conductivity of water and steam/8/

41

 

Figure 3.7 Prandtl number of water and steam/8]

Chapter 4 The Test Stand

4.0 Introduction

The test stand used to generate steam and create the air flow for the tests can be
separated into two sections which operate independent of each of each other. First is the
air blower section which simulates hot gas flow in a turbine by drawing in ambient air and
blowing it through an air duct. After it passes through the section of the duct where the
test blade is mounted, the air exits out into the ambient air again. This .151m x .151m
rectangularshapedduct thencanbethought ofasasmallwindtunnelwithastationary
test blade mounted in it. The second section of the test stand provides steam as a blade
coolant. The steam passes through the test blade which in this case is a round 3/4” copper
tube. Figure 4.1 illustrates the actual configuration of the test stand.

The test stand on which all of the equipment for testing is attached, is mounted on
a four wheel dolly so that it can be moved around as needed. Figure 4.2 shows the test
stand on the dolly. The open fiamework of the test stand will allow new equipment to be
added and existing equipment to be modified in fiiture work. The stand needs only to be
attached to 240V electrical power and a source of tap water with a hose in order to
operate. In this initial test stand a superheater was not needed because it was found that
the steam through the test blade was at superheat temperatures and pressures. The thick
insulation on the piping fi'om the steam generator to the test blade prevented premature

condensation. In an actual turbine the combustion gases theoretically can reach over

42

43

 

Steam Generator

 

 

 

 

 

 

 

AIr Compressor
’
_______ pfi --——-—-——--1 __________.__...__
$ 4
Water
5
Steam 6

 

 

 

 

 

 

 

 

 

Condenser

 

 

 

 

Figure 4. 1
Actual configuration of the teat stand

 

 

 

2000 °C degrees centigrade. To create combustion gases for this test stand would have
meant using a combustion chamber . To simplify things for this initial set up a
combustionchamberwasnot used. Air insteadwasused,whichisactuallycoolerthan
the test blade. Because heat flows from an area of high temperature to one of lower
temperature, it isacomparisonofheat flowrates whichwasanalyzedinthistest set up,
not the direction of heat flow. Therefore, the direction of heat flow is opposite, in this set

up, to that of an actual cooled turbine blade.

 

 

 

 

Figure 4.2

 

45
4.1 Steam Circuit

Steam for the test stand is produced in a Chromalox Electric Steam
Generator(Model # CMB9), which is fed by ordinary tap water. The incoming water must
be at least 0.7 bar pressure(lO psi) greater than the operating pressure of the system.

The generator has an electric capacity of 9 kW and will supply saturated steam up to 7 bar
pressure( 1 00 psi), depending on the feed water pressure and temperature. Actually the
operating pressure in the test stand was about 3 bar which resulted in the pressure in the
test blade to be about 2 bar pressure. Once the steam passes through the test blade it
passes through a water cooled condenser. Then finally it is collected as condensed water
in a beaker. The mass flow rate of the steam is calculated by measuring the time it takes

to collect 500 ml of water. See Figure 4.3.

4.2 Air Circuit

The air that passes across the test blade in the duct is provided by a 15 kW FUGI
Blower. The blower will produce a mass flow rate of about 0.3 kg/s . To vary the mass
flow rate circular bafile plates with different diameter holes in them are mounted
downstream from the blower. By using a different size hole in the bafile plate the air flow
rate can be varied. For the tests run holes sizes varied from 1.5” to 2.75”. Smaller
diameter hole bafiles were tried but the pressure developed was too great for the clamped
piped joints The test blade was placed on the suction side of the compressor. This

allowed a higher temperature difference between the test blade and the flowing air which

46

was at ambient air temperature. Compressed air at the outlet side of the compressor was

 

 

Z

 

 

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Ala-Elf!

 

 

 

 

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to
n
1-
8

0

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J. . o; ._.
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ttttttttttttttttttttttttttttttttttttt

. 00....0000...000.00.000.000000000000

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sch

 

 

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cozm—gF: .ceeeooeeeeeoeeoee009.000.000.000.eeeeeeoeoeeeeeeeeoeeeeeeoeoeeoee

DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

 

 

33.2.50
Seem

 

 

Figure 4.3 The test stand showing the position of the temperature and pressure sensors.

47
4.3 Measurement Technique

Before each test the atmospheric pressure was read in inches of mercury using a
barometer located in the turbomachinery laboratory. The atmospheric temperature was
also recorded in the turbomachinery lab at the same time. On the test stand
thermocouples are placed at the desired locations to measure the temperatures of interest.
The thermocouple measurements are displayed on OMEGA DP116 meter in degrees
Celsius. The DP116 is a miniature economical temperature meter with a large display for
easy recording of data. It has a linearized analog output that is supplied as a standard
feature. It can also provide an analog output signal which can be recorded automatically
on a PC with the proper software.

At the blade there are six self adhesive thermocouples placed on the surface of the
blade. Two of them are placed on the surface of the blade at the inlet and outside of the
test section. They are just outside of the test section under heavy insulation. Because of
the thin wall of the blade and its high conductivity temperature measurements recorded
fi'om these two represent the inlet and outlet temperature of steam in the test section.
Just inside the air flow of the duct the other four thermocouples are mounted. Two are
mounted at the front of the test blade and the other two are mounted at the rear of the
test blade. Another two thermocouples were mounted in the air stream. They were
located upstream in front of the test blade and downstream fiom it(See Fig. 4.3). It was
found that alter sweeping the area at the positions shown, the temperature remained
nearly constant. Therefore, by using these two temperature measurements and averaging
them an average air stream temperature at the blade can be determined. The temperature

differences between the two are not significant enough and the flow is not uniform to

48
allow the heat transferred from the blade to be calculated. This heat transfer, however, is

calculated using the steam temperature measurements fi'om the blade. For this reason the
pressure of the steam is monitored just before and just after the test section. Three steam
pressm'es are recorded using pressm'e transducers supplied with 10 volts. One is the
absolute pressure at the entrance to the test section. The second is the absolute pressure
just alter the test section. The third is done with a differential pressure transducer which
serves to easily give the AP for the section, and also verify that other two transducers are
working properly.

Because the transducers don’t read pressure directly their output is in volts
proportional to the pressure. The transducers are calibrated to be sure that the voltage
read reflects actual pressure sensed by the transducer. The following equations were used
in cah’brating the transducers:

For the steam inlet pressure transducer:

 

 

 

pee = palm +13259'3 X (Ilse — I[II-re) where 7.7 111V was SCI to correspond to

 

zero(atmospheric) pressure by adjusting the supply voltage.

For the steam outlet pressure transducer:

 

 

 

pso 2 Pan» +13259-3 x (K10 - V030) and the supply voltage was adjusted to 7.5

mV to correspond to zero(atmospheric) pressure.

The differential pressure transducer was calibrated using:

 

Pa
A P, = 6516;}; X Vs where zero(atmospheric) pressure was set to 0 mV.

 

 

 

49
Appendix 8, Table 8.1 shows the cahhration data for Figure 8.1 to 8.3 of the calibration

charts. Below Figure 4.4 shows the backside of the test cell and the rack mounted

temperature and pressure readout meters.

21“

.. Inside this
square air duct
is the test section

l igital readout
meters for

emperature and

.ressure sensors

 

50
To compare the mass flow rate of steam to that ofair, the mass flow rate ofair

was determined first by measuring the pressure drop across the bafile plates that were
used to vary the air flow. A differential pressure transducer was used on each side of the
baffle plate. Both transducers used atmospheric pressure as their common reference
pressure and both digital meters readouts are in inches of water. The density of the air
was determined using these pressure readings and a temperature measurement from a
thermocouple placed in the air flow before it passes through the hole of the bafile.

To calculate the air pressure, p, in N/m"2, for the blower side of the bafile orifice:

 

 

 

m
P =pdm +(pinl-120 x (10254; pr-IZO x g) was used, and therefore,

 

 

m kg m
p=pm +(pinH20 X00254; X 10(1); X9815?) .

 

 

 

The pressure change from one side of the baffle to the other was found similarly:

 

 

 

m
A per] =A Fargo x0.0254-iI—1 XPH20 xg or

 

 

 

 

m kg m
A Pay =A Pair/,0 x0.0254i71x10m;x9.806;2-

 

51
To compute the density of the air in fiont of the baflle, the ideal gas assumption for air is

 

 

= P
'0 RxT

 

used: vaszRXT and thus:

 

 

 

 

 

 

Knowing density the mss flow rate, kg/sec =volume flow rate(m"3/s) x density(kg/m"3)
can be found once the volume flow rate is determined. The actual flow rate, Vacmal, is

found using an iterative procedure. The theoretical or ideal flow rate, Vided is calculated

 

Jim

. d2 [APO
from: Video! = X x If x C
4 d“ p
x/“BI

 

 

 

 

 

where ,d_ and D_ represent the diameters of the orifice and inside diameter of the pipe
duct. Because the actual rate of flow through a differential pressure orifice is not nearly
the same as the theoretical a correction factor, C, called the discharge coefficient is used
where C = actual flow rate/theoretical flow rate. To find C the Reynolds number, Re,

must be found:

 

 

 

R, = 4.1297 x 101 x (1 — 0.008 x (1; — 293K» x VW

 

where the subscript _1___denotes that the property was measure a distance D in fiont ofthe
orifice and the APO“, from above denotes that the pressure difference was measure fiom

_1_ to a distance 1/2D after the orifice. So now C can be calculated:

 

7
C = 0.60694 + 3 5977

 

 

 

e

 

To correct for expansion after the orifice an expansion coeficient, Y, is used in

conjunction with C. Y is related to AP.“ and P, by:

52

 

M0,,
1’.

 

Y=l—0.353x

 

 

 

Vm, is then calculated:

 

C x Y
0.640

 

Vadual = Video/x

 

 

 

So now the mass flow rate of air is found:

 

 

 

in“? =mepaaual

 

Because Va... is defined as a fimction ofC, which in turn is defined in terms of Va”, an
iterative procedure is used to find that value of C which works in both expressions. This
hasbeendoneandtypically C 5 0.64 .

As explained previously the mass flow rate of steam is calculated by the volume of

condensed steam collected per unit time:

 

Vm >< pm

At

m steam —

 

 

 

 

Figure 4.2 shows the positions on the test stand where the measurements were taken.
Also the temperature sensors just ahead and behind the test section can be seen in Figure
4.3 and their readings are recorded in the columns Tum. and Tm“ of the test results in the

Appendix.

53

4.4 Test stand operating procedures

4.4.1 Steps to starting up the test stand

1.

9.

Open the three gauge valves on the steam generator; these must be left open.

(Valves #1, #2, and #3 in Figure 4.5)

Check to be sure all downstream steam path valves are open(Figure 4.6 valves

#4, #5, and #6)

Make sure the steam bypass valve is closed(Valve #7 in Figure 4.7)

Close the main drain valve(Valve #8 in Figure 4.8)

Open water supply faucet and main water supply for the steam generator
(Valves # 10 and #9 in Figure 4.9)

Wait for the water to reach the proper level automatically by checking the sight

gauge, Figure 4.10

Close the steam outlet valve # 11, Figure 4.11.

Make sure the main power switch is off before plugging the cord into a 240V

outlet, Figure 4.11.

Set the steam generator thermostat to 275° F, Figure 4.10.

10. Recheck steps 1-9 again and thentum on the main power switch, Figure 4.11.

11. Wait for the generator to build up to the required steam pressure; *note that it

will automatically shut ofi‘.

12. Openthemainsteamoutletvalve# 11 andusethesteam, Figure 11.

54

4.4.2 Turning on the temperature and pressure measuring devices

1.

2.

Turn on the measuring equipment power supply, Figure 4.4

Adjust the supply voltage so that the meters are at their calibrated zero point.

4.4.3 Blow down procedures for shutting the equipment of!

1.

Afier the required measurements are taken turn off the power supply to the

measuring equipment.

Shut off the main power supply switch, Figure 11.

. Reset the steam generator thermostat to the ofl‘ position, Figure 4.10.

Close the water supply valves #9 and #10 in Figure 4.9.

Open the drain valve, valve # 8, Figure 4.8.

55

Open the three gauge valves shown

 

 

Valve #3
Valve #1
Valve #2

 

 

Always leave these three open

Figure 4.5

 

56
Check to be sure all of the downstream steam path valves are open

 

 

Figure 4.6

 

57
Make sure bypass valve is closed

Valve # 7
By-Pass valve

 

Figure 4.7

58
Close main drain valve

 

Figure 4.8

59
Open main water supply faucet and steam generator supply valve

 

 

 

Valve # 9
Steam Generator
Main water supply

   

  
 

 

 

Figure 4.9

 

60
As the steam generator fills check the water sight gauge to see when it

reaches the proper level

 

Figure 4.10

 

 

 

Valve # l 1
Steam Outlet Valve
*open before turning
on generator

 

 

 

Main Power Switch
*must be off before
plugging cord

into 240V outlet

 

 

 

 

Figure 4.11

 

Chapter 5 Analysis and Results
5.0 Theoretical Analysis

By using the simple model of a gas flowing through a cylindrical hollow tube
oriented in a cross flow of gas of uniform temperature, a difl‘erential equation for blade
cooling can be derived. As shown in Figure 5.1 below the gas inside the blade is
flowing from top to bottom with an assumed uniform temperature, Tc, in cross section and
changing in temperature as it flows through the blade, It exchanges heat through the wall
of the tube with the gas in cross flow. An elemental section of the tube is also assumed to
have a uniform temperature, Tb, in cross section due to axial symmetry and the highly
conductive thin wall . A summation of heat fluxes into and out of the two differential
elements shown in Figure 5.1 should each equal zero by the first law of thermodynamics,
assuming axial symmetry. For the elemental cross section of the tube there are four
different heat fluxes. Two are convective heat transfers and two are conductive heat

transfers.

62

63

 

 

 
 

' a
me cnew“):

 
   

‘1cmIa"i"'|:""r:l"dx
‘—

a,*u,*(r,-r.,rdx , ac-ugrrb- crdx

 

 

mc*cpc*Tcx+dx

 

\\\\\\\\\\\x

Qx+dx

 

 

 

 

 

 

 

 

 

Figure 5.1. Heat flows using a thin wall tube as a simplified blade model

The two convective heat fluxes, d Q,“ and d Q is can be written:

 

[dQ'n =a.-(Tb-£)-Ub.-°dx| (5.1)

 

 

E9“! =ag-(7'g-7;)-U,,o-dx| (5.2)

 

where a denotes the convective heat transfer coefficient and U denotes the

circumference.

64

The two conductive heat fluxes are Q I and th , where:

 

 

 

 

 

 

 

 

- dT
__ e *_b_
91‘ lb A Ch (5'3)
- - dQ dT dzT
= + *d =— *A*-—”—+—-—”-*d 5.4

 

Itisassumed 7],, =Tbo dueto thehighconductivityofthetubewallandthisis

illustrated in Figure 5.2 where the relative temperatures a typical cross section are

shown.

 

Therefore, for the wall of the tube element, Q, — Qng. + dQ'k — dQ.)lg = 0 . (5.5)

 

 

 

Substituting for each term of (5.5) its equivalent expression, the following differential

 

 

equationcanbewritten:
dsz a rub. a .Ubo

+ c__.(T _Tc)+L__. T "T =0 (5.6)
dx2 hb-A, " hb-A, (" 8)

 

 

 

For the cross sectional element of gas flow inside the tube there are three heat
fluxes, koc , inflow *Ta , and anagram, where "tn isthermssflowrate

and 0,, isthe specific heat capacity ofthe gas(See Figure 5.1).

 

 

 

mcxcpchmd,=—(mcxcpcha-mcxcpcx-dx—axdx) (5.7)

 

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ bladewan000mm,W
. / I
9330‘” 4 /
temperature 11 /
/ l
/ v
T9 1, /
\ / I
\ /
TM Tbi '
I ll GTc
/ ;
/

 

 

 

 

 

Figure 5.2 Typical temperature profile of a cross section of the tube .

Again by the first law of thermodynamics:

 

koc+nicxcpcha+nicxcpcham=0 (5.8)

 

 

 

and again substituting the equivalent expression for each term of (5.8), the following

differential equation can be written:

 

 

_ . . dT
a, -(1;, -7;).U,,,. -dx + mac“ *Tc, - mncpgrc, + mgcpgf'idbc =0 (5.9)

 

 

66

Simplifying:

 

me x cpc at];r
x
ac x Uh, dx (5'10)

 

(Tb—72'):—

 

 

 

This can now be substituted into equation (5.6) with the resulting difl‘erential

equation:

 

CI

d27;_rtte*cpc *dT +ag-Ub.
ah:2 Ab*A,, dx ,ib-A,

 

 

(n—T)=0 GAD

 

 

 

To further simplify this equation, if it is assumed that the change in conductive heat

 

 

 

 

 

 

 

 

 

dZT

transferalongthelengthofthetubeis linear, then dx; iszero. Thus(5.ll)isnow:

{we dT a ~U,,
_ pC * C1 8 0 . _ =

Ab*A,, dx +ib.A,, (Tb T8) 0 (512)
Therefore, equation (5.6) becomes:

ac.Ubt' a8.UbO
'A,.A,,'(Tb-Tc)+,i,,.A,'(73‘72)-0 (5'13)

 

 

 

67

 

 

*T (5.14)

 

 

 

 

Since it was assumed the cross flow of gas to be ofuniform temperature by taking the

 

dT
derivative with respect to x of equation (5.13) g is thus zero and (5.14) can be

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

dx
rewritten:
dT ag‘Ubo d];
c = *
dx (new...) dx (5.15)
Now by substituting (5.15) into (5.12) and rearranging:
*c a *U afl‘ a ~U
Ab*Ab ac* [1' fl Ab Ab g I
dT a *U
”= g fifty *(Tg—n) (5.17)
*(1+ 3 ”°)
m CFC ac#Ubi
(IT (IT dT T d T —T
Since ——g-iszerothen ” = g +d b = (g b) and (5.18)

 

 

dx dx dx dx dx

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

d(T - T)
gdx b +n‘(Tg-'Tb)=0 (5.19)
ag .UbO
where n = *U (5.20)
. * ag b0
mc'cpc (1+"a—c—*Ubl)
. 4(Tg - Tb) .
Rearrangmg, = —n * dx and solvmg:
T8 - Tb
_. :1: -""‘x
E-Q+Ce um
Atx=0, Tb = 720 , and therefore, C = Tbo - Tg (5.22)
_ __ * —n"x
I; — I; + (E0 7;) e (5.23)

 

 

 

Finally substituting (5.20) into (5.12) the coolant temperature, To, is found to be :

 

ag *Ubo) ag *Ubo *
ac :1: Us ac :1: Ubi a (5-24)

 

T =(T +(T,0 —T)*e-""‘ *(1+

 

 

 

69

5.1 Expected Results and Calculation of Heat Transfer

In the previous section a differential equation was developed which theoretically
represented a simplified model of a turbine blade being cooled. The blade was represented
as cylindrical tube being cooled internally by one gas and transferring heat through the
tube wall with another gas. To prove the theoretical model correct, results found by
applying it an actual model should approximate results found by experiments on the same
model. The actual blade model for the experiments that follow is a copper tube with an
inner diameter of 14.5 mm and an outer diameter of 15.9 mm. A steam generator supplies
a steady flow of steam through the copper tube while a steady cross flow of air moves
outside the tube.

If the experimental results compare favorably with the theoretical results, then the
principles of similarity from dimensional analysis can be applied. Similarity principles
will allow the theoretical results to be applied to other fluids with different velocities, and
to scale the geometry of the model to suit different design configurations. Dimensional
analysis reduces the number of parameters in a theoretical expression by using
dimensionless variables. The dimensionless numbers most applicable to this experiment
are the Nusselt number, the Prandtl number, and the Reynolds number.

The Nusselt number is defined as:

 

a xD
Nu= 2 (5.25)

 

 

 

 

70
for flow over a cylinder, where D is the diameter of the cylinder, 6.7 is the average

convection heat transfer coeflicient, and 11 is the thermal conductivity. Thus the
Nusselt number is the ratio of the convective heat flux to the conductive heat flux and

directly proportional to the diameter of the tube.

 

 

The Prandtl number is defined as
c e
Pr: ” ”=3. (5.26)
,1 a

 

 

 

The Prandtl number is a ratio of fluid properties. It relates the relative thickness of the

hydrodynamic and thermal boundary layers. For a Prandtl number of one the momentum

 

 

 

 

 

 

 

 

 

 

 

é’u flu €211
equation ux_0"_x+VX§—y— = Vx(0"y2) and the energy equation
aT 6T 52T . _
uxZ+vx-a-;=ax(ay2) areidentical.
The Reynolds number is defined as
-U-D
Re=£—n—. (5.27)

 

 

 

The Reynolds number gives a measure of the relative magnitudes of the inertia and viscous
forces in the fluid. The Reynolds number determines the character of the flow process.

Re is the Reynolds at which the flow changes fi'om laminar to turbulent. At Re < Re the
low is laminar and at Re > Re the flow becomes turbulent. The larger the Reynolds
number the steeper the velocity gradient at the wall, tlmt means also a larger convective

heat transfer coeflicient.

71
From similarity theory for forced convectional heat transfer processes, if the values for

Nu, Re and Pr stay the same, the processes are physically similar for similar geometries/W

 

This implies for example, that the effectiveness O( Na, Re, Pr, geometry) = 0 (5.28)

 

 

 

for cross flow heat exchangers for constant values of Nu, Re, Pr, and constant geometric
ratios.

Similarity theory yields only the ftmctional relationship of the dimensionless variables of a
process. To actually apply it to the basic equations and determine whether it correctly

predicts the actual behavior of a physical system cannot be done without doing

 

experiments. For example Eu = f(Re,Pr,geometry)] (5.29)
describes that the Nu number is a fimction of Re, Pr, and geometry. However, by
experiment for turbulent fully developed flow in a tube, it has been determined that the

average Nusselt number given by Holeman /10/

014
\

N_u = 0.027Re08Pry3(“i) . (5.30)

 

 

 

 

which describes the actual experimental results of this frmctional relationship which can be
applied to similar physical systems. The temperature difl‘erence between the pipe surface
and pipe center may lead to variable fluid properties. This influence is accounted for in
(5.30) by the relationship between bulk dynamic viscosity, [4, and wall dynamic
viscosity, u...

The average convective heat transfer coefficient for the inside of the tube is calculated

with the definition of the Nusselt number equation, (5.25) and used with equation (5.30)

 

_ N— 2
to yield: a, = —-“I‘)—-& (5.31)

 

 

 

72
For cylinder in a transverse flow the following form for the average Nusselt number is

given by Elsner /7/

 

Pr 0.25
"Iv—u = 021 Re” Fr“8 — . (5.32)
Pr”,

 

 

 

Figure 5.3 and Figure 5.4 illustrate the circumferential variation of the local Nusselt
number for difl‘erent Reynolds numbers for a circular cylinder in cross flow. In the
calculations the average Nusselt number is used. Figure 5.5 shows the distribution of heat
transfer coeficient and adiabatic wall temperature around a typical turbine blade.

The average convective heat transfer coefficient for the outside of the tube is calculated

with the Nusselt number definition given in equation (5.25). This is applied to equation

 

 

(5.32) so that:
0.25
2
a, = D“ x 021x Rem x P613843] (5.33)

 

 

 

For calculating the Reynolds number, the flow velocity of the fluid is needed. It is

determined using the equation of continuity.

 

, 71'
m. = V. '10, 7-03‘ (5.34)

 

 

 

 

V. = —— (5.35)

 

 

 

73

 

 

 

 

 

 

Figure 5.3. Circumferential variation of the Nusselt number at low Reynolds number for a

circular cylinder in a cross flow /9/

 

 

 

 

“ o-mmmm

 

Figure 5.4. Circumferential variation of the Nusselt number at high Reynolds number for a

circular cylinder in a cross flow /9/

 

 

 

5/
\‘}§_

/ \\' / \
/ \\\ __ // \
/ e""""’///I// >24;
. m / /

,4:— — x

/ / l \ \ "30' ~

/ / l 7 \

/ ‘ liar trader enamel-rt / \\
/’\ Adtabatlc In}! amnion \ (OWN-FL“ / \ l
t F) l / 3‘20
‘ . \
l

 

\ /\%5= "“."\ \l / /
"377‘ \ / /

 

 

Figure 5.5. Distribution of heat transfer coefficient and adiabatic wall temperature around

a typical turbine blade /10/

The test section can also be considered as a cross flow heat exchanger. Elsner /7/ gives a

calculation model for this. Figure 5.6 shows a diagram for the cross flow heat exchanger

 

 

wherethefunction
k-A k-A
“Mic—J =f[m.-c..] (5'34)

 

 

 

figured at different mass flows ratios, where E is defined as

 

Tci _ Tea
— (5.35)

G—n1_];i.

 

 

 

The in
The 0

intern

wh:

Ci

75
The index 1 stands for the fluid, which delivers the heat.

The overall heat coefficient for a tube, which can be considered a simple model of a

internally cooled turbine blade, is defined as

11+8T+1

k'Am _aa'Ab AT.Ahn as°Au.

 

 

 

(5.36)

 

 

 

 

 

1
k= (5.37)
a A‘T.Abm as'Abi

 

 

 

The corresponding heat flux can then be calculated using

 

Q = k - A AT," (5.38)

 

 

 

where the averaged steam temperature is determined by

.—T. _ T —T
Mfg“ °‘) ('° °°. (5.39)

In T.-T.]
Too—Too

 

 

 

Both the cross flow heat exchanger method and the cylinder in cross flow method of

calculation yield almost identical results for the resulting steam and blade temperature.

0,6

05

J

0,4

0,3

0,2.

 

 

Figure 5.6

76

0,3 0,4 0,5 0,6 08

Kreuzsrrom (Crossflowl

¢ _'1"’1:m
"’ ti—rz’

 

0,04 0,06 0,’ 0,2 0,3 0.4 050,6“.08 1,0
(:1

Figure 5.6. Characteristic of a cross flow heat exchanger /7/

ten
Fig:
Clfic.
dissip
tempe
ofthe 1
14001.3I

ConSlde]

77
5.3 Comparison of Air and Steam as Coolants

A quick comparison of the specific heat capacities, cp, of steam and air in Figure
(5.7) shows that steam has more value than air as a coolant. Steam has about the double
mespecificheatcapacnyofair.AhigherspecificheMeapacnymemsahigherhem
transfer rate can be achieved. The plot of the heat conduction coefficient for steam to that
of air shows little difference between the two. However, a comparison of the calculated
values of blade cooling effectiveness for a set up similar to that of the test stand, shows a

large difference between both coolants. The classical definition of bhde cooling

 

 

effectiveness is /1 1/
T - T
g b
('9 = T _ T . (5.40)
g c

 

 

 

Figure (5.11) shows how the blade temperature varies compared to a changing mass flow
ratio of coolant to hot gas. The calculations were done for a simple blade where the
temperatme ofthe coolant was 500° K and the gas temperature was 1400° K.

Figure (5.12) is a plot of the cooling effectiveness for both steam and air versus, their
efliciency, A. A is the ratio of energy diverted to blade cooling to the actual heat
dissipated by blade cooling . Again the calculations were rmde with the hot gas
temperature at l400° K and the coolant temperature at 500° K for the simple blade model
of the test stand.

Looking at Figure (5.11) steam performs better than air as a coolant. The difference is

considerable. For example the blade temperature of the steam cooled blade is 80° K below

that of

steam

 

 

 

 

 

 

 

Fl

78
that of the air cooled blade at a coolant to gas mass flow ratio of 0.02. This means a

steam cooled blade could last four times longer than an air cooled bklde.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CommrbonofStsamandAlratLowm .
Specific ”Capacity
2.5
1”
/'I
/
2
1.5
Cp
T ............... t ..... L- .....
1 --------------- 1- - — —
—steam
0.5 - - - at
o
300 400 500 600 7m am 900 1a» 11m
tomperflmepq

 

 

 

Figure 5.7. Specific heat transfer coeflicients of steam and air

79

 

 

0.95

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5

Comparbonofsuamandflratmm .
PrandflNunbsr

 

 

 

e\\

m‘

 

 

 

 

 

—---.-.lr

 

"'---+ ----- p---"'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1M 1100

 

Figure 5.8. Prandtl numbers of steam and air

 

 

0.1

0.09

0.08

0.07

0.x

0.05

0.04

0.03

0.02

0.01

Comparison of Steam and Alt at Low Pronouns
Thoma! Conductivity

 

 

 

 

 

 

 

 

 

 

 

 

steam

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

700
tanner-tun [K]

1100

 

Figure 5.9. Thermal conductivities for steam and air

 

 

 

NJ! . 3
4 5

4 m wE\mv_ mm r

 

5

_ @6083 2:556

80

 

Comparison of Steam and Airat Low Preaaurea .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dynamic Viscosity
5
5.5 c ’
U) 4 v ‘ a " fl ’ .
g a ' ' ‘ ' a
x 3.5 " :‘a 1' [I
In , — "
LU 3 0‘ ' /
‘- 4'
s
2.5 ‘7'
.5 ’0,
§ 2 I ///
i
'5 15 /
o .
(u 1 —ate-n
c " " " II?
>.
'O 0.5
0
300 400 500 600 700 000 900 1000 1100
temperature“)
Figure 5.10. Dymmic viscosities for steam and air
Theoretical Comparison of Steam and Air aa Coolant 1
of a Simple Blade (Gas: 1400K 8r Coolant: 600K)
1400
K
1300 “ ""_“°"“
- - - air
\
52" ~.
H 1200 \‘
a \ ~.
3 \
d-D \ L
g 1100 \ “
E \ ~. _ _.
m \ ~. _
H 1000 "e
m “.
.o \\ ~ - -.
9 ‘ ‘ - .
.0 ‘ - .. .
mo \ \ u _ - v
\\
000
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

 

maaai'lew coolant I mm In H

 

Figure 5.11. Blade temperature ofsteam and air cooled blade

 

 

0,7

06

0.5

O D 0
3 32.2500... 95.000

0.1

Anoth

coolin

81

 

Theoretical Comparison of Steam and Air aa Coolant .
of a Sknple Blade (Gas: 1400K 8r Coolant: 600K)
0.7

/
0.0 //

 

 

 

.°
0-

 

.0
;

 

 

 

cooling Mama [-1
P
0

.°
N

 

 

 

0.1 8'.“
Air

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.12. Cooling effectiveness for a steam and an air cooled blade

Another factor which affects the performance of a blade coolant is the pressure drop in the

cooling passages of the blade caused by fluid friction. This pressure drop is

 

L p
A =x.-.._2
P d 2

 

 

 

 

8.L-1;.Z(s)
den; '1). (5.41)

 

=zl-R 4522-

C

h

 

 

 

wherel isthefi'ictionfactor,Lthelengthofthecoolingpassage,anddthediameterof
the cooling passage. For the theoretical comparison of the pressure drop of steam to air in

the blade, the coolant is considered as an ideal gas. The coolant temperature and pressure

areas

is deg

Fig

bl:

tel

82
are assumed the same for both, and the fiiction factor, it, a constant. Thus pressure drop

isdependentonlyonthegasconstantofthecoolantandthesquareofthemassflow.

40:11; hi ~CtInS't (5.42)

The resulting comparison is illustrated in Figure (5.13). The pressure drop is plotted

 

 

 

 

against the calculated blade temperature, which is dependent on the coolant mass flow.
Thepressuredropofsteamissmallerthanthatofairatthesamebladetemperatm'e. This
meansthatlessmassflowofsteamisneededto reachthesamebladetemperature. In
Figure (5.14) the pressure drop of steam is larger than that ofair for the same coolant
mass-flow. What is important in looking at the results ofFigure (5.13) to Figure (5.14) to
blade cooling is that steam requires less coolant mass flow to reach the same blade

temperature. This is steams big advantage over air as a blade coolant.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

111eoreticalCompariaonof8teamandAiraaCoolant .
otaSimpleBiade(Gaa:1400K8-Cooiart:500i()
25
I
\
\
\
. ate-n
20 .‘ ___ at
\
|
'— I
3315 x
'3' ‘~
9 ‘~
'0 \
10 ‘
2 x
a ‘r
\
a) s‘
95)- 5 ‘x
§~‘ ‘
o W _
000 900 1000 1100 1200 1300 1400
Mum-elk]

 

 

 

Figure 5.13. Pressure dr0p in a steamand an air cooled blade against blade temperature

 
 

C

.mn: no.6 muammmcu

Y3;

83

 

25

5‘. 8

pressure drop [Pa]

0

 

Theoretical Comparison of Steam and Air as Coolant .
of a Simple Blade (Gas: 1400K 8r Coolant: 500K)

 

 

 

 

 

 

 

 

 

 

 

 

0

 

0.005

 

//.
(”u/“J,
.__._J=§MP

 

 

 

 

 

 

 

0.01

0.015 0.02 0.025 0.03 0.035 0.04
mass flow coolant I mace new one [-1

 

Figure 5.14. Pressure drop in a steam and an air cooled blade against mass flow ratio.

Their viscosity’s shown in Figure (5.9) and Figure (5.10) are about the same.

 

5.4

results

theAp

84
5.4 Results of the tests:

The results of the tests are plotted in the following charts. A discussion of the

results follows in Chapter 6. The actual test data results in an Excel format are included in

theAppendix.

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88

Temperature of the Blade, the
Air, and the Steam(degrees K)

275 295 31 5 335 355 375 395
Le—in 1 1 1 4 1

 

Air

 

Blade wi 1.
differing fl 1‘
rate rati - r.

  

Steam

 

 

 

 

 

 

Le-out

 

Blade Cooling Effect

Chart3

89

Temperature of the Blade, the Air, and

 

 

 

 

 

 

 

 

 

 

 

the Steam(degreees K)
275 295 315 335 355 375 395
Te-in 1 i i i i. l
Arr Blade
differi
rate
Te-out

Blade Cooling Effect

Chart4

Chapter 6 Discussion of the Results
and Conclusions

6.0 Discussion of Results

The charts of the results in Cha ter 5 re resent :

 

1. Thechangeinthebladetemperatureoveritslengthasafimctionoftheratio ofthe
mass flow rate of steam to the mass flow rate of air.

2. The effectiveness of the cooling and heating involved in the heat transfer across the
blade surface as a fimction of the ratio of the mass flow rate of steam to the mass flow rate
of air.

3. The blade cooling effect of the difi‘erence in air temperature to steam temperature.

As can be seen in Chart 1 the cooling effect of the air dominates, evident by the
higher change in the blade temperature at lower ratios of steam to air. Then the effect of
the steam begins to become dominant as the temperature change of the blade begins to
decrease with the steadily increasing ratio of steam to air. The actual change in steam
temperature is nearly immeasurable as seen by its near insignificant plot on the chart.

T — T
Chart 2-A and 2-B reflect the effectiveness 6) = M for the leading and trailing
g _ cr‘

90

91
edge of the blade respectively as a function of the ratio of mass flow of steam to mass

flow rate of air. At the entrance of the blade the effectiveness is lower than at the exit
of the blade for both the leading and trailing edge cases. This is reasonable since at the
exit the blade temperature is going to be lower due to the convective heat transfer with the
airalongitslength. Thismeans (7}5 —T,,.) will behigherattheexitandsincetheterm

(Te—12,)isnearlyconstant,thismeanstheratioofthetwoattheexitwillbehigher.

Thebladecooling effect oftheaircanbeseeninCharts3 and4. Inarealturbine blade
situation the positions of the air and steam would be reversed on the chart with the air
temperature being higher than that of the blade, and the steam, as coolant, less than that of
the bLade. The blade cooling effect of the air is evident by the temperature drop of the

blade between entrance and exit of the steam flow for both charts.

6.1 Conclusions

Looking at Chart 3 and 4 it is clear that less steam is needed for the same heat
transferred across the blade, when compared to air. As such steam would definitely
perform better than air as a turbine blade coolant. Also by charts 2-A and 2-B because of
the lower blade temperature at the exit, a higher steam effectiveness can be expected
when the temperature difference of the steam and the blade is higher. Finally looking at
Chart 3 and 4, the large temperature difl‘erence between the air and the blade compared to
the steam and the blade means that a more uniform blade temperature should be possible

when steam is used as a coolant.

92
6.2 Suggestions for further work

In future work on the project I would suggest that a combustion chamber be added
sothat theairtemperature ofthetest standcanberaisedhigherthatthatofthe steam.
This would simulate actual turbine operating conditions. A variety of blade models could
then be tested by varying the mass flow rate of the steam. The mass flow rate of steam
could be varied by putting a valve at the outlet of the steam generator. If higher steam
temperatures were needed a super heater could be added to the steam generator.

To predict the results of fiiture work a finite element model of the test set up would assist

in planning experiments.

LIST OF REFERENCES

/1/

/2/

/3/

/4/

/5/

/6/

7.0 References

Bohn, D.

Zysin, V. A.

Wilson, G. W.

Arts, T.

Van Fossen, Jr.

Moore, M.J., Sieverding,C.H.

"Gasturbinen", Vorlesungsumdruck, Institur fiir
Dampf- und Gasturbinen, RWTH Aachen, 1994

Steam-Gas Plants and Cycles, pp 1-186
Gasenergoizdat, Leningrad

"The Design of High-Efficiency Turbomachinery
and Gas Turbines", The Massachusetts Institute of
Technology, 1993

"Introduction to Heat Transfer Phenomena in
Gas Turbines", Course Note 127, von Karman
Institute for Fluid Dynamics, Rhode Saint Genése

NASA Reference Publication 1038, Technical
Report 78-21 April 1979

"Two Phase Steam Flow in Turbines and
Separators", Hemisphere Publishing Corporation,
Washington, London, 1976

93

/7/

/8/

/9/

/10/

/11/

/12/

Elsner, N.

Schmidt, E.

Kreith, F.

Harman,T. C.

Le Grivés, E.

CengeL Yunus A.
Boles, Michael A.

94

"Grundlagen der Technischen Thermodynamik",
Akamedie-Verlag, Berlin, 1985

"Properties of Water and Steam in S-I Units",
Springer Verlag New York Inc., 1969

"Principles of Heat Transfer", Intext Educational
Publishers, New York, 1973

"Gas Turbine Engineering", Halsted Press, New
York, 1981

“Advanced Topics in Tmbonmchinery Technology”,
Principal Lecture Series No. 2, Concepts ETI, 1986

“Thermodynamics, An Engineering Approach”,
McGraw-Hill, New York, 1989

8.0 Appendix

8.0 Appendix

Table 8.1. Calibration of the transducer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pressure [bar]

 

Pressure Voltage TDl Voltage TD2 Voltage TD3

[Psi] [bar] [111V] [111V] [111V]
0.0 0.000 7.7 7.5 0.0

5.0 0.345 10.3 10.1 51.9
10.0 0.689 12.9 12.7 105.6
15.0 1.034 15.5 15.3 158.4
20.0 1.379 18.1 17.9 211.0
25.0 1.724 20.7 20.5 265.0
30.0 2.068 23.3 23.1 319.0

Calibration Transducer 1
2.5
I

 

 

..a
Q

 

d

 

0.5

 

 

/

 

/

 

 

 

 

v
10

Voltair- [11M

20

25

 

Figure 8.1. Calibration curves for transducer 1

95

 

96

 

 

Calibration Transducer 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.0
or

 

 

 

 

 

g... /
9

3

m

a) 1

93

0.

0.5 f
0 /
5 1O 15 20 25
Value-rum
Figure 8.2. Calibration curves for transducer 2
Calibration Transducer 3
2.5
2 /

'E‘ /

(u 1.5
a /

9 /

3

(D 1

a)

2

1:1

 

 

 

 

 

 

 

 

 

 

50 100 150 200 250

VON-00 [I'M

 

Figure 8.3. Calibration curves for transducer 3

 

 

a; can...

>E>E0000000
3223.8

u. 0 NR 5.0..

9.... 8.3 Mecca
.. cod ”00.0505

.00. .00 H

._.mm.._. 023000 mofim - m<r_ >mmz_IO<_>_OmmD._. Ems.

 

 

98

MSU TURBOMACHINERY LAB — BLADE COOLING TEST

OF TEST;

Figure 8.4b

Test #1-Initial test

mA3/s

 

0.0385 m.
Diem—pipe 0.0762 m.
Patm: 98408 Pa

Tatm: 22.2 ° C
air—in air—out orf b1 02 b4
K K K K K K K Pa Pa Pa

 

 

 

«3 2am...

0 O

u. o méo ”.52.

9+. 58 Ema
.. ood ”maaémfi

.mm ”

._.mm_.r 023000 maxim - m<._ >mmz_IO<S_0mm3._. Dm_>_

 

 

 

100

MSU TURBOMACHINERY LAB - BLADE COOLING TEST
- Test 2

stm-in1
m"3/s K

Figure 8.5b

 

stm-in2

K

stm—out2

K

Diam-pipe
99120 Pa

P’atm:

Tatm:
air—in

K

0.0699 m.
0.0762 m9

w2°C

air-out

K

orf
K

 

k

 

3.. 05mm

>E>Eooooooo
Emnmnzto

"— 0 Wow HEN—w

9... .38 mean.
.. ooh ”85.830

.3 H

._.wm_._. 023000 mojm - m<._ >mm2__.._0<_>_0mm3._. 3m:

 

 

102

MSU TURBOMACHINERY LAB — BLADE COOLING TEST
TYPE OF TEST: Test # 3

0.0254 m.
Diam-pipe 0.0762 m.
2pm Patm: 99120 F’a

Tatm: 192 ° C
Re C Y1 stm—in1 Tstm—out1 stm—in2 stm-out2 air-in orf

mA3/s K K K K K K K

 

Figure 8.6b

 

 

at. ”am...

0 0

n. o Nam HEEL.

9... 3mm Ema
.. ooh ”029.55

v % «mo... H

._.wm_._. 023000 mofim - m5 >mm2_10<_>_0mm3._. 30.2

 

 

104

MSU TURBOMACHINERY LAB - BLADE COOLING TEST

Test # 4
Diam-orf: 0.0445 m.

Diam—pipe 0.0445 m.
Patm: 98747 Pa

10/2/96

2pm

Tatm: 20.1 ° C

stm-in1 stm-out1 stm—inZ stm—outz air—in orf

mA3/S K K K K K K K

 

Figure 8.7b

 

 

a... 2%....

u. o Nam ESP

9+. 3% ES
.. ooh ”099630

m t 30... n

..wmz. 023000 wo<3m .. m<._ >mm2=._0<_20mm3._. Ems.

 

 

 

106

MSU TURBOMACHINERY LAB - BLADE COOLING TEST

OF Test 5

10/2/96 Diam-orf: 0.0508 m.
Diam-pipe 0.0508 m.
2pm Patm: 98747 Pa

3: Tatm: 20.1 ° C

stm—in1 stm—out1 stm—inZ stm—outZ air-in air-out orf b1 b4

mAS/S K K K K K K K K K K K

 

Figure 8.8b

 

 

..3. 25mm

0 0

n. o Nam H..:.mh

9.... 2.8 San.
.. oo.m 0&9Em5

323» H
..mm._. 023000 mofim - m<n_ >mm2_10<_>_0m~”_3._. Ems—

 

 

108

MSU TURBOMACHINERY LAB - BLADE COOLING TEST

Test # 6
10/2/96 Diam—orf: 0.0572 m.
Diam—pipe 0.0572 m.

2pm Patm: 98747 Pa

Tatm: 20.1 ° C

stm-in1 stm—out1 stm—in2 sIm-out2 air—in air—out orf b1 b3 b4

m"3/S K K K K K K K K K K K Pa Pa

 

Figure 8.9b

 

 

3:. new...

0 0 0

~c_-E.m

u. 0 Now “Efih

9.... 2.3 Ema
.. ooh “33.8.30

:28. H
._.mm_._. 023000 mo<3m - m<3 >mm2=.._0<_>_0mm3._. Ems.

 

 

 

110

MSU TURBOMACHINERY LAB — BLADE COOLING TEST
: est 7

10/2/96 Diam—orf: 0.0635 m.
Diam-pipe 0.0635 m.
2pm Patm: 98747 Pa

3: Tatm: 20.1 o C

stm—in1 stm-out1 sIm-inZ air-In orf

m"3/s K K K K K K

 

Figure 8.1%

 

 

2 ..w 2&3

0 0

n. a on ”ch—wk

or. 3.8 Ema
.. oo.m bufiémfi

3.3» 2
ohm... 023000 mo<3m - m<3 >mm_2_I0<_>_0mmD._. Ems.

 

 

MSU TURBOMACHINERY LAB - BLADE COOLING TEST

est 8
10/30/96

2pm

3:
stm—In1

m"3/s K

Figure 8.1 lb

stm—outI

K

stm-in2

K

stm-out2

K

Diam-orf: 0.0318 m.
Diem—pipe 0.0318 m.
Patm: 97359 Pa

Tatm: 21.1 ° C
air-in

K K K

 

 

 

 

as... 05w...

0 0

n. c on HE.m._.

or. 2.8 Ema.
.. oo.m nanEmE

m u «no... N

._.wm_._. 023000 m0<3m - m<._ >2m2=._0<_>_0mm_3._. 302

 

 

 

 

114

MSU TURBOMACHINERY LAB - BLADE COOLING TEST

TYPE OF TEST: Test # 9
'10/30/96 Diam-orf: 0.0381 m.

Diam-pipe 0.0381 m.
Patm: 97359 Pa

Tatm: 21.1 ° C

Y] Vaclual stm-in1 stm-outt sIm—in2 stm-out2 air-In air-out orf b1 03 b4

mA3/s K K K K K K K K K K K Pa Pa

 

Figure 8.12b

 

 

IGQN STnTE UNIV.

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