Acknowledgements
I would like to thank the members of the group working with aerodynamics and cooling of blades and vanes, GRCTA at Siemens in Finspång for always taking time to answer my questions. Also, special thanks to my supervisors at Siemens Mats Annerfeldt and Yuri Mamon and to my supervisors at LiTH Dan Loyd and Johan Svensson for your support. In the Siemens office in Lincoln, I would like to thank John Maltson, Anthony Davis and Andrew Down for helping me with the Multipass program code. I would also like to thank Mats Kinell for helping me with the Q3D program code and Xiufang Gao and Daniel Lörstad for your help with correlations
vanes and blades 1 and 2 on different Siemens Gas Turbines. The cooling methods increase the heat transfer in the cooling channels by increasing the heat transfer coefficient and/or increasing the heat transfer surface area. The penalty paid for the increased heat transfer is higher pressure losses.
Three cooling methods, called rib turbulated cooling, matrix cooling and impingement cooling were investigated. Rib turbulated cooling and impingement cooling are typically used in the leading edge or mid region of the airfoil and matrix cooling is mostly applied in the trailing edge region.
Literature studies for each cooling method, covering both open literature and internal reports, were carried out in order to find correlations developed from tests. The correlations were compared and analyzed with focus on suitability for use in turbine conditions. The analysis resulted in recommendations about what correlations to use for each cooling method.
For rib turbulated cooling in square or rectangular ducts, four correlations developed by Han and his co-workers [3.5], [3.8], [3.9] and [3.6] are recommended, each valid for different channel and rib geometries. For U-shaped channels, correlations of Nagoga [3.4] are recommended.
Matrix cooling is relatively unknown in west, but has been used for many years in the former Soviet Union. Therefore available information in open literature is limited. Only one source of correlations was found. The correlations were developed by Nagoga [4.2] and are valid for closed matrixes. Siemens Gas Turbines are cooled with open matrixes, why further work with developing correlations is needed.
For impingement cooling on a flat target plate, a correlation of Florschuetz et al. [5.7] is recommended for inline impingement arrays. For staggered arrays, both the
correlations of Florschuetz et al. [5.7] and Höglund [5.8] are suitable. The correlations for impingement on curved target plate gave very different results. The correlation of Nagoga is recommended, but it is also advised to consult the other correlations when calculating heat transfer for a specific case.
Another part of the work has been to investigate the codes of two heat transfer programs named Q3D and Multipass, used in the Siemens offices in Finspång and Lincoln, respectively. Certain changes in the code are recommended.
method. Therefore, one parameter sometimes has multiple meanings. For those cases, the cooling method it is valid for is written after the explanation of the parameter. General
a = channel cross-section area [m2]
aA = channel flow cross-section area at matrix side bound [m2]
A = area [m2]
Af = open area ratio, i.e. ratio of jet hole area to opposing heat transfer surface area [-] Ai = index of alloy heat resistance, see equation (4.11), =2.6⋅106
i
A for ally of interest here [Pa]
Ar = coefficient in Q3D for Nu calculation on ribbed side wall [-] Arow = area of all holes in a spanwise impingement row [m2] As = coefficient in Q3D for Nu calculation on smooth side wall [-] b = width of a 2D slot with equivalent area of a single row of impingement [m]
C = friction enhancement factor [-]
Cd = discharge coefficient [-]
Cd,s = discharge coefficient for a thin orifice [-]
Cp = specific heat at constant pressure [J/(KgK)]
Cv = specific heat at constant volyme [J/(KgK)]
cbs = vector in function Sfun in the Q3D program code [-]
cfs = vector in function Sfun in the Q3D program code [-]
d = hydraulic diameter of channel (matrix cooling) [m]
d = hole diameter (impingement cooling) [m]
D = effect of centrifugal force on flow in matrix side bound [-]
Dh = hydraulic diameter in ribbed channel [m]
Dp = diameter of curved target plate [m]
e = rib height [-]
e = rib height [m]
+
e = roughness Reynolds number [-]
2 r
f = average friction factor for flow in duct with ribs on 2
opposite sides [-]
F = total area increase for SR- and SSR- schemes [-]
f = friction factor [-]
C
F = mass exchange effect of opposite sub channels through the inter-ribs windows,
C
F =z [-]
CD
F = effect of flow contraction-diffusion in matrix side bound [-]
ρ
F = heat transfer area of ribs themselves [-]
F1 = total leading edge air outlet area [m2]
F4 = total trailing edge air outlet area [m2]
Gc = channel crossflow mass velocity based on channel cross section area [kg/(m2s)]
Gf = summary of cooling air mass flow [kg/(m2s)]
Gg = mass flow after the compressor [kg/(m2s)]
Gj = jet mass velocity based on jet hole area [kg/(m2s)]
j
G = average jet mass velocity [kg/(m2s)]
) (e+
G = heat transfer roughness function, non-dimensional temperature at rib tip [-]
h = rib height [m]
H = channel height [m]
Ic = cross flow interference paramterer [-]
k = width of rib top [m]
K = heat transfer enhancement factor [-]
KA = heat transfer enhancement due to increased heat transfer surface area [-] ∗
K = heat transfer enhancement factor, including effect of increased heat transfer surface area [-]
l = length of matrix channel (matrix cooling) [m]
l = length of control section (rib turbulated cooling) [m]
l = lenght of target surface arc on curved target plate (impingement cooling) [m]
L = length of matrix (matrix cooling) [m]
L = channel length (rib turbulated cooling) [m]
L = length of impingement hole (impingement cooling) [m]
Lc = characteristic length according to Table 2.1 [m]
Les = lenght of equivalent slot [m]
LE = Leading Edge
m = distance between ribs, m = t-k (matrix cooling) [m]
m = distance from stagnation line (impingement cooling) [m]
M* = cross flow-to-jet flow mass velocity ratio,
j c m
m& & [-] n = index of alloy heat resistance in equation (4.11), n = 6060 for alloy of interest here [-]
nc = number of streamwise rows in an impingement array [-]
Np = number of holes in a spanwise impinement row [-]
nr = Reynolds number exponent in Q3D Nu calculation for ribbed side wall [-] ns = Reynolds number exponent in Q3D Nu calculation for smooth side wall [-]
Nu = Nusselt number [-]
s
Nu = average Nu over the full length of a smooth duct [-]
Nu = averaged Nu over an impingement array [-]
Nu1 = Nu for the first row, without cross flow [-]
p = pressure [N/m2]
p0 = plenum pressure (impingement cooling) [N/m2]
p2 = channel pressure (impingement cooling) [N/m2]
P = rib pitch [m]
PS = Pressure Side
Q = heat transfer [W]
R = radius of U-shaped channel (rib turbulated cooling) [m]
R = radius of curved target plate (impingement cooling) [m]
r = specific gas constant, r = 283.9 [kJ/(kgK)]
R.A.M = Reduced Area Method
Re = Reynolds number [-]
) (e+
R = heat transfer roughness function, non-dimensional velocity at rib tip [-]
s = width of rib base [m]
S = perimeter of blade or vane cross-section (rib turbulated cooling) [m] S = area of blade cross section with intensifiers of the cooling method (S<S0) (matrix cooling) [m2] S = with of equivalent slot according to Nagoga’s definition (impingement cooling)
S* = area of through flow section in matrix [m2]
S0 = area of shell cross section of initial smooth channel without intensifiers [m2]
SS = Suction Side
SSR = Segmented Rib cooling scheme SR = Surrounding Rib cooling scheme
ST = rib top area [m2]
St = Stanton number [-]
t = rib pitch [m]
T = temperature [K]
Tdiff = temperature difference between the core flow and in the flow near the wall [K] ∗
f
T = cooling air temperature in the sub channels [K]
∗ G T = stagnation temperature [K] w T = metal temperature [K] T ∆ = temperature difference [K] w T
∆ = temperature change in the blade wall in control section [K]
0 , w
T = initial temperature in the blade wall in a smooth channel [K]
TE = Trailing Edge
u = mean axial velocity of fluid [m/s]
) ( + + e Ue = R(e+) [-] v = velocity [m/s] v = mean velocity [m/s]
w = cooling air velocity in channel (matrix cooling) [m/s]
w = rib width (rib turbulated cooling) [m]
x
w∗, = maximum value of w [m/s]
W = channel width (rib turbulated cooling) [m]
W/H = aspect ratio [-]
Wr = ribbed wall width at a cross-section [m]
Ws = smooth wall width at a cross-section [m]
x = local distance measured from channel inlet [m]
x = for U-shaped channel: distance from duct inlet to the control section (rib turbulated cooling) [m]
x = distance from stagnation line (impingement cooling) [m]
x = x/d [-]
xn = streamwise hole spacing [m]
xbs = vector in function Sfun [-]
xfs = vector in function Sfun [-]
yn = spanwise hole spacing [m]
z = number of channels in matrix (matrix cooling) [-]
z = jet plate-to-impingment plate spacing (impingement cooling) [m]
za = streamwise location from impingement line [m]
Z = 2W/(W+H) [-] Greek Symbols
α = heat transfer coefficient [W/(m2K)]
α = rib angle (rib turbulated cooling) [rad]
β = angle of longitudinal rib [rad]
δ = distance between matrix top and bottom [m]
ε = surface roughness
∆ = matrix end clearance, see Figure 4.2 [m]
φ = rib flank angle [-]
Φ = rotation parameter [-]
ϕ = angle of flow rotation [rad]
T
ϕ = ability to carry load of section ST [-]
η = rib efficiency [-]
κ
= relative depth of matrix channel, channel width-to-height ratio [-]κ
= specific heat ratio, κ =Cp Cv [-]λ = thermal conductivity of fluid [W/(mK)]
µ = dynamic viscosity of fluid [kg/(ms)]
ν = kinematic viscosity of fluid [m2/s]
Π = portion of the duct perimeter covered by the rib system,
s
F F =
Π [-]
Θ = cooling effectiveness, relative cooling depth Θ=
(
∗−) (
∗− ∗)
f G w G T T T T [-]ρ
= density [kg/m3]σ
= effect of tension stresses of cooling method [-]τε = blade life with cooling method used [cycles]
τ = effect on life on turbine blade or vane [-]
m
ξ = hydraulic resistance in the spatial turns at matrix side bound [-]
Ψ = streamfunction [-]
Ψ = hydrodynamic energy effectiveness [-]
∗
air = cooling air
AV = average
b = bulk
b = rib base (matrix cooling)
rib = total rib heat transfer surface
c = corrected
c = cross flow (impingement cooling)
conv = convective
d = jet hole diameter
e = reduced area method
f = film (fluid)
j = jet flow
l = channel length
n = normal distance
new = value calculated with one of the correlations from the literature study original = value used in Q3D today
r = ribbed side in channel with 1, 2, 3 or 4 ribbed walls rc = circular channel
r4 = channel with four ribbed sides
s = smooth channel
s4 = channel with four smooth sides
ST = line along concave matrix side wall w = wall
x = local value
x = local distance in channel from matrix side wall (matrix cooling)
x- = axial component
0 = smooth duct
0 = jet discharge condition (impingement cooling)
∗ = value near the wall
Table of Contents
1 INTRODUCTION...1 1.1 BACKGROUND...1 1.2 PROBLEM DESCRIPTION...2 1.3 OBJECTIVE...2 1.4 LIMITATIONS...2 1.5 METHOD...2 1.5.1 Method Criticism ...31.6 DISPOSITION AND READING INSTRUCTIONS...3
2 THEORY...5
2.1 FLOW AND HEAT TRANSFER BASICS...5
2.1.1 Heat Transfer ...5
2.1.2 Friction...5
2.1.3 Flow...6
2.2 GAS TURBINE VANES AND BLADES...8
2.3 REFERENCES THEORY...10
3 RIB TURBULATED COOLING ...11
3.1 THEORY...11
3.2 CORRELATIONS FROM ARTICLES...12
3.2.1 Results ...12 3.2.2 Analysis ...12 3.2.3 Conclusions...12 3.3 CORRELATIONS IN Q3D ...12 3.3.1 Results ...12 3.3.2 Analysis ...12 3.3.3 Conclusions...12 3.4 CORRELATIONS IN MULTIPASS...12 3.4.1 Results ...12 3.4.2 Analysis ...12 3.4.3 Conclusions...12
3.5 REFERENCES RIB TURBULATED COOLING...12
4 MATRIX COOLING...12
4.1 THEORY...12
4.1.1 What is Matrix Cooling? ...12
4.1.2 Fin Effect of Ribs ...12
4.1.3 Summary of Literature Study...12
4.2 CORRELATIONS FROM LITERATURE...12
4.2.1 Results ...12 4.2.2 Analysis ...12 4.2.3 Conclusions...12 4.3 RIB EFFECTIVENESS IN Q3D ...12 4.3.1 Results ...12 4.3.2 Analysis ...12 4.3.3 Conclusions...12
4.4 REFERENCES MATRIX COOLING...12
5 IMPINGEMENT COOLING ...12
5.1 THEORY...12
5.1.1 What is Impingement Cooling? ...12
5.1.2 Summary of Literature Survey...12
5.2 FLAT TARGET PLATE...12
5.2.1 Results ...12
5.2.2 Analysis ...12
5.3.1 Results ...12
5.3.2 Analysis ...12
5.3.3 Conclusions...12
5.4 REFERENCES IMPINGEMENT COOLING...12
6 CONCLUSIONS...12
6.1 RIB TURBULATED COOLING...12
6.2 MATRIX COOLING...12
6.3 IMPINGEMENT COOLING...12
7 FUTURE WORK ...12
APPENDIX 1 - RIB TURBULATED COOLING ...12
APPENDIX A–CORRELATIONS...12
APPENDIX B–CORRELATIONS FOR U-SHAPED CHANNELS...12
APPENDIX C–RESULTS FOR CASE A ...12
APPENDIX D–EFFECT OF RIB ANGLE...12
APPENDIX E–EFFECT OF PITCH-TO-RIB HEIGHT...12
APPENDIX F–EFFECT OF ASPECT RATIO...12
APPENDIX G–EFFECT OF RIB HEIGHT...12
APPENDIX H–Q3DCORRELATIONS...12
APPENDIX I–MULTIPASS RESULTS...12
APPENDIX J–INTERESTING ARTICLES...12
APPENDIX 2 - MATRIX COOLING...12
APPENDIX A–ZINC TEST...12
APPENDIX B–CORRELATIONS AND RANGES OF [4.2] ...12
APPENDIX C–CORRELATIONS AND RANGES OF [4.5] ...12
APPENDIX D–RESULTS FOR A TYPICAL TURBINE BLADE...12
APPENDIX E–INTERESTING ARTICLES...12
APPENDIX 3 – IMPINGEMENT COOLING...12
APPENDIX A–CORRELATIONS AND RANGES...12
APPENDIX B–FLAT TARGET PLATE,CASE B...12
APPENDIX C–FLAT TARGET PLATE,COMPONENTS...12
APPENDIX D–FLAT TARGET PLATE,RANDOM TESTS...12
APPENDIX E–FLAT TARGET PLATE,EFFECT OF PARAMETERS...12
APPENDIX F–ANALYSIS OF CORRELATIONS...12
APPENDIX G–CURVED TARGET PLATE,COMPONENTS...12
APPENDIX H–CURVED TARGET PLATE,RANDOM TESTS...12
APPENDIX I–CURVED TARGET PLATE,EFFECT OF PARAMETERS...12
Table of Figures
Figure 2.1 Boundary Layer [2.3]. ______________________________________________________6 Figure 2.2 Velocity Profiles in Pipe Flow [2.1]. ___________________________________________7 Figure 2.3 Schematics of a Gas Turbine [[2.6]. ___________________________________________8 Figure 2.4 Schematic Drawing of SGT -800 [2.7]. _________________________________________8 Figure 2.5 Turbine Blade (Right), and Turbine Vane (Left ) [2.8]._____________________________9 Figure 2.6 Typical Cooling Concept [2.9] _______________________________________________9 Figure 3.1 A Ribbed Channel. ________________________________________________________11 Figure 3.2 Flow around Ribs [3.1]. ___________________________________________________11 Figure 3.3 Comparison of K and C. Ribbed Duct is Number 3 [3.3].__________________________12 Figure 3.4 Geometry of SR-Scheme, Front View (Left) and Top View (Right).___________________12 Figure 3.5 Geometry of SSR-Scheme, Front View (Left) and Top View (Right).__________________12 Figure 3.6 Secondary Flow induced by Angled Ribs[3.1]. __________________________________12 Figure 3.7 Flow Patterns for Different Rib Spacings [3.13]. ________________________________12 Figure 3.8 Triangular Ducts Investigated by Metzger & Vedula [3.1]. ________________________12 Figure 3.9 Triangular Ducts Investigated by Zhang et al [3.1]. ______________________________12 Figure 3.10 Ranges for Correlations and Channels in SGT -700 and SGT -800._________________12 Figure 3.11 Nu on Ribbed Side Wall for Case A. _________________________________________12 Figure 3.12 Friction Factor on Ribbed Side Wall for Case A. _______________________________12 Figure 3.13 Nu on Smooth Side Wall in Ribbed Duct for Case A. ____________________________12 Figure 3.14 K on Smooth Side Wall in Ribbed Duct for Case A. _____________________________12 Figure 3.15 Results for SR- and SSR-Scheme Calculations. _________________________________12 Figure 3.16 Cross-Section 4, Vane 2, SGT -700. _________________________________________12 Figure 3.17 Temperature in Vane 2, SGT -700. __________________________________________12 Figure 3.18 Temperature Difference in Vane 2, SGT -700. _________________________________12 Figure 3.19 Q3D Interface for Ribbed Channels. _________________________________________12 Figure 3.21 Original Interface (Left) and Corrected Interface (Right). ________________________12 Figure 4.1 Example of a Matrix Geometry [4.1]__________________________________________12 Figure 4.2 Open Matrix. ____________________________________________________________12 Figure 4.3 Geometry of Longitudinal Rib. ______________________________________________12 Figure 4.4 Geometry in Matrix Side Bounds [4.2].________________________________________12 Figure 4.5 Line ST on Matrix Shell inner Concave Surface._________________________________12 Figure 4.6 Comparsion of Cooling Depht [4.2].__________________________________________12 Figure 4.7 Three Matrixes Investigated by Jurchenko and Malkov [4.3]. ______________________12 Figure 4.8 Nusselt Number Enhancement for the Tests with End Clearances [4.3]. ______________12 Figure 4.9 Height and Chord of an Airfoil.______________________________________________12 Figure 4.10 Alfa as a Function of Red in Initial Section, Red = 15 000. ________________________12
Figure 4.11 Alfa as a Function of x/d in Inital Section, Red = 15 000. _________________________12
Figure 4.12 Alfa as a Function of x/d for Intial and Basic Sections, Re= 11000._________________12 Figure 4.13 Rib effectiveness interface in Q3D. __________________________________________12 Figure 4.14 Q3D Rib Geometry. ______________________________________________________12 Figure 5.1 Impingement Cooling Setup. ________________________________________________12 Figure 5.2 Curved Target Plate[5.1]. __________________________________________________12 Figure 5.3 Impingement Cooling in Turbine Vane [5.2]. ___________________________________12 Figure 5.4 Impinging Jet (Left, [5.3]) and Free Jet (Rigth) [5.4]. ____________________________12 Figure 5.5 Re and Gc/Gj as a Function of Row Number for xn/d=yn/d =3, z/d=2.75 and Red=29900 and
57800 [5.14]._____________________________________________________________________12 Figure 5.6 Alfa for Case C. __________________________________________________________12 Figure 5.7 Q3D Comparison for Case C. _______________________________________________12
1 Introduction
In this opening chapter, the background, problem description and objective of the work is presented, together with an explanation of the methods used. The limitations of the work and the disposition of the report are also offered.
1.1 Background
The efficiency and power output of a gas turbine increases with higher turbine inlet gas temperature. Modern gas turbine vanes and blades are exposed to gas with temperatures which far exceeds the melting point of the component material. Thus, the blades and vanes have to be cooled in order to lower the temperature. When cooling the component it is important to know the correct boundary conditions, to avoid creating too large temperature gradients. Large temperature gradients cause thermal stresses and significantly decrease the component life.
Both internal and external cooling is used in turbine blades and vanes. The cooling air is extracted from the compressor. The cooling affects the gas turbine in two ways. First, less mass flow is available for combustion in the combustion chamber. Second, the trailing edge thickness has to be increased, which creates a larger wake behind the trailing edge which affects the aerodynamics negatively.
The extraction of air decreases the efficiency of the turbine, since less air is available for power generation. Maximum cooling with minimum cooling air is therefore desired.
This work concerns internal cooling of turbine vanes and blades 1 and 2 on Siemens Gas Turbines 700 and 800, shortly called SGT -700 and SGT -800. These components are situated next to the combustor chamber, and are therefore exposed to the highest temperatures. The report is primarily addressed to gas turbine cooling engineers. Blades and vanes are cooled by internal channels, through which the cooling air flows in different schemes and configurations. The cooling air decreases the channel wall temperature by convective cooling. A number of cooling methods are applied to different part of the vane or blade. To make the cooling systems more efficient and spend a minimum of air, the cooling systems nowadays usually include features that increase the heat transfer coefficient and/or increasing the heat transfer surface area. The heat transfer coefficient is increased by enhancement of the flow turbulence and by breaking the flow boundary layer. The penalty paid for the increased heat transfer is higher pressure loss.
Many methods exist in theory, but only a handful are widely used in practice. Three cooling methods are investigated here. They are called rib turbulated cooling, matrix cooling and impingement cooling. The flow of these cooling methods is complicated. Heat transfer coefficients and pressure losses can be calculated by Computational Fluid Dynamics programs, or CFD, but modeling is very time consuming. Since it is often necessary to investigate many different cases, it is convenient to use semi empirical correlations based on experiments.
Introduction
2
To evaluate how effective these cooling methods are, the heat transfer and friction of the cooling methods are compared to a corresponding smooth channel. The
augmentation of heat transfer and friction are expressed by the heat transfer enhancement factor and the friction enhancement factor. These factors are used in heat transfer programs for flow and temperature calculations of gas turbine components.
1.2 Problem Description
The enhancement factors are calculated from correlations based on tests or approximated from experiments. A large number of correlations exist in open literature, and it is not obvious which ones are most suitable for different flow schemes and geometries. There is a need to gather information about correlations and to evaluate them, in order to find out which correlations to use for different cases.
1.3 Objective
The objective of this work is to create a first part of a “Heat Transfer Handbook” for internal cooling of gas turbine vanes and blades. This part of the “Heat Transfer Handbook” will contain recommendations for how to calculate the heat transfer- and friction enhancement factors for rib turbulated cooling, matrix cooling and
impingement cooling. A sub objective is to investigate the code of two heat transfer programs used at Siemens, in order to examine how well the code agrees with open literature correlations.
1.4 Limitations
The effect of rotation is not considered. Only articles with correlations based on tests are considered, so for example articles about CFD analysis are not in the scope of this work.
Concerning ribbed channels, correlations for ribs with 30° to 90° angles to the air flow velocity vector are investigated. Only continuous ribs with inline pattern are considered. Investigated ducts have rectangular, U-shaped or square cross-section. The limitations of matrix cooling have been that there are limited sources of information and that the work has a time limit.
For impingement cooling, the average heat transfer of impingement of multiple jets on a concave or flat surface is investigated. The target plate is solid without roughness elements, film cooling holes or other irregularities. The jets have circular cross-section and impinge perpendicular to the jet target. Both single rows of jets and staggered or inline array patterns are investigated.
1.5 Method
One cooling method was investigated at the time, first rib turbulated cooling, second matrix cooling and third impingement cooling. Literature studies were performed for each area, which covered both open literature and in-house reports. The information from the literature studies were summarized for each cooling method. Much
information was also gathered by personal communication with cooling engineers in the Turbine Aerodynamic and Cooling department at Siemens, GRCTA. Articles and
had been performed, correlation ranges and the applicability to turbine conditions. For each cooling method, the correlations were compared and analyzed. The agreement between the correlations was also investigated, since if independent investigators have come to the same conclusion the correlations are more likely to be accurate.
Conclusions about the correlations were drawn based on information in the sources of the correlations and from analyzing the results of the comparisons.
Parallel to the investigation of correlations in literature, the codes of two in-house programs used at Siemens were investigated for each cooling method. In Finspång, a heat transfer program called Q3D is used for heat transfer calculations. In the Siemens office in Lincoln, a heat transfer program called Multipass is used. Q3D was studied for all three cooling methods. Multipass cannot be used for heat transfer for matrix and impingement cooling, and thus was only studied for rib turbulated cooling. The code was checked against the correlations it was based upon.
1.5.1 Method Criticism
The recommendations of correlations are partly based on the results of a limited number of flow cases and geometries that are relevant for turbine conditions. It is possible that the correlations behave somewhat different for other test cases. It has not been doable to test all cases possible for all correlations.
Parts of the Q3D code consist of numerical approximations of correlations, why it is hard to analyze. This can cause misinterpretations.
The Multipass program itself was not available for use, but the subroutines were investigated separately from the program. That can cause mistakes in the code
interpretations. However, the results were checked and accepted by the Lincoln office.
1.6 Disposition and Reading Instructions
All information about each cooling method is gathered in one place, to facilitate use of the report for cooling design. Chapter 1 gives an introduction to the work and presents background, problem description, objective, limitations and the disposition of the report. Chapter 2 shortly presents basic flow and heat transfer theory and also the geometry and cooling fundamentals of turbine blades and vanes. The next three chapters summarize the work on rib turbulated cooling, matrix cooling and impingement cooling, in that order. Each chapter contains basic theory about the cooling method, a summary of the literature study, results, analysis and discussion and finally conclusions. Both the work about correlations and the program codes are presented in each cooling method chapter. References for the cooling methods are also included in each separate chapter. Next, Chapter 6 summarizes the conclusions drawn for all cooling methods. Chapter 7 presents future work.
2 Theory
This chapter presents basic flow and heat transfer relationships. A brief introduction to gas turbines and blade cooling is also offered.
2.1 Flow and Heat Transfer Basics
Definitions of flow, friction and heat transfer parameters and terms used are shortly presented.
2.1.1 Heat Transfer
Much of the heat transfer in blades and vanes internal cooling systems takes place by convective cooling, where heat is transferred from the hot wall to the cooling air. The heat transfer coefficient - α is defined by equation (2.1) [2.1].
(
w air)
conv A T T
Q =α⋅ ⋅ − (2.1)
To generalize heat transfer correlations, it is common to use non-dimensional parameters. The heat transfer coefficient is often made non-dimensional by the Nusselt number, defined in equation (2.2).
λ α Lc
Nu= ⋅ (2.2)
The characteristic length Lc varies for different geometries and some examples are given in Table 2.1 [2.2].
Table 2.1 Examples of Characteristic Lengths.
Flow Case Lc =
flat plate, local value x flat plate with length L, the hole plate L
cylindrical pipe d
non-cylindrical pipe Dh
Another parameter that describes convective heat transfer is the Stanton number, see equation (2.3). Pr Re⋅ = Nu St (2.3)
2.1.2 Friction
The fanning friction factor is defined from the pressure loss according to equation (2.4). 2 4 2 v D L f p h ⋅ ⋅ ⋅ = ∆ ρ (2.4)
The Darcy friction factor is defined according to equation (2.5).
2 2 v D L f p h D ⋅ ⋅ ⋅ = ∆ ρ (2.5)
Theory
6
The relationship between the fanning and the Darcy friction factor is displayed in equation (2.6). 4 D f f = (2.6)
2.1.3 Flow
Flow can be turbulent, laminar or in the transitional region between laminar and turbulent. Laminar flow occurs for non-disturbed flow with relatively low velocities and is characterised by even velocities and orderly motions. The opposite, turbulent flow, occurs at higher velocities and is characterised by velocity fluctuations and disordered motions. The Reynolds number describes the flow regime, see equation (2.7). For example, flow in a pipe is laminar for Re < 2300 and turbulent for Re > 4000 approximately.
The Reynolds number is defined as the ratio of the inertia forces to the viscous forces in the fluid. The inertia forces depend on the flow kinetic energy and are a function of the fluid density and the square of flow velocity. The viscous forces depend on the fluid viscosity and the flow velocity. The characteristic length is the same as for the Nusselt number, see Table 2.1.
µ ρ⋅v⋅Lc
=
Re (2.7)
Flow in a pipe or over a flat plate can be divided into two regions. First the boundary layer region, where the friction from the surface below affects the velocity profile. Second, the inviscid flow region, where the friction effect is negligible, see Figure 2.1.
Figure 2.1 Boundary Layer [2.3].
In a pipe, where flow enters with uniform velocity, the boundary layer will grow thicker and thicker further from the pipe entrance and thus, the inviscid region will decrease. After a certain length from the inlet, the hydrodynamic entry length, the velocity profile is uniform and the flow is said to be hydrodynamically developed, see Figure 2.2 .
Figure 2.2 Velocity Profiles in Pipe Flow [2.1].
If also the temperature profile is constant, the flow is called fully developed. If neither cooling nor heating occurs, hydrodynamically developed flow is equivalent of fully developed flow. [2.1]
The Prandtl number describes the thickness of the boundary layer, see equation (2.8).
(
⋅Cp)
= ρ λ ν Pr (2.8)The definition of mass flow is important for correlations. Mass flow is defined in equation (2.9).
v A
m& =
ρ
⋅ ⋅ (2.9)A discharge coefficient is often used for mass flow definitions in correlations. It is defined in equation (2.10) [2.4]. ideal real d m m C & & = (2.10)
Mass velocity – G is defined in equation (2.11) [2.5].
A m G= & (2.11) Hydrodynamically developed region Hydrodynamic entry region x
Theory
8
2.2 Gas Turbine Vanes and Blades
Gas turbines consist of three main parts; the compressor, the combustor and the turbine see numbers (1), (2) respectively (3) in Figure 2.3.
Figure 2.3 Schematics of a Gas Turbine [2.6].
The compressor increases the pressure of the inlet air before the air enters the combustion chamber. In the combustor, air is mixed with fuel and the gas mixture combusts at high temperatures. The temperature increase makes the gas expand. In the turbine, the gas first reaches vane 1, in which the expanding gas is directed towards blade 1. In blade 1, the gas stream is deflected, which causes a torque on the shaft. The torque brings the shaft to rotate, which is the useful movement of the engine. The rotational movement can then be used for various purposes, such as working oil and gas pumps or, as in Figure 2.3 operating a generator (4) that produces electricity which is transformed to high tension by a transformer (5). A picture of SGT -800 is seen in Figure 2.4.
Figure 2.4 Schematic Drawing of SGT -800 [2.7].
Figure 2.6 shows the nomenclature for a blade or vane. The front part is called the leading edge and the back part the trailing edge. Low pressure and high pressure sides are called suction side and pressure side, respectively.
Figure 2.5 Turbine Blade (Right), and Turbine Vane (Left ) [2.8].
Figure 2.6 describes a typical cooling concept of a turbine blade.
Figure 2.6 Typical Cooling Concept [2.9]
Impingement cooling is often applied at the leading edge. In the mid chord region, rib turbulated cooling is common and in the trailing edge, pin fin cooling or matrix cooling is used. Platforms on vanes are often cooled by impingement. Exampes of a blade and a vane are displayed in Figure 2.5.
Theory
10
2.3 References Theory
[2.1] Çengel, Y. A. and Turner, R. H. (2001). Fundamentals of Thermal-Fluid Sciences, McGraw-Hill Companies, New York (ISBN 0-07-118152-0) [2.2] Storck, K., Karlsson, M., Andersson, I., Loyd, D. Formelsamling i termo- och
fluiddynamik,(2001), Institutionen för Konstruktion och Produktion, Linköpings Tekniska Högskola
[2.3] Appelqvist, B. and Loyd, D. Grundläggande teknisk strömningslära, (1979), Institutionen för Konstruktion och Produktion, Linköpings Tekniska Högskola [2.4 ] Höglund, H. Experimental Investigation of Impingement Cooling Under a
Staggered Array of Circular Jets, Thesis Work at the Department of Energy Tehnology Royal Institute of Technologi, KTH (1999)
[2.5] Holman, J. P. (2002). Heat Transfer Ninth Edition, McGraw-Hill Companies, New York (ISBN 0-07-112230-3)
[2.6] Vattenfall (2005).
http://www.vattenfall.se/om_vattenfall/energikunskap/gas/gasturbin.asp (2005-12-14)
[2.7] Siemens Industial Turbomachinery, Finspång
[2.8] Vontobel (2005). http://people.web.psi.ch/vontobel/images/turb8_tn.jpg (2005- 12-13)
[2.9] Han, J.C., Dutta, S., & Ekkad S.V. (2000). Gas Turbine Heat Transfer and Cooling Technology, Taylor & Francis, New York (ISBN 1-56032-841-X)
3 Rib Turbulated Cooling
The concepts of rib turbulated cooling are described, together with a summary of the literature study. After that, the results, analysis and conclusions of investigated correlations and program codes are presented.
3.1 Theory
In turbine vanes and blades, ribs are mostly used in the internal cooling channels in the middle of the component. The ribs are situated on opposite walls, almost always towards the pressure side and suction side, see Figure 3.1 [3.1]. Sometimes only one side has ribs, because the internal cooling has to match the external load, which can be different on pressure and suction side.
Figure 3.1 A Ribbed Channel.
The ribs cause separation from the flow at the rib tops, and reattachment to the flow between the ribs. This disturbs the boundary layer, which leads to increased heat transfer, see Figure 3.2. Separation and reattachment increases the turbulence of the flow, which mixes the fluid elements near the wall with the cooler ones in the middle of the flow.[3.1] A new thin boundary layer is started at the reattachment point after every rib.
Figure 3.2 Flow around Ribs [3.1].
The increase of heat transfer depends mainly on the aspect ratio of the duct, the flow Reynolds number and the rib configuration [3.2]. Figure 3.2 shows the setup of a ribbed duct, and the important rib parameters such as rib height - e, pitch, and rib angle. Ribs that are orthogonal to the flow direction are called transverse ribs.
Due to the complex flow that the ribs create, the flow has to be described by empirical correlations from experiments, instead of by analytical solutions [3.1].
To compare the results from different experiments and with turbine blade channels, certain dimensionless ratios of the geometry is of extra interest. Important
H
W
Ribs
Rib Turbulated Cooling
12
dimensionless parameters for ribbed ducts are the channel aspect ratio, the pitch-to-rib height ratio and the rib height-to-hydraulic diameter ratio. The definition of rib
angleα is also important, see Figure 3.2.
The disadvantage of ribbed duct is that the pressure drop is increased by the ribs. However, since the ribs are relatively small the pressure drop is often acceptable. The largest pressure drop usually occurs in the channel bends. A comparison of the heat transfer to the pressure drop was made for different cooling methods [3.3]. Curve number 3 in Figure 3.3 represents a duct with ribs on two opposing walls. It is clear that the friction grows faster than the heat transfer.
Figure 3.3 Comparison of K and C. Ribbed Duct is Number 3 [3.3].
The Nusselt number in a smooth duct is highest near the inlet, due to the turbulent developing flow. Further from the inlet the Nusselt number decreases. However, the smooth wall Nusselt number in a ribbed duct is about 20% to 60% higher than that in a smooth duct. In a ribbed duct, the Nusselt number on both the ribbed and smooth walls are also fluctuating, due to the separation from and reattachment between the ribs. The ribbed walls have higher fluctuations and higher Nusselt number than the smooth walls. [3.1]
The leading edge channels are often U-shaped. Rib turbulated cooling of U-shaped ducts were investigated by Nagoga, [3.3]. He tested two different cooling methods, called the SR-scheme and the SSR-scheme. Both the SR- and SSR-scheme consist of a periodic array of ribs that are spaced at a pitch P either perpendicularly or at angle
α to the flow. The ribs are attached to the concave side of the duct. SR stands for Surrounding Ribs, and the geometry can be seen in Figure 3.4. [3.4]
Figure 3.4 Geometry of SR-Scheme, Front View (Left) and Top View (Right).
The SSR-scheme consists of segmented ribs, which are placed in a semi-circular longitudinal duct. Figure 3.5 describes the geometry of the SSR-scheme. [3.4]
C
K
Rib Turbulated Cooling
14
Summary of Literature Study
The heat transfer enhancement decreases with increased Re [3.5] [3.6]. The reason is that flow reattaches faster for higher Re [3.5]. For Re = 60 000, the flow reattached approximately 2 rib heights downstream, compared to 6 rib heights for Re = 10 000 [3.5].
[3.7] found that for a rib angleα of 45°, Nu is increased but f remains the same as for
α=90 °. [3.8] and [3.9] reported that angled ribs create a
Figure 3.6 Secondary Flow induced by Angled Ribs[3.1].
secondary flow according to Figure 3.6. For α= 60° to 30°, the secondary flow makes Nu decrease along the rib axes, from left to right in Figure 3.6 Secondary Flow induced by Angled Ribs[3.1]. [3.9].
The ribs cause Nu to have a periodic distribution, due to the continuous separation and reattachment of the flow. For a square duct with transverse ribs, Nu decreases from the inlet along the channel in the streamwise direction, until x/Dh > 3 where the periodic Nu reaches a constant value. For a square duct with angled ribs, Nu also decreases after the inlet, but for x/Dh > 3 Nu increases again, due to the secondary flow induced by the rib angle. For ducts with larger W/H than 1, this effect is gradually decreased. [3.9]
Han et al. [3.8] investigated the same phenomenon as described above but in channels with aspect ratios less than 1. They found that for α= 90° or 30°, local Nu is
periodically distributed between the ribs after x/Dh > 3, i.e. Nu neither increase nor decrease. For α= 60° or 45° [3.8] found that the periodic Nu increases along the channel due to the secondary flow described above.
Han and Park [3.9] also found that for a duct with square cross-section, highest Nu and f were obtained for α=60° . For a duct with W/H = 4, the highest Nu and f were obtained for α= 90°. The best heat transfer performance, i.e. high Nu and low f, were obtained for α= 30° and 45° [3.10]. Ribs with 60° and 45° angle to the flow had 25 to 30 % better heat transfer performance than transverse ribs [3.8].
Concerning aspect ratio, [3.5] investigated ducts with aspect ratios from ¼ to 4 and found that ducts with small aspect ratios had better heat transfer performance than large aspect ratio ducts. [3.8] investigated ducts with aspect ratios less than 1, and also found that channels with smaller aspect ratios perform better.
The effect of rib height was investigated by [3.7]. It was concluded that increased e/Dh led to increased friction factor. An experimental study took place at Siemens in Finspång in 2002, which aimed to investigate the effect of rib height [3.11]. The outcome was that the influence of rib height on the Nu heat transfer decreases with an
heat transfer coefficient, but increased the friction factor by 2 [3.11].
The effect of rib pitch was discussed in many articles, and many investigators came to the same conclusions. For P/e no less than 10, Nu increases with decreased P/e [3.7],[3.5],[3.12]. Maximum heat transfer is obtained for P/e =10 [3.7], [3.10]. For smaller rib spacing, the reattachment between ribs cannot occur, see Figure 3.7 [3.13].
Figure 3.7 Flow Patterns for Different Rib Spacings[3.13].
[3.6] investigated the effect of number of ribbed walls. They found that Nu and f increased with the number of ribbed walls. For example, K increased from 2.04 for 1 ribbed wall to 2.63 for 4 ribbed walls when Re = 30 000. They also found that a duct with 4 ribbed wall and W/H = ½ , obtained 29% higher Nu than a duct with 1 ribbed wall and Re = 30 000. A duct with 4 ribbed walls and W/H = 2 obtained 4% higher Nu than a duct with 2 ribbed walls when Re= 30 000. [3.6]
In 1987, Metzger and Vedula studied heat transfer performance in ribbed channels with a triangular cross-section. Different configurations of angled ribs were used, which created secondary flow according to Figure 3.8. [3.1]
Figure 3.8 Triangular Ducts Investigated by Metzger & Vedula [3.1].
Metzger and Vedula found that the downstream angled ribs transported the main flow towards the ribbed sides, and the upstream angled ribs carried the main flow towards the smooth side wall. This resulted in higher heat transfer coefficient on the ribbed
Rib Turbulated Cooling
16
sides for the downstream angled ribs, and higher heat transfer coefficient on the smooth side wall for the upstream angled ribs. [3.1]
Experiments for the spiral ribs showed that for 60° angle, all three walls reached nearly the same Nusselt number for fully developed flow. They also found that the ribbed side wall for spiral ribbed had lower Nusselt number than the ribbed side wall of the downstream and upstream angled ribs. [3.1]
Zhang et al. investigated channels with triangular cross-section in 1994. Experiments were made on six geometries, see Figure 3.9.
Figure 3.9 Triangular Ducts Investigated by Zhang et al [3.1].
They found that Nu for the three-wall partial ribs were approximately 10 % higher than for three-wall full ribs. For transverse ribs K=2 - 2.3 and C = 3.6-6.6 and for 45° angled ribs K = 1.6-1.8 and C = 1.6-2.5. In the 55° corner, K = 1.4-1.7 for transverse ribs and K = 1.2-1.5 for 45° angled ribs. In the 35° corner, heat transfer enhancement was low for all configurations, both transverse and for 45° angled ribs. [3.1]
3.2 Correlations from Articles
The results, analysis and conclusions drawn of the investigation of correlations from articles are presented below.
3.2.1 Results concerning Correlations from Articles
Investigated CorrelationsFollowing correlations from published articles were examined. • Webb, Eckert &Goldstein, 1970 [3.13]
• Han, 1988 [3.5]
• Chandra, Niland & Han, 1997 [3.6] • Han, Glicksman & Rohsenow, 1978 [3.7] • Han & Park, 1988 [3.9]
• Han, Ou, Park & Lei, 1989 [3.8] • Han, 1984 [3.12]
• Han, Park and Lei, 1985[3.10] • Nagoga, 2001 [3.4]
The correlations are summarized in Appendix A. The correlation ranges are showed in Figure 3.10, together with ranges of interest for turbine cooling. The investigated reports from Siemens did not contain correlations for ribbed ducts. More articles about rib turbulated cooling are listed in Appendix J. The correlations are valid for different ranges of Reynolds number - Re, rib angle, aspect ratio, pitch-to-rib height ratio and rib height-to-hydraulic diameter ratio. Ranges for the correlations derived from articles are shown in Figure 3.10, together with ranges that are of interest for typical gas turbine blades and vanes in the first and second stages. The ranges of Nagoga’s correlations for U-shaped ducts are displayed in Appendix B.
Rib Turbulated Cooling 18 Reynolds Number 0 20 40 60 80 100 120 140 160 Re*10-3 Aspect Ratio 0 5 10 15 20 W/H Pitch-to-Rib Height Ratio
5 10 15 20 25 30 35 40 P/e W ebb et al. 1970 Han et al. 1978 Han 1984 Han 1985 Han & Park 1987 Han 1988 Han et al. 1989 Chandra et al 1997 Turbine components
Rib Height-to-Hydraulic Diameter Ratio
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
e/Dh
Rib Angle
20 30 40 50 60 70 80 90
Rib Angle
The correlations were compared and analyzed by using Matlab. The effect of rib angle, aspect ratio, pitch-to-rib height ratio, rib height-to-hydraulic diameter ratio and Reynolds number was investigated. To be able to compare as many correlations as possible in their valid ranges, a test case with rib- and duct geometry according to Table 3.1 was chosen. This case is referred to as Case A. All correlations except for Webb et. al’s 1970, Chandra et. al’s 1997 and Han et. al’s 1978 are valid for Case A. The latter are therefore analyzed separately.
Table 3.1 Case A, Test Case for Ribbed Ducts.
P [mm] 3.15
e [mm] 0.315
Dh [mm] 5
W [mm] 5
H [mm] 5
Number of ribbed walls 2
Re [-] 10 000- 80 000
α [°] 90
W/H [-] 1
P/e [-] 10
e/Dh [-] 0.063
Figure 3.11 and Figure 3.12 display the results for the Nusselt number and friction factor for Case A. Nu for a smooth channel is calculated with the Dittus-Boelter equation, see equation (3.1). The Q3D correlations will be handled in chapter 3.2.3 but they are also presented here to avoid displaying almost the same figures twice.
1 2 3 4 5 6 7 8 x 104 0 50 100 150 200 250 300 350 400
Nusselt Number for a Ribbed Duct
Reynolds Number Nu ss el t N um be r Han 1988 Han & Park 1988 Han et. al 1989
Han 1984,OBS! Nuaverage
Han et al. 1985 Q3D
Smooth Channel
Rib Turbulated Cooling 20 4 . 0 8 . 0 Pr Re 023 . 0 ⋅ ⋅ = Nu (3.1)
As can be seen in Figure 3.11, Han 1984 results in a lower Nusselt number than the other correlations. The reason for this is that this correlation concerns the average Nusselt number for the ribbed and smooth walls in a duct with two ribbed walls. The other correlations are for the Nusselt number on the ribbed side wall, which is of more interest for turbine blade design.
1 2 3 4 5 6 7 8 x 104 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Friction factor for a Ribbed Duct
Reynolds Number Fr ic tio n Fa ct or Han 1988 Han & Park 1988 Han et. al 1989
Han 1984, OBS! Nuaverage
Han et al. 1985 Q3D
Smooth duct
Figure 3.12 Friction Factor on Ribbed Side Wall for Case A.
The results concerning the friction factor are displayed in Figure 3.12. All correlations except Q3D result in approximately the same value for the friction factor. All
correlations of Han et al. calculate an average friction factor, which is based on a weighted average between a totally smooth duct and a totally ribbed duct, see Appendix A.
Figure 3.13 and Figure 3.14 presents Nu and K for a smooth wall in a duct with two ribbed walls.
1 2 3 4 5 6 7 8 x 104 0 50 100 150 200 250 300 Reynolds Number Nus selt Num ber Han 1988 Han & Park 1988 Han et al. 1985 Q3D
Smooth Channel
Figure 3.13 Nu on Smooth Side Wall in Ribbed Duct for Case A.
1 2 3 4 5 6 7 8 x 104 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Nusselt Number Enhancement K on Smooth W all in a Ribbed Duct
Reynolds Number Heat T ran sf er E nha nc em en t F ac tor Han 1988 Han & Park 1988 Han et al. 1985 Q3D
Rib Turbulated Cooling
22
Figure 3.14 shows that there is quite a large difference on the enhancement factor between the correlations. Results for K, C and eff of a ribbed side wall are presented in Appendix E.
The effect of α, P/e, e/Dh and W/H on Nusselt number enhancement, K, friction factor enhancement, C and efficiency, eff for Case A has been studied. The results are presented in Appendices C to G.
U-shaped Channels
The friction factors and enhancement factors in U-shaped ducts cooled by SR- and SSR-schemes are displayed in Figure 3.15 for the geometry according in Table 3.2.
Table 3.2 Geometry for SR- and SSR- Calculations.
e Dh R P α Tf Tw 0.3 2.5 1.08 3.3 45 ° 800 400 0 5 10 15 x 104 0 5000 10000 15000 Nusselt Number Re Nu 0 5 10 15 x 104 0 0.05 0.1 0.15 0.2 Friction Factor Re f 0 5 10 15 x 104 1 1.5 2 2.5
Nusselt Number Enhancement Factor K
Re K 0 5 10 15 x 104 2 2.5 3 3.5
Friction Enhancement Factor C
Re C SR SSR SR SSR SR SSR SR SSR
Figure 3.15 Results for SR- and SSR-Scheme Calculations. Temperature Analysis
A temperature analysis was made in order to investigate the effect on surface temperature for a change of K. Vane 2 on SGT -700 was chosen since the duct’s geometries are easily approximated to fit the correlations. A cross-section in the middle of the vane, named section 4 in Q3D, was used, see Figure 3.16.
Figure 3.16 Cross-Section 4, Vane 2, SGT -700.
The K values in channels 1, 2 and 3 were altered, see Figure 3.16. The temperatures are calculated for the 2D-section, and are shown as the temperatures of the external surface. Temperature is calculated at points along the perimeter. The distance along the external perimeter, S, starts with 0 at the suction side trailing edge and is defined as Smax at the pressure side trailing edge. The points along the perimeter are made dimensionless by dividing S by Smax.
For channel 1, only the Nagoga correlation was applicable, for channel 2, only Han & Park 1988 was valid, and for channel 3 only Han et al. 1989 was valid. Table 2 display the geometries and both original and new K values. The dimensions of the channel are taken from the CAD program Catia. Channels 2 and 3 were approximated to have a rectangular cross-section. The Reynolds number and enhancement factors were taken from a Q3D model of the vane. The formula used for the calculations of the original K values is not known. Index s indicates value for smooth wall and index r value for ribbed wall.
Table 3.3 Parameters for Channels in Vane 2, SGT -700.
Channel 1 Channel 2 Channel 3
Correlation Nagoga [3.4] Han & Park [3.9] Han et al. [3.8]
W - 6.33 3.89 H - 5.39 4.63 e 0.3 0.3 0.3 P 3.3 3.3 3.3 Dh 2.52 5.82 4.23 α 45 45 45 R 1.08 - - W/H - 1.17 0.84 P/e 11 11 11 e/Dh 0.12 0.052 0.071 Re 68 591 58 025 48 881 Kr,orig 2.78 2.68 2.750 Kr,new 2.272 2.157 2.634 Ks,orig 1.670 1.610 1.650 Ks,new 1.670 1.463 1.430 Kr,new/Kr,orig 0.817 0.805 0.958 Ks,new /Ks,orig 1 0.909 0.867
Rib Turbulated Cooling
24
The Nagoga correlations does not consider the smooth side wall, therefore the original value was kept for channel 1 for the smooth side wall.
Figure 3.17 and Figure 3.18 display the results of the temperature calculations.
SGT 700 Vane 2 Section 4 800 810 820 830 840 850 860 870 880 890 900 0 0,2 0,4 0,6 0,8 1 1,2 Position S/S_max T em p er at u re [ K ] Original SGT700 New SGT700
Figure 3.17 Temperature in Vane 2, SGT -700.
Temperature Difference, New-Original
-15 -10 -5 0 5 10 15 20 25 0 0,2 0,4 0,6 0,8 1 Position, S/Smax T e m p . D if fer ence [ K ] Temp. differences
3.2.2 Analysis and Discussion of Correlations from Articles
Correlations from eight articles have been investigated, in order to find which ones are most reliable to use in turbine blade and vane cooling channels with ribs. Figure 3.10 gives an overview of the different ranges of the correlations together with the ranges of interest for turbine design. Unfortunately, no correlation covers the total area of interest. Therefore different correlations could be of use for different cooling channels.The friction factors in the correlations are the average friction factors, weighed between f of a fully smooth duct and that of a fully ribbed duct. The friction factor on a ribbed side wall is therefore higher than the values displayed in Figure 3.12. Webb et al.’s correlation from 1970 covers a lot of interesting ranges. However, the experiments it is based on were performed on fully ribbed circular pipes, instead of rectangular or square ducts with only two ribbed sides. This makes the correlation unsuitable for turbine blade design.
The correlations of Han 1988 cover a wide range of parameters. J.C. Han has made a large amount of research in this area, and when it comes to correlations of this kind, it is difficult to find articles that he has not been involved in. His results from 1987, 1988 and 1989 are similar but valid for different duct- and rib geometries. The main difference is that Han 1988 only is valid for transverse ribs and the other two for both transverse and angled ribs, see Figure 4. The correlations from 1987 are valid for aspect ratios between 1 and 4, and those from 1989 are valid for smaller aspect ratios, between ¼ and 1. Experiments from these articles are comparable to each other and all aim to gather information to use for turbine blade cooling.
Figure 3.11 shows that the Han 1988 correlations give a slightly lower value of Nu compared with Han & Park 1988 and Han et al. 1989. Since it is safer to choose a too low Nu than a too high, it would be wiser to use the correlation from 1988 for
transverse ribs.
Figure 11 in Appendix D shows that for W/H = 1, where both the correlations from 1987 and 1989 are valid, the later gives a higher value of the Nusselt number. Therefore it would be safer to use the 1987 correlation for an aspect ratio of one. His earlier work, in 1984 and 1985, also aims for turbine blade design. However, the correlations from 1984 only concerns average values for the Stanton number and friction factor, instead of the actual St and f of a ribbed or smooth wall which are used in heat transfer programs. It is therefore not suitable for turbine blade design.
The correlation from 1985 concerns angled ribs, but is valid for a smaller range for e/Dh and W/H, than the correlations from 1987 and 1989. The values of St and f of Han 1985 differs from those of Han et al. 1989 and 1987, Figure 3.11 and Figure 3.12. The difference between the correlations is that in Han 1985, calculations are made with the average roughness Reynolds number, e+ and the average roughness function, R
( )
e+ and in the other Han correlations calculations are based on theRib Turbulated Cooling
26
parameters is found in Appendix A. Since the most recent and the majority of articles use the later way of calculations, that method it likely to be the most reliable.
The article of Han, Glicksman and Rohsenow from 1978 covers a relatively small range of Reynolds number and is valid for very large aspect ratios, see Figure 3.10. Therefore the correlations are often not applicable for turbine vane and blade design. The experiments were performed using parallel plate geometry instead of a
rectangular or square duct, which also contributes to the unsuitability of using these correlations for the turbine components of interest. However, it can be of interest for other areas, for example combustor cooling.
Chandra, Niland and Han performed experiments to investigate the effect of different number of ribbed walls in 1997. The correlations are only valid for a small range of W/H and e/Dh and may therefore not be suitable to use for duct with two ribbed walls, where there exist more applicable correlations. However, the correlations can be useful for ducts with one, three or four ribbed walls.
Effect of Rib Angle
The correlations from articles all display similar trends concerning rib angle,
according to Figure 1 to Figure 3 in Appendix D. The highest Nusselt number appears for α = 60° for all correlations except for Han et al. 1989, which calculates the highest Nusselt number for α = 75° . However, the experiments from 1989 were only made for α = 30°, 45°, 60° and 90°, therefore it is difficult to say how correct the value is for α = 75° .
The highest Nusselt number is unfortunately followed by the highest friction factor, as seen in Figure 5, Appendix D. Therefore the efficiency, Figure 3 in Appendix D, has a minimum for α around 60° and 75°. Even thought Figure 3 in Appendix D show a minimum of eff for α around 60° and 75°, rib angles of 60° are often used in turbine vanes and blades. This is because the pressure loss due to the ribs in cooling ducts in are relatively small compared to other losses, for example that caused by the channel bends. Therefore rib angle is often chosen with respect to the highest Nusselt number instead of efficiency.
Effect of Pitch-to-Rib Height Ratio
Appendix E show the results concerning P/e. These correlations are not valid for P/e < 10, but for the valid range it is clear that the highest heat transfer coefficient occur for P/e = 10. The correlation of Han et al. 1978 is valid for a larger span of P/e. Figure 4, Appendix E indicates that P/e = 10 is the optimal pitch-to-rib height ratio. However, this correlation is not valid for Case A, so the result should be handled with caution. The Han correlations agree well with the theory in chapter 3.2.
Effect of Aspect Ratio
The effect of aspect ratio is displayed in Appendix F. The Han correlations from 1987, 1988 and 1989 give similar results, whereas that from 1985 deviate from the trend. The graphs confirm the theory that smaller aspect ratios results in higher efficiency than larger aspect ratios. An increased aspect ratio leads to increased K and C, according to Figures 1 and 2, Appendix F. The increase of C is larger than the increase of K. Therefore, the highest efficiency is received for small aspect ratios.
Figure 14 to Figure 16 in Appendix G display the effect upon C, K and eff for various e/Dh. Han 1988 and 1985 returns a lower value than Han et al. 1987 and 1989. Han 1984 returns lower values than the other correlations, which is the same pattern as for previous results.
The effect on K is relatively low compared with the other dimensionless parameters investigated. The friction factor is more sensitive to rib height according to Figure 2, Appendix G. It is logical that increased rib height leads to increased pressure drop. This agrees well with the theory about the effect of e/Dh. The fact that the friction factor increases while the Nusselt number is rather unaffected by increased rib height, makes the highest efficiency for small rib height-to-hydraulic diameter ratios, as seen in Figure 16, Appendix G.
Temperature Analysis
As seen in Figure 3.17 and Figure 3.18, the changes of K values affect the surface temperature on the vane. Since the values of Knew where all lower than the original values, it should result in higher surface temperatures. Since Koriginal is higher than Knew, the model was not based on calculations from Q3D, since the Q3D enhancement
factors result in lower values than all Han correlations except that from 1984, see Figure 3.11. The model of Vane 2, SGT -700 was built in Moscow several year ago, and it is not known what correlation the enhancement factor is bases on.
The surface temperature became higher with Knew implemented, except at the trailing edge. At the trailing edge, the temperature in the original model is approximately 12 °C higher than in the modified model. The explanation is that since the K values are lowered in channels 1 to 3, less heat is transferred to the cooling air which results in colder cooling air in the trailing edge. Colder trailing edge cooling air results in colder surface temperature in this region, which is displayed in Figure 3.17 andFigure 3.18.
The largest temperature difference appears next to the leading edge at the pressure side. This is natural since the K values are lowered most in channel 1 and 2. The new revised model’s surface temperature is 20 °C higher than the original model.
Since the enhancement factor K has such impact on the surface temperature, and the difference of the original and new value of K for this example is as much as 18.3 %, it is recommended to look into the routine of choosing Nusselt number enhancement factors.
Rib Turbulated Cooling
28
3.2.3 Conclusions concerning Correlations from Articles
In conclusion, following recommendations are made for what correlations to use. • Han 1988 [3.5] for transverse ribs in ducts with two opposing ribbed walls • Han et al. 1989 [3.8] for angled ribs in ducts with two opposing ribbed walls
with 14≤W H <1.
• Han & Park 1988 [3.9] for angled ribs in ducts with two opposing ribbed walls with 1≤W H ≤4.
• Chandra et al. 1997 [3.6] for duct with one, three or four ribbed walls. • Nagoga 2001 [3.4] for U-shaped ducts with SR- or SSR-schemes.
3.3 Correlations in Q3D
The results from an investigation of the Q3D program code are presented and analyzed below.
3.3.1 Results concerning Q3D
The correlation in Q3D is an in-house correlation based on Han test data. Q3D calculates the Nusselt number and the friction factor. The input variables are duct height, duct width, rib height and the hydraulic diameter. The Nusselt number is calculated according to equation (3.2). The Q3D correlations are used to choose A and n.
n
A
Nu = ⋅Re (3.2)
The Q3D interface for ribbed channels is showed in Figure 3.19.
Figure 3.19 Q3D Interface for Ribbed Channels.
The path to the Channel box is
H_Hydro → Hydraulic Net → HN Branches-›FE Grid → Channels As seen in Figure 3.19, both the Nusselt number for a ribbed duct, Nur and for a smooth duct, Nus are calculated. The exact values and expressions used in Q3D were extracted from the code and are displayed in Appendix H.
Reduced Area Method
The area and hydraulic diameter used in Q3D to calculate the friction factor and pressure drop are calculated by the so called Reduced Area Method - R.A.M. This means that the area and hydraulic diameter are calculated by the reduced height He, instead of the total height H according to equation (3.3) and (3.5) and Figure 3.20.
