Linköping Studies in Science and Technology Thesis No. 1593
CFD Simulations for Film Cooling
Reduced Models at Engine Like Conditions
Andreas Bradley
Division of Applied Thermodynamics and Fluid Mechanics Department of Management and Engineering
CFD Simulations for Film Cooling
Reduced Models at Engine Like Conditions
Linköping Studies in Science and Technology Thesis No. 1593
Department of Management and Engineering Linköping University
SE-581 83, Linköping, Sweden
Printed by:
Liu-Tryck, Linköping, Sweden ISBN 978-97-7519-608-4 ISSN 0280-7971
Copyright c 2013 Andreas Bradley, unless otherwise noted
No part of this publication may be reproduced, stored in a retrieval system, or be transmitted, in any form or by any means, electronic, mechanic, photocopying, recording, or otherwise, without prior permission of the author.
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Abstract
In gas turbines some parts are exposed to combustion gases with temperatures well above the melting temperature of the material. Therefore, various cooling techniques are utilized in order to protect the parts exposed to these hot gases. One such technique, film cooling, is a common and well established way to protect the exposed parts. Film cooling involves the ejection of cold air on the surface of the parts that are to be protected, thus creating a film of colder air between the surface and the hot gases.
Computational Fluid Dynamics (CFD) is a way of calculating fluid flow, and can be used to calculate the effectiveness of a cooling film in film cooling applica-tions. CFD is demanding in terms of computer power, especially when advanced methods are to be used. Even the simpler methods, such as Reynolds Average Navier-Stokes (RANS), can be quite demanding, time and computer power-wise, and require resources not always available. Finding ways of limiting the needed computer power is therefore of large interest.
The aim of this thesis is to reduce the computational time of film cooling CFD-simulations, by using reduced models. To achieve this, simulations has been conducted and compared to experiments. The investigated setup is of an engine-like equipment, where a guide vane is investigated for heat transfer coefficient and film effectiveness. The geometry in the experimental setup is constructed in such a way as to give the same pressure distribution around the guide vane as can be seen in a real gas turbine, although at lower temperatures than those in the real turbine. The CFD-simulations conducted on the test rig includes RANS-simulations using the realizable k- and the SST k-ω turbulence models.
The reduced model contains only the central part of the vane. The walls of the test rig is replaced with periodic boundary conditions. This narrow model gives good agreement with the full model for heat transfer coefficient. Due to the large computational cost required to conduct simulations with cooling on the full model no comparison were made between the cooled narrow and cooled full model.
To further reduce the size of the computational domain, two additional models were investigated. The first one involves a reduction of the full domain to only include the section being studied, in this case the suction side of the guide vane.
This infers a reduction of the mesh size to less than ten percent of the size of what a mesh of the cooled full domain would be. The next step to reduce the size of the model and mesh is to make a narrow version of the already shortened model. The results for these two models show that they perform adequately to each other and (in the cases where a comparison is possible), to the full domain.
Populärvetenskaplig
Sammanfattning
Gasturbiner används för flera olika uppgifter, exempelvis för drivning av flygplan och båtar, eller ihopkopplade med en generator för framställning av elektricitet. Det är en ständigt pågående uppgift att konstruera effektivare och bättre turbiner och på så sätt minska bränsleförbrukningen, öka uteffekten och därmed få en min-dre miljöpåverkan.
För att öka effektiviteten i moderna gasturbiner är det önskvärt att höja tem-peraturen i brännkammaren, då en högre förbränningstemperatur innebär att mer av bränslets energi kan utnyttjas. Då förbränningstemperaturen kan nå värden som är högre än den temperatur som materialen i gasturinens komponenter tål, krävs att delarna skyddas på olika sätt för att inte gasturbinen ska fallera. Särskilt utsatta är blad och ledskenor i turbinen, som kommer direkt efter brännkammaren och därmed utsätts för mycket höga temperaturer. Dessa delar förses med ett isolerande lager (s.k. thermal barrier coatings, TBC) som tål högre temperaturer än materialet de appliceras på. Detta räcker dock inte utan även aktiv kylning med hjälp av luft är nödvändig. Det går vanligast till så att luft leds från kompressorn direkt till turbinen där den används för att kyla blad och ledskenor. Kylluften får ofta passera genom gångar inuti komponenterna (inre kylning) för att sedan ledas ut till utsidan där luften bildar en “film” som ska skydda från de heta gaserna (s.k. filmkylning).
Hur effektiv filmkylningen är beror främst av två saker, dels hur mycket kylluft som används samt hur effektivt den luften sprids över ytan. Då kylluften tas från kompressorn och leds förbi brännkammaren är det luft som kräver, men inte bidrar med, arbete. Det är därför ett mål att använda luften så effektivt som möjligt och därigenom minimera mängden som behöver tas från kompressorn.
I dagens designprocess av gasturbiner används ofta matematiska modeller, korrelationer och samband för att beräkna hur effektiv kylfilmen är. Dessa mod-eller har vanligtvis tagits fram experimentellt och kan ge relativt goda resultat. De är dock ofta begränsade i hur mycket detaljer som går att få fram. Beräkningar (simuleringar) med hjälp av datorer (s.k. Computational Fluid Dynamics, CFD) är
ett kraftfullt sätt att beräkna hur luft i rörelse beter sig och därför väldigt lämpligt att använda vid studier av filmkylning. CFD lider dock av att det är väldigt krä-vande när det gäller datortid och datorkraft. Som exempel så har en beräkning som utförts i denna avhandling krävt över 10 timmars beräkningstid på en su-perdator med 80 beräkningskärnor (processorer). En vanlig modern hemdator har 2-8 kärnor och samma beräkning skulle således kunna ta 100-400 timmar i beräkningstid. En hemdator har dock sällan den minneskapacitet som krävs för dessa beräkningar, vilket gör att de ändå inte skulle vara möjliga att genomföra.
Den här avhandlingen handlar primärt om att ta fram sätt att minska beräkn-ingstiden och datorkraften som krävs för att göra simuleringarna. Detta göres genom att modellen/geometrin som ska undersökas reduceras i storlek och att bara de delar som är av allra störst intresse undersöks. Genom att minska storleken på modellen på detta sätt kan beräkningstiden reduceras.
Resultaten visar att de reducerade modellerna ger likvärdiga resultat som den fulla modellen. De metoder som presenteras här kan således användas för att minska beräkningstiden för CFD-beräkningar.
Acknowledgements
There are many people that deserve a thank you for helping me with the work pre-sented in this thesis. First I like to thank all my colleges at the Division of Applied Thermodynamics and Fluid Mechanics. A thank you to you all for making my time here memorable and fun. A special thanks to professor Matts Karlsson. You are an everlasting source of encouragement and ideas. Not all ideas were feasible, but there was always at least one that made the work move forward. Also a thank you to associate professor Joakim Wren for always being there when I needed a second opinion on something, for your invaluable help with this thesis and for supporting me with my teaching -We made quite a good team in the TMMV04-course. I want to thank Jonas Lantz for providing the template for this thesis, and Roland Gårdhagen for always being there when I needed help wrapping my head around some problem. Thanks to Hossein Nadali Najafabadi for helping me with the third paper and understanding the experiments. Thanks also to Anna Wahlund for administrating everything in the division. Without you I don’t think anything would have worked.
I want to thank the people at Siemens Industrial Turbines in Finspång, especially Dr Mats Kinell and Dr Esa Utriainen, for their knowledge and for conducting the experimental work.
A big thank you to all my friends, both near and far, for reminding me that there is a life outside of work and that we are supposed to work to live and not live to work.
The final thank you goes out to my family. First my sister, Hanna, who, probably without knowing it, has always spurred me forward to achieve greater things. All the way from elementary school up to, and beyond, college. Last, but definitely not least, I like to thank my mother and father, Ann-Sofie and Gerth, for always believing in and encouraging me. You have never doubted me, even when I have done so myself.
Thank you all!
Andreas Bradley April 2013
Funding
This research has been funded by the Swedish Energy Agency, Siemens Industrial Turbomachinery AB, Volvo Aero Corporation, and the Royal Institute of Technol-ogy through the Swedish research program TURBOPOWER, the support of which is gratefully acknowledged.
List of Papers
The following papers are included in this thesis. When necessary they will be referred to by their roman numerals.
I. Fan Shaped And Cylindrical Holes Studied in a Vane Film Cooling Test Rig
Mats Kinell, Esa Utriainen, Jonas Hylén, Jonas Gustavsson, Andreas Bradley, Matts Karlsson, Joakim Wren
ASME Turbo Expo 2010, June 14-18, 2010, Glasgow, UK
II. Towards Efficient CFD-Simulations of
Engine Like Turbine Guide Vane Film Cooling
Andreas Bradley, Hossein Nadali Najafabadi, Matts Karlsson, Joakim Wren, Esa Utriainen, Mats Kinell
49th AIAA Aerospace Science Meeting January 4-7, 2011, Orlando, Florida, USA
III. CFD Simulations Using Reduced Models for Film Cooling Design Hossein Nadali Najafabadi, Andreas Bradley, Joakim Wren, Matts Karlsson, Esa Utriainen, Mats Kinell
49th AIAA Aerospace Science Meeting January 4-7, 2011, Orlando, Florida, USA
Contents
Abstract v
Populärvetenskaplig Sammanfattning vii
Acknowledgements ix
Funding xi
List of Papers xiii
Contents xv
1 Introduction 1
2 Aims 3
3 Film cooling 5
3.1 Film effectiveness . . . 5
3.2 Film cooling hole geometry . . . 6
4 Parameters in Film cooling 7 4.1 Blowing ratio (M) . . . 7
4.2 Downstream distance (x/D) . . . 9
4.3 Turbulence (Tu) . . . 9
4.4 Coverage ratio (t/P) . . . 10
4.5 Area ratio (AR) . . . 11
4.6 Distance between holes (hole spacing) (P/D) . . . 11
4.7 Hole angle (α) . . . 12
4.8 Hole length (L/D) . . . 12
4.9 Momentum ratio (I) . . . 13
4.10 Density ratio (DR) . . . 13
CONTENTS
5 Correlations and Experiments 15
5.1 Correlations . . . 15
5.2 Experiments . . . 18
5.2.1 Experiments in literature . . . 18
5.2.2 Project specific experiments . . . 20
6 Computational Fluid Dynamics (CFD) 23 6.1 Introduction to CFD . . . 23 6.2 Mesh . . . 24 6.3 Project specific CFD . . . 24 6.3.1 Full domain . . . 26 6.3.2 Narrow domain . . . 30 6.3.3 Short domain . . . 37 6.3.4 Conclusions . . . 40 7 Included Papers 45 Paper I . . . 49 Paper II . . . 59 Paper III . . . 69 Appendix 77 Updated Experimental Results . . . 77
Chapter 1
Introduction
When designing gas turbines, a high combustion temperature is desirable to obtain a good thermal efficiency. At the same time, the thermal limitations of the gas turbines components must not be exceeded. High temperatures can lead to large thermal stresses that can reduce the life span of the components and increase the risk of fatigue and failure.
The trade-off between efficiency on the one hand, and reliability, life span, service interval etc. on the other hand, must be handled early in the design process. At the same time, many other aspects such as aerodynamics, structural strength, manufacturing and assembly must be considered simultaneously.
To not risk putting too high thermal loads on the components different cool-ing techniques are becool-ing used. For the turbine blades and guide vanes in the high pressure turbine (which experiences the highest temperatures) two primary cool-ing techniques are utilized -internal and external coolcool-ing. The internal coolcool-ing is executed by passing cool air through canals in the blade, thus cooling from the inside. This is not always enough and to obtain increased cooling, external cool-ing is utilized. The external coolcool-ing, or film coolcool-ing, is executed by ejectcool-ing cool air on the outside of the vane, creating a protecting film of cool air on the surface of the blade/vane. The ejected air is often the same air as has previously been circulated inside the blade for internal cooling.
Chapter 2
Aims
The work conducted and presented in this thesis aims at developing and investigat-ing methods for reducinvestigat-ing the computational time when conductinvestigat-ing Computation Fluid Dynamics (CFD) simulations of gas turbine film cooling. Today, many ad-vanced methods exist for CFD, but they demand large amounts of computational resources that are often not available for gas turbine designers. Therefore, it is desirable to find ways to reduce the cost while maintaining the accuracy of the simulations.
Thus the goal of this work is double.
• Find ways to reduce the computational time of CFD simulations to an indus-trially acceptable time frame while not losing any accuracy in the solution. • Investigate the similarities between experiments and simulations for film
cooling heat transfer applications, quantified by the film effectiveness and heat transfer coefficient
Chapter 3
Film cooling
Film cooling is a way of protecting surfaces in gas turbines that are being exposed to hot gases. This is done by ejecting cold air onto the surface, thus creating a cooling film.
Cooling through film cooling is a complex process, influenced by many pa-rameters related to the hole geometry, the flow through the hole, and the free stream above the surface of interest, see e.g. [1]. A number of governing parame-ters have been identified, and their effect has been analyzed, see e.g. [2, 3].
In order to handle the design of film cooling along with the rest of the design process, fast and relatively accurate tools for prediction and comparison of film cooling configurations are essential. One early attempt to describe film cooling by a correlation was carried out in the sixties [4]. Since then a number of correlations have been developed and scrutinized, but most of them have considered flat plates without pressure gradients, a case that is not always representative for gas turbine film cooling.
3.1
Film effectiveness
The efficiency of film cooling is most commonly measured with a parameter known as film effectiveness. Film effectiveness is defined by equation 1, where T∞is the free stream temperature, TC the coolant temperature and Tawthe
adia-batic wall temperature.
η=T∞− Taw T∞− TC
CHAPTER 3. FILM COOLING
From equation 1 it is evident that if the wall temperature equals the free stream temperature, a film effectiveness η = 0 is obtained, while if the wall temperature equals the coolant temperature, the effectiveness is equal to 1.
3.2
Film cooling hole geometry
Film cooling holes (the holes in the surface from which the cooling air is ejected) are usually divided in two categories; cylindrical holes and shaped holes. Cylin-drical holes are the simplest hole geometry and can be angled in both the lateral (perpendicular to the flow) and longitudinal (aligned with the flow) directions. This type of geometry were for a long time the most utilized for film cooling applications, but are more and more being replaced by shaped holes.
Shaped holes come in many forms, the most common being fan-shaped holes, with a lateral expansion, and laidback holes, with a longitudinal expansion. Other forms exist, e.g. conical holes. Figure 1 shows a hole with both lateral and longi-tudinal expansion, a so called laidback fan-shaped hole. The figure shows some geometrical parameters that can influence film effectiveness. The coverage or breakout length, t are only available for shaped holes. Also, for a cylindrical hole, the hole exit area, Aout, and inlet area, Ain, are the same. The distance between
two holes, P, hole length, L, hole diameter, D, and hole angle, α, are present for both cylindrical and shaped holes.
Figure 1: Geometry of a shaped film cooling hole. Some parameters also exist for cylin-drical holes and some are exclusive for shaped holes.
Chapter 4
Parameters in Film cooling
Baldauf and Scheurlen [1] investigated what parameters effect film cooling per-formance, and they concluded that the following parameters are influencing the film effectiveness. ¯ η= f M, x D, T u, P D, α, L D, I, δ D (2) This study was made for cylindrical holes. For shaped holes some new pa-rameters can be added to the list, namely Pt and AR. Another parameter that is influencing the film effectiveness is density ratio, DR, so that parameter is also included in the list. The following sections summarize these parameters and how they affect film effectiveness.
The parameters can be divided in two categories depending on whether they are dependent on the geometry of the cooling hole (or hole surrounding) or on flow properties. Geometrical parameters include cooling hole length, hole angle and downstream distance, while flow parameters are such as blowing ratio, turbulence intensity and density ratio.
4.1
Blowing ratio (M)
Blowing ratio is a measure of how much, and with what velocity, cooling air is being used to create the cooling film. Blowing ratio is defined as:
M = ρcUc
ρ∞U∞ (3)
where ρcand ρ∞is the coolant and free stream density while Ucand U∞is the
CHAPTER 4. PARAMETERS IN FILM COOLING
Baldauf et. al. [3] studied the film effectiveness for rows of cylindrical holes. With a low blowing ratio the coolant spreads immediately after ejection, creating a covering film. This results in a maximum film effectiveness close to the hole exits. The effectiveness diminishes further downstream, ending in a low effectiveness far from the ejection location.
A slight increase in blowing ratio results in higher overall and peak film ef-fectiveness. The position of the maximum effectiveness shifts further downstream with increasing M as the more compact jets need some downstream distance to spread.
Further increase of the blowing ratio, up to what Baldauf et. al. call moder-ate blowing rmoder-ates, the peak effectiveness is beginning to decrease. The cause is given by jet lift-off, allowing hot gas to slip in between the jet and the surface. The interaction between adjacent jets and increased amount of injected coolant do result in an increased effectiveness downstream of the peak and give a higher overall effectiveness. In Baldaufs experiment the overall maximum effectiveness occurred at a blowing ratio of M= 1.0.
At higher blowing rates the effect of jet lift off becomes more pronounced. Jet lift-off causes a reduction in effectiveness at the hole, and adjacent jet interaction an increase downstream. At M= 1.7 the effectiveness reaches its minimum over-all value. At even higher blowing ratios, M >1.7, the effectiveness is very low at the hole exit but increases with downstream distance.
Baldauf concludes that the flow at low blowing ratios is dominated by the single jet in cross flow effect, giving a high cooling effectiveness close to the ejection location, while at high blowing ratios the flow is dominated by adjacent jet interaction, resulting in high effectiveness further downstream.
Colban et. al. [5] studied film effectiveness from a row of laidback fan-shaped film cooling holes, and concluded that there are some major differences between shaped and cylindrical hole film cooling. One major difference is the absence of jet separation with shaped holes. Colban showed that even for blowing ratios as high as M= 4, no evident jet separation occurred. Instead the film effectiveness close to the ejection location increases with blowing ratio up to M≈1.5. After this the effectiveness remains the same close to ejection, but rises somewhat further downstream.
Another difference noticed by Colban [5] between shaped and circular holes, is the location of the peak effectiveness. For circular holes, the peak location moves downstream with increased blowing ratio, due to the separation and reat-tachment of the jet, while it for shaped holes remains at the ejection location. 8
4.2. DOWNSTREAM DISTANCE (X/D)
4.2
Downstream distance (x/D)
The downstream distance is, like many parameters in film cooling, scaled with the hole diameter, D, to create a dimensionless distance. Downstream distance is an essential parameter in film cooling and in graphs the film effectiveness is most commonly plotted versus this parameter. Thus, these graphs show how the film effectiveness changes with downstream distance from the hole, and a number of plots like this will be presented later in this thesis.
As long as no jet separation occurs at the hole exit, film effectiveness will peak at the exit and decrease with downstream distance, as the cooling air mixes with the free stream. When jet separation occurs, the effectiveness peak at the hole is reduced and the location of the maximum film effectiveness is moved further downstream. This is caused by mixing between the free stream and the separated coolant, bringing cold gases back to the surface. The increased mass flow at higher blowing ratios results in a higher thermal capacity of the coolant, and thus often gives a higher downstream effectiveness despite the fact that the coolant is mainly ejected into the free stream.
4.3
Turbulence (Tu)
Baldauf et al. [3] investigated the effect of increased free stream turbulence on the film effectiveness. They concluded that an augmented turbulence increased the effectiveness close to the ejection location for low blowing rates. This is caused by an increased mixing, and thereby spreading, between coolant and free stream. At high blowing rates the turbulence in the coolant jet increases and the flow is dominated by this turbulence. Thus the importance of the free stream turbulence is reduced.
Downstream from the point of ejection, the increased mixing between coolant and free stream caused by the higher turbulence results in a larger amount of hot gas reaching the surface, and thus a reduction in effectiveness. This reduction is most pronounced at low blowing ratios, where the turbulence from the jet injection is low.
The importance of free stream turbulence is also dependent on hole geometry. For instance, an increase in turbulence with an ejection angle of90◦relative to
the surface results in a larger increase in film effectiveness close to the hole, than what is obtained with the same increase in turbulence for an ejection angle of30◦.
Saumweber and Schulz [2] investigated the effects of turbulence on both cylin-drical and shaped holes. They only investigated the area close to the ejection lo-cation and came to somewhat different conclusions than Baldauf et. al. For cylin-drical holes, Saumweber and Schulz states that the film effectiveness is reduced
CHAPTER 4. PARAMETERS IN FILM COOLING
for low blowing ratios if the turbulence is increased. This is due to the mixing of coolant and free-stream leading more hot gases to the surface. For high blowing ratios, where jet lift of is present, the increased mixing result in more coolant be-ing transported to the surface, and thus an increase in effectiveness. These results are consistent with those obtained by Bons et. al. [6] who investigated turbu-lence intensities up to17% and blowing ratios up to M = 1.7. They found that at higher blowing ratios, where jet lift-off is present, the increased mixing caused by higher turbulence result in the coolant spreading quicker back to the surface. Their study also showed that increased turbulence results in increased mixing of jets from neighboring holes, thus an earlier adjacent jet interaction effect.
Shaped holes work differently with increased turbulence. Saumweber and Schulz [2] show that the film effectiveness is always reduced for shaped hole ejection if the turbulence is increased. Since no coolant jet detachment is present with shaped holes, the increased turbulence only leads to more hot gases being transported into the boundary layer through mixing with the coolant, resulting in higher surface temperatures.
4.4
Coverage ratio (t/P)
Coverage ratio only exists for shaped holes where it is defined as the breakout length (width of the hole exit), t, divided by the distance between adjacent holes, P , see figure 1. The coverage ratio can be seen as a limit for the film effectiveness in the near hole region [5], i.e. η x
D= 0
=t
P. This requires that the jet is spreading
over the whole breakout length and that no jet separation occurs. A study by Gritsch [7] showed that for blowing ratios up to M= 1.5, the coverage ratio has no influence on the film effectiveness. For blowing ratios higher than this, there is a minor change in effectiveness with coverage ratio, but it is small. It should be noted that the interval of examined t/P values in this study where quite narrow, and that the area ratio is kept constant as the coverage ratio changed. The range of coverage ratios investigated were t
P= 0.31−0.39 for AR =2.5 and t
P= 0.43−0.63
for AR= 4.2.
4.5. AREA RATIO (AR)
4.5
Area ratio (AR)
Area ratio is another parameter only used with shaped holes. It is defined as the ratio of the outlet to inlet area of the cooling hole, AR=Aout
Ain. Thus a cylindrical
hole has an area ratio of 1. The purpose of having an AR >1 is to reduce the velocity, and thus the momentum, of the coolant prior to ejection, thereby reduc-ing the jets penetration into the free stream. Reducreduc-ing the penetration into the free stream results in more coolant at the surface, thus giving a higher film effec-tiveness than with lower area ratios. Gritsch [7] showed that with a constant hole spacing, P/D, the area ratio has a negligible influence on the film effectiveness for the range of AR investigated in the study (AR= 3.5, 4.2, 4.7).
4.6
Distance between holes (hole spacing) (P/D)
Bauldauf et al. [3] investigated the influence from hole spacing on the film ef-fectiveness and found that, as can be assumed, a closer hole spacing resulted in a higher effectiveness. This is caused by the larger coolant mass flow per unit length obtained with narrower hole spacing. A narrower hole spacing also leads to an increased influence from adjacent jet interaction while a wider spacing re-sults in more single jet in cross-flow effects. For a large hole spacing of P/D= 5, Baldauf et al. discovered that there were no influence from adjacent jet interaction within the examined downstream range (x/D= 80).
Colban et al. [5] states that the same effects that are visible for cylindrical holes, can also be seen with shaped holes. Close to the ejection location, the film effectiveness is dominated by the coverage ratio, but further downstream (x/D > 10) the flow is primarily influenced by the hole spacing. Gritsch [7] showed that even though a narrower hole spacing increases the film effectiveness, a to small spacing does not provide an efficient usage of the coolant.
CHAPTER 4. PARAMETERS IN FILM COOLING
4.7
Hole angle (α)
Colban et al. [5] states that a shallower hole angle reduces the jet separation, thereby increasing film effectiveness. Shallow ejection angles may however lead to problems with machining and can cause higher pressure losses in the hole due to an increased L/D ratio.
Baldauf et al. [3] investigated three different hole angles, 30◦, 60◦ and 90◦, for a number of blowing ratios. That investigation showed that with a steeper ejection angle, the peak effectiveness at the ejection location is reached with a lower blowing ratio, but also that the effectiveness decline faster downstream. The steeper angles also encouraged earlier adjacent jet interaction at increased blowing ratios, resulting in higher overall effectiveness compared to the inclined jets.
4.8
Hole length (L/D)
Lutum and Johnson [8] investigated the influence of hole length on film effective-ness for cylindrical holes. They studied L/D from 1.75 to 18 and showed that hole length to diameter ratios higher than 5 only have small to moderate influence on the film effectiveness. Shorter hole lengths (the study investigated L/D of 1.75 and 3.5) resulted in a lower film effectiveness than with higher L/D ratios. The dif-ference in cooling effectiveness between the long and short holes were increased with higher blowing ratios. Lutum and Johnson explain this decrease with two effects. Firstly the undeveloped character of the flow inside the cooling hole gives a different flow structure at the hole exit compared to completely developed flow. Once the flow is fully developed it will not change if the hole length is further in-creased, and thus the small influence from larger L/D. The second effect causing the reduced film effectiveness with shorter holes is the increased effective ejection angle that arise as the flow do not have time to completely align with the direction of the hole.
Gritsch et al. [7] investigated the influence of hole length to diameter ratio on film effectiveness for shaped holes. Their conclusion was that Lutum and John-sons results for cylindrical holes are also applicable to shaped holes. Gritsch et al. investigated L/D values between 7.5 and 11.5 and found minor to no impact on the film effectiveness. No investigation were conducted on hole lengths smaller than 7.5 so no conclusion can be made on whether the film effectiveness decreases with shorter hole length, as it does for cylindrical holes.
4.9. MOMENTUM RATIO (I)
4.9
Momentum ratio (I)
The momentum ratio is defined as
I = ρcU 2 c ρ∞U2 ∞ (4) where ρc and ρ∞ is the coolant and free stream density while Uc and U∞ is
the coolant and free stream velocity. As can be seen this closely resembles the blowing ratio.
Both momentum and blowing ratios has been used to scale results from simu-lations and experiments. Baldauf et al. [3], for instance, investigated scaling with both M and I. Their study showed that scaling with the blowing ratio gave good results far downstream from the ejection location. Also, when scaling with blow-ing ratio, the maximum effectiveness occurs at the same downstream distance. Scaling with the momentum ratio, on the other hand, gave a good overlap of the different flow cases close to the ejection location.
4.10
Density ratio (DR)
The density ratio, DR, is defined as the ratio of coolant and free stream density,
ρc
ρ∞, and in a gas turbine it is larger than or equal to one, DR≥ 1. Baldauf et
al. [3] investigated the effect of density ratio on film effectiveness for a large number of blowing ratios. The study included two different density ratios and they found that a lower density ratio between coolant and free stream reduces the peak effectiveness, but also the blowing ratio at which the peak is reached. Worthy to note is that both density ratios produce a similar value for the maximum overall effectiveness. The difference here being that with lower density ratio (1.2) this overall effectiveness is reached at a blowing ratio of 0.7, while for the higher density ratio (1.8) it is reached at a blowing ratio of 1.0. Thus, with a lower density ratio the same overall effectiveness can be reached but while using a lesser amount of coolant.
CHAPTER 4. PARAMETERS IN FILM COOLING
4.11
Boundary layer thickness (δ/D)
Baldauf et. el. [1] states that the boundary layer thickness influences the film effectiveness. The boundary layer thickness falls into the flow properties category and is hard for the gas turbine designer to affect. It is mostly dependent on the distance from the leading edge stagnation point and whether the flow is laminar or turbulent. Cutbirth and Bogard [9] stated that a thicker (implying turbulent) boundary layer generally decreases the film effectiveness. The random motions in the turbulent boundary layer induce a transport of cool air away from the surface, thus lowering the film effectiveness.
Chapter 5
Correlations and Experiments
5.1
Correlations
As stated earlier, correlations are a common tool, used early in the design process to determine the cooling of vanes and blades in gas turbines. Correlations are usu-ally developed using experimental data, both when developing the correlation and when evaluating it. Since it is hard to mimic engine like conditions in an exper-imental setup, correlations tend to be developed for prerequisites quite far from what is present in the actual turbine. For instance, when looking at correlations available in open literature, many are derived for flat plates. A flat plate makes creating and conducting the experiments easier, but is quite far from the curved surfaces of the blades and vanes found in the turbines.
To get an idea of how correlations are built and how they work, a number where collected from open literature and compared to each other. The correla-tions investigated where those by Brown and Saluja [10], L’Ecuyer and Soecht-ing [11], Baldauf et. al. [12], Bunker [13], Baldauf and Scheurlen [3] and Colban et. al. [5]. All of these correlations are developed for cylindrical holes, except for the correlation by Colban et. al. [5], which is for shaped holes. The structure of these correlations varies, some are very complex and some are sim-pler. The Baldauf 2002 correlation is an example of a very complex structure and it consists of more than 25 equations.
CHAPTER 5. CORRELATIONS AND EXPERIMENTS
Equations 5 and 6 show examples of how some of the simpler correlations can look. Equation 5 is from Colban [5] and thus developed for shaped holes.
¯ η= t 1 P + C1M C 2ξ3C (5) Where ξ=4 π X D P D
M·AR and C1, C2and C3 are coefficients based on the current case
the correlation are to be used for.
Equation 6 is one of the correlations presented by Bunker [13] and are used for cylindrical holes. Originally this correlation was intended for cooling from slots, rather than discrete holes, but it has been modified to work for holes as well.
¯ η= x C1 M s+ C2 (6) Where s=Aexit P = πD 4 AR P D
is the equivalent slot width [5].
Figure 2 and 3 show all correlations used for low and high blowing ratios, respectively. Figure 2 and 3 also presents two sets of experimental data by Yuen [14]. Both data sets are for flat plates and one has an inclined plane as “roof”, creating an acceleration in the flow and thus a pressure gradient. This is intended to more resemble the curved surface of the blades and vanes in the gas turbine. L’Ecuyer and Soechtings correlation uses the experimental data to which it is compared as input, and thus, since the figures presents two sets of experimental data, it appears twice.
The figures show that no correlation gives a particularly good prediction of the experimental data. For the low blowing ratio, basically all correlations have the correct shape, with high effectiveness close to the point of ejection (x/D= 0). The exception might be Baldauf 02 that peaks at around x/D= 3−4. Worth to notice is that there is a big spread between all the correlations, even though they are intended to predict the same case. For the high blowing ratio the difference between the correlations becomes even clearer. This visualizes the problems with creating a correlations that works, not only for different experimental data, but also for different levels of blowing ratios.
5.1. CORRELATIONS
Figure 2: Comparison of correlations. Film effectiveness versus distance from cooling hole (i.e. point of coolant ejection) in cooling hole diameters. Low blowing ratio, M=0.5.
Figure 3: Comparison of correlations. Film effectiveness versus distance from cool-ing hole (i.e. point of coolant ejection) in coolcool-ing hole diameters. High blowcool-ing ratio, M=1.67.
CHAPTER 5. CORRELATIONS AND EXPERIMENTS
When comparing the different correlations to each other, it becomes obvious that they did not perform as expected as the difference between them are very large, even for the same input parameters. Still, most of the correlations had been shown to give good results in the papers in which they were presented, so they had the predictive capability of the film effectiveness at least for these cases. One reason for the large deviations might be that the correlations were used slightly outside the parameter span for which they were derived. The very large deviations, however, cannot likely be solely explained by this. The next section investigates another possible cause of the large deviations between the correlations, namely the experiments.
5.2
Experiments
In the previous section it was shown how correlations can differ from each other even though they perform well compared to the experiments for which they were derived. It was therefore suspected that there were large deviations between the experiments, and to investigate this a number of experimental data was collected from open literature, all conducted with similar parameter settings (i.e. blowing ratio, hole angle, hole pitch, etc.).
5.2.1
Experiments in literature
The experiments used were those by Baldauf et. al. [12], Baldauf and Scherlen [3], Lutum and Johnson [8], Schmidt and Bogard [15], Sinha et.al. [16] and Yuen [14].
Figure 4 and 5 shows a comparison of the selected experiments for high and low blowing ratios. In the figures it is seen that the experiments show almost as much spread as the correlations. This is in line with the finding that correlations have a large spread even though they are being used for similar conditions. Since the differences between experiments are so large, the differences in correlations based on these experiments will also be large. No clear explanation for why the different experiments vary this much has been found, but it is possible that differ-ences in how the experiments are conducted, or parameters other than those listed, affect the results.
5.2. EXPERIMENTS
Figure 4: Comparison of experiments with similar parameter settings. Film effectiveness versus distance from the cooling hole (i.e. point of coolant ejection) in cooling hole diameters. (M=Blowing ratio, A=Hole angle, P=Hole spacing, DR=Density ratio)
Figure 5: Comparison of experiments with similar parameter settings. Film effectiveness versus distance from the cooling hole (i.e. point of coolant ejection) in cooling hole diameters. (M=Blowing ratio, A=Hole angle, P=Hole spacing, DR=Density ratio)
CHAPTER 5. CORRELATIONS AND EXPERIMENTS
5.2.2
Project specific experiments
Due to the fact that experiments available in open literature differs so much, and to get better control, experiments were conducted in a test rig at Siemens Indus-trial Turbomachinery AB in Finspång, Sweden. The experiments were conducted to investigate both film effectiveness, η, and heat transfer coefficient, h, for an engine like geometry. The test setup incorporates a single guide vane that can be changed to investigate different cooling hole geometries. The surface temperature is measured using an IR-camera and a transient evaluation method is used to ob-tain η and h. The temperature read from the IR-camera is then processed using Matlab (Mathworks, Natick, MA, USA) to compensate for background radiation, window reflection, etc.
The test rig consists of a test section with a complete guide vane surrounded by walls that give the same pressure distribution around the guide vane as can be found in the actual gas turbine. The air to the rig is heated and supplied using a compressor giving a mass flow rate of 3 kg/s. Cooling air is obtained from a local supply of compressed air and led into the plenum chambers and out through the cooling holes prior to the guide vane being exposed to the hot air. Before the test starts the hot free stream is led through a bypass valve, and thus not passing the guide vane. The hot air is then instantaneous led into the test chamber and temperature measurements are taken from the surface of the vane.
The experimental procedure starts with the heat transfer differential equation, seen in equation 7 (as presented in paper I), which is combined with the heat trans-fer coefficient in equation 10 (see section 6.3.1) and the film effectiveness (equa-tion 1). These equa(equa-tions, together with boundary condi(equa-tions and the assump(equa-tion that heat transfer only occur in one direction (perpendicular to the surface) results in the equation seen in equation 8. This equation together with transitional temper-ature data from the thermal camera results in an overdetermined equation system (two unknowns and one equation for each time-step.) This equation system is solved in Matlab using least squares to obtain values for h and η.
∆(kT ) = ρcp ∂T ∂t (7) TW(t) = Ti+(η (TC− Ti) + (1− η) (Tm− Ti))× 1− erfcx h√Λt k !! (8) 20
5.2. EXPERIMENTS
In equation 8, Tmis the mainstream temperature, which is compensated for
the friction heating that arises close to the surface. Λ is dependent on the ther-mal conductivity, density and heat capacity of the surface. For a more thorough description of the experiments, see paper I.
Chapter 6
Computational Fluid Dynamics
(CFD)
6.1
Introduction to CFD
Computational fluid dynamics is a way to compute and simulate how a fluid in motion behaves. The basis for the simulations is the so called Navier-Stokes equations. These equations are non-linear partial differential equations without any (known) analytical solution, but must instead be solved using numerical iter-ative methods. To solve these equations completely is associated with large costs in computational power, and not practically doable.
Especially the turbulence, i.e. small random fluctuations in the flow, is very hard to resolve. These fluctuations are usually modeled using any of many avail-able so called turbulence models (e.g. the k-, Spalart-Allmaras or k-ω turbulence models). Some methods don’t utilize any modeling at all (so called Direct Numer-ical Simulation, DNS), and there also exists combinations of the DNS and turbu-lence models, so called Large Eddy Simulations (LES), where the large scales in the flow are resolved but the small vortices are modeled. But for practical appli-cations even LES mostly infer to large computational cost to be applicable. Thus, turbulence models are the most widely used method. They utilize an averaging method where an average is calculated for all fluctuating parts of the flow.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
6.2
Mesh
The mesh is the grid used for calculations in the simulations. There exists two general types of computational grids, structured and unstructured. The structured grids are usually created manually, consisting of hexahedral elements. Unstruc-tured grids are generated automatically and can consist of a number of different element types, the most common being tetrahedrons.
The meshes, as stated earlier, consist of a number of elements and in each corner of these elements is a node located (thus hexahedral elements have eight nodes and tetrahedral four). Nodes are shared with neighboring elements (i.e. a node in a hexahedral mesh is shared between eight elements.) and it is in these nodes that the fluid properties are calculated. The solution is iterated in each node based on the values in the neighboring nodes. Thus, a higher number of elements results in a higher number of nodes and ultimately more calculations necessary (i.e. higher calculation costs). This results in a trade-off between reduced mesh size, giving faster computations, and higher mesh densities required for capturing the details of the flow.
Manually created structured grids usually allows for better control for the user over the generated mesh and allows for denser node concentration in parts where better resolution is deemed necessary. This better control comes at a cost since making the grid usually requires significant time and work. Also, structured grids tend to have a higher number of nodes compared to a comparable unstructured grid.
6.3
Project specific CFD
Extensive CFD-simulations have been performed on the test rig, with investiga-tions of both film effectiveness and heat transfer coefficient, as well as an aero-dynamic validation of the pressure around the guide vane. The simulations were conducted using different turbulence models and different geometries based on the test rig. The main objective has been to reduce the mesh size by reducing the model and thus limit the computational cost.
The reduction in the model is not meant to be a simplification (i.e. less details in the geometry), but instead use a smaller domain with the same level of detail. This is made by “cutting” the full domain into smaller segments. Basically two different cutting methods have been used. The first is that the center piece of the test rig has been extracted, and thus the walls omitted. For this geometry, a piece wide enough to include two cooling holes (one from each row in a two row setup) is extracted from the geometry, and the walls are replaced by periodic boundary conditions. That means that the domain includes a full length inlet and outlet, but 24
6.3. PROJECT SPECIFIC CFD
that any influence the wall has on the flow are not captured.
The second method for reducing the domain is to cut out only the part that is being studied, in this case the guide vane (specifically the suction side of the guide vane). This means that large portions of the domain are being left out, e.g. the inlet and outlet, which in turn means that the boundary conditions will be put close to the part being investigated. Normally when conducting CFD simulations, the boundaries are being placed well away from the object being studied, so that the flow has time to “adapt” and no traces of the boundary condition affect the results (e.g. velocity profiles have time to develop). Having the boundary conditions close to the investigated object means that the flow will not have time to adjust, which in turn puts higher demands on the boundary conditions being correct. To accomplish this, the boundary condition for this reduced model is taken from a simulation of the full domain. Thus a simulation is run on the full domain and the solution from this is taken as boundary condition for the reduced model. Then different cooling configurations can be tested on the smaller model.
Using these techniques it is possible to greatly reduce the mesh size, and thus computational time, while not making any simplifications of the physics of the flow.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
6.3.1
Full domain
The full domain used for simulations of the entire test rig can be seen in ure 6(a) and the mesh created for this model consists of 10 Million elements. Fig-ure 6(b) shows the vane geometry and how the coordinate system of the vane is oriented. The normalized coordinate S (goes from 0 to 1) starts at the trailing edge and moves over the suction side to the leading edge and via the pressure side back to the trailing edge. The suction and pressure side are so named since the pres-sure in these locations are low respectively high. The stagnation point is located at approximately S=0.55. (For a more thorough description of the experimental equipment, see paper I).
(a) Geometry used for simulations of the full domain.
(b) Figure showing the vane, the coordinate system orientation and the location of suction and pressure side of the vane.
Figure 6: Geometry of the full uncooled model.
For a first evaluation of the accuracy of the simulations, an aerodynamic com-parison were made. The pressure coefficient from the experiments were compared to the simulations and the results can be seen in figure 7.
The figure shows that the incompressible simulation is not able to capture the flow characteristics on the suction side of the guide vane (S=0-0.45). This is supported by the flow velocity which in this region reach as high as Mach 0.5, thus implying compressible flow. (The rule of thumb is that velocities higher than Mach 0.3 results in compressible flow. [17]). Because of this all simulations conducted in this study are made using compressible flow, utilizing the ideal-gas law to calculate the air density.
Two different turbulence models were tested, the realizable k- (rke) and the
SST k-ω (SST), and as can be seen in figure 7 both models give similar results,
and reasonable accuracy with experiments. The Normalized Root Mean Square error (NRMS) is calculated for each simulation and the results can be seen in the 26
6.3. PROJECT SPECIFIC CFD
Figure 7: Comparison of pressure coefficient for experiments and simulations. The in-compressible simulations clearly fails to capture the flow on the suction side of the vane.
legend in figure 7. The NRMS-error is calculated as the root of the sum of the square of the difference in each measured point. This value is then normalized with the difference between highest and lowest experimental data. The equation for calculating NRMS can be seen in equation 9.
N RM S= v u u u t n X 1 (Cpexp,n− Cpsim,n) 2 n Cpexp,max− Cpexp,min (9) Once the aerodynamic verification had shown that the simulations were able to match the flow characteristic of the experiments, simulations were conducted to investigate whether the simulations were able to also predict the heat transfer characteristics. For the uncooled configuration, only the heat transfer coefficient can be investigated. Since no film cooling is present no film effectiveness can be evaluated.
The convective heat transfer equation, equation 10, states that the amount of heat transported between a solid and a fluid is dependent on the temperature dif-ference between the two, as well as the heat transfer coefficient, h. The value of the fluid temperature, Tf luid, is not obvious since it, in film cooling applications,
temper-CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
atures. This dependence makes the fluid temperature vary greatly downstream of the coolant hole [18]. The heat transfer coefficient is dependent on many external factors connected to flow and surface properties. The heat transfer coefficient is very sensitive to these factors and thereby hard to assess.
Q= h(Tsolid− Tf luid) (10)
To evaluate the heat transfer coefficient, two simulations has been conducted for each investigated configuration. One where the surface temperature of the vane is kept constant, and one where the vane surface is modeled as an adiabatic surface. The simulation with constant temperature results in a temperature differ-ence between surface and the passing flow, and thus, according the equation 10, results in heat being transferred. This gives one of the temperatures and the heat transfer in the equation, but the temperature of the flow is still necessary to be able to calculate h. This temperature is obtained in the second simulation where the vane surface is assumed to be adiabatic. To ensure that no heat transfer oc-curs between the surface and the fluid, they need to have the same temperature and thus the surface temperature obtained from this simulation is the same as the fluid temperature close to the wall, and gives the last temperature. This method to obtain the fluid temperature has, for instance, been used by Harrison and Bogard [19]. The two temperatures and the heat transfer obtained from these simulations can be used together with equation 10 to obtain the heat transfer coefficient.
As stated earlier the objective of film cooling is to keep the temperature of the material low to avoid failure. The temperature is dependent on the amount of heat transferred into the material, and as can be seen in equation 10 the heat transfer is in turn dependent on the heat transfer coefficient and the temperature difference between fluid and solid. Thus, both the heat transfer coefficient and the film temperature is of interest when studying film cooling. The film temperature is, as stated previously, normally scaled and displayed as the film effectiveness (see equation 1). Therefore both these parameters are studied.
Figure 8 shows the obtained heat transfer coefficient from the full domain simulations together with the experiments. The data in this graph is taken from the center section of the vane. The section where data is extracted from has the same width as the narrow domain presented later, and this is done to make the comparison between the two models easier and more fair.
As can be seen in figure 8, a general discrepancy exist between the experi-mental and the simulated values for HTC. The simulations generally overpredict the experimental values. Harrison and Bogard [20] stated that when comparing experiments with simulations, trends rather than absolute values should be con-sidered. The trends for these simulations show quite clear resemblance with the 28
6.3. PROJECT SPECIFIC CFD
Figure 8: Heat transfer coefficient for experiments and simulations of the uncooled full domain. Simulations generally overpredict the experimental data, except for the peak at the transition region.
experiments. For instance, at the stagnation point (S≈0.55) the experiments show a small but distinct “bump” that can also be seen in the SST-simulation. Also, the maximum peak (S≈0.4) appears at the same location for both experiments and simulations.
On the suction (low S) and pressure (high S) sides the trends of the simulations clearly follows the experiments, with the exception being the SST close to the peak on the suction side. The rke also misses the peak close to S=0.4, although not as big as the SST. Also, both models fail to capture the rapid increase of HTC from the stagnation point over to the suction side (S=0.55-0.4). This is expected, however, as one of the limitations of these turbulence models is that transition from laminar to turbulent flow is not adequately captured, and that is exactly what happens here. As the flow accelerates from the stagnation point over to the suction side it experiences transition from laminar to turbulent, where the latter is associated with much higher heat transfer coefficient. The turbulence models don’t make any clear distinct difference between laminar and turbulent flow, and thus are unable to correctly capture the transition between these two.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
6.3.2
Narrow domain
Figure 9 shows the geometry used for simulations of the narrow domain. As stated, the narrow domain consists of the center part of the full domain. Instead of the walls of the full domain, the narrow uses periodic boundary conditions on the sides. This implies an infinitely long guide vane, but as only the center part is of interest, and the objective of this study is to investigate if this simplifica-tion/assumption is acceptable, this narrow domain is a good representative of the full domain.
Figure 9: Geometry of the narrow model. Only the mid-section of the full model is extracted, and periodic boundary conditions are used on the sides.
Figure 10 shows the aerodynamic verification for the narrow domain com-pared to the experiments. As for the full domain, and as expected, the incom-pressible simulation fails to correctly capture the pressure coefficient on the suc-tion side of vane. This is, as for the full domain, caused by the high flow velocity giving compressible flow in this region.
6.3. PROJECT SPECIFIC CFD
If the narrow domain in figure 10 is compared to the full domain in figure 7, no noticeable difference can be seen between the two. Worthy to notice is also that the incompressible simulations have the exact same NRMS-error. This does not mean that they are exactly the same, but that they have the same deviation from the experimental data. For the two compressible simulations the NRMS-error is not exactly the same, but very similar.
Figure 10: Comparison of pressure coefficient for experiments and simulations with the narrow domain. Results show clear resemblance with those for the full domain (figure 7).
Using the narrow model obviously works fine for the aerodynamics of the test rig. Does it also work adequately for the heat transfer? The heat transfer coefficient for the narrow domain is presented in figure 11. The figure shows that the differences between the narrow and full model are quite small. As with the full model, the narrow fails to capture the significant rise in HTC at the beginning of the suction side, as well as the peak appearing at S≈0.4. The difference between the two turbulence models is more significant than the difference between the two geometries. For instance the small “bump” visible at S≈0.55 with the SST model is visible for both geometries (although not as distinct for the narrow). Close to the leading edge the two turbulence models give similar results, while downstream on the pressure and suction side, the similarities lies more with the different geometries.
That the full and narrow domain differs away from the leading edge is (at least partially) caused by wall effects in the full domain. The interaction between the vane and the side walls of the full domain give rise to vortices that grows as they
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
progress over the vane. As the vortices reach the trailing edge they have grown and covers a large portion of the vane. The narrow domain doesn’t experience these effects, and thus there is a difference between the two models close to the trailing edge. Even though the vortices themselves are not included in the data taken from the central parts of the full domain, their effects on the flow can still be seen. Figure 12 shows the contours of the heat flux on the suction side of the vane as obtained from the simulations. The leading edge is located to the right in the figure and the influence of the wall effect can clearly be seen, starting at the leading edge and growing towards the trailing edge.
Figure 11: Heat transfer coefficient for both narrow and full domain together with experi-mental results. Only data for the same width as the narrow domain are compared, thus all data are for similar domains.
Overall the effects from the walls are quite small, at least when looking at the center section of the vane. If contours from the narrow domain where to be projected on top of the full domain, only minor differences would be visible between the two models. Also, the differences seen in the data presented in figure 11 are relatively minor.
6.3. PROJECT SPECIFIC CFD
Figure 12: Heat flux on the suction side of the guide vane. The leading edge is located to the right and the wall effect vortices due to the interaction between wall and vane can be seen, starting at the walls at leading edge and growing towards the center of the vane as the move towards the trailing edge.
Narrow Cooled Domain
Cooling holes were added to the narrow domain to simulate a vane with film cool-ing. Two staggered holes were added that, together with the periodic boundary conditions, simulated an infinitely long vane with two rows of cooling holes. As with the uncooled narrow domain, the wall effects are missing. The decision to use the narrow domain for the cooled simulations is necessary. This model requires a mesh size of 20 Million cells, for only two cooling holes. If all 18 cooling holes that exist in the test rig were to be simulated, the mesh would consist of almost 200 Million cells. Added to that is the number of cells needed to resolve the boundary layer at the side walls. This would give a mesh size of over 200 Million, which is too large for most applications. Figure 13 shows the cooled domain (left) and details of the mesh (right).
Since no simulation of a cooled full domain has been made, a comparison between that and the narrow is not possible. Thus it is hard to say whether the narrow domain is a good representative for the full domain when it comes to cooling. The results presented in this section should instead mainly be viewed as an example of what these models are supposed to be used for: a fast and straight-forward way of testing different cooling configurations.
The aerodynamic verification of the cooled model can be seen in figure 14. It shows that the only differences between the cooled and uncooled simulations lies after the cooling holes (located at about S=0.4). On the pressure side and suction side prior to the cooling holes, the two simulations gives exactly the same result. That the difference between the cooled and uncooled domain is small can also be seen in the NRMS-error that, rounded, is exactly the same for both simulations. The only visible differences lie behind the cooling holes, which indicates that the simulations are very similar except for just the ejection of coolant.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
(a) Guide vane of the cooled narrow model. Same width as the uncooled narrow model, but with two cooling holes and cooling supply chamber added.
(b) Close-up of the mesh of the cooling hole exit at the guide vane. Shows how many cells are necessary to resolve the details at the hole exit.
Figure 13: The cooled narrow model.
Figure 14: Pressure coefficient for the cooled narrow model and uncooled narrow model. Effects of the cooling holes can be seen at S=0.4.
6.3. PROJECT SPECIFIC CFD
Figure 15 shows the heat transfer coefficient for the cooled model compared to experiments for the part downstream of the cooling holes. Close to the cooling hole the simulations underestimate the heat transfer coefficient, but further down-stream the difference between simulations and experiments is small. Whether the discrepancy is caused by the narrow model or the computational method in itself is hard to say. To know that it would be necessary to have a simulation of the cooled full domain, which is, for reasons explained earlier, not available. Some conclu-sions can still be drawn about the behavior of the different simulations. This is seen more clearly in figure 16 that shows the film effectiveness (defined in equa-tion 1). The figure shows that all simulaequa-tions overpredict the value obtained in the experiment, and whether this is caused by the model or method is hard to tell. Interesting to note is that the three blowing ratios follow the theories explained earlier. The low blowing ratios peak at the hole and diminishes downstream as the coolant diffuses away from the surface, while the high blowing ratio acts in the opposite way. The coolant is ejected into the free stream giving a low effec-tiveness close to the hole, but then diffuses back to the surface, giving a higher effectiveness further downstream.
As can be seen in figure 16, the simulated values are generally overpredicting the experimental. This might be due to a limitation in the computational method. RANS turbulence model are well known to mispredict the lateral spreading of the coolant [21], and thus the mixing between coolant and free stream is not ade-quately simulated, resulting in a to high absolute value of the cooling.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
Figure 15: Heat transfer coefficient for the cooled full narrow domain compared to exper-iments. Only the cooled part of the guide vane is shown. Cooling holes is located at about S=0.4 and the flow moves from right to left.
Figure 16: Film effectiveness for the cooled full-narrow domain. Three different blowing ratios for the simulations together with one blowing ratio for the experiments. Only the cooled part of the guide vane is shown. Cooling holes is located at about S=0.4 and the flow moves from right to left.
6.3. PROJECT SPECIFIC CFD
6.3.3
Short domain
The short domain consists of only the suction side of the guide vane between the S-coordinates 0.007 and 0.475, and can be seen in figure 17(a). Having the inlet so close to the area being investigated means that the flow cannot fully adjust and form the correct wall boundary layers, pressure gradients, etc., thus putting high demands on the boundary condition. Therefore, the inlet boundary condition is taken from the full domain simulations.
The mesh of the short domain consists of 18 Million elements. This is still a quite high number of cells, but far less than the 200 Million estimated necessary for the full domain with cooling. Also, the smaller domain allows for better node density and easier control of node placement, i.e. a more efficient cell usage.
(a) The short model is a cut-out of the suction side of the full model with cooling.
(b) A narrowed version of the short model. Wide enough to include two cooling holes.
Figure 17: The short models. Left shows the short and right the short narrow model.
Figures 18 and 19 show the heat transfer coefficient and film effectiveness, respectively, for the short domain. The figures give two sets of data, both for a narrow domain (i.e. for a section wide enough to contain two cooling holes) and for a model with full width. Figure 18, showing the heat transfer coefficient, give that close to the hole, all results, both simulations and experiments, show a somewhat uneven and jagged behavior. This implies a disturbed flow in this area, as the coolant exits the cooling holes. Further downstream a number of interesting phenomenona can be seen. The first is the clear difference between the simulations for full span and mid-section. The reason for this difference has been mentioned previously, i.e. the wall effects, and was shown in figure 12. The wall effects forces the coolant towards the mid-section of the vane, and thus leaves uncooled sections on the sides. This gives completely different flow situations in the center compared to the sides, and thus a big difference between the full span and mid-section measurements. Any difference in the experimental data for
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
full and mid-sections is barely seen at all, implying that the wall effects is not as distinct in the experiments as in the simulations.
The film effectiveness in figure 19 show similar behavior as the heat transfer coefficient. A clear difference can be seen between the simulations for the full span and those for the mid-section. The full span simulations gives lower effec-tiveness than the mid-section ones. This is caused by the wall effect vortices, that leaves completely uncooled sections at the vane sides that lowers the effectiveness when it is averaged over the full span.
Figure 18 and 19 show that the results from the full span coincides and moves together as the flow closes in on the trailing edge. Once again the cause is the uncooled areas at the vane side. Since all cooling are forced towards the center part of the vane, the flow properties at the side will be the same, regardless of what the cooling properties looks like. Thus these unaffected areas will act to even out the average.
The wall effects mentioned in the previous sections is a well known phe-nomenon in gas turbines. Even though they are not so prominent in the exper-iments performed in this project, they can be seen in experexper-iments e.g. [22, 23]. The vortices start at the intersection of wall and vane at the leading edge and cre-ates what is known as a “passage vortex” on the pressure side of the vane. This vortex leaves the pressure side of the vane and moves over to the suction side of the next vane [24]. Thus the vortices seen is actually created at the vane next to the vane being studied. In this case the vortex is created at the wall of the experimental equipment imitating the next guide vane (see figure 6(a)).
6.3. PROJECT SPECIFIC CFD
Figure 18: Heat transfer coefficient for the short model. One set of data taken for the full span, the other for a mid-section with the same width as the narrow model.
Figure 19: Film effectiveness for the short model. One set of data taken for the full span, the other for a midsection with the same width as the narrow model.
CHAPTER 6. COMPUTATIONAL FLUID DYNAMICS (CFD)
Short narrow domain
To further reduce the model size, the short model were cut into a narrow strip, just like the full model was. The resulting model can be seen in figure 17(b). This, of course, further reduced the mesh size, which for this model were no larger than 3.5 Million cells.
The results for this simulation showed similar behavior as those presented for the full narrow and short models. The big difference lies close to the cooling holes where the short narrow models shows a fluctuating and jagged behavior. This is probably caused by a combination of the model slice being thin, that the flow in the region close to the cooling holes is very disturbed and that the averaging needs more points to smooth out these large variations. The results for the short narrow can be seen in paper III.
6.3.4
Conclusions
The results presented here shows that it is possible to reduce the model size while maintaining the accuracy of the simulations. Making this reduction will drasti-cally shorten the computational time of the simulations. To accurately predict the absolute values of film effectiveness and heat transfer coefficient, however, is a tricky objective. The simulations presented in this thesis are able to capture the behavior of the heat transfer coefficient and film effectiveness, but not always the exact values. It can be concluded that CFD is a powerful tool to use, for example, when parameter studies are conducted, for instance to compare different cooling configurations, but that other tools are needed to qualitatively determine the exact performance of the cooling.
