Analysis of Design of an Intermediate Turbine Duct

Submitted in partial fulfillment of the requirementsof the degree of

Bachelor of technology

By

Rakshit CRoll No.110010044

Under the Guidance of

Prof. A M Pradeep

Aerospace EngineeringIndian Institute of Technology

Bombay

November 2014

ii

Approval Sheet

This report entitled ’Analysis of Design of an Intermediate Turbine Duct’ by RakshitC is approved for the degree of Bachelor of Technology

Examiner

_______________

Supervisor

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Date: ______________

Place: ______________

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Declaration

I declare that this written submission represents my ideas in my own words and whereothers’ ideas or words have been included, I have adequately cited and referenced the orig-inal sources. I also declare that I have adhered to all principles of academic honesty andintegrity and have not misrepresented or fabricated or falsified any idea/data/fact/sourcein my submission. I understand that any violation of the above will be cause for disci-plinary action by the Institute and can also evoke penal action from the sources whichhave thus not been properly cited or from whom proper permission has not been takenwhen needed.

_____________________

(Signature)

_____________________

(Name of Student)

_____________________

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Date:_______________

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Abstract

Intermediate turbine duct represents the flow path between the high pressure and thelow pressure turbine of a high-bypass ratio turbofan engine. There is a growing demandin the aviation industry for higher efficiency engines which leads to increase in bypassratio. The radial offset causes these duct to have a pronounced S- shaped design. Due tothe difference in rotational speed of differnt spools, this duct needs to diffuse the flow tolarger turbine with minimal pressure loss and flow distortions. As the trend of increasingbypass ratio continues, the design of these diffusers becomes more significant,as the shapeof these duct can affect the net weight of an engine.

Shape optimization used for turbomachinery applications has become a powerful aero-design tool. In this paper we discuss the preliminary considerations for the design of anInter Turbine Duct. Parametrization approach of Response surface methodology alongwith a simple Genetic Algorithm is used to design and optimize the length of the duct.The choice of length optimisation with constrained limits, is preffered as it is a low fidelityand less computational intensive method. The optimized duct is then analysed externally,for its pressure recovery and presence of wakes. The final goal is to create a inter turbineduct which is smaller in length , and has comparable flow charecteristics of the initialduct may be with active/passive flow control.

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Aknowledgements

I take this oppportunity to express my sincere thanks to my guide Prof. A M Pradeep.He has been very resourseful and supportive, and has motivated me throught. I wouldlike to thank Mr. Shyam Sundar Shukla, M.tech student, for providing the computationalflow analysis of the ducts. Also, I am grateful to Prof. Lars Erik Eriksson of ChalmersUniversity of technology for providing us a copy of the papers that he had worked onand for his quick reply. I would like to thank, Kangal or The Kanpur Genetic Algorithmlaboratory at IIT Kanpur for their robust algorithm, which helped us in optimization ofthe duct.

I like to thank my friends Varun Sudharshanan for his support during this semesterinn many academic and non academic matters and Sai Krishna for his assistance in codingthe program for optimization of the duct. At last but not the least, I would like to thankmy parents, all my friends for their continuous and everlasting motivation and support.

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Contents

List of Figures viii

List of Tables ix

1 Introduction 1

2 Literature Review 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Review of literature on Interturbine Ducts: . . . . . . . . . . . . . . . . . 22.3 Review on Optimization: . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Preliminary Considerations 43.1 Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1.2 Methods of Parametrization . . . . . . . . . . . . . . . . . . . . . 4

3.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.1 Objective function and Optimization Approach . . . . . . . . . . 63.2.2 Optimization Method used . . . . . . . . . . . . . . . . . . . . . . 7

4 Problem Definition 84.1 Defining the Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1.1 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.1.2 Parametrization and the Geometry . . . . . . . . . . . . . . . . . 10

4.2 Objective function and Constraints . . . . . . . . . . . . . . . . . . . . . 114.2.1 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.2 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Optimized Design 135.1 Performance of the Baseline Duct . . . . . . . . . . . . . . . . . . . . . . 13

5.1.1 Pressure Contours . . . . . . . . . . . . . . . . . . . . . . . . . . 135.1.2 Velocity Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2 Optimized Duct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Flow Charecteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.4 Comparision with Baseline Geometry . . . . . . . . . . . . . . . . . . . . 16

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6 Conclusion 176.1 Scope of Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Bibliography 18

A Understanding the Optimisation Program 20A.1 The Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . 20

A.1.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20A.2 The Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

viii

List of Figures

4.1.1 The Center-line and Area variation Data obtained from Chalmer’s Literature[10] 9

5.1.1 Pressure Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.1.2 Total Pressure Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.1.3 Velocity Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.3.1 Velocity Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

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List of Tables

4.1.1 Tabulated data of Center-line and Area variation . . . . . . . . . . . . . 10

5.2.1 Table containing values of Mean line and Area at given length . . . . . . 15

1

Chapter 1

Introduction

Most of the multi spool jet engines of today consist of low pressure turbines whichare at a lower speed and higher radius than high pressure turbines. The duct thatconnects these two is annular and will result in having a pronounced S-shape. Increasingtrend in higher bypass ratio jet engines is resulting in longer intermediate ducts andhigher variation of rotational speed between the two turbines. This difference leads tocomplicated flow patterns, and in order to tackle this longer ducts were sought. Theextra weight that is contributed by the length of these duct is of major importance. Flowcomplications are caused by the strong curvature with swirling and diffusive flow. Thereis a risk that end wall separation occurs and these separations could cause unwantedlosses and asymmetric flow distortions. Shape optimization in turbomachinery design isan important tool, and is possible due to the advent of powerful computational machinesfor performing complex CFD routines.

In Chapter 2 we discuss on the literature that is available on Inter turbine duct andshape optimization. Intermediate turbine ducts are fairly new topic of research and onlya handful of literature is available, where as Shape optimization has become a majordesign tool in the modern era due to the advent of faster computers. In chapter 3,The optimization and parametrization model for the geometry is discussed. GeneticAlgorithm is one of the widely used optimization method for finding a global minima.New and much complicated evolutionary algorithms promise better result but are verytaxing on the resources. In chapter 4, we discuss the problem that is being put up andthe initial model, baseline geometry and the scheme is defined. In chapter 5, the obtainedlow fidelity optimization duct is presented. A CFD analysis done on the same externallyis put and is compare with the baseline geometry. Finally, in chapter 6, scope of futurework is discussed as the project moves to its second stage and a brief summary of thewhole is presented.

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Chapter 2

Literature Review

2.1 IntroductionThe advent of higher bypass ratio engines1, in recent years have sparked interest in

the field of Intermediate turbine ducts. There are numerous works carried out in shapeoptimization in design of turbomachinery, and thus proving it to be a robust approach.A lot of research work has been carried out on diffuser flows but only fewer studies of theflow within annular S-shaped ducts are available in open literature. Many of them dealthe flow in intermediate compressor ducts.

Intermediate ducts on the other hand have limited literary work although a goodamount of study, both analytical and experimental, is done at Chalmers university ofTechnology by Arroyo Osso C[1], Wallin F[2] , Alexson L-U [3] and many papers by MarnA, Gottlich E et al of TU Graz[4, 5, 6]. Apart from these there are few other importantwork on this field. Few of these work which are essential for design and optimization ofthe intermediate duct were studied.

2.2 Review of literature on Interturbine Ducts:One of the first study of diffuser flows was done by Sovran and Klomp in 1967[7],

it provides a performance chart for straight-walled annular diffusers and is still used asa reference to classify intermediate turbine diffusers regarding their criticality. Later in1978, the Energy Efficient Engine Component Development and Integration Program(E3program) between NASA and Pratt and Whitney, the need of more aggressive tur-bine transition ducts was considered to be an enabling factor for high-bypass turbofanengines[8]. The pioneer study in open literature on Inter turbine duct, was on the in-fluence of swirl on the performance of duct, carried out by Dominy RG,et al[9]. Lateron many studies, both experimental and computational, were carried out on the flowaerodynamics of an annular S-shaped duct.

The first attempt on design of an Intermediate duct was carried out by Wallin F etal[10]. Design of Intermediate duct, is carried out by shape optimization method. Shapeoptimization method, unlike analytical method, is a recent method in obtaining optimizedmodels for various applications. It was possible due the rise of modern computationalmachines with higher computational capabilities. It involves changing the shape of themodel to be optimized every run and is then computed for its performance characteristics,

1Rolls-Royce Trent 1000(bypass ratio of 10.9), being used in Boeing 787 Dreamliner, [21]

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then based on selected method of optimization change in shape is carried out in a recursiveloop until the stopping criterion is reached. The several works by Wallin F, Eriksson L-E,et al[10, 11, 12, 13], are done on the same basis. Shape optimization is used along withResponse Surface Methodology(RSM) for optimization. The robustness of RSM can beseen from the work of Madsen et al[14]. The work by Gottlich E [15], on summarizingthe current stage at which research on intermediate turbine duct and where it is headed,is a useful source of information on various aspects of the duct.

As ducts are made more aggressive, the flow will experience swirls and separationwhich will result in pressure loss and flow distortion. These losses are not desired as theybring down the overall efficiency of the engine. Flow control is a method to reduce theseeffects, various active and passive flow controls are studied as active research. Differentmethods of flow control are documented and vortex generators is one of the popularpassive control methods, the large study on it asserts the same. The use of vortexgenerators for passive flow control in intermediate turbine ducts is studied byWallin F andEriksson L-E[16]. Flow control can improve the performance characteristics significantlyand will most likely be incorporated in future engine designs.

2.3 Review on Optimization:Study was done on the optimization techniques that existed and were being used, a

sound knowledge in this area would be helpful during the entire period of the project. Thetextbooks referred were Optimization for Engineering Design[17], and Multi-ObjectiveOptimization Using Evolutionary Algorithms[18] both written by Prof. Kalyanmoy Deb.In order to understand the optimization approaches used in shape optimization the workby E. Taskinoglu et al[19, 20] on Design of a Submerged Air Intake was studied. Sincethe objective function of our design problem is not an explicit function of the designvariables, the function evaluation of optimization needs to be done externally. Thus, useof simple gradient methods for optimization will not suffice. Sequential Programmingmethod would be a less computational intensive algorithm for optimization, and is idealfor low fidelity analysis. Evolutionary Algorithms, although being computational taxing,have evolved to reach global minima very precisely. The new methods, like particle swarmmethod, promise better results than traditional genetic algorithms.

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Chapter 3

Preliminary Considerations

Any design problem, or any problem, needs few initial conditions defining the ques-tions posed and constraints specified. It was planned that the whole design processwould be done in two parts, first Low fidelity approach and second a high fidelity ap-proach along with validation. It was assumed that for low fidelity analysis a gradientbased solver with objective function as pressure loss will be used. The parametrizationmodels, and optimization methods were later decided.

3.1 Parametrization

3.1.1 IntroductionThe first step in the shape optimization process is the parametrization. Parametriza-

tion, as the name would suggest, the process of deciding and defining the parametersnecessary for a complete or relevant specification of a model or geometric object. Mostoften, parametrization is a mathematical process involving the identification of a com-plete set of effective coordinates or degrees of freedom of the system, process or model,without regard to their utility in some design. Parametrization helps in breaking downthe problem into set of few parameters which govern the design, and may be propertiesrelevant to the component. Selection of optimization parameters has to be done withcare so as to reduce the computational burden of CFD calculations

3.1.2 Methods of ParametrizationFor our case, Intermediate turbine duct, the parametrization of geometry can be

done in a couple of different methods. The work by Gräsel, Jürgen titled, "Parametricinterturbine duct design and optimization."[23], deals with the topic of parametrizationof the ducts. Two approaches are studied in this literature, and the merits and de-meritsof each are stated.

3.1.2.1 B-spline methods

For Case-1, Duct mean line and Area(height) was considered and for Case -2, huband casing endwalls was considered. It was found that, Hub and Casing method reducedthe parameters that we deal with as effect of some of the parameters can be ignored

5

contrary to the first case. Both approaches used, few points as parameters and B-splinesto interpolate the geometry variation.

3.1.2.2 Perturbation method

There is alternative method to parametrize for optimization and this can be seen in theperturbation analogy approach used by Wallin F[11]. The idea is to apply perturbationsto a reference duct, we know that there exists a perturbation such that it optimizes theduct geometry with respect to our defined goal-function. Hence an approximation tothis perturbation is sought. A linear combination of basis functions is used to constructthis approximate perturbation. T o ensure that this approximation is the best possible,orthogonal polynomials (Pi ) are used as basis functions. All polynomials are defined onthe interval 0 ≤ x ≤ L. In order not to change the reference design conditions at inlet oroutlet, the boundary conditions are imposed on the orthogonal polynomials.

Pi(x) = dPi

dx= d2Pi

dx2 = 0 atx = 0,x = L

(3.1.1)

The first basis function is defined as the lowest-order nonzero polynomial satisfyingthese boundary conditions. The basis functions are orthogonal to each other accordingto the norm

ˆ L

0Pi(x)Pi(x)dx

= 0 as i 6= j

6= 0 as i = j(3.1.2)

The next basis function is the lowest-order non-zero polynomial that satisfies theboundary conditions (1) and is orthogonal to all previously defined basis functions ac-cording to (2) and so on. An infinite number of orthogonal polynomials can be defined,but in the present work only the two first polynomials (P1 and P2) have been used. Thereference geometry is modified by adding (or subtracting) perturbations to functions.

The Polynomials P1 and P2 are defined as

P1(x) = x3(x− L)3 (3.1.3)

P1(x) = x3(x− L)3(x− L

2 (3.1.4)

3.1.2.3 Conclusion

To summarize, of the two methods used, the method of perturbation model feels morepromising than just plain hub and shroud. It deals with lower constraints number anda lesser complex parameters. On the contrary other approach requires more numberof parameter to be able to create a spline. Hence, Perturbation model was chosen.The parameter themselves will be discussed in the next chapter along with the baselinegeometry.

3.2 OptimizationThere numerous approaches and methods exist for optimization of a given problem.

Optimization schemes can be broadly classified into 2 categories

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1. Schemes to find local Minima (eg: Newton Raphson method)

2. Schemes to find global minima (eg: Evolutionary Algorithms)

Local minima although seeming useless, can be very useful for short searches and quickresults. The obtained extremum may not be the global optimum but the amount ofresources needed for the same is minimal. This might not seem significant for simplerproblems. When real world problems are considered, due to the complexity of the problemposed, the computation time and resources become more significant. There is a need tocut down cost intensive approaches to the minimum.

Searching for global extremum is a must for any complex problem as the offset betweenthe values of local and global extremum can be quite significant, in many cases. Thesemethods are computationally intensive compared to gradient methods. Some of themethods like genetic algorithm, have been used extensively and the robustness of theirsolution is proven. Extensive research is still going strong in this area even today. Forcomplex systems like Aircraft engine, even a single percent improvement in the overallsystem can be helpful in making it more cost effective in the long run.

3.2.1 Objective function and Optimization ApproachShape optimization, optimizes the shape or geometry of a given object subject to con-

straints and the optimizing function. As with most shapes which needs to be optimized,the performance characteristics of each shape generally do not have a proper equationin most complex scenarios. This is especially true with shapes that are subject to fluidflow with turbulence, most of the cases CFD and/or experimental data is used to assesthe performance. This leaves us with no explicit function to be an objective function foroptimization.

For low fidelity optimization of the duct, we generally prefer simple and quick methodfor optimization, which then be used in a high fidelity approach to obtain optimizedduct. A simple gradient based optimization would be sufficient at this stage for analysis.Due to the very nature of the problem that is,no explicit function for calculating flowcharacteristics, or performance parameters the optimization method that can be usedfor optimization becomes restricted in type. This is mentioned in the work done byTaskinoglu et al[19], on shape optimization of submerged intakes.

Two different approaches can be used for optimization

3.2.1.1 CFD solver and Simple optimizer

This method despite being more accurate than the alternative, is computationallyintensive and time consuming. The data from CFD solver needs to be fed to the optimizerevery time and it optimizes based on the data. This approach also restricts the type ofoptimizers that can be used, as no explicit objective function exist. None of the gradientbased methods work, only optimization models that can be used are the ones which donot depend on objective function at all. Most of regression based methods, EvolutionaryAlgorithms fit into this category.

3.2.1.2 Different Objective function

Consider a different parameter instead of performance parameter, which can be linkedto the parametrization or the constraints directly. In this case a function can be defined

7

and simpler and easier methods can be used for optimization.The optimization of shapefor a low fidelity analysis without the use of CFD, led us to choose length as objectivefunction. Length being an important parameter which needs to be optimized for anintermediate duct, can be directly linked to it’s geometry and easier low fidelity analysiscan be done.

3.2.2 Optimization Method usedGenetic algorithm (GA) is a search heuristic that mimics the process of natural selec-

tion. This heuristic (also sometimes called a meta-heuristic) is routinely used to generateuseful solutions to optimization and search problems. Genetic algorithms belong to thelarger class of evolutionary algorithms (EA), which generate solutions to optimizationproblems using techniques inspired by natural evolution, such as inheritance, mutation,selection, and crossover

Kangal, or The Kanpur Genetic Algorithm laboratory at IIT Kanpur is generousenough to provide source codes for many of the popular evolutionary algorithm, as freeaccess to all, in their website.These sources codes were extremely useful in reducing theworkload involved in coding the optimizer. Time and again GA’s have proven theirrobustness in many studies. It is due to this robustness and the ease of availability ofsource code for the optimizer, they are implemented in our optimization.

A simpler gradient based optimization could have been used, but due to the simpleobjective function of length, and constraints that were defined a global optimizationmethod was chosen1. The computation time of this method, due to the objective function,is less than 60 seconds. Hence, it is ideal for a low fidelity analysis.

1Refer Appendix A for more details on the code that was used for defining objective function andconstraints

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Chapter 4

Problem Definition

In the chapter, the optimization problem is going to be defined. The geometry, con-straints, objective function and the optimizer etc. Once they are defined, we look at theflow pattern in the baseline that was used.

4.1 Defining the GeometryBaseline geometry that will be used should be such that its close to the optimum duct

and thus helping us reach the extremum easily. Various literature have different baselinesfor their desgn, but in most of the cases these baseslines were defined from somethingthat existed physically (like a test facilty). Most of the baseline designs are checked forSrovan and Klomp’s criterion, generally a conservative duct is chosen.

4.1.1 BaselineFor our case, we needed a baseline which is closer to an optimized case, and if possible

data on experimental studies of the same. Hence it was decided that we would use theoptimized duct mentioned in the work of Wallin F., Eriksson L-E et al [10]. The dataon the variation of Area and center-line alogwith length was available as a graph1(Figure4.1.1). This was then converted into tabulated data2, (table 4.1.1). This was the baselineintermediate turbine duct that was defined.

By this data we can write both variations with respect to x as a polynomial of x byinterpolating the data. Thus we get the polynomials h(x) and A(x) for center-line andArea variation respectively, they are

h(x) = 66.43x6 − 92.187x5 − 35.103x4 − 2.659x3 + 0.696x2 + 0.02x+ 0.4949A(x) = (−972.23)x6 + 1241.2x5 − 528.87x4 + 76.607x3 + 0.4116x2 − 0.0378x+ 0.3431

1Fig 5 and 6, Page no 7, [10]2Computed by Mr. Shyam Sundar Shukla

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(a) Center-line Variation

(b) Area Variation

Figure 4.1.1: The Center-line and Area variation Data obtained from Chalmer’sLiterature[10]

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Sl.No Length Center-line Area1 0 0.495 0.34212 0.025 0.4955 0.3453 0.05 0.4975 0.354 0.075 0.5 0.365 0.1 0.504 0.37756 0.125 0.51 0.398757 0.15 0.515 0.428 0.175 0.525 0.449 0.2 0.53625 0.45510 0.225 0.55 0.4637511 0.25 0.565 0.4662512 0.275 0.58325 0.462513 0.3 0.6 0.4614 0.325 0.61875 0.457515 0.35 0.6375 0.4587516 0.375 0.65625 0.4687517 0.4 0.67 0.487518 0.425 0.68375 0.5112519 0.45 0.6925 0.53520 0.475 0.697 0.5462521 0.5 0.6975 0.54781

Table 4.1.1: Tabulated data of Center-line and Area variation

4.1.2 Parametrization and the GeometryThe whole geometry is parametrized as,

Baseline Geometry(Length) + Pertubation = New Geometry

In this kind of approach the parameters that are defining the geometry are control-ling only the perturbation. Two perturbation functions are defined as explained in theprevious sections, P1 and P2, Four independent parameters are now defined α1, α2, β1, β2.These parameters are bound between 0 and 1 and the parameters that control P1 and P2

P1(x) = x3(x− L)3

P2(x) = x3(x− L)3(x− L

2

)If we call the equations pertaining to new geometry as, h∗ and A∗, Now we define

length parameter len, this parameter is also bound between 0 and 1 and defines thelength of the duct. This will change the functions h(x) and A(x), to make the change tonew length all one has to do is to replace x∗. Hence for the new parameter len, we define

x∗ = x

len

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The final equations that define the new geometry’s center-line and area variationare the sum of the perturbation functions and the modified geometry with length. Theequations of h∗ and A∗are

h∗(x) = h(x∗) + α1P1(x) + α2P2(x)

A∗(x) = A(x∗) + β1P1(x) + β2P2(x)

4.2 Objective function and ConstraintsFor a problem to be clearly defined, it should have proper objective function and

constraints.

4.2.1 ConstraintsThe only constraints that were defined was on the wall angles of both, hub and shroud.

The wall angles in the baseline geometry itself exceed 50at some points. Hence a relaxedwall angle constraint was defined as , that is

• Wall Angles< 100 .In order to obtain wall angles, first we are required to compute radius of hub and

shroud at different location and this was easily obtained by

rh(x) = h∗(x)− A∗(x)4πh∗(x) and rs(x) = h∗(x) + A∗(x)

4πh∗(x)

Now by computing at 20 different locations the value of radius and using simpletrigonometric relations the wall angle could be found and it is then checked if it satisfiesthe constraint.

4.2.2 Objective functionIn the current case, the objective function is very simple. Its just the length factor,

f(x) = len. Such a simple function is possible since the parameter len controls thegeometry of the entire duct significantly and it can have effect on the wall angles. This,in turn, lets us perturb the shape such that the constraints are satisfied. Thus, whilelooking as a simple function will function as a good enough objective function. Themathematical simplicity of the objective function also helps us reduce the computationalload significantly and even optimization models like GA can work quick enough,( under60 seconds for each run).

4.2.2.1 Inputs and Outputs

The inputs that are defined to the program are, the baseline geometry and constraints.Along with that other parameters for the optimizer needs to be defined. For GeneticAlgorithm, in our case we have considered

• Number of Generations is taken as 100

12

• Number of Population, it is generally 10 times the number of variables, i.e., 50

• Crossover Probability as 80%

• Mutation Probabilty as 5%

There are different output files generated from the program. They are

• h1.out, center-line variation for 20 different points along the length of the new duct

• a1.out, area variation for 20 different points along the length of the new duct

• hub.out, wall angles of the hub at 20 locations in radians

• shroud.out, wall angles of the shroud at 20 locations in radians

• Paramaters.out, all the parameters that are being varied for the optimization in therespective order α1, α2, β1, β2, len

• Result.out, indicating the maximum, minimum and the average value of the gener-ation. Also the number of mutations and crossovers made.

13

Chapter 5

Optimized Design

5.1 Performance of the Baseline Duct

5.1.1 Pressure ContoursBy the CFD simulations that is done externally we observe for the baseline duct the

pressure loss to be around 4%.

Figure 5.1.1: Pressure Contours

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Figure 5.1.2: Total Pressure Contours

5.1.2 Velocity ContoursThe velocity contours that are plotted show that small amount of seperation that

occurs at the shroud near the end of the duct.But this seperation is not significant.

Figure 5.1.3: Velocity Contours

5.1.3 ConclusionThe Baseline gometry has the following charecteristics

• A very good pressure recovery of 96%,

• Also the flow seperation that exist is very minimal.

15

5.2 Optimized Duct

5.2.1 IntroductionThe optmized duct is obtained after running the optimizer with the constraints and

conditions specified in the previous chapter. Genetic Algorithm is used for the optimiza-tion of the duct.

5.2.2 GeometryAfter five runs, the geometry obtained, for the specified conditions and constraints,

has the following parameters as shown in table 5.1. These values are directly extractedfrom the values of h1.out and a1.out

Sr. No Length Centerline Area1 0 0.4949 0.34312 0.0175 0.495356 0.3434153 0.035 0.496599 0.3488824 0.0525 0.498745 0.3609365 0.07 0.502052 0.3785926 0.0875 0.506835 0.3994717 0.105 0.513403 0.4206588 0.1225 0.522001 0.4393899 0.14 0.532767 0.4535610 0.1575 0.545701 0.46207411 0.175 0.560642 0.46501412 0.1925 0.577261 0.46364213 0.21 0.595063 0.46023314 0.2275 0.613401 0.45773115 0.245 0.631506 0.45924116 0.2625 0.64852 0.46734617 0.28 0.663546 0.48325518 0.2975 0.675715 0.50577619 0.315 0.684251 0.53012620 0.3325 0.688564 0.54656521 0.35 0.688338 0.538856

Table 5.2.1: Table containing values of Mean line and Area at given length

5.3 Flow CharecteristicsThe obtained duct is then anaysed in CFD externally and the following resultsa are

obtained

• Pressure recovery is relatively low at 92%

• Large seperation of flow exist at hub and shroud near the exit

16

It can be seen from velocity contour in fig 5.3.1 that the seperation occuring is significant.

Figure 5.3.1: Velocity Contours

5.4 Comparision with Baseline GeometryIn comparision to baseline geometry, thi duct has

• Lower Pressure recovery, with a pressure recovery of 92%. This is significantly lowerfor a duct of this type.

• Flow seperation in this case is quite significant, and this can be the main reasonfot the pressure loss that is being caused.

• While the baseline is better in the previous cases, the optimized duct has 30%shorter duct.(i.e., 70% of original length)

17

Chapter 6

Conclusion

6.1 Scope of Future work• Further improvisations on the optimization methods and constraints can be done

to get a better result.

• The optimized duct can be analyzed for its performance, and thus can be used forfurther optimization through a High fidelity analysis that is coupled with CFD

• When the duct becomes more aggressive, flow control methods can be used toreduce separation and decrease the effect of the pressure loss.

• Non axis symmetric and inclusion of struts can be considered for a more realisticanalysis of the Duct and optimization of the same can be carried out.

6.2 SummaryIntermediate turbine ducts are essential components, and they are quickly finding a

niche of their own. In the present work, the basic ideas required for the understandingand optimization of a Intermediate Turbine duct were established. The obstacles facedgave us an idea on what can be achieved and what approaches are not feasible. The studyon various optimization and parametrization methods will be very helpful when furtheroptimizations and constraints are carried out.

The baseline duct which was considered was already an optimized duct and showedgood pressure recovery along with minimal flow seperation. The first optimized duct, wasobtained by optimizing length purely by considering design space defined by constraints.The obtained duct had length 70% of the original length. This method gave us a feasiblepoint but there was no guarantee that this duct would perform well as flow performancewas not the objective function. The duct used had poor pressure recovery and largeseparation. Thus indicating further improvements for the same can be made in thefuture to obtain a duct with favorable characteristics.

18

Bibliography

[1] Arroyo Osso C. Aerothermal investigation of an intermediate turbine duct. Doctoralthesis, Department of Applied Mechanics of Chalmers University of Technology,2009. ISBN:978-91-7385-351-4

[2] Wallin F. Flow control and shape optimization of intermediate turbine ducts forturbofan engines. Doctoral thesis, Department of Applied Mechanics of ChalmersUniversity of Technology, 2008. ISBN:978-91-7385-205-0

[3] Axelsson L-U. Experimental investigation of the flow field in an aggressive interme-diate turbine duct. Doctoral thesis, Department of Applied Mechanics of ChalmersUniversity of Technology, 2009. ISBN:978-91-7385-264-7

[4] Gottlich E, Malzacher FJ, Heitmeir FJ, Marn A. Adaptation of a transonic testturbine facility for experimental investigation of aggressive intermediate turbine ductflows. AIAA paper ISABE-2005-1132, 2005

[5] Gottlich E, Marn A, Malzacher FJ, Schennach O, Heitmeir F. Experimental investi-gation of the flow through an aggressive intermediate turbine duct downstream of atransonic turbine stage. In: Papailiou K, Martelli F, Manna M, editors. Proceedings7th European conference on turbomachinery fluid dynamics and thermodynamics,2007, p. 383–9

[6] Marn A, Gottlich E, Pecnik R, Malzacher FJ, Schennach O, Pirker HP. The influenceof blade tip gap variation on the flow through an aggressive S-shaped intermediateturbine duct downstream a transonic turbine stage— Part I: time-averaged results.ASME paper GT2007-27405, 2007

[7] Sovran G, Klomp ED. Experimentally determined optimum geometries for rectilineardiffusers with rectangular conical or annular cross section. In: Sovran G, editor. Fluidmechanics of internal flow. Elsevier; 1967. p. 270–319

[8] Gardner WB. Energy efficient engine (E3) technology status. AIAA paper AIAA-82-1052, 1982

[9] Dominy RG, Kirkham DA. The influence of swirl on the performance of interturbinediffusers. In: VDI Berichte 1186, 1995, p. 107–22

[10] Wallin, Fredrik, Lars-Erik Eriksson, and Martin Nilsson. "Intermediate turbine ductdesign and optimization." ICAS Paper No. ICAS 5.1 (2006).

[11] Wallin, Fredrik, and Lars-Erik Eriksson. "Response surface-based transition ductshape optimization." ASME Turbo Expo 2006: Power for Land, Sea, and Air. Amer-ican Society of Mechanical Engineers, 2006.

19

[12] Wallin, Fredrik, and Lars-Erik Eriksson. "Non-axisymmetric endwall shape optimiza-tion of an intermediate turbine duct." 18th ISABE Conference. 2007.

[13] Wallin, Fredrik, and Lars-Erik Eriksson. "Design of an aggressive flow-controlledturbine duct." ASME Turbo Expo 2008: Power for Land, Sea, and Air. AmericanSociety of Mechanical Engineers, 2008.

[14] J. I. Madsen, W. Shyy , and R. T . Haftka. Response Surface T echniques for DiffuserShape Optimization. AIAA Journal, 38:1512–1518, 2000

[15] Göttlich, Emil. "Research on the aerodynamics of intermediate turbine diffusers."Progress in Aerospace Sciences 47.4 (2011): 249-279.

[16] Wallin F, Eriksson L-E. A tuning-free body-force vortex generator model. AIAApaper AIAA-2006-0873, 2006.

[17] Kalyanmoy Deb, Optimization for Engineering Design: Algorithms and Examples,2nd Edition (English), PHI Learning Pvt. Ltd-New Delhi, ISBN:9788120346789

[18] Kalyanmoy Deb ,Multi-Objective Optimization Using Evolutionary Algorithms, 1stEdition, Wiley India Pvt Ltd, 2010, ISBN: 9788126528042

[19] E. Taskinoglu, D. Knight. Design Optimization for Submerged Inlets-Part I. AIAAPaper 2003-1247, January, 2003.

[20] Taskinoglu, Ezgi S., et al. "Design optimization for submerged inlets-Part II." 21stApplied Aerodynamics Conference. 2003.

[21] Rolls Royce Trent 1000 fact sheet VCOM13797 Issue 5 March 2009.http://www.rolls-royce.com/Images/brochure_Trent1000_tcm92-11344.pdf

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[23] Gräsel, Jürgen, Manuel Pierré, and Jacques Demolis. "Parametric interturbine ductdesign and optimisation." Proceedings of 25th international congress of the aeronau-tical sciences, ICAS. 2006.

20

Appendix A

Understanding the OptimisationProgram

A.1 The Optimization MethodA genetic algorithm (GA) is a search heuristic that mimics the process of natural

selection. This heuristic is routinely used to generate useful solutions to optimization andsearch problems. Genetic algorithms belong to the larger class of evolutionary algorithms(EA), which generate solutions to optimization problems using techniques inspired bynatural evolution, such as inheritance, mutation, selection, and crossover.

A.1.1 MethodologyIn a genetic algorithm, a population of candidate solutions (called individuals, crea-

tures, or phenotypes) to an optimization problem is evolved toward better solutions. Eachcandidate solution has a set of properties (its chromosomes or genotype) which can bemutated and altered; traditionally, solutions are represented in binary as strings of 0sand 1s, but other encodings are also possible.

The evolution usually starts from a population of randomly generated individuals,and is an iterative process, with the population in each iteration called a generation. Ineach generation, the fitness of every individual in the population is evaluated; the fitnessis usually the value of the objective function in the optimization problem being solved.The more fit individuals are stochastically selected from the current population, and eachindividual’s genome is modified (recombined and possibly randomly mutated) to form anew generation. The new generation of candidate solutions is then used in the nextiteration of the algorithm. Commonly, the algorithm terminates when either a maximumnumber of generations has been produced, or a satisfactory fitness level has been reachedfor the population.

A.1.1.1 Crossover

In genetic algorithms, crossover is a genetic operator used to vary the programmingof a chromosome or chromosomes from one generation to the next. It is analogous toreproduction and biological crossover, upon which genetic algorithms are based. Crossover is a process of taking more than one parent solutions and producing a child solution

21

from them. There are methods for selection of the chromosomes. Those are also givenbelow.

A.1.1.2 Mutation

Mutation is a genetic operator used to maintain genetic diversity from one generationof a population of genetic algorithm chromosomes to the next. It is analogous to biologicalmutation. Mutation alters one or more gene values in a chromosome from its initial state.In mutation, the solution may change entirely from the previous solution. Hence GA cancome to better solution by using mutation. Mutation occurs during evolution accordingto a user-definable mutation probability. This probability should be set low. If it is settoo high, the search will turn into a primitive random search.

A.2 The CodeThe entire code was written in C, as the sorce codes available for genetic algorithm

from KANGAL was only in C.The code that is presented below is the section that iswritten as objective function and constraints for the GA source code that was available.

double compute(double* pol,double q) {

double ret=0,val=1.0;

int i;

for(i=0;i<8;i++) {

ret+=val*pol[i];

val*=q;

}

return ret;

}

void objective(indv)

INDIVIDUAL *indv;

{

int i;

double term1,term2, term3, pi, your_func;

double g[MAXCONSTR], gsum, x[2*MAXVECSIZE];

// if (indv == NULL) error_ptr_null("x in objective()");

for (i=0; i < nvar_bin; i++)

x[i] = indv->xbin[i];

for (i=nvar_bin; i < nvar_bin+nvar_real; i++)

x[i] = indv->xreal[i-nvar_bin];

MINM = 1; // for maximization use -1

double len=x[4];

// double H[8]={0,66.42,-92.19,35.103,-2.659,0.696,0.002,0.4949};

double h[8]={0.4949,0.002,0.696,-2.659,35.103,-92.19,66.42,0};

// double A[8]={0,-972.23,1241,-528.87,76.607,0.412,-0.0378,0.3431};

double a[8]={0.3431,-0.0378,0.412,76.607,-528.87,1241,-972.23,0};

double H[8],A[8];

double P1[8],P2[8];

double rs[21],rh[21];

double h1[21],a1[21];

double th_s[20],th_h[20];

double h1_x,a1_x;

double sum;

H[0]=h[0];

H[1]=h[1]/(len);

H[2]=h[2]/(len*len);

H[3]=h[3]/(len*len*len);

H[4]=h[4]/(len*len*len*len);

H[5]=h[5]/(len*len*len*len*len);

H[6]=h[6]/(len*len*len*len*len*len);

H[7]=h[7]/(len*len*len*len*len*len*len);

A[0]=a[0];

A[1]=a[1]/(len);

A[2]=a[2]/(len*len);

A[3]=a[3]/(len*len*len);

A[4]=a[4]/(len*len*len*len);

A[5]=a[5]/(len*len*len*len*len);

A[6]=a[6]/(len*len*len*len*len*len);

A[7]=(a[7]/(len*len*len*len*len*len*len));

for (i=0;i<8;i++)

{

sum+= A[i];

}

//printf("%.7f ",A[1]);

for(i=0;i<8;i++) {

P1[i]=0;P2[i]=0;

}

double val=(len/(double)2.0);

P1[6]=1.0;

P1[5]=-3*val;

P1[4]=3*val*val;

P1[3]=-val*val*val;

val*=-1.0;

for(i=0;i<7;i++)

P2[i]=P1[i]*(val/(double)2.0);

for(i=1;i<8;i++)

P2[i]+=P1[i-1];

// P1 and P2 are generated

double b=0.0;

pi=acos(0)*2.0;

double pi_by36=pi/(double)5.0;

double ms;

double mh;

double l=(len/(double)2.0);

for(i=0;i<21;i++) {

h1[i]=compute(H,b);

h1[i]+=x[0]*compute(P1,b)+x[1]*compute(P2,b);

a1[i]=compute(A,b);

a1[i]+=x[2]*compute(P1,b)+x[3]*compute(P2,b);

rs[i]=h1[i]+(a1[i]/(4.0*pi*h1[i]));

rh[i]=h1[i]-(a1[i]/(4.0*pi*h1[i]));

if(i>0) {

ms=(rs[i]-rs[i-1])/((double)0.1*l);

mh=(rh[i]-rh[i-1])/((double)0.1*l);

th_s[i-1]=atan(ms);

th_h[i-1]=atan(mh);

}

b+=(0.05*l);

}

your_func=len;

nc=40;

for(i=0;i<20;i++){

g[i]=(th_s[i]-(pi_by36));

}

for(i=10;i<40;i++){

g[i]=((th_h[i-20]-pi_by36));

}

FILE* ths;

ths= fopen("shroud.out","w+");

for(i=0;i<20;i++) {

fprintf(ths, "%f ",th_s[i] );

// printf("%.7f ",x[i] );

}

fprintf(ths, "\n" );

fclose(ths);

FILE* thh;

thh= fopen("hub.out","w+");

for(i=0;i<20;i++) {

fprintf(thh, "%f ",th_h[i] );

// printf("%.7f ",x[i] );

}

fprintf(thh, "\n" );

fclose(thh);

FILE* hf;

hf= fopen("h1.out","w+");

for(i=0;i<21;i++) {

fprintf(hf, "%f ",h1[i] );

// printf("%.7f ",x[i] );

}

fprintf(hf, "\n" );

fclose(hf);

FILE* af;

af= fopen("a1.out","w+");

for(i=0;i<21;i++) {

fprintf(af, "%f ",a1[i] );

// printf("%.7f ",x[i] );

}

fprintf(af, "\n" );

fclose(af);

FILE* fp2;

fp2= fopen("krish.out","w+");

for(i=0;i<5;i++) {

fprintf(fp2, "%f ",x[i] );

// printf("%.7f ",x[i] );

}

fprintf(fp2, "\n" );

fclose(fp2);