Fluid Structure Interaction Analysis Of Tapered Wing And Rectangular Plate

Fluid Structure Interaction Analysis of Tapered Wing And Rectangular Plate Submitted by Jyoti Rathore Roll no. 16017504005

Under the guidance of Er. Rahul Malik (Head of Department) in partial fulfillment of the requirements for the award of the degree of MASTER OF TECHNOLOGY in MECHANICAL ENGINEERING (Computer Aided Design)

Department of Mechanical Engineering Deenbandhu Chotu Ram University of Science & Technology, Murthal (Sonipat – 131039)

DECLARATION This is certified that the matter embodied in the present work entitled “Fluid Structure Interaction Analysis of Tapered Wing and Rectangular Plate” is based on my original research work. It has not been submitted in part of fully for any diploma or degree of any other university. My indebtedness to other in this work has been duly acknowledged at relevant palaces.

Jyoti Rathore Roll No. 16017504005

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CERTIFICATE I hereby certified that the work being presented in the “Fluid Structure Interaction Analysis of Tapered Wing and Rectangular Plate” in partial fulfillment of the requirements for the award of the degree of Master of Technology (Mechanical Engineering) in Computer Aided Design submitted in the department of Mechanical Engineering at P.M. College of Engineering, Sonipat is an authentic record of Jyoti Rathore’s own record carried out during a period from Jan 18 to Nov 18 under the supervision of Er. Rahul Malik, Head cum Assistant Professor (Department of Mechanical Engineering, PMCE). The matter presented in thesis has not been submitted in any other university or institute for the award of M.Tech. Degree.

Signature of Student (Jyoti Rathore)

This is to certify that the above statement made by the candidate is correct to the best of my knowledge.

Signature of Supervisor (Er. Rahul Malik) Head cum Assistant Professor Mechanical Engineering Department P.M. College of Engineering, Sonipat

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ACKNOWLEDGEMENTS I feel blessed for having the privilege of working with my guide, Er. Rahul Malik, Head cum Assistant Professor of Mechanical Engineering Department, whose dedication to academics has been a constant motivation for carrying out my project to the best of my abilities. I am thankful to him for giving me this opportunity. All the thought-provoking discussions I had with him enriched my understanding of the engineering fundamentals and helped me to complete my project at a faster pace. I would also like to thank my guide for sharing his valuable knowledge and constant encouragement provided to me during the course of project. I would also like to thank P. Rama Krishana (Assistant Professor), Vinod Kumar (Laboratory Instructor) for their deep involvement and guidance in this research work. I express my gratitude to my mates who helped in resolving some of the issues related to off the shelf availability of crucial software and data which saved me a lot of precious time. I am grateful to all my classmates for creating a homely atmosphere and being there during good and bad times. All the wonderful moments shared with them will remain in my memory forever. Finally, I am indebted to my family who were always a great source of encouragement in providing a peaceful state of mind during my entire duration of M Tech.

I

happily

dedicate

this

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thesis

to

my

family.

DEDICATED TO

MY PARENTS

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ABSTRACT

This project work deals with fluid structure interaction (FSI) analysis, which is the most emerging area of numerical simulation and calculation. FSI occurs due to flow of fluid influences the properties of a structure or vice versa. It is very important task to researchers to find a good technique so that complex problems such as interaction of fluid flow over the solid object can be dealt out by keeping in mind the resources available. The fluid structure interaction phenomenon is not specific it occurs in almost every field of engineering and always remains attraction of engineers and researcher of different fields. Present work dealt with FSI analysis of tapered wing made by NACA2412 aerofoil having different chord length from root to tip and a flat plate. The researchers and engineers develops a variety of techniques to deal FSI analysis. A comparative study has been made on the stress strain, deformation of structure and stress time analysis of wing and plate. The fluid and structural model have been created with appropriate dimensions in design modeller in ANSYS. Transient structural and CFD fluent is used as a pre-processing tool for creating the whole computational domain and volume mesh. For the structural model, ANSYS Mechanical (transient structural) is used to determine the dynamic response of a structure under unsteady fluid pressure loads. In order to understand the dynamics of a structural member, modal analysis has been conducted to determine the flutter velocities and deformation.

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CONTENTS

DECLARATION

PAGE NO. ii

CERTIFICATE

iii

ACKNOWLEDGEMENT

iv

ABSTRACT

vi

LIST OF FIGURES

x

LIST OF TABLES

xii

SYMBOLS AND NOTATIONS

xiii

CHAPTER 1

INTRODUCTION

1

1.1

Static Problems

2

1.2

Dynamic Problems

4

1.3

Aircraft Wing

5

1.4

Fluid-Structure Interaction

6

CHAPTER 2

LITERATURE REVIEW

10

CHAPTER 3

THEORITICAL BACKGROUND

14

3.1

CFD and Fluid Model

14

3.2

Mass Conservation Principle

14

3.3

Newton’s Second Law and Momentum Eqation Finite Volume Method

14

3.4

vii

15

3.5

Turbulence Model

16

3.6

16

3.8

Reynold’s Averaged NavierStokes (RANS) Equations K-Epsilon (K-ɛ) Turbulence Model Realizable K-ɛ Model

3.9

K-ω Turbulence Model

18

3.10

18

3.11

Finite Element Method and Structural Model System Coupling

3.12

Data Transfer

20

3.13

Time Advancement Schemes

22

3.14

Re-Meshing

23

3.7

CHAPTER 4

RESEARCH METHODOLOGY

17 18

20

24

4.1

Geometry

24

4.2

Computational Mesh

25

4.3

Simulation Setup

26

4.4

Material Properties

26

4.5

Turbulence Modelling Setup

27

4.6

Boundary Conditions

27

4.7

Solver Setup

27

4.8

ANSYS Mechanical Setup

28

4.9

System Coupling Setup

28

CHAPTER 5 5.1

RESULTS AND DISCUSSION FSI Analysis of Rectangular Plate

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31 31

5.2

FSI Analysis of Wing

35

CHAPTER 6

CONCLUSION

39

CHAPTER 7

FUTURE SCOPE OF WORK

41 42

REFERENCES

ix

LIST OF FIGURES

Page No. Figure 1.1

Collar’s aero-elastic triangle

2

Figure 1.2

Cross-section of aircraft wing

3

Figure 1.3

Rotation and plunge motion for an airfoil subjected to flutter A typical wing and its parts

4

Figure 1.5

Fluid structure interaction

7

Figure 3.1

System coupling flowchart

20

Figure 3.2

Conservative nature of GGI algorithm

21

Figure 3.3

Profile preserving nature of smart bucket algorithm

21

Figure 4.1

Wing inside a fluid domain

25

Figure 4.2

Meshing over the wing

25

Figure 4.3

Meshing over fluid domain

26

Figure 4.4

Structural member setup

28

Figure 4.5

FSI analysis setup using system coupling

29

Figure 4.6

Properties of data transfer

30

Figure 5.1

Total deformation contour of rectangular plate

31

Figure 1.4

x

6

Figure 5.2

Elastic strain contour of rectangular plate

32

Figure 5.3

Maximum shear stress contour of rectangular plate

32

Figure 5.4

Displacement vs time curve of rectangular plate

33

Figure 5.5

Stress vs strain curve of rectangular plate

34

Figure 5.6

Stress vs time curve of rectangular plate

34

Figure 5.7

Total deformation contour of wing

35

Figure 5.8

Equivalent stress contour of wing

36

Figure 5.9

Equivalent elastic strain contour of wing

37

Figure 5.10

Displacement vs time curve of wing

37

Figure 5.11

Stress vs Strain plot of wing

38

Figure 5.12

Stress vs time plot of wing

38

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LIST OF TABLES

S.N.

Name of Table

Page no.

Table 4.1

Fluid property

26

Table 4.2

Turbulence modelling setup

27

Table 4.3

Discretization scheme used in fluent

27

xii

SYMBOLS AND NOTATIONS

ρ: Density of fluid µ: Dynamic viscosity of fluid U: Velocity vector SM: Momentum source Φ: Variable function CV: Control volume Ϭ: Stress tensor Eij: Component of rate of deformation µt: Eddy viscosity Ke: Element stiffness matrix Ne: Number of elementc

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CHAPTER 1 INTRODUCTION

Aero elasticity is an aerodynamic phenomenon in which we study the effect of the aerodynamic forces on elastic bodies, when solid body interact with fluid. During analysis of dynamic system of structure, if aerodynamic loading is taken into account then the resultant phenomenon is classified as aeroelastic. Theory of elasticity deals with the effect of external displacement and aerodynamic forces on deformation and stress of an elastic body. Deformation of a structure of body is generally not depends on the extent of external forces acts on it so in most of the case deformation is to be assumed as a very small and presume it will not affect by the action of forces acts externally. Based on this assumption the change in dimension of body was neglected often and calculations are purely consider by taking the initial shape of the object, in other words initial dimensions of object is taken for calculation. While reality is different in most of the problems of aero elasticity. The extent of aerodynamic forces depends upon structure body attitude relative to the flow. External loading of body is generally determined by elastic deformation of the body. In other words to determine the magnitude of aerodynamic force pre knowledge of elastic deformation is required. So design of flight vehicles is strongly influenced by aero elastic phenomenon and hence its analysis is very important. Collar made a triangle of forces in which the vertex of triangle represents a specific force. By pairing two of three corners he formulates a new discipline.

1

Figure-1.1: Collar’s aero-elastic triangle

For example   

Aerodynamics + Dynamics = Aerodynamic Stability Dynamics + Structural Mechanics = Mechanical Vibration or Structural dynamics Aerodynamics + Structural Mechanics = Divergence or Static aeroelasticity

Since all these forces are considered special cases of aeroelasticity. Hence for occurrence of dynamic aeroelastic effects, all three forces are required. Different types of aeroelastic problems occur in aeronautical field are given in the following subsection: 1.1 Static Problems The interaction between aerodynamics and elastic forces may leads to divergent tendencies in a very flexible structure, which eventually leads to failure of structure. While on the other hand, if the structure is adequately stiff, a stable equilibrium condition is reached. The static aeroelastic problems occur due to interaction of aerodynamic forces and elastic forces. These problems are further classified as: Divergence, Static Flight Stability, Distribution of Lift and Aileron Effectiveness. 2

When moment produced by the air loads will be greater than the torsional stiffness of the wing then it twisted the structure of wing. This phenomenon is known as divergence. The speed at which divergence failure occurs is known as divergence speed and it will be much higher than the normal operational speed of the vehicle. This particular problem generally occurs in case of swept forward wings because they have relatively low divergence speed. To understand this phenomenon considers a simple case of wing shown in figure 1.2. When speed of flow increases then lift forces increases, which acts to the aerodynamic centre of wing.

Figure 1.2: Cross section of aircraft wing Due to increase in lift, the twisting moment about the centre of twist also increases which increase the local angle of attack of the wing. Hence the lift forces and twisting moment further increase and this process continues. Above a certain limiting speed i.e. divergence speed the torsional speed of the structure will not be capable to balance the aerodynamic moment of wing and structure becomes unstable. This phenomenon is known as torsional divergence. Other structural divergence also occurs on the system but this is the critical ones. Aileron reversal occurs due to deflection of aileron. Aileron is used to produce the rolling moment on aircraft. It is attached at the outboard of trailing edge of the wing through the hinge support. So when it is deflected downward cause additional upward lift in the wing near the tip. This additional lift also creates additional moment, which results in nose down twisting moment and hence local angle of attack reduces. When a particular speed reached i.e. aileron reversal speed, then the aileron deflection does not produce further rolling moment. This condition is known as aileron reversal. Finally the distribution of lift due to uneven distribution of pressure over the surface of wing causes elastic deformation of the wing, which may be divergence of nature. Static flight stability deals with this elastic deformation in terms of flight controllability namely static margin. 3

1.2 Dynamic Problems The time dependent situation of system enters in dynamic aeroelasticity, which leads to structural oscillation of system. Since elastic stiffness of the system remains independent with the wind speed past over it, but aerodynamic forces strongly dependent on the wind speed and increases rapidly with the increment of wind speed. Hence there must be consists a critical wind speed at which structure of the system becomes unstable. This instability might be caused of excessive oscillatory deformations in structure, which increases exponentially and leads to damage or destruction of the structure. Flutter is one of the major problem which may exists in aircraft structure, suspension bridges etc. It is dynamic in characteristics and small disturbance may leads to small or more violent oscillation. It is characterized by the interaction of elastic, inertia and aerodynamic forces and is known as problem of dynamic aeroelastic instability. A particular case of oscillation with zero frequency, in which in inertia force is neglected generally is called as steady state or static aero-elastic instability.

Figure-1.3: Rotation and Plunge Motion for an Airfoil Subjected to Flutter

The basic type of flutter of aircraft wing is described above. Flutter might be initiated by rotation of the airfoil. Consider rotation starts at time t=0, as shown in figure 1.3. The aerodynamic force on airfoil increases and rises the airfoil, but due to torsional stiffness of the structure it again returns to zero rotation condition at time t = T/4. The airfoil tries to return to neutral condition due to bending stress of the structure, but it starts rotating in nose down sense (shown at t = T/2 in figure). Again aerodynamic forces will increase causes the airfoil to plunge and due to torsional stiffness of structure returns to zero rotation (t=3T/4). The cycle will be completed, when the airfoil returns to the neutral position with a nose-up sense. We can notice here that the maximum rotation leads to maximum rise or plunge by 90 degrees (T/4). With increase in time the plunge motion tends to damp out, while the rotation motion diverges. If 4

this motion is allowed to continue, then the forces due to the rotation will leads to structural failure. Coalescence of two structural modes leads to flutter and these modes are pitch and plunge motion. The plunge is also known as bending. The pitch mode leads to rotational motion, while bending mode leads to vertical up and down motion at the wing tip. As the airfoil flies with increasing speed of air, the frequencies of these modes coalesce and created one mode, the frequency of the resulting mode is known as flutter frequency and this condition is called flutter condition of airfoil. This condition occurs at the flutter resonance. Airfoil has many applications in aircraft. It is primarily used to decide the cross section of wing but also used in tail, control surfaces such as aileron, elevator and rudder and propeller blades. Therefore flutter analysis of airfoil is very important because it can affect the overall performance of the aircraft.

1.3 Aircraft Wing In aviation field effort is continuously made to decrease the weight of the wing while increasing its strength, so that it can supports the weight of whole aircraft by producing the enough lift force. The cross section of wing is known as airfoil, which may be symmetrical or cambered. Thick end of wing is called as leading edge and thin end is trailing edge. Length of straight line joining the leading edge to trailing edge of airfoil is known as chord length of airfoil. Line joining the locus of points which is equidistant from upper surface to lower surface is known as camber line of airfoil. When camber line is coincide with the chord line, the airfoil will be symmetrical. If camber line lies above the chord line of airfoil, it will be positive cambered airfoil. Present work has been carried out on NACA2412 airfoil, which is positive cambered airfoil. The figure 1.4 shows the main structural parts of the wing. Which are ribs, spars, stringers and skin. According to the application, one can change their materials, quantity and location of the components.

5

Figure 1.4: A typical wing and its parts Ribs are chordwise elements that provide airfoil shape to the wing and used to resist the concentrated loads acted on the wing. While spars and stringers are spanwise elements which provides strength to the wing and provide strength to the wing against torsional and bending loads. The thickness requirement of the skin is provided by the spars. For example in case of two spar wing, the thickness of the skin of the wing is higher and spars to manipulate the torsional characteristics of the wing spars can be adjusted. 1.4 Fluid-structure interaction (FSI) Fluid Structure Interaction is a multi-physics coupling between the laws that describe structural mechanics and fluid dynamics. This phenomenon can be characterized by stable or oscillatory interactions between a moving or deformable structure and internal fluid flow or surrounding. Stresses exerted on the structure due to passing of airflow over the structure and it leads to strains are on the solid object. This induced stress and strains causes body will deformed. The extent of deformation totally depends upon the velocity and pressure of flow of fluid and also on the properties of material of the actual structure.

6

Figure 1.5: Fluid structures interaction

For the past ten years, the simulations of multi-physics problems have become more important in the field of numerical simulations and analyses. In order to solve such interaction problems, structure and fluid models i.e. equations which describe fluid dynamics and structural mechanics have to be coupled. If the deformations of the structure are quite small and the variations in time are also relatively slow, the fluid's behaviour will not be greatly affected by the deformation, and we can concern ourselves with only the resultant stresses in the solid parts. However, if the variations in time are fast, greater than a few cycles per second, then even small structural deformations will lead to pressure waves in the fluid. These pressure waves lead to the radiation of sound from vibrating structures. Such problems can be treated as an acousticstructure interaction, rather than a fluid-structure interaction. Yet, if the deformations of the structure are large, the velocity and pressure fields of the fluid will change as a result, and we need to treat the problem as a bidirectionally coupled multiphysics analysis: The fluid flow and pressure fields affect the structural deformations, and the structural deformations affect the flow and pressure.

Fluid-structure interactions can be classified into three groups: 1. Zero strain interactions: such as the transport of suspended solids in a liquid matrix. 2. Constant strain steady flow interactions: The constant force exerted on an oil-pipeline due to viscous friction between the pipeline walls and the fluid. 7

3. Oscillatory interactions: In this interaction the induced strain in the solid structure will move in such a way that the source of strain is diminished and the structure will returns to its previous state only for the process to repeat. One-way and two-way fluid-structure interaction modelling: The Problems Which involves the interaction between fluids and structures can be modelled as uncoupled problems and can be consider within their separate domains. In the uncoupled problems one domain is driven by the other domain. The domain which drives the system is called as driven domain and the other domain is called driving domain. The driven domain having no feedback effect on the driving domain and hence it is called, one-way fluid structure interaction. For example the acoustic propagation of air being driven by a speaker can be consider without considering the feedback effects of the driven air on the structural deflection of the loud speaker surface. That is therefore an example of a classical fluid structural interaction problem where the coupling effect of the interaction between the fluid and structural domains needs to be consider in one direction only namely the effect of the fluid on the structure. Modelling of complex structure analytically has limited scope and difficult so numerical analysis is generally required. Therefore most of the complex engineering problems widely adopted the numerical solutions such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) numerical simulations in the structural and fluid domains respectively. One way to couple the model numerically in fluid structure interaction problems is to couple two computational domain i.e. FEM and CFD together with independent solvers for each domain, while boundary conditions is passed from each domain to the other at every computational step. Other example of one way fluid structure interaction situation is the dynamic wind loading on civil structures, where fluid is the driving domain and the structure is being driven, while the structural part has almost no feedback effect on the domain of fluid. In these problems, the motion of fluid and displacement of the structure have not major effect on the wind loads which drive this motion and separate analysis of structure can be possible or can be uncoupled from the wind under the given load conditions. This will be not always occurs in all engineering problems. In some problems the motion of fluid further enhance the fluid forces due to displacement of structure .In these system the structure and fluid must be coupled in such a way that they are interacting through a feedback system. 8

These types of problems required two way fluid structure interaction analyses. This is often occurs when the amplitude of the structural deflection is large.

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CHAPTER-2 LITERATURE REVIEW Fluid structure interaction (FSI) analysis, which is the most emerging area of numerical simulation and calculation. FSI occurs due to flow of fluid influences the properties of a structure or vice versa. It is very important task to researchers to find a good technique so that complex problems such as interaction of fluid flow over the solid object can be dealt out by keeping in mind the resources available. The fluid structure interaction phenomenon is not specific it occurs in almost every field of engineering and always remains attraction of engineers and researcher of different fields. It is a major topic of research from the past few decades in the area of research in aeronautical and mechanical stream. Fluid- Structure interaction problems have been investigated by Goud et. al (March, 2014) on AGARD 445.6 wings at transonic flow regime. The simulated result of wing at this speed was compared by previous result. The tip motion of wing was noted during flutter test at M=0.9, while dynamic pressure is varied. At each Mach number they observed a flutter boundary means tip displacement maintains its amplitude, it will be neither increasing nor decreasing. The region above flutter boundary has been found as unstable and region below flutter boundary was found to be stable. Jian Tang et. al (January,2008) explained the computational FluidStructure Interaction of a Deformable Flapping Wing for Micro Air Vehicle Applications and in that he tells that the structural model is based on an asymptotic approximation to the equations of elasticity. Considering the slenderness as the small parameter, the equations are categorised into two independent variation problems, corresponding to the (i) crosssectional, small deformation and (ii) longitudinal and large deformation analyses. Computational test has been carried out for fluid structure interaction between an elastic body and laminar incompressible flow by Turek and Hron (2015). They used a configuration consisting of incompressible laminar channel flow around an elastic object which leads to self-induced oscillation in the structure. The solid body with elastic part was submerged in channel flow which results in self-induced oscillation and deformation in body. They provide many displacement – Time graph at different working condition and along different direction. Sangeetha et. Al (July-August,2015) explains the Fluid-Structure Interaction on AGARD 445.6 wing at Transonic Speeds. Since extensive research has been done in the field of aero-elasticity using this model, this configuration was chosen. The main objective of this paper was to study the fluid structure interaction over the wing of aircraft and determine the 10

aero elastic properties through modelling as well as analysing the AGARD 445.6 wing structure using CATIA V5 to generate the solid model and the stress analysis was done using ANSYS-FLUENT. Schuster et al (1990) analysed the aeroelastic static effect on fighter aircraft by using 3-dimensional Navier-Stoke’s algoritham. They developed and tested an aeroelastic analysis method for extreme flight conditions for fighter aircraft, which is operating at flight conditions where shock, boundary layer separation, vortices and even high unsteady flow might be present. They found very encouraging result when compared their results with static tunnel data on an aeroelastically tailored wing and fuselage configuration. Aeroelastic analysis of transonic wings were done by Garcia and Guruswamy (1999). They adopted Navier-Stokes equations and a nonlinear beam finite element model for analysis of wing. The nonlinear beam element result was validated with analytical solutions. They studied three different high aspect ratio wings and demonstrate the tightly coupled approach on these wings. Result showed that by shortening the effective span and twist of the wing, will affects the aeroelastic properties of swept and unswept wings. R. S. Raja (2012) explains the FSI analysis that has been conducted on a typical slender cylindrical structural member used either as a leg or brace of truss structure of offshore. The members supported the structure were subjected to loads induced by the wave. They observed fatigue in existing structure due to this gradual interaction. The analysis was done by using partitioned method, where two ways coupling was adopted to simulate the flow over the cylindrical object subjected by ocean wave loads. Wing design was optimized for large endurance unmanned aerial vehicle by Lee et. al (2016) by Fluid structure interaction analysis. FSI and some other techniques was adopted to optimise the aspect ratio of wing shape on an unmanned aerial vehicle (UAV) with the aim of minimum cruise drag. The fluid solution was solved by Euler’s solver and structural analysis was performed by using FEM solver. Sample points were selected by Design of Experiment (DOE) method to generate an approximate model. M. C. Reese (July,2010) presented an experimental assessment of twodimensional theories and trends concerning hydro-elastic response of a cantilever hydrofoil in uniform flow. An aluminium NACA 66 hydrofoil with geometry similar to those found on sea-surface and an undersea vehicle was used to determine modal parameters under the conditions of both flow-induced and mechanical vibrations. He also analysed the in-air structural damping factors, fluid-loaded and uniform flow cases. 11

Glauret published data on the force and moment acting on a cylindrical body due to an arbitrary motion. In 1934, Theodorsens provide exact solution for wing with a flap and oscillated harmonically. Flutter due to torsion was first investigated by Glauret in 1929, which was further discussed in detail by Smilg. Several kinds of single degree of freedom flutter of control surfaces at both subsonic and supersonic speeds have been found. All flutter fulfilled the special criteria such as condition of location of rotational axis, condition of reduced frequency and condition of moment of inertia of the system. They observed Pure bending flutter is in cantilever swept wing, when wing was at high swept angle and relatively heavier than the surrounding air. Mechanical pressure loading due to fluid flow over turbine blade causes torque on the turbine shaft of hydro turbine was explained by Schmucker et. al (October-November,2010). This fluid loading leads to structural load on the component which in deflects the blade of turbine. Finite element analysis was used to calculate the mechanical stresses and deflection of the turbine blade by using commercial software ANSYS CFD with one way coupled approach and reverse influence of deformation of fluid was neglected. They analysed the influence of fluid deformation by two-way coupled Fluid structure interaction simulations of propeller turbine. The FSI simulation has done by coupling of commercial solvers ANSYS CFX for the fluid mechanical simulation and ANSYS Classic for the structure mechanical simulation and much comparative result was presented for various stiffness of blade and by changing the Young’s modulus of the blade. Coupled effect of hydrofoil and flowing fluid was investigated by Liaghat et. al (November,2010) by using two way fluid structure interaction by ANSYS. Logarithmic decrement method was adopted to estimate the damping co-efficient of the hydrofoil by considering damped free vibration. Different types of meshes were used to solve the problem and to see influence of mesh. They concluded that finer mesh must be used to solve high fluid velocity problems. They also observed the effect of time step and based on this concludes that by choosing small time step results can be approximated with experimental results. To predict and simulate the flutter characteristics of an aeroelastic system, a coupled CFD-CSD programme was used by the Liu et. al (MarchApril,2001). They simulate two-dimensional airfoil and three dimensional AGARD 445.6 wing at transonic speed of flow. Good agreement with experimental data was observed for flutter speed and frequency, on AGARD 445.6 wing at subsonic as well as transonic speed, while at supersonic speed both flutter speed and frequency had been found greater than the results found by experiment. Coupled fluid structure method was used by Yun and Hui (April,2011) to analyse the flutter characteristics of vibration in turbomachinery blade. 12

An aeroelastic model of blade vibration was developed to solve the threedimensional RANS equations and to evaluate aerodynamic forces on the blade. The equation of fluid dynamics and structure dynamics was integrated for simulation. Rotor blade was seen to be stable at peak efficiency and at stall with 100 percent rotational speed in flutter analysis of blade. They concluded that coupled fluid-structure method was capable in predicting the blade stability and also in computing the magnitude of amplitude and frequency. Hydraulic instabilities ofa slide gate chain was analysed by Hubner et. al (2010) by adopting monolithic coupling of fluid and structure. They said that natural frequency of system might be 50 percent less in water than in air and damping effect due to induction of flow might be higher than structural damping. They concluded that flowing fluid should be consider while identifying the hydrodynamic damping effects and hydroelastic instabilities. Matthew et al (Oct 2005) gives studied modern numerical techniques for simulation of aero-elastic phenomena is presented. This review was focused to coupling computational fluid dynamics codes to computational structural mechanics codes by arbitrary Lagrangian-Eulerian (ALE) method. Based on literature review we can observe that the method of fluid structure interaction plays a vital role in the analysis of many complex problems, especially in the case of research in mechanical and aeronautical stream. The details of present studies given in the following chapters.

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CHAPTER-3 THEORITICAL BACKGROUND

3.1 CFD and Fluid Model The fluid flow problems and transport phenomena are governed by basic conservation principles such as mass conservation, energy and momentum conservation. These are the partial differential equations which are solved at each grid point and gives the mean value of physical properties at each node of grid. All these conservation equations are solved which is based upon the fluid model and formed a set of partial differential equations known as governing equations of the fluid. 3.2 Mass Conservation Principle and Continuity Equation The mass conservation principle states that mass will remains conserved in the system, it means the rate of mass entering in a fluid element is equal to the net rate of flow of mass going out to the fluid element. When we apply this physical principle to a fluid model a differential equation is formed, which is called as continuity equation. For a compressible fluid flow the continuity equation can be written as follows: 𝜕𝜌 𝜕𝑡

+div (ρu) = 0

Where,  is the fluid density and u is the velocity of the flowing fluid. First term of equation is known as rate of change of density with respect to time and the second term is net flow of mass going out of the element boundaries. 3.3 Newton’s Second Law and Momentum Equation Newton’s second law states that the rate of change of momentum of a fluid particle equals to the sum of the forces acting on the particle. The forces acting on a body are a combination of both surface forces and body forces. When this law is applied for Newtonian fluid where viscous stress is proportional to the rates of deformation, the resulting equations are called as Navier-Stokes equations and it is valid for both compressible 14

flow and incompressible flow. The equations given below shows the momentum conservation principle 𝜕(𝜌𝑢) 𝜕𝑡 𝜕(𝜌𝑣) 𝜕𝑡 𝜕(𝜌𝑤) 𝜕𝑡

𝜕𝜌

+div (ρUu) = -𝜕𝑥 + div (µ grad u) +𝑆𝑀𝑥 𝜕𝜌

+div (ρUv) = -𝜕𝑦 + div (µ grad v) +𝑆𝑀𝑦 𝜕𝜌

+div (ρUw) = - 𝜕𝑧 + div (µ grad w) +𝑆𝑀𝑧

Where,  is the density of fluid, U represents the velocity vector and u, v and w, are the velocity components in X, Y and Z direction respectively.  Represents dynamic viscosity of fluid and 𝑆𝑀 represents the momentum source term which could be occurs due to body forces.

3.4 Finite Volume Method Finite volume method is a numerical technique used in well-established commercial computational fluid dynamics codes for the purpose of solving the governing differential equations of the fluid flow. The first step involved in CFD is to divide the domain of computation into number of smaller regions, they are called as control volumes or cells and the collection of these cells is known as grid or a mesh. Fluent uses the finite volume technique to convert the general transport equation in to a system of algebraic equations and it uses different iterative methods to solve the algebraic equations. Key steps involves to find the solution for the transport equation of a physical quantity are mentioned below The steps are as follows:  Division of geometry in to smaller regions (control volumes) using a computational mesh.  Integration of the governing equations of fluid over all the control volumes of the domain.  Discretization – conversion of the resulting integral equations in to a system of algebraic equations.  Finding a solution to the system of algebraic equations by an iterative method.  The general form of transport equation in conservative form can be written as 𝜕(𝜌Ø) 𝜕𝑡

+div (ρ Ø u) = div (Ʈ grad Ø) +𝑆Ø 15

Where the variable Ø can be replaced by any scalar quantity, is the diffusion coefficient. The left hand side of the equation contains the rate of change term and convective term, whereas the diffusive term and source term lie on the right hand side of the equation. Integrating over the control volume and applying the Gauss’s divergence theorem on the general transport equation gives 𝜕 𝜕𝑡

∫ρ Ø

dV

+

∫𝐴 𝑛 (ρ Ø u)dA

= ∫𝐴 𝑛 (Ʈ grad Ø) dA +

∫𝐶𝑉 𝑆Ø 𝑑𝑉

3.5 Turbulence Model The present study deals with turbulent flow. Turbulent flows consist of fluctuations in the flow field in time and space. Turbulent flow is a very complex flow. The complexity in flow arises mainly because of three dimensional, unsteady and it consists of more than one scales. It could have significant effects on the flow characteristics. Turbulent flow occurs when the inertia forces in the fluid will be greater or dominating when compared to viscous forces, which leads to flow of high Reynolds Number. The Navier-Stokes equations describe laminar flow as well as turbulent flow without the need of additional information. Turbulence models was developed to account the effects of turbulence without recourse to a prohibitively fine mesh and direct numerical simulation. The most important approaches to simulate turbulence are Reynolds-averaged Navier-Stokes (RANS) models, large eddy simulation (LES) models and detached-eddy simulation (DES) models. In present case, the RANS models are used. 3.6 Reynolds Averaged Navier-Stokes (RANS) Equations Assuming that the density fluctuations are negligible, the equations for transient flow can be averaged. A modified set of transport equations is formed by taking averaged and fluctuating components of velocity and can be solved for transient simulation. V= 𝑉̅ +𝑉′ 𝜕(𝜌) 𝜕𝑡

+

̅𝑗 ) 𝜕(𝜌𝑉 𝜕𝑥𝑗

16

=0

̅𝑖 ) 𝜕(𝜌𝑉 𝜕𝑡

+

̅̅̅̅𝑗 ) 𝜕(𝜌𝑉𝑉 𝜕𝑥𝑗

𝜕𝜌

= -𝜕𝑥 +

̅̅̅̅̅̅𝑗 ) 𝜕(σ𝑖𝑗 −𝜌𝑉′𝑉′ 𝜕𝑥𝑗

𝑖

+ 𝑆𝑀

Where 𝑉𝑖 are the velocity components, σ is the stress tensor including both normal and shear components of the stress, p is the pressure, 𝑆𝑀 is the momentum source. 3.7 K-Epsilon (k-ε) Turbulence Model This model has very good convergence rate and its required relatively less memory when compared to other available turbulence model hence for simulation of mean flow characteristics of turbulent flow it is widely adopted in computational fluid dynamics. It uses two transport partial differential equation to completely simulate the turbulent flow and to provide general information of turbulence. Its main purpose is to improve the mixing-length of model, as well as to form an alternative way for prescribing the turbulent length scales in moderate to high flow complexity. 

The first transported variable (k) represents the turbulence kinetic energy.



The second transported variable (ε) represents the rate of dissipation of turbulence kinetic energy. For turbulent kinetic energy k

𝜕(𝜌𝜅) 𝜕𝑡

+

𝜕(𝜌𝜅𝑢𝑖) 𝜕𝑥𝑖

𝜕

µ

𝜕𝜅 ] 𝜕𝑥 𝑘 𝑗

=𝜕𝑥 [𝜎 𝑡 𝑗

+ 2µ𝑡 𝐸𝑖𝑗 𝐸𝑖𝑗 – ρε

For dissipation ε

𝜕(𝜌ε) 𝜕𝑡

+

𝜕(𝜌ε𝑢𝑖) 𝜕𝑥𝑖

𝜕 µ𝑡 𝜕ε [ ] 𝜕𝑥𝑗 𝜎ε 𝜕𝑥𝑗

=

ε 𝜅

𝜀2 𝜅

+ 𝐶1ε 2µ𝑡 𝐸𝑖𝑗 𝐸𝑖𝑗 – 𝐶2ερ

Where 𝑢𝑖, Represents velocity component in corresponding direction 𝐸𝑖𝑗, Represents component of rate of deformation µ𝑡, Represents eddy viscosity. The k-ε model has been used specifically for planar shear layer and flows with recirculation zone. This model is used widely and validated turbulence model with wide range of applications in industrial and environmental flows, its shows its popularity. It is generally useful in free-shear layer flows with small pressure gradients as well as in confined 17

flows where the Reynolds shear stresses are important. It required supply of only initial and/or boundary conditions so we can say it is relatively simple than other available turbulence model.

3.8 Realizable k-ε Model An immediate benefit of the realizable k-ɛ model is that it provides improved predictions for the spreading rate of both planar and round jets. It also exhibits superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation. In virtually every measure of comparison, Realizable k-ɛ demonstrates a superior ability to capture the mean flow of the complex structures. 3.9 K-ω Model This model is similar to the k-ɛ model, but the difference is, it solve for the specific rate of dissipation of turbulence kinetic energy. In this model ω represents the specific rate of dissipation of kinetic energy. It is generally a low Reynold’s number model and more nonlinear than k-ɛ model, therefore relatively difficult to converge. The K-ω model employed in many cases, where k-ɛ model does not provides accurate results. Such as in the case of internal flow. 3.10 Finite Element Method and Structural Model Study of behaviour of structures under the influence of loads is known as structural dynamics. The current work involves the transient dynamic analysis which determines the structural response under the impulse load. In general two types of loads acts on any structural member. The first one is static load which do not vary with time and provide enough time to structure to respond against the load, while the second one is dynamic load, which changes with time quickly when compared to the static loads. Impulse load is a kind of dynamic loads which acts on the structure or system with greater magnitude within a short interval of time. Through this analysis, the time history of responses such as displacement, stress, strain of structure can be calculated. The equilibrium equation for multi degree of freedom system is given as 𝜕𝜎𝑥𝑥 𝜕𝑥

+

𝜕𝜎𝑥𝑦 𝜕𝑦

+

𝜕𝜎𝑥𝑧 𝜕𝑧

𝜕2 𝑢

+𝑓𝑥 = 𝜌 𝜕2 𝑡 18

in x-direction

𝜕𝜎𝑥𝑦 𝜕𝑥 𝜕𝜎𝑥𝑧 𝜕𝑥

+ +

𝜕𝜎𝑦𝑦 𝜕𝑦 𝜕𝜎𝑦𝑧 𝜕𝑦

+ +

𝜕𝜎𝑦𝑧 𝜕𝑧 𝜕𝜎𝑧𝑧 𝜕𝑧

𝜕2 𝑣

+ 𝑓𝑦 =

𝜌 𝜕2 𝑡

+ 𝑓𝑧 =

𝜌

𝜕2 𝑤 𝜕2 𝑡

in y-direction in z-direction

Where, 𝑓𝑥 , 𝑓𝑦 , 𝑎𝑛𝑑 𝑓𝑧 are the body forces in x, y and z direction respectively. It is normal practice to use a numerical technique called finite element method (FEM) to find the solution for equation. The basic principle behind this method of finding an approximate solution to the differential equations is to divide the volume of a structure or system in to smaller (finite) elements such that infinite number of degree of freedoms is converted to a finite value. The sequence of steps involved in solving the equation of motion is as follows: First steps involve conversion of a structure member into a system of finite elements, which are connected at the nodes and then defining the degree of freedom at these nodes. Second step involves determination of stiffness matrix, mass matrix, and force vector for each element in a mesh with reference to the degree of freedom for the elements The force –displacement relationship and inertia force- acceleration relationship for each elements can be written as (𝑓𝑠 ) = 𝑘𝑒 𝑢𝑒

(𝑓𝑠 ) = 𝑚𝑒 𝑢𝑒

Where, 𝑘𝑒 is the element stiffness matrix, 𝑚𝑒 is the element mass matrix , 𝑢𝑒 and 𝑢̈ are the displacement and acceleration vector for the element respectively. Formation of transformation matrix (Boolean matrix contains zeros and ones) that connects the values of each element in to the global finite element assemblage. It simply locates the elements of, 𝑘𝑒 , 𝑚𝑒 and 𝑢𝑒 at the proper places of the global matrices. For instance the elemental displacements 𝑢𝑒 can be related to global matrix u through the following expression 𝑢𝑒 = 𝑎𝑒 u Assembling of element matrices to evaluate the global stiffness, mass matrices and applied force vector for the final assemblage k=𝐴𝑁 𝑒=1 𝑘𝑒

m=𝐴𝑁 𝑒=1 𝑚𝑒 19

p(t)=𝐴𝑁 𝑒=1 𝑝𝑒 (t) Where A is an operator responsible for assembly process. According to the transformation matrix 𝑎𝑒 , the element mass matrix, element stiffness matrix and element force vector are placed in the respective global matrices and the arrangement is based on the number of an each element e  1 to Ne, where Ne is the number of elements. The final equation of motion with the global matrices is formulated as in the form of basic governing equation. This equation can be solved for u (t) using an appropriate iteration schemes which gives the response of system in term of nodal displacement values. 3.11 System Coupling In ANSYS Workbench, the FSI (two-way coupling) analysis can be performed by connecting the coupling participants to a component system called System Coupling. A participant system is a system which either feeds or receives data in a coupled analysis. Here, Fluent (participant 1) and ANSYS Mechanical (participant 2) are acting as coupling participants. Figure-3 depicts the work flow of a FSI simulation using System Coupling with coupling participant. Initially, system coupling collects information from the participants to synchronize the whole set up of simulation and then the information to be exchanged are given to the respective participant. The next step of the work process is organizing the sequence of exchange of information. The solution part of the chart varies for different ways of coupling. Finally, the convergence of coupling step is evaluated at end of the every coupling iteration.

Figure-3.1: System Coupling Flowchart Two-way coupling has a more intrinsic solving facility as any time step (coupling step) is launched, Fluent acquires a converged solution according to its own criterion of the convergence and transfers the fluid forces to ANSYS Mechanical. Then the displacement value of a structural member is obtained with help of the solution provided by Fluent for the same time step. The calculated solution of ANSYS Mechanical is given 20

back to the Fluent to determine a new set of fluid forces according to nodal displacements of previous time step. This is said to be a coupling iteration and continues until the convergence criterion of data transfer is reached. 3.12 Data Transfer Data transfer between the coupled participants is one of the critical parts of an FSI analysis. At the interface of the two mediums, the information has to be exchanged between two different meshes of different mediums. This is carried out by a systematic sequence and it includes some sub processes. The first process of the data transfer is to match or pair the source and target mesh to generate weights. The source mesh feeds the data to the target mesh and this matching is done by two different mapping algorithms in System Coupling according to the nature of the data transferred. The first algorithm is called the General Grid interface (GGI) which uses the method of dividing the element faces of both target and source sides into n (number of nodes on each side) integration points (IP). These three dimensional IP faces are converted into two dimensional quadrilaterals, which are made up of rows and columns of pixels. Pixels of both target and source sides are intersected to get overlapping areas called control surfaces. Finally, mapping weight contributions are determined for each control surface by the amount of pixel interactions, these interactions are accumulated to get the value of mapping weights for each node. The mapping weights generated by this algorithm are conservative in nature, so it is used as a default algorithm in Workbench for transferring the quantities like forces, mass and momentum. The conservative nature of GGI algorithm is shown Figure 3.2.

Figure-3.2: conservative nature of GGI algorithm

21

The next one is the `Smart Bucket algorithm’ shown in Figure-5; in this algorithm, the process of computing the mapping weights starts by dividing the target mesh in to a grid of buckets (simple group of elements on a mesh). Then mapping weights are computed for each node on the source mesh which is already associated with the buckets of target mesh. Two cases of buckets can exist i.e. empty (no element inside it) and nonempty (contain elements) bucket. In the latter case, the source node is matched to one or more elements in the bucket of target mesh and this is executed by iso-parametric mapping. For the case of an empty bucket, the closest non-empty bucket is identified and the same procedure is followed using iso-parametric mapping. Due to the profile preserving nature of the generated mapping weights, this is used as a default algorithm in Workbench for transferring the non-conserved quantities such as displacement, temperature and stress.

Figure-3.3: Profile preserving nature of smart bucket algorithm

It can be concluded that the fine mesh must be used on the sending side when conservative algorithm is used in order to send as much information as possible, on other hand for the profile preserving algorithm, the receiving side should have the refined mesh for the purpose of capturing sufficient information. Finally, interpolation algorithms are accountable for target node values with the help of source data and mapping weights generated by any one of the above algorithms 3.13 Time Advancement Schemes There are three classes of methods for advancing a time-accurate fluid/structure simulation forward in time: the monolithic approach, the fully coupled approach, and the loosely coupled approach. In the monolothic approach for aeroelasticity problems, the fluid and structure equations of motions are viewed as a single equation set and solved using a unified solver. From the computer code’s point of view, a structural element is differentiated from a fluid element or control volume 22

only by the difference in variables and spatial representation scheme for each type of element. The primary advantage of a monolithic approach is that fully consistent coupling is preserved; that is, the fluid and structure are perfectly synchronized while advancing a single time step. This usually leads to enhanced robustness, stability, and larger allowable time steps. The fully coupled approach also synchronizes the fluid and structure systems at each time step, but does so using a partitioned scheme. In a partitioned scheme, the fluid and structure code modules are separate, with fluid loads and structural displacements transferred back and forth within a single time step. The solvers for the fluid and structure systems are entirely separate and may be constructed for efficiency in each case. In the fully coupled approach, sub-iterations are performed until the entire system is fully converged. The fully coupled approach retains the synchronicity property of the monolithic scheme but also has the advantages of a partitioned scheme, namely improved code maintainability and algorithmic flexibility for physically disparate systems. The loosely coupled approach is similar to the fully coupled approach because it, too, is a partitioned method. However, the fluid/structure system is not sub-iterated to full convergence at each time step. Instead, the fluid and structure system exchange data one, or maybe two, times within a time step. The fluid and structure solution updates are lagged, or staggered, resulting in lower computational cost per time step than a fully coupled approach. The two systems are never fully in phase, and this introduces a temporal error in addition to the truncation error of the fluid and structure integration schemes. Care must be taken to maintain both accuracy and stability when constructing a loosely coupled scheme. A lagged approach not only introduces additional error, but may also result in a system that is not dynamically equivalent to the physical system. Unless the time lag is sufficiently small, spurious numerical solutions may exist. However, loosely coupled approaches have been successfully demonstrated on an array of aero-elasticity problems and the dynamic equivalence argument does not appear to be of great practical importance. In addition to the already mentioned advantages of a partitioned approach, the primary advantage of a loosely coupled scheme is the relatively small computational expense per time step. 3.14 Re-Meshing Re-meshing of the volume mesh is an alternative to the spring and structural analogy methods. Re-meshing techniques generate a new mesh 23

each time the boundary moves based on the prescribed boundary motion and the geometry of the problem, rather than on any type of structural analogy.

CHAPTER 4 RESEARCH METHODOLOGY

A brief introduction to the overall method is given in this section. Initially, geometric models of both fluid and solid domains are created with appropriate dimensions. Design modeller OF ANSYS are used to create the geometries models. The surface and volume mesh of fluid domain are formed using ANSYS Fluent and the finite element mesh is created by ANSYS Meshing. The two computational meshes differ with parameters such as cell type, cell size and mesh resolution. The completed meshes are imported to the respective numerical solvers where the simulation setup of a model is implemented. The simulation setup includes essential steps such as assigning the material properties, boundary conditions and numerical schemes for the two different models. At the end of the simulation setup, the fluid model consists of mediums air where the wing is placed inside the fluid domain such that the flow passes the plate within desired time period, whereas the structural model is a simple plate member with one ends fixed in position. Finally, the two solvers are coupled in Workbench using System Coupling to exchange the data according to the type of coupling. 4.1 Geometry Wing is generated by using NACA 2412 aerofoil of chord length 500 mm and span of 1000 mm in design modeller. The NACA 2412 aerofoil is part of the NACA 4 digit series of airfoil classifications. The four digits are determined the characteristics of the airfoil in terms of percentage of length of the chord. NACA 2412 determines that the airfoil has a maximum camber of 2% of chord length, located at 40% of chord from 24

the leading edge, with a maximum thickness of 12%. Of chord. The fluid domain is made as a square prism of 2m in which the rectangular plate of dimension 7.5m x 2m x 0.2m is placed inside at 20 degree angle of attack. Figure shows a closer view of the plate fixed at one side. Fluid domain is created in order to make a refined mesh around the structural member.

Figure-4.1: Wing inside a fluid domain 4.2 Computational Mesh In CFD mesh, the surface mesh is first created by taking triangular elements, which is then used to create a volume mesh. The volume mesh is made up by tetrahedral cells which belongs in category of unstructured mesh. Unlike the structured mesh, the cells of unstructured mesh cannot be identified using i, j, k index. The mesh of the entire computational fluid domain is shown below.

25

Figure-4.2: Meshing over the wing

Figure-4.3: Meshing over fluid domain 4.3 Simulation Setup The computational work of this project is divided in to two parts, the first part deals with the CFD model and the other is with the structural model. Subsequently, the simulation setups of this work also follow the same partition which is explained in the below sections. 4.4 Material Properties The important properties of both air used in this simulation are shown in Table

Table-4.1: Fluid property

26

4.5 Turbulence Modelling Setup The theoretical explanation of turbulent flow and its modelling is given in Table Turbulent model

K-epsilon model

Near wall treatment

Scalable wall function

Table-4.2: Turbulence modelling setup

4.6 Boundary Conditions The boundary conditions applied on the boundaries of the fluid domain i.e velocity inlet and pressure outlet in span wise direction and the rest of the faces of fluid domain are wall. 4.7 Solver Setup Commercial available software FLUENT were used as a numerical solver to solve the fluid structure interaction over rectangular plate and tapered wing. Computation were performed using finite element method to solve the continuity, momentum and Reynold’s averaged navier stroke equation at different grid point. The table 4.3 shows the method adopted for temporal and spatial discretization schemes used in analysis in fluent. The number of time steps used is 100 with step size of 0.01.

Temporal Discretization

Second order implicit

Pressure-Velocity Coupling

Simple

Spatial Discretization Pressure

Second order

Momentum

Second order upwind

Volume Fraction

Compressive

Turbulent Kinetic energy (κ)

First order upwind

Turbulent Dissipation rate (ε)

First order upwind 27

Table-4.3: Discretization Scheme used in fluent

4.8 ANSYS Mechanical Setup

Figure-4.4: Structural member setup

Figure-4.4: shows the overall simulation setup of the structural member. The one edges of the wing are fixed and the calculated fluid forces are applied on the surface of the wing which is described as a fluid solid interface. Apart from this, it follows the same transient setups like time step size and end time as in Fluent. 4.9 System Coupling Setup System coupling is a coupling tool used in Workbench to integrate different domain solvers in multi-physics simulations. The working principle and procedure of System Coupling is shown in Figure.

28

Figure-4.5: FSI analysis setup using system coupling

Figure-4.5: depicts the FSI analysis setup of this project work using System coupling with Fluent and ANSYS mechanical as numerical solvers. Initially, the simulation setups of both solvers in the preceding sections are executed, and then the setup component of the solvers is integrated into the setup component of System Coupling as shown. This makes the System Coupling to synchronize the numerical conditions of both solvers and to identify the fluid structure interface. The next step is to assign the simulation setups in System coupling. This consists of three main steps .  Analysis Settings: This setting includes time step size, end time and maximum & minimum number of coupling iteration for each time step. Generally, other than the coupling iteration for each time step, the required information is automatically fed in to System Coupling once the solvers are coupled.  Data transfer: This is the most vital part of the coupling device which includes and manages the data transfer sequence between two numerical solvers. This data transfer process varies with the type of coupling. Figure4.6: shows the data transfer for one-way and two-way coupling analyses. One-way coupling analysis is carried out with single-way data transfer from Fluent to ANSYS Mechanical which transfers the forces, whereas two-way coupling has data transfer in both direction i.e. first one from Fluent to ANSYS Mechanical (forces) and the second one is from ANSYS Mechanical to Fluent (nodal displacements).

29

 Simulation sequence: The working sequence of the numerical solvers should be given here as an input.

Figure-4.6: Properties of Data Transfer

30

CHAPTER 5 RESULTS AND DISCUSSION

5.1 FSI Analysis of Rectangular Plate:

FSI analysis was made on rectangular plate at flow speed taken as Mach = 0.46, the one end of plate was kept clamped while the other end remains free. The contour of total deformation, elastic strain and maximum shear stress obtained by post processing is shown in figure 5.1, 5.2 and 5.3 respectively. From figure 5.1 we can see that the free end is deformed more as compare to fixed end, as we expected. Deformation intensity of the plate reduces from tip to fixed end.

Figure 5.1: Total deformation contour

31

Figure 5.2: Elastic Strain Contour

Figure5.3:Maximum Shear Stress Contour

The displacement or deformation pattern of the rectangular plate structure with the time series is shown in figure 5.4. Here plot shows with increase in time deformation on structure reduces. Initially plate deformation is maximum but with respect to time it reduces exponentially on both 32

positive and negative sense. In other word we can say that deformation is damped out and achieved the some equilibrium mean deformation. This shows the dynamic nature of system which we already named as flutter tendency in chapter 1.

Figure-5.4: Displacement vs time curve

Linear relationship has been observed between stress and strain on the system shown in figure 5.5. The equivalent stress of the system was almost 80 MPa with corresponding strain is 0.004. Point “B” represents equivalent state of system. The co-ordinate of point “B” gives the exact magnitude of equivalent strain and stress respectively.

33

Figure-5.5: Stress vs Strain curve

Figure-5.6: Stress vs time curve Figure 5.6 represents the post processing result of stress variation with time. The pattern of this graph is similar to the graph of figure 5.4 i.e. deformation versus time graph. From stress vs time graph we can see the fluctuating characteristics of stress in some interval of time. It will also dampen out exponentially and finally reached to equivalent state after 6.5 seconds, as shown by vertical bold line. Point “B” in the graph represents the time required to reach in equivalent state.

34

5.2 FSI Analysis of wing FSI analysis of swept back wing has been done by passing the flow over it at Mach 0.46. Chord length of wing is greater at the root, which is considered here as fixed end. At the free end chord length is smaller compared to root. Same airfoil of NACA 2412 series has been taken from root to tip to design the wing, with varying chord length. The post processing results are presented in this section. The data was collected after the 10 sec from flow starts to accelerated. Figure 5.7 represents the total deformation contour of swept wing after the 10 sec of flow of air passing over it with a speed of around 150 m/s. The contour shows the maximum deformation at the tip of the wing, which is around 2.5 mm. Displacement of structure, reduces from tip to root and it went to almost zero at the root as we expected.

Figure-5.7: Total deformation contour Figure 5.8 and 5.9 represents the equivalent stress and equivalent strain contour of the system. Maximum stress has been observed at the root of the wing, near the centre of the chord. The magnitude of stresses has been seen reducing from this point as parabolic zones. A parabolic region of same colour represents the same value of equivalent stress. Near the 35

leading edge, trailing edge and tip of the wing, least value of equivalent stress has been observed. Since strain will always be directly proportional to the strain, so same pattern of equivalent strain can be seen

Figure 5.8: Equivalent stress contour

In figure 5.9. Maximum value of equivalent elastic strain of magnitude 0.00019 was found at the root of wing near the half of chord of wing. Variation of displacement with respect to time has plotted in figure 5.10. We can see the transient condition of displacement during the time interval 0 sec to 1.5sec. After 1.5 sec the transient condition dies out and system becomes stable with an equivalent displacement of the system was around 2.5mm. So after initial transient dies out the system represents the static characteristics of aeroelasticity.

36

Figure 5.9: Equivalent Elastic Strain contour

Figure 5.10: Displacement vs time curve

Figure 5.11 shows the variation of stress with strain plot and sit shows the linear variation of stress with strain or vice-versa or in other words we can say that there would be a linear relationship exists between stress and strain. 37

Figure 5.11: Stress vs Strain Plot

The variation of equivalent stress with time has represented in figure 5.12. Initial variation in equivalent stress can be observed by the plot. When flow started over the wing, initial magnitude of equivalent stress was around 26 MPa but after some interval of time it becomes stable and reached to maximum value of around 40 MPa.

38

Figure 5.12: Stress vs time curv CHAPTER 6 CONCLUSION Post processing result of FSI analysis over both rectangular plate and wing structure gives the contour of total deformation, Elastic strain, Maximum shear stress and plot of Displacement vs Time, Stress vs Time, Stress vs Time and Stress vs time. Comparison of graph, plots and contour of plate and wing are listed in current section.  Total deformation contour of rectangular plate shows the maximum deformation of magnitude 53.448 mm near the tip and minimum is 6 mm near the root. Contour shows the uniform deformation along the chord at each section of plate. While deformation contour of wing shows the abruptly reduced value of both maximum and minimum deformation. The magnitude of maximum and minimum deformation is 2.5 mm and 0 mm respectively.  Result of elastic strain contour of rectangular plate shows the maximum value is 0.00038 at the trailing edge of plate near the root and minimum value is 4.447 × 10-8 near the tip of the plate. While maximum value of elastic strain on the wing is 0.00019 at the root near the half of the chord and minimum value is 2.12 × 10-8. Minimum value of elastic strain in the plate remains uniform along the chord of plate while value of elastic strain remains minimum in small region of leading edge and trailing edge of wing along the span and remains uniform at the tip along the chord. So here again we conclude that the magnitude of maximum and minimum strain on the wing is lower than that of the plate.  Maximum value of equivalent shear stress on the plate is occurs at the trailing edge of the plate near thee root and near the tip section value of shear stress is minimum. While in the maximum shear stress acts at the root near the half of chord of the airfoil and shear stress is minimum in small region of leading edge and trailing edge of the wing along the whole span and remains uniform at the tip along the chord. The maximum value of equivalent shear stress is almost same on both plate and wing while the minimum value is lower for the wing section.  Displacement versus time plot also provides concluding remarks that small deformation persists on the wing. Equivalent displacement on the plate reached to equilibrium condition by dampening exponentially. While on the wing it first increases and reached to equivalent condition and remains same for the remaining time of flow.

39

 Stress versus time plot of rectangular blade shows the maximum value of equivalent shear stress is 75 MPa, which will reach after 6.5 seconds when the initial transient is dies out. It also dampens exponentially. While on the wing it keep increasing in a short interval of time, reached to maximum value of around 39 MPa and remains same for the rest of the time. The value of equivalent stress is also observed minimum for the wing compared to plate from stress versus time plot.

40

CHAPTER 7 FUTURE SCOPE OF WORK

The flutter analysis of wind turbine blade using fluid structure interaction. The aero-elastic stability analysis gives aero-elastic frequency and damping of blade, where the negative damping in mode shapes gives prone to ability of flutter, thereby neglecting negative damping it is possible to overcome the fluttering phenomenon of the blade.

41

REFERNCES

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