Engineering Resarch Paper On Fluid Structure Interaction (fsi)

A MAJOR PROJECT REPORT ON

“FLUID-STRUCTURE INERACTION ON AN AIRCRAFT WING” A project report submitted in partial filfillment of the requirement for the award of the bachelor’s degree In AERONAUTICAL ENGINEERING Under the guidance of INTERNAL GUIDE

Dr.S.Srinivas Prasad

By SANA KAUSER

(09R21A2143)

P. TARA SRIVALLI

(09R21A2154)

V. AKHITHA

(09R21A2106) At

(Affiliated to JNTU, Hyderabad and approved by AICTE – New Delhi)

Jawaharlal Nehru Technological University Hyderabad (Kukatpally, Hyderabad - 500 085, Andhra Pradesh, India)

MLRInstitute of Technology (Approved by AICTE, Affiliated to JNTU) Laxman Reddy Avenue, Dundigal, Qutbullapur (M), Hyderabad-43 R. R. DistPh:9949774842, 9866755166, 9652226061 Website: www.mlrinstitutions.ac.in

CERTIFICATE This is to certify that the Industry oriented major project report titled

“FLUID-STRUCTURE INTERACTION ON AN AIRCRAFT WING ” has been carried out by SANA KAUSER

(09R21A2143)

P. TARA SRIVALLI

(09R21A2154)

V. AKHITHA

(09R21A2106) At

MLR Institute of Technology, Hyderabad Submitted in partial fulfillment of the requirement for the award of the B. Tech degree in Aeronautical Engineering under

Jawaharlal Nehru Technological University

Dr. S. Srinivas Prasad

Dr. S. Srinivas Prasad

Head of Department Aeronautical Engineering

Head of Department Aeronautical Engineering

INTERNAL EXAMINER

EXTERNAL EXAMINER

ACKNOWLEDGEMENT “Task successful” makes everyone happy. But the happiness will be gold without glitter if we didn’t state the persons who supported us to make it a success. Foremost, we would like to express my sincere gratitude to my advisor Dr. Srinivas Prasad for the continuous support of our major project work, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped us in all the time of project and writing of this documentation. We could not have imagined having a better advisor and mentor for major project work. We are thankful to our principal Mr. P. Bhaskar Reddy for encouraging us throughout the course. We highly appreciate our colleagues for their constant friendship and intellectual input. It would have been all work and no play in the lab, if it were not for their friendly and humorous demeanor. We are thankful to all faculty members and staffs of the Department of Aeronautical engineering who assisted us in research, as well as in our graduate studies. Our sincere thanks also goes to Mr. J Ravinder Rao sir, M.D of Arya systems for supporting us to do the many projects in their groups and leading me working on diverse exciting projects. His technical advice and suggestions helped me overcome hurdles and kept me enthusiastic and made this work a wonderful learning experience.

Sana kauser

- 09R21A2143

P.Tara Srivalli - 09R21A2154 V. Akhitha

- 09R21A2106

ABSTRACT Fluid–structure interaction problems in general are often too complex to solve analytically and so they have to be analyzed by means of experiments or numerical simulation. Studying these phenomena requires modeling of both fluid and structure. Many approaches in computational aero elasticity seek to synthesize independent computational approaches for the aerodynamic and the structural dynamic subsystems. This strategy is known to be fraught with complications associated with the interaction between the two simulation modules. AGARD 445.6 wing will be generated along with the fluid domain. The transonic flow in subsonic flow regime (M= 0.9) over the wing will be simulated and the results will be validated by comparing the computational results with the previously published results. The stresses induced corresponding to the flow will be computed using the ANSYS Workbench. This project provides basic knowledge of FSI in aerodynamics.

TABLE OF CONTENTS ACKNOWLEDGEMENT

iii

LIST OF FIGURES

vi

LIST OF TABLES

vii

ABSTRACT

ix

CHAPTER1. INTRODUCTION 1.1Concept of Fluid-Structure Interaction

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1.1.1Classification of FSI

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1.1.2 Types of FSI

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1.2 Brief History of Fluid-Structure Interaction

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1.3 Advantages

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1.4 Physics of Fluid-Structure Interaction

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1.5 Problem Definition

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1.6 Objective

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1.7 Scope of the project

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1.8 Organization of thesis

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1.9 Software package used

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CHAPTER2. LITERATURE REVIEW 2.1 Range of Computational aero-elastic model

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2.1.1 Fully coupled model

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2.1.2. Loosely coupled model

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2.1.3. Closely coupled model

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2.2 Weakly coupled fluid-structure system 2.2.1 Strongly coupled fluid-structure system 2.3 Aerodynamic Models

11 11 13

2.3.1 Physical Model

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2.3.2 Reduced-Order Models

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2.4 Inference from the literature survey

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2.5 Motivation to the work

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CHAPTER3. PROBLEM DESCRIPTION 3.1AGARD 445.6 Wing

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3.1.1 Airfoil Description

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3.1.2 NACA six-digit 65a004 airfoil

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3.2 Model Description

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3.2.1 Wing Specifications

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3.2.2 Material Properties

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3.3 Operating conditions

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3.4 Coupling

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CHAPTER4. EXPERIMENTAL PROGRAM 4.1 Modeling

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4.2 Meshing

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4.3 Flow Setup

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4.4 Structural set up

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CHAPTER5. RESULTS AND VALIDATION

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CHAPTER6. CONCLUSION

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CHAPTER7. BIBLIOGRAPHY

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LIST OF FIGURES Figure 3.1 Airfoil Geometry

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Figure 3.2: Airfoil generated using foilsim software

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Figure 3.3: Airfoil data of AGARD wing with a=1

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Figure 3.4: Airfoil point data for the airfoil at wing root

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Figure 3.5: Airfoil point data of the airfoil at wing tip

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Figure 3.6: AGARD 445.6 wing model

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Figure 4.1: Design of AGARD 445.6 wing in CATIA

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Figure 4.2: Representing one of the custom systems in ANSYS WORKBENCH

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Figure 4.3: Representing the procedure to import the geometry to the fluent

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Figure 4.4: Generated wing in Design modeler

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Figure 4.5: Wing with Domain

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Figure 4.6: Represents the wing subtracted from the domain

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Figure 4.7: Wing with domain after Boolean operation is performed

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Figure 4.8: Representing mesh on the fluid domain

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Figure 4.9: Showing mesh over the wing using wireframe view

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Figure 4.10: Created wing root named selection

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Figure 4.11: Showing Fluent launcher

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Figure 4.12: Geometry in fluent setup

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Figure 4.13: showing the setup for the solver

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Figure 4.14: Setting the dimensions

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Figure 4.15: Represents the selection of energy equation in fluent

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Figure 4.16: Selection of k-epsilon method under viscous models

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Figure 4.17: showing materials properties in problem setup

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Figure 4.18: specifying the cell zone conditions

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Figure 4.19: defining the boundary conditions

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Figure 4.20: specifying the reference values

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Figure 4.21: Specifying the solution methods

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Figure 4.22: Specifying lift, drag and moment monitors

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Figure 4.23: Solution initialization to compute from wall-solid

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Figure 4.24: Specifying the iterations and time step in run calculations

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Figure 4.25: Scaled residuals graph

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Figure 4.26: Drag plot

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Figure 4.27: lift plot

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Figure 4.28: Pressure contour on wall solid (wing)

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Figure 4.29: Contour of static temperature

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Figure 4.30: contour of Turbulent Kinetic energy

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Figure 4.31: Wireframe model of the geometry in CFD post

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Figure 4.32: Plane located on wall-solid showing pressure distribution

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Figure 4.33: Represents that coupling of flow with structural analysis

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Figure 4.34: Material added in engineering data

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Figure 4.35: Meshed geometry in static structural

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Figure 4.36: Fixed support applied at root chord of the wing

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Figure 4.37: showing imported pressure acting on a wing

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Figure 4.38: Contour of total deformation on wing

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Figure 4.39: Contour of total deformation on wing

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Figure 4.40: Contours for vonmisses strain

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Figure 4.41: Representing the 6 modes of frequency

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Figure 4.42: Shows the tabular data of the frequencies obtained

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Figure 4.43: shows the tabular data of the frequencies

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Figure 5.1First mode of frequency

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Figure 5.2: mode shape of 2nd frequency

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Figure 5.3: mode shape of 3rd frequency

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Figure 5.4: mode shape of 4th frequency

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Figure 5.5: mode shape of 5th frequency

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Figure 5.6: mode shape of 6th frequency

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Figure 5.7: temperature Vs turbulent kinetic energy graph

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Figure 5.8: pressure Vs temperature graph

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Figure 5.9: pressure Vs turbulent kinetic energy graph

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Figure 5.10: pressure Vs velocity magnitude graph

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Figure 5.11: imported pressure Vs vonmises stress

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Figure 5.12: pressure Vs vonmisses strain

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LIST OF TABLES Table 5.1 Material Properties

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Table 5.2 Minimum and Maximum Deformation

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Table 5.3 Deformation at different flutter frequencies

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Table 5.4 Flutter frequency comparison

63

CHAPTER 1. INTRODUCTION 1.1 Background of Fluid-Structure Interaction In Fluid-structure interaction (FSI) problems, solid structures interact with an internal or surrounding fluid flow. FSI problems play prominent roles in many scientific and engineering fields, yet a comprehensive study of such problems remains a challenge due to their strong nonlinearity and multidisciplinary nature. Fluid-structure interaction (FSI) occurs when a fluid interacts with a solid structure, exerting pressure on it which may cause deformation in the structure. As a return, the deformed structure alters the flow field. The altered flowing fluid, in turn exerts another form of pressure on the structure with repeat of the process. This kind of interaction is called Fluid-Structure Interaction (FSI). Such interactions may be stable or oscillatory, and are a crucial consideration in the design of many engineering systems, especially aircraft. Failing to consider the effects of FSI can be catastrophic, especially in large scale structures and those comprising materials susceptible to fatigue. One of the typical problems, the fluid flow in either inside or outside of pipe or vessels exerts steady or oscillatory pressure on the wetted surface of pipes or vessels which may deform or vibrate them. Another one is that the flow of air around an Airplane wing causes the wing to deform, and as the wing deforms it causes the air pattern around it to change. In application of, Fluid-Structure interaction covers such subjects as Aero-elasticity, hydro-elasticity, flow induced vibration, thermal deformations. Aero-elasticity can be defined as the phenomena associated with the interaction of aerodynamic forces and inertial forces within elastic structural systems. There are also aeroelastic phenomena associated with interaction between aerodynamic and elastic forces alone. Aero-elastic problems mainly arise from the flexible nature of the structure. In other words, rigid structures do not experience aero-elasticity of any sort. It is well known that external forces acting on a flexible structural system (such as a wing) lead to a deformation in the 1

wing geometry, and this structural deformation thereby leads to additional aerodynamic loads. Fluid-Structure Interaction problems in general are often too complex to solve analytically and so they have to be analyzed by the means of experiments or numerical simulation. Many approaches in computational aero-elasticity seek to synthesize independent computational approaches for the aerodynamic and structural dynamic systems. This strategy is known to be fraught with complications associated with the interaction between the two simulation modules. In this project the fluid–structure interaction problem will be illustrated using the AGARD 445.6 wing by Predicting its initial boundary condition. AGARD 445.6 wing is used because the experimental results are available. This configuration was chosen because extensive research has been done in the field of aero-elasticity using this model. A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometry is presented. The computations are performed for AGARD 445.6 by considering the transient flow at subsonic mach numbers. 1.1.1 Classification of FSI In general, a fluid-structure interaction system is classified as either strongly or weakly coupled. Weakly coupled fluid-structure system: if a structure in the flow field or containing flowing fluid deforms slightly or vibrates with small amplitude, it will affect negligibly the flow field because of the relatively low pressure. These fluid-structure interaction systems are called weakly coupled systems. For these FSI systems, it is assumed that the force acting on the fluid due to the structural motion can be linearly super-imposed onto the original forcing function in the fluid.

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Strongly coupled fluid-structure system: Fluid-structure systems are called strongly coupled systems if alteration of the flow field due to large deformation or high amplitudevibration of the structure cannot be neglected. In such strongly coupled fluid-structure systems in which large structural deformation or displacement results in a significant alteration of original flow field, both altered and original flow fields cannot be linearly superimposed upon each other .

1.2 Types of FSI There are three types of fluid-structure interactions Zero strain interactions: Such as the transport of suspended solids in a liquid matrix. Constant strain steady flow interactions: The constant force exerted on an oil-pipeline due to viscous friction between the pipeline walls and the fluid. Oscillatory interactions: Where the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.

1.3 Brief History of Fluid-Structure Interaction In 1828, the concept of hydrodynamic mass (or added mass) was proposed first by Friedrich Bessel who investigated the motion of a pendulum in a fluid. He found out that a pendulum moving in a fluid had longer period than in a vacuum even though the buoyancy effects were taken into account. This finding meant that the surrounding fluid increased the effective mass of the system. Thereafter, in 1843 Stokes performed a study on the uniform acceleration of an infinite cylinder moving in an infinite fluid medium and concluded that the effective mass of the cylinder moving in the fluid increased due to the effect of surrounding fluid by the amount of hydrodynamic mass equal to the mass of the fluid displaced. It was known that this finding proposed the concept of fluid-structure interaction.

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In 1960’s some designers of nuclear reactor systems found that the hydrodynamic mass of a structure in a confined fluid medium resulting from the fluid-structure interaction was much larger than that for the structure in an infinite fluid medium which was equal to the mass of fluid displaced by the structure.

1.4 Advantages Practical uses fluid film interaction  FSI is responsible for countless useful effects in engineering.  It allows fans and propellers to function.  Sails on marine vehicles to provide thrust.  Aerofoil's on racecars to produce down force.

1.5 Physics of Fluid-Structure Interaction FSI is a true multi physics phenomenon where a fluid flowing around or within a structure causes it to move, spin or even change shape due to flow-induced pressure and shear loads. Multi physics - The ability to combine the effects of two or more different, yet interrelated physical Phenomena, within one, unified simulation environment. In FSI Numerical coupling is established between the different “physics” modules, Fluidstructure interactions (FSI) are those that involve the coupling of fluid mechanics and structural mechanics. Fluid–structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. This deformation, in turn, changes the boundary conditions of the fluid flow. Fluid–structure interactions can be stable or oscillatory. In oscillatory interactions, the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.

4

FSI results in the cause of Flutter. Flutter is a dangerous phenomenon encountered in flexible structures subjected to aerodynamic forces. This includes aircraft, buildings, telegraph wires, stop signs, and bridges. Flutter occurs as a result of interactions between aerodynamics, stiffness, and inertial forces on a structure. In an aircraft, as the speed of the wind increases, there may be a point at which the structural damping is insufficient to damp out the motions which are increasing due to aerodynamic energy being added to the structure. This vibration can cause structural failure and therefore considering flutter characteristics is an essential part of designing an aircraft.

1.6 Problem Definition AGARD 445.6 is widely used benchmark in computational Aero-elasticity. FSI arises in transient flow experiments are highly expensive and can be destructive. AGARD 445.6 wing is selected as it is regarded as benchmark in dynamic aero-elastic analysis. The transient flow in subsonic regime (M= 0.9) over the AGARD 445.6 wing will be simulated and the results will be validated by comparing the computational results with the previously published results. The stresses induced corresponding to the flow will be computed using the ANSYS Workbench.

1.7 Objectives Aim: To study the FSI on an aircraft wing. This project consists of the following major categories which encompasses.  To obtain a numerical study of FSI  To study the effect of fluid on the structure and vice versa.  Providing exposure to the FSI problem.

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While it is realized that a larger quantum of work is required to make the study more meaningful, this project was largely aimed at gaining a basic understanding and better overview of the fundamental structural behavior of the AGARD 445.6 wing under practical load conditions.

1.8 Scope of the project The scope of interest is to study of fluid structure interaction (FSI) on AGARD 445.6 (structure).The goal of this project is to explore ways through ANSYS WORKBENCH to compute the effect of the fluid over the wing and hence the changes in the structure of the wing by computing static structural analysis.

1.9 Organization of thesis Chapter 1 gives an introduction to the problem and focuses on the objectives of this project. In chapter 2, literature work on AGARD wing, fluid solvers, and fluid -structure interaction, fluid and structure mechanics had been reviewed. Chapter 3 discusses in detail the Methodology used. Chapter 4 describes the experimental program, analysis using ANSYS workbench and results are obtained. In chapter 5, the experimental results have been validated with the published results. In chapter 6 gives the conclusion drawn from the above analysis and future work have been documented in chapter 7.

1.9 Software package used ANSYS stands for Analysis System product. Dr. John Swanson was the founder of ANSYS Inc. In the year 1970 ANSYS was founded in order to establish a technology that facilitates several companies/industries to compute or simulate analysis issues. ANSYS is a generalpurpose finite element analysis (FEA) software package that is extensively used in industries to resolve several mechanical problems. FEA is a method of fragmenting a composite system in to small pieces called elements. The ANSYS software carries out equations that regulate 6

the performance of these elements and solves them resulting in an overall description of how system works integrally. The obtained results are displays in a tabulated or graphical form.  ANSYS is a dedicated general purpose Finite Element package used for determining the temperature, stress and strains.  ANSYS offers a comprehensive range of engineering simulation solution sets providing access to virtually any field of engineering simulation that a design process requires.  ANSYS is uses in industries in order to solve several mechanical problems and fluidstructure interaction problems,  ANSYS is a flexible and cost effective tool.

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CHAPTER2. LITERATURE REVIEW 2.1 Introduction This chapter includes description of cases that are studied for static aero-elasticity of AGARD 445.6 wing. AGARD 445.6 wing is being chosen because the experimental results are available and various aspects and modules related to the field of computational aeroelasticity are reviewed. To understand the fluid-structure interaction problem, we need to model both the structure and the fluid efficiently, and then we review various classes of CAE models.

2.1 Range of Computational aero-elastic model Computational aero-elasticity can be classified broadly under three major categories: fully coupled, closely coupled, and loosely coupled analyses. Before looking at the various CAE models in detail, it is useful to look at the generalized equations of motion [1] to explain CAE methodologies better.

[M]{q (t)}+[C] {q(t) +[K]{q(t)}={F(t)}………………………..… (2.1)

{W(x, y, z, t)}=

qi(t){Φi(x, y, z)…………………………… (2.2)

Here, {w(x, y, z, t)} is the structural displacement at any time instant and position and {q(t)} is the generalized displacement vector. The matrices [M], [C], [K] are the generalized mass, damping, and stiffness matrices; respectively and Φi are the normal modes of the structure, with N being the total number of modes of the structure. The term on the right-hand side of Eq. (2.1), {F (t)} is the generalized force vector, which is responsible for linking the unsteady

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aerodynamics and inertial loads with the structural dynamics. Eq. (2.1) shows that there are distinct terms representing the structures, aerodynamics, and dynamics disciplines. 2.1.1 Fully coupled model In this kind of approach, the governing equations are reformulated by combining fluid and structural equations of motion, which are then solved and integrated in time simultaneously. While using a fully coupled procedure, one must deal with fluid equations in an Eulerian reference system, and structural equations in a Lagrangian system. This leads to the matrices being orders of magnitude stiffer for structure systems as compared to fluid systems, thereby making it virtually impossible to solve the equations using a monolithic computational scheme for large-scale problems. Initially, combined Euler flow equations with plate finiteelement structures, and later combined the Navier-Stokes equations with shell finite-element structure to perform fluid-structure calculations. They used a domain decomposition method, wherein fluids and structures are solved in separate modules. And latter computations were on transonic aero-elastic response of 3-D wings by coupling a nonlinear-beam finite-element model with Navier- Stokes equations. This kind of fully coupled method has limitations on grid size, and is currently limited to 2-D problems as they are computationally expensive. 2.1.2. Loosely coupled model In this class of methodologies, unlike the fully coupled analysis, the structural and fluid equations are solved using two separate solvers. This can result in two different computational grids (structured or unstructured), which are not likely to coincide at the boundary. This calls for an interfacing technique to be developed, to exchange information back and forth between the two modules. The loosely coupled approach has only external interaction between the fluid and structure modules; or the information is exchanged after partial or complete convergence. This approach is like a multidisciplinary computing 9

environment, where one effectively controls the interaction between two commercial codes for each of the modules by means of interfacing techniques. This gives us the flexibility of choosing different solvers for each of the modules but the coupling procedure leads to a loss in accuracy as the modules are updated only after partial or complete convergence. 2.1.3. Closely coupled model This is one of the most widely used methods in the field of CAE as it not only paves way for the use of different solvers for fluid and structure models but also couples the solvers in a tight fashion thereby making it an efficient method for complex nonlinear problems. In this approach, the fluid and structure equations are solved separately using different solvers but are coupled into one single module with exchange of information taking place at the interface or the boundary via an interface module thereby making the entire CAE model tightly coupled. The information exchanged here are the surface loads, which are mapped from CFD grid onto CSD grid, and displacement field, which are mapped from CSD grid onto CFD grid. The transfer of surface displacement back to the CFD module implies deformation of the CFD boundary mesh and this call for a moving boundary technique to enable re-meshing the entire CFD domain for further computations as we march in time. Several models have been combined for individual modules to arrive at a coupled model. On the other hand, models ranging from linear beam finite elements to nonlinear solid finite elements have been used for structure module. These models are interlinked via necessary interfacing techniques, complexity of which depends on what two models are used for the individual modules. Ramji Kamakoti [1, 2]. According to Jong Chull Jo [3] fluid-structure interaction system is classified as either strongly or weakly coupled.

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2.2 Weakly coupled fluid-structure system: if a structure in the flow field or containing flowing fluid deforms slightly or vibrates with small amplitude, it will affect negligibly the flow field because of the relatively low pressure. These fluid-structure interaction systems are called weakly coupled systems. For these FSI systems, it is assumed that the force acting on the fluid due to the structural motion can be linearly super-imposed onto the original forcing function in the fluid. 2.2.1 Strongly coupled fluid-structure system: Fluid-structure systems are called strongly coupled systems if alteration of the flow field due to large deformation or high amplitudevibration of the structure cannot be neglected. In such strongly coupled fluid-structure systems in which large structural deformation or displacement results in a significant alteration of original flow field, both altered and original flow fields cannot be linearly superimposed upon each other. In 2004 and 2005 Kamakoti developed a closely coupled CAE model based on a threedimensional, multi-block, structured CFD solver for the RANS equations. Structural modal dynamic equations were solved simultaneously and were strongly coupled with the flow equations using fully implicit (iterative) and semi-implicit (non-iterative) time-marching methods. A linear structure model based on beam finite elements was employed to perform flutter analysis on the AGARD 445.6 wing. The flow solver used was based on the full 3-D RANS equations with well-validated turbulence models. A suitable method to evaluate Jacobians via the geometric conservation law was invoked in the model as well. The solver also has capabilities to include effects for multi-block moving boundary treatment based on master/slave concepts and transfinite interpolation techniques. Robust interfacing techniques were also embedded in the coupled solver to account for transfer of information between the two modules.

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In 2002 F. Liu, J. Cai, and Y. Zhu, Calculation of Wing Flutter by a Coupled Fluid-Structure Method [6], An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed for the simulation and prediction of • utter. The CFD solver is based on an unsteady, parallel, multiblock, multigrid finite volume algorithm for the Euler/Navier–Stokes equations. The CSD solver is based on the time integration of modal dynamic equations extracted from full Ž finite element analysis. A general multiblock deformation grid method is used to generate dynamically moving grids for the unsteady • flow solver. The solutions of the • flow- field and the structural dynamics are coupled strongly in time by a fully implicit method. The coupled CFD–CSD method simulates the aero-elastic system directly on the time domain to determine the stability of the aero-elastic system. The unsteady solver with the moving grid algorithm is also used to calculate the harmonic and/or indicial responses of an aero-elastic system, in an uncoupled manner, without solving the structural equations. Flutter boundary is then determined by solving the flutter equation on the frequency domain with the indicial responses as input. Computations are performed for a two-dimensional wing aero-elastic model and the three-dimensional AGARD 445.6 wing. Flutter boundary predictions by both the coupled CFD–CSD method and the indicial method are presented and compared with experimental data for the AGARD 445.6 wing. Daron A. Isaac, Michael P. Iverson [7], An automated Fluid-Structure Interaction (FSI) analysis procedure has been developed at ATK Thiokol Propulsion that couples computational fluid dynamics (CFD) and structural finite element (FE) analysis to solve FSI problems. The procedure externally couples a steady-state CFD analysis using Fluent® and a structural FE analysis using ABAQUS®. Pressure results from the CFD solution are interpolated and applied as pressure boundary conditions on the structural model. Displacements from the structural analysis are interpolated and applied to the boundary of the

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CFD mesh. Iteration between the CFD and the structural analysis continues until a solution is reached. The FSI procedure provides controls to monitor the solution and define termination criteria, as well as manage output. Automatic report generation of the solution is another feature of the FSI procedure. Plans and funding are in place to extend the FSI procedure to include coupling with thermal analysis as well. Previous studies mostly cover development of solution techniques for the solution of aeroelastic problems such as wing flutter analysis. Lui et al. developed a method for simulation and prediction of wing flutter problems by integrating CFD and CSD tools. Euler and NavierStokes equations are modeled by a CFD solver which is an unsteady, parallel, multi-block, multi-grid finite volume solver. CSD solver extracts modal equations and integrates over time. Both solutions are implicitly coupled with a strong coupling algorithm. A two dimensional and a three dimensional AGARD 445.6 wing are used for computations and the results are compared with experiments. 2.3 Physical Models Physical models used for treating fluid-structure interaction problems can vary enormously in their complexity, based on the applications. One of the simplest models is based on piston theory which expresses the pressure, p, at some point x, y at time t on the oscillating body, as a simple function of the motion at the same point and instant. It can be expressed as follows P= (ρU/M) (δw/δt +U δw/δx)………………………………………………………. (2.3) Where w is a function of x, y and t and it is the instantaneous deflection of the body. The symbols ρ, U and M represent free-stream density, velocity, and Mach number, respectively. This simple method is only useful for a limited set of flow conditions, and is usually used to verify more complex models in the appropriate limit. An improved model to the piston theory is the full-potential flow theory, which works under the assumption that the flow is in-viscid

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and irrotational. The potential flow model solves the nonlinear wave equation for the velocity potential, from which the velocity (and thereby the pressure) can be obtained using Bernoulli’s equation. If the body profile is assumed to be thin, the nonlinear equation can be cast into a linear convected-wave equation, which has found uses for many fluid-structure interaction problems such as flutter and gust response analysis. The linear convected-wave equation has trouble satisfying the boundary conditions because in the boundary condition, both the velocity potential and its gradient over different portions of the fluid domain are unknown (leading to a mixed-boundary problem). This is resolved by reducing the convected-wave equation (partial differential equation) to an integral equation using Green’s theorem or Fourier transform. This is also referred to as the boundary element approach. Another well-known model is based on small perturbation theory but it was found to fail when the flow is transonic (when shock waves may appear and disappear). Another class of models is the time-linearized or dynamically linear model, in which a steady state nonlinear solution is used as a starting point; then a small dynamic perturbation about this steady flow is considered, and all subsequent flow variables and shock motion are assumed to vary in a linear fashion. This model leads to an order of magnitude reduction in computer resources compared to the nonlinear model, and was found to be sufficient for many problems. However, this method was found to be less useful for turbo machinery problems. This approach can be extended to determine a full dynamically nonlinear solution, which involves solving a nonlinear convected-wave equation for potential flow or Euler or Navier-Stokes models. Either finite-difference or finite-volume schemes in spatial variables can be used to convert the system of partial difference equations to ordinary differential equations, which forms the basis for CFD. Additional models must be developed to account for turbulence flow features and for transition from laminar to turbulent flows. Another class of models beginning to gain interest

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in the field of fluid-structure interaction is reduced-order modeling (ROM) techniques, discussed next. Ramji kamakoti et al [1, 2] and Mehmet Akgul et al [8], For the past several decades, researchers have worked in the field of CFD to develop models for complex unsteady flows. The computational cost for high dimensionality model, especially for aero-elastic problems, has limited the use of full CFD models for such applications. Recently, advances are being made to develop a novel technique for unsteady flows based on the modal character of flows, which can be termed reduced-order models. In the structural dynamics world, over the years, finite element models for structural dynamics have been reduced in size by using the normal or Eigen modes of the structure, thereby reducing the model to a few degrees of freedom from thousands of degrees of freedom .This reduces the computation time for solving such problems, while maintaining the accuracy of the physical phenomena. This method has also gained interest in the field of fluid dynamics, because such an approach gives us great benefits (saving computational costs and giving insight into the dynamics of the fluid models by considering their different modal structures). This method involves constructing a computational aerodynamic model using the dominant Eigen modes of unsteady aerodynamic flows. Combining such a reduced-order aerodynamic model with a structural modal model is an efficient way to form an aero-elastic modal model with a modest number of degrees of freedom. Extracting the dominant Eigen modes for large dimensional systems can be potentially difficult. Hence another modal approach that seeks to include more information on the flow response to enhance the accuracy of the reduced model has been developed and it is called the proper orthogonal decomposition (POD) method. It is a much simpler approach than the Eigen mode approach, and it uses a methodology based on nonlinear dynamics and signal processing. One disadvantage of this method is that determining the POD modes can be computationally expensive compared to determining the Eigen modes. Extensive research

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is being done to construct nonlinear aerodynamic ROMs and to use the Eigen mode ROM approach to develop better turbulence models. However, it is still unknown whether ROM or POD approach can accurately predict all the length scales associated with the turbulence models.

2.2 Inference from the literature survey AGARD 445.6 is widely used computational Aero-elasticity. Aero-elastic experiments are highly expensive and can be destructive, thus this case is one of the few benchmark cases available in the literature. Many experimental results from the previously published thesis have been review and understood that FSI is responsible for countless useful effects in engineering. This project involves the FSI analysis performing structural analysis in the Mechanical application taking into account the interaction with the corresponding fluid analysis. After the completion of literature survey, this chapter helps us to understand the phenomena and mechanism of fluid-structure interaction and get a fundamental knowledge and information for the analysis of fluid-structure interaction problems occurring on the various structures, and mainly on the AGARD 445.6 wing from the previously published thesis.

2.3 Motivation to the work Aero-elastic analysis has a critical impact on the design and performance of an aircraft. The coupling between the aerodynamic loading due to the fluid surrounding the aircraft and its structural properties can lead to instabilities that cause important damage or failure. The class dealing with problems where more than one physical effect is involved comprises the socalled “multi-physics problems”, among the most important of which is fluid-structure interaction (FSI), challenging with respect to both modeling and computational issues. Coupling here is a very tough task to be accomplished i.e. coupling of fluid and structural 16

solver. AGARD 445.6 wing is used as many static and dynamic aero-elastic results are available and this helps us out to understand the FSI and carry out the static structural analysis using ANSYS workbench and validating the results with the available results.

17

CHAPTER3. PROBLEM DESCRIPTION This chapter includes description of AGARD wing model and its airfoil series, model specifications and operating conditions that are to be conducted on the wing and the coupling definition and techniques.

3.1AGARD 445.6 Wing AGARD stands for Advisory group for Aeronautics Research and development and was an agency of NATO that existed from 1952 to 1996. The first configuration to be tentatively accepted as an AGARD standard is designated "Wing 445.611. Wing 445.6 identifies the shape of a set of sweptback, tapered research models which were flutter tested in both air and Freon-12 gas in the 16 foot x 16 foot NASA Langley Transonic Dynamics Tunnel( ref.5 ) . The first digit of this numerical designation is the aspect ratio; the second and third digits indicate the quarter-chord sweep angle; and the last digit is the taper ratio. These wing had 65a004 airfoil sections with no twist and nor camber and were tested at zero angle of attack (fully symmetrical conditions). They were of solid homogeneous construction.

3.1.1 Airfoil Description An airfoil (in American English) or aerofoil (in British English) is the shape of a wing or blade (of a propeller, rotor, or turbine) or sail as seen in cross-section. The lift on an airfoil is primarily the result of its angle of attack and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air, resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and can be resolved into two components: Lift and drag. Most foil shapes require a positive angle of attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This "turning" of the air in the vicinity of the airfoil creates curved streamlines which results in lower pressure on one side 18

and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flow field about the airfoil has a higher average velocity on the upper surface than on the lower surface. The lift force can be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta-Joukowski theorem. The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA). The shape of the NACA airfoils is described using a series of digits following the word "NACA." The parameters in the numerical code can be entered into equations to precisely generate the cross-section of the airfoil and calculate its properties.

Figure 3.1 Airfoil Geometry Profile geometry – 1: Zero lift line; 2: Leading edge; 3: Nose circle; 4: Camber; 5: Max. Thickness; 6: Upper surface; 7: Trailing edge; 8: Camber mean-line; 9: Lower surface

3.1.2 NACA six-digit 65a004 airfoil Six digit series

is an improvement over 1-series

airfoils

with

emphasis on

maximizing laminar flow. The airfoil is described using six digits in the following sequence:  The number "6" indicating the series. 19

 One digit describing the distance of the minimum pressure area in tens of percent of chord.  The subscript digit gives the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces  A hyphen.  One digit describing the design lift coefficient in tenths.  Two digits describing the maximum thickness in tens of percent of chord.

The shape 65a004 airfoil using foilsim software with a=1 is shown below where subscript a represents the range of lift coefficient in tenths above and below the design lift coefficient in which favorable pressure gradients exist on both surfaces.

Figure 3.2: Airfoil generated using foilsim software Airfoil point data is obtained using Foilsim software with reference as a=1 is shown in figure below. As the wing is a swept back wing the airfoil chord length varies from wing root to wing tip. Also airfoil point data for airfoil at wing root and wing tip is shown below.

20

Figure 3.3: airfoil data of agard wing with a=1.

Figure 3.4: showing airfoil point data for the airfoil at wing root.

21

Figure 3.5: showing airfoil point data of the airfoil at wing tip

3.2 Model Description AGARD 445.6 wing is widely used for many aero-elastic analysis, as its experimental results are available in open literature. It is an experimental wing that has 65a004 airfoil and an aspect ratio of 4, sweep of 45˚ and taper 0.6. This model is homogeneous and orthotropic in nature. Figure below shows the plan form of the AGARD 445.6 wing used in the experiment. Material properties of the wing are shown below. The material use here is laminated mahogany as considered in previously available results.

Figure 3.3: AGARD 445.6 wing model(with reference to Ramji kamakoti thesis)

22

3.2.1 Wing Specifications  Root chord Cr = 0.558m  Half-wing span b = 0.762m  Quarter chord sweepback angle λ = 45˚  Aspect ratio AR = 1.65  Taper ratio T = 0.66

Material  Laminated mahogany.  Density ρ = 381.98 kg/m^3.  Parallel young’s modulus Ep = 3.151e9 pa.  Orthogonal young’s modulus Eo = 4.162e8 pa.  Tangential modulus G = 4.392e8 pa.  Poisson’s coefficient η = 0.31.

3.3 Operating conditions Domain of this dimension is generated around the wing, Flow property such as that of air at 25deg is considered in the domain. Steady state is conducted for better accuracy and boundary conditions such as inlet, outlet, wall and opening has to be assign, k-epsilon turbulence model is selected as it has proven stable and numerically robust and has well established regime of predictive capability. Subsonic flow regime (M=0.9) over the wing will be simulated.

23

3.4 Coupling Coupling here is a very tough task to be accomplished i.e. coupling of fluid and structural solver. The coupled analysis described in this project couples finite element structural analysis and computational fluid dynamics. The term “coupled solution” has several different meanings that are primarily differentiated by the level of integration. Coupled solutions may be described as: 1) Manual–the analyst manually extracts data from one analysis for input to the next analysis, 2) Interfaced–programmatic interfaces to analysis codes transfer data but the analyst manually directs the analysis process, 3) External–interfaces to analysis codes are created and the analysis process is automated, and 4) Internal or monolithic–one analysis code does it all.

24

CHAPTER 4. EXPERIMENTAL PROGRAM This chapter gives the step by step experimental procedure to solve the one way fluidstructure interaction using ANSYS workbench.

4.1 Modeling STEP-1: The AGARD 445.6 wing is generated in CATIA by importing the point data in to the software using MACROS; AGARD 445.6 wing is a swept back wing with root chord as 558mm and wing tip as 368.2mm. Geometry wing in CATIA is shown in figure below.

Figure 4.1: Design of AGARD 445.6 wing in CATIA This designed wing should be save in .igs format in order to import the file in ANSYS workbench. This generated wing is imported to the custom systems in ANSYS WORKBENCH i.e. FSI: fluid flow (FLUENT) static structural. The link shown below between solutions of fluent and setup of static structure is used to import the pressure load on the wing from fluent to the static structural as shown in figure 4.2. 25

STEP 2:  Go to ANSYS 13.0 – Workbench – fluid flow(FLUENT) – save  Geometry – import geometry – browse-select wing in .igs format - select plane – generate – wing is imported to the Design modeler in FLUENT.

Figure 4.2: representing one of the custom systems in ANSYS WORKBENCH

Figure 4.3: Representing the procedure to import the geometry to the fluent

26

The generated wing is design modeler is shown below in the figure. It provides an easy way to model complex geometries and has most of the features that commercial modeling software offer. The best advantage of Design modeler is that we don’t need to clean geometry for meshing and further processing.

Figure 4.4: Generated wing in Design modeler STEP 3: Creating Domain on the wing in Design modeler using symmetry plane.

 Select new plane

– generate.

 Go to – tools – enclosure – select no. of planes as 1 – select symmetry plane - enter the cushion length as – 800mm. While selecting the symmetry plane ensure that the type of the cushion be as uniform and selecting the no. of planes as 1 and click on generate wing is generated as shown in the figure 4.5.

27

, the domain around the

Figure 4.5: wing with Domain STEP 4: Applying Boolean operation to subtract the wing from the Domain  Go to create - select Boolean – subtract – select the target body as domain and tool body as wing and click on generate. The wing is subtracted from the Domain as shown in the figure.

28

Figure 4.6: represents the wing subtracted from the domain

Figure 4.7: wing with domain after Boolean operation is performed

4.2 Meshing STEP 5: CFX-mesh method is used for meshing; Mesh is generated on the domain with the wing as wall-solid.  Mesh – select mesh method – CFX-mesh method- generate 29

Figure 4.8: representing mesh on the fluid domain

Figure 4.9: Showing mesh over the wing using wireframe view 30

STEP 6: Creating named selections as Inlet, Outlet, Wing root, Wing tip, Top and Bottom.

Figure 4.10: Created wing root named selection 4.3 Flow Setup STEP 7: Creating SETUP for the solution

Figure 4.11: Showing Fluent launcher

31

 Click on set up FLUENT launcher window opens- ok as shown in above figure 4.11.  In FLUENT under problem setup check is performed to check the geometry and scale is changed to mm.  In solver select the type as pressure-based, the velocity formulation as absolute and st the time as transient.

Figure 4.12: geometry in fluent setup

Figure 4.13: showing the setup for the solver

32

Figure 4.14: changing the scale to mm STEP 8: In model under model setup select the energy equation and viscous as standard kepsilon method. The standard k- ε model is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). The model transport equation for k is derived from the exact equation, while the model transport equation for

was obtained using physical reasoning and bears little resemblance to its

mathematically exact counterpart. In the derivation of the k- ε model, it was assumed that the flow is fully turbulent, and the effects of molecular viscosity are negligible. The standard k- ε model is therefore valid only for fully turbulent flows.

Figure 4.15: represents the selection of energy equation in fluent. 33

Figure 4.16: selection of k-epsilon method under viscous models  In materials select fluid – density – ideal gas click on change/create – close. Controls Name shows the name of the material. If you edit this field, the new name will take effect when you click on Change/Create. Chemical Formula displays the chemical formula for the material. You should generally not edit this field unless you are creating a material from scratch. Material Type is a drop-down list containing all of the available material types. By default, fluid and solid will

be

the

only

choices.

If

you

are

modeling

species

transport/combustion, mixture will also be available. For problems in which you have

34

defined

discrete-phase

injections, inert-particle, droplet-particle,

and/or combusting-

particle will also appear. FLUENT Fluid Materials allows you to choose the fluid material for which you want to modify properties. This option is available when fluid is selected in the Material Type dropdown list. FLUENT Solid Materials allows you to choose the solid material for which you want to modify properties. This option is available when solid is selected in the Material Type dropdown list. FLUENT Mixture Materials allows you to choose the mixture material for which you want to modify properties. This option is available when mixture is selected in the Material Type drop-down list. FLUENT Droplet Particle Materials allows you to choose the droplet-particle for which you want to modify properties. This option is available when droplet-particle is selected in the Material Type drop-down list. Order Materials by allows you to order the materials in the Materials list alphabetically by Name or alphabetically by Chemical Formula. FLUENT Database... opens the FLUENT Database Materials dialog box, from where you can copy materials from the global database into the current solver. User-Defined Database... opens the Open Database dialog box, where you can specify the user-defined database to be used. Properties contain input fields for the material properties that are required for the active physical models.

35

Density sets the material density. You may set a constant value, or select one of the other methods from the drop-down list above the real number field. Cp sets the constant-pressure specific heat of the material. You may set a constant value, or select one of the other methods from the drop-down list above the real number field. Thermal Conductivity sets the thermal conductivity of the material. You may set a constant value, or select one of the other methods from the drop-down list above the real number field. Viscosity sets the viscosity of the material. You may set a constant value, or select one of the other methods from the drop-down list above the real number field. Molecular Weight sets the molecular weight of the material. It is used to derive the gas constant of the material.

Figure 4.17: showing materials properties in problem setup 36

STEP 9: Selecting the cell-zone conditions as fluid.

Figure 4.18: specifying the cell zone conditions The Cell Zones Conditions task page allows you to set the type of a cell zone and display other dialog boxes to set the cell zone condition parameters for each zone. Controls Zone contains a selectable list of available cell zones from which you can select the zone of interest. You can check a zone type by using the mouse probe on the displayed physical mesh. This feature is particularly useful if you are setting up a problem for the first time, or if you have two or more cell zones of the same type and you want to determine the cell zone IDs. To do this you must first display the mesh with the Mesh Display dialog box. Then click

37

the boundary zone with the right (select) mouse button. ANSYS FLUENT will print the cell zone ID and type of that boundary zone in the console window. Phase specifies the phase for which conditions at the selected cell Zone are being set. This item appears if the VOF, mixture, or Eulerian multiphase model is being used. Type contains a drop-down list of condition types for the selected cell zone. The list contains all possible types to which the cell zone can be changed. ID displays the cell zone ID number of the selected cell zone. (This is for informational purposes only; you cannot edit this number.) Edit... opens the appropriate dialog box for setting the conditions for that particular cell zone type. Copy... opens the Copy Conditions dialog box, which allows you to copy conditions from one cell zone to other cell zones of the same type. See Section 7.1.5 for details. Profiles... open the Profiles dialog box. Parameters... open the Parameters dialog box. Operating Conditions... opens the Operating Conditions dialog box. Display Mesh... opens the Mesh Display dialog box. Porous Formulation contains options for setting the velocity in the porous medium simulation. Superficial Velocity enables the superficial velocity in a porous medium simulation. This is the default method.

38

Physical Velocity enables the physical velocity in a porous medium simulation for a more accurate simulation. This option is available only for a pressure-based solver. STEP 10: In boundary conditions specify bottom and top as interface, inlet as velocity-inlet, outlet as pressure-outlet, wing tip and wing root as wall condition. The Boundary Conditions task page allows you to set the type of a boundary and display other dialog boxes to set the boundary condition parameters for each boundary.

Figure 4.19: defining the boundary conditions.  Giving Wall-solid as pressure-far-field condition with mach 0.9 and velocity 297 m/s.

39

Controls Zone contains a selectable list of boundary zones from which you can select the zone of interest. You can check a zone type by using the mouse probe on the displayed physical mesh. This feature is particularly handy if you are setting up a problem for the first time, or if you have two or more boundary zones of the same type and you want to determine the zone IDs. To do this you must first display the mesh with the Mesh Display dialog box. Then click the boundary zone with the right (select) mouse button. ANSYS FLUENT will print the zone ID and type of that boundary zone in the console window. Phase specifies the phase for which conditions at the selected boundary Zone are being set. This item appears if the VOF, mixture, or Eulerian multiphase model is being used. Type contains a drop-down list of boundary condition types for the selected zone. The list contains all possible types to which the zone can be changed. ID displays the zone ID number of the selected zone. (This is for informational purposes only; you cannot edit this number.) Edit... opens the appropriate dialog box for setting the boundary conditions for that particular boundary type. Copy... opens the Copy Conditions dialog box, which allows you to copy boundary conditions from one zone to other zones of the same type. Profiles... open the Profiles dialog box. Parameters... open the Parameters dialog box. Operating Conditions... opens the Operating Conditions dialog box. Periodic Conditions... opens the Periodic Conditions dialog box. 40

STEP 11:  Specifying mesh interfaces as top and bottom.  Under reference value in problem setup mention wall-solid to compute the solution and select the reference zone as fluid as specified in cell-zone conditions.

Figure 4.20: specifying the reference values  In solution method select the scheme as coupled. The coupled algorithm solves the momentum and pressure-based continuity equations together. The full implicit coupling is achieved through an implicit discretization of pressure

41

gradient terms in the momentum equations, and an implicit discretizations of the face mass flux, including the Rhie-Chow pressure dissipation terms.

Figure 4.21: specifying the solution methods In monitors put on the residuals, lift, drag and moment plot,

Figure 4.22: Specifying lift, drag and moment monitors 42

 In solution initialization enter wall-solid in compute from tab and then click on initialize.

Figure 4.23 solution initialization to compute from wall-solid  In Run calculation enter the no. of iterations as 20 and then check case, then click on calculate to start the iterations. Specifying the time step and number of time steps as shown in the figure below 4.2.4.

43

Figure 4.24: specifying the iterations and time step in run calculations After completion of the iterations the lift, drag and moment graphs are obtained with respect to the iteration, as shown in below figures.

Figure 4.25: scaled residuals graph

44

Figure 4.26: Drag plot

Figure 4.27: lift plot Pressure, Temperature and turbulence contours are display below showing minimum and maximum values for the pressure, temperature and turbulence.  Go to Graphics and animations – click on contours –set up - select the variable as pressure – display.  Now select the variable as temperature on wall-solid select display  Select turbulence – turbulent kinetic energy – display.

45

Figure 4.28: pressure contour on wall solid (wing) The pressure contour obtained above shows the pressure variation on the wing, different colors here shows the different values of pressure on the wall solid.

Figure 4.29: contour of static temperature

46

Figure 4.30: contour of Turbulent Kinetic energy

Figure 4.31: contour of velocity magnitude Now go to results CFD post window opens showing the wireframe structure of the geometry.  Go to insert location – plane – set the Z value to 0.5m.  Select colors – variable – select pressure as the variable then click on apply A plane at 0.5m distance is located on the wall solid with pressure variation on it. 47

Figure 4.32: wireframe model of the geometry in CFD post.

Figure 4.33: plane located on wall-solid showing pressure distribution After the solution is done in fluid flow (FLUENT) pressure obtained as output in the flow analysis is the input for the structural analysis. The FSI carried out here is an automated approach.

48

Figure 4.34: represents that flow analysis has been completed

4.4 Structural set up In ANSYS workbench under Analysis system select STATIC STRUCTURAL (ANSYS) click on engineering data to give the material properties. STEP 12: Giving material properties  Go to outline toolbar enter the material name select physical property in the tool box as density enter the value for density as discussed above in chapter 3 section 3.2.1.  Include linear elastic properties such as young’s modulus, poison’s ratio, and shear modulus as the material is orthotropic in nature select orthotropic properties.

Figure 4.35: material added in engineering data

49

STEP 13: after specifying the material properties in engineering data import the wing geometry saved in .igs format to generate the geometry in the design modeler. Now meshing the geometry with same grid as used in flow analysis i.e. CFX-mesh method. The mesh used in the flow analysis and structural analysis must be same. After the wing geometry is generated in design modeler of static structural analysis, specifying the material as laminated mahogany. Then right click on mesh and select Generate mesh.

Figure 4.36: Meshed geometry in static structural STEP 14: In outline tool bar under static structural insert fixed support on the root chord of the wing as shown below.Go to static structural in outline tool bar select insert – fixed support – select the geometry where the fixed support has to be apply.

50

Figure 4.37: fixed support applied at root chord of the wing STEP 15: Now inserting the pressure on the wing as an input which we got as output in the flow analysis as shown in figure below 4.37 by using import pressure from outline tool bar.

Figure 4.38: showing imported pressure acting on a wing. STEP 16: Solving the problem  Right click on the static structural in outline toolbar select solve.

51

 After solving under solution select total deformation – the total deformation on the wing is displayed. In the similar way insert von-misses stress and von misses strain.

Figure 4.39: Contour of total deformation on wing

Figure 4.40: Contour of vonmises stress

52

Figure 4.41: Contour of vonmises strain In order to know the flutter frequency of the wing the static structural solution is coupled with the modal analysis where we obtained 6 modes of frequency for the total deformation of the wing. The graph below in the figure 4.41 shows the graph of 6 modes of frequency with values, the mode shapes for this frequency is discussed in next chapter i.e. results and validation.

Figure 4.42: representing the 6 modes of frequency

53

Figure 4.43: shows the tabular data of the frequencies From the above obtained frequency the starting flutter frequency will be validated in next chapter by comparing it with the previously published thesis.

54

CHAPTER 5. RESULTS AND VALIDATION The objective of the project is successfully achieved. One-way FSI has been demonstrated in ANSYS- WORKBENCH. The object of this test is to show deflection of the wing due to pressure due to aerodynamic loads and resulting change in frequency due to deflection of wing. AGARD 445.6 wing is a benchmark for Aero-elastic analysis as its experimental flutter results are available in open literature. This wing is to be checked for dynamic structural stability by carrying out dynamic Aero-elastic study and then validate the results with experimental results. The wing is tested for flutter at Mach=0.9 and dynamic pressure is varied and resulting tip motion is noted. At each Mach number there is a dynamic pressure at which the tip displacement maintains its amplitude, i.e. it is neither increasing nor decreasing, is called Flutter Boundary for that Mach. The region above flutter boundary is unstable i.e. amplitude of deformation increases; while the region below flutter boundary is stable region i.e. deformation decreases. Material properties of the wing are not fully specified in the NASA’s paper so these properties are picked because using these properties we get the modal frequencies very close to those that were found experimentally. Property

Value

Ex

3.1511E9

Ey

4.162E8

Ez

4.162E8

55

Poison’s Ratio XY

0.31

Poison’s ratio YZ

0.31

Poison’s Ratio XZ

0.31

GXY

4.392E8

GYZ

4.392E8

GXZ

4.392E8

Table 5.1 Material Properties The first step after modeling is modal frequency and mode shape matching. The following figures shows the modal shapes obtained in ANSYS.

Figure 5.1 mode shape of 1st frequency

56

Figure 5.2: mode shape of 2nd frequecy

Figure 5.3: mode shape of 3rd frequency

57

Figure 5.4: mode shape of 4th frequency

Figure 5.5: mode shape of 5th frequency

58

Figure 5.6: mode shape of 6th frequency

3.50E+04 3.00E+04 2.50E+04 2.00E+04 temperature 1.50E+04

turbulent kinetic energy

1.00E+04 5.00E+03 0.00E+00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Figure 5.7: temperature vs turbulent kinetic energy graph

59

3.50E+04 3.00E+04 2.50E+04 2.00E+04 1.50E+04 1.00E+04

pressure

5.00E+03

temperature

0.00E+00 1

3

5

7

9

11 13 15 17 19 21

-5.00E+03 -1.00E+04 -1.50E+04 -2.00E+04

Figure 5.8: pressure vs temperature graph

2.00E+04

1.50E+04

1.00E+04

5.00E+03 pressure 0.00E+00 1

3

5

7

9

11 13 15 17 19 21

turbulent kinetic energy

-5.00E+03

-1.00E+04

-1.50E+04

-2.00E+04

Figure 5.9:pressure vs turbulent kinetic energy graph 60

2.00E+04 1.50E+04 1.00E+04 5.00E+03 pressure

0.00E+00 1

3

5

7

9 11 13 15 17 19 21

velocity magnitude

-5.00E+03 -1.00E+04 -1.50E+04 -2.00E+04

Figure 5.10: pressure vs velocity magnitude graph

35000000 30000000 25000000 20000000 von-mises stress imported pressure

15000000 10000000 5000000 0 1

2

3

4

5

6

7

8

9

10

Figure 5.11: imported pressure vs vonmises stress

61

pressure vs von-mises strain imported pressure

strain

38816 34769 30721 26674 22627 18580 14532 10485 6438 2390.7 0.0353790.0314490.0275190.0235890.0196590.01573 0.0118 0.00787 3.94E-03 1.03E-05 1 2 3 4 5 6 7 8 9 10

Figure 5.12: pressure vs vonmises strain Results: Maximum value (m)

Minimum value(m)

Total deformation

0.21256

0

Equivalent stress

3.2277e7

15705

Equivalent strain

0.035379

1.0315e-5

Flutter frequency

Maximum deformation(m)

Minimum deformation (m)

16.691

2.1375 m

0

78.583

3.245

0

82.015

2.3012

0

62

151.49

2.9814

0

191.9

3.9414

0

338.07

3.085

0

Validation

Value from Flutter frequency

Computed value

%age error

16.691Hz

0.018

Reference thesis 17 Hz

Table 5.3 Flutter frequency comparison

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CHAPTER 7: CONCLUSIONS This project was largely aimed at gaining a basic understanding and better overview of the fundamental structural behavior of the AGARD 445.6 wing under practical load conditions, As from the previously discussed chapter we can say that Fluid-structure interaction plays prominent roles in many ways in the engineering fields. These problems are often too complex. In this project the FSI problem was successfully solved using the AGARD445.6 wing. The computations were performed for AGARD 445.6 wing by considering the transonic flow at subsonic mach numbers. The stresses induced corresponding to the flow has been successfully computed using the ANSYS Workbench. Validation of flutter frequency also accomplished by comparing it with the previously published thesis. This project provides the complete exposure to the FSI problem and gives the complete study of fluid on structure and vice-versa. A larger quantum of work has been done to make the study more meaningful. 7.1 Future Directions The current project can be extended in the following direction:  Extend the methodology to investigate nonlinear structural dynamics models to address issues related to larger and more complicated deformation characteristics. Issues such as limit cycle oscillations, buffeting, etc, can be investigated in detail.  Refine both spatial and temporal resolutions, including possibly adopting higher order time marching schemes. Coupled fluid and structure simulations are very time consuming. Priority should be given to help reduce the computational cost, including higher order schemes, parallel computational capabilities, and adaptively updated grid distributions.

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CHAPTER 8: REFERENCES 1. Ramji Kamakoti, Wei Shyy*1, Fluid–structure interaction for aero-elastic applications Department of Mechanical and Aerospace Engineering, University of Florida, in 2005. 2. RAMJI KAMAKOTI Computational Aero-elasticity using a Pressure-based solver at university of Florida, in 2004. 3. Jong Chull Jo, fluid structure interactions, Korea institute of Nuclear safety, Republic of Korea. 4. Elizabeth M. Lee-Rausch *John T. Batina** CALCULATION OF AGARD WING 445.6 FLUTTER USING NAVIER-STOKES AERODYNAMICS, NASA

Langley Research centre.

5. E. Carson Yates, Jr. AGARD STANDARD AEROELASTIC CONFIGURATION FOR DYNAMIC RESPONSE, NASA Langley Research Center Hampton, Virginia. 6. F. Liu,¤ J. Cai,† and Y. Zhu‡ Calculation of Wing Flutter by a Coupled FluidStructure Method, University of California, Irvine, Irvine, California 92697-3975. 7. Daron A. Isaac, Micheal P. Iverson Automated Fluid-Structure Interaction, ATK Thiokol Propulsion, Brigham city, Utah. 8. MASTERARBEIT zur Erlangung des akademischen Grades Fluid-Structure Interaction – Coupling of flexible multibody dynamics with particle-based fluid mechanics. 9. MEHMET AKGÜL Static Aero-elastic analysis of a Generic slender missile using a loosely coupled Fluid-Structure interaction method, The Graduate school of Natural and Applied sciences of Middle-east Technical university.

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