Numerical Study of a Flapping Wing Flight PDF

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Numerical Study of a Flapping Wing Flight submitted by Snehasis Chowdhury (511317001) Kunal Ghosh (511317014) Arijit Singha(511317019) Mentor Dr. Prince Raj Lawrence Raj Indian Institute of Engineering Science and Technology, Shibpur January 28, 2021 Acknowledgement We are extremely thankful to Dr. ...

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Numerical Study of a Flapping Wing Flight

submitted by

Snehasis Chowdhury (511317001) Kunal Ghosh (511317014) Arijit Singha(511317019) Mentor

Dr. Prince Raj Lawrence Raj

Indian Institute of Engineering Science and Technology, Shibpur

January 28, 2021

Acknowledgement We are extremely thankful to Dr. Prince Raj Lawrence Raj, Assistant Professor in the Department of Aerospace Engineering and Applied Mechanics at Indian Institute of Engineering, Science and Technology, Shibpur for his constant guidance and supervision, during the preparation of thesis. We would like to extend our sincere gratitude to Dr. Joydeep Bhowmik, Assistant Professor, Department of Aerospace Engineering and Applied Mechanics IIEST Shibpur, for his valuable experimental data and guidance. This study will never be possible without the softwares from Ansys Inc. and MathWorks.

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ABSTRACT The present study is devoted to the study of the flapping wing of an ornithopter using computational fluid dynamics (CFD) and the experimental data from the obtained from the experiments. With this bigger picture in mind, the problem is divided into three sub-problems. Firstly, the flapping and the twisting of the wings are modelled with fourier series using the experimental data obtained. The geometry of the wing is considered as a thin plate with no thickness. This is modelled using tetrahedron elements to mesh the computational domain. For the motion of the mesh we are using the overset meshing technique. The forces and moments about all the axes are estimated in the simulation. In the next phase of this study we are planning to implement the same simulation techniques to more complex flapping wing mechanisms. All of these CFD simulations are performed in 3-Dimensional computational domain using ANSYS FLUENT and the post-processing is done using ANSYS CFD-Post. The k-ω SST model is used to model the turbulence of the flow. The solver used in this study is Roe fluxdifference splitting (Roe-FDS). Keywords: Flapping Wing, Overset Meshing, CFD

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Contents 1 Introduction 1.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 The million dollar problem: Solving the NavierStokes Equations . . . . . . . . . . . . . . . . . 1.2.2 CFD . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 ANSYS Fluent . . . . . . . . . . . . . . . . . .

1 1 1

2 Literature Review

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1 1 7

3 Applications of the ornithopter

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4 Wing Kinematics

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5 Mesh and Computation 5.1 Geometry Description . . 5.2 Mesh . . . . . . . . . . . . 5.2.1 y+ value . . . . . 5.2.2 Method of meshing 5.3 Schematic . . . . . . . . . 5.4 Setup . . . . . . . . . . . . 5.5 Criteria for Convergence .

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6 Results : AOA = 00 23 6.1 Data Obtained from Simulation: . . . . . . . . . . . . . 23 6.2 Post Processing: . . . . . . . . . . . . . . . . . . . . . . 27 7 Results : AOA = 30 31 7.1 Data Obtained from Simulation: . . . . . . . . . . . . . 31 7.2 Post Processing: . . . . . . . . . . . . . . . . . . . . . . 31 8 Conclusion

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A MATLAB Code for transformation of the angular velocities for the fluent 40 B UDF

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Chapter 1

Introduction 1.1

Aim

We will try to review the theory underlying the simulations to be performed in this study. 1.2 1.2.1

Theory The million dollar problem: Solving the Navier-Stokes Equations

ρ

dV~ ~ ) + µ∇2 (V~ ) + f~ = −(∇P dt

(1.1)

∂ρ ~ ~ + ∇.(ρV ) = 0 (1.2) ∂t Although these seemingly simple equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations. But till date no generalised analytical solution to Navier-Stokes equation is known to us. So, only option we are having is to solve these equations numerically (i.e. using CFD) as the analytical solution is something which is yet to be achieved. 1.2.2

CFD

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Basically we will be solving Navier Stokes Equation numerically using Fluent. Here the form of Navier Stokes Equation, we are choosing is very crucial for whether we are converging to right solution or not. The forms of the Navier Stokes Equation are : 1

1.2. THEORY

CHAPTER 1. INTRODUCTION

On the basis of the fluid element considered: 1. Conservation form 2. Non-conservation form On the basis of the mathematical form: 1. Differential form 2. Integral form

Forms of the Navier Stokes Equation Conservation form and Non-conservation form Conservation Form : (Fluid element has fixed dimensions) Continuity Equation: ∂ρ ~ ~ + ∇.(ρV ) = 0 ∂t

(1.3)

Momentum Equation: ∂ρu ~ ~ ) = − ∂P + ∂ ((λ∇. ~ V ~ ) + (2µ ∂u )) + ∂ (µ( ∂v + ∂u )) + ∂ (µ( ∂u + ∂w )) + ρfx + ∇.(ρuV ∂t ∂x ∂x ∂x ∂y ∂x ∂y ∂z ∂z ∂x (1.4)

∂ρv ~ ~ ) = − ∂P + ∂ (µ( ∂v + ∂u )) + ∂ ((λ∇. ~ V ~ ) + (2µ ∂v )) + ∂ (µ( ∂w + ∂v )) + ρfy + ∇.(ρv V ∂t ∂y ∂x ∂x ∂y ∂y ∂y ∂z ∂y ∂z (1.5)

∂ρw ~ ~ ) = − ∂P + ∂ (µ( ∂u + ∂w )) + ∂ (µ( ∂w + ∂v )) + ∂ ((λ∇. ~ V ~ ) + (2µ ∂w )) + ρfz + ∇.(ρwV ∂t ∂z ∂x ∂z ∂x ∂y ∂y ∂z ∂z ∂z (1.6)

Non - Conservation Form: (Fluid element has deforming dimensions) Continuity Equation: Dρ ~ V ~)=0 + ρ∇.( Dt

(1.7)

Momentum Equation: ρ

Du ∂P ∂ ~ V ~ ) + (2µ ∂u )) + ∂ (µ( ∂v + ∂u )) + ∂ (µ( ∂u + ∂w )) + ρfx =− + ((λ∇. Dt ∂x ∂x ∂x ∂y ∂x ∂y ∂z ∂z ∂x 2

(1.8)

1.2. THEORY

Dv ∂P ∂ ∂v ∂u ∂ ~ V ~ ) + (2µ ∂v )) + ∂ (µ( ∂w + ∂v )) + ρfy =− + (µ( + )) + ((λ∇. Dt ∂y ∂x ∂x ∂y ∂y ∂y ∂z ∂y ∂z

(1.9)

Dw ∂P ∂ ∂u ∂w ∂ ∂w ∂v ∂ ~ V ~ ) + (2µ ∂w )) + ρfz =− + (µ( + )) + (µ( + )) + ((λ∇. Dt ∂z ∂x ∂z ∂x ∂y ∂y ∂z ∂z ∂z

(1.10)

ρ

ρ

CHAPTER 1. INTRODUCTION

Integral form and Differential form Differential Form: (Fluid element has infinitesimal dimensions) Continuity Equation: Dρ ~ V ~)=0 + ρ∇.( Dt

(1.11)

Momentum Equation:

ρ

Du ∂P ∂ ~ V ~ ) + (2µ ∂u )) + ∂ (µ( ∂v + ∂u )) + ∂ (µ( ∂u + ∂w )) + ρfx =− + ((λ∇. Dt ∂x ∂x ∂x ∂y ∂x ∂y ∂z ∂z ∂x

(1.12)

ρ

Dv ∂P ∂ ∂v ∂u ∂ ~ V ~ ) + (2µ ∂v )) + ∂ (µ( ∂w + ∂v )) + ρfy =− + (µ( + )) + ((λ∇. Dt ∂y ∂x ∂x ∂y ∂y ∂y ∂z ∂y ∂z

(1.13)

∂P ∂ ∂u ∂w ∂ ∂w ∂v ∂ Dw ~ V ~ ) + (2µ ∂w )) + ρfz =− + (µ( + )) + (µ( + )) + ((λ∇. Dt ∂z ∂x ∂z ∂x ∂y ∂y ∂z ∂z ∂z

(1.14)

ρ

Integral Form: (Fluid element has finite dimensions) Continuity Equation: ZZZ V

Dρ dV + Dt

ZZ

~ =0 ~ .(dS) ρV

(1.15)

S

Momentum Equation: ∂

R

ui dV = ∂t

V

Z V

∂ui dV = − ∂t

∂P

Z [ V

3

∂(uj ui ) ∂ 2 ui + ∂xi − ν ]dV ∂xj ρ ∂xj ∂xj

(1.16)

1.2. THEORY

CHAPTER 1. INTRODUCTION

Comparison Conservation form VS Non-conservation form: Conservation Form is better for CFD applications because it can take care of the both shock capture and shock fitting approach while Non - Conservation Form not well suited for shock capture approach. The solution starts oscillating when non-conservation form is used for shock capture approach. More over the method of falls apart when it encounters the discontinuity as in case of the shock capture approach. Integral form VS Differential form: Integral Form is better for CFD applications because it can take care of the discontinuity of the flow variable in flow field while Differential Form not well defined for the discontinuity of the variables. This follow from the usual laws of differentiation. Partial Differential Equation In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. Navier Stokes equation is a second order partial differential equation (PDE). Suppose we have a second order PDE like the one shown below a(x1 , x2 )

∂2u ∂2u ∂u ∂2u ∂u + b(x1 , x2 ) + c(x1 , x2 ) 2 + d(x1 , x2 ) + e(x1 , x2 ) + f (x1 , x2 )u = g(x1 , x2 ) 2 ∂x1 ∂x1 x2 ∂x2 ∂x1 ∂x2 (1.17)

Classification of Partial Differential Equation Elliptic PDE (If b2 –4ac < 0)

The information in P is transmitted to the whole shaded region of the flow field. Example : Steady subsonic flow Parabolic PDE (If b2 – 4ac = 0) 4

1.2. THEORY

CHAPTER 1. INTRODUCTION

Fluid in shaded region is influenced by point P. While point P is dependent on the region enclosed. But any information in region outside the boundary in not transmitted to point P. Example : Steady Boundary Layer flow Hyperbolic PDE (If b2 –4ac > 0)

Fluid in region 1 is influenced by point P. While point P is dependent on the region 3. But any information in region 2 in not transmitted to point P. While the left running characteristic and right running characteristic are the characteristic curve along which the partial differentiation is indeterminant. Examples: 1. Steady inviscid supersonic flow 2. Unsteady inviscid flow Navier Stokes equation is a mixed type PDE it elliptic about any two of the spaitial directions while parabolic about the time and any one of the spaitial directions.

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1.2. THEORY

CHAPTER 1. INTRODUCTION

Turbulence Modelling Numerous turbulence models are proposed to model the turbulence in the flow. In this study we will be using, k-ω SST turbulence model, which is a Reynolds Average Navier Stokes (RANS) turbulence model. RANS Equations: Continuity Equation: ∂ui =0 ∂xi

(1.18)

Momentum Equation : ρ

∂P ∂ ∂Ui ∂Ui + ρUj =− + ((2µSji ) − (ρu0j¯u0i )) ∂t ∂xj ∂xi ∂xj

(1.19)

where, ∂uj ∂ui sij = 12 (( ∂x ) + ( ∂xi )) j and for any quantity let ‘a‘ in the above equations we use the following notations : a = A + a’ Quantity = Average Value + Perturbation Transport Equations of k-ω SST turbulence model: ∂ ∂ ∂ ∂k (ρk) + (ρkui ) = (Γk ) + Gk − Yk + Sk ∂t ∂xi ∂xj ∂xj

(1.20)

∂ ∂ ∂ω ∂ (ρω) + (ρωuj ) = (Γω ) + Gω − Yω + Sω ∂t ∂xj ∂xj ∂xj

(1.21)

where, ui = Velocity along ith direction P = Pressure k = Turbulence Kinetic Energy ω = Specific dissipation rate Γi = Effective diffusivity of i Gi = Generation of i due to mean velocity Yi = Dissipation of i due to turbulence Si = User defined source terms of i 6

1.2. THEORY

1.2.3

CHAPTER 1. INTRODUCTION

ANSYS Fluent

ANSYS Fluent is a commercial CFD code which is used in numerous industries like aerospace, marine, chemical and many more along with the academia. It uses finite volume method to numerically solve the Navier Stokes equation. All the simulations presented here are performed in ANSYS Fluent using it’s density based solver.

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Chapter 2

Literature Review Most flying insects are equipped with an exemplary aerodynamics propulsion system rivaled by no known man-made system. An insect’s maneuverability, mobility, autonomy, agility, and recoverability in seemingly impossible flight conditions obviously impressed us from aerodynamics standpoint. A strong effort has been made to manufacture flying craft that have some of the flight characteristics, stealth, and maneuvering advantages of biological flyers. Since, the 19th century there has been an interest in micro-sized man-made flyers that eventually lead to controlled effort after the development of Unmanned Aerial Vehicles (UAVs) to create Micro Air Vehicles (MAVs). We have been through many thesis papers and journals to grasp the idea. Starting with • Experimental investigation on lift generation of flapping MAV with insect wings of various species: Purpose: The purpose of this paper is to experimentally analyze the effect of wing shape of various insects of different species in a flapping micro aerial vehicle (MAV). Result: This study shows that the wing “Tipsula sp” has better value of lift than other insect wings, except for negative angle of attack. Conclusion: The paper lays foundation for the development of flapping MAVs with the insect wings. This type of wing can be used for spying purpose in the military zone and also can be used to survey remote and dangerous places where human cannot enter. • CFD analysis and design optimization of flapping wings flows: Purpose: The study performs CFD analysis of the 3-D flow around a flapping wing in a gusty environment and to optimize its kinematics and shape to maximize aerodynamics characteristics of a rigid wing undergoing insect-based flapping motion are analyzed numerically. Approach: The turbulent, low-Re flow near a flapping wing was solved using 3-D unsteady RANs based Spalart-Allmaras turbulence model. 8

CHAPTER 2. LITERATURE REVIEW

Conclusion: Downward gust drastically reduces the thrust generated when the ratio of the gust velocity to the wing tip velocity is around 0.5. The flapping-wing MAVs can alleviate the frontal gust if the mean gust velocity is less or comparable with the wing tip velocity. A two-wing MAV may experience a significant rolling moment under side gust conditions. • Clap-and-Fling mechanism in a hovering insect like twowinged flapping-wing micro air vehicles: Purpose: The study investigates the role played by the clap-andfling mechanism in enhancing force generation during hovering. Approach: A CFD simulation was conducted in Fluent 16.2 and the results are compared with experimental data of a Flapping wing MAV (high flapping amplitude 192°). An incompressible laminar model was chosen to simulate the airflow around the wing. Conclusion: Clap and flings at both stroke reversals augments the average vertical force by approximately 16.2% The estimated forces using CFD differ from experimental data by approximately 7.5% and 7.7% for vertical (Fz ) and horizontal (Fy ) forces, respectively. • Three-dimensional simulation for fast forward fight of a calliope hummingbird: Purpose: Computational study of fapping-wing aerodynamics of a calliope hummingbird (Selasphorus calliope) during fast forward fight. Conclusion: Both downstroke and upstroke in a wingbeat cycle produce thrust for the bird to overcome drag on the body. Negative lift is induced during upstroke. Its upstroke further enhances thrust (which is not found in other birds and insects). • Aerodynamic evaluation of wing shape and wing orientation in four butterfly species using numerical simulations and a low-speed wind tunnel, and its implications for the design of flying micro-robots: Purpose: To optimize wing design for next generation flying microrobots, we analyse butterfly wing shapes and wing orientations at full scale using numerical simulations and in a low-speed wind tunnel. Conclusion: The results indicate that wing orientations which maximize wing span lead to the highest glide performance, with lift to drag ratios up to 6.28, while spreading the fore-wings forward can increase the maximum lift produced and thus improve versatility.

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Chapter 3

Applications of the ornithopter Practical applications capitalize on the resemblance to birds or insects. Colorado Parks and Wildlife has used these machines to help save the endangered Gunnison sage grouse. An artificial hawk under the control of an operator causes the grouse to remain on the ground so they can be captured for study. Because ornithopters can be made to resemble birds or insects, they could be used for military applications such as aerial reconnaissance without alerting the enemies that they are under surveillance. Several ornithopters have been flown with video cameras on board, some of which can hover and maneuver in small spaces. In 2011, AeroVironment, Inc. demonstrated a remotely piloted ornithopter resembling a large hummingbird for possible spy missions. Led by Paul B. MacCready (of Gossamer Albatross), AeroVironment, Inc. developed a half-scale radio-controlled model of the giant pterosaur, Quetzalcoatlus northropi, for the Smithsonian Institution in the mid1980s. It was built to star in the IMAX movie On the Wing. The model had a 5.5-metre (18 ft) wingspan and featured a complex computerized autopilot control system, just as the full-sized pterosaur relied on its neuromuscular system to make constant adjustments in flight. Researchers hope to eliminate the motors and gears of current designs by more closely imitating animal flight muscles. Georgia Tech Research Institute’s Robert C. Michelson is developing a reciprocating chemical muscle for use in microscale flapping-wing aircraft. Michelson uses the term ”entomopter” for this type of ornithopter. SRI International is developing polymer artificial muscles that may also be used for flapping-wing flight. In 2002, Krister Wolff and Peter Nordin of Chalmers University of Technology in Sweden, built a flapping-wing robot that learned flight techniques. The balsa-wood design was driven by machine learning software technology known as a steady-state linear evolutionary algorithm. Inspired by natural evolution, the software ”evolves” in response to feedback on how well it performs a given task. Although confined to a laboratory apparatus, their ornithopter evolved behavior for maximum sustained lift force and horizontal movement. 10

CHAPTER 3. APPLICATIONS OF THE ORNITHOPTER

Since 2002, Prof. Theo van Holten has been working on an ornithopter that is constructed like a helicopter. The device is called the ”ornicopter” and was made by constructing the main rotor so that it would have no reaction torque. In 2008, Amsterdam Airport Schiphol started using a realistic-looking mechanical hawk designed by falconer Robert Musters. The radiocontrolled robot bird is used to scare away birds that could damage the engines of airplanes. In 2012, RoBird (formerly Clear Flight Solutions), a spin-off of the University of Twente, started making artificial birds of prey (called RoBird®) for airports and agricultural and waste-management industries. Adrian Thomas (zoologist) and Alex Caccia founded Animal Dynamics Ltd in 2015, to develop a mechanical analogue of dragonflies to be used as a drone that will outperform quadcopters. The work is funded by the Defence Science and Technology Laboratory, the research arm of the British Ministry of Defence, and the United States Air Force.

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Chapter 4

Wing Kinematics The wing used in experimental study was made nearly elliptical having a straight leading edge. Chord lengths at seven distinct locations were provided from which the wing shape has been modelled. Wing length(R) is approximately 469.9 mm. Actual wing was made of thin polythene membrane; therefore in computation also it is modelled as a thin impermeable wall.

Figure 4.1: Stroke plane orientation

An actual flapping motion is a combination of t...