1

CHAPTER 1

INTRODUCTION

.

Thrust vector control system or thrust vectoring is a technology that deflects the mean

flow of an engine jet from the centerline to transfer some force to the aimed axis. By that

imbalance, a momentum is created and used to control the change of attitude of the

aircraft. Among other things, thrust vector greatly improves maneuverability, even at

high angle of attack or low speeds where conventional aerodynamic control surface loses

are effectiveness. A propulsive system not only provides thrust but also a means in

controlling its flight path by redirecting its thrust vector to provide directional control.

This is known as THRUST VECTOR CONTROL (TVC).

Thrust vectoring, also Thrust vector control or TVC, is the ability of an aircraft or rocket,

or other vehicle to manipulate the direction of the thrust from its engine or motor in order

to control the attitude or angular velocity of the vehicle

There are several methods of thrust vectoring system available but Thrust Vectoring by

JET DEFLECTION method is chosen as it satisfies the requirement of our system.

2

1.1 AIM:

To analyze the thrust vectoring control system using JET DEFLCTION method.

1.2 SCOPE:

Jet deflection thrust vector controlling method is with light weight and has high response.

This can be controlled using manual gears or RC. This method can be applied to small

scale and low thrust available engines.

1.3 SOFTWARES USED:

SOLIDWORKS

ANSYS

FLUENT

1.4 TYPES OF THRUST VECTORING

GIMBALED ENGINE:

In this case, the engine has a hinge or a gimbal ( a universal joint) that allows

rotation about its axis – that is the whole engine is pivoted on a bearing.

Flexible Laminated Bearing

The swiveled nozzle changes the direction of throat and nozzle. It is similar to

gimbal engine. The main drawback in using this method is the difficulty in

fabricating the seal joint of the swivel since the swivel is exposed to extreme high

pressure and temperature.

3

JET VANES

JET VANES are small airfoils located at the nozzle exit plane, and behave like

aileron or elevator on an aircraft, and cause the vehicle to change the direction.

This control system causes a loss of thrust (2 to 3%), and erosion of vanes.

JETAVATORS

This system has rotating airfoil shaped collar, and gives an unsymmetrical

distribution of gas flow. This provides a side force thereby changing the direction

of the flight.

.

JET TABS

This system has tabs rotated by hydraulic actuators. Power is supplied from

compressed nitrogen. Usually, this type of TVC methods is used in military

missiles.

1.5 BENEFITS OF THRUST VECTORING

Enhanced performance in conventional flight.

Extended flight envelope.

Increased safety

Reduction of aero controls

4

CHAPTER 2

2. LITERATURE STUDY

Our aim is to design lightweight with fast response RC type thrust vectoring system.

2.1 SELECTION OF THRUST VECTORING METHOD

Secondary fluidic injection TVC system requires modifying the engine nozzle to

create a cavity for flow manipulation as well as injection ports, the lack of readily

available source of engine bleed air necessitates the use of storage tank which

would have a large weight and occupies large area and also plumbing work

required for this system increases weight and increases the design difficulties.

Gimbal engine is relatively higher in weight and complex in design makes it

difficult for this application.

Jetavators and paddles posses high thermal stress and bulky which results in high

weight hence it is not suitable for the design.

Adjustable internal nozzle contouring does not produce satisfactory degrees of

vectoring, this method also greatly reduces the overall thrust level hence it is not

valuable.

5

Post nozzle exit exhaust flow manipulation leaves the original engine design intact

and has small weight penalties. Thrust loss associated with supersonic flow

turning will not be an issue since our system is designed for subsonic flow turning.

Hence vectoring method using airfoils mounted directly on exhaust flow is

selected for TVC system. This method reduces the available thrust but care has

been taken to ensure that sufficient thrust is produced.

2.2 AIRFOIL DESIGN:

S.No.

Type

Cause

Result

Decision

1. Circular leading edge

which directly extends

into flat section before

tapering to a sharp trailing

edge

In pressure

distribution there are

two rise in pressure.

One at leading edge

and at transition region

of taper region

Flow separation

starts at low angle

of attack

No

2. Circular leading region

without flat region but

start tapering

Rise in pressure

distribution is very

high at leading edge

Flow separation

starts at low angle

of attack

No

3. Cambered airfoil No uniform flow after

passing the airfoil

No

4. Symmetrical airfoil Rise in pressure

distribution

is not so high

No flow

separation at low

angle of attack

Yes

Hence symmetrical airfoil is chosen.

6

2.2.1 NACA 0012 AIRFOIL

From classical thin airfoil theory 0f symmetrical airfoil

Coefficient of lift (Cl) = 2πα

Lift slope = 2π

The center of pressure and the aerodynamic center are both located at the

quarter – chord point.

Hence,

From thin airfoil theory – quarter chord is the point where center of

pressure and aerodynamic center are present.

For the required geometry fitting should be at the quarter chord.

Thickness should be around 12% of the airfoil

NACA 0012 satisfies all the above requirements.

Since thickness above 12% does not satisfy thin airfoil theory, our selection

is NACA 0012 airfoil.

7

CHAPTER 3

3. THEORY

3.1 CFD (Computational Fluid Dynamics)

CFD is a technology that enables us to study the dynamics of things that

flow. Using CFD we can develop a computational model of the system or device that we

want to study. Fluid flow physics is applied along with some chemistry and the software

will output the fluid dynamics and the related physical phenomena. With the advent of

CFD, one has the power to simulate the flow of gases and liquids, heat and mass transfer

moving bodies, multiphase physics, chemical reaction, fluid structure interaction and

acoustics through computer modeling. A virtual prototype of the system can be built

using CFD (Fluent Inc.). Thus CFD can be applied for predicting the fluid flow

associated with the complications of simultaneous flow of heat, mass transfer, phase

change, chemical reaction etc. using computers. CFD has now become an integral part of

the engineering design and analysis. Engineers can make optimal use of the CFD tools to

simulate fluid flow and heat transfer phenomena in a system model and can even predict

the system performance before actually manufacturing it.

3.2 Navier-Stokes Equation:

It is named after Claude-Louis Navier and George Stokes

and describes the motion of fluid substance. It’s also a fundamental equation being used

by ANSYS and even in the present project work being carried out. These equations arise

from applying second law of Newton to fluid motion, together with the assumptions that

the fluid stress is the sum of a diffusing viscous term (proportional to the gradient of

velocity), plus a pressure term.

8

The derivation of the Navier-Stokes equation begins with an application of second law of

Newton i.e. conservation of momentum (often alongside mass and energy conservation)

being written for an arbitrary portion of the fluid. In an inertial frame of reference, the

general form of the equations of fluid motion is

Where

V is the flow velocity,

is the fluid density,

P is the pressure,

T is the (deviatoric) stress tensor

F represents body forces (per unit volume) acting on the fluid.

stands for del operator.

This equation often written using the material derivative, denoted as Dv/Dt, making it

more apparent that is a statement of second law of Newton:-

The left side of the equation describes acceleration, and may be composed of time

dependent or convective effects (also the effects of non-inertial coordinates if present).

The right side of the equation is in effect a summation of body forces (such as gravity)

and divergence of stress (pressure and shear stress).

9

3.3 Benefits of CFD

Insight- if there is a design or system design which is difficult to analyze or test

through experimentation, CFD analysis enables us to virtually sneak inside the

design and see how it performs. CFD gives a deep perception into the designs.

There are many occurrences that we can witness through CFD which wouldn’t be

visible through any other means.

Foresight- under a given set of circumstances, we can envisage through the CFD

software what will happen. In short time we can predict how the design will

perform and test many variants until we arrive at an ideal result.

Efficiency- the foresight we gain help us to design better to achieve good results.

CFD is a device for compressing the design and development cycle allowing for

rapid prototyping

.

3.4 Advantages of CFD can be summarized as

The effect of various parameters and variables on the behavior of the system can

be studied instantaneously since the speed of computing is very high. To study the

same in an experimental setup is not only difficult and tedious but also sometimes

may be impossible.

In terms of cost factor, CFD analysis will be much cheaper than setting up

experiments or building sample model of physical systems.

Numerical modeling is flexible in nature. Problems with different level of

complexity can be simulated.

It allows models and physical understanding of the problem to be improved, very

much similar to conducting experiments.

In some cases it may be the only practicable ancillary for experiments.

10

3.5 CFD Process

The steps underlying the CFD process are as follows:

Geometry of the problem is defined.

Volume occupied by fluid is divided into discrete cells.

Physical modeling is well-defined.

Boundary conditions are defined which involves specifying the fluid behavior and

properties at the boundaries.

Equations are solved iteratively as steady state or transient state.

Analysis and visualization of resulting solution is carried out.

3.6Limitations of CFD

Even if there are many advantages of CFD, there are few shortcomings of it as follows :-

CFD solutions rely upon physical models of real world processes. Solving

equations on a computer invariably introduces numerical errors.

Truncation errors due to approximation in the numerical models.

Round-off errors due to finite word size available on the computer.

The accuracy of the CFD solution depends heavily upon the initial or

boundary conditions provided to numerical model.

3.7 Comparative Study of Experimental, Analytical and Numerical Methods

Experimental Method - Experimental methods are used to obtain consistent

information about physical processes which are not clearly understood. It is the

most realistic approach for problem solving. It may involve full scale, small scale

or blown up scale model. However disadvantages are high cost, measurement

difficulties and probe errors.

11

Analytical Method - These methods are used to obtain solution of mathematical

model which consists of a set of differential equations that represent a physical

process within the limit of conventions made. The systematic solution often

contain infinite series, special functions etc. and hence their numerical evaluation

becomes difficult to handle.

Numerical method – Numerical prediction works on the results of the

mathematical model. The solution is obtained for variables at distinct grid points

Within the computational field. It provides for greater handling of complex

geometry and nonlinearity in governing equations or boundary conditions. The

kind of ease provided by numerical methods makes it the powerful and widely

applicable. The above said discussion is represented in tabular form in table 3.1.

3.8 Table Comparison of Experimental, Analytical and Numerical Methods of Solution

Name of the Method Advantages Disadvantages

1.Experimental Capable of being most

realistic

Equipment required

Scaling problem

Measurement

difficulties

Probe errors

High operating costs

2.Analytical Clean, general information

which is usually in

formula form

Restricted to simple

geometry and physics

Usually restricted to

linear problems

Cumbersome results-

difficult to compute

12

3.Numerical No restriction to linearity.

Ability to handle irregular

geometry and complicate

physics.

Low cost and high speed

of computation

Truncation and round-

off errors

Boundary condition

problems

An assessment of advantages and disadvantages of numerical methods vis-à-vis

analytical and experimental method shows that even though the Numerical Method has

few shortcomings but it has many advantages associated with it and is hence suited.

13

CHAPTER 4

4. EXPERIMENTAL THEORY OF COMPUTATIONAL FLUID DYNAMICS

4.1 SOLVER

4.1.1 DENSITY BASED SOLVER:

This method was developed for low speed incompressible flows, while density –

based is used for high speed compressible flows.

In both methods the velocity field is obtained from the momentum equations.

In the density – based approach, the continuity equation is used to obtain the

density field while the pressure field is determined from the equation of state.

In pressure based approach, the pressure field is extracted by solving a pressure or

pressure correction equation which is obtained by manipulating continuity and

momentum equations.

Hence the pressure based solver has been mainly used for incompressible and

mildly compressible flows.

4.1 SOLVER

4.1.2K- EPSILON TURBULENT MODEL:

K-epsilon (k-ε) turbulence model is the most common model used in Computational

Fluid Dynamics (CFD) to simulate mean flow characteristics for turbulent flow

conditions. It is a two equation model which gives a general description of turbulence by

means of two transport equations (PDEs). The original impetus for the K-epsilon model

was to improve the mixing-length model, as well as to find an alternative to algebraically

prescribing turbulent length scales in moderate to high complexity flows.

14

The first transported variable determines the energy in the turbulence and is

called turbulent kinetic energy (k).

The second transported variable is the turbulent dissipation ( ) which determines the

rate of dissipation of the turbulent kinetic energy.

The k-ε model has been tailored specifically for planar shear layers and recirculation

flows. This model is the most widely used and validated turbulence model with

applications ranging from industrial to environmental flows, which explains its

popularity. It is usually useful for free-shear layer flows with relatively small

pressure gradients as well as in confined flows where the Reynolds shear stresses are

most important. It can also be stated as the simplest turbulence model for which only

initial and or boundary conditions needs to be supplied.

However it is more expensive in terms of memory than the mixing length model as it

requires two extra PDEs. This model would be an inappropriate choice for problems such

as inlets and compressors as accuracy has been shown experimentally to be reduced for

flows containing large adverse pressure gradients. The k-ε model also performs poorly in

a variety of important cases such as unconfined flows, curved boundary layers, rotating

flows and flows in non-circular ducts.

4.3 BOUNDRY CONDITIONS:

General: Pressure inlet, Pressure outlet.

Incompressible: Velocity inlet, Outflow.

Compressible: Mass flow inlet, Pressure far-field, Mass flow outlet.

Other: Wall, Symmetry, Axis.

Special: Inlet vent, Outlet vent, Intake fan, Exhaust fan.

15

4.3.1 Velocity Inlet:

1. Define velocity and other properties at the inlet.

2. The flow is incompressible.

3. The velocity is applied at the inlet.

4.3.2 Pressure inlet:

1. Define total pressure and other properties at the inlet.

2. The flow direction is also defined.

3. If the inlet is Supersonic, then the static pressure is also to be specified.

4.3.3 Pressure outlet:

1. The static pressure is defined at the inlet.

2. This process works well in case there if is a back flow.

3. This condition is used the model is set up with pressure inlet.

4. This condition is suitable for compressible and incompressible flow.

4.3.4 Pressure far-field:

1. This condition is used in free stream compressible flow at infinity, with free

stream Mach number and static conditions are specified.

2. This condition is applied for compressible flow when density is calculated by

ideal gas.

16

4.3.5 Outflow:

1. It is used when flow velocity and pressure are not known before the flow.

2. This condition cannot be used for compressible flow with pressure inlet.

3. This condition cannot be used for unsteady flow with variable density.

4.3.6 Mass flow inlet:

1. This condition is used in compressible flow to find mass flow rate.

2. Not mostly used in incompressible flow since velocity will fix the mass flow

rate.

4.4 MATERIAL PROPERTIES:

4.4.1 STAINLESS-STEEL (SOLID MEDIUM)

Density ( = 7480-8000 / 3

Specific heat ( = 510 /

Thermal conductivity (k) = 15 /

4.4.2 AIR (FLUID MEDIUM)

Density ( = 1.225 / 3

Specific heat ( = 1006.43 /

Thermal conductivity (k) = 0.0242 /

17

4.5 SOLUTION METHODS

4.5.1 EXPLICIT AND IMPLICID METHODS:

These are approaches used in numerical analysis for obtaining numerical solutions of

time dependent ordinary and partial differential equations, as is required in computer

simulation of physical processes.

Y (t+ = F(Y (t))

While for an implicit method one soles an equation

G (Y (t), Y (t+ )) = 0 (1)

To find Y (t+ .

It is clear that implicit methods require an extra computation (solving the above

equation), and they can be much harder to implement. Implicit methods are used because

many problems arising in practice are stiff, for which the use of an explicit method

requires impractically small time steps t to keep the error in the result bounded. For

such problems to achieve given accuracy, it takes much less computational time to use an

implicit method with larger time steps even taking into account that one needs to solve an

equation of the form( 1) at each time step . These explain, whether one should use an

explicit or implicit method depend upon the problem to be solved.

4.5.2 UPWIND SCHEME

In computational physics, upwind schemes denote a class of

numerical discretization methods for solving hyperbolic partial differential equations.

Upwind schemes use an adaptive or solution-sensitive finite difference stencil to

numerically simulate the direction of propagation of information in a flow field. The

upwind schemes attempt to discretize hyperbolic partial differential equations by using

18

differencing biased in the direction determined by the sign of the characteristic speeds.

Historically, the origin of upwind methods can be traced back to the work of Courant,

Isaacson, and Rees who proposed the CIR method.

4.5.2.1MODEL EQUATION

To illustrate the method, consider the following one-dimensional linear advection

equation

which describes a wave propagating along the -axis with a velocity . This equation is

also a mathematical model for one-dimensional linear advection. Consider a typical grid

point in the domain. In a one-dimensional domain, there are only two directions

associated with point – left and right. If is positive the left side is called upwind side

and right side is the downwind side. Similarly, if is negative the left side is

called downwind side and right side is the upwind side. If the finite difference scheme for

the spatial derivative, contains more points in the upwind side, the scheme is

called an upwind-biased or simply an upwind scheme.

4.5.2.2 FIRST ORDER UPWIND

The simplest upwind scheme possible is the first-order upwind scheme. It is given by[2]

19

4.5.2.2.1Compact form

Defining

and

The two conditional equations (1) and (2) can be combined and written in a compact

form as

Equation (3) is a general way of writing any upwind-type schemes.

4.5.2.2.2Stability

The upwind scheme is stable if the following Courant–Friedrichs–Lewy condition (CFL)

condition is satisfied.

A Taylor series analysis of the upwind scheme discussed above will show that it is first-

order accurate in space and time. The first-order upwind scheme introduces

severenumerical diffusion in the solution where large gradients exist

4.5.3 SECOND ORDER UPWIND SCHEME

The spatial accuracy of the first-order upwind scheme can be improved by including 3

data points instead of just 2, which offers a more accurate finite difference stencil for the

approximation of spatial derivative. For the second-order upwind scheme, becomes

the 3-point backward difference in equation (3) and is defined as

20

and is the 3-point forward difference, defined as

This scheme is less diffusive compared to the first-order accurate scheme and is called

linear upwind differencing (LUD) scheme.

21

CHAPTER 5

5. DESIGN AND MODELLING

INTRODUCTION TO SOLIDWORKS

The geometry is modeled as per the required dimensions.

5.1 DIMENSIONS

5.1.1 Cylinder

Main

Length = 880 mm

Diameter = 117 mm

CONNECTING RODS:

Length = 130 mm

Diameter = 3.3 mm

5.1.2 Jet vane:

Chord length = 44 mm

Span = 33 mm

Thickness = 5.16 mm

Separation distance = 16 mm

22

5.1.3 FLAT PLATE

Length = 43 mm

Breadth = 33 mm

Width = 5.16 mm

Separation distance = 16 mm

5.2 THRUST VECTORING USING FLATE PLATE:

23

5.3 THRUST VECTORING USING SYMMETRIC AEROFOIL:

5.4 MESH MODELING

In order to analyze the flow after the exit there is a need of an ambient cylinder

ABIENT CYLINDER

Diameter - 2500 mm

Length - 2500 mm

24

CHAPTER 6

6. COMPUTATIONAL SET-UP

6.1 INTRODUCTION TO ANSYS:

The modeled geometry is imported to ANSYS for further analysis.

6.2PRE-PROCESSING

Step 1: Creating the domain

The geometry is designed in Solid Works for the required THRUST VETORING

SYSTEM (JET DEFLECTION TYPE) and it is exported to ANSYS.

6.2.1GRID GENERATION

Step 2: Meshing the edges

The geometry is meshed.

25

6.3PROCESSING

Step 1: Creating the domain

The geometry is designed in Solid Works for the required THRUST VETORING

SYSTEM (JET DEFLECTION TYPE) and it is exported to ANSYS.

6.3.1 SOLVER

1. Enable energy equation

2. Reynolds number calculation

Re =

= density of the material

v = velocity

= diameter of the tube

= dynamic viscosity

for air flowing through a duct

= 1.225

v = 265.5 m/s

= 117

= 1.846 * Kg/m s

Hence our case is a turbulent case

3. Turbulence selection - K EPSILON MODEL

.

6.3.2 BOUNDARY CONDITIONS

Step 3 : Set Boundary Types

General : Pressure inlet, Pressure outlet.

Incompressible : Velocity inlet, Outflow.

Compressible : Mass flow inlet, Pressure far-field, Mass flow outlet.

26

Other : Wall, Symmetry, Axis.

Special : Inlet vent, Outlet vent, Intake fan, Exhaust fan.

6.3.3 OPERATING CONDITIONS

Step 4: Operating condition

Operating pressure = 0 Pa

Give the value for x, y, z based on flow direction

6.3.4 MATERIAL PROPERTIES

Step 5: MATERIAL PROPERTIES

1. Stainless Steel (Solid Medium)

Density = 7480-8000 / 3

Specific heat = 510 /

Thermal conductivity = 15 /

2. Air (Fluid Medium)

Density = 1.225 / 3

Specific heat = 1006.43 /

Thermal conductivity = 0.0242 /m

6.4 POST PROCESSING

1. Display contour.

2. Display vectors.

3. Display path lines

27

4. Take input summary and results

5. File - write - case and data.

6. File – exit.

The step by step solution consists of 7 major steps discussed as follows:-

Step 1 - Pre-analysis and start-up

1. Start workbench.

2. Drag and drop “Fluid Flow (FLUENT)” on “Project Schematic”.

3. Select “3D”.

Step 2 - Geometry

The required geometry is imported from SlidWorks.

Now for creating Named Selection

1. Select Face Selection– Select th inlet – Right click – Create name selection –

Define as INLET.

2. Select Face Selection – Select the first cylinder – Right click – Create name

selection – Define as MAIN CYLINDER.

3. Select Face Selection – Select the Second Cylinder’s inner face – Right click –

Create name selection – Define as PRESSURE OUTLET.

4. Select Face Selection – Select the Second Cylinder’s outer face – Right click –

Create name selection – Define as PRESSURE OUTLET.

5. Select Face Selection – Select the Second Cylinder’s Body – Right click – Create

name selection – Define as AMBIENT CYLINDER.

6. Close geometry.

Step 3 – Mesh

1. Double click on Mesh

28

2. Sizing – Relevance center – Fine

3. Generate mesh

4. Save – Exit – Update.

Step 4 - Setup

1. Double click on setup – Select "Double Precision“.

2. Define - Material – fluid – Air

(Here, set Density = 1.225 , Cp=1006.43 J/kgK, k=0.0242 W/m K)

3. Define – Material – Solid – Aluminum.

(Here, Set Density= 7500

, Cp=510J/kg-K, k=16 W/m K

4. Set – Boundary conditions

I. Inlet - Pressure inlet

At mach no =0.8 with total pressure of 1atm

M = mach no

Hence

II. Main Cylinder – Wall

III. Outlet – Pressure Outlet

IV. Ambient Cylinder – Pressure Outlet

V. Outer Cylinder – Pressure Outlet

VI. Object 1 – Wall

VII. Object 2 – Wall

VIII. Object – Wall

IX. Object 4 – Wall

29

Step 5 – Solutions

1. Solution Methods – Momentum – Second order upwind method

2. Solution Initialization – Initialize

3. Run Calculations – Number of iterations – Calculate

4. Save project

The remaining two steps in the simulation procedure consist of

i. Results

ii. Verification and Validation

These steps are further discussed in detail and the conclusion is drawn from them

30

CHAPTER 7

RESULT AND DISCUSSION

7.1 RESULT

7.1.1 NO PLATE RESULTS

7.1.1.1 Velocity magnitude sectional view

7.1.1.2 Velocity vector sectional view

31

7.1.1.3 Total pressure sectional view

32

7.1.2FLAT PLATE AT ZERO DEGREE ANGLE ATTACK

7.1.2.1 Velocity magnitude sectional view

7.1.2.2 Velocity magnitude closer sectional view

33

7.1.2.3 Velocity vector sectional view

7.1.2.4 Total pressure sectional view

34

7.1.3FLAT PLATE AT FIVE DEGREE ANGLE OF ATTACK

7.1.3.1 Velocity magnitude sectional view

7.1.3.2 Velocity magnitude closer sectional view

35

7.1.3.3 Velocity vector sectional view

7.1.3.4 Total pressure sectional view

36

7.1.4AIRFOIL AT ZERO DEGREE ANGLE OF ATTACK

7.1.4.1 Velocity magnitude sectional view

7.1.4.2 Velocity magnitude closer sectional view

37

7.1.4.3 Velocity vector sectional view

7.1.4.4 Velocity vector closer sectional view

38

7.1.4.5 Total pressure sectional view

39

7.1.5AIRFOIL AT FIVE DEGREE ANGLE OF ATTACK

7.1.5.1 Velocity magnitude sectional view

7.1.5.2 Velocity magnitude closer sectional view

40

7.1.5.3 Velocity vector sectional view

7.1.5.4 Velocity vector over the wall

41

7.1.5.5 Total pressure sectional view

42

7.2 DISCUSSION

VELOCITY VECTOR AT ZERO DEGREE ANGLE OF ATTACK FOR FLAT PLATE

Deflecting Angle = 0.502 degree

VELOCITY PATH LINE AT FIVE DEGREE ANGLE OF ATTACK FOR FLAT

PLATE

43

Deflecting Angle = 5.73 degree

VELOCITY PATH LINE AT ZERO DEGREE ANGLE OF ATTACK FOR AN

AIRFOIL

Deflecting Angle = 0.85 degree

VELOCITY PATH LINE AT FIVE DEGREE ANGLE OF ATTACK FOR AN

AIRFOIL

44

Deflecting Angle = 7.6 degree

CAMPARISON:

Table 7.1 Flow angle

COMPONENT ANGLE OF ATTACK

(degree )

EXIT VELOCITY V2

(m/s)

FLOW ANGLE

(degree )

NO PLATE 0∘ 380 0.02

FLAT PLATE 0∘ 330 0.5

FLAT PLATE 5∘ 320 5.3

NACA 0012 0∘ 310 0.85

NACA 0012 5∘ 300 7.6

THRUST

T= ṁ(V2- V1)

ṁ=3.5 Kg/s

Table 7.2 Thrust

COMPONENT INLET VELOCITY

V1 (m/s)

EXIT VELOCITY

V2 (m/s)

THRUST

T (N)

NO PLATE 265.5 380 400

FLAT PLATE 265.5 330 225

FLAT PLATE 265.5 320 190

NACA 0012 265.5 310 155

NACA 0012 265.5 300 120

45

CHAPTER 8

CONCLUSION

From the above tabulation and calculations, parameters such as the velocity magnitudes,

flow deflection angle and thrust for the THRUST VECTORING SYSTEM using the Jet

Vane method has been analyzed and it is concluded that a system with THRUST

VECTORING METHOD using a symmetrical airfoil has better results for mach 0.8 at

pressure of 6.64 atm as flow deflected by airfoil is comparatively higher than flat

plate of same dimension and condition.

46

Reference

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11. http://www.afs.enea.it/fluent/Public/Fluent-Doc/PDF/chp10.pdf

12. http://en.wikipedia.org/wiki/Upwind_scheme

13. http://en.wikipedia.org/wiki/Power_law

14.http://www.cfd-online.com/Forums/main/8398-pressure-based-density-based-

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15. http://en.wikipedia.org/wiki/Reynolds_number