Numerical simulation of Fluidic thrust vectoring by transverse injection flow in

a De Laval nozzle

Under the guidance of

Mr. K Ramesh,

Assistant Professor,

BMSCE

Abhiram D 1BM12ME004

Arvind D R 1BM12ME026

Ashvij Narayanan 1BM12ME028

Asish James 1BM12ME029

Objectives

• Design a CD nozzle for shock free supersonic primary exit flow

• Simulation of nozzle in third critical and under-expanded mode of operation

• Create analytical model for thrust vectoring using Shock Vector Control (SVC)

• Design the transverse inlet port based on MFR and SPR iteratively

• Analysis of the performance of SVC for various parameters

Thrust Vectoring

• What is Thrust Vectoring?

• Need for Thrust Vectoring

Source: Numerical simulation of fluidic thrust vectoring

Source: www.nasa.gov

• Types

Source: https://pritamashutosh.wordpress.com

Source: www.nasa.gov

Source: www.america.pink/9k720

• Advantages• Increased payload fraction• Elimination of high temperature flux joints• Reduction of IR signature

• Applications

What is a C-D nozzle?

It is a device used to convert the sub sonic flow to a super sonic flow.

The need for one is because combustion takes place at only sub sonic conditions.

[Source: http://sahil34935.blogspot.in/2013/03/nozzles.html]

Modes of operation

• First critical mode • Second critical mode • Third critical mode

[Source: Fundamentals of Gas dynamics by Zucker 2nd edition]

Nozzle designThe nozzle specifications are as follows:

• Inlet area ratio: 2.0346• Exit area ratio: 6.7877• Length of diverging section(L) obtained was 1.03m

Inlet Throat OutletArea(m2) 0.07068 0.0347388 0.2358

Pressure(bar) 72.377 40.69 1.01Mach 0.3 1 3.5

Source: http://www.math.iitb.ac.in/~neela/cp.pdf

𝐴2

𝐴1=𝑀 1

𝑀 2(1+[(𝛾−1)/2]𝑀 2

2

1+[(𝛾−1)/2]𝑀 12 )

(𝛾+1 )/2(𝛾− 1)

𝑒𝛥𝑠 /𝑅

The converging section is essentially a frustum of a cone

Whose height is about 0.25 to 0.16 times the diverging section length

The design of the divergent section is critical due to the following reasons• The flow should accelerate to super sonic conditions• The flow should be shock free• The flow should achieve the required Mach number

The method uses a time and position dependent PDE.

The coefficient of the position derivative determines whether the PDE is:• Hyperbolic PDE• Parabolic PDE• Elliptical PDE

Method of Characteristics

Methodology

The nozzle is of minimum length.The points of intersection are considered shock pointsThe boundary points are obtained by an iterative process of averaging slopes

[Source: Fundamentals of Gas dynamics by Zucker 2nd edition]

The code was first generated for a rectangular cross section, which expands in one directionThen modifications were made for them to generate a circular profile with expansion in two directions.

Governing Equations

• General governing equations of Compressible flow

Continuity Equation

Momentum Equation

Energy Equation

• Governing equations for laminar inviscid compressible flow

Continuity Equation

Momentum Equation

Energy Equation

Equation of State

Compatibility equations

• Methods of turning Supersonic flow

• Oblique Shock Relation

Prandtl Meyer Compression Source: Fundamentals of Gas dynamics by Zucker

Oblique ShockPrandtl Meyer Expansion

Design of SVC• Design Parameters

• Area• Mass flow rate• Secondary Inlet Port Position

Known NPR and SPR

Transverse injection Area

and Temperature

Transverse injection port

position

Reflecti-ng bow

shock

Get NPR, SPR, As, T and Xs

Source: Numerical simulation of fluidic thrust vectoring

• OpenFOAM• Free Software• C++ Tool Box• Open Source Codes• Entropy Conservation Schemes

• Solver “rhocentralfoam” Compressible Solver Density based Central Upwind Scheme

Numerical Simulation

• 15deg Wedge (normalized gas)

Benchmarking

• 150 Ramp (normalized gas)

• Half-Cylinder (un-normalized gas)

• Forward Step (normalized gas)

• Flow at 3rd critical mode of operation

• Grid Generation blockMeshDict.m4 – to establish

parametric relationship Hexahedra Mesh Grading Number of Cells : 41600

• Flow Properties Inviscid flow Laminar flow

• Numerical scheme

Flux scheme KurganovTime scheme EulerGradient Gauss linearDivergence Gauss linearDefault Interpolation Schemes LinearTolerance 1e-09

Boundary conditions • Boundary conditions

Nozzle Pressure Ratio(NPR) of 75 Secondary Pressure Ratio(SPR) was set to 1 Transverse injection for various NPR and SPR values Chamber pressure (static) and temperature was set to ~75bar and

300K

Simulation test cases

• Variation of transverse injection position• Position of secondary inlet tested: 0.6L, 0.85L and 0.9L • Constant MFR of 4.07%• Constant SPR of 0.9

• Variation of Secondary Pressure Ratio• Position of secondary inlet tested at 0.9L • Constant MFR of 4.07%• SPR 0.6, 0.75 and 0.9

• Variation of Secondary Mass Flow Rate• Position of secondary inlet tested at 0.9L • Constant SPR of 0.9• MFR of 1%, 2%, 4%, 8% and 12%

Performance Parameters for SVC

• Deflection Angle

• Vectoring efficiency

• Systems Thrust Ratio

• Thrust Loss

Results

• Variation of transverse injection position

Performance Characteristics for

Transverse Injection Position

• Variation of Secondary Pressure Ratio

Performance Characteristics for

Secondary Pressure Ratio

• Variation of Secondary Mass Flow Rate

Performance Characteristics for

Secondary Mass Flow Rate

Thank You