NOZZLE FLOW SEPARATION STUDY

Submitted in Partial Fulfillment of the Requirements for the Degree of

Bachelor of Technology

in

Aerospace Engineering

by

LALA SURYA PRAKASH

SC08B019

JANMEJAY JAISWAL

SC08B072

Department of Aerospace Engineering

INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY

THIRUVANANTHAPURAM

April 2012

ii

BONAFIDE CERTIFICATE

This is to certify that this project report entitled “NOZZLE FLOW

SEPARATION STUDY” submitted to Indian Institute of Space Science

and Technology, Thiruvananthapuram,is a bonafide record of work done by

LALA SURYA PRAKASH and JANMEJAY JAISWAL under my

supervisionfrom 9th

JANUARY to 27th

APRIL 2012.

Dr. AravindVaidyanathan Mr. Biju Kumar K.S.

Assistant Professor Eng./Sci-SF

Aerospace Department Cryogenic Engines Division

IIST LPSC

Dr.V.Narayanan

Group Head

Cryogenic Engines Group

LPSC Valiamala

Place: LPSC Valiamala

Date: 02/05/2012

iii

Declaration by Authors

This is to declare that this report has been written by us. No part of the

report is plagiarized from other sources. All information included from other

sources have been duly acknowledged. We aver that if any part of the report is

found to be plagiarized, we shall take full responsibility for it.

LALA SURYA PRAKASH

SC08B019

JANMEJAY JAISWAL

SC08B072

Place : Trivandrum

Date : 02/05/2012

iv

ACKNOWLEDGEMENT

This project report could have been prepared, if not for the help and

encouragement from the various people. We take immense pleasure in thanking

Prof. Kurien Issac and Dr. G. Rajesh who have helped us getting our project topic

in LPSC. We would like to thank Dr. Aravind Vaidyanathan who has kindly

agreed to be our internal guide for our project and helped a lot in experimental part

of project. We are very grateful to Mr. Biju Kumar K.S. of Cryogenic Engines

Division (LPSC), who has helped us a lot in our numerical study of nozzle flow

separation. We would also like to extend our thanking to Mr. Thomas Vargheese

and Mr. Kurup for their help in fabrication of nozzle flow setup. We are grateful to

Mr. Vinil Kumar for his help in modeling of nozzle flow setup. We would also like

to thank helpful people at Manufacturing Lab, IIST for their support.

v

ABSTRACT

Nozzle flow separation remains a fundamental problem in rocket nozzle design. Flow separation

leads to performance loss and sometimes generates large side forces which can damage the

nozzle. The current work is an attempt towards understanding the physics behind the flow

separation and exploring a means of avoiding it. CFD analysis has been carried to simulate the

effect of throat radius and wall flow injection on flow separation. A modular experimental setup

was designed to validate the numerical simulations. Throat radius study indicated the

independent nature of flow separation and shock wave-boundary layer interaction. Wall injection

had a significant effect on separation location. It was also found that the separation always

remained ahead of injection location and becomes symmetric when point of injection is moved

downstream. However this was not found to be valid when flow injection point was moved to

close to the nozzle exit.

vi

Table of Contents

ABSTRACT ...............................................................................................................................v

List of Figures ......................................................................................................................... viii

List of Abbreviations................................................................................................................. ix

List of Tables ............................................................................................................................ ix

Nomenclature ..............................................................................................................................x

1. Introduction .............................................................................................................................1

2. Literature Survey .....................................................................................................................3

3. Objective of the Study .............................................................................................................5

4. CFD Analysis ..........................................................................................................................6

4.1 Introduction .......................................................................................................................6

4.2 Governing Equations .........................................................................................................6

4.3 Turbulence Modeling .........................................................................................................7

4.4 Grid Generation ............................................................................................................... 10

4.5 Grid Independence ........................................................................................................... 10

4.6 Boundary Conditions ....................................................................................................... 10

5. Validation of CFD code for Flow Separation ......................................................................... 12

6. Experiment and Simulation ................................................................................................... 16

6.1 Set up .............................................................................................................................. 16

6.2 Fabrication ....................................................................................................................... 18

6.3 Instrumentation ................................................................................................................ 20

6.3.1 Schlieren photography ............................................................................................... 20

6.3.2 Pressure Transducer .................................................................................................. 21

6.4 CFD Simulation ............................................................................................................... 21

7. Computation Studies for Flow Separation.............................................................................. 25

7.1 Effect of Throat Radius on Nozzle Flow Separation ......................................................... 25

7.2 Secondary Jet Flow Injection ........................................................................................... 29

8. Conclusion ............................................................................................................................ 34

vii

9. Recommendation .................................................................................................................. 35

APPENDIX .............................................................................................................................. 36

REFERENCES ......................................................................................................................... 50

viii

List of Figures Figure 1: Schematic of principal phenomena in supersonic nozzle flow separation [5] ................2

Figure2: FSS and RSS [2] ...........................................................................................................2

Figure 3 Normalized Wall Static Pressure vs Axial Position ...................................................... 10

Figure 4: Computational domain for validation ......................................................................... 12

Figure 5: Wall Static Pressure with default constant .................................................................. 13

Figure 6: Wall Static Pressure with modified constant ............................................................... 14

Figure 7: Computed Mach field: Validation .............................................................................. 15

Figure 8: Designed Nozzle Flow Separation Setup for PIV........................................................ 17

Figure 9: Nozzle Flow Separation Setup for Pressure Measurement ......................................... 17

Figure 10: Assembly Drawing ................................................................................................... 18

Figure 11 Fabricated Nozzle Flow Setup ................................................................................... 19

Figure 12: Nozzle connected to Settling Chamber ..................................................................... 19

Figure 13: Schlieren 'z' configuration [McGraw Hill Encyclopedia] .......................................... 20

Figure 14: Mesh of 2D model .................................................................................................... 21

Figure 15: Mesh detail of CD nozzle ......................................................................................... 22

Figure 16: Detail of computed Static pressure field (Pa): Experimental design .......................... 23

Figure 17: Detail of computed Mach field: Experimental design ............................................... 23

Figure 18: Plot of Normalized Static Wall Pressure ................................................................... 24

Figure 19: Plot of TKE (m2/s

2) at 76mm from throat ................................................................. 26

Figure 20: Plot of TKE (m2/s

2) at 81mm from throat ................................................................. 26

Figure 21: Plot of TKE (m2/s

2) at 87mm from throat ................................................................. 27

Figure 22: Plot of Normalized Static Wall Pressure for different throat radius .......................... 27

Figure 23 Mach Contour (radius=102mm) ................................................................................ 29

Figure 24 Comparison of Shock Location ................................................................................. 30

Figure 25: Injection at 16mm from throat .................................................................................. 31

Figure 26: Injection at 38mm from throat ................................................................................. 31

Figure 27: Injection at 67mm from throat .................................................................................. 32

Figure 28: Injection at 86mm from throat .................................................................................. 32

Figure 29 : Plot of Normalized Wall Static Pressure for both upper and lower wall ................... 33

ix

List of Abbreviations

APLD Advanced Propulsion and Laser Diagnostic Lab

CFD Computational Fluid Dynamics

FSCD Flow Separation Control Device

FSS Free Shock Separation

NPR Nozzle Pressure Ratio (P0/P)

PIV Particle Image Velocimetry

RANS Reynolds Averaged Navier-Stokes Equation

RSS Restricted Shock Separation

SST Shear Stress Transport

TKE Turbulent Kinetic Energy

List of Tables Table 1: Boundary Conditions for validation of code ................................................................. 13

Table 2: Available conditions in the lab ..................................................................................... 16

Table 3: Nozzle configuration ................................................................................................... 16

Table 4: Boundary conditions for simulation of Experimental setup .......................................... 22

x

Nomenclature

A Cross-sectional area

A*

Throat area

Cp Specific heat at constant pressure

F Body forces

g Acceleration due to gravity

ht Throat height

I Unit tensor

K Thermal conductivity

k Turbulent Kinetic Energy

M Mach number

m Mass flow rate

p Static pressure

p0 Stagnation pressure

p Time average pressure

gq Heat generation per unit volume

R Gas constant

T Temperature

t Time

u,v,w Velocity components

, ,u v w Time average velocity components

, ,u v w Fluctuating velocity components

y Y plus

ρ Density

τ Shear stress

µ Dynamic Viscosity

β Thermal expansion coefficient

Dissipation

ω Dissipation per unit TKE

γ Specific heat ratio

Γ Effective diffusivity

1. Introduction

Flow separation in nozzles is a basic and yet a very challenging fluid-dynamic problem. A lot of

studies have been conducted to understand this phenomenon and still its behavior cannot be

comprehended completely[1]. This may be primarily attributed to complex interaction of shock

wave and boundary layer interaction in the flow field. Flow separation in a nozzle is a process by

which the viscous flow adjusts to an adverse pressure gradient caused due to higher back

pressure at the exit.

In rocket design community, shock-induced separation is considered undesirable as the

asymmetry in flow separation and fluctuating pressure can generate large unbalanced lateral

forces (side loads) which can in turn damage the nozzle[2]. To eliminate flow separation, one

may continuously adjust the nozzle contour like extendable nozzle, during the flight to

accommodate changes in ambient and chamber pressure. The significant weight penalty and

mechanical complexity which such systems attract make them unsuitable for practical

application. The other option is to avoid flow separation and can be achieved by Flow Separation

Control Devices (FSCD). However for implementing such devices, flow physics governing flow

separation has to be thoroughly understood[3].

Flow separation redefines the effective geometry to lower the expansion ratio. Flow separation

takes place due to coupled effect of negative pressure gradient and viscous effects. From purely

gas-dynamics point of view, this problem involves basic structure of shock interactions with

separation shock, which consists of incident shock, Mach reflections, reflected shock, triple point

and slip lines as shown in fig.1. Near the wall, the lambda-foot like structure that consists of

incident and reflected oblique waves merge into a Mach stem at a point. This point is called the

Triple Point of shock system. The adverse pressure gradient due to shock separates the boundary

layer at the point where the incident oblique shock originates, forming separation regions

downstream. The oblique shock structures are of weak type that results in low supersonic flow

downstream. The Mach stem is a strong normal shock resulting in subsonic flow downstream.

Shape and size of Mach discs depend on upstream conditions. Mach disc can be curved

depending on sign of radial pressure gradient. This shock structure or shock cell can repeat until

it is totally disrupted by viscous effects[4]

2

The subsonic flow downstream of the normal portion of the shock reaccelerates back to

supersonic. It is due to emergence of wavy slipstreams from the triple points that form a

convergent-divergent fluidic channel. The trailing shocks reflect off of the separation shear

layers emerging as expansion fans that are then transmitted across the test section to the opposite

shear layers where they are reflected again as compression waves. These reflections continue

downstream, resulting in a series of alternating regions of expansion and compression through

the separation jet.

Figure 1: Schematic of principal phenomena in supersonic nozzle flow separation [5]

There are two types of flow separation phenomena - Free Shock Separation (FSS) and Restricted

Shock Separation (RSS) as shown in fig.2. In FSS flow remains separated after the separation

point but in RSS flow reattaches to the wall after some distance forming a closed recirculation

bubble. The transition from FSS to RSS occurs at well-defined pressure ratios.

Figure2: FSS and RSS [2]

3

2. Literature Survey

Several experimental and computational studies have been performed on nozzle flow separation.

Flow pattern is asymmetric in case of flow separation for area ratio of 1.4 and NPR greater than

1.4[6]. For Ae/At > 1.2 and NPR > 1.4, the separation shock has a well-defined lambda shape.

For large values of Ae/At(>1.4) and NPR(>1.3), one lambda foot is always larger than the other,

i.e., separation occurs asymmetrically. The asymmetry does not flip during a given test run, but

can change side from run to run. The flow asymmetry which occurs in both planar and

axisymmetric nozzle geometries is still an open question, and is clarified neither by experiment

nor by CFD[1].

The asymmetry is computationally validated by Xiao et.al.[7]. Computations are conducted for a

series of exit-to-throat area ratios (Ae/At) from 1.0 to 1.8 and a range of nozzle pressure ratios

(NPR) from 1.2 to 1.8. The results are compared with available experimental data in a nozzle of

the same geometry. Various turbulence models predictions are compared with the experimental

result. SST k-ω model is predicting the most accurate of all models[7,8]. According to

Menter[9], turbulence models with default constant values do not give correct results always.

Small changes in modeling constants can lead to significant improvement (or deterioration) of

model predictions. In that case one has to modify the default constant values to get correct

result[10]. Dembowski and Georgiadis[11] conducted a numerical study for supersonic

axisymmetric jet flow using the two-equation shear stress transport (SST) and k-ω models, with

and without compressibility correction. Their results indicated that these models do not predict

supersonic nozzle flows accurately without the compressibility correction. After applying

compressibility correction, solution improves significantly. The graph of centerline Mach

number and centerline stagnation temperature are plotted to show the improvement in results in

[11]. Hunter [12] has done a detailed experimental, theoretical and computational study of

separated nozzle flows. He proposed that shock/boundary-layer interaction and separation are

mutually dependent results in contrast to a typical view that SBLI is the cause of separation. The

experimental results indicate that separation had two regimes; for NPR<1.8, the separation was

3D and steady and confined to bubble. For NPR >2.0, separation was steady and fully attached

and it became more 2D as NPR increased.

4

Boccaleto and Dussuage [13] have found a solution to prevent separation. They positioned a

small aerospike device around the nozzle lip. The aerospike flow acts like a high momentum

fluidic barrier which prevents the external air to get inside the nozzle and therefore prevent

separation. This new concept can allow wide throttling range at low altitude without incurring

flow separation phenomena and associated side loads.

In spite of many studies on this subject, no nozzle flow separation controls devices exist which

are implemented in practical uses [13]. Majority of present launch systems use conventional bell-

shaped nozzles due to lack of models which can accurately predict the flow separation fully.

There is a need to understand the flow physics to avoid flow separation in rocket nozzles.

5

3. Objective of the Study

The objective of the current work is to study the effect of nozzle geometry and downstream

secondary jet injection in rectangular nozzle. The throat radius will be varied to analyze the

resulting flow field. It is planned to do experiments to get wall static pressure distribution and

total pressure along centerline and separated region. Experimental studies provide pressure

distribution and shock structure but to get more details out of the flow field, computational

studies are necessary[7]. CFD simulation of wall flow injection will be done to analyze its effect

on flow separation. Flow visualization technique like Schlieren will be carried out to observe the

separated flow and shock structure.

In chapter 4, generalized approach for computation of nozzle flow is specified. Chapter 5 deals

with the validation of CFD code. Experimental setup and CFD simulation for experimental setup

for flow separation is described in chapter 6. Effect of throat radius and secondary jet flow

injection on flow separation is analyzed in chapter 7.

6

4. CFD Analysis

4.1 Introduction

CFD analysis is performed using commercially available software ANSYS 13, FLUENT. 2D

compressible Navier-Stokes equations are solved. Additional transport equations are solved to

incorporate the effect of turbulence. For compressible flows energy equations incorporates the

coupling between velocity and static temperature.

Velocity field is obtained from the momentum equation. In density based approach density field

is obtained from continuity equation and pressure field from equation of state.

4.2 Governing Equations

The equation for conservation of mass, momentum and energy, can be written as follows:

. 0vt (4.1)

. .

vvv p g F

t (4.2)

Where p is the static pressure, is the density, is the stress tensor and g and F are

gravitational and external body forces respectively. The stress tensor is defined as

2.

3

T

v v v I (4.3)

Where is the viscosity and I is a unit tensor.

7

. :p g

DT Dpc q K T T v

Dt Dt (4.4)

where

.D

vDt t

(4.5)

There are basically pressure based and density based solvers. Pressure based solver is applicable

for low speed incompressible flows whereas density based solver is used for compressible flows.

In Pressure based solver, density variations are not linked to the pressure. The mass conservation

is a constraint on the velocity field. This equation (combined with the momentum) can be used to

derive an equation for the pressure. In density based solver, mass conservation is a transport

equation for density. With an additional energy equation, pressure can be specified from a

thermodynamic relation (ideal gas law). In both cases control volume based technique is used.

Density based solver is selected for the current study as the flow is compressible. All the

computations are done with steady method since the transient nature of shock get damped out

due to numerical damping[7]. Second order upwind schemes are used for spatial discretization

for better accuracy. Other discretization schemes like QUICK and third order MUSCL schemes

are also available but it gives better result for rotating and swirling flows[14]. Convergence

criteria for continuity, energy, x-velocity, y-velocity, k and ω are of the order of 10-6

.

4.3 Turbulence Modeling

Turbulence denotes a motion in which an irregular fluctuation is superimposed on the main

stream. Turbulent flow instantaneously satisfies the Navier-Stokes equations. However it is

virtually impossible to predict the flow in detail because of very small length and time scales. In

computing the turbulent motion it is useful to decompose the motion into a mean motion and a

fluctuating motion and then time averaging of the equations are done to get a new set of

equations called Reynolds Averaged Navier-Stokes (RANS) equation. In the new set of

equations, number of unknowns (quadratic fluctuation terms, Reynolds Stresses) is more than

equations. So to solve the problem, additional equations are required.

8

Continuity equation

0

u v w

x y z (4.6)

Momentum Equation

2u u u p u u v u wu v w u

x y z x x y z (4.7)

2v v v p u v v v wu v w v

x y z y x y z (4.8)

2w w w p u w v w wu v w w

x y z z x y z (4.9)

Thermal Energy Equation

2 2 2

2 2 2

2 2 22 2 2

2 2 2

p p

T T T T T T u T v T w Tc u v w c

x y z x y z x y z

u v w u v u w v w

x y z y x z x z y

(4.10)

Where

2 2 22 2 2

2 2 2u v w u v u w v w

x y z y x z x z y (4.11)

The wall boundary layer is assumed to be turbulent since flow. Available models to incorporate

turbulence include k-ε, Spalart-Allmaras, k-ω,etc. SST k-ω is selected for all the simulations. It

is selected because it is valid throughout the boundary layers and it accurately predicts the results

in case of adverse pressure gradient and separated flows[9]. Also from literature survey, it is

9

found that SST k-ω predictions are closer to experimental results as compared to other

turbulence models [5,7]. SST k-ω has a number of advantages over other turbulence models. The

SST model employs a k-ω formulation in the inner region of wall boundary layers and switches

to a transformed k-ε formulation in the outer region of boundary layers and in the free shear

layer. To achieve this k-ε is transformed into k-ω formulation. The two equations are added with

the help of blending functions to generate new model.

The transport equations for the new model are:

i k k k k

i j j

kk ku G Y S

t x x x (4.12)

i

i j j

u G Y D St x x x (4.13)

Where , kG represents the generation of turbulence kinetic energy due to mean velocity gradients,

G represents the generation of ω, k and represent effective diffusivity of k and ω

respectively, kY and Y represent the dissipation of k and ω due to turbulence. D represents the

cross-diffusion term. kS and S are user defined source terms.

Blending function is modeled in such a way that its value is one near wall and zero away from

wall. The k-ω model is the model of choice in the boundary layer because of its simplicity and

numerical stability as compared to other models. In the wake region of the boundary layer, the k-

ε model is more favorable. The reason for this switch is that k-ω model has a very strong

sensitivity to the free stream values specified for ω outside the boundary layer [9].

SST k-ω is valid throughout the boundary layer, provided near wall mesh resolution is sufficient.

So near wall modeling is applied as given in [15,16]. Non dimensional wall y is a suitable

criteria for determining the appropriate mesh configuration and turbulence model[16].Physically

it represent the ratio between turbulent and laminar influences. To resolve viscous sub layer, wall

y+

is chosen in the range of 1 to 5.

10

4.4 Grid Generation

Structured grid is generated using the ANSYS Meshing utility in workbench. Initial grid of about

35000 cells is created. Based on the y+

value, distance of the first cell from the wall is calculated

and keeping gradient of cells smooth, mesh is adapted near wall to capture near wall

physics(Fig.4,15) using y-plus adaption in FLUENT. The grid is clustered in the divergent

portion to capture the flow separation phenomena. Structured grid is selected because of its

several advantages over unstructured grid. Structured grid offers better accuracy, more user

control, and less memory usages.

4.5 Grid Independence

Simulations are done for three grid resolution i.e for 4000 nodes, 35000 nodes and 50000 nodes.

The wall static pressure for different cases are plotted in fig. 3.It is found that solution becomes

independent of grid after 35000 nodes.

Figure 3 Normalized Wall Static Pressure vs Axial Position

4.6 Boundary Conditions

Pressure inlet boundary condition is used at inlet. It is suitable for both compressible and

incompressible flows and is used where velocity is unknown. Supersonic initial gauge pressure is

specified to compute initial values in conjunction with specified stagnation pressure according to

isentropic relations for compressible flows. In contrast, velocity inlet is not suitable for

11

compressible flows and leads to non-physical result because it allows the pressure to float[14].

Pressure outlet boundary conditions are implemented at all outlets. No slip condition is imposed

at the walls.

12

5. Validation of CFD code for Flow Separation

To validate FLUENT, simulation of the experiment performed by D. Papamoschou et. al.[17] is

done. The experiment was performed for nozzle area ratio ranging from 1 to 1.5 and NPR

ranging from 1.2 to 1.8. To measure wall static pressure, 24 equally spaced pressure ports were

mounted on each wall. Centerline pressure was also measured using pitot tube. Numerical

investigation of the same experiment has been done by Xaio et. al.[7].

To validate CFD code, geometry is selected as a 2D planar convergent-divergent nozzle with

area ratio of 1.5 and NPR of 1.6. The nozzle contour is extracted from [7]. Computational

domain used for the study is shown in fig.4.Grid is generated as explained in sec.2.4. Also,

boundary condition of domain is given in table 2.7.1.

Figure 4: Computational domain for validation

13

Table 1: Boundary Conditions for validation of code

Boundary Type Conditions

Inlet Pressure 1.6 bar

Wall Stationary No slip

Outlet Pressure 1 bar

Stagnation temperature is kept at 300K.

Wall pressure distribution is obtained from CFD and its comparison with the experimental result

[17] is shown in fig 5. It is observed that flow separation occurred at a distance of x/Ht ~2.1 in

CFD against x/Ht~2.3 in experiment.

Figure 5: Wall Static Pressure with default constant

Initially the simulation is done with default values of constants in SST k-ω model and the result

is as shown in fig. 5. It is observed that separation point is not matching, hence the default value

14

of constant a1 in turbulence model is changed from 0.31 to 0.32[10] and the new result is shown

in fig. 6.

Figure 6: Wall Static Pressure with modified constant

The computational result is compared with Papamoschou et. al. paper[17]. The static pressure

along the wall is plotted for comparison. The result is very close to the experimental data. To

compute root mean square error between the numerical and experimental result, Python program

is made (Appendix 4) and error is found to be 3%. Some deviations are there which may be due

to inability to regenerate the exact contour used in the experiment. Mach number contour is

plotted which show the lambda shock structures (fig.7). The separation is asymmetric which is in

accordance with experimental result. The structure of the shock is inverted in comparison with

Schlieren results[17].

15

Figure 7: Computed Mach field: Validation

Thus the CFD code is validated for flow separation. To verify it further an experiment is planned

using 2D nozzle. Design and analysis details are given in next section.

16

6. Experiment and Simulation

6.1 Set up

Experimental setup is made to study nozzle flow separation which utilizes facilities available in

APLD lab, IIST.

Table 2: Available conditions in the lab

Mach Number 1.5-2.0

Mass Flow Rate <0.4 kg/s

Compressor Discharge Rate 1.56 m3/min @10bar

Based on the above conditions, exit Mach number (perfect expansion case) of 1.8,mass flow rate

of 0.3 kg/s ,chamber pressure of 2.0 bar and chamber temperature 300K are selected for the

present study. From this throat area (A*) is calculated using isentropic mass flow rate equation

1

2 120

0

11

2

pm A M M

RT

Table 3: Nozzle configuration

Area Ratio 1.4375

Throat Area 642 mm2

Exit Area 920 mm2

NPR 1.6

Based on the above calculation, nozzle flow setup is designed in commercially available CAD

software.(fig 8)

17

Figure 8: Designed Nozzle Flow Separation Setup for PIV

Design Features

(1) Side optical windows for Schlieren.

(2) Pressure measurement ports in divergent section.

(3) Optical access on top and bottom for PIV.

(4) Modular design for variable geometry.

Experimental setup is designed for implementing flow visualization techniques like Schlieren

and PIV. But due to instrumentation non availability, setup is designed and fabricated for

Schlieren and wall pressure measurement as shown in fig 9,10.

Figure 9: Nozzle Flow Separation Setup for Pressure Measurement

18

Figure 10: Assembly Drawing

6.2 Fabrication

Nozzle flow set up consists of following parts whose CAD drawings are shown in Appendix 1

and 2.

(1) Nozzle

(2) Nozzle Connector

(3) Side plate

(4) Optical access (Side glass)

(5) Flange

All the above parts are fabricated in manufacturing lab in IIST. Entire setup is made of

Aluminium except flange which is of Mild Steel. Nozzle contour and flange are fabricated in

CNC. CNC codes are given in Appendix 3. Fabricated nozzle setup is shown in fig.11.

19

Figure 11 Fabricated Nozzle Flow Setup

Nozzle apparatus consists of two nozzle connector on which planar nozzle is mounted. Using

this design, flow field of planar nozzles with different geometry and area ratio can be studied.

Based on the above calculation, nozzle dimension are 20mm width, 32mm height at throat and

46mm height at exit. To visualize flow separation using Schlieren technique, nozzle side walls

are incorporated with glass windows. Glass windows are arrested using side plates. The entire

apparatus is connected to the settling chamber using flange as shown in fig 12.

Figure 12: Nozzle connected to Settling Chamber

20

6.3 Instrumentation

6.3.1 Schlieren photography

Schlieren photography is a way of visualizing density variations in a gas and is useful in wind

tunnel studies and investigations into heat flow. It employs a shadowgraph principle. A

collimated (i.e. parallel) beam of light passes through the test space and is brought to a focus at a

knife edge; it then diverges on to a screen or a camera system. Any gas density gradient with a

component perpendicular to the knife edge will deviate the light from the region, so that it either

clears the edge, giving a bright area on the screen, or is intercepted by it, giving a dark area. The

resolution can be improved by a further knife edge at the first focus of the system.

There are many techniques for optically enhancing the appearance of the Schlieren in an image

of the field of interest. In this case, a point or slit source of light is collimated by a mirror and

passed through a field of interest, after which a second mirror focuses the light, reimaging the

point or slit where it is intercepted by an adjustable knife edge (commonly a razor blade). The

illustration (fig 13) shows the “z” configuration which minimizes the coma aberration in the

focus. Mirrors are most often used because of the absence of chromatic aberration.

Figure 13: Schlieren 'z' configuration [McGraw Hill Encyclopedia]

In this experiment, Schlieren system consists of two concave mirror of 6 inches diameter and 60

inches focal length of Edmund Schlieren Systems, mercury light source and PCO PIXELFLY

camera. Each mirror is protected by aluminized front surface over coated with Silicon Monoxide

and mounted on metal stands.

21

6.3.2 Pressure Transducer

To make time resolved measurement, high frequency pressure transducer are required. Kulite

XCQ 152 peizo-resistive pressure transducer are flush mounted on upper and lower walls in

divergent section of nozzle. Natural frequency of transducer is 240kHz.

To measure wall static pressure, 8 pressure transducers are connected to each upper and lower

walls of nozzle from throat up to exit. These transducers are equally spaced along axial direction

and connected along mid width of nozzle wall. The diameter of each pressure transducer is

3.8mm.

6.4 CFD Simulation

To study the flow field inside the nozzle in the experiment, CFD analyses is carried out using

ANSYS, FLUENT.

Based on the validation of computational scheme adopted from experiment specified in previous

section, similar schemes are used to simulate nozzle flow. Nozzle area ratio is 1.44 and NPR is

kept at 1.6. Also throat radius of nozzle is 100mm. Computational domain is shown in fig 14.

To capture shockwave boundary layer interaction, mesh is adapted near wall with y+

values

between 1 to 5. In the nozzle section, mesh is fine and it gradually becomes coarser outside the

nozzle (fig.15).

Figure 14: Mesh of 2D model

22

Figure 15: Mesh detail of CD nozzle

Boundary condition used is given in table 6.1.

Table 4: Boundary conditions for simulation of Experimental setup

Boundary Type Conditions

Inlet Pressure 1.6 bar

Wall Stationary No slip

Outlet Pressure 1 bar

23

Figure 16: Detail of computed Static pressure field (Pa): Experimental design

Figure 17: Detail of computed Mach field: Experimental design

24

To solve the flow field, the method described in Sec.2.7 is used. Contour plots of pressure and

Mach number is given in fig. 16 and 17 respectively. Flow separation is observed at x/Ht~2.4.

Shock form inside the nozzle is asymmetric lambda shock. Normalized wall static pressure

distribution is shown in fig.18.This result is consistent with the observation made by

Papamoshchou[17] that flow becomes asymmetric for NPR greater than 1.4. At throat region

(x/Ht ~1.2), static pressure slightly increases due to compression waves (fig.18). When flow

reattaches in lower wall, static pressure becomes more compare to upper wall.

To validate these results, it is proposed to compare the wall static pressure value with those

obtained from measurements. Nozzle flow setup is manufactured but facility for nozzle flow in

lab is not yet fully commissioned.

Figure 18: Plot of Normalized Static Wall Pressure

25

7. Computation Studies for Flow Separation

7.1 Effect of Throat Radius on Nozzle Flow Separation

Nozzle flow separation depends on area ratio, wall angle, nozzle pressure ratio etc. The effect of

area ratio and nozzle pressure ratio was investigated by Papamoschou et.al.[6] . In the present

study, the effect of throat radius on flow separation is studied.

Different nozzle contours with throat radius ranging from 88mm to 104mm are simulated using

FLUENT, ANSYS. The grid is generated and boundary conditions are given as described in the

Sec.2.4 and Sec.2.6 respectively. All the cases are of similar nature since in all cases lambda

shock forms and asymmetric flow separation is observed. The only difference is in the location

of large separation side. Some of cases have large separation on upper wall while others have on

lower wall. So three cases are selected to be investigated; two cases for which the large

separation is on the lower wall (radius 90mm and 104mm) and third case where it is on the upper

wall. (radius 92mm).

The shock/boundary layer interaction effects turbulence level in boundary layer [18]. TKE is

selected to quantify the turbulence level and hence SBLI near wall. Turbulence kinetic energy

(TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. The

turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity

fluctuations. Physically it represents turbulence level.

2 2 21

2k u v w

When throat radius is increased the flow smoothly changes its direction from converging to

diverging section. This causes decrease in turbulence level. So to observe the effect of throat

radius on separation, TKE is plotted for different radius near the wall.

The Total Kinetic Energy (TKE) vs. position from centerline is plotted using MATLAB in the

boundary layer region on the large separation side at a distance of 76mm(behind shock), 81mm

(middle of shock)and 87mm(after shock) from throat for different cases (fig.19-21). The

distances from throat are selected in such a way that the shock wave boundary layer interactions

can be captured fully.

26

Figure 19: Plot of TKE (m2/s

2) at 76mm from throat

Figure 20: Plot of TKE (m2/s

2) at 81mm from throat

27

Figure 21: Plot of TKE (m2/s

2) at 87mm from throat

Fig. 21 indicates the variation in shockwave boundary layer interaction in three different cases.

The TKE is decreasing with increase in radius of curvature. The same trend is observed for all

the three plots.

Figure 22: Plot of Normalized Static Wall Pressure for different throat radius

28

The normalized wall static pressure for different throat radius is plotted in fig. 22. The above

graphs show that separation location is a very weak function of shock wave boundary layer

interaction and throat radius. This reinforces the hypothesis given by C.A. Hunter. According to

Hunter[12], separation is not a result of strong shock/boundary-layer interaction but instead it

came about through the natural tendency of an overexpanded nozzle flow to separate to adjust to

the exit pressure. Mach contour for different throat radius are given in Appendix 6.

29

7.2 Secondary Jet Flow Injection

There are different techniques to avoid flow separation in nozzles like dual bell nozzles and

deployable nozzle. But due to increase in weight and mechanical complexity, such systems are

unsuitable for practical application. Another approach to control flow separation is to inject air in

direction of flow to compensate for momentum loss after separation.

To analyze the effect of flow injection on separation, simulations are done with injection point

ranging from 16mm to 86 mm from throat with throat radius 102mm. From the velocity contour

(fig . 23) (simulation without injection), it is found that velocity loss due to shockwave is around

450m/s. Hence flow injection is selected as same.

Figure 23 Mach Contour (radius=102mm)

In the following figures, Mach contour for different position of velocity inlet are shown. Pressure

contour for all the cases are given in Appendix 5. From these figures, observations are obtained.

1. Boundary layer separation is a natural tendency of an over expanded nozzle to adjust the

exit pressure. From simulation, it is observed that shock location or separation nature is

not changing when injection is done earlier than the shock location (fig 24,25). When

injection is done after shock, separation and shock shifts downstream (fig 24,26,27).

Injection avoids this ambient flow recirculation and the separation location moves

30

downstream. This pattern is broken when the injection is done very near to exit (fig.

24,28).

Figure 24 Comparison of Shock Location

2. The Mach number contours (fig 25-28) clearly show that the location of lambda shock

system is governed by the separation point. The oblique shock wave originates at the

separation point to divert the flow parallel to separated flows. The region between the

mid flow and the separated layer forms a convergent channel like structure. The portion

of flow diverted by oblique shocks is supersonic and gets decelerated when it passes

through the convergent channel. This results in increase in pressure. To match this

pressure. The mid flow has to pass through normal shock.

3. As the injection point is moved downstream at 67 mm from throat, the separation

becomes much less (fig 27). This leads to much shorter oblique shock structure

formation.

4. Flow separation become symmetric when injection point is moved downstream. This can

be confirmed by plotting the wall static pressures for upper and lower wall which are

overlapping as shown in fig 29. This results in reduction in side loads.

31

Figure 25: Injection at 16mm from throat

Figure 26: Injection at 38mm from throat

32

Figure 27: Injection at 67mm from throat

Figure 28: Injection at 86mm from throat

33

Figure 29 : Plot of Normalized Wall Static Pressure for both upper and lower wall

Once flow separation occur, recirculation bubble is formed which is continuously fed by the

ambient air and flow separation is sustained [13]. When secondary jet is injected along direction

of flow in separated area, kinetic energy of particle in boundary layer region increases. This

opposes incoming ambient air and leads to smaller recirculation bubble. However when jet is

injected near exit of nozzle, injection flow is unable to stop ambient air flow to move inside and

recirculation bubble increases in size.

34

8. Conclusion

CFD code is validated from the experiment performed by Papamoschouet. al.. The same method

is applied for the study of effect of throat radius and wall injection on flow separation.

Different nozzle contours with throat radius ranging from 88mm to 104mm are simulated using

FLUENT, ANSYS. It is found that change in throat radius does not have any significant effect

on shock location and shock structure. It is also found that shock/boundary-layer interaction and

flow separation is an independent phenomenon. Shock/boundary-layer interaction is quantified

by turbulence kinetic energy.

From simulation, it is observed that shock location or separation nature is not changing when

injection is done earlier than the shock location. When injection is done after shock, separation

and shock shifts forward Flow separation become symmetric when injection point is moved

downstream. This is confirmed by plotting the wall static pressures for upper and lower wall .

This results in reduction in side loads. The Mach number contours show that lambda shock

system location is governed by the separation point.

A 2D nozzle is designed and realized for the flow separation experiment.

35

9. Recommendation

To get detailed flow field, PIV can be done to get velocity vectors. Experimental setup can be

modified to capture the effect of side walls by adding pressure port adjacent to centerline

pressure port. If 3D effects are observed during experiment, CFD simulation of same cabe done

to get detailed information of flow field. Also wall flow injection experiment can be done to

validate numerical simulation done in the present study. In this study, analysis of planar

convergent nozzle is performed. However, computation and experiment can be performed for

axisymmetric nozzle. Scale analysis of axisymmetric nozzle can be done, so that results obtained

can be extended to actual nozzles.

36

APPENDIX

1. Detailed design of fabricated Nozzle flow setup

a. Nozzle

37

b. Nozzle Connector

38

c. Side plate

39

d. Optical access (Side glass)

40

e. Flange

41

2. Detailed design of Nozzle flow setup for PIV

a. Nozzle

42

b. Nozzle Connector

43

c. Laser window

44

d. Quartz glass holder

e. Side plate – Same design as Appendix Sec.1.c

f. Optical access-Same design as Appendix Sec.1.d

g. Flange-Same design as Appendix Sec.1.e

45

3. CNC code to generate nozzle contour

N10 G75 Z0

N20 G75 X0 Y0

N30 G71 G95

N40 G54 G00 X-20 Y-20 Z5

N50 M03 S1500

N60 CYCLE72(“SUB:SUB_E”, 1.0, -18.0, -27.5, 0.5, 0.0, 0.0, 0.5, 0.1,11,42,1,2, , 1, 2.0)

N70 G00 Z5

N80 G00 X-20 Y-20

N90 M05

N100 M30

****CONTOUR****

N110 SUB:

N120 G01 X-20Y-20

N130 G01 Y18

N140 G01 X10.67

N150 G03 X68.64 Y0 CR=100

N160 G01 X171 Y7.696

N170 G01 X181

N180 Y-20

N190 X-20

N200 G17

SUB_E:

******CONTOUR ENDS******

46

4. Error calculation

A python program is made to calculate the RMS error between the experimental data and

computational result.

#!/usr/bin/python

from math import sqrt

fid=open("t2.txt"); #t2 is the file containing computational result

lines=fid.readlines()

#List initialization

x1=[];y1=[];p_num=[]

#experimental data

x3=[-1.06498,-0.805054,-0.534296,-

0.263538,0.00180505,0.267148,0.532491,0.803249,1.06859,1.32852,1.59928

,1.87004,2.14621,2.40072,2.55776,2.94224,3.19675,3.46751,3.73827,4.003

61,4.26895,4.53971,4.79964,5.0704]

y3=[.739731,.678451,.610101,.555107,.52211,.487542,.455331,.423906,.39

4837,.371268,.350056,.328844,.31156,.300561,.396409,.467116,.503255,.5

33109,.550393,.56532,.580247,.591246,.60303,.6156]

for line in lines:

var1=(float(line.split("\t")[0])+0.0045)/0.023

var2=(float(line.split("\t")[1]))/(1.6*10**5)

x1.append(round(var1,5))

y1.append(round(var2,5))

for j in x3:

ll=j-0.0005

rl=j+0.0005

cmp=1

for i in x1:

if (i>=ll) & (i<=rl):

if abs(j-i)<cmp:

cmp=j-i

ins=i

ind=x1.index(ins)

p_num.append(y1[ind])

#Root Mean Square Error Calculation

error=0

for i in range(24):

error=error+(y3[i]-p_num[i])**2

error=sqrt(error/len(y3))

print("ERROR=",error*100,"%")

47

5. Pressure contours of flow for Wall flow injection

Xt=16mm Xt=29mm

Xt=38mm Xt=48mm

48

Red- 1.5 bar

Blue- 0.382 bar

Xt=67mm Xt=77mm

Xt=86mm

49

6. Effect of throat radius

Rt=90mm Rt=95mm

Rt=102mm Rt=104mm

50

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