Project Presentation June2010

7/29/2019 Project Presentation June2010

1/62

METHODS OF CHARACTERISTIC

DESIGNS OF PLANAR ANDAXISYMMETRIC DUAL BELL NOZZLES

ASHISH GARG

Project Advisor : Prof. JOSEPH MATHEW

DEPARTMENT OF AEROSPACE ENGINEERING

INDIAN INSTITUTE OF SCIENCE

BANGALORE

28TH JUNE 2010


2/62

Introduction

Dual bell nozzle is a concept of altitude adaptive nozzle Flow transition from base bell to extension bell occur at high altitude

No side load generation hence stability point of view its good, which is the main issue forother adaptive nozzles such as spike nozzles

Reasons for significant performance gain

Weak over expansion at low altitude so shocks are weak

No moving part

Higher expansion ratio of extension bell than conventional nozzle giving moreperformance gain at high altitude

Nozzle weight is comparatively very less than optimum contour

Some issues

Fast flow transition is required

Aspiration drag due to recirculation zone


3/62

-20

0

20

0 50 100 150 200

-60

-40

-20

0

20

40

60

WidthX

Y

inflection point

base nozzle

extension nozzle

0 50100 150 200

-50

050

-25

-20

-15

-10

-5

0

5

10

15

20

25

X

R

base nozzle

extension nozzle

inflection point


4/62


5/62

About Method of characteristic

Its a numerical method for solving nonlinear inviscid,irrotational flow.

Used to convert partial differential equation into ordinary

differential equation

Exist only in super sonic flow

Coincident with mach line

While derivatives of flow properties are discontinuous but

flow properties are continuous Along given line they satisfy compatibility equation


6/62

Region OTR: Starting of source flow

Region TRDC: Radial flow region

Region CDE: Transition region Region EDX: Flow is fully parallel and uniform

Used linearized approximate integral form of MOC

Foelsch Analytical Method

Different procedures used to design

nozzles using MOC


7/62

Anderson Method

Use MOC equations in discretize form along characteristicline


nozzles using MOC


8/62

Shapiro method

Use MOC equations in discretize form along characteristic line

Shapiro use backward c- characterstic to define more accurate

profile


nozzles using MOC


9/62

Comparision of lengths

0 1 2 3 4 5 6-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

X

R

Re

Me=2.5

C+

Length of centered expansion axis symm. nozzleC- characterstic

backward C-

max

-1 0 1 2 3 4 5 6 7 81

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

X

R

Nozzle length comparison for axis symm Me=2.5

Foesch Analytical Method

SOAM with centered expansion

SOAM with Radius of expansion =1.161


10/62

Types of single

and dualbell nozzles

discussed inthesis

Sr.NO. NOZZLE TYPE BASE NOZZLE EXTENSION NOZZLE

1

single bell

optimum wall

2 parabolic bell

3 wedge/straight line bell

4 pressure boundary wall

5 mach number boundary wall

6

double bell

optimum wall optimum wall

7 parabolic bell parabolic bell

8 parabolic bell wedge/straight line bell

9 parabolic bell pressure boundary wall

10 parabolic bell mach number boundary wall

11 wedge/straight line bell wedge/straight line bell

12 wedge/straight line bell pressure boundary wall

13 wedge/straight line bell mach number boundary wall

14 wedge/straight line bell parabolic bell

15 pressure boundary wall pressure boundary wall

16 pressure boundary wall mach number boundary wall

17 pressure boundary wall parabolic bell

18 pressure boundary wall wedge/straight line bell

19 mach number boundary wall mach number boundary wall

20 mach number boundary wall parabolic bell

21 mach number boundary wall wedge/straight line bell

22 mach number boundary wall pressure boundary wall


11/62

2D planar nozzles

Expansion arc boundary condition


12/62

Axis boundary condition = 0, y = 0

Prandtl-Meyer function

Mach angle equation


13/62


14/62

Optimum dual bell

Inflection point conditions


15/62

Parabolic Raos bell


16/62


17/62

Parabolic dual bell



18/62

Wedge dual bell


Wedge nozzle wall equation


19/62

PW and WP nozzle contours


20/62

Linear pressure variation along nozzle wall


21/62

Characteristic equation of Axisymmetric

nozzles


22/62

Axisymmetric boundary condition


23/62

Axisymmetric Parabolic dual bell nozzle


24/62

Treatment of Special Conditions


25/62


26/62


27/62

Nozzle weight calculation


28/62

Validation of Coding through FLUENT


29/62

Validation from1D flow relation


30/62


31/62


32/62

Boundary layer correction[17]


33/62

Boundary layer correction


34/62



35/62

Typical characteristics of dual bell

nozzles


36/62

2D planar optimum dual bell nozzle

INPUTS

base nozzle exit mach number = 3.5

extension bell exit mach number = 5

base bell exit area ratio w.r.t throat = 6.79

extension bell exit area ratio w.r.t. throat = 25

total pressure = 200 bar

total temperature = 2000k

atmospheric pressure = 0.38 bar

Specific heat = 1.4

Throat height = 1


37/62


38/62

2D planar parabolic dual bell nozzle


39/62

2D planar parabolic dual bell nozzle

INPUTS

base nozzle exit mach number = 3







reference wedge angle = 15 degree

fraction length used of this reference wedge = 0.8


40/62


41/62

INPUTS :

base nozzle exit mach number = 3







reference wedge angle = 15 degree

fraction length used of this reference wedge = 0.8

Comparisions of PC, CP, PP, CC nozzles


42/62

For PP the parameters are:slope1 : 0.34, slope2 : 0.21, slope3 : 0.41,

and slope4 : 0.25

For PC the parameters are:

slope1 : 0.34, slope2 : 0.21, slope3 : 0.39,

and slope4 : 0.39

For CP the parameters are:


and slope4 : 0.25

For CC the parameters are:


and slope4 : 0.39

Comparisions of PC, CP, PP, CC nozzles


43/62


44/62


45/62


46/62


47/62


48/62

Shock captured by

MOC solution asRef. [8]


49/62

Axisymmetric nozzle

INPUTS

Nozzle type= Dual parabolic nozzle

Total pressure = 200 bar

Total temperature = 2000k

Reference cone angle = 15 degree

Fraction length used of this reference cone = 0.8

Specific heat =1.4

Mach number at the exit of base bell= 4.8

Pressure at the exit of base bell = 0.47 bar

Mach number at the exit of extension bell = 6.6

Area ratio extension = 80.2

Atmospheric pressure = 0.07 bar = desired pressurefor 6.6 mach number

For PP Axisymmetric nozzle, the parameters are:

slope1 : 0.34, slope2 : 0.2, slope3 : 0.5, and slope4 :

0.3


50/62


51/62


52/62

Separation criteria and calculation of

transition altitudes[9]


53/62

Goals Achieved and Future Work

From the discussion so far in the presentation. MOC code for 2D Planar and

Axisymmetric Dual Bell Nozzles completed with Boundary Layer Correction

and CFD validation of MOC results.

Transition point calculation with respect to altitude has been formulated in

the thesis.

Experiments need to be done on designed contour by MOC to validate

transition analysis and results on Dual Bell Nozzles.

As we have located the shock where the MOC lines are coalescing. Now the

another future task is to incoporate entropy gradient after this shock in MOC

solution for better appoximation of flow field.

For other researchers working on MOC, Unsteady and 3D effect of flowfield can be modelled and can extend this code further with that.


54/62

References

Foelsch, K., The Analytical Design of an Axially Symmetric Laval Nozzle for a Parallel and Uniform Jet, Journalof the Aeronautical Sciences, Volume 16, 1949, pp.161-166,pp.188

Emanuel, G. and Argrow, B. M., Comparison of Minimum Length Nozzles, Journal of Fluid Engineering, Trans.ASME, Volume 110, 1988, pp.283-288.

Anderson, JD., 2001, Fundamentals of Aerodynamics, 3rd Edition, pp. 532-537, pp.555-585.

Anderson, JD., 1982, Modern Compressible Flow with Historical Perspective, pp. 268-270,pp. 282-286.

Shapiro, AH., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol.I, pp. 294-295.

Shapiro, AH., 1954, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol.II, pp. 694-695.

Frey, M. and Hagemann, G., Critical Assessment of Dual-Bell Nozzles, Journal of Propulsion and Power, Vol.15,No.1, 1999,pp. 137-143.

Masafumi Miyazawa and Hirotaka Otsu, An Analytical Study on Design and Performance of Dual-Bell Nozzles,AIAA, 2004

J.O stlund and B. Muhammad-Klingmann, Supersonic Flow Separation with Application to Rocket EngineNozzles, Applied Mechanics,2005,Vol 58,pp 143-177


55/62

Sibualkin, M. Heat Transfer to an Incompressible Turbulent. Boundary Layer and Estimation of HeatTransfer Coefficients at Supersonic nozzle Throats. J. Aeronaut. Sci., 23, No. 2, pp. 162-172, 1956.

A. MCCABE, Design of a Supersonic Nozzle, Reports and Memoranda No. 3440,March, 1964

Abdellah Hadjadj , Marcello Onofri, Nozzle flow separation, Shock Waves (springer) pp.163169,2009

Coles, D. E. "The Turbulent Boundary Layer in a Compressible Fluid." RAND Corporation Report R-403-PR, September 1962.

J.C. Sivells, Design of two-dimensional continuous-curvature supersonic nozzles. J. Aeronaut. Sci., 22,No. 10, pp. 685, 692, 1955.

J. Ruptash, Supersonic wind tunnels-theory, design and performance, UTIA Review No. 5, 1952.

J.C. Sivells , A Computer Program For The Aerodynamic Design OfAxisymmetric And Planar of NozzlesFor Supersonic And Hypersonic Wind Tunnels, Aedc,Dec1978

E.W.E. Rogers and. Miss B. M. Davis. A note on turbulent boundary layer allowances in supersonicnozzle design. A.R.C.C.P. 333, 1957.

References


56/62

THANKS!!!


57/62


58/62



59/62



60/62



61/62



62/62


Documents

Project Presentation June2010