1 “CFD Analysis of Inlet and Outlet Regions of Coolant Channels in an Advanced Hydrocarbon Engine Nozzle” Dr. Kevin R. Anderson Associate Professor California.

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“CFD Analysis of Inlet and Outlet Regions of Coolant Channels in an Advanced

Hydrocarbon Engine Nozzle”

Dr. Kevin R. AndersonAssociate Professor

California State Polytechnic University at PomonaDepartment of Mechanical Engineering

Thermal/Fluids Engineer, Swales AerospaceFaculty Part Time T&FSE, NASA-JPL

TFAWS 2004Thermal & Fluids Analysis Workshop Aerothermal / CFD Paper 109-A0019

JPL Pasadena, CA August 30 – September 3, 2004Pasadena Center, Pasadena, CA

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CFD Analysis Required to Model Channel Outlet Regions

Background:

AHEP – Advanced Hydrocarbon Engine Program

Air Force sponsored research contracted Swales Aerospace to perform CFD analysis

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CFD Analysis Required to Model Channel Outlet Regions

Goal: Estimate Convective Heat Transfer Coefficient On Hot Gas Wall At Inlet And Outlet

Region Of Rectangular Channel

A

A

Coolant Inlet

Section A-A

Coolant Outlet

Combustion Chamber Geometry

4

Injector MountingFlange Stresses

Copper Combustor LinerStresses

Electroformed NickelStructural Closeout Stresses

Copper/EF NickelBond Joint Stresses

Inje

cto

r E

xit

Pla

ne

Combustion ChamberCross-Section

Combustor Geometry

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Combustor Liner Dimensions

Vacuum Plasma Sprayed GRCop-84 Combustor Liner

CoolantChannel

ElectroformedNickel Structural Closeout

300 R

Throat Cross-section

All Dimensions are in Inches

1210 R

270 R

0.140

0.30

0.0350.050

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Bounding Calculations• Based upon inlet flow rates and LN2 properties

– Reynolds Number

2300~3 ,4

,4

transhh

Rew

h

P

AD

D

mRe

Flow Rate (lb/s) Re inlet ×105 Re outlet ×105

0.7 0.815 38.6

1.0 1.165 55.1

1.2 1.398 66.1

• Thus, flow is modeled as Turbulent

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Bounding Calculations• Based upon inlet and outlet speed of sound in LN2

– Mach Number

Flow Subsonic 1 , , MaA

mu

c

uMa

Flow Rate (lb/s) Ma inlet Ma outlet

0.7 0.073 0.171

1.0 0.105 0.244

1.2 0.126 0.293

• Thus, flow is modeled as Incompressible

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CFD Modeling Methodology• GAMBIT© 2.0 Used to Build Computational Grid

• FLUENT© 6.0 3-D Finite Volume

• Incompressible, Viscous Internal flow

• Standard k- Turbulence Model

• Internal Flow Convective Heat Transfer

• FLUENT User Defined Fluid Option for LN2

• NIST 12 Database Used to Obtain LN2 Properties:ckccsh p ,,,,,,,

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CFD Modeling MethodologyLN2 DENSITY NIST 12 DATA CURVE FITS

T;p=6000 psia) = 9E-05T2 - 0.1429T + 73.415(T;p=5000 psia) = 0.0001T2 - 0.1594T + 75.011(T;p=4000 psia) = 0.0001T2 - 0.1844T + 77.658

0

10

20

30

40

50

60

0 100 200 300 400 500 600

TEMPERATURE (R)

DE

NS

ITY

(L

BM

/FT

3 )

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Governing Equations• Conservation of Mass

• Conservation of Momentum

0)(

t

I

pt

T ~

3

2)(~

~)()(

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Governing Equations• Conservation of Energy

K 15.298

flows ibleincompressfor

2

~)()(

,

2

ref

T

T

jpj

jj

j

effeff

TdTch

phYh

phE

TkpEt

E

ref

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Governing Equations• Conservation of Energy

- Segregated solver does not include Pressure Work or Kinetic Energy terms, which are negligible for incompressible flows

- Viscous Dissipation terms which describe the thermal energy created by the viscous shear in the flow must be included since Brinkman number:

- Br ~ 1.14, 2.3, 3.4, Viscous Heating present

1 2

Tk

uBr stream

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Governing Equations• Standard k- Turbulence Model

)()(

)()(

2

21 kC

x

uuu

kC

xxx

u

t

x

uuu

x

k

xx

ku

t

k

i

jji

j

t

ji

i

i

jji

jk

t

ji

i

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Governing Equations• Turbulent Eddy Viscosity

• Model Constants

2

kCt

31 ,0.1

09.0 ,92.1 ,44.1 21

.σσ

CCC

εk

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CFD Model Solution• FLUENT© Segregated Solver

- Finite Volume Discretization

- Linearization of Discretized Equations

• Implicit Linearization results in a system of linear equations for each cell in the domain

• Point implicit Gauss-Seidel linear equation solver used in conjunction with an Algebraic Multigrid Method (AMG) to solve the resultant scalar system

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CFD Model Solution• Overview of the Segregated Solution Method

• Mesh independence study showed approx. 70,000 Finite Volumes required for grid independent converged results

UPDATE PROPERTIES

SOLVE MOMENTUM EQUATIONS

SOLVE PRESSURE-CORRECTION (CONTINUITY) EQUATION

UPDATE PRESSURE,

FACE MASS FLOW RATE

SOLVE ENERGY, TURBULENCE AND OTHER SCALAR

EQUATIONS

CONVERGED ?STOP

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Boundary ConditionsA

A

Coolant Inlet

Section A-A

Coolant Outlet

Mass Flow Rate Inlet BC

Supply LN2:

140 R

6000 psia

Pressure Outlet BC

Exit LN2:

285 R

4870 psia

Heat Flux BC

97 BTU/in2-s

(50.3×106 BTU/hr-ft2)

k- log-law of the wall

wall functions

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3-D FLUENT CFD Model Grid Surfaces Outline

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Detail View of Mesh Near Channel Inlet Region

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Detail View of Mesh Near Channel Outlet Region

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Flow rate = 0.7 lb/s Velocity Vectors Near Inlet

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Flow rate = 0.7 lb/s Velocity Vectors Near Outlet

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Flow rate = 0.7 lb/s Contours of h (BTU/hr-ft2-R)

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Flow rate = 0.7 lb/s Contours of h (BTU/hr-ft2-R) Near Inlet

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Flow rate = 0.7 lb/s Contours of h (BTU/hr-ft2-R) Near Outlet

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30


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36


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40


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LOCAL HEAT TRANSFER COEFFICIENT h(x) VS. DISTANCE ALONG CHANNEL(CURVE SHOWN FOR UPPER HALF OF COMBUSTOR WALL)

3000

5000

7000

9000

11000

13000

15000

17000

19000

21000

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

DISTANCE ALONG CHANNEL

h(x)

(B

TU

/hr-

ft2 -R

)

Flow Rate = 0.7 lb/s



1 2

1

2

2

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Comparison of Overall Convective Heat Transfer Coeff. hFLUENT CFD Model Surface Description

Flowrate = 0.7 lb/s Area Weighted Average Surface Heat Transfer

Coefficient (BTU/hr-ft2-R)

Flowrate = 1.0 lb/s Area Weighted Average Surface

Heat Transfer Coefficient

(BTU/hr-ft2-R)

Flowrate = 1.2 lb/s Area Weighted Average Surface Heat Transfer

Coefficient (BTU/hr-ft2-R)

combustorback 6448 8702 10541 combustorbottom 3986 5124 5815 combustorfront 6187 8885 10450 combustorinnerwall 5206 7507 8922 combustortop 3989 5159 5840 Net area weighted average 5868 8149 9681

1 “CFD Analysis of Inlet and Outlet Regions of Coolant Channels in an Advanced Hydrocarbon Engine Nozzle” Dr. Kevin R. Anderson Associate Professor California.

Documents

cfd analysis slide

incompressible slide

ca slide

turbulent slide

turbulence model slide

cfd modeling methodology

cfd analysis of inlet

viscous heating present