N9412S O5O - NTRS - NASA

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in rocket engine coolant channels are analyzed by means of a numerical model. .... results for the slug flow inlet show a peak velocity of 4.0 m/s in the exit plane ...
O5O

N9412S CFD

ANALYSES

Jennifer

OF

COOLANT

CHANNEL

A. Yagley t, Jinzhang Propulsion

Feng 1:, and Charles

Engineering

Department

FLOWFIELDS

Research

of Mechanical

L.Merkle

§

Center

Engineering

The Pennsylvania State University University Park, PA 16802

SUMMARY The flowfield characteristics The channels

are characterized

At representative developed coolant,

by large length to diameter

flow conditions,

conditions the strong

the channel

would be reached property

variations

ence on the flow and the resulting tial differences.

In addition,

fluid in the channels configuration

by means of a numerical

numbers,

twice the hydraulic

and asymmetrical entrance

fluid. For the supercritical

secondary

and variable

fully developed

drop without an accompanying

model. heating.

so that fully

that is used as the

which have a major influ-

property

solutions

show substan-

flow. The density

variation

accelerates

increase

can affect the development work is focused

length

hydrogen

flows in the cross-plane

of constant

prevent

that side entry from a manifold

in heat flux. Analyses

of the velocity

on studying

the

of the inlet

profile because of vor-

the effects of channel

bifurcation

characteristics.

DISCUSSION

Regenerative mal environment

cooling

is normally

of the combustion

length of the combustor near the injector

Although

process.

engines,

that the fluid remains the design

transfer

characteristics

sociated

heat transfer

characteristics

in these coolant passages,

functions

t Graduate

Research

_tResearch

Associate

§ Distinguished

variations

conditions

is critical

heating,

to the operation

the limiting

the throat region, and exiting

and temperature

(density,

occurs

viscosity,

106

rectangular

the flowfield

Because channel

are

their heat and the as-

channel

(which

inside the tubes re-

of a supercritical of the complex

coolant

with

three-dimen-

aspect ratio exists, and a vali-

under different

thermal conductivity

[1]. These variations

Professor

of the fluid dynamics

geometries,

that an optimum

where this optimum

pressures

passage.

and life of the engine,

case of a straight

numbers.

in shape and run the

and the elevated

the fin effect, the presence

it is anticipated

Assistant

Alumni

through

our understanding

Even with straight

all fluid properties

of both pressure

are rectangular

liquid hydrogen,

and the high Reynolds

tool in assessing

passages

end, passing

is generally

To maximize

is studied.

sional flow patterns

come strong

passages

of the asymmetrical

to protect the wails from the severe ther-

over the entire length of the cooling

of the coolant passages,

strong property

At supercritical

the coolant

understood.

its characteristically

dated CFD code is an important

at the supersonic

supercritical

being tested at NASA LeRC) because

engine combustors

In most cases, the coolant

of these coolant

are only poorly

mains quite complex

used in rocket

with the coolant entering

face. In cryogenic

to ensure

is currently

variations

as the flow enters the channel.Current

TECHNICAL

sufficient

property

create significant

on the flow field and the heat transfer

are analyzed

ratios, high Reynolds

heat transfer. Comparison

the pressure

channels

length is approximately

for a constant

the property

increasing

suggest

tices generated

in rocket engine coolant

are particularly

conditions. and specific strong

heat) be-

near the critical

point. Temperature

dependence

is especially

dients near the hot wall of the coolant In the presence

of property

must be solved simultaneously.

significant

in the present problem

because

variations,

the Navier-Stokes

The corresponding

equations

system of governing

and the energy

equations

T is the vector of dependent

Fis a pre-conditioning vectors

and pressure.

modate

auxiliary

equations

for the pressure

flow. The turbulent

Although

our interest

and are solved

tions are represented small amount

is in steady flow, the equations

by a four stage Runge-Kutta

by centered

differences.

the process

state Navier-Stokes

system;

algebraic

turbulence

scheme

model

thermal

[3] is used to accom-

the calculation. in unsteady

[4]. All derivatives is used to achieve odd-even

flux

maximum

splitting.

equa-

convergence

and a

Since the time derivatives

the stiffness

zero and the numerical

form for computational

of the Navier-Stokes

caused

expression

solution

dis-

by the low Mach num[5,6]. During

satisfies the proper

steady

equations.

As boundary inlet, and uniform the Riemann

coordinate

of the viscosity,

using an artificial compressibility

approach

and

to the local temperature

dependence

as 0.9/.hroughout

is added to prevent

all the time derivatives

the density

and temperature

time stepping

is circumvented

non-orthogonal

of state relating

may be taken with them to counter

fluid. This stiffness

of convergence,

a general

of motion are written

explicit

Local

of fourth order artificial dissipation

appear in the steady state, some license bers in the supercritical

is chosen

are coupled

flux vectors while E_, Fv and Gv are the viscous

The Baldwin-Lomax

Prandtl number

equation

= 0

_, _) represents

by a tabular equation

and specific heat are also specified.

turbulent

purposes

set is completed

Additionally,

conductivity

variables;(_,

matrix; E, F, and G are the conservative

[2]. The equation

gra-

is:

F_--Q+0--%(E-Ev)+_-_(F-Fv)+_-0-_(G-Gv) Q=(P,u,v,w,T)

of the strong temperature

passage.

conditions

pressure

variables

calculations,

at the exit plane. The remaining

determined

sage wall are the traditional

for the present

from the method

no-slip conditions.

we specify the velocity flow variables

of characteristics

and temperature

profiles

at the

at the inlet and outlet are computed

from

[4]. The velocity

These are augmented

by enforcing

boundary

conditions

the normal

momentum

on the pasequation

to

obtain the wall pressure. Heat transfer propriate

Dirichlet

tions are assigned temperature

conditions

(temperature)

representative boundary

of those in combustor

conditions

on both the inner (combustor)

the periphery

and outer (ambient)

is used on the side walls to simulate

are to couple the present fluids solution

around

coolant

passages

of the duct. Uniform

sides of the passage

the fin effect. The inlet temperature

with a heat conduction

are simulated

formulation

by selecting

temperature

ap-

condi-

while a linear distribution

is specified

for the combustor

as 40 K. Future

walls to obtain

of

plans

the cou-

pled solution. The straight properties,

turbulence

investigate in Figure

duct study was conducted modeling,

the effects of channel

to give an understanding

of the fundamental

high length

to diameter

ratios and inlet conditions.

bifurcation

on the flow and temperature

physical

effects of variable

The next step in the study is to

fields. A representative

geometry

is shown

1.

RESULTS The geometry

for this study were chosen to parallel

conducted

at NASA LeRC [7]. The length of the experimental

channel

diameters.

The Reynolds

and hydraulic

we also studied channels been completed

--

and flow conditions

number based on the inlet conditions

and variable

(supercritical

107

hydrogen)

study currently

is 137 mm which corresponds

of shorter lengths and flow at the lower Reynolds

for both constant

an experimental

diameter

is 500,000.

to 112 hydraulic

For the current study

number of 10,000. Computations

property

flows.

being

have also

One of the important and heat transfer

issues in the straight

characteristics

of the channels.

the flow field characteristics these differences parison

ations are shown

number

streamwise

in Figure

variation

hydrogen

cooling.

2. The constant

contour

property

direction

cause the velocity

plots of the pressure, results are shown

has been stretched

layers were significantly

transfer.

The inlet conditions

condition

issue

property).

represents

of fully developed

velocity

effect on the velocity results

was the effect of inlet velocity

The first two represents

a bounding

the tube, and in addition,

profiles

number. Despite

inlet show a peak of 3.3 m/s. The corresponding

the fact that the thermal

on the downstream

velocity

profiles

two extremes

pressure

configuration.

profile shows that the inlet condition

those

the same. Both calculations

show that the fluid has been heated to the point where the minimum

latter observation, percent)

has a measurable similar, but the

for the fully developed

drop for the slug flow inlet is about

inlet profile.

The last

A comparison

in the exit plane are qualitatively

the fluid temperatures

and heat

a 90 degree

in inlet profiles.

that for the fully developed

plane is 45 K, although

variations

fluid dynamics

and entry through

of 4.0 m/s in the exit plane whereas

By contrast,

shows the viscous

of the flow due to the density

study between

in the exit plane (Fig. 3). The contours

for the slug flow inlet show a peak velocity

lead to an

effect on the temperature.

10,000 and 500,000

to the type of entry that is used in the experimental

profile with the slug flow velocity

contours

15 percent

larger than

at the exit plane for both cases are about temperature

in the exit

more of the fluid appears to have been heated in the slug flow inlet case. In agreement

computation

of the heat flux through

for the slug flow inlet case. These differences

that care should be taken in defining

results

number.

studied were slug flow, fully developed

an approximation

numbers

there is still an acceleration

as in the lower Reynolds

studied

Reynolds

across

thinner at the higher Reynolds

to a small portion of the flowfield

not as significantly Another

to be very non-uniform

of the flow fields for the two different

although

bend (constant

profiles

property

vari-

by a factor of five in theses figures. As can be seen,

by a factor of about two. The higher flow speeds cause a lesser, but noticeable

effect are limited

This com-

and the temperature

on the right while the variable

acceleration

boundary

alters

the nature of

was conducted.

the axial velocity

properties

and thermal

drop

significantly

To evaluate

and variable properties

the variable

A comparison

on the pressure

of 10,000.

direction

are shown on the left. The cross-stream

of super-critical

to assess its effect on the channel

of the flowfields based upon constant

was made at a Reynolds The mid-plane,

The property

and it is important

a comparison

tube studies is the effect of variable properties

the walls shows that the heat addition

between

the inlet conditions

the two calculations

with this

is larger (by about

15

are not major, but they do suggest

to be sure to obtain maximum

accuracy

in the coolant channel

predictions. The results locity contours ric. Similar

for the second inlet condition,

are quite similar in magnitude,

comparison

temperature

of the temperature

although

profiles

from 90 K to 110 K, suggesting

the inlet with a 90 degree bend are presented

in Figure 4. The ve-

the profiles for the 90 degree bend inlet are slightly asymmet-

shows the presence

of the bend in the inlet increases

the minimum

that the vortex created by the turn at the inlet has some effect on the heat

flux. Comparisons The pressure

drop predictions

itself), suggesting downstream boundary

of the streamwise

gradient.

layer downstream

The presence

of the vortices

The velocity

developed

flow characteristics

(not counting

are given on Figs. 5 and 1.

the pressure

drop across the inlet bend

by the bend in the inlet was not sufficient

profile in the bent inlet calculation

shows a dramatic

and the vortex generated

and the coolant channels

by the curved inlet suggests

can have an effect on the downstream

108

to affect the

thickening

of the inside portion of the curved inlet. This arises from a flow separation

of flow separation

tween the manifold

of the various

for the two cases is nearly identical

that the strength

pressure

development

of the

near the bend.

that the type of connection

be-

heat n'ansfer.

--

REFERENCES [I]

McCarty,

R.D., "Hydrogen

Technological

Survey-Thermophysical

Properties",

NASA SP-3089,

1975, Wash-

ington D.C. [2] ASEE

Yagley,J.A.,

[3]

Baldwin,

Flows",

AIAA

[4]

Merkle,

Conference,

B.S. and Lomax

16th Aerospace

AIAA-86-0553, [5]

Feng, J. and Merkle, C.L., "CFD Analyses

29th Joint Propulsion

C.L.

and

H., "Thin Layer

Sciences Tsai,

Merkle,C.L.

and Athavale,

Meeting,

Y.L.

AIAA 24th Aerospace

Compressibility",

AIAA-93-1830,

Approximation

Meeting,

M., "Time-accurate

Channel

Unsteady

Fluid Dynamics

January

AIAA/SAE/ASME/

Model

for Separated

1978, Huntsville,

of Runge-Kutta

January

FIowfields",

CA.

and Algebraic

AIAA Paper 78-257,

Peter, "Application

Sciences

AIAA 8th Computational

of Coolant

June 1993, Monterey,

Schemes

Turbulent

AL.

to Incompressible

Flows",

1986, Reno, NV. Incompressible

Conference,

Flow Algorithms

AIAA Paper 87-1137,

based on Artificial

June 1987, Honolulu,

HA. [6]

Choi, Y.-H. and Merkle, C.L., "The Application

tion Physics, [7]

Voi 105, No2, April

in Viscous

Flows",

Journal

of Computa-

1993.

Carlile, J.A. and Quentmeyer,

AIAA-92-3154,

of Preconditioning

R.J., "An Experimental

AIAA/SAE/ASME/ASEE

Investigation

28th Joint Propulsion

Top

Conference,

of High-Aspect-Ratio July 1992, Nashville,

Cooling

Passages",

TN.

View q

l"

I

i

Figure

---

1:

Representative

sketch of channel

bifurcation

geometry.

109

1"

!

Variable Properties

_u_

Constant

Properties

[JJl llllll Velocity

Temperature

Figure 2: Steamwise contours of the pressure, velocity, and temperature on the centerplane for an L/D h of 28. Variable Properties: Pine = 20., Pm_x = 220.; Uinc = 0.5, ureax -- 4.0; Tin c = 70, Tma x = 600 (top wall). Constant Properties: Pinc = 6., Pmax = 42 .; Uinc = 0.17, Ureax = 1.4; Tin c = 70, Tma x = 600 (top wall). Slug Flow Inlet Velocity

Fully Developed

Inlet

Bend Inlet

Slug Flow Inlet

Velocity

1

Figure 3: Contour of axial velocity and temperature at the exit plane (L/D h = 28) for slug flow and fully developed inlet with variable properties. Slug: Uinc = 0.4, urea x = 4.0, Tree = 70, Train = 45. Fully Developed: uinc = 0.4, Umax= 3.3; Tinc= 70, Tmax = 600 (right wall).

Figure 4: Contour of axial the exit plane (L/Dh=28) for inlet with constant properties. Tint = 70, Tmin = 45. Bend Tree = 70, Tmax = 600 (right

velocity and temperature in slug flow and bend entrance Slug: uinc = 0.4, Umax= 4.0, Inlet: uinc = 0.4, Umax = 3.3; wall).

Velocity

Temperature

Figure 5: Effects of bend on flowfield (constant properties). There are 28 hydraulic diameters after the bend. Pinc= 0.5, Pmax = 5; uinc = 0.1, umin = 4). 1, Umax= 1.5; Tint = 70, Tma x = 600 (at bottom wall), Tmin = 40 (at inlet).

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