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
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June 1993, Monterey,
Schemes
Turbulent
AL.
to Incompressible
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1986, Reno, NV. Incompressible
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AIAA Paper 87-1137,
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June 1987, Honolulu,
HA. [6]
Choi, Y.-H. and Merkle, C.L., "The Application
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Voi 105, No2, April
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Carlile, J.A. and Quentmeyer,
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R.J., "An Experimental
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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).
Ii0