Prediction of strongly-heated internal gas flows Page: 8 of 17
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matching -- may be considered to be indirectly deduced
data [Shehata and McEligot, 1995]. This approach
could be thought to be an extension of the earlier
technique of deducing eddy diffusivity profiles for
simple fully-developed, adiabatic flows by fitting mean
velocity profiles. That is, by adjustment of the
turbulent models which give -UWv, -vt, etc., the
velocity and temperature distributions have been fit.0
0
0
0
0
0
0
01 . .
Ru 6' -:
.8 Unteated
x0 .3.2
.6 --
8.7
.4 -
.2 14.2
\2 24.5
0 -{
Run 635 3
8 Unheate d
.6.'
xfD=. *I
8.7
.2 '-
r /~~ 14.2 , .
0
1
--0.5
0.- -2
0.2
* ---
0-+
Figure 6 Axial behavior of Reynolds shear stress
profiles as deduced from velocity and temperature
measurements via numerical diagnostic technique
[Shehata and McEligot, 19951.
The Reynolds shear stress or turbulent shear
stress distributions, -p uv, which are required in order
to obtain agreement between predictions and
measurements, are shown normalized by the local wall
shear stress in Figure 6. For fully-developed, adiabatic
turbulent flow the total shear stress, g(aU/ ay) - p v,
decreases linearly from the wall to the centerline.
Therefore, across the viscous layer the normalizedReynolds stress increases from zero to approach the
value for the total shear stress, as molecular effects
become less important, and then follows this decreasing
ramp-like function to zero at the centerline. For each of
Shehata's runs, one can discern the beginning of this
behavior in the adiabatic entry profile of -p v /t .
With the significant heating of Runs 618 and 635, the
deduced levels of these Reynolds stress profiles decrease
from the entry to x/D = 3.2, the first heated profile.
For the "turbulent" run (618), the normalized Reynolds
stress settles to an approximately constant profile from
x/D = 9 to 25 with slight variation. For the other two
runs at higher heating rates, these profiles decrease to
negligible values as the axial distance increases. For
Run 445 the deduced reduction in the first few diameters
is more severe than for Run 635; in a sense, Run 445
laminarizes more quickly (as might be expected for
lower Re. and higher q i).
6. SIMULATIONS WITH GAS PROPERTY
VARIATION
Mikielewicz [1994] examined eleven turbulence models
developed for forced turbulent flow with the constant
property idealization as discussed earlier. For fully-
developed flow with constant properties at Reynolds
numbers in the range 4000 < Re < 60,000, only the
model by Launder and Sharma agreed with the Dittus-
Boelter correlation for common gases (coefficient =
0.021) within its estimated experimental uncertainty
over the full range; several k-e models designed for
low-Reynolds-number conditions gave poor agreement.
A number of turbulence models, developed for
turbulent flows under conditions of uniform fluid
properties, were applied by Mikielewicz for the
purposes of simulating experiments with strongly-
heated, variable property gas flows at low Reynolds
numbers in a vertical circular tube [Shehata, 1984].
The selection of models included a mixing length
model, eddy diffusivity models, a one-equation k model
and two-equation models of k-E type with low-
Reynolds-number treatments; this selection is
representative of models which have been widely used
but obviously is not all-inclusive. Thermal energy
transport was modeled using a turbulent Prandtl number
with its value held constant (0.9).
To illustrate the predictions of integral heat
transfer, Figure 7 presents the resulting wall
temperature distributions for eight models for the three
runs. For the thermal design engineer, these predictions
are of key importance. In this figure the distance z/D is
labeled from the start of the calculation, so the nominal
start of heating (usually called x = 0) is at z/D = 14.8
and the near-uniform wall heat flux range is in the
region 20 < z/D < 41. The expected sharp rise of wall
temperature after the abrupt increase in wall heat flux
(near z/D = 15) is demonstrated by all the models.
In Figure 7 the identification of the various
models is via letter labels; the square symbols are the
measurements from Shehata [1984]. For the lowest
heating rate, "turbulent" Run 618, the trends from6
.
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McEligot, D. M.; Shehata, A. M. & Kunugi, Tomoaki. Prediction of strongly-heated internal gas flows, article, December 31, 1997; Idaho Falls, Idaho. (https://digital.library.unt.edu/ark:/67531/metadc691775/m1/8/?rotate=90: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.