Prediction of strongly-heated internal gas flows Page: 4 of 17
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that "the first essential in modeling such flow is to
adopt a low-Reynolds-number model for the sublayer
region." The reader is referred to these reviews for
general background on computational fluid dynamics
(CFD), circa 1995.
In our terminology, the viscous layer is
operationally defined to include both the so-called
"linear" layer, where molecular effects dominate, and the
next region where molecular effects are still significant
but not dominant. For unheated flows, these regions
typically extend to y+ (= Y[gcwP]1/2/V) of about five
and thirty, respectively. This usage follows that
suggested by Bradshaw [1971]. Emphasis must often
be centered on the viscous layer because it tends to
provide the greatest uncertainty in predicting the
convective thermal resistance [McEligot, 19861.
2. CONSTANT PROPERTY LIMIT
As will be seen later, simulations of some effects of
strong heating of a gas involve the low-Reynolds-
number turbulent range. In fact, Kawamura [1979
demonstrated nicely that adequate predictions of some
phenomena with significant property variation were
obtained when their results were also good in the low
temperature-difference limit as the gas properties
become effectively constant (his Figure 1). Therefore,
it is appropriate that codes and their turbulence models
be initially examined for fully-developed flow in a
circular tube with the constant properties idealization
to assess their capabilities to simulate low-Reynolds-
number flows in the simplest case. In any event, most
engineers would want both heat and momentum transfer
to be handled adequately for constant properties before
treating cases with property variation.
McEligot, Ormand and H. C. Perkins [1966]
showed by measurements that for common gases the
Dittus-Boelter correlation [1930], with the coefficient
taken as 0.021 [McAdams, 1954], is valid to within
about five per cent for Pr - 0.7 and Reynolds numbers
greater than about 2500. Thus, this correlation may be
employed as a standard of comparison.
Mikielewicz [1994] conducted simulations of
the predictive capabilities of a range of turbulence
models for fully-developed flow in a circular tube with
uniform wall heat flux and the constant properties
idealization; eleven models were considered. The
Reynolds number range covered was 4000 < Re < 6 x
104 and the Prandtl number used was 0.7, for air. His
tabulated results are plotted in Figure 2. Based on his
predictions for Nusselt number, several popular models
could be immediately eliminated from further
consideration. Some models do not even handle high-
Reynolds-number flows well for heat transfer. Several
k-e models designed for use at low Reynolds numbers
also gave poor results. At Re = 5000, the Jones and
Launder version is over thirty per cent high and
predictions by Lam and Bremhorst and by Shih and Hsu
are over fifteen per cent above the correlation. The only
model considered which gave acceptable results was that
of Launder and Sharma; their predictions fall within theestimated experimental uncertainty in the Nusselt
number over the full range.
Reasonable predictions have also been provided
in the low-Reynolds-number range for this case by
McEligot, Ormand and Perkins [1966], McEligot and
Bankston [1969], Kawamura [1979], Torii et al. [1991],
Ezato et al. [1997] and Nishimura and Fujii [Nishimura
et al., 1997] and others. These calculations have
covered a range of types of turbulence models, from
modified mixing length approaches to a Reynolds stress
model coupled to a two-equation model for heat transfer.a
, .2
0
0.93000
*P Re
6" 10
Figure 2. Simulations by Mikielewicz [1994] using
various turbulence models (curve labeled KP is the
Kurganov-Petukhov correlation).
3. EFFECTS OF LARGE HEAT FLUXES
The effects of temperature on the transport properties of
helium are presented in Figure 3. From the perfect gas
"law", one recalls that the density also varies
significantly -- approximately inversely with the
absolute temperature. These trends are typical of most
common gases and of binary mixtures of gases; for the
former, the Prandtl number is around 2/3 or 0.7, while
for the latter in may be as low as 0.2 [McEligot, Taylor
and Durst, 1977].t
.0
0
U
N1000
T (R)-
v
E
c.
d .
(3T (R)
Figure 3. Transport properties of helium.
From Figure 3 it can be seen that the
temperature dependencies of the viscosity and thermal
conductivity can also be approximated by power laws
/lref (T/Tref)a and k/kref =(T/Tref)b
for convenience in numerical predictions.
We consider the idealization of a uniform wall
heat flux for convenience in the presentation. With2
Constant properties
.-- .
--E
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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/m1/4/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.