Medhat Sharabi, Walter Ambrosini, Discussion of heat transfer
phenomena in fluids at supercritical pressure with the aid of CFD
models, Annals of Nuclear Energy 36 (2009) 60–71
Introduction
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Qualitative similarity of the fluid property transition during boiling at subcritical pressure and
the continuous but dramatic changes observed across the pseudo-critical temperature 
analogies and differences between the 2 phenomena
The presence of maxima and minima in the HTC that occur or nor occur (depending on the
operating conditions) is a challenge for many researchers and is still not fully understood
HT ENHANCEMENT  is intuitively justified on the basis of the large value of cp (as many HT
correlations suggest that Nu rises with increasing Pr)
HTD (local minima)  Less clear
o Depends on up- or downwards flow direction  possible buoyancy effects
For T_w > T_pc  fluid in contact with it becomes rapidly a gas-like fluid  progressive
decrease in HT efficiency is expected (similar for subcritical boiling at the wall which is an
obstacle for higher conductivity fluid to reach the wall)
o Suggestion for applicability of pseudo two-phase models for predicting HT in SC fluids
 Hsu, Y.-Y., Graham, R.W., 1976. Transport Processes in Boiling and TwoPhase Systems–Including Near Critical Fluids. McGraw-Hill Book Company.
 Hendricks, R.C., Graham, R.W., Hsu, Y.-Y., Medeiros, A.A., 1962. Correlation
of hydrogen heat transfer in boiling and supercritical pressure states. ARS J.
32 (2), 244–252
  presence of gas-like layer close to the wall which is regarded as a
sort of inverted annular film, controlling the effects of HTD and
recovery
 McEligot, D.M., et al., 2008. Fundamental thermal fluid physics for cooling
channels of supercritical-pressure reactors. International Students’
Workshop on High Performance Light Water Reactors, March 31–April 3,
2008. Karlsruhe, Germany
 Similar ideas
o Importance of buoyancy effects due to density changes across the boundary layer at
T_pc
 Hall, W.B., Jackson, J.D., 1969. Laminarization of a Pipe Flow by Buoyancy
Forces. ASME paper 69-HT-55.
 For q/G >>  the effects deform the velocity profiles so heavily in the
boundary layer that the turbulence generated by shear stress is reduced 
laminarization of the flow follows  strong Decrease in HT
 M-shapes velocity profiles also occur in turbulent gas buoyancy flows
 the definition of ‘aided’ mixed convection in turbulent flows then
becomes misleading
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By this, this effect should not occur in downward flow, because here
buoyancy doesn’t decrease the shear stresses, maintaining a
sufficient degree of turbulence intensity
 Recent experiments show this: HTD for upward flow and a very weak
and restarted reduction for downward flow
 Pis’menny, E.N., Razumovskiy, V.G., Maevskiy, A.E., Pioro, I.L.,
2006. Heat transfer to supercritical water in gaseous state or
affected by mixed convection in vertical tubes. In: Proceedings of
the ICONE14 Conference, July 17–20, Miami, USA
 Criteria for occurrence of such laminarization proposed by:
 Jackson, J.D., Hall, W.B., 1979. Influence of Buoyancy on Heat
Transfer to Fluids in Vertical Tubes under Turbulent Conditions,
Turbulent Forced Convection in Channels and Bundles, Hemisphere,
New York, PP. 613–640.
 McEligot, D.M., Jackson, J.D., 2004. ‘‘Deterioration” criteria for
convective heat transfer in gas flow through non-circular ducts,
Short communication. Nucl. Eng. Design 232 (2004), 327–333
o Acceleration also considered to play a role
 Large density decrease  Increase in local velocity  weakens turbulence
CONCLUSION:
o Different phenomena play a role for HTE and HTD
o Similarity between pseudo-critical transition and boiling
HERE: CFD Turbulence models for prediction of experimental data of:
o Yamagata, K., Nishikawa, K., Hasegawa, S., Fujii, T., Yoshida, S., 1972. Forced
convection heat transfer to supercritical water flowing in tubes. Int. J. Heat Mass
Trans. 15, 2575–2593
o Kim, J.K., Jeon, H.K., Yoo, J.Y., Lee, J.S., 2005. Experimental study on heat transfer
characteristics of turbulent supercritical flow in vertical circular/non-circular tubes.
In: Proceedings of the 11th NURETH-11, Avignon, France, October 2–6
PREVIOUS works by Sharabi on data of Pis’menny and Kim already gave some indication of
the available turbulence models in predicting HTD
o Sharabi, M.B., Ambrosini, W., Forgione, N., He, S., 2007. Prediction of experimental
data on heat transfer to supercritical water with two-equation turbulence models.
In: 3rd Int. Symposium on SCWR – Design and Technology, March 12–15, 2007,
Shanghai, China.
o Sharabi, M., Ambrosini, W., He, S., Jackson, J.D., 2008. Prediction of turbulent
convective heat transfer to a fluid at supercritical pressure in square and triangular
channels. Annals Nucl. Energy 35 (6), 993–1005.
o Pis’menny, E.N., Razumovskiy, V.G., Maevskiy, A.E., Pioro, I.L., 2006. Heat transfer
to supercritical water in gaseous state or affected by mixed convection in vertical
tubes. In: Proceedings of the ICONE14 Conference, July 17–20, Miami, USA
o Kim, J.K., Jeon, H.K., Yoo, J.Y., Lee, J.S., 2005. Experimental study on heat transfer
characteristics of turbulent supercritical flow in vertical circular/non-circular tubes.
In: Proceedings of the 11th NURETH-11, Avignon, France, October 2–6
Conclusions from previous studies:
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turbulence models relying on wall functions to deal with the near-wall region have
no capability to predict heat transfer deterioration;
different low-Reynolds number k–e models are capable to qualitatively predict the
onset of deterioration in upward flow, though they tend to overestimate the effect
of laminarization, providing wall temperatures well above the values observed in
experiments;
k–x models respond more slowly in predicting laminarization effects in upward flow
and do not provide a qualitatively acceptable prediction of the observed
deterioration;
in the addressed cases, the adopted models did not show any evidence of the
possibility of occurrence of heat transfer deterioration in downward flow.
Conclusions
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heat transfer enhancement is due only to the lambda-shaped trend of specific heat as a
function of temperature, whenever buoyancy effects are relatively important;
on the other hand, heat transfer deterioration is caused by laminarization effects and occurs
only in upward flow when buoyancy effects are relatively important;
at low flow rate, heat transfer enhancement can be masked by the simultaneous presence of
deterioration; on the other hand, at large flow rate heat transfer deterioration does not take
place, since buoyancy is relatively weak with respect to inertia.