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Tom SKS, Hauptman EG, The feasibility of cooling heavy-water reactors with supercritical fluids,
Nuclear engineering and design 53, p 187-196, 1979
Tom et al. uses in his feasibility study the heat transfer correlation introduced by Kranoshchekov and
Protopopov modified by a density-ration correction factor, which was later refined for calculation of
heat transfer to supercritical CO2 at a normalized pressure (p/pcrit) 1.02 to 5.25.
The pressure drop was calculated using the Kurawa and Protopopov correlation.
Adelt M, Micielewicz, Heat transfer in a channel at supercritical pressure, International Journal of
Heat and Mass Transfer, Vol.24, pp. 1667-1674, 1981
Kurganov VA, Katil’ny AG, Velocity and enthalpy fields and eddy diffusivities in a heated
supercritical fluid flow, Experimental Thermal and Fluid Science 1992; 5:465-478
Kurganov et al. investigated the velocity and temperature fields in a supercritical CO2 flow through a
heated vertical circular tube (22.7mm). A comparative analysis is made for normal and deteriorated
heat transfer flow structures, as well as in upward and downward direction. From these data, the
profiles of shear stresses, heat fluxes and gradient coefficients of turbulent diffusivity in various cross
sections of the tube have been found. In the conditions of normal heat transfer the flow structure
resembles the structure of the one at constant properties, so that simple models of flow and heat
transfer can be used to calculate the normal heat transfer. The tendency to develop deteriorated
heat transfer, which only occurred with an upward flow, are associated with the reconstruction of
the velocity and shear stress fields under the combined influence of the Archimedes forces
(buoyancy) and the negative pressure gradient that accelerates the heated fluid flow. The formation
of a fluid layer in the turbulent flow core with lower turbulent diffusivities causes the lowering value
of the heat transfer coefficient. In that particular layer, the low values of the turbulent shear stresses
and radial gradient of the velocity exist together with the maximum values of the convective
acceleration of the flow. The formation of M-shaped velocity profiles in the upward flow reduces the
tendency towards heat transfer deterioration. The Archimedes forces (buoyancy forces) compensate
the effects of the thermal acceleration for a downward flow, which is favourable for keeping the flow
structure near the normal heat transfer regime.
Jiang PX, Zhang Y, Xu YJ, Shi RF, Experimental and numerical investigation of convection heat
transfer of CO2 at supercritical pressures in a vertical tube at low Reynolds numbers, International
Journal of Thermal Sciences 47 (2008) 998–1011
Jiang et al. performed an experimental and numerical investigation of the convection heat transfer of
C02 at supercritical pressures in a vertical tube for laminar to turbulent flow. The influence of the
inlet temperature, pressure, mass flow, heat flux, buoyancy and flow direction were investigated. An
M-shape velocity distribution develops across the tube with increasing heat flux, due to the property
variations and the buoyancy. This phenomenon becomes more evident as the heat flux and as x/d
increases. For an upward flow and moderate heat fluxes, the local wall temperature does not
increase continuously. For higher heat fluxes, the local wall temperature first increases along the
tube, then decreases, and then increases again, with a second small decrease at the outlet due to the
conduction along the wall. The first decrease of the the local wall temperature is due to transition
from laminar to turbulent flow. The local wall temperature then increases again along the tube due
to laminarization of the flow by the very strong buoyancy which reduces the convection heat
transfer. For downward flow and high heat fluxes, the local wall temperature increases continuously
along the tube with small decreases at the outlet due to conduction in the wall. The convection heat
transfer did not deteriorate along the tube for downward flow as was observed for upward flow. The
results indicate that for downward flow the buoyancy induces very early transition from laminar to
turbulent flow (much earlier than for upward flow) which increases the heat transfer coefficient
compared to that for upward flow with the same conditions. For the outer surface fluid temperature
<Tpc, the HTC increases with increasing heat flux and then decreases with further increases in the
heat flux for both upward and downward flows. For downward flow the decreases of the HTC with
increasing heat flux for the higher heat fluxes were caused by variations of the thermophysical
properties (sharp decreases of cp,λ,ρ). However, for upward flows, the decreases of the HTC with
increasing heat flux for the higher heat fluxes were caused not only by the variations of the
thermophysical properties, but also by laminarization of the turbulence by the buoyancy. Therefore,
the HTCs for upward flow are less than for downward flow. For very high heat fluxes (e.g., 90.0
kW/m2), the HTCs for both upward and downward flows were very similar because the heat transfer
is mainly controlled by the natural convection. For downward flow the buoyancy enhanced the heat
transfer coefficients along the entire tube, while for upward flow the buoyancy enhanced the heat
transfer coefficients only in the latter part of the tube. Generally, the difference between the local
heat transfer coefficients for downward and upward flows was not evident in the latter part of the
tube when very strong buoyancy effects were present.