# Theoretical and Numerical Study of Heat Transfer Deterioration in High Performance Light Water Reactor

Authors: David Palko; Henryk Anglart
Journal: Science and Technology of Nuclear Installations
 (2008)

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## Abstract

A numerical investigation of the heat transfer deterioration (HTD) phenomena is performed using the low-Re k-ω turbulence model. Steady-state Reynolds-averaged Navier-Stokes equations are solved together with equations for the transport of enthalpy and turbulence. Equations are solved for the supercritical water flow at different pressures, using water properties from the standard IAPWS (International Association for the Properties of Water and Steam) tables. All cases are extensively validated against experimental data. The influence of buoyancy on the HTD is demonstrated for different mass flow rates in the heated pipes. Numerical results prove that the RANS low-Re turbulence modeling approach is fully capable of simulating the heat transfer in pipes with the water flow at supercritical pressures. A study of buoyancy influence shows that for the low-mass flow rates of coolant, the influence of buoyancy forces on the heat transfer in heated pipes is significant. For the high flow rates, buoyancy influence could be neglected and there are clearly other mechanisms causing the decrease in heat transfer at high coolant flow rates.


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## Body

## 1. Introduction

High performance light water reactor (HPLWR) is one of the six Gen-IV reactor concepts, based on the
existing boiling and pressurized water reactors. Water at high pressures
(p>22.1MPa), used as a cooling medium, allows significant increase of the
system thermal efficiency. As the reactor is designed to operate at supercritical
pressure, there is no phase change between liquid and vapor phase and,
therefore, the boiling crisis is inherently avoided. However, close to the
pseudocritical point, where the thermophysical properties vary significantly,
the heat transfer shows unusual behavior. Enhanced, normal, or deteriorated
heat transfer regime may exist depending on the flow parameters and the applied
heat flux.In the
deteriorated region, the heat transfer coefficient decreases causing the
increase in wall temperature. As shown by several experiments (Shitsman [1],
Kirillov et al. [2], or Ornatskij et al. [3]), the increase in wall temperature is not as rapid as
in case of boiling crisis in classical light water reactors. Due to the
relatively mild increase in wall temperature, the onset of HTD is not well
defined. Many different definitions are used in the literature. For example, Koshizuka
et al. [4] defined the onset of HTD as the following ratio:
(1)Dr=αα0<0.3,
where α0 is the heat transfer coefficient
calculated numerically by Jones-Launder’s k-ε model using constant properties at bulk liquid
temperature. Heat transfer is considered to be deteriorated when Dr<0.3.The modified Koshizuka’s criterion for the
onset of the HTD is frequently used. Here,α0 is calculated using the
Dittus-Boelter [5] correlation:
(2)Nu=0.023Re0.8Pr0.4with thermophysical properties evaluated at the
bulk liquid temperature. Differences in the definition of the onset of the HTD
could lead to the relevant differences in its prediction. However, for the
present study the exact definition is not relevant, as all the simulations are
performed in the highly deteriorated region.


## 2. Numerical Modeling Issues

The effect of
buoyancy and its influence on the heat transfer is simulated numerically, using
the Ansys-CFX 11.0 computational code, for steady-state flow within heated
pipes. Computational domain consists of 30 degree slide of a pipe and the mesh
is a standard hexahedral with approximately 2500000 grid points with refinement
close to the wall, such as the nondimensional distance from the wally+ is
below 1. All simulations which
include heat transfer require proper resolution of the boundary layer. The
standard k-ε turbulence model offers very robust and
reliable modeling of turbulence for the bulk flow. However, for the near wall
region (y+<30),
the flow is approximated by wall functions. This means that the whole viscous
sublayer and part of the buffer layer is not resolved numerically with the k-ε model.The standard k-ω turbulence model, as developed by Wilcox [6], allows resolving the viscous sublayer. However, this
model is known to be sensitive to the free stream conditions. Strong variations
of final results could occur depending on the value of the turbulent frequency
specified at the inlet.The shear stress transport (SST) model, as developed by Menter [7], combines the robustness of the k-ε model for the bulk flow and the low-Re
treatment of the boundary layer using the modified Wilcox k-ω model.As the validation of different cases against the experimental data
proves, the low-Re SST model is fully capable of modeling the heat transfer to
supercritical water (including the deteriorated region) and the calculated
results are in a very good agreement with the experimental data. This is
demonstrated in Figure1, where the comparison of SST and k-ε turbulence models is shown for the experiment
by Ornatskij et al. [3] (described later). The heat transfer coefficient is
plotted against the bulk fluid temperature.Figure 1
Comparison of SST turbulence model,
k-ε model and experiment by Ornatskij et
al. [3]. Flow conditions: p=25.5MPa, d=3mm, G=1500kg/m2s, q=1810kW/m2, vertical
upward flow in a pipe.The k-ε model fails to calculate the heat transfer to
supercritical fluid in deteriorated region. The SST model predicts the heat
transfer coefficient in a very good agreement with the experimental results.
The main reason for the substantial difference in results for these two
turbulence models is the near wall treatment. SST model allows resolving the
boundary layer numerically. Standard k-ε turbulence model approximates the boundary
layer by wall functions (for coarse grid, y+>5), which are not
suitable for the flows where the thermophysical properties changes rapidly
close to the wall. For the very fine grids (y+<1), the nonlinear
damping functions, required for the k-ε model, cause the loss of accuracy and so the
final results differ substantially from the experimental values.Sensitivity analysis for the grid size is also made for the SST model.
In order to resolve the boundary layer, the nondimensional distance of the
first computational cell from the wall (y+) should be kept below 1. Figure 2 proves that if this condition is fulfilled, the
results are insensitive to the grid size. This behavior results from the
implementation of the wall treatment by SST turbulence model in Ansys CFX-11.0
computational software. Here, if the nondimensional distance of the first
computational cell y+ is bigger than 1, the near wall region is
approximated by wall functions, which leads to the similar behavior of results
as in the case of k-ε model. If the distance is smaller than y+=1,
boundary layer is resolved numerically leading to the correct solution.Figure 2
Sensitivity analysis on the grid size for the SST turbulence model, comparison
with the experiment by Ornatskij et al. [3]. Flow conditions: p=25.5MPa, d=3mm, G=1500kg/m2s, q=1810kW/m2, vertical
upward flow in a pipe.


## 3. Influence of Buoyancy on Heat Transfer

Once the correct numerical results are obtained, the influence of
buoyancy on heat transfer could be studied by the comparison of the solution
obtained with and without the buoyancy terms in the governing equations. The
expected influence of buoyancy can be examined by the ratio of Grashof and
Reynolds numbers(3)GrRe2=gβLΔTU2,
where g is the
gravitational constant, β is
the thermal expansion coefficient, L is the characteristic length, ΔT is the temperature change, and U is the velocity of coolant. For the
normal operating conditions in the pressurized water reactors (PWRs), this
ratio is small due to the very high flow velocities, relatively small change in
temperature and the low value of the thermal expansion coefficient. Therefore,
the buoyancy influence on heat transfer could be neglected in conditions
typical for PWRs.However, for the HPLWR conditions, even though, the flow velocity is
relatively high, there is a strong change in thermophysical properties, namely,
density and thermal expansion coefficient, thus the ratio of Grashof and
Reynolds numbers may be relevant. It should be pointed out that the buoyancy is
not the only phenomenon causing the HTD. Its influence strongly depends on the
flow conditions. Several resources show that other effects, such as the streamwise
acceleration (McEligot and Jackson [8]) or the direct change of the thermophysical properties
(Koshizuka et al. [4]), could cause the heat transfer to deteriorate.In the vertical
pipes with upward flow, the buoyancy accelerates the flow close to the wall,
where there is the highest density difference. The increase of velocity causes
the decrease of the velocity gradient and thus the decrease of the turbulent
kinetic energy. Loss of the turbulence close to the wall then decreases the
heat transfer coefficient. In order to examine this effect, Mikielewicz et al. [9] proposed the following nondimensional number:
(4)Bo=Gr*δM+(νw/νb)(ρw/ρb)0.52NuDhReDh3(fτ/2)1.5Pr0.4
which
applies for arbitrary heated surfaces in a vertical duct (δM+ is a distance near the edge of the viscous layer, Jackson [10] proposed 26). Gr* is defined as:
(5)Gr*=gβqwallD′′h4/kν2.
Here, g=9.81ms−2 is the
gravitational constant, ν is the kinematic viscosity, ρ is density, subscripts
w and b correspond to the wall and bulk conditions, respectively, NuDh is
the Nusselt number, ReDh is the Reynolds number, Pr is the Prandtl
number and fτ is the friction factor. All of these nondimensional
quantities are evaluated at bulk conditions.According to Mikielewicz et. al. [9], Bo>0.1 corresponds to the onset of significant
buoyancy effects. When applying the Dittus-Boelter correlation (2) and Blasius correlation for the friction factor, (4) can be written as follows (neglecting the
differences between wall and bulk densities, resp., viscosities):
(6)Bo*=Gr*ReDh3.425Pr0.8,
where Bo*=Const*Bo. Then the onset of significant buoyancy influence
is expressed as
(7)Bo*>6.10−7.


## 4. Numerical Results and Discussion

Two different experiments are numerically simulated with Ansys CFX-11.0
computational software, using the SST turbulence model in order to examine the
influence of buoyancy on the heat transfer. Experiments by Shitsman [1] and Ornatskij et al. [3] were chosen due to the following reasons.Both experiments measure the heat transfer in the highly deteriorated
region. The experiment by Ornatskij et al. [3] is performed for very high-coolant flow rate, where
the buoyancy force should have no effect on the heat transfer according to (7). On the other hand, experimental data by Shitsman [1] are in the region of high-buoyancy influence.


### 4.1. Heat transfer at Low-Coolant Flow Rates

Flow simulation at low-coolant flow rate is demonstrated in the experiment
by Shitsman [1]. This experiment is performed with supercritical
water at p=233bar in a pipe with inner diameter d=8mm. The pipe is uniformly
heated with a heat flux of 319.87kW/m2 and the coolant flow rate is
G=430kg/m2s. For these flow parameters, Mikielewicz condition for
the influence of buoyancy is fulfilled.These flow conditions are modeled on a 30 degrees slice of pipe geometry
with approximately 2500000 computational hexahedral cells. Boundary conditions
consist of specification of constant pressure at the outlet, mass flow rate,
respectively, velocity at the inlet and no slip + constant heat flux boundary
conditions at the walls. Symmetry b.c is applied at the symmetry walls.Comparison of the numerical results with the experimental data is shown
in Figure3, where the wall temperature is plotted against the
bulk enthalpy. There is a very good agreement between CFX-11.0 results and
experimental data. The solver is capable of capturing also the deteriorated region
represented by the two peaks in the wall temperature.Figure 3
Comparison of the numerical results
with the experiment by Shitsman [1] and the correlation by Dittus-Boelter. Flow
conditions: p=23.3MPa, d=8mm, G=430kg/m2s, q=319.87kW/m2, vertical
upward flow in a pipe.Solving the same equations on an identical numerical grid without the
buoyancy terms in the NS equations leads to substantial underprediction of the
wall temperature. This means that the buoyancy terms in Navier-Stokes equations
are responsible for the increase in the wall temperature and hence the heat
transfer deterioration is caused by the buoyancy force, as was predicted by (7). A possible explanation of this phenomenon is that
the buoyancy accelerates the flow close to the wall leading to the more flat
velocity profile, decrease in the velocity gradient and decrease of turbulence.
Decrease in turbulence then leads to the decrease of the heat transfer
coefficient, and thus to the increase in wall temperature.The Dittus-Boelter correlation (2) prediction of the wall temperature is plotted to
visualize how the heat transfer regime differs from the normal regime.


### 4.2. Heat Transfer at High Coolant Flow Rates

For the high flow rates, when the conditionBo*>6.10−7 is
not fulfilled, the buoyancy could be neglected according to Mikielewicz et al. [9]. Such a flow is demonstrated by the experiment of
Ornatskij et al. [3]. Here, the flow parameters of supercritical water at
p=255bar are measured in a pipe with inner diameter d=3mm. The pipe is
uniformly heated with heat flux of 1810kW/m2 and the coolant flow
rate is G=1500kg/m2s.Even though the buoyancy should not be relevant, heat transfer is still
deteriorated (as measured by Ornatskij et al. [3]) according to the definition:(8)Dr=αα0<0.3,
where α0 is an ideal heat transfer
coefficient calculated with the Dittus-Boelter correlation (2) with the properties evaluated at the bulk
temperature.Numerical results and the comparison with the experiment and
Dittus-Boelter correlation are shown in Figure4. The influence of buoyancy is small and there are
clearly other mechanisms which cause the decrease in heat transfer. According
to Koshizuka et al. [4], change in the thermophysical properties, such as
viscosity and thermal conductivity, may lead to the decrease in heat transfer
coefficient. The influence of these phenomena could be demonstrated in the same
way as the influence of buoyancy, if numerical simulations with constant and
variable properties are compared.Figure 4
Comparison of the numerical results
with the experiment by Ornatskij [3] and the correlation by Dittus-Boelter. Flow
conditions: p=25.5MPa, d=3mm, G=1500kg/m2s, q=1810kW/m2, vertical
upward flow in a pipe.


## 4.1. Heat transfer at Low-Coolant Flow Rates

Flow simulation at low-coolant flow rate is demonstrated in the experiment
by Shitsman [1]. This experiment is performed with supercritical
water at p=233bar in a pipe with inner diameter d=8mm. The pipe is uniformly
heated with a heat flux of 319.87kW/m2 and the coolant flow rate is
G=430kg/m2s. For these flow parameters, Mikielewicz condition for
the influence of buoyancy is fulfilled.These flow conditions are modeled on a 30 degrees slice of pipe geometry
with approximately 2500000 computational hexahedral cells. Boundary conditions
consist of specification of constant pressure at the outlet, mass flow rate,
respectively, velocity at the inlet and no slip + constant heat flux boundary
conditions at the walls. Symmetry b.c is applied at the symmetry walls.Comparison of the numerical results with the experimental data is shown
in Figure3, where the wall temperature is plotted against the
bulk enthalpy. There is a very good agreement between CFX-11.0 results and
experimental data. The solver is capable of capturing also the deteriorated region
represented by the two peaks in the wall temperature.Figure 3
Comparison of the numerical results
with the experiment by Shitsman [1] and the correlation by Dittus-Boelter. Flow
conditions: p=23.3MPa, d=8mm, G=430kg/m2s, q=319.87kW/m2, vertical
upward flow in a pipe.Solving the same equations on an identical numerical grid without the
buoyancy terms in the NS equations leads to substantial underprediction of the
wall temperature. This means that the buoyancy terms in Navier-Stokes equations
are responsible for the increase in the wall temperature and hence the heat
transfer deterioration is caused by the buoyancy force, as was predicted by (7). A possible explanation of this phenomenon is that
the buoyancy accelerates the flow close to the wall leading to the more flat
velocity profile, decrease in the velocity gradient and decrease of turbulence.
Decrease in turbulence then leads to the decrease of the heat transfer
coefficient, and thus to the increase in wall temperature.The Dittus-Boelter correlation (2) prediction of the wall temperature is plotted to
visualize how the heat transfer regime differs from the normal regime.


## 4.2. Heat Transfer at High Coolant Flow Rates

For the high flow rates, when the conditionBo*>6.10−7 is
not fulfilled, the buoyancy could be neglected according to Mikielewicz et al. [9]. Such a flow is demonstrated by the experiment of
Ornatskij et al. [3]. Here, the flow parameters of supercritical water at
p=255bar are measured in a pipe with inner diameter d=3mm. The pipe is
uniformly heated with heat flux of 1810kW/m2 and the coolant flow
rate is G=1500kg/m2s.Even though the buoyancy should not be relevant, heat transfer is still
deteriorated (as measured by Ornatskij et al. [3]) according to the definition:(8)Dr=αα0<0.3,
where α0 is an ideal heat transfer
coefficient calculated with the Dittus-Boelter correlation (2) with the properties evaluated at the bulk
temperature.Numerical results and the comparison with the experiment and
Dittus-Boelter correlation are shown in Figure4. The influence of buoyancy is small and there are
clearly other mechanisms which cause the decrease in heat transfer. According
to Koshizuka et al. [4], change in the thermophysical properties, such as
viscosity and thermal conductivity, may lead to the decrease in heat transfer
coefficient. The influence of these phenomena could be demonstrated in the same
way as the influence of buoyancy, if numerical simulations with constant and
variable properties are compared.Figure 4
Comparison of the numerical results
with the experiment by Ornatskij [3] and the correlation by Dittus-Boelter. Flow
conditions: p=25.5MPa, d=3mm, G=1500kg/m2s, q=1810kW/m2, vertical
upward flow in a pipe.


## 5. Conclusions

The present work demonstrates the ability of the low-Re RANS turbulence
treatment to model the heat transfer under supercritical pressure. Proper grid
resolution of the boundary layer and the accuracy in thermophysical properties
show very high influence on final results.Buoyancy influence on the heat transfer deterioration was demonstrated.
The results proved that under some conditions, buoyancy is the phenomenon that
governs the heat transfer deterioration, mainly for relatively low coolant flow
rates and high heat fluxes. However, for high coolant flow rates, there exist
clearly other mechanisms which have to be identified and examined in order to
be able to successfully predict the onset of HTD.



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*Source: 405072-2008-09-23.xml*