XI. Void fraction in boiling channels..
The characteristic feature of boiling channels is the presence The characteristic feature of boiling channels is the presence
of two phases: the liquid and the vapor phase.
of two phases: the liquid and the vapor phase. 8585
THERMAL-HYDRAULIC IN NUCLEAR REACTOR
Clearly, the presence of two phases changes the fluid flow and Clearly, the presence of two phases changes the fluid flow and heat transfer processes as compared to the non-boiling heat transfer processes as compared to the non-boiling channels. In addition, the density changes of coolant are channels. In addition, the density changes of coolant are more significant in boiling channels due to the dramatic more significant in boiling channels due to the dramatic change of density once liquid transforms into vapor. Thus, change of density once liquid transforms into vapor. Thus, to be able to predict the local value of the coolant density it to be able to predict the local value of the coolant density it is required to determine the local volume fraction of both is required to determine the local volume fraction of both phases. Typically, the void fraction (that is the volume phases. Typically, the void fraction (that is the volume fraction of the vapor phase) is determined using various fraction of the vapor phase) is determined using various
models, as described below.
models, as described below.
The various two-phase flow and heat transfer regimes in a The various two-phase flow and heat transfer regimes in a boiling channel, such as BWR fuel assembly, is shown in boiling channel, such as BWR fuel assembly, is shown in
figure( XI.1).
figure( XI.1).
THERMAL-HYDRAULIC IN NUCLEAR REACTOR
Figure XI.1: Two-phase flow & heat transfer regime in a Figure XI.1: Two-phase flow & heat transfer regime in a boiling channel ONB (Onset of Boiling), OSV (Onset of boiling channel ONB (Onset of Boiling), OSV (Onset of Significant Void, OAF (Onset of Annular Flow).
Significant Void, OAF (Onset of Annular Flow).
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THERMAL-HYDRAULIC IN NUCLEAR REACTOR
Figure XI.2: Two-phase flow & heat transfer regime in a Figure XI.2: Two-phase flow & heat transfer regime in a boiling channel ONB (Onset of Boiling), OSV (Onset of boiling channel ONB (Onset of Boiling), OSV (Onset of Significant Void, OAF (Onset of Annular Flow).
Significant Void, OAF (Onset of Annular Flow).
THERMAL-HYDRAULIC IN NUCLEAR REACTOR
The heat exchange coefficient depends on the local properties The heat exchange coefficient depends on the local properties of coolant flow, which evolve all along the hot channel. This of coolant flow, which evolve all along the hot channel. This
coefficient is characterized by its F
coefficient is characterized by its FΔΔh and the coolant by:h and the coolant by:
- Ti: the inlet temperature - Ti: the inlet temperature
- g: the mass flow rate - g: the mass flow rate
- Tsat: the saturation temperature - Tsat: the saturation temperature
- X: the quality = steam mass/ mixture mass - X: the quality = steam mass/ mixture mass
- α- α: the void fraction = steam volume/mixture volume: the void fraction = steam volume/mixture volume
* A first assumption is made that the channel is isolated &
* A first assumption is made that the channel is isolated &
exchanges neither mass nor energy with neighboring exchanges neither mass nor energy with neighboring channels. This hypothesis, in fact highly penalizing, is not channels. This hypothesis, in fact highly penalizing, is not
verified in a real PWR.
verified in a real PWR.
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THERMAL-HYDRAULIC IN NUCLEAR REACTOR
As the coolant rises along the channel (see following As the coolant rises along the channel (see following figure), its physical properties are modified because its figure), its physical properties are modified because its temperature increases, along with the temperature of the temperature increases, along with the temperature of the channel wall. The height of the channel can be divided into channel wall. The height of the channel can be divided into
a certain number of zones with different properties:
a certain number of zones with different properties:
1) A lower zone, in which the wall temperature and the 1) A lower zone, in which the wall temperature and the coolant temperature are below the saturation temperature.
coolant temperature are below the saturation temperature.
In this zone, the flow is single phase and the heat exchange In this zone, the flow is single phase and the heat exchange
regime is one of forced convection.
regime is one of forced convection.
The heat exchange between the cladding & the coolant is The heat exchange between the cladding & the coolant is good & the temperature difference
good & the temperature difference ΔΔT remains small, not T remains small, not exceeding tens of degrees.
exceeding tens of degrees.
THERMAL-HYDRAULIC IN NUCLEAR REACTOR
2) Starting from a certain length of the tube, the wall 2) Starting from a certain length of the tube, the wall temperature exceeds the coolants saturate temperature, temperature exceeds the coolants saturate temperature, Tsat, whereas the coolant remains at a temperature less Tsat, whereas the coolant remains at a temperature less than Tsat. Bubbles then begin to appear along the cladding than Tsat. Bubbles then begin to appear along the cladding wall, while the coolant remains strongly under saturation.
wall, while the coolant remains strongly under saturation.
These bubbles improve the thermal exchange, because they These bubbles improve the thermal exchange, because they do not stuck to the wall but are carried along by coolant do not stuck to the wall but are carried along by coolant flow. Consequently they transmit calories from the wall to flow. Consequently they transmit calories from the wall to
the coolant.
the coolant.
3) Since the coolant continues to heat up, the density & the 3) Since the coolant continues to heat up, the density & the size of the bubbles increase. Suddently, there is a size of the bubbles increase. Suddently, there is a coalescence of the bubbles and the creation of a stable coalescence of the bubbles and the creation of a stable vapor film along the cladding wall. From this moment on, vapor film along the cladding wall. From this moment on, the heat exchange degenerates (h decreases, Tcladding the heat exchange degenerates (h decreases, Tcladding
increases).
increases). 91
THERMAL-HYDRAULIC IN NUCLEAR REACTOR
This degraded heat exchange is explained, among other This degraded heat exchange is explained, among other reasons, by the fact that steam has lower thermal reasons, by the fact that steam has lower thermal conductivity than water. It occurs when a certain value of conductivity than water. It occurs when a certain value of thermal flux has been reached, and leads to ô Departure thermal flux has been reached, and leads to ô Departure
from Nucleate Boiling ằ & burn-out.
from Nucleate Boiling ằ & burn-out.
- Zone 0 to 1:
- Zone 0 to 1: corresponds to the forced convection regime. corresponds to the forced convection regime.
The fluid is under the unsaturated liquid form (quality equal The fluid is under the unsaturated liquid form (quality equal zero), its exchange coefficient is relatively constant at zero), its exchange coefficient is relatively constant at given mass flow. The temperature difference between the given mass flow. The temperature difference between the surface and the center of the fluid flow is proportional to surface and the center of the fluid flow is proportional to
calorific flux to be transferred.
calorific flux to be transferred.
THERMAL-HYDRAULIC IN NUCLEAR REACTOR