Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF
Abstract
:1. Introduction
2. Liquid Sublayer Dryout Model and Its Application to an Annulus
3. Prediction of CHF in an Annulus
4. Predictions of the Changes in Liquid Sublayer Thickness and Heater Surface Temperature at the CHF
4.1. Modeling of Near Wall Vapor–Liquid Structure at the CHF
4.2. Modeling of Heat Transfer Modes over Heated Surface near the CHF
4.3. Analysis Case
4.4. Calculation of Transient Heater Surface Temperature Change at CHF
5. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Latin symbols: | |
ratio of the area where boiling occurs on the heating surface, dimensionless | |
coefficient in Equation (3) | |
drag coefficient, dimensionless | |
specific heat of the heater, ] | |
equivalent diameter of test section, [m] | |
thickness of the vapor clot, [] | |
friction factor, dimensionless | |
buoyancy force, [N] | |
drag force, [N] | |
G | mass flux, [] |
heat transfer coefficient in liquid single-phase flow, [] | |
heat transfer coefficient of liquid, [] | |
latent heat, [] | |
heat transfer coefficient of vapor steam, [] | |
thermal conductivity of the heater, [] | |
thermal conductivity of the liquid sublayer, [] | |
thermal conductivity of the vapor, [] | |
heating length of test section, [m] | |
length of the elongated vapor clot, [] | |
region where the liquid sublayer has been completely evaporated under the vapor clot, [] | |
region where the liquid sublayer presents under the vapor clot, [] | |
length of nucleate boiling region, [] | |
NVG | net vapor generation point |
P | system pressure, [] |
heat flux transferred by liquid single-phase, [] | |
heat flux transferred by boiling, [] | |
calculated CHF, [] | |
wall surface heat flux, [] | |
volumetric heating density, [] | |
Reynolds number, dimensionless | |
radius direction in heat conduction equation in cylindrical coordinate, [] | |
heater inner radius in Figure 4, [] | |
heater outer radius, and the inner radius of annulus flow channel, as shown in Figure 4, [] | |
heater temperature, [] | |
liquid temperature at the inlet of test section, [] | |
steam vapor temperature, [] | |
saturation temperature, [] | |
wall temperature at the heater surface, [] | |
time, [] | |
velocity of the vapor clot, [] | |
average velocity of liquid bulk, [] | |
liquid velocity at the centerline of the vapor clot, [] | |
velocity profile inside liquid phase, [m/s] | |
velocity of the liquid sublayer, [] | |
dimensionless velocity in liquid phase | |
friction velocity, [] | |
distance form heated wall to the centerline of vapor clot, [m] | |
dimensionless distance from heated wall | |
Greek Symbols: | |
void fraction, dimensionless | |
initial thickness of liquid sublayer, [] | |
δ | thickness of the liquid sublayer, [] |
Helmholz instability wavelength at the interface between the liquid sublayer, [] | |
Helmholz instability wavelength at the interface between vapor clot and liquid bulk, [] | |
subcooling of the liquid phase in enthalpy, [] | |
subcooling of the liquid phase in temperature, [] | |
surface wall superheat, [] | |
surface wall superheat in the fully developed nucleate boiling region (Equation (17)), [] | |
the minimum wall superheat necessary for boiling, [] | |
average density of liquid bulk, [] | |
liquid density, [] | |
vapor density, [] | |
heater density, [] | |
surface tension, [] | |
liquid viscosity, [] | |
passage time of the vapor clot, [] | |
passage time of the nucleate boiling region, [] | |
wall shear stress, [] | |
difference of the specific volumes between the vapor and liquid phases, [] |
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Data Source | Hino CHF data in annulus [25] |
Fluid | R113 |
Pressure | 0.147 MPa |
Mass flux | 1239 kg/m2·s |
Inlet subcooling | 30 K |
Experimental CHF | 332 kW/m2 |
Data Source | Hino CHF Data in Annulus [25] |
Fluid | R113 |
Calculated CHF, | 335.29 |
Initial liquid sublayer thickness | 4.371 |
Length of the elongated vapor clot | 3.889 |
Velocity of the elongated vapor clot | 1.436 |
Void fraction | 0.726 |
Length of the nucleate boing region, | 1.468 |
Passage time of the vapor clot | 2.709 |
Passage time of the boiling region | 1.022 |
Volumetric heating density corresponding to | 7.224 × 105 |
Initial wall superheat (Jens–Lottes correlation (Equation (20))) | 18.65 |
Saturation temperature for R113 at 0.147 MPa, | 332.42 |
Heater density specific heat, | 3.386 E6 |
Thermal conductivity of heater | 16.2 |
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Liu, W. Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF. Fluids 2022, 7, 230. https://doi.org/10.3390/fluids7070230
Liu W. Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF. Fluids. 2022; 7(7):230. https://doi.org/10.3390/fluids7070230
Chicago/Turabian StyleLiu, Wei. 2022. "Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF" Fluids 7, no. 7: 230. https://doi.org/10.3390/fluids7070230