Natural convection cooling of a hot vertical wall wet by a falling liquid film (original) (raw)
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Passive Containment Cooling: Model Experiments
The feasibility of using a closed cylindrical twophase thermosyphon and a closed loop Pulsating Heat Pipe (PHP) for containment cooling application is experimentally studied in this work. The reactor containment at the time of accident is presently mimicked by administering steam in the evaporator chamber ~ 1 bar/ 100 o C (high pressure tests will be reported later). The condenser chamber is modeled as heat sink containing a stagnant pool of water. The latent heat of condensation of the steam is transferred to the stagnant pool of water through the thermosyphon or the PHP, as per the case. The axial cross-sectional area and the radial surface area for heat transfer are kept identical for both the thermosyphon and the PHP. In this way a direct comparison of the thermal performance of these two devices was possible. We find that while both the devices transferred approximately the same amount of heat (~500W), the average Nusselt number for PHP was higher than the thermosyphon, indicating that it operated at a lesser temperature difference between the wall and the coolant fluid, i.e., PHP had a higher effective thermal conductivity than the thermosyphon.
Nuclear Engineering and Design, 1997
The long term containment cooling of GE's passive BWR design is based on a new safety system called PCCS (passive containment cooling system). Performance of this system relies on the pressure difference between the drywell and wetwell in case of an accident and on the condensation of steam moving downward inside vertical tubes fully submerged in a water pool initially at room temperature. In this paper a model based on the resolution of momentum equations of both phases, the application of the heat and mass transfer analogy, and the consideration of the presence of a noncondensable gas by diffusion theory in a boundary layer is presented. Assumptions and approximations taken resulted in new methods to estimate film thickness and heat transport from the gas to the interface. Influence of phenomena such as suction, flow development, film waviness, and droplet entrainment has been accounted for. Based on this formulation, a computer programme called HVTNC (heat transfer in vertical tubes with noncondensables) has been built up. HVTNC results have been compared to the experimental data available. Experimental trends have been reproduced. Heat transfer has been found to be severely degraded by the presence of noncondensables whereas high Reynolds numbers of gas flow have been seen to enhance shear stress and therefore, heat transmission. The average error of HVTNC is essentially located at regions where only a residual fraction of heat remains to be transferred, so that minor deviations can be anticipated in the overall heat transfer in the tube. Comparison of HVTNC to other models show a substantial gain of accuracy with respect to earlier models. © 1997 Elsevier Science S.A.
Heatline analysis on thermal management with conjugate natural convection in a square cavity
Chemical Engineering Science, 2013
Conjugate natural convection finds various thermal applications in chemical industries, where the heat transfer is controlled by the presence of solid walls such as heat exchanger, nuclear reactors, fin type cooling and solar storage systems. Heat flow distribution within square cavity enclosed by vertical conducting walls of definite thickness ðt 1 and t 2 Þ is analyzed for various fluids (Pr) in this study based on the location of the wall thickness [left wall (case 1)/ right wall (case 2)/ both side walls (case 3)] and conductivity ratios between solid and fluid regions (K). At Ra ¼ 10 5 , circular heatlines are observed near core of the cavity at K¼ 0.1 whereas they are distorted and pushed towards the hot wall at K¼ 10 with low Pr (Pr¼0.015). On the other hand, heatlines are horizontally stretched at core of the cavity for higher Pr (Pr¼ 0.7 and 1000) at K¼ 10. End to end heatlines are highly compressed near top portion of the cavity at K¼ 10 irrespective of Pr. Closed loop heatlines are absent for case 2 at Ra ¼ 10 3 whereas closed loop heatlines with lesser magnitude than cases 1 and 3 are observed for case 2 at Ra ¼ 10 5 due to less heat transfer from the hot solid wall irrespective of Pr at K¼ 0.1 and 1. The heat transfer rate can be maintained constant at low thermal conductivity ratio (K) even for the high convective regime ðRa ¼ 10 5 Þ irrespective of wall thickness (t 1 and t 2). Average Nusselt number shows overall larger heat transfer rate for higher K (K¼ 10), which is almost identical with classical natural convection (zero wall thickness) compared to lower K (K¼ 0.1 and 1) irrespective of location of wall thickness (cases 1-3). In order to achieve almost invariant or lower fluid temperature at Ra ¼ 10 5 for t 1 þ t 2 ¼ 0:2 and 0.8, solid wall at hot side (case 2) may be useful. This heating strategy may be viewed for high temperature shielding or minimization of thermal runaway for temperature sensitive applications, such as environmental control system, chemical storage reservoirs, etc., where heat flow is controlled by solid wall resistance.
NUCLEAR TECHNOLOGY, 2024
The presented work deals with the improvement of the evaporation model of the ATHLET (Analysis of Thermal and Hydraulics of Leaks and Transients) system code to be applied to a passive containment cooling system of a nuclear power plant. For the model validation, INTRAVIT (Investigation of Passive Heat Transfer in a Variably Inclined Tube) test facility setup at the University of Luxembourg was used. The first part of the paper presents a review of the existing literature on evaporation models that revealed that those models significantly simplify the physical processes that occur. Next, a modified evaporation model is proposed that offers a realistic description of various evaporation processes and the start of bubble formation using a nucleation model, and a surface density calculation model is introduced that is necessary for evaporation simulation. The final part of this work explored five different system configurations to test the evaporation model: three condenser tube inclinations (5 deg, 60 deg, and 90 deg), two riser lengths (1 m and 2.5 m), and different thermal loads. They made it possible to simulate several experiments for stable and unstable natural circulation and to verify the proposed model.
Numerical investigation of passive cooling in open vertical channels
Applied Thermal Engineering, 2012
Numerical simulations have been carried out in order to investigate natural convection flow and heat transfer in vertical channels which are relevant to passive cooling of building-integrated photovoltaics (BIPV) systems. The numerical results have been validated against existing experimental data available in literature. It has been found that narrow vertical channels with different aspect ratios exhibit varied heat transfer behaviours, implying its significance in the design of passive cooling applications. In addition, the different behaviours of heat transfer may be explained by the turbulence quantities obtained through large-eddy simulations (LES). Based on the current numerical results, a correlation for turbulent natural convection in vertical channel has been determined to predict the average Nusselt number in terms of the relevant dimensionless parameters for the geometry considered in this study.
Numerical prediction of cooling margins for a fluid with internal heat generation
Advanced Computational Methods in Heat Transfer V
Reactor pressure vessel lower plenum retention problem was studied to determine external cooling margins of the plenum walls. The accumulated melt was modelled as an incompressible fluid with internal volumetric heat generation in a rectangular cavity. A Smagorinsky type of Large-Eddy Simulation model for buoyancy flows was implemented. Because of uncertainty about the upper wall thermal boundary conditions, isothermal and adiabatic boundary conditions were used to assess heat transfer margins (Nusselt number) at each boundary of the simulation domain. It was found out in both calculated cases that the Nusselt number is the lowest at the bottom of the simulation domain and increases with height. In the future nuclear safety studies, the most severe wall thermal conditions from both simulated cases will have to be considered.
Energies
This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.
Nuclear Engineering and Design, 2022
This paper presents the steps followed to implement and validate a hybrid multiphase flow model in the open-source code, OpenFOAM. The modeling approach couples the interface capturing model with the dispersed flow model. The resulting multiphase model can be used to predict the slug flow boiling regime. The flow regime in question occurs during the external cooling of a core-catcher and in-vessel retention (IVR) which are severe accident mitigation strategies. A distinctive key feature of this multiphase-type flow is the coexistence of large-scale slug vapor bubbles with both dispersed vapor bubbles and the carrying liquid phase. The slug vapor bubbles are generated from the coalescence of the smaller dispersed bubbles. Also, due to the tilted orientation of the core-catcher and reactor vessel lower head (for the IVR option), these large-scale bubbles remain in the vicinity of the heated surface, while being transported by the flow. This is due to the buoyancy force acting upward in these two design configurations. The latter phenomenon engenders the fact that a liquid film is occupying a thin layer separating the large bubbles from the heated surface. Under such flow conditions, the existing wall boiling model, commonly known as the (Rensselaer Polytechnic Institute) RPI model, has been demonstrated to be inadequate for the determination of the boiling heat transfer characteristics. Therefore, an extended near-wall boiling model accounting for the conduction heat flux across the liquid film (trapped underneath the slug bubbles) is formulated and implemented in this study. Using this enhanced model, the simulation of a slug flow boiling on a downward-facing heated surface produces a better prediction of the wall superheat than the original model. In addition, the morphologies of the vapor slug coexisting with dispersed bubbles are adequately captured and compared fairly well with experimental visualizations. This new multiphase model is then used to simulate a prototypical core-catcher cooling channel. Once again, a fair representation of the wall heat transfer is predicted in good agreement with measurements. Finally, it has been also successfully proven that under subcooled nucleate flow boiling conditions, the present model can reproduce the RPI model predictions.