Two peculiar convection patterns–re-oscillation and stable non-centrosymmetric convection–are observed when two-dimensional double-diffusive convection in a porous enclosure (aspect ratio=1.5) is analysed numerically. The top and bottom walls of the enclosure are insulated; constant and opposing heat and mass fluxes are prescribed on the vertical walls. Re-oscillation occurs when the convection pattern changes from centrosymmetric to non-centrosymmetric. When the buoyancy ratio, which generates re-oscillation convection, is marginally lower, the convection pattern changes to stable non-centrosymmetric. These two convection patterns can be observed only for limited values of the Rayleigh number, Lewis number, and buoyancy ratio.

The present paper deals with a theoretical analysis of the spray cooling of a Reactor Pressure Vessel (RPV) head in a Boiling Water Reactor (BWR). To this end a detailed computational model has been developed. The model predicts the trajectories, diameters and temperatures of subcooled droplets moving in saturated vapor. The model has been validated through comparison with experimental data, in which droplet temperatures were measured as functions of the distance that they cover in saturated vapor from the moment they leave the sprinkler outlet to the moment they impact on the RPV head inner wall. The calculations are in very good agreement with measurements, confirming the model adequacy for the present study. The model has been used for a parametric study to investigate the influence of several parameters on the cooling efficiency of the spray system. Based on the study it has been shown that one of the main parameters that govern the temperature increase in a subcooled droplet is its initial diameter. Comparisons are also made between conclusions from the theoretical model and observations made through flow and temperature measurements in the plant (Forsmark 1 and 2). One of these observations is that the rate at which the RPV head temperature decreases on the way down from hot to cold standby is constant and independent of the sprinkling flow rate as long as the flow rate is above a certain minimum value. Accordingly, the theoretical model shows that if one assumes that the cooling of the RPV head is through a water film built on the inner wall due to sprinkling, the heat removal rate is only very weakly dependent on the sprinkling flow rate.

New data was obtained for a previously studied T-junction experimental setup [1] for a range of flow ratios between hot and cold flows in order to validate new Large Eddy Simulations (LES). The instantaneous velocity field downstream of the T-junction was measured with two-component Particle Image Velocimetry (PIV) in several horizontal and vertical planes at the centre line downstream of the T-junction. The generated PIV database enables a thorough validation of CFD turbulence statistics. The turbulence statistics are shown to be well predicted despite the fact that the mesh in the LES is rather coarse. By usage of time resolved PIV the temporal evolution of the predominant low frequent large-scale structures, responsible for much of the mixing and the high amplitude temperature fluctuations on the walls, were captured. Those structures are, however, weaker in LES than in PIV, being in line with the fact that the wake region behind the penetrating vertical hot jet is underpredicted in LES. Tests regarding the influence of the LES-results to the shape of the inlet boundary conditions (developed or flat symmetric mean-velocity profiles) were carried out and the sensitivity in the results was shown to be small. Furthermore, the results show good agreement with the experimental data independent of the flow ratio between the hot and the cold flows.

The present paper describes new experimental data of thermal mixing in a T-junction compared with results from Large-Eddy Simulations (LES) and Detached Eddy Simulations (DES). The experimental setup was designed in order to provide data suitable for validation of CFD-calculations. The data is obtained from temperature measurements with thermocouples located near the pipe wall, velocity measurements with Laser Doppler Velocimetry (LDV) as well as single-point concentration measurements with Laser Induced Fluorescence (LIF).The LES showed good agreement with the experimental data also when fairly coarse computational meshes were used. However, grid refinement studies revealed a fairly strong sensitivity to the grid resolution, and a simulation using a fine mesh with nearly 10 million cells significantly improved the results in the entire flow domain. The sensitivity to different unsteady inlet boundary conditions was however small, which shows that the strong large-scale instabilities that are present in the mixing region are triggered independent of the applied inlet perturbations.A shortcoming in the performed simulations is insufficient near-wall resolution, which resulted in poor predictions of the near-wall mean velocity profiles and the wall-shear stress. Simulations using DES improved the near-wall velocity predictions, but failed to predict the temperature fluctuations due to high levels of modeled turbulent viscosity that restrained the formation of small scale turbulence.

Peculiar oscillating convection is observed when two-dimensional double-diffusive convection in porous medium is analysed numerically. The top and bottom walls of an enclosure are insulated, and constant and opposing heat and mass fluxes are prescribed on the vertical walls. The peculiar oscillations are of three types: (1) Chaotic oscillations wherein the main flow is due to temperature; however, the convection due to concentration is strong enough to generate this peculiar oscillation. (2) The ‘sudden steady state case’ caused by the shifts from thermally-driven to concentration-driven forces. (3) The ‘re-oscillation case’ caused by the convection pattern changes from centrosymmetric to non-centrosymmetric.

Fuel damages are commonly caused by grinding of the cladding due to debris entering the reactor pressure vessel. In order to reduce the probability for fuel damages so-called particle traps have been developed and are currently in operation in two Swedish nuclear power plants. The particle traps are of type axial centrifugal separators, and are characterized by a robust design, high separation rate and low pressure drop (typically less than 1 bar). Special care has been taken in the design of the flow straightener, which efficiently eliminates the swirl in the flow. The model tests show that the Swirl number downstream of the particle trap is typically the same order of magnitude or less than that downstream of a pipe bend. The particles are separated from the main flow and collected in a separate chamber, which is emptied only during the outages. Traps have been developed for both upward or downward flow direction, with feedwater flows from 300 to 900 kg/s. The present paper describes the development work, which is primarily based on full-scale model tests supported by CFD-calculations. Some operating experiences from plants in which particle traps currently are in use are also reported.

Thermal mixing in a T-junction has been studied for validation of CFD-calculations. Experiments were carried out in a 2/3-scale model of a typical T-junction in a nuclear power plant, and temperature fluctuations were measured near the pipe walls by means of thermocouples. Three different flow ratios between the hot and cold water were considered. The computational results show that both steady and unsteady RANS fail to predict a realistic mixing between the fluids. The results were significantly better with scale-resolving methods such as LES and DES, showing fairly good predictions of the mean temperatures near the wall. The calculations did however predict larger fluctuations and different frequencies than observed in the model tests. Grid refinements showed that more small-scale fluctuations appeared in the calculated flow fields, although the predicted mean and temperature fluctuations near the walls were only moderately affected.

This article adopts lattice Boltzmann method to investigate the double diffusive natural convection around a heated cylinder in an enclosure filled with porous medium. The heated cylinder is located at the center of the enclosure with high temperature and concentration. Four surrounding walls are assumed to be low temperature and concentration. The distributions of velocity, temperature and concentration are solved by three independent lattice Bhatnagar-Gross-Krook (LBGK) equations. The influence of Darcy number Da (10–4 ≤ Da ≤ 10− 2), Lewis number Le (0.2 ≤ Le ≤ 10.0) and buoyancy ratio Br (− 10.0 ≤ Br ≤ 10.0) on the double diffusive natural convection are inspected numerically. Results are presented in terms of isotherms, streamlines, isoconcentrations, average Nusselt and Sherwood numbers. At Br = − 50.0, the effect of Darcy number on unsteady flow characteristics is also investigated by the time history and phase space trajectory. It is found that the flow undergoes steady-state, unsteady doubling periodic oscillation, quasi-periodic oscillation and non-periodic oscillation when Darcy number Da is varied from 10− 4 to 10− 2.

Unsteady electrolysis of a dilute solution of a metal salt made up of two ions in a system with vertical electrodes is considered for large values of the Rayleigh and Schmidt numbers. The mass transfer at the electrodes is assumed to be related to the local charge transfer potential and concentration by a nonlinear Butler–Volmer law. Free convection of the electrolyte appears owing to the variation of the concentration field. After a short initial period, the electrolyte becomes strongly stratified and the motion takes place in boundary layers at the solid boundaries. An approximate model equation for the evolution of the stratification is derived by using perturbation theory. Predictions from the simplified model are found to be in good agreement with numerical solutions of the complete problem. Significant differences compared with earlier studies for linear kinetics, i.e. cases in which the electric current density at the electrodes is constant, are found. Among other things, for large values of the difference ΔV in electric potential between the electrodes, most of the dissolved salt eventually collects near the bottom of the cell. The concentration in the bulk of the electrolyte is, for large values of ΔV, approximately given by a ninth-order polynomial to be compared with a linear behaviour for linear kinetics.

Some theoretical and experimental results for the concentration and velocity fields that appear during unsteady electrolysis in small electrochemical cells are given. Two systems are considered: ¦Cu¦CuSO4(aq)¦Cu¦ and ¦PbO2,PbSO4¦H2SO4(aq)¦Pb,PbSO4¦. For the former system, in which the electrodes are solid, both linear and nonlinear electrode kinetics are considered. For the more complicated latter system, where the electrodes are porous, attention is restricted to linear kinetics. Theoretical results are obtained by using both perturbation methods and numerical analysis. Experimental results are obtained by Laser Doppler Velocimetry and Image Laser Holography. It is shown that the evolution of the concentration and velocity fields is controlled by stratification of the electrolyte. The boundary layer structure is similar to that appearing during nonlinear spin up of a homogeneous fluid. Theoretical and experimental results are in good agreement.

A two-dimensional mathematical model for buoyancy-driven flow and mass transfer in a rectangular cell for copper electrolysis is proposed. The cell contains an excess of sulfuric acid as a supporting electrolyte. The electrodes are placed vertically and the electric current density along them is assumed to be constant and uniform. Effects of migration are accounted for in the laws for conservation of mass. A set of coupled nonlinear partial differential equations for describing the electrolysis is derived, and solved by numerical methods. It is shown that, after an initial and rather short period of time, the electrolyte becomes vertically stratified, with light electrolyte at the top and heavy electrolyte at the bottom of the enclosure. Thereafter, the system evolves slowly on a long time scale. The concentrations of the cupric and the hydrogen ions decrease in the upward and the downward directions respectively. Strong horizontal gradients of concentration appear in boundary layers adjacent to the electrodes. Electrolyte motion is confined to vertical and horizontal boundary layers on the solid walls of the container. The electrolyte in the core region is practically stagnant. Although Sc ⪢ 1 and D2 ⪢ D1, the vertical boundary layers for the velocity and the concentration fields have the same thicknesses. It is also demonstrated that the hydrogen ions carry the major part of the electric current. Moreover, and perhaps somewhat unexpectedly, it is shown that, at least for intermediate values of copper sulfate concentration (c*1/c*2 ≈ 0.3 as is the case dealt with in this work), migration plays a more important role than diffusion in the transport of the minority ions (Cu2+).

Unsteady convection of an initially homogeneous fluid in a vertical slot is investigated theoretically in the limit of large Rayleigh and Prandtl/Schmidt numbers. The motion is driven by prescribed fluxes of heat or mass at the vertical walls of the slot. The 'heat-up' problem is considered, i.e. the fluxes are specified to change instantaneously from zero to finite constant values. Perturbation methods are used to compute approximate solutions for the initial period and for the slow approach to the asymptotic state. Numerical solutions of the full problem are also given. It is shown that a significant stratification is set up after short time and that the system thereafter evolves as a strongly stratified fluid on a timescale that is proportional to Ra2/9. During the latter part of the process, linear buoyancy layers of thickness approximately Ra-2/9 appear on the vertical walls. On the horizontal walls, there are nonlinear boundary layers of thickness approximately Ra-1/9, whose structure is akin to that of a Stewartson E1/4 layer. The theoretical predictions are found to be in good agreement with experimental results.

The concentration and the velocity fields in a small copper refining cell with plane vertical electrodes were studied experimentally. The electrolyte was an aqueous solution of 0.3 M CuSO4 with 1.0 M H2SO4 as a supporting electrolyte. The electrolysis was done under galvanostatic conditions. The development in time of the concentration and velocity fields was measured for different values of the current density. The concentration field was measured by Holographic Laser Interferometry (HLI) and the velocity field by Laser Doppler Velocimetry (LDV). Experimental results were compared with numerically obtained concentration and velocity profiles based on a mathematical model developed earlier. The agreement was found to be good.

Free convection and stratification of the electrolyte in a lead-acid cell with porous electrodes and during recharge were studied theoretically and experimentally. The concentration field was measured by means of Holographic Laser Interferometry (HLI) and the velocity field by means of Laser Doppler Velocimetry (LDV). A two-dimensional mathematical model was also developed for mass transfer and electrolyte motion during the process. It was assumed for simplicity that the electric current density and porosities of the electrodes were constant and uniformly distributed in the electrodes. The results from the experiments were compared with numerical results obtained from the mathematical model. The agreement was found to be good. A simplified mathematical model, as an alternative to the full numerical problem, was also developed. The results of the simplified model proposed here proved to be in good agreement with the results from the full numerical solution, albeit for sufficiently large times.