Hopf bifurcations to quasi-periodic solutions for the two-dimensional plane Poiseuille flow

This paper studies various Hopf bifurcations in the two-dimensional plane Poiseuille problem. For several values of the wavenumber $\alpha$, we obtain the branch of periodic flows which are born at the Hopf bifurcation of the laminar flow. It is known that, taking $\alpha\approx1$, the branch of periodic solutions has several Hopf bifurcations to quasi-periodic orbits. For the first bifurcation, previous calculations seem to indicate that the bifurcating quasi-periodic flows are stable and go backwards with respect to the Reynolds number, $Re$. By improving the precision of previous works we find that the bifurcating flows are unstable and go forward with respect to $Re$. We have also analysed the second Hopf bifurcation of periodic orbits for several $\alpha$, to find again quasi-periodic solutions with increasing $Re$. In this case the bifurcated solutions are stable to superharmonic disturbances for $Re$ up to another new Hopf bifurcation to a family of stable 3-tori. The proposed numerical scheme is based on a full numerical integration of the Navier-Stokes equations, together with a division by 3 of their total dimension, and the use of a pseudo-Newton method on suitable Poincar\'e sections. The most intensive part of the computations has been performed in parallel. We believe that this methodology can also be applied to similar problems.Comment: 23 pages, 16 figure

Numerical analysis of re-oscillation and non-centrosymmetric convection in a porous enclosure due to opposing heat and mass fluxes on the vertical walls

金沢大学環日本海域環境研究センターエコテクノロジー研究部門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. © 2009 Elsevier Ltd. All rights reserved

Numerical analysis of double-diffusive convection in a porous enclosure due to opposing heat and mass fluxes on the vertical walls - Why does peculiar oscillation occur?

金沢大学環日本海域環境研究センターエコテクノロジー研究部門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 \u27sudden steady state case\u27 caused by the shifts from thermally-driven to concentration-driven forces. (3) The \u27re-oscillation case\u27 caused by the convection pattern changes from centrosymmetric to non-centrosymmetric.. © 2007 Elsevier Ltd. All rights reserved

High-cycle thermal fatigue in mixing tees. Large-eddy simulations compared to a new validation experiment

ABSTRACT 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

Study of spray cooling of a pressure vessel head of a boiling water reactor

The present paper deals with a theoretical analysis of the spray cooling of a Reactor Pressure Vessel (RPV) head in 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.</p