We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards th...We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.展开更多
In this paper, we investigate the thermal and turbulent behaviour of incompressible Newtonian flow, by numerical simulation, combining two physical phenomena, namely, the heat-transfer by mixed convection and the onse...In this paper, we investigate the thermal and turbulent behaviour of incompressible Newtonian flow, by numerical simulation, combining two physical phenomena, namely, the heat-transfer by mixed convection and the onset of turbulence, around different isothermal complex geometries, using the immersed boundary method coupled with the virtual physical model, in order to model the presence of the isothermal body. Boundary conditions of the Dirichlet and Neumann type are implemented. For turbulence modelling, the Smagorinsky and Spalart-Allmaras models are used, for Reynolds and Richardson numbers ranging up to 5000 and 5, respectively. This work confirms that, downstream of the immersed body, the recirculation: 1) increases with the increase in the number of Reynolds, keeping the number of Richardson constant, and 2) decreases with the increase in the number of Richardson, preserving the number of Reynolds constant. It also confirms the generation of thermal plumes moving upwards. For Reynolds numbers in the order of a few hundred and Richardson numbers around 5, it is observed, for tandem cylinders, the vortex wake being established in the downstream region. Interactions within the vortex wake, with the shear layer separated from the downstream cylinder, create two vortices near the downstream cylinder. The shear layer separating from the upstream cylinder creates a vortex behind the downstream cylinder.展开更多
文摘We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.
文摘In this paper, we investigate the thermal and turbulent behaviour of incompressible Newtonian flow, by numerical simulation, combining two physical phenomena, namely, the heat-transfer by mixed convection and the onset of turbulence, around different isothermal complex geometries, using the immersed boundary method coupled with the virtual physical model, in order to model the presence of the isothermal body. Boundary conditions of the Dirichlet and Neumann type are implemented. For turbulence modelling, the Smagorinsky and Spalart-Allmaras models are used, for Reynolds and Richardson numbers ranging up to 5000 and 5, respectively. This work confirms that, downstream of the immersed body, the recirculation: 1) increases with the increase in the number of Reynolds, keeping the number of Richardson constant, and 2) decreases with the increase in the number of Richardson, preserving the number of Reynolds constant. It also confirms the generation of thermal plumes moving upwards. For Reynolds numbers in the order of a few hundred and Richardson numbers around 5, it is observed, for tandem cylinders, the vortex wake being established in the downstream region. Interactions within the vortex wake, with the shear layer separated from the downstream cylinder, create two vortices near the downstream cylinder. The shear layer separating from the upstream cylinder creates a vortex behind the downstream cylinder.
