Ioannis Sarris

Natural convection in a 2D enclosure with sinusoidal upper wall temperature

Natural convection in a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated. The applied sinusoidal temperature is symmetric with respect to the midplane of the enclosure. Numerical calculations are produced for Rayleigh numbers in the range 10 2 to 10 8 , and results are presented in the form of streamlines, isotherm contours, and distributions of local Nusselt number. The circulation patterns are shown to increase in intensity, and their centers to move toward the upper wall corners with increasing Rayleigh number. As a result, the thermal boundary layer is confined near the upper wall regions. The values of the maximum and the minimum local Nusselt number at the upper wall are shown to increase with increasing Rayleigh number. Finally, an increase in the enclosure aspect ratio produces an analogous increase of the fluid circulation intensity.

On the Limits of Validity of the Low Magnetic Reynolds Number Approximation in MHD Natural-Convection Heat Transfer

In the majority of magnetohydrodynamic (MHD) natural-convection simulations, the Lorentz force due to the magnetic field is suppressed into a damping term resisting the fluid motion. The primary benefit of this hypothesis, commonly called the low-R m approximation, is a considerable reduction of the number of equations required to be solved. The limitations in predicting the flow and heat transfer characteristics and the related errors of this approximation are the subject of the present study. Results corresponding to numerical solutions of the full MHD equations, as the magnetic Reynolds number decreases to a value of 10−3, are compared with those of the low-R m approximation. The influence of the most important parameters of MHD natural-convection problems (such as the Grashof, Hartmann, and Prandtl numbers) are discussed according to the magnetic model used. The natural-convection heat transfer in a square enclosure heated laterally, and subject to a transverse uniform magnetic field, is chosen as a case study. The results show clearly an increasing difference between the solutions of the full MHD equations and low-R m approximation with increasing Hartmann number. This difference decreases for higher Grashof numbers, while for Prandtl numbers reaching lower values like those of liquid metals, the difference increases.

Large-eddy simulations of the turbulent Hartmann flow close to the transitional regime

A series of large-eddy simulations (LES) of turbulent and transitional channel flows of a conductive fluid under the effect of a uniform magnetic field applied in the wall-normal direction, usually referred to as Hartmann flows, are performed using the dynamic Smagorinsky model. The flow is characterized by the hydrodynamic Reynolds number Re and the Hartmann number Ha that is related to the strength of the external magnetic field. Previous measurements and works on stability analysis have shown that a critical modified Reynolds number, based on the Hartmann layer thickness R=Re∕Ha, exists at approximately R=380. Here, the LES are used to investigate the laminarization of flow when decreasing R. Also, similarities of the turbulent flows are explored for different values of Re and Ha but the same values of R or of the interaction parameter N=Ha2∕Re. The LES confirm that R is the relevant parameter that describes the transition and a critical Reynolds number for relaminarization is observed at R≈500. Howeve...

Dispersed-phase structural anisotropy in homogeneous magnetohydrodynamic turbulence at low magnetic Reynolds number

A new tensor statistic, the dispersed-phase structure dimensionality Dp, is defined to describe the preferred orientation of clusters of discrete bodies. The evolution of Dp is calculated via direct numerical simulations of passive, Stokesian particles driven by initially isotropic, decaying magnetohydrodynamic turbulence. Results are presented for five magnetic field strengths as characterized by magnetic interaction parameters, N, in the range 0–50. Four field strengths are studied at a grid resolution of 1283. The strongest field strength is also studied at 2563 resolution. In each case, the externally applied magnetic field was spatially uniform and followed a step function in time. Particles with initially uniform distributions were tracked through hydrodynamic turbulence for up to 2800 particle response times before the step change in the magnetic field. In the lower resolution simulation, the particle response time, τp, matched the Kolmogorov time scale at the magnetic field application time t0. Th...

Transient Laminar MHD Natural Convection Cooling in a Vertical Cylinder

A numerical study is presented of transient laminar natural convection cooling of an electrically conductive fluid, placed in a vertical cylinder in the presence of an axial magnetic field. The cylindrical wall is suddenly cooled to a uniform temperature, thus setting the fluid to motion. The cooling process starts with the development of momentum and thermal boundary layers along the cylindrical cold wall, followed by the intrusion of the cooled fluid into the bulk, and finally, by fluid stratification. A range of Hartmann, Rayleigh, and Prandtl numbers are studied for which the flow remains laminar in all stages. It is found that the increase of the magnetic field reduces the heat transfer rate and decelerates the cooling process. This can be attributed to the damping of the fluid motion by the magnetic field, which results in the domination of conduction over convection heat transfer. The increase of the Rayleigh number enhances heat transfer, but the cooling process lasts longer due to the higher temperature of the hot fluid. The flow deceleration and the reduction of heat transfer are less intense for fluids with low Prandtl number.

Laminar Free Convection in a Square Enclosure Driven by the Lorentz Force

A numerical study is presented of laminar free convection flow driven by magnetic forces. An external magnetic field with one spatially varying component is applied to an electrically conducting fluid in a square enclosure. This magnetically-driven flow is controlled by the intensity and the wave number of the applied magnetic forcing. In addition, when the enclosure is heated laterally in a non-zero gravity environment, the resulting buoyant forces may contribute or resist the magnetically-driven fluid motion. The present results show that a strong magnetic field can even reverse the buoyant flow. The circulation intensity of the flow and the heat transfer from the sidewalls is increased with increasing magnetic field or with decreasing magnetic Reynolds number. The wave number of the magnetic forcing is also an important parameter that determines the vortex patterns and, consequently, the convection heat transfer.

Box-size dependence and breaking of translational invariance in the velocity statistics computed from three-dimensional turbulent Kolmogorov flows

The Kolmogorov flow generated by a stationary one-dimensional forcing varying sinusoidally in space is studied using direct numerical simulations with periodic boundary conditions. The velocity statistics are considered for various computational domains ranging from the minimal cubic box with size equal to the forcing wavelength to significantly larger domains. For the minimal computational domain, the velocity statistics exhibit symmetries that are directly imposed by the forcing properties. However, for larger domains, the translational invariance in the streamwise direction appears to be broken and the turbulence statistics depend on the computational box aspect ratio.

Dynamo transition in low-dimensional models

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.

Magnetohydrodynamic Natural Convection of Liquid Metal Between Coaxial Isothermal Cylinders Due to Internal Heating

Direct numerical simulation results are presented of magnetohydrodynamic liquid metal flow between two vertical coaxial cylinders under the effect of internal heating and a horizontal magnetic field. The end walls are thermally insulated, while the cylindrical walls are at the same temperature. The flow is driven by the heat sources under the stabilizing effect of the external magnetic field. The problem is characterized by the internal Rayleigh number, expressing the internal heating, and the Hartmann number corresponding to the magnetic field. Depending on their value laminar, transitional or turbulent flow may occur. The heat sources create bi-cellular flow patterns as the maximum temperature in inside the fluid bulk. Te flow is azimuthally asymmetric due to the Hartmann and Robert layers formed on the walls normal and parallel to the magnetic field, respectively.

Magnetic field effect on the cooling of a low-Pr fluid in a vertical cylinder

Results of direct numerical simulations are presented for the transient and turbulent natural convection cooling of an initially isothermal quiescent liquid metal placed in a vertical cylinder in the presence of a vertical magnetic field. The electrically conductive low-Prandtl number fluid is put to motion when the cylindrical wall is suddenly cooled to a uniform lower temperature. For this particular cooling process, the flow is characterized by three sequential almost discrete stages: (a) development of momentum and thermal boundary layers along the cylindrical cold wall, (b) intrusion of the cooled fluid into the main fluid body, and (c) flow and thermal stratification. The selected Rayleigh numbers in the present study are high enough so that turbulent convection is established. The numerical results show that the magnetic field has no observable effect at the initial stage of the vertical boundary layer development and conduction heat transfer is favored during the intrusion stage. An interesting ef...