Limits of strong magneto-convective fluctuations in liquid metal flow in a heated vertical pipe affected by a transverse magnetic field

Abstract

It is known from experimental and numerical studies that in channel flows of liquid metals, strong buoyancy forces, provided by temperature gradients, generate in magnetic field specific structures, which manifest themselves in the form of large-scale magneto-convective fluctuations (MCFs), accompanied by temperature fluctuations of anomalously large amplitude. The specific structure of MCFs depends on the properties of the liquid metal, on the channel configuration and its orientation to gravity and to the magnetic field, and on the combination of governing parameters of the flow. In this work we made the first attempt to define the domain of existence of MCFs in the parameter space for one specific configuration of the heated magnetohydrodynamic (MHD) flow. We studied experimentally a downward flow of mercury in the one-sided heated pipe in a transverse magnetic field, which can be considered as a first approximation to channels within a blanket module of a tokamak. We found that for this configuration, the weak buoyancy limit is defined by the critical Richardson number Rimin≈0.08, which indicates the value of required buoyancy, which should be strong enough to manifest itself in MCFs. The weak magnetic field limit is defined by the critical Stuart number Nmin≈1.5, which indicates the value of the required magnetic field that affects the developed turbulence and provides the transition from homogeneous turbulence to MCFs. The high magnetic field limit, which determines the boundary of MFs suppression by a strong magnetic field, depends on the flow rate and on the heating rate and has a clearer configuration in terms of a Reynolds number Rh, defined through the Hartmann layer thickness. At moderate Richardson numbers, the boundary is confined by a line Ri=6/Rh. With further increase of Ri, the border line rises more steeply and tends to an absolute upper limit Rh−1=2/25, above which the magnetic field completely laminarizes the flow for any buoyancy forces. We have shown, that MCFs strongly affect the heat transport, being able to essentially enhance it.