Several engineering applications involve flows of liquid metals which are, at least partially, driven by thermal gradients and influenced by magnetic fields. Such flows are termed magnetoconvection, and they occur in, for example, electromagnetic stirring of melts in casting processes, liquid metal batteries, and cooling blankets in nuclear fusion reactors. The flow in these applications is highly turbulent; hence, cost-effective but accurate numerical simulations of such flows require appropriate subgrid-scale models. The relevant parameters for these models can be determined from the statistics of small-scale turbulence in magnetoconvection. These statistics are the energy spectrum, rate of energy transfer through different scales, and structure functions.
Studies on small-scale turbulence statistics exist for either thermally-driven flows without magnetic field effects or purely magnetohydrodynamic flows without thermal forcing [J. Phys. A. 55, 013002 (2022)]. However, turbulence in liquid metal flows that are both thermally driven and influenced by magnetic fields becomes more intricate due to the combined effects of buoyancy and magnetic fields on the small-scale statistics and has not been addressed before. In this project, we will, for the first time, study the small-scale statistics of liquid metal convection for a wide range of thermal forcing (due to buoyancy) and magnetic field strengths.
In this work (funded by Anusandhan National Research Foundation, Government of India), we conduct direct numerical simulations of the above flow in a cube of unit dimensions that is heated from below and cooled from above for different governing parameters. Two configurations for the imposed magnetic field are considered: a horizontal magnetic field (perpendicular to the direction of gravity) and a vertical magnetic field (parallel to the direction of gravity). We compute the anisotropic energy spectra, the rates of energy injection, cascade, and dissipation at different scales. The effects of anisotropy on the energy transfer mechanisms will be analyzed, and the scaling of the aforementioned spectral quantities with wavenumber will be obtained. We will also compute the structure functions to quantify the dynamics of turbulent flow in real space. Further, the viscous and thermal dissipation rates in the bulk and boundary layers of the flow will be determined, and their dependence on the governing parameters will be analyzed. Finally, we will arrive at phenomenologies for liquid-metal magnetoconvection, which will help determine the parameters for subgrid-scale models for simulating such flows in complex geometries.
Predicting and understanding climate change along with extreme weather events have motivated large-scale computing for decades, as the frontier of “extreme” advances through hardware and software technology. The weather forecast is typically done by employing numerical weather prediction (NWP) models that involve solving a set of dynamical equations for atmospheric flows. However, due to elusive ranges of physical and temporal scales, the simulations employed using these models are inevitably under-resolved and use approximate parameterizations for turbulent diffusion, convection, radiation, clouds and precipitation. These parameterizations themselves have constituted fields of active research. Most of the NWP models employ hydrostatic or anelastic approximation to filter out vertically propagating acoustic waves and hence reduce computational costs. Although these assumptions are reasonable for global and mesoscale flows, they are inaccurate at smaller scales (~ 2 km or less) where vertical acceleration becomes important. In this proposed project, we follow a different approach to study atmospheric flows which involves direct numerical simulations (DNS) of fully compressible convection. Note that convection is a crucial component in atmospheric flows and plays an important role in Earth’s climate and weather. Sustainability translations of this research include improved weather forecasts and more effective pollution mitigation strategies.
This work was conducted in Department of Physics, Indian Institute of Technology Kanpur, with Prof. Mahendra K. Verma. This work was started after the successful defense of my doctoral thesis. In this work, we applied machine-learning techniques to estimate the large-scale heat transport in turbulent RBC.
We developed a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in RBC using 62 sets of data obtained from direct numerical simulations. These simulations were conducted during my doctoral work. We compared the predictions of the models developed by us with those of earlier models of convection: Grossmann-Lohse [Phys. Rev. Lett. 86, 3316 (2001)], revised Grossmann-Lohse [Phys. Fluids 33, 015113 (2021)], and Pandey-Verma [Phys. Rev. E 94, 053106 (2016)] models. We observed that although the predictions of all the models are quite close to each other, the machine-learning models developed in this work provide the best match with the experimental and numerical results. Our work has been published in Physics of Fluids 34, 025102 (2022).
My doctoral research was on turbulent Rayleigh-Bénard Convection (RBC) under the joint supervision of Prof. Mahendra K. Verma and, in the first two years of my Ph.D., by Prof. Anirban Guha (who is currently in the University of Dundee, U.K.). The objective of my work was to numerically analyze the small-scale statistics of RBC (velocity structure functions, kinetic energy and entropy spectra and fluxes, and the dissipation rates) and their impact on heat and momentum transport. The simulations were conducted using a finite-volume solver "OpenFOAM" and a finite difference solver ``SARAS". The findings from my doctoral work are summarized as follows.
For small and moderate Prandtl numbers (Pr), the velocity structure functions are similar to those of three-dimensional homogeneous and isotropic turbulence [Phys. Fluids 31, 115107 (2019)]. Further, the amplitudes of the kinetic energy spectrum and structure functions increase with the decrease of Pr, thus exhibiting strong nonlinearity for flows with small Prandtl numbers. On the other hand, the fluctuations of the local heat flux are stronger for flows with large Prandtl numbers [Phys. Rev. Fluids 6, 063501 (2021)]. We observed that contrary to popular belief, the kinetic energy dissipation rate (viscous dissipation rate) is dominant in the bulk rather than in the boundary layers [Phys. Fluids 30 031702 (2018)]. On the other hand, the thermal dissipation rate dominates in the boundary layers [Phys. Fluids 31, 075104 (2019)]. It is currently held that the viscous and the thermal dissipation rates in the bulk region of RBC scale as U^3/d and U Δ^2/d respectively [Phys. Rev. Lett. 86, 3316 (2001)], similar to 3D homogeneous isotropic turbulence (Here, U is the large scale velocity, and Δ and d, respectively, are the temperature difference and the distance between the top and bottom walls). A major finding from our work is these rates exhibit an additional Rayleigh number (Ra) dependence of approximately Ra^-0.2 [Phys. Fluids 33, 015113 (2021)]. This modification, which is due to the suppression of nonlinear interactions by walls and buoyancy, assumes importance for high Rayleigh numbers where the large-scale heat transport is expected to be significantly impacted by the aforementioned additional factor. Using these results and employing a machine-learning algorithm on 60 training datasets obtained from numerical simulations of RBC, we improved the well-known Grossmann and Lohse's model to predict the Reynolds and Nusselt numbers for a given set of governing parameters [Phys. Fluids 33, 015113 (2021)].
The findings from my doctoral work should help in more accurate prediction of atmospheric flows, developing better turbulence models, and an improved understanding of the convective heat transfer mechanism in liquid metal batteries, heated chambers, heat sinks, etc.
This work was carried out at the Institute for Energy Systems, Technical University of Munich (TUM), chaired by Prof. H. Spliethoff. A model for simulating the flow of coal ash slag in an entrained flow gasification system was developed using the CFD software ANSYS Fluent. Although several models of slag flow have been proposed in the literature, the regime of the slag flow between the temperature of critical viscosity and the solidus temperature, where the slag becomes a non-Newtonian shear-thinning fluid, has not been worked on before. Therefore, special attention was given to the non-Newtonian regime of slag flow. The results of the simulations were then compared with those of the models which did not account for non-Newtonian nature of slag flow. Significant differences were found, which showed that the new model is promising. However, the simulation requires very high computational costs, and therefore the model should be researched upon further so as not to make it very computation-intensive.
This work was carried out under the supervision of Prof. Jyotirmay Mathur in the Mechanical Engineering Department, Malaviya National Institute of Technology, Jaipur, India. The task involved the simulation of a grid-connected zero energy house and the effects of energy conservation measures (such as thermal insulation) on the reduction of annual energy consumption. The economics of these energy conservation measures was also studied with the goal of finding out the most optimal measure. The building was modeled and simulated using EnergyPlus software, developed by the Department of Energy (DOE), USA. It has been found that the most economical energy conservation measure involved the installation of thermal insulation on the roof of the building, while wall insulation and energy-efficient glazing proved to be uneconomical.
This work was carried out in the Fluid Mechanics Group (led by Prof. J. Schumacher), Ilmenau University of Technology, and supported by the Alexander von Humboldt Foundation, Germany. In this work, we studied the effects of strong magnetic fields on liquid metal flows. We primarily studied large-scale structures and heat transport in magnetoconvection, which is thermal convection under the influence of magnetic fields. It is a known fact that an imposition of horizontal magnetic fields results in the convection rolls becoming quasi-two-dimensional. On the other hand, vertical magnetic fields suppress convection, and above a certain critical magnetic field, bulk convection ceases completely with residual convective motion attached to sidewalls. Magnetoconvection finds extensive applications in industries such as in liquid metal batteries for energy storage, cooling blankets in fusion reactors, and the growth of high-precision semiconductor monocrystals. Thus far, previous work on magnetoconvection has been restricted to spatially uniform magnetic fields which is a highly idealized configuration. However, in realistic situations, there are spatial and even temporal variations of magnetic fields, which is the motivation of our current research.
We studied the influence of fringing magnetic fields on turbulent convection in a horizontally extended rectangular domain. The magnetic field was created in the gap between two semi-infinite planar magnetic poles. The convection layer is located near the edge of the gap. We employed direct numerical simulations in this setup for fixed Rayleigh and small Prandtl numbers but varied the fringe width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets was strong enough to cease the flow in high magnetic flux region of the convection cell. We observed that as the local vertical magnetic field strength increases, the large-scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determined the local Nusselt and Reynolds numbers as functions of the local Hartmann number based on the vertical component of the magnetic field and estimated the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe width for strong magnetic fields but increases with increasing fringe width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion became confined to the vicinity of the sidewalls, as expected. Interestingly, however, the amplitudes of these wall modes showed a non-monotonic dependence on the fringe-width. A manuscript on our work has been published in the Journal of Fluid Mechanics 964, A31 (2023).
Although there had been a few studies on convection with inclined magnetic fields, there was no work on the above in the wall-attached convection regime before. We employed a linear stability analysis and direct numerical simulations to study the characteristics of the wall-modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell were electrically insulated. The stability analysis assumed periodicity in the direction perpendicular to the plane of the homogeneous magnetic field. Our study showed that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes became tilted along the direction of the resulting magnetic fields and, therefore, extended further into the bulk as the horizontal magnetic field was increased. Once the modes localized on the opposite walls started to interact, the critical Rayleigh number decreased again and eventually dropped below the value for onset with a purely vertical field. We found that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk, and therefore, convection is no longer restricted to the sidewalls. The above results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection. A manuscript on our work has been published in the Journal of Fluid Mechanics 979, A53 (2024).
In addition to convection, we also studied the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number was low such that the wake of the stationary magnetic obstacle was steady. The transverse oscillation of the magnet created a sinusoidal time-dependent wake reminiscent of the vortex shedding behind solid obstacles. We examined the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force was twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid showed a non-monotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding. The above work has been published in the Proceedings in Applied Mathematics and Mechanics, e202300153 (2023).