Convection and Solidification in Constant and Oscillating Thermal Gradients: Measurements and Simulations

Abstract

An experimental and numerical study of natural convection and solidification in a two-dimensional cavity driven by constant and oscillating temperature gradients is presented. Finite element models are developed to predict the flowfield, the temperature distribution, and the solid-liquid interphase shapes during solidification. Both the fixedgrid and moving-grid methods are applied in the numerical simulations, using the former to illustrate the oscillating thermal gradient conditions and using the latter to illustrate the constant temperature gradient conditions. An experimental system is set up where succinonitrile is used as a working fluid. The flow pattern, the velocity field, and the solidification interface shape are measured using the laser-based particle-image-velocimetry system. Numerical simulations and experiments are conducted for various configurations and different thermal gradients. In most cases, convection is dominated by one recirculating loop. With an inverted temperature gradient, however, multiple convection loops are observed. Both the convective flow pattern and the velocity strongly affect the solid-liquid interface shapes during solidification. In a majority of the cases studied, the model predictions are in good agreement with the experimental measurements. NomenclatureC p = specific heat f = frequency of temperature modulation g 0 = terrestrial gravity H = height of the cavitŷ i,ĵ = unit vectors in the x and y directions, respectively k = thermal conductivity L = length of the cavity Pr = Prandtl number p = pressure q T = boundary heat flux Ra = Rayleigh number S = interface St e = Stefan number T = temperature T m = melting point t = time U max = absolute value of maximum velocity u = velocity α = thermal diffusivity β = thermal expansion coefficient H = latent heat T = temperature difference between two sidewalls ε p = penalty parameter for pressure θ = shape function for temperature µ = dynamic viscosity ν = kinematic viscosity ρ = density τ = stress tensor φ = shape function for velocity ψ = shape function for pressure , ∂ = computational domain and boundary of the domain Subscripts B, T, L , R = bottom, top, left, and right sidewalls l = liquid n = normal direction s = solid t = tangential direction

Freezing Front Propagation on Microgrooved Substrates

“…Stelian et al [12] conducted a numerical study of a temperature oscillation effect on the freezing front speed in the vertical Bridgman growth process using the finite element analysis software FIDAP. Shu et al [13] experimentally and numerically investigated the solid-liquid interface under the conditions of constant and oscillating temperature gradients, and their prediction was in good agreement with their experimental measurement. Furthermore, other effects (e.g., magnetic fields [14], capillary forces, and the solid-liquid contact angle [15]) on the solidifying interface have also been studied.…”