Assessing non-Oberbeck-Boussinesq effects of convection in cryogenic helium

Abstract

The present study investigates the non-Oberbeck-Boussinesq (NOB) effects which arise due to the temperature dependence of material properties in cryogenic helium experiments of turbulent Rayleigh-B\'enard convection. They are manifest as a difference of the measured mean temperature at the center of the closed cell, $T_c$, from the arithmetic mean temperature obtained from the prescribed fixed and uniform temperatures at the top and bottom copper plates of the apparatus, $T_m = (T_{bot} +T_{top})=2$. Therefore, the material properties such as specific heat at constant pressure, dynamic viscosity, thermal conductivity, the isobaric expansivity, and the mass density are expanded into power series with respect to temperature up to the quadratic order with coeffcients obtained from the software package HEPAK. A subsequent nonlinear regression that uses deep convolutional networks delivers a dependence of the strength of non-Oberbeck-Boussinesq effects in the pressure-temperature parameter plane. Strength of the NOB effects is evaluated via the deviation of the mean temperature profile $\xi_{NOB} = T_m - T_c$ from the top/bottom-symmetric Oberbeck-Boussinesq case $\xi_{NOB} = 0$. Training data for the regression task are obtained from 236 individual long-term laboratory measurements at different Rayleigh numbers which span 8 orders of magnitude.