Thermal convection in the van der Waals fluid

TL;DR

This paper investigates the van der Waals fluid model for liquid-vapor flows, demonstrating its ability to simulate phase transitions, boiling phenomena, and heat transport properties through advanced numerical methods.

Contribution

It introduces a numerical framework using entropy-stable schemes and isogeometric analysis to study the thermodynamics and flow behaviors of the van der Waals fluid.

Findings

Successful simulation of liquid-vapor phase transitions.

Model applicability to nucleate and film boiling regimes.

Derived scaling law for Nusselt number versus Rayleigh number.

Abstract

In this work, the van der Waals fluid model, a diffuse-interface model for liquid-vapor two-phase flows, is numerically investigated. The thermodynamic properties of the van der Waals fluid are first studied. Dimensional analysis is performed to identify the control parameters for the system. An entropy-stable numerical scheme and isogeometric analysis are utilized to discretize the governing equations for numerical simulations. The steady state solution at low Rayleigh number is presented, demonstrating the capability of the model in describing liquid-vapor phase transitions. Next, two-dimensional nucleate and film boiling are simulated, showing the applicability of the model in different regimes of boiling. In the last, the heat transport property of the van der Waals model is numerically investigated. The scaling law for the Nusselt number with respect to the Rayleigh number in the van der Waals model is obtained by performing a suite of high-resolution simulations.