Modelling heat transfer in two‐fluid interfacial flows

Abstract

SUMMARYThis paper presents a method to calculate heat transfer across an interface separating immiscible fluids. A volume tracking method was used to model the simultaneous movement of mass, momentum and energy across cell boundaries. Both first-and second-order methods were used to approximate temperature fields with sharp gradients that exist near the fluid-fluid interface. Temperature distributions around hot droplets surrounded by a colder fluid with uniform velocity were calculated and the magnitude of false diffusion identified. The effect of changing the thermal diffusivity of the surrounding fluid was studied. It was found that in most cases a second-order approximation, such as the van Leer scheme, is sufficient for estimating advection temperatures. To demonstrate the capabilities of the model we modelled molten tin droplets falling in an oil bath. The development of vortices behind droplets was modelled and the effect of fluid re-circulation and oil thermal conductivity on heat dissipation studied.

Modeling transport of scalars in two-phase flows with a diffuse-interface method

“…Pericleous et al (1995) used the SEA method for modeling free-surface flows and adopted the Van Leer total-variation diminishing (TVD) scheme for the discretization of the energy equation instead of an upwinding scheme to avoid the artificial heat loss across the interface due to numerical smearing. However, the mere use of a Van Leer TVD scheme for the discretization of the scalar-transport equation does not completely eliminate the artificial diffusion of the scalar across the interface (Mehdi-Nejad et al, 2004). Most VOF methods tackle the issue of artificial numerical diffusion of the scalar across the interface by geometrically advecting the scalar concentration field in a manner consistent with the advection of the volume fraction field (Davidson and Rudman, 2002, Alke et al, 2009, Bothe and Fleckenstein, 2013, Berry et al, 2013.…”

Inertia dominated flow and heat transfer in liquid drop spreading on a hot substrate

“…It was shown that even at temperatures below the boiling point the temperature rise in the liquid may cause changes in thermophysical properties leading to a significant increase in the spreading ratio, indicating that neglecting the heat transfer in the spreading stage of motion, as commonly done in modeling spray impact, may therefore lead to erroneous initial conditions for the subsequent analysis of the evaporation process. Interfacial heat transfer from multiple molten tin droplets falling in oil was numerically simulated in (Mehdi-Nejad et al, 2004, 2005 using a VOF-based computational model. Results showed a considerable change in the temperature distribution of the upstream droplet due to heat dissipation from the downstream droplet.…”

Regularized Dirac delta functions for phase field models

“…In interface tracking methods (front tracking [9,10] and immersed boundary [11,12]), Lagrangian particles are used to track the interface and are advected by the velocity field. In interface capturing methods (volume of fluid [VOF] [11,13,14], level set [15][16][17][18], and phase field [19][20][21][22]), the interface is implicitly captured by a contour of a particular scalar function. Many numerical techniques, including immersed boundary [23][24][25][26][27][28][29][30], VOF [31][32][33][34][35][36][37][38][39][40], and level set [41][42][43][44][45][46][47][48], use the concept of a regularized Dirac delta function to account for interfacial effects (this is described in more detail in Section 2), and many previous studies show that an appropriate delta function is required to obtain more accurate results.…”