Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer

Abstract

In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.

A lattice Boltzmann model for heat transfer in heterogeneous media

“…There is no obvious difference between them. The continuity of temperature and of temperature gradient across the interface of solid media can be guaranteed exactly in the present numerical prediction, which is important for conjugate heat transfer simulation [17][18][19][20][21]. Furthermore, in the models proposed in Refs.…”

“…(3) is an advection-diffusion equation for which a simpler lattice is sufficient [2,4]. For example, a D2Q5 lattice for two-dimensional problems and a D3Q7 lattice for three-dimensional domains [18,24]. Such choice can save computational cost efficiently, which is crucial for industrial-level simulation, as explained in our previous work [24].…”

“…Moreover, the present model can be directly used for conjugate heat transfer simulation, without any modification. Compared with some of the available LB approaches for conjugate heat transfer simulation [17][18][19][20], the present model is easier to be implemented as here no interface should be treated explicitly. Although the complexity induced by interface treatment can be avoided in several previous LB models [21,22], they suffer a number of obvious shortcomings.…”

“…combustion), these two assumptions can hardly be met. Recently, some scholars discussed how to model conjugate heat transfer by the LB method [17][18][19][20][21][22]. For conjugate heat transfer, the investigated domain is consisted of several different medium layers, and the specific heat capacity and/or thermal conductivity of the medium layers may be different with each other.…”

“…As shown by the above literature survey, this issue has been ignored by the LB community although it is extremely critical for practical applications. What should be emphasized is although in the present study we only take a single-relaxation-time LB model as an example to show how to address the variation of thermophysical properties of working media, the extension to its multiple-relaxation-time counterpart is straightforward [5,18]. …”