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TECHNICAL PAPERS

# A Thermal Lattice Boltzmann Two-Phase Flow Model and Its Application to Heat Transfer Problems—Part 2. Integration and Validation

[+] Author and Article Information
Peng Yuan

Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261pey1@pitt.edu

Laura Schaefer

Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261laschaef@engr.pitt.edu

J. Fluids Eng 128(1), 151-156 (Aug 10, 2005) (6 pages) doi:10.1115/1.2137344 History: Received December 18, 2004; Revised August 10, 2005

## Abstract

In the previous paper (Part 1) (P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 142–150), the multiphase isothermal lattice Boltzmann equation (LBE) model and single phase thermal LBE (TLBE) model were described. In this work, by combining these two models, the thermal two-phase LBE model is proposed. The coupling of the two models is through a suitably defined body force term. Due to the external nature of this coupling, the new model will have the same stability as the isothermal two-phase model. The applicability of the model is shown by the numerical simulation results of a thermal two-phase flow system in a rectangular channel. Our preliminary studies show that different equations of state, variable wettability, gravity and buoyancy effects, and relatively high Rayleigh numbers can be readily simulated by this new model.

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## Figures

Figure 1

Isotherms, density contours, and velocity vectors at Ra=10,000 and Re=100: (a) isotherms and density contours and (b) velocity vectors

Figure 2

Isotherms and density contours at different Rayleigh number: (a) Ra=5000 and (b) Ra=15,000

Figure 6

Isotherms and density contours at Ra=10,000 and Re=500: (a) xz plane (y=25) and (b) yz plane (x=25)

Figure 3

Nusselt number of the bulk flow, at the top wall, and at the bottom wall as functions of the time step (Ra=10,000, Re=100)

Figure 4

The bulk Nusselt number changing with time step at different Rayleigh numbers

Figure 5

The bulk Nusselt number changing with time step at different Reynolds numbers

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