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ABSTRACT
In this paper, a new two-dimensional simulation model was developed for the falling film flow under low Reynolds number (below 20). The phase-field multiphase lattice Boltzmann model was developed to simulate the flow pattern of the two-phase falling film with high density ratio. The approaches to treating the liquid-gas interface with high density ratio (up to 775), surface tension, gravity, inlet and outlet open boundary conditions as well as solid-liquid interface considering contact angle were developed firstly, and then implemented in the model. The dynamic characteristics of the film flow, including the development of the liquid-gas interface and the film thickness, were simulated under the Reynolds numbers between 1.0 and 20. The results show that the film is fully laminar under low Reynolds numbers. The falling film flow model developed in this study lays the foundation for the study of heat and mass transfer in the falling film based liquid desiccant dehumidifier.
Acknowledgements
The research work presented in this paper is financially supported by a grant (ECS/533212) of the Research Grant Council (RGC) of the Hong Kong SAR. The support is gratefully acknowledged.
Nomenclature
| C | = | composition of liquid phase, dimensionless |
| Cs | = | composition of liquid phase at the solid surface, dimensionless |
| c | = | lattice speed, ms−1 |
| cs | = | lattice sound speed, ms−1 |
| E0 | = | bulk energy density, J.m−3 |
| e | = | lattice discrete velocity, ms−1 |
| f | = | distribution function of density, kg.m−3 |
| F | = | force vector, N |
| g | = | distribution function of pressure, Pa |
| g | = | gravitational acceleration, ms−2 |
| h | = | distribution function of composition, dimensionless |
| hfilm | = | film thickness, m |
| M | = | mobility, dimensionless |
| NX, NY | = | grid number, dimensionless |
| n | = | unit vector normal to the boundary, dimensionless |
| p | = | dynamic pressure, Pa |
| Re | = | Reynolds number, dimensionless |
| S | = | area, m−2 |
| t | = | time, s |
| t0 | = | viscous time, s |
| U | = | initial velocity, ms−1 |
| u | = | local velocity, ms−1 |
| um | = | local velocity of fluid m, ms−1 |
| V | = | volume, m−3 |
Greek symbols
| β | = | constant related with bulk energy, J.m−3 |
| Γ | = | normalized equilibrium distribution function, dimensionless |
| δx | = | lattice length, m |
| δt | = | lattice time, s−1 |
| θ | = | contact angle, rad |
| κ | = | constant related with surface energy, J.m−3 |
| λ | = | relaxation time, s |
| μ | = | chemical potential, J.m−3 |
| = | viscosity of the liquid, ms−2 | |
| ξ | = | interface thickness, m |
| ρ | = | density, kg.m−3 |
| ρ* | = | density ratio, dimensionless |
| ρH | = | density of liquid, kg.m−3 |
| ρL | = | density of gas, kg.m−3 |
| = | local density of fluid m, kg.m−3 | |
| σ | = | surface tension, N.m−1 |
| τ | = | relaxation factor, s−1 |
| ϕ0, ϕ1… | = | surface energy density, J.m−2 |
| Φb | = | bulk energy, J |
| Φs | = | surface energy, J |
| ω | = | wetting potential, dimensionless |
| ωa | = | weight factor, dimensionless |
Subscripts
| m | = | type of fluid in multiphase flow |
| s | = | solid surface |
| α | = | discrete direction |
| = | opposite direction of α | |
| l | = | liquid phase |
Superscripts
| CD | = | central difference |
| eq | = | equilibrium state |
| film | = | liquid film |
| gas | = | gas phase |
| liquid | = | liquid phase |
| MD | = | mixed difference |
| x, y, z | = | coordinates components |
Additional information
Notes on contributors
Tao Lu
Tao Lu is a Ph.D. candidate in Building Services Engineering of the Hong Kong Polytechnic University, Hong Kong. He received his bachelor's degree from Shanghai Jiao Tong University in 2014. His main research direction is the heat and mass transfer process in falling film using the Lattice Boltzmann Method and the falling film based liquid desiccant air conditioning.
Fu Xiao
Fu Xiao is an Associate Professor in Department of Building Services Engineering of the Hong Kong Polytechnic University (PolyU), Hong Kong. She received her Ph.D. degree in BSE in 2004 from PolyU. She is an active researcher in building energy efficiency and modelling and enhancement of heat and mass transfer in energy-related equipment in buildings.