An original algorithm for VOF based method to handle wetting effect in multiphase flow simulation
Introduction
The numerical simulation of two-phase flows involving wetting effects is of interest for numerous fundamental and applied researches in fluid mechanics applied to material selection, surface treatment, heat exchangers, energy production or lubrication in industrial processes. The unsteadiness and complex optical properties of two-phase flows make the experimental measurements difficult to achieve and have encouraged research efforts to build efficient physical models and numerical methods.
Among the wide variety of physical approaches, two main fundamental modeling strategies exist, based on microscopic considerations or continuous fluid mechanics. Molecular dynamics of multiphase flows involve molecular interfacial forces [1], [2], which act on a smaller scale than the minimum numerically resolved structures and are responsible for an interface energy excess. Microscopic models integrate molecular forces into continuous models. These latter models introduce diffuse interfaces and contain a complete description of capillary effects – including wetting-through thermodynamically consistent equations. The resolution of diffuse interfaces can only be applied to problems involving small ranges of interfacial scales to keep reasonable computational grids in three dimensions.
The models based on continuous fluid mechanics are the most commonly used in academic and industrial CFD tools. They are built by integrating the Navier–Stokes equations in each phase and by defining jump relations at the interface to ensure mass and momentum conservation [3]. Considering fixed structured grids, the interface is not explicitly discretized on the mesh used to solve the Navier–Stokes equations. Kataoka [4] introduce a phase function variable C to define the local volume fraction in each grid cell. The Navier–Stokes equations in each phase are generalized to the whole two-phase medium by convolving the conservation equation by C and integrating them among all the control volumes. Finally, a single fluid model, also called 1-fluid model, is obtained, which contains a new force in the momentum equations accounting for the surface tension effects. This single fluid model requires the solving of an advection equation on C to describe the time and space evolutions of the interface. A wide variety of methods have been proposed over the last 20 years to numerically treat the advection of C, such as the Front Tracking method [5], the level set technique [6], or the volume of fluid (VOF) approach [7]. We choose to use the single fluid model and to improve VOF methods to simulate wetting effects as these approaches are among the most popular in the field of two-phase flow simulation. In the VOF methods, the surface tension force is classically approximated with the continuum surface force (CSF) of Brackbill et al. [8], which formulates the interfacial force as a function of the gradients of C. An extension of the CSF approach is proposed in this work to treat the dynamic contact angle in VOF methods. The reader can refer to the work of Manservisi and Scardovelli [9] for a review of two-phase flow models dedicated to contact angle on fixed grids.
First, the filtered 1-fluid model is presented briefly. An original extension of the CSF method, which uses an auxiliary diffuse VOF variable, is then detailed and the numerical implementation of the single fluid CSF model for wetting effects is explained. Several test cases are done to show the advantages of this model. Then, the regularized CSF approach on the impact of a droplet on a dry surface for various wetting conditions is illustrated. These numerical tests are used to validate the physical meaning of the numerical model for wetting. Finally, concluding remarks are provided.
Section snippets
The 1-fluid model
As previously explained, the modeling and the simulation of two-phase flows involving separated phases, i.e. the characteristic interfacial length scale is larger than the smallest spacing of the computational grid, is classically achieved by introducing the Navier–Stokes equations in each phase [10] and by insuring the connection of the velocity field at the interface by defining jump conditions on the velocity and the stress tensor [3]. Another point of view, chosen in this work, consists in
Numerical tests and validations
The impact of a droplet on a flat surface is associated to complex two-phase flow phenomena involving dramatic interface deformations, which mainly depends on contact angle and surface tension. The fluid dynamics are directly dependent on the physical and chemical properties of interfaces through capillary effects. The wetting properties of the target solid surface, the height and diameter of the droplet during time, as well as the contact angle between the droplet and the surface are
Concluding remarks
A new Eulerian model based on a Volume Of Fluid has been proposed to handle capillary effects, in particular wetting properties of solid surfaces. The model relies on a regularized VOF function for estimating the surface tension forces including the contact line with a Continuum Surface Force model of Brackbill et al. [8], called “Smooth VOF”. The imposition of the contact angle at the solid-fluid interfaces uses a penalty method applied to the Smooth VOF function, which is finally obtained by
Acknowledgements
We acknowledge the Aquitaine Regional Council for the financial support dedicated to a 432-processor cluster investment, located in the I2M Institute. This work was also granted access to the HPC resources of CCRT, CINES and IDRIS by GENCI (Grand Equipement National de Calcul Intensif) under reference number x2009026115 and x2010026115.
References (33)
- et al.
On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method
J. Comput. Phys.
(2002) - et al.
Numerical simulations of spontaneous capillary rises with very low capillary number using front tracking method combined with generalized navier boundary condition
Int. J. Multiph. Flow
(2013) Jump conditions and entropy sources in two-phase systems. Local instant formulation
Int. J. Multiph. Flow
(1974)Local instant formulation of two-phase flow
Int. J. Multiph. Flow
(1986)- et al.
A front-tracking method for viscous, incompressible, multi-fluid flows
J. Comput. Phys.
(1992) - et al.
A level set approach for computing solutions to incompressible two-phase flow
J. Comput. Phys.
(1994) - et al.
Volume of fluid (VOF) methods for the dynamics of free boundaries
J. Comput. Phys.
(1981) - et al.
A continuum method for modelling surface tension
J. Comput. Phys.
(1992) - et al.
A variational approach to the contact angle dynamics of spreading droplets
Comput. Fluids
(2009) - et al.
A volume of fluid method based on multidimensional advection and spline interface reconstruction
J. Comput. Phys.
(2004)
An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows
J. Comput. Phys.
A high-order projection method for tracking fluid interfaces in variable density incompressible flows
J. Comput. Phys.
A new volume of fluid advection algorithm: the stream schemes
J. Comput. Phys.
An accurate adaptive solver for surface-tension-driven interfacial flows
J. Comput. Phys.
Volume of fluid interface tracking with smoothed surface stress methods for three dimensional flow
J. Comput. Phys.
Simulating compressible gas bubbles with a smooth volume tracking 1-fluid method.
Int. J. Multiph. Flow
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