Continuum surface force

In order to properly solve (17.5), sharp changes in the properties as well as pressure forces due to surface tension effects have to be resolved. In particular, surface tension results in a jump in pressure across a curved interface. The pressure jump is discontinuous and located only at the interface. This singularity creates difficulties when deriving a continuum formulation of the momentum equation. The interfacial conditions should be embedded in the field equations as source terms. Once the equations are discretized in a finite-thickness interfacial zone, the fiow properties are allowed to change smoothly. It is therefore necessary to create a continuum surface force (CSF) equal to the surface tension at the interface, or in a transitional region, and zero elsewhere. Therefore, the surface integral term in (17.5) could be rewritten into an appropriate volume integral... 

In Eq. 5, the surface tension force p is modeled using the continuum surface force model [5]. It is reformulated as an equivalent body force acting within a band of 2a at the interface using a smeared-out Dirac delta function D(iJ). The surface tension force can be expressed as... 

The phase-indicator or color function x can be related to a level set function (p which changes sign across the interface. For instance, if (p is negative in fluid 1 and positive in fluid 2, the appropriate relation is x = H Heaviside step function. Note that with the help of the phase-indicator function the combination 8511 that appears in the continuum surface force model is given by 856 = — V%. 

Surface Tension Calculation in VOF Method Modeling interfacial tension effects is important because it is a potentially large force which is concentrated on the interface. There are two different approaches to modeling surface tension forces. The first mie is continuum surface force (CSF) defined as... 

Once the surface between the fluids has been determined, there remain two important additional steps before surface forces can be included. First, the curvature of the surface must be calculated from the discrete location values available on the computational grid. Then the surface tension force is applied by replacing a surface force by an equivalent volume force in a zone adjacent to the interface, with most commercial software using a version of the Continuum Surface Force (CSF) method derived by Brackbfll et al. [40]. The manner in which this force is implemented can lead to the appearance of spurious velocities, known as parasitic currents. A recent study by Harvie et ol. [41] has shown that these parasitic currents cannot be removed by mesh refinement alone and they can have a significant effect in certain conditions. 

The bubble-fluid interaction force, /bf, is obtained by using a continuum surface force (CSF) model (Brackbill et al., 1992)... 

According to the applied Continuum Surface Force (CSF) method we approximate the Dirac Delta function 5 by a continuous regularized one, which is a smooth function in the vicinity of e of the interface ... 

The third term on the left hand side of (18.1) is an artificial compression term which is active only in the interface region. U ei is a velocity field suitable to compress the interface. The gas-liquid flow is governed by the incompressible Navier—Stokes (N-S) equations in which the parameters about physical properties such as density ip) and dynamic viscosity (//) are calculated as weighted averages by the linear interpolation of the volume fraction. The continuum surface force (CSF) method is employed to calculate the surface tension force [2]. Therefore, the N-S equatimis can be expressed as follows ... 

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