Ashley Jean James

An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids

We present an adaptive coupled level-set/volume-of-fluid (ACLSVOF) method for interfacial flow simulations on unstructured triangular grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a discontinuous Galerkin finite element method. The volume fraction advection is performed using a Lagrangian-Eulerian method. The interface is reconstructed based on both the level set and the volume fraction information. In particular, the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction. Different from previous works, we have developed an analytic method for finding the line constant on triangular grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. The level set function is finally reinitialized to the signed distance to the reconstructed interface. Since the level set function is continuous, the normal vector calculation is easy and accurate compared to a classic volume-of-fluid method, while tracking the volume fraction is essential for enforcing mass conservation. The method is also coupled to a finite element based Stokes flow solver. The code validation shows that our method is second order and mass is conserved very accurately. In addition, owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately.

Vibration-induced drop atomization and bursting

A liquid drop placed on a vibrating diaphragm will burst into a fine spray of smaller secondary droplets if it is driven at the proper frequency and amplitude. The process begins when capillary waves appear on the free surface of the drop and then grow in amplitude and complexity as the acceleration amplitude of the diaphragm is slowly increased from zero. When the acceleration of the diaphragm rises above a well-defined critical value, small secondary droplets begin to be ejected from the free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected from the vibrating diaphragm in the form of a spray. This event is the result of an interaction between the fluid dynamical process of droplet ejection and the vibrational dynamics of the diaphragm. During droplet ejection, the effective mass of the drop–diaphragm system decreases and the resonance frequency of the system increases. If the initial forcing frequency is above the resonance frequency of the system, droplet ejection causes the system to move closer to resonance, which in turn causes more vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting. In this paper, the basic phenomenon of vibration-induced drop atomization and drop bursting will be introduced, demonstrated, and characterized. Experimental results and a simple mathematical model of the process will be presented and used to explain the basic physics of the system.

Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection

Vibration-induced droplet ejection is a novel way to create a spray. In this method, a liquid drop is placed on a vertically vibrating solid surface. The vibration leads to the formation of waves on the free surface. Secondary droplets break off from the wave crests when the forcing amplitude is above a critical value. When the forcing frequency is small, only low-order axisymmetric wave modes are excited, and a single secondary droplet is ejected from the tip of the primary drop. When the forcing frequency is high, many high-order non-axisymmetric modes are excited, the motion is chaotic, and numerous small secondary droplets are ejected simultaneously from across the surface of the primary drop. In both frequency regimes a crater may form that collapses to create a liquid spike from which droplet ejection occurs. An axisymmetric, incompressible, Navier–Stokes solver was developed to simulate the low-frequency ejection process. A volume-of-fluid method was used to track the free surface, with surface tension incorporated using the continuum-surface-force method. A time sequence of the simulated interface shape compared favourably with an experimental sequence. The dynamics of the droplet ejection process was investigated, and the conditions under which ejection occurs and the effect of the system parameters on the process were determined.

Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids

In volume of fluid methods for interfacial flow simulations, one essential process is the so-called interface reconstruction, in which an approximate interface is reconstructed from a given discrete volume fraction field. In [J. Comput. Phys. 164 (2000) 228-237], Scardovelli and Zaleski presented analytical relations connecting linear interfaces and volume fractions in rectangular grids. Here, we present analytical relations connecting linear interfaces and volume fractions in triangular and tetrahedral grids. For computing the volume of fluid in an arbitrary polygonal or polyhedral fluid element, we also cite some of the most efficient formulas for polygon area and polyhedron volume computations. Simple test cases show that this analytic method of interface reconstruction is about 18 times faster than an iterative method in two dimensions, and four to six times faster in three dimensions. The results can be in general applied to other fields as well.

Numerical Modeling of Surfactant Effects in Interfacial Fluid Dynamics

Surfactants are substances that preferentially accumulate at interfaces between two fluids, altering the local surface tension. An imposed flow can produce a non-uniform distribution of surfactant. In regions of high surfactant concentration the surface tension is low, so the interface offers less resistance to deformation and can become highly curved, allowing very small droplets or bubbles to pinch off. A numerical method to simulate interfacial surfactant mechanics within a volume of fluid method has been developed. To conserve surfactant, the surfactant mass and the interfacial surface area are tracked as the interface evolves, and then the surfactant concentration is reconstructed. The algorithm is coupled to an incompressible flow solver that uses a continuum method to incorporate both the normal and tangential components of the surface tension force into the momentum equation.

Head-on Collision Of Two Equal-sized Drops With Van Der Waals Forces

Drop collision is significant not only in natural processes, such as raindrop formation, but also in various engineering applications, such as chemical separation, spray coating, encapsulation, and drug delivery. In this study, head on collision of two equal-sized drops in a hyperbolic flow is investigated numerically. It is well known that van der Waals forces become important and govern coalescence when the thickness of the fluid film between the two drops falls into the range of several hundreds of Angstroms, 100-1000 A. We have developed two new numerical methods to introduce non-retarded van der Waals forces into the Navier-Stokes equations. An axisymmetric volume of fluid (VOF) method is used to simulate the motion of a drop toward a symmetry plane where it interacts with, and possibly coalesces with, its mirror image. A hyperbolic flow imposed initially and at the domain boundaries drives the motion. In the absence of van der Waals forces, the VOF boundary condition on the symmetry plane determines whether the two drops coalesce or bounce. One method used to include van der Waals forces is to apply the force on the drop as the negative gradient of van der Waals potential between the drops. The other method computes the force in terms of a disjoining pressure in the film which depends on the film thickness. A cut-off is used as the thickness of the film approaches zero to avoid singularity. Comparisons of the results of the two methods at various values of the Hamaker constant are presented. A comparison to results without van der Waals forces is also reported. In future work mesh adaptivity will be used to better resolve the film between the two drops. Transactions on Engineering Sciences vol 42,