Direct Numerical Simulation of dilute droplet-laden flows

MSc graduation project of Tjerk Vreeken
Location: Lab. for Aero & Hydrodynamics
Supervisors: M. Kwakkel & W.-P. Breugem
Defense: August 22 2011, 14.00

Project description:

Dispersed multiphase flows are found in a large variety of industrial processes. For example, emulsification of two immiscible fluids in the food industry and mixing of petrochemicals in the oil industry. To be able to simulate such flows in great detail, an accurate and efficient numerical method is necessary. A proven combination is Direct Numerical Simulations (DNS) for the fluid with a front-tracking or front-capturing method for the deformable interfaces. In front-tracking methods the interface is tracked in an explicit way by marker particles; in front-capturing the interface is captured by some implicit marker functions. Up to now, most research on systems with multiple droplets have been done using the front-tracking method [1, 2, 3].

The aim of this project is to investigate the ability of the multiple marker Coupled Level-Set and Volume-of-Fluid (CLSVOF) method [4] to simulate flows with multiple droplets. By using separate marker functions for each interface, numerical (artificial) coalescence is impossible. Interface capturing is achieved by using a Level-Set function as a measure for the distance to the interface, and a Volume-of-Fluid function for mass conservation during interface advection. The CLSVOF method is integrated in a finite-difference method, in which the full Navier-Stokes equations are solved for both fluid phases. The efficiency of the method as used by [4] has been improved in several ways by Kwakkel, which enables the possibility to simulate dilute droplet-laden flows.

In this project, the accuracy and efficiency of the CLSVOF method will be determined for systems with multiple droplets. First, the buoyant rise of an array of droplets in a periodic domain will be studied, which will be validated with [1]. Next, the distribution of equally sized droplets in a laminar vertical channel when the solution is at steady state for both upflow and downflow of the medium will be investigated. These results will be validated with [5]. After extensive validation of the multiple marker CLSVOF method, the method may be applied to study droplets with varying sizes or droplets in a turbulent vertical channel.

[1] A. Esmaeeli and G. Tryggvason, “Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays”, Journal of Fluid Mechanics, vol. 385, pp. 325–358, 2000.
[2] B. Bunner and G. Tryggvason, “Effect of bubble deformation on the properties of bubbly flows,” Journal of Fluid Mechanics, vol. 495, pp. 77–118, 2003.
[3] A. Esmaeeli and G. Tryggvason, “A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number”, Physics of Fluids, vol. 17, no. 9, 093303, 2005.
[4] E. Coyajee and B. Boersma, “Numerical simulation of drop impact on a liquid-liquid interface with a multiple marker front-capturing method”, Journal of Computational Physics, vol. 228, pp. 4444–4467, July 2009.
[5] J. Lu, S. Biswas, and G. Tryggvason, “A DNS study of laminar bubbly flows in a vertical channel”, International Journal of Multiphase Flow, vol. 32, pp. 643–660, June 2006.


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