L.E. Patruno

Finite-difference stable stencils based on least-square quadric fitting

In this paper a procedure to obtain new finite difference stencils is given. We investigate the particular branch of cases where the order of the finite difference stencil is lower than the amount of grid points. New finite difference stencils are obtained and compared with traditional ones from literature. General properties and advantages of the proposed stencils are investigated, in particular the improvements obtained in stability when solving ill-posed problems.

Modelling and Simulation of Droplet Distribution from Entrained Liquid Film in Gas-Liquid Systems

The description of the interaction between phases in multiphase flow is of major interest for the oil and gas industry. The presence of droplets in the gas phase can produce erosion and breakdown of equipment. The use of conventional separators may not be enough since new droplets may be created from entrained liquid films at the walls. Previous work [ANSSZZ04] presented possible frameworks to describe the interaction between one sized droplets and wall films by using a two dimensional (time plus space) transport equation for the liquid film. This work presents a possible framework to model the droplet-film interaction using a population balance type of equation in which the mathematical formulation is

Analysis of breakage kernels for population balance modelling

\left\{ \begin{gathered} \tfrac{\partial } {{\partial z}}u_f f_f (z) = \int_{\xi _{min} }^{\xi _{max} } {\lambda (\hat \xi )f_d (\hat \xi ,z)d\hat \xi - \beta f_f (z) in \Omega _z = (z_{min} ,z_{max} )} \hfill \\ \tfrac{\partial } {{\partial z}}u_d f_d (\xi ,z) = - \lambda (\xi )f_d (\xi ,z) + \chi (\xi )\beta f_f (z) in \Omega = (\xi _{min} ,\xi _{max} ) \times \Omega z \hfill \\ f_d (\xi ,z) = f_d^0 (\xi ) on \Gamma _\xi = [\xi _{\min } ,\xi _{\max } ] \hfill \\ f_f (z) = f_f^0 on \Gamma _z = [z = z_{\max } ] \hfill \\ \end{gathered} \right.

Experimental and Numerical Investigations of Liquid Fragmentation and Droplet Generation for Gas Processing at High Pressures

(1) where f d is the droplet concentration, f f is the film height, u d and u f are the corresponding velocities, γ is the deposition rate, β is the entrainment rate and η is the entrainment spectrum. The variable ξ is the droplet mass and z is the position along the pipe.