Arthur Soucemarianadin

The matching of a "one-dimensional" numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up

This paper develops a model for fast filament stretching, thinning, and break-up for Newtonian and non-Newtonian fluids, and the results are compared against experimental data where fast filament relaxation occurs. A 1D approximation was coupled with the arbitrary Lagrangian Eulerian (ALE) formulation to perform simulations that captured both filament thinning and break-up. The modeling accounts for both the initial polymer stretching processes from the precise movement of the two moving pistons and also the subsequent thinning when the pistons are at rest. The simulations were first validated for a low viscosity Newtonian fluid matched to experimental data obtained from a recently developed apparatus, the Cambridge Trimaster. A non-Newtonian polymer fluid, with high frequency linear viscoelastic behavior characterized using a piezoaxial vibrator rheometer, was modeled using both an Oldroyd-B and FENE-CR single-mode constitutive models. The simulations of the filament deformation were compared with experiment. The simulations showed a generally reasonable agreement with both the stretch and subsequent relaxation experimental responses, although the mono mode models used in this paper were unable to capture all of the details for the experimental time evolution relaxation profile of the central filament diameter.

The matching of polymer solution fast filament stretching, relaxation, and break up experimental results with 1D and 2D numerical viscoelastic simulation

This paper is concerned with the comparison of two numerical viscoelastic strategies for predicting the fast filament stretching, relaxation, and break up of low viscosity, weakly elastic polymeric fluids. Experimental data on stretch, relaxation, and breakup were obtained using a Cambridge Trimaster for a Newtonian solvent (diethyl phthalate) and three monodisperse polystyrene polymer solutions. Two numerical codes were tested to simulate the flow numerically. One code used a one-dimensional approximation coupled with the arbitrary Lagrangian–Eulerian approach and the other a two-dimensional axisymmetric approximation for the flow. In both cases, the same constitutive equations and mono and multimode parameter fitting were used, thereby enabling a direct comparison on both codes and their respective fit to the experimental data. Both simulations fitted the experimental data well and surprisingly the one-dimensional code closely matched that of the two-dimensional. In both cases, it was found necessary to...

Simulation of coalescence with stratified sampling

We analyze a stratified strategy for numerical integration and for simulation of coalescence. We use random points which are more evenly distributed in the unit cube than usual pseudo-random numbers. They are constructed so that only one point of the set lies in specific sub-intervals of the cube. This property leads to an improved convergence rate for the variance, when they are used for integrating indicator functions. A bound for the variance is proved and assessed through a numerical experiment. We also devise a Monte Carlo algorithm for the simulation of the coagulation equation. We start with an initial population of particles whose sizes are sampled from some initial distribution, and these sizes evolve according to the coalescence dynamics; the random numbers used are the stratified points described above. The results of some numerical experiments show a smaller variance, when compared to a Monte Carlo simulation using plain random samples.

Numerical simulation of the drop size distribution in a spray

Classical methods of modeling predict a steady-state drop size distribution by using empirical or analytical approaches. In the present analysis, we use the maximum of entropy method as an analytical approach for producing the initial data; then we solve the coagulation equation to approximate the evolution of the drop size distribution. This is done by a quasi-Monte Carlo simulation of the conservation form of the equation. We compare the use of pseudo-random and quasi-random numbers in the simulation. It is shown that the proposed method is able to predict experimental phenomena observed during spray generation.

Monte Carlo Method for Predicting a Physically Based Drop Size Distribution Evolution of a Spray

We report in this paper a method for the evolution of a physically-based drop size distribution of a spray, by coupling the Maximum Entropy Formalism and the Monte Carlo scheme. Using the discrete or continuous population balance equation, a Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After deriving a kernel for coalescence, we solve the time dependent drop size distribution equation using a Monte Carlo method. We apply the method to the spray of a new print-head known as a Spray On Demand (SOD) device; the process exploits ultrasonic spray generation via a Faraday instability where the fluid/structure interaction causing the instability is described by a modified Hamiltons principle. This has led to a physically-based approach for predicting the initial drop size distribution within the framework of the Maximum Entropy Formalism (MEF): a three-parameter generalized Gamma distribution is chosen by using conservation of mass and energy. The calculation of the drop size distribution evolution by Monte Carlo method shows the effect of spray droplets coalescence both on the number-based or volume-based drop size distributions.

Physically-based drop-size distribution evolution of atomized drops

We report in this work the evolution of a physically-based drop size-distribution of atomized drops coupling the Maximum Entropy Formalism (MEF) and the Monte Carlo method. The atomization is performed using a Spray On Demand (SOD) print-head which exploits ultrasonic generation via a Faraday instability. The physically-based distribution is a result of the coupling of a MEF specific formulation and a general Gamma distribution. The prediction of the drop size distribution of the new device is performed. The dynamic model which prediction capability is fairly good is shown to be sensitive to operating conditions, design parameters and physico-chemical properties of the fluid. In order to achieve the drop size-distribution evolution, we solve the distribution equation, reformulated via the mass flow algorithm, using a convergent Monte Carlo Method able to predict coalescence of sprayed droplets.Copyright