The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive mesh generation technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration in agreement with a derived theoretical model, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a master curve is derived when normalizing the mobility for both the carbonate and the sandstone

Prediction and evolution of drop-size distribution for a new ultrasonic atomizer

International audienceComplete modeling of a new ultrasonic atomizer, the Spray On Demand (SOD) printhead, was carried out to enable its optimization. The modeling was focused on various factors, including nozzle vibrations and a theoretical prediction of the SOD drop-size distribution. Assuming that the spray is generated based on Faraday instability, a prediction of the drop-size distribution within the framework of a specific and general Maximum Entropy Formalism (MEF) was developed. This prediction was formulated using the conservation laws of energy and mass, as well as the three-parameter generalized Gamma distribution. After establishing an analytical expression to estimate the Sauter Mean Diameter, a qualitative validation of the model was performed by comparing predictions with experimental measurements of the dropsize distribution. The dynamic model is shown to be sensitive to operating conditions and physical properties of the fluid. The prediction capabilities of the model were found to be adequate, paving the way for optimization of the atomizer. The evolution of the drop-size distribution, under the coalescence effect, was also assessed using a convergent Monte Carlo method to solve the distribution equation. This was formulated in a mass flow algorithm, leading to a more physically relevant distribution

Monte Carlo method for predicting a physically based drop-size distribution evolution of a spray

International audienceWe 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 Hamilton's 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

Generation of a spray on demand using a vibrating micro-channel

International audienc

Theoretical study of a new spray on demand print-head

Abstract—In this paper a theoretical study of a new Spray On Demand print-head (SOD) is performed. This work leads us to study (i) fluid structure/interaction with a vibrating tube conveying fluid, assimilated to a cantilever beam excited by a pointwise piezoactuator (PZA) (ii) fluid film instability with spray generation. After establishing a more general equation of the motion of a vibrating tube filled with fluid using Hamilton’s modified principle, an analytical solution is proposed allowing to determine the volume flow rate generated by the motion of the tube motion. The maximum entropy formalism (MEF) is used to predict the drop size distribution and the Sauter Mean Diameter of the SOD. The coupling of the three-parameter generalized Gamma distribution with physical based-distribution constraints is proposed leading to new predictions in the framework of the MEF formalism

Monte Carlo Method for Physically-Based Drop Size Distribution Evolution

Abstract—We report in this paper the evolution of a physically based drop size distribution coupling the Maximum Entropy Formalism and the Monte Carlo method to solve the coagulation equation. Using the discrete or continuous population balance equation, the Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After proposing a kernel for coalescence, we solve the time dependent drop size distribution equation using a Monte Carlo method which is convergent. The evolution of the drop size distribution shows the effect of spray droplets coalescence

Supercooled Water Droplet Impacting Superhydrophobic Surfaces in the Presence of Cold Air Flow

In the present work, an investigation of stagnation flow imposed on a supercooled water drop in cold environmental conditions was carried out at various air velocities ranging from 0 (i.e., still air) to 10 m/s along with temperature spanning from −10 to −30 °C. The net effect of air flow on the impacting water droplet was investigated by controlling the droplet impact velocity to make it similar with and without air flow. In cold atmospheric conditions with temperatures as low as −30 °C, due to the large increase of both internal and contact line viscosity combined with the presence of ice nucleation mechanisms, supercooled water droplet wetting behavior was systematically affected. Instantaneous pinning for hydrophilic and hydrophobic surfaces was observed when the spread drop reached the maximum spreading diameter (i.e., no recoiling phase). Nevertheless, superhydrophobic surfaces showed a great repellency (e.g., contact time reduction up to 30% where air velocity was increased up to 10 m/s) at temperatures above the critical temperature of heterogeneous ice nucleation (i.e., −24 °C). However, the freezing line of the impacting water droplet was extended up to 2-fold at air velocity up to 10 m/s where substrate temperature was maintained below the aforementioned critical temperature (e.g., −30 °C)

Physically-based drop-size distribution evolution of atomized drops

International audienceWe 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

Numerical simulation of the drop size distribution in a spray

International audienceClassical 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