Solitary waves on falling liquid films in the inertia-dominated regime

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development

Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver

A novel hybrid multiphase flow solver has been used to conduct simulations of a vertical plunging liquid jet. This solver combines a multifluid methodology with selective interface sharpening to enable simulation of both the initial jet impingement and the long-time entrained bubble plume phenomena. Models are implemented for variable bubble size capturing and dynamic switching of interface sharpened regions to capture transitions between the initially fully segregated flow types into the dispersed bubbly flow regime. It was found that the solver was able to capture the salient features of the flow phenomena under study and areas for quantitative improvement have been explored and identified. In particular, a population balance approach is employed and detailed calibration of the underlying models with experimental data is required to enable quantitative prediction of bubble size and distribution to capture the transition between segregated and dispersed flow types with greater fidelity

Simulation of Single Vapor Bubble Condensation with Sharp Interface Mass Transfer Model

Pure numerical simulation of phase-change phenomena such as boiling and condensation is challenging, as there is no universal model to calculate the transferred mass in all configurations. Among the existing models, the sharp interface model (Fourier model) seems to be a promising solution. In this study, we investigate the limitation of this model via a comparison of the numerical results with the analytical solution and experimental data. Our study confirms the great importance of the initial thermal boundary layer prescription for a simulation of single bubble condensation. Additionally, we derive a semi-analytical correlation based on energy conservation to estimate the condensing bubble lifetime. This correlation declares that the initial diameter, subcooled temperature, and vapor thermophysical properties determine how long a bubble lasts. The simulations are carried out within the OpenFOAM framework using the VoF method to capture the interface between phases. Our investigation demonstrates that calculation of the curvature of interface with the Contour-Based Reconstruction (CBR) method can suppress the parasitic current up to one order

Fundamental understanding of swirling flow pattern in hydrocyclones

This work is concerned with establishing and validating a physics-based model that describes the swirling flow inside hydrocyclones. The physics is embedded in a Computational Fluid Dynamics (CFD) simulation model whose key features are presented and justified in the paper. Some features are selected in such a way that the model can eventually be used to simulate dense flow inside hydrocyclones. Nevertheless, its underlying physics is here within validated against dilute flow conditions. The model applies a Eulerian multi-fluid modelling approach for fluid–particle turbulent flows, and is computed using the semi-industrial code NEPTUNE_CFD. Simulation results are successfully compared to water split, velocity profiles inside the hydrocyclone and partition function measurements, either produced using our own experimental setup or from the literature. The work finds velocity profiles to be the most discriminating parameter for validation of the physics that describes the swirling flow inside the hydrocyclone. Water split on the other hand shows no relation to the choice of turbulence model and hence cannot be used to validate a mechanistic model of the hydrocyclone. The physics-based model presented here is the first building block towards describing and understanding hydrocyclone flow under dense regime

Effective permeability of an immiscible fluid in porous media determined from its geometric state

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process/path dependent with an underlying dependency on pore structure. For applications, fuel cells to underground $CO_2$ storage, it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modelling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an Artificial Neural Network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. The developed ANN is based on a prescribed set of state variables based on physical insights that predicts the effective permeability of 4,500 unseen pore-scale geometrical states with $R^2 = 0.98$.Comment: 6 Pages, 2 Figures, and Supporting Materia

Direct numerical simulation of bubble-bubble and droplet-droplet interaction using a Surface Thin Film model

This dissertation deals with the simulation of dispersed multiphase flow. The particle-particle and particle-fluid interactions in this class of flows play an important role on the hydrodynamics and fluid transport phenomena that govern the overall flow behaviour. Accurate computational modelling of the particle-particle and particle- fluid interactions is thus required to correctly model the flow. The aim of this study is to use a Direct Numerical Simulation approach based on a smoothed Volume Of Fluid method to model particle-particle interactions in a dispersed multiphase flow at a fundamental level, and employing a surface thin film model, to drastically reduce the computational effort required. A multiscale modelling approach is followed with the smoothed Volume Of Fluid simulation on the particle scale and the surface thin film model simulation on the thin- film scale. The resulting governing equations are the Navier-Stokes equations for an incompressible viscous multiphase Newtonian fluid undergoing laminar and isothermal three-dimensional flow, the interface advection equation and the reduced order surface thin film equation. The model equations are discretized using the Finite Volume Method and implemented into the open source software OpenFOAM®. The numerical solution is obtained by solving the resulting non-linear system of equations implicitly on a structured computational grid on parallel processors using a pressure correction algorithm to converge the pressure at each time step. The study is restricted to gas-liquid systems where particles could either be bubbles or droplets; rigid particles are not considered. The model is tested against experimental results from binary collision of hydrocarbon droplets. Good qualitative numerical results are obtained at a practical computational cost

A hybrid lagrangian-eulerian approach for simulation of bubble dynamics

A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolution: (i) fully resolved simulations (FRS) wherein the bubble dynamics and deformation are completely resolved, and (ii) subgrid, discrete bubble model where the bubbles are not resolved by the computational grid. For fully resolved simulations, a novel approach combining a particle-based, mesh-free technique with a finite-volume flow solver, is developed. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. Interpolation kernel based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Unlike front-tracking methods, connectivity between the marker points is not necessary. For underresolved bubbles, a mixture-theory based Eulerian-Lagrangian approach accounting for volumetric displacements due to bubble motion and size variations is developed. The bubble dynamics is modeled by Rayleigh-Plesset equations using an adaptive timestepping scheme. A detailed verification and validation study of both approaches is performed to test the accuracy of the method on a variety of single and multiple bubble problems to show good predictive capability. Interaction of bubbles with a traveling vortex tube is simulated and compared with experimental data of Sridhar and Katz [1] to show good agreement.http://deepblue.lib.umich.edu/bitstream/2027.42/84270/1/CAV2009-final74.pd

Modeling multiphase flow and substrate deformation in nanoimprint manufacturing systems

Nanopatterns found in nature demonstrate that macroscopic properties of a surface are tied to its nano-scale structure. Tailoring the nanostructure allows those macroscopic surface properties to be engineered. However, a capability-gap in manufacturing technology inhibits mass-production of nanotechnologies based on simple, nanometer-scale surface patterns. This gap represents an opportunity for research and development of nanoimprint lithography (NIL) processes. NIL is a process for replicating patterns by imprinting a fluid layer with a solid, nano-patterned template, after which ultraviolet cure solidifies the fluid resulting in a nano-patterned surface. Although NIL has been demonstrated to replicate pattern features as small as 4 nm, there are significant challenges in using it to produce nanotechnology. Ink-jet deposition methods deliver the small fluid volumes necessary to produce the nanopattern, and drop volumes can be tuned to what the pattern requires. However the drops trap pockets of gas as they merge and fill the template, and due to relatively slow gas dissolution, reduce processing throughput. Capillary forces that arise from the gas-liquid interfaces drive non-uniform gap closure and the resulting variations in residual layer reduces process yield or degrades product performance. This thesis develops reduced-order models for fluid flow and structural mechanics of the imprint process for NIL. Understanding key phenomena of gas trapping and residual layer non-uniformity drives model development to better understand how throughput and yield can be improved. Reynolds lubrication theory, the \textit{disperse} type of multiphase flow, and a lumped-parameter model of dissolution unite to produce a two-phase flow model for NIL simulations of 10,000 drops per $\text{cm}^2$. Qualitative agreement between simulation and experiment provides a modicum of validation of this model for flow in NIL simulations. The two-phase model simulations predicts that both dissolution and viscous resistance affect throughput. The coupling of a reduced-order model for 3D structural mechanics with the two-phase flow model enables simulations of drop merger on a free-span tensioned web. Challenges in improving the structural model lead to formulation of a 2D model for which sources of instability are more easily discovered and understood. Inextensible cylindrical shell theory and lubrication theory combine into a model for the elastohydrodynamics of a rolling-imprint modality of NIL. Foil-bearing theory describes the lubrication layer that forms between a thin, tensioned web moving past another surface. Reproduction of the results of foil-bearing theory validates this coupled model and reveals a highly predictable region of uniformity that provides low shear stress conditions ideal for UV-cure. These results show theoretical limitations that are used to construct a processing window for predicting process feasibility

Numerical Study of Cloud-Sized Droplet Impact and Freezing on Superhydrophobic Surfaces

In-flight icing is a serious meteorological hazard caused by supercooled cloud particles (with an average size of 20–50 µm) that turn into ice as an immediate consequence of impact with an aircraft, and it poses a serious risk to the safety of the aircraft and its passengers. Anti-icing surface treatment is a potential solution to mitigate ice accretion and maintain optimal flying conditions. Superhydrophobic coatings inspired by nature (e.g., lotus leaf) have attracted much attention in recent years due to their excellent water repellent properties. These coatings have been extensively applied on various substrates for self-cleaning, anti-fogging, and anti-corrosive applications. The performance of these coatings depends on the chemical composition and their rough hierarchical surface morphology composed of micron and sub-micron-sized structures. Recently, there has been an increased interest to fabricate superhydrophobic coatings that can repel droplets of cloud-relevant sizes (20–50 µm) before they freeze to the surface in practical flight conditions (i.e., icephobic surfaces). The main goal of this work was to numerically model the hydrodynamic and thermal behaviour of cloud-sized droplets on superhydrophobic surfaces when interacting with micron-sized surface features. Consequently, by correlating the hydrophobicity and the icephobicity of the surface, we found viable solutions to counteract icing and to prevent ice accumulation on critical aerodynamic surfaces. For this purpose, we developed a computational model to analyze the hydrodynamics of the impact of the micro-droplet on a micro-structured superhydrophobic surface under room temperature and freezing (including rapid-cooling and supercooling) conditions. All coding and implementations were carried out in the OpenFOAM platform, which is a collection of open-source C++ libraries for computational continuum mechanics and CFD analysis. Superhydrophobic surfaces were directly modelled as a series of fine, micro-structured arrays with defined cross sections and patterns. Surface chemistry was included in the simulations using a dynamic contact angle model that describes well the hydrodynamics of a micro-droplet on rough surfaces. A multi-region transient solver for incompressible, laminar, multi-phase flow of non-isothermal, non-Newtonian fluids with conjugate heat transfer boundary conditions between solid and fluid regions was developed to simulate both the dynamics of the micro-droplet impact on the substrate and the associated heat transfer inside the droplet and the solid bulk simultaneously. In addition, a phase change (freezing) model was added to capture the onset of ice formation and freezing front of the liquid micro-droplet. The computational model was validated using experimental data reported in the literature. In addition, an analytical model was derived using the balance of energy before impact and at the maximum spreading stage, which we found to be in good agreement with the data obtained from simulations. Since aluminum (Al) is the base material used in aerospace industries, the thermo-physical properties of aluminum were extensively used in our simulations. Comparing laser-patterned aluminum substrates with a ceramic base composite material that has a low thermal diffusivity (such as titanium-dioxide), we showed that the onset of icing was significantly delayed on the ceramic-based substrate, as the droplet detached before freezing to the surface. Finally, a freezing model for the supercooled water droplet based on classical nucleation theory was developed. The model is an approximation for a supercooled droplet of the recalescence step, which was assumed to be initiated by heterogeneous nucleation from the substrate. This research extended our knowledge about the hydrodynamic and freezing mechanisms of a micro-droplet on superhydrophobic surfaces. The developed solvers can serve as a design tool to engineer the roughness and thermo-physical properties of superhydrophobic coatings to prevent the freezing of cloud-sized droplets in practical flight conditions

CFD modelling of flow-induced vibration under multiphase flow regimes.

Internal multiphase flow-induced vibration (MFIV) in pipe bends poses serious problems in oil and gas, nuclear and chemical flow systems. The problems include: high amplitude displacement of the pipe structure due to resonance; fatigue failure due to excessive cyclic stress, induced by fluctuating forces; and structural wear, due to the relative motion of the pipe and its support. Current industry guidelines are based on single phase flows, while the few existing MFIV models in literature are based on small scale laboratory experiments, which do not completely address the complexities in multiphase flows, or the differing multiphase flow mechanisms between small and large pipes. Therefore, numerical simulations of two-phase flow induced fluctuating forces, stresses, displacements and natural frequencies at 900 bends have been carried out, in order to investigate the characteristics of MFIV in pipes of 0.0525m, 0.1016m and 0.2032m internal diameters (I.D.). An integrated high-fidelity CFD and FEA-based numerical-analytical modelling framework was applied, to predict the defining characteristics of MFIV in the pipes. The CFD simulations of thirty-five cases of slug, cap bubbly and churn turbulent flow-induced fluctuations at the bends were carried out using the volume of fluid (VOF) model for the two-phase flows, and th