arXiv subjects

Omar K. Matar

Publications and source records attributed to Omar K. Matar.

36 records · Page 2Linked to original sources

arXiv2022

The transition to aeration in two-phase mixing in stirred vessels

We consider the mixing of a viscous fluid by the rotation of a pitched blade turbine inside an open, cylindrical tank, with air as the lighter fluid above. To examine the flow and interfacial dynamics, we utilise a highly-parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation strategy. Our numerical technique is designed to capture faithfully complex interfacial deformation, and changes of topology, including interface rupture and dispersed phase coalescence. As shown via transient, three-dimensional direct numerical simulations, the impeller induces the formation of primary vortices that arise in many idealised rotating flows as well as several secondary vortical structures resembling Kelvin-Helmholtz, vortex breakdown, blade tip vortices, and end-wall corner vortices. As the rotation rate increases, a transition to `aeration' is observed when the interface reaches the rotating blades leading to the entrainment of air bubbles into the viscous fluid and the creation of a bubbly, rotating, free surface flow. The mechanisms underlying the aeration transition are probed as are the routes leading to it, which are shown to exhibit a strong dependence on flow history.

physics.flu-dyn↗

arXiv2022

Time-dependent modelling of thin poroelastic films drying on deformable plates

Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. The cantilever experiment allows the stress in a drying film that has been deposited onto a thin plate to be quantified. Mechanical stresses in the film are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Foppl-von Karman (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from $t$ to $t^{1/2}$, in agreement with experiments.

physics.class-ph↗

arXiv2022

Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional CFD application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.

cs.LG↗

arXiv2022

Drying-induced stresses in poroelastic drops on rigid substrates

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a non-monotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localise the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.

cond-mat.soft↗

arXiv2022

Rule-based Evolutionary Bayesian Learning

In our previous work, we introduced the rule-based Bayesian Regression, a methodology that leverages two concepts: (i) Bayesian inference, for the general framework and uncertainty quantification and (ii) rule-based systems for the incorporation of expert knowledge and intuition. The resulting method creates a penalty equivalent to a common Bayesian prior, but it also includes information that typically would not be available within a standard Bayesian context. In this work, we extend the aforementioned methodology with grammatical evolution, a symbolic genetic programming technique that we utilise for automating the rules' derivation. Our motivation is that grammatical evolution can potentially detect patterns from the data with valuable information, equivalent to that of expert knowledge. We illustrate the use of the rule-based Evolutionary Bayesian learning technique by applying it to synthetic as well as real data, and examine the results in terms of point predictions and associated uncertainty.

stat.ML↗

arXiv2022

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

The modelling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of kilometres versus a pipe diameter of just a few inches. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM) which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by using domain decomposition; dimensionality reduction; training a neural network to make predictions for a single subdomain; and by using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we explore several types of autoencoder networks, known for their ability to compress information accurately and compactly. The performance of the autoencoders is assessed on two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1, and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the success of our approach.

physics.flu-dyn↗

arXiv2021

Multiphase flow applications of non-intrusive reduced-order models with Gaussian process emulation

Reduced-order models (ROMs) are computationally inexpensive simplifications of high-fidelity complex ones. Such models can be found in computational fluid dynamics where they can be used to predict the characteristics of multiphase flows. In previous work, we presented a ROM analysis framework that coupled compression techniques, such as autoencoders (AE), with Gaussian process (GP) regression in the latent space. This pairing has significant advantages over the standard encoding-decoding routine, such as the ability to interpolate or extrapolate in the initial conditions' space, which can provide predictions even when simulation data are not available. In this work, we focus on this major advantage and show its effectiveness by performing the pipeline on three multiphase flow applications. We also extend the methodology by using Deep Gaussian Processes (DGP) as the interpolation algorithm and compare the performance of our two variations, as well as another variation from the literature that uses Long short-term memory (LSTM) networks, for the interpolation.

physics.comp-ph↗

arXiv2021

Direct numerical simulations of transient turbulent jets: vortex-interface interactions

The breakup of an interface into a cascade of droplets and their subsequent coalescence is a generic problem of central importance to a large number of industrial settings such as mixing, separations, and combustion. We study the breakup of a liquid jet introduced through a cylindrical nozzle into a stagnant viscous phase via a hybrid interface-tracking/level-set method to account for the surface tension forces in a three-dimensional Cartesian domain. Numerical solutions are obtained for a range of Reynolds (Re) and Weber (We) numbers. We find that the interplay between the azimuthal and streamwise vorticity components leads to different interfacial features and flow regimes in Re-We space. We show that the streamwise vorticity plays a critical role in the development of the three-dimensional instabilities on the jet surface. In the inertia-controlled regime at high Re and We, we expose the details of the spatio-temporal development of the vortical structures affecting the interfacial dynamics. A mushroom-like structure is formed at the leading edge of the jet inducing the generation of a liquid sheet in its interior that undergoes rupture to form droplets. These droplets rotate inside the mushroom structure due to their interaction with the prevailing vortical structures. Additionally, Kelvin-Helmholtz vortices that form near the injection point deform in the streamwise direction to form hairpin vortices, which, in turn, trigger the formation of interfacial lobes in the jet core. The thinning of the lobes induces the creation of holes which expand to form liquid threads that undergo capillary breakup to form droplets.

physics.flu-dyn↗

arXiv2021

Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves

This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to the approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE) although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with an SFC. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.

math.NA↗

arXiv2020

Data-driven surrogate modelling and benchmarking for process equipment

In chemical process engineering, surrogate models of complex systems are often necessary for tasks of domain exploration, sensitivity analysis of the design parameters, and optimization. A suite of computational fluid dynamics (CFD) simulations geared toward chemical process equipment modeling has been developed and validated with experimental results from the literature. Various regression-based active learning strategies are explored with these CFD simulators in-the-loop under the constraints of a limited function evaluation budget. Specifically, five different sampling strategies and five regression techniques are compared, considering a set of four test cases of industrial significance and varying complexity. Gaussian process regression was observed to have a consistently good performance for these applications. The present quantitative study outlines the pros and cons of the different available techniques and highlights the best practices for their adoption. The test cases and tools are available with an open-source license to ensure reproducibility and engage the wider research community in contributing to both the CFD models and developing and benchmarking new improved algorithms tailored to this field.

cs.CE↗

arXiv2020

Numerical simulation, clustering and prediction of multi-component polymer precipitation

Multi-component polymer systems are of interest in organic photovoltaic and drug delivery applications, among others where diverse morphologies influence performance. An improved understanding of morphology classification, driven by composition-informed prediction tools, will aid polymer engineering practice. We use a modified Cahn-Hilliard model to simulate polymer precipitation. Such physics-based models require high-performance computations that prevent rapid prototyping and iteration in engineering settings. To reduce the required computational costs, we apply machine learning techniques for clustering and consequent prediction of the simulated polymer blend images in conjunction with simulations. Integrating ML and simulations in such a manner reduces the number of simulations needed to map out the morphology of polymer blends as a function of input parameters and also generates a data set which can be used by others to this end. We explore dimensionality reduction, via principal component analysis and autoencoder techniques, and analyse the resulting morphology clusters. Supervised machine learning using Gaussian process classification was subsequently used to predict morphology clusters according to species molar fraction and interaction parameter inputs. Manual pattern clustering yielded the best results, but machine learning techniques were able to predict the morphology of polymer blends with $\geq$ 90 $\%$ accuracy.

cs.CE↗

arXiv2020

Three-dimensional dynamics of falling films in the presence of insoluble surfactants

We study the effect of insoluble surfactants on the wave dynamics of vertically-falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (2003). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi two-dimensional shape. In addition, the presence of Marangoni stresses are found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near complete rigidification of the interface is observed.

physics.flu-dyn↗

arXiv2020

Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number

The effect of surfactants on the tail and film dynamics of elongated gas bubbles propagating through circular capillary tubes is investigated by means of an extensive three-dimensional numerical study using a hybrid front-tracking/level-set method. The focus is on the visco-inertial regime, which occurs when the Reynolds number of the flow is much larger than unity. Under these conditions, `clean' bubbles exhibit interface undulations in the proximity of the tail \cite{Magnini_prf_2017}, with an amplitude that increases with the Reynolds number. We perform a systematic analysis of the impact of a wide range of surfactant properties, including elasticity, bulk surfactant concentration, solubility, and diffusivity, on the bubble and flow dynamics in the presence of inertial effects. The results show that the introduction of surfactants is effective in suppressing the tail undulations as they tend to accumulate near the bubble tail. Here, large Marangoni stresses are generated, which lead to a local `rigidification' of the bubble. This effect becomes more pronounced for larger surfactant elasticities and adsorption depths. At reduced surfactant solubility, a thicker rigid film region forms at the bubble rear, where a Couette film flow is established, while undulations still appear at the trailing edge of the downstream `clean' film region. In such conditions, the bubble length becomes an influential parameter, with short bubbles becoming completely rigid.

physics.flu-dyn↗

arXiv2020

Numerical simulations of a falling film on the inner surface of a rotating cylinder

A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterised by the Reynolds, Froude, Weber and Ekman numbers. The variation of the Ekman number ($Ek$), defined to be proportional of the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of $Ek$ values ($0 \leq Ek \leq 484$) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing $Ek$, which leads to a rise in the magnitude of centrifugal forces, produces a stabilising effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilisation, and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally- and centrifugally-driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

physics.flu-dyn↗

arXiv2019

Transport Properties of Water Confined in a Graphene Nanochannel

Equilibrium molecular dynamics simulations are used to investigate the effect of phase transitions on the transport properties of highly-confined water between parallel graphene sheets. An abrupt reduction by several orders of magnitude in the mobility of water is observed in strong confinement, as indicated by reduced diffusivity and increased shear viscosity values. The bulk viscosity, which is related to the resistance to expansion and compression of a substance, is also calculated, showing an enhancement compared to the bulk value for all levels of confinement. An investigation into the phase behaviour of confined water reveals a transition from a liquid monolayer to a rhombic frozen monolayer at nanochannel heights between 6.8-7.8 Å; for larger separations, multilayer liquid water is recovered. It is shown how this phase transition is at the root of the impeded transport.

physics.comp-ph↗

arXiv2017

On the missing link between pressure drop, viscous dissipation, and the turbulent energy spectrum

After decades of experimental, theoretical, and numerical research in fluid dynamics, many aspects of turbulence remain poorly understood. The main reason for this is often attributed to the multiscale nature of turbulent flows, which poses a formidable challenge. There are, however, properties of these flows whose roles and inter-connections have never been clarified fully. In this article, we present a new connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum, which, to the best of our knowledge, has never been established prior to our work. We use this finding to show analytically that viscous dissipation in laminar pipe flows cannot increase the temperature of the fluid, and to also reproduce qualitatively Nikuradse's experimental results involving pressure drops in turbulent flows in rough pipes.

physics.flu-dyn↗

arXiv2017

An Interface-Tracking Technique for Multiphase Flow with Soluble Surfactant

We adapt and extend a formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737-757) to the context of the Level Contour Reconstruction Method (Shin et al. IJNMF 60 (2009) 753-778) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that our adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows. We also demonstrate that this approach applies easily to massively parallel simulations.

cs.CE↗

arXiv2015

Impact of Droplets on Inclined Flowing Liquid Films

The impact of droplets on an inclined falling liquid film is studied experimentally using high-speed imaging. The falling film is created on a flat substrate with controllable thicknesses and flow rates. Droplets with different sizes and speeds are used to study the impact process under various Ohnesorge and Weber numbers, and film Reynolds numbers. A number of phenomena associated with droplet impact are identified and analysed, such as bouncing, partial coalescence, total coalescence, and splashing. The effects of droplet size, speed, as well the film flow rate are studied culminating in the generation of an impact regime map. The analysis of the lubrication force acted on the droplet via the gas layer shows that a higher flow rate in the liquid film produces a larger lubrication force, slows down the drainage process, and increases the probability of droplet bouncing. Our results demonstrate that the flowing film has a profound effect on the droplet impact process and associated phenomena, which are markedly more complex than those accompanying impact on initially quiescent films.

physics.flu-dyn↗