arXiv subjects

Ali Mani

Publications and source records attributed to Ali Mani.

At least 37 records · Page 2Linked to original sources

arXiv2023

Effects of operator nonlocality on closures for multicomponent reactive flows based on dispersion analysis

Algebraic closure models with spatially nonlocal operators that are associated with both unresolved advective transport and nonlinear reaction terms in a Reynolds-averaged Navier-Stokes context are presented in this work. In particular, a system of two species subject to binary reaction and transport by advection and diffusion are examined by expanding upon analysis originally developed for binary reactions in the context of Taylor dispersion of scalars. This work extends model forms from weakly-nonlinear extensions of that dispersion theory and the role of nonlocality in the presence of reactions is studied and captured by analytic expressions. These expressions can be incorporated into an eddy diffusivity matrix that explicitly capture the influence of chemical kinetics and flow conditions on the closure operators and we demonstrate that the model form derived in a laminar context can be directly translated to an analogous setup in homogeneous isotropic turbulence, which has implications as a subgrid scale model. We show that this framework can improve prediction of mean quantities compared to previous purely local results, but does not fully close unresolved terms.

physics.flu-dyn↗

arXiv2022

Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods

Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order equation, allowed for the derivation of surface tension models through thermodynamic arguments. In contrast, the second-order phase field models do not follow a known energy law, and deriving a surface tension term for these models using thermodynamic arguments is not straightforward. In this work, we justify that the energy-based surface tension model from the Cahn-Hilliard context can be adopted for second-order phase field models as well and assess its performance. We test the surface tension model on three different second-order phase field equations; the conservative diffuse interface model of Chiu and Lin [1], and two models based on the modified Allen-Cahn equation introduced by Sun and Beckermann [2]. Additionally, we draw the connection between the energy-based model with a localized variation of the continuum surface force (CSF) model. Using canonical tests, we illustrate the lower magnitude of spurious currents, better accuracy, and superior convergence properties of the energy-based surface tension model compared to the CSF model, which is a popular choice used in conjunction with second-order phase field methods, and the localized CSF model. Importantly, in terms of computational expense and parallel efficiency, the energy-based model incurs no penalty compared to the CSF models.

physics.flu-dyn↗

arXiv2022

Direct 3D observation and unraveling of electroconvection phenomena during concentration polarization at ion-exchange membranes

A decade ago, two-dimensional microscopic flow visualization proved the theoretically predicted existence of electroconvection roles as well as their decisive role in destabilizing the concentration polarization layer at ion-selective fluid/membrane interfaces. Electroconvection induces chaotic flow vortices injecting volume having bulk concentration into the ion-depleted diffusion layer at the interface. Experimental quantification of these important flow patterns have so far only been carried out in 2D. Numerical direct simulations suggest 3D features, yet experimental proof is lacking. 3D simulations are also limited in covering extended spacial and temporal scales. This study presents a new comprehensive experimental method for the time-resolved recording of the 3D electroconvective velocity field near a cation-exchange membrane. For the first time, the spatio-temporal velocity field can be visualized in 3D at multiples of the overlimiting current density. In contrast to today's simulations, these experiments cover length and time scales typical for actual electrodialytic membrane processes. We visualize coherent vortex structures and reveal the changes in the velocity field and its statistics during the transition from vortex rolls to vortex rings with increasing current density. The transition is characterized by changes in the rotational direction, mean square velocity, and temporal energy spectrum with only little influence on the spatial spectrum. These findings indicate a more significant impact of EC's structural change on the mean square velocities and temporal spectra than on the spatial spectra. This knowledge is a prerequisite for engineering ion-selective surfaces that will enable the operation of electrically driven processes beyond the diffusion-limited Nernst regime.

physics.flu-dyn↗

arXiv2022

Eddy diffusivity in homogeneous isotropic turbulence

We use the recently developed Macroscopic Forcing Method [Mani and Park, Physical Review Fluids, 6:054607, 2021] to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in incompressible homogeneous isotropic turbulence. For scales larger than the energy containing eddies, eddy diffusivity is found to be constant and consistent with the Boussinesq approximation. However for small scales eddy diffusivity is found to vanish inversely proportional to the wavenumber. Behavior at all scales is reasonably captured by a non-local eddy diffusivity operator modeled as $D/\sqrt{\mathcal{I}-l^2\nabla^2}$, where $D$ is the eddy diffusivity in the Boussinesq limit, and $l$ is a constant on the order of the large-eddy length. These results present the first direct measurement of eddy diffusivity in turbulence with implications in turbulence modeling.

physics.flu-dyn↗

arXiv2021

Closures for Multi-Component Reacting Flows based on Dispersion Analysis

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters (Turbulent Combustion, 2000) and based on work by Corrsin (JFM, vol. 11, p.407-416) beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly-nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of non-reactive species and linear reactions, respectively.

physics.flu-dyn↗

arXiv2021

On the convergence of statistics in simulations of stationary turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: 1) What is the appropriate range of sampling frequency in large eddy time units? and 2) How long should a simulation be performed in terms of large eddy time so that the statistical error could be reliably reported. Our results indicate that proper sampling frequency is on the order of 10 large eddy time scale. More importantly, we find that reliable reporting of statistical errors requires simulation durations orders of magnitude longer than typically performed. Our observations of sampling frequency for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

physics.flu-dyn↗

arXiv2021

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook (2007), Subramaniam et al., (2018), and Adler and Lele (2019), in which artificial diffusion terms are added to the conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., (2010) and Tiwari et al., (2013), in which the diffusion and sharpening terms (together called regularization terms) are added to the conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., (2020), in which the regularization terms are added to the conservation equations. The primary objective of this work is to compare these three methods in terms of their ability to maintain: constant interface thickness; the conservation property; and accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer-Meshkov instability of a copper-aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. This is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

physics.comp-ph↗

arXiv2021

Macroscopic forcing method: a tool for turbulence modeling and analysis of closures

This study presents a numerical procedure, which we call the macroscopic forcing method (MFM), which reveals the differential operators acting on the mean fields of quantities transported by underlying fluctuating flows. Specifically, MFM can precisely determine the eddy diffusivity operator, or more broadly said, it can reveal differential operators associated with turbulence closure for scalar and momentum transport. We present this methodology by considering canonical problems with increasing complexity. Starting from the well-known problem of dispersion of passive scalars by parallel flows we elucidate the basic steps in quantitative determination of the eddy viscosity operators using MFM. Utilizing the operator representation in Fourier space, we obtain a stand-alone compact analytical operator that can accurately capture the nonlocal mixing effects. Furthermore, a cost-effective generalization of MFM for analysis of nonhomogeneous and wall-bounded flows is developed and is comprehensively discussed through a demonstrative example. Extension of MFM for analysis of momentum transport is theoretically constructed through the introduction of a generalized momentum transport equation. We show that closure operators obtained through MFM analysis of this equation provide the exact RANS solutions obtained through averaging of the Navier-Stokes equation. We introduce MFM as an effective tool for quantitative understanding of non-Boussinesq effects and assessment of model forms in turbulence closures, particularly, the effects associated with anisotropy and nonlocality of macroscopic mixing.

physics.flu-dyn↗

arXiv2021

Deionization Shocks in Crossflow

Shock electrodialysis is a recently developed electrochemical water treatment method which shows promise for water deionization and ionic separations. Although simple models and scaling laws have been proposed, a predictive theory has not yet emerged to fit experimental data and enable system design. Here, we extend and analyze existing "leaky membrane" models for the canonical case of a steady shock in cross flow, as in recent experimental prototypes. Two-dimensional numerical solutions are compared with analytical boundary-layer approximations and experimental data. The boundary-layer theory accurately reproduces the simulation results for desalination, and both models predict the data collapse of the desalination factor with dimensionless current, scaled to the incoming convective flux of cations. The numerical simulation also predicts the water recovery increase with current. Nevertheless, both approaches cannot quantitatively fit the transition from normal to over-limiting current, which suggests gaps in our understanding of extreme electrokinetic phenomena in porous media.

physics.flu-dyn↗

arXiv2020

Modeling transport of scalars in two-phase flows with a diffuse-interface method

In this article, we propose a novel scalar-transport model for the simulation of scalar quantities in two-phase flows with a phase-field method (diffuse-interface method). In a two-phase flow, the scalar quantities typically have disparate properties in two phases, which results in effective confinement of the scalar quantities in one of the phases, in the time scales of interest. This confinement of the scalars lead to the formation of sharp gradients of the scalar concentration values at the interface, presenting a serious challenge for its numerical simulations. To overcome this challenge, we propose a model for the transport of scalars. The model is discretized using a central-difference scheme, which leads to a non-dissipative implementation that is crucial for the simulation of turbulent flows. Furthermore, the provable strengths of the proposed model are: (a) the model maintains the positivity property of the scalar concentration field, a physical realizability requirement for the simulation of scalars, when the proposed criterion is satisfied, (b) the proposed model is such that the transport of the scalar concentration field is consistent with the transport of the volume fraction field, which results in the enforcement of the effective zero-flux boundary condition for the scalar at the interface; and therefore, prevents the artificial numerical diffusion of the scalar across the interface. Finally, we present numerical simulations using the proposed model in a wide range of two-phase flow regimes, spanning laminar to turbulent flows; and assess: the accuracy and robustness of the model, the validity of the positivity property of the scalar concentration field, and the enforcement of the zero-flux boundary condition for the scalar at the interface.

physics.flu-dyn↗

arXiv2020

Time-Accurate and highly-Stable Explicit operators for stiff differential equations

Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical stiffness originating from convection, diffusion and source terms (typically related to reaction) can be handled by a set of predefined Time-Accurate and highly-Stable Explicit (TASE) operators in a unified framework. The proposed TASE operators act as preconditioners on the stiff terms and can be deployed to any existing explicit time-marching methods straightforwardly. The resulting time integration methods remain the original explicit time-marching schemes, yet with nearly unconditional stability. The TASE operators can be designed to be arbitrarily high-order accurate with Richardson extrapolation such that the accuracy order of original explicit time-marching method is preserved. Theoretical analyses and stability diagrams show that the $s$-stages $s$th-order explicit Runge-Kutta (RK) methods are unconditionally stable when preconditioned by the TASE operators with order $p \leq s$ and $p \leq 2$. On the other hand, the $s$th-order RK methods preconditioned by the TASE operators with order of $p \leq s$ and $p > 2$ are nearly unconditionally stable. The only free parameter in TASE operators can be determined a priori based on stability arguments. Unlike classical implicit methods, the TASE methodology allows for solving non-linear problems with arbitrary order without requiring solving a nonlinear system of equations. A set of benchmark problems with strong stiffness is simulated to assess the performance of the TASE method. Numerical results suggest that the proposed framework preserves the high-order accuracy of the explicit time-marching methods with very-large time steps for all the considered cases.

math.NA↗

arXiv2020

A conservative diffuse-interface method for compressible two-phase flows

In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the system. We use the baseline five-equation model and propose interface-regularization (diffusion--sharpening) terms in such a way that the resulting model maintains the conservative property of the underlying baseline model; and lets us use a central-difference scheme for the discretization of all the operators in the model, which leads to a non-dissipative implementation that is crucial for the simulation of turbulent flows and acoustics. Furthermore, the provable strengths of the proposed model are: (a) the model maintains the boundedness property of the volume fraction field, which is a physical realizability requirement for the simulation of two-phase flows, (b) the proposed model is such that the transport of volume fraction field inherently satisfies the total-variation-diminishing property without having to add any flux limiters that destroy the non-dissipative nature of the scheme, (c) the proposed interface-regularization terms in the model do not spuriously contribute to the kinetic energy of the system and therefore do not affect the non-linear stability of the numerical simulation, and (d) the model is consistent with the second law of thermodynamics. Finally, we present numerical simulations using the model and assess (a) the accuracy of evolution of the interface shape, (b) implementation of surface tension effects, (c) propagation of acoustics and their interaction with material interfaces, (d) the accuracy and robustness of the numerical scheme for simulation of complex high-Reynolds-number flows, and (e) performance and scalability of the method.

physics.comp-ph↗

arXiv2019

Consistent, energy-conserving momentum transport for simulations of two-phase flows using the phase field equations

Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving momentum transport scheme in the context of a second order mass-conserving phase field method. This is achieved by (1) accounting for the mass flux associated with the right-hand-side of the phase field equation in the convective flux of the conservative form of the momentum transport equation---a correction absent in previous phase field simulations (2) utilization of non-dissipative spatial discretization. We demonstrate accuracy and robustness improvements from our proposed scheme via numerical tests, including a turbulent case of a water jet subject to air cross-flow. Our proposed modifications to the momentum transport equation can be quite readily extended to general conservative phase field methods. Additionally, in the framework of this phase field method, we present a free energy-based surface tension force calculation scheme. This scheme, which significantly reduces spurious currents, is based on a general paradigm that can also be extended to other two-phase flow methods.

physics.flu-dyn↗

arXiv2019

Secondary Concentration Plateau and Formation of Flow Stagnation by Ion Concentration Polarization in Microchannels

Ion transport in perm-selective media has been extensively investigated in recent years owing to its applications in advancements of fundamental understanding of nanoscale electrokinetics as well as innovative engineering applications. A key phenomenon in this context is ion concentration polarization (ICP) that occurs near perm-selective nanoporous membranes or nanochannels under dc bias. In classical settings, involving voltage-driven transport of ions through perm-selective membranes, concentration polarization is well understood as formation of steep concentration drop to reach near zero concentration (depletion layer) at the anodic side of cation-selective membranes. In contrast to this classical description, we demonstrate here that when ICP is driven in a microchannel and coupled with electroosmotic flows a long-tailed fluorescent layer in front of diffusion layer is formed, which can be characterized as an additional plateau in the concentration profile. Using a micro/nanofluidic platform, in situ visualizations, and local concentration measurements by microelectrode arrays we quantify that this plateau layer has a concentration of 60 % of bulk electrolyte concentration, regardless of the bulk concentration itself. Using a mathematical analysis of conservation laws for flow, charge, and salt, we demonstrate that this plateau region is related to the formation of a flow stagnation point due to the competition between electro-osmotic and induced pressure driven flows. Consistent with the experiments, this analysis predicts the plateau concentration to be 60% of the bulk electrolyte. Thus, this plateau concentration region completes the picture of ICP in microchannels which has drawn significant attention from the fields of electrokinetics and micro/nanofluidics.

physics.flu-dyn↗

arXiv2019

Overlimiting current in non-uniform arrays of microchannels

Overlimiting current (OLC) through electrolytes interfaced with perm-selective membranes has been extensively researched in recent years for understanding the fundamental mechanisms of transport and developing efficient applications from electrochemistry to sample analysis and separation. Predominant mechanisms responsible for OLC include surface conduction, convection by electro-osmotic flow, and electro-osmotic instability depending on input parameters such as surface charge and geometric constrictions. This work studies how a network of microchannels in a non-uniform array, which mimicks a natural pore configuration, can contribute to OLC. To this end, micro/nanofluidic devices are fabricated with arrays of parallel microchannels with non-uniform size distributions. All cases maintain the same surface and bulk conduction to allow probing the sensitivity only by the non-uniformity of the channels. Both experimental and theoretical current-voltage relations demonstrate that OLCs increase with increasing non-uniformity. Furthermore, the visualization of internal recirculating flows indicates that the non-uniform arrays induce flow loops across the network enhancing advective transport. These evidences confirm a new driving mechanism of OLC, inspired by natural micro/nanoporous materials with random geometric structure. Therefore, this result can advance not only the fundamental understanding of nanoelectrokinetics but also the design rule of engineering applications of electrochemical membrane.

physics.app-ph↗

arXiv2019

A conservative and non-dissipative Eulerian formulation for the simulation of soft solids in fluids

Soft solids in fluids find wide range of applications in science and engineering, especially in the study of biological tissues and membranes. In this study, an Eulerian finite volume approach has been developed to simulate fully resolved incompressible hyperelastic solids immersed in a fluid. We have adopted the recently developed reference map technique (RMT) by Valkov et. al (J. Appl. Mech., 82, 2015) and assessed multiple improvements for this approach.These modifications maintain the numerical robustness of the solver and allow the simulations without any artificial viscosity in the solid regions (to stabilize the solver). This has also resulted in eliminating the striations ("wrinkles") of the fluid-solid interface that was seen before and hence obviates the need for any additional routines to achieve a smooth interface. An approximate projection method has been used to project the velocity field onto a divergence free field. Cost and accuracy improvements of the modifications on the method have also been discussed.

physics.comp-ph↗

arXiv2019

A modal analysis of the behavior of inertial particles in turbulence

The clustering of small heavy inertial particles subjected to Stokes drag in turbulence is known to be minimal at small and large Stokes number and substantial at $\rm St = \mathcal O(1)$. This non-monotonic trend, which has been shown computationally and experimentally, is yet to be explained analytically. In this study, we obtain an analytical expression for the Lyapunov exponents that quantitatively predicts this trend. The sum of the exponents, which is the normalized rate of change of the signed-volume of a small cloud of particles, is correctly predicted to be negative and positive at small and large Stokes numbers, respectively, asymptoting to $τQ$ as $τ\to 0$ and $τ^{-1/2} |Q|^{1/4}$ as $τ\to \infty$, where $τ$ is the particle relaxation time and $Q(τ)$ is the difference between the norm of the rotation- and strain-rate tensors computed along the particle trajectory. Additionally, the trajectory crossing is predicted only in hyperbolic flows where $Q<0$ for sufficiently inertial particles with a $τ$ that scales with $|Q|^{-1/2}$. Following the onset of crossovers, a transition from clustering to dispersion is predicted correctly. We show these behaviors are not unique to three-dimensional isotropic turbulence and can be reproduced closely by a one-dimensional mono-harmonic flow, which appears as a fundamental canonical problem in the study of particle clustering. Analysis of this one-dimensional canonical flow shows that the rate of clustering, quantified as the product of the Lyapunov exponent and particle relaxation time, is bounded by $-1/2$, behaving with extreme nonlinearity in the hyperbolic flows and always remaining positive in the elliptic flows. These findings, which are stemmed from our analysis, are corroborated by the direct numerical simulations.

physics.flu-dyn↗

arXiv2019

Impact of Network Heterogenity on Nonlinear Electrokinetic Transport in Porous Media

We present a numerical study of nonlinear electrokinetic transport in porous media, focusing on the role of heterogeneity in a porous microstructure on ion concentration polarization and over-limiting current. For simplicity, the porous medium is modeled as a network of long, thin charged cylindrical pores, each governed by one-dimensional effective transport equations. For weak surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by electroconvection via internally induced flow loops, which is not properly captured by existing homogenized models. We systematically vary the topology and "accessivity" of the pore network and compare with simulations of traditional homogenized parallel-pore (capillary-bundle) models, in order to reveal the effects of regular and hierarchical connectivity. Our computational framework sheds light on the complex physics of nonlinear electrokinetic phenomena in microstructures and may be used to design porous media for applications, such as water desalination and purification by shock electrodialysis.

physics.flu-dyn↗