Shankar Subramaniam

• Iowa State University

Solvent removal by thermal drying of granular mixtures is encountered in many industrial operations. A mixture model that treats the granular solid and the liquid solvent along with any interstitial gas phase as a single phase, is a useful first approximation to estimate the time required to heat the system to the wet-bulb temperature at which the...

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modelling the neighbour-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration–velocity distribution function 𝑃(𝑣′,𝑎′;𝑡...

A mixing index based on solid volume fraction fields is developed for gas‐solid flows. Conventional mixing indices are based on particle realizations of granular mixing and are applicable to experimental data or discrete element method simulations. However, these indices cannot be used as‐is for multifluid models, and an index for characterizing mi...

Standard Eulerian–Lagrangian (EL) methods generally employ drag force models that only represent the mean hydrodynamic force acting upon a particle-laden suspension. Consequently, higher-order drag force statistics, arising from neighbor-induced flow perturbations, are not accounted for; this has implications on the predictions for particle velocit...

Infectious respiratory diseases such as the current COVID-19 have caused public health crises and interfered with social activity. Given the complexity of these novel infectious diseases, their dynamic nature, along with rapid changes in social and occupational environments, technology, and means of interpersonal interaction, respiratory protective...

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modeling the neighbor-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration-velocity distribution function P(v',a';t)....

A three-dimensional (3D) multi-segment hand-specific thermoregulation model was developed as a fundamental tool for spatial and temporal skin temperature prediction. Cold-induced vasodilation in fingers was simulated by superimposing symmetrical triangular waveforms onto the basal blood flow. The model used realistic anatomical, physiological, and...

Standard Eulerian--Lagrangian (EL) methods generally employ drag force models that only represent the mean hydrodynamic force acting upon a particle-laden suspension. Consequently, higher-order drag force statistics, arising from neighbor-induced flow perturbations, are not accounted for; with implications on predictions for particle velocity varia...

Creating next-generation pyrotechnic emitters capable of dynamically controllable light output requires a paradigm shift away from emission control via formulation. This work demonstrates the ability to modulate light emission intensity of a pyrotechnic flame with 2.46 GHz microwave energy within a multimodal cavity. Stoichiometric mixtures of thre...

The objective of this study is to understand the dynamics of freely evolving particle suspensions over a wide range of particle-to-fluid density ratios. The dynamics of particle suspensions are characterized by the average momentum equation, where the dominant contribution to the average momentum transfer between particles and fluid is the average...

Granular mixing is important to many industries, but the mixing process is still poorly understood. In this study, motion of a single intruder particle introduced in a shallow bed of native particles was investigated. A parametric investigation was carried out to quantify the effects of initial intruder particle location, blade speed, and density d...

Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water, and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called particle-laden suspensions involving nondeforming particles in a carrier fluid. The hydrodynamic interactions in these flo...

This study provides a detailed account of stochastic approaches that may be utilized in Eulerian-Lagrangian simulations to account for neighbour-induced drag force fluctuations. The frameworks examined here correspond to Langevin equations for the particle position (PL), particle velocity (VL) and fluctuating drag force (FL). Rigorous derivations o...

Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called particle-laden suspensions involving non-deforming particles in a carrier fluid. The hydrodynamic interactions in these flo...

Fully resolved simulation of flows with buoyant particles is a challenging problem since buoyant particles are lighter than the surrounding fluid, and as a result, the two phases are strongly coupled together. In this work, the virtual force stabilization technique introduced by Schwarz et al. [Schwarz, S., Kempe, T., & Fröhlich, J. (2015). A tempo...

Screw feeders and conveyors are mainly used in industries like minerals, agriculture, chemicals, pharmaceuticals, pigments, plastics, cement, sands, and food processing for transporting and mixing the granular materials. The system looks mechanically simple but the physics of particle transport in the system is complex; problems like bridging and b...

The Eulerian–Eulerian two-fluid model is widely used for computational fluid dynamics simulations of gas–solid flows. For non-isothermal flows, the averaged conservation equations solved in the two-fluid model require closures for drag, gas–solid heat transfer, pseudo-turbulent velocity fluctuations and the pseudo-turbulent heat flux (PTHF). Howeve...

Velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation. The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for $\Re_m=20$ and a wide range of dispersed phase volume fractions...

We use particle-resolved direct numerical simulation (PR-DNS) as a model-free physics-based numerical approach to validate particle acceleration modelling in gas-solid suspensions. To isolate the effect of the particle acceleration model, we focus on point-particle direct numerical simulation (PP-DNS) of a collision-free dilute suspension with soli...

Immersed cohesive particles that aggregate under shear are commonly encountered in chemical engineering contexts. This work concerns the rheology of a particular set of systems, cement pastes, that have been difficult to treat from first-principles. In practice, these pastes exhibit large polydispersity with micron to millimeter sized particles, co...

The rheology of homogeneous cohesive granular assemblies under shear at moderate volume fractions is investigated using the discrete element method for both frictionless and frictional granules. A transition in rheology from inertial to quasistatic scaling is observed at volume fractions below the jamming point of noncohesive systems, which is a fu...

In this work, a detailed comparison of velocity fields obtained from Particle Image Velocimetry (PIV) experimental measurement and Particle-Resolved Direct Numerical Simulation (PR-DNS) of flow inside a square duct around a train of five spherical particles at a Reynolds number of 100 based on the particle diameter Dp for two different particle sep...

This work aims to study the interaction of a shock wave with a cloud of particles to quantify flow unsteadiness and velocity fluctuations using particle-resolved direct numerical simulation (PR-DNS). Three cases are studied, with each case revealing one aspect of the intricate flow phenomena involved in this interaction. The unsteady interaction of...

The goal of modeling dispersed multiphase flows is to predict spatial distributions of the volume fraction, velocities and other properties of interest of the dispersed and continuous phases in geometries of practical interest. In this chapter we summarize key advances that have enabled progress towards this goal by starting with the development of...

Most gas–solid flows encountered in nature and industrial applications are polydisperse, and the segregation or mixing of particle classes in polydisperse gas–solid flows is a phenomenon of great practical importance. A statistically homogeneous gas–solid flow with a bidisperse distribution (in size or density) of particles is a canonical represent...

We present an in-depth study on the restitution coefficient and sticking behavior of two models commonly used in the Discrete Element Method (DEM) community for simulating fine cohesive powders. The cohesion in this study is the result of the van der Waals force and is added to commonly used contact force models. We obtain a collapse of the restitu...

A constitutive model is developed to capture the complex rheological behavior of dense granular flows (solid volume fraction ranging from 0.45 to 0.62) in the quasi-static, intermediate, and inertial regimes. The principal contribution of this work is the development of a contact stress model (CSM) that is a statistical closure for the average cont...

Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. ( J. Fluid Mech. , vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flu...

The slip velocity between particle size classes in a homogeneous bidisperse gas-solid flow is quantified using particle-resolved direct numerical simulation (PR-DNS). This slip velocity is the key characteristic of size segregation in industrial devices. The ability of current gas-particle drag models to predict this slip velocity is examined by si...

Particle-resolved direct numerical simulation (PR-DNS) is used to quantify the drag force on clustered particle configurations over the solid phase volume fraction range of and the mean slip Reynolds number range of . The particle configurations and flow parameters correspond to gas-solid suspensions of Geldart A particles in which formation of clu...

Cement is the most widely used man-made material. In slurry form and in absence of rheological modifiers, cement is a dense suspension of attractive microparticles. At even small shear rates, e.g. 10s^-1, thermal effects are small, producing aggregated systems and with Peclet numbers O(10^4). Such athermal attractive systems are interesting from th...

The acceleration of an inertial particle in a gas–solid flow arises from the particle’s interaction with the gas and from interparticle interactions such as collisions. Analytical treatments to derive a particle acceleration model are difficult outside the Stokes flow regime, but for moderate Reynolds numbers (based on the mean slip velocity betwee...

The stability of a statistically homogeneous gas-solid flow is still incompletely understood in spite of several advances in our understanding of this fundamental problem. The stability of a homogeneous gas-solid flow is closely related to the formation of spatial patterns in the particle field, i.e. clusters. Although the precise definition of sta...

The purpose of this work is to develop gas-solid heat transfer models using Particle-resolved Direct Numerical Simulations (PR-DNS). Gas-solid heat transfer in steady flow through a homogeneous fixed assembly of monodisperse spherical particles is simulated using the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PURe...

An analytical framework for calculating the filtration efficiency of polydisperse aerosols in a granular bed is developed for cases where inertial impaction and interception are the principal filtration mechanisms. This framework is used to develop a model for the polydisperse single-collector efficiency from monodisperse single-collector efficienc...

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pse...

We treat the case of an undriven gas of inelastic hard-spheres with short-ranged attractive potentials via an extension of the pseudo-Liouville operator formalism. New evolution equations for the granular temperature and coordination number are obtained. The granular temperature exhibits deviation from both Haff’s law and the case of long-ranged po...

The characteristic features of sprays pose unique challenges to multiphase flow methods that are used to model and simulate their behavior. This article reviews the principal modeling challenges posed by sprays, and discusses the capabilities of different modeling approaches by classifying them according to the basis for their statistical represent...

Heat transfer is important in many gas-solid flow applications such as fluidized beds that are used for biomass fast pyrolysis or CO2 capture using dry sorbents. Current computational fluid dynamics models solve evolution equations for the mean fluid and solid temperature that contain unclosed terms such as the average gas-solid heat transfer rate...

Examples of microparticle suspensions occur frequently in both industry and nature. For example, concrete reigns as the most abundant man made material in existence. Yet, the rheology of its key ingredient, cement ­- a microparticle suspension -­ , remains poorly understood. Indeed, the simulation of microparticle suspensions, much more simple than...

The presented work is focused on developing closure models for simulation of multiphase flow using multi-fluid models. In the two-fluid model, pseudo turbulent terms appear in both the heat transfer term in the energy equation and the mass transfer term in the species equation. These terms are often neglected due to lack of information, but recent...

Aggregation of colloidal particles under shear is studied in model systems using a Langevin dynamics model with an improved interparticle interaction potential. In the absence of shear, aggregates that form are characterized by compact structure at small scales and ramified structure at larger scales. This confirms the structural crossover mechanis...

Lagrangian point-particle models are widely used to model particle-laden flows in Reynolds Average Navier-Stokes (RANS) simulation, Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) codes. Point-particle models do not impose the exact boundary conditions corresponding to particle-fluid interaction, but rather they employ a particle...

Gas-solid flows in nature and industrial applications are characterized by multiscale and nonlinear interactions that manifest as rich flow physics and pose unique modeling challenges. In this article, we review particle-resolved direct numerical simulation (PR-DNS) of the microscale governing equations for understanding gas-solid flow physics and...

Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle–wall friction coefficient and particle coefficient of restitution) and syst...

This review article aims to provide a comprehensive and understandable account of the theoretical foundation, modeling issues, and numerical implementation of the Lagrangian–Eulerian (LE) approach for multiphase flows. The LE approach is based on a statistical description of the dispersed phase in terms of a stochastic point process that is coupled...

Heat transfer is important in gas–solid flows that are encountered in many industrial applications such as energy generation. Computational fluid dynamics (CFD) simulations of heat transfer in gas–solid flow are based on statistical theories that result in averaged equations (e.g., the Eulerian–Eulerian two-fluid model). These averaged equations re...

The Enskog kinetic theory is used as a starting point to model a suspension of solid particles in a viscous gas. Unlike previous efforts for similar suspensions, the gas-phase contribution to the instantaneous particle acceleration appearing in the Enskog equation is modelled using a Langevin equation, which can be applied to a wide parameter space...

A coarse-graining (CG) approach is developed to infer mesoscale interaction potentials in aggregating systems, resulting in an improved potential of mean force for Langevin dynamics (LD) and Brownian dynamics (BD) simulations. Starting from the evolution equation for the solute pair correlation function, this semi-analytical CG approach identifies...

Experiments [Powder Technol. (2003), vol. 131, pp. 23-39; Phys. Rev. E 78 (041306)] and discrete element simulations (DEM) [J. Fluid Mech. (2002), vol. 465, pp. 261-291; Powder Technol. (2006), vol. 169, pp. 10-21] have established that dense granular flow exhibit three different kinds of rheological behavior. In the quasi-static regime the granula...

Turbulent two-phase flows are characterized by the presence of multiple time and length scales. Of particular interest in flows with non-negligible interphase momentum coupling are the time scales associated with interphase turbulent kinetic energy transfer (TKE) and inertial particle dispersion. Point-particle direct numerical simulations (DNS) of...

The Mechanical Engineering department at Iowa State University started the 'Women in Mechanical Engineering' (WiME) program 3 years ago. WiME is a student run, faculty moderated, and department funded program with a three pronged approach to enhance women participation in mechanical engineering - retention, outreach, and recruitment. WiME organizes...

This report describes in detail the technical findings of the DOE Award entitled 'Development, Verification, and Validation of Multiphase Models for Polydisperse Flows.' The focus was on high-velocity, gas-solid flows with a range of particle sizes. A complete mathematical model was developed based on first principles and incorporated into MFIX. Th...

Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ϕ and the Reynolds number based on the mean slip velocity Rem. In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow p...

The apparent particle dispersion in a granular medium due to the combined effects of random granular arrangements and interstitial fluid flow was studied. The particle motion was a two-dimensional random walk on the transverse plane. The corresponding dispersion coefficient was found by sampling all possible trajectories with the aid of two granula...

Gas–phase velocity fluctuations in statistically homogeneous gas–solids flow are quantified using particle–resolved direct numerical simulation (DNS). The kinetic energy associated with the gas–phase velocity fluctuations kf in steady flow past fixed random assemblies of monodisperse spheres is characterized as a function of solid volume fraction φ...

Rheology of dense granular material in an annular Couette cell is studied by experimentation and simulation. A transition from quasi-static to intermediate behavior is identified when a secondary vertical flow is induced. This secondary flow-induced transition and a power–law relation between stress and shear rate in the intermediate regime are ver...

In this chapter, the Direct numerical simulation (DNS) of flow past particles is described. DNS is a first-principles approach for modeling interphase momentum transfer in gas-solids flows that does not require any further closure as the flow around the particles is fully resolved. In this chapter, immersed boundary method (IBM) is described where...

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas...

Predictive device-level computational fluid dynamics (CFD) simulation of gas–solid flow is dependent on accurate models for unclosed terms that appear in the averaged equations for mass, momentum and energy conservation. In the multifluid theory, the second moment of particle velocity represents the strength of particle velocity fluctuations and is...

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. T...

A third-order quadrature-based moment method (Fox, 2008) for simulating poly-disperse fluid-particle flows has been implemented in a computational fluid dynamics code, accounting for the full coupling between the gas and the dispersed phase. The particle phase is described by solving the moments transport equations obtained from kinetic theory, usi...

Fluctuations in the number of particles, and consequently the fraction of volume occupied by them, are observed in experiments as well as simulations of granular and multiphase flows. The mathematical representation of these fluctuations is described, and compared with the standard average number density representation in kinetic theory of granular...

Particle granular temperature plays an important role in the prediction of core annular structure in riser flows. The covariance of fluctuating particle acceleration and fluctuating particle velocity governs the evolution of the granular temperature in homogeneous suspensions undergoing elastic collisions. Koch and co--workers (Phys. Fluid. 1990, J...

We study the shear motion of granular material in an annular shear cell operated in batch and continuous modes. In order to quantitatively simulate shear behavior of granular material composed of spherical shaped grains, a 3D discrete element method (DEM) is used. The ultimate goal of the present work is to compare DEM results for the normal and sh...

a flow intensification model is proposed. We first give an estimation of the flow intensification factor, and then the velocity field in the vicinity of a single granule subject to the intensified flow is obtained. Creeping flow is assumed and Happel's model is used to represent the granular media. Based on the flow field, the initial collector eff...

A theoretical foundation for two widely used statistical representations of multiphase flows, namely the Eulerian–Eulerian (EE) and Lagrangian–Eulerian (LE) representations, is established in the framework of the probability density function (p.d.f.) formalism. Consistency relationships between fundamental statistical quantities in the EE and LE re...

In Lagrangian–Eulerian (LE) simulations of two-way coupled particle-laden flows, the dispersed phase is represented either by real particles or by computational particles. In traditional LE (TLE) simulations, each computational particle is assigned a constant statistical weight, which is defined as the expected number of real particles represented...

Nanoparticle synthesis in turbulent reactors subjects anoparticle aggregates to a homogeneous, time-varying shear flow. The shear flow results in anisotropic clusters and it is of interest to characterize the structural properties of these clusters and their effects on initiation and acceleration of aggregation, the restructuring of clusters, and t...

Classical Euler-Euler two-fluid models based on the kinetic theory of the granular flow assume the particle phase to be dominated by collisions, even when the particle volume fraction is low and hence collisions are negligible. This leads to erroneous predictions of the particle-phase flow patterns and to the inability of such models to capture phe...

Direct simulation of passive scalar transport in steady flow past arrays of spheres is performed using the immersed boundary method. We investigate the dependence of the Nusselt number on different sphere arrangements (simple cubic, face--centered cubic and random) as a function of solid volume fraction and Reynolds number (0.01 < Re < 20) for Pran...

Direct numerical simulations (DNS) of monodisperse suspensions with high particle inertia and moderate fluid inertia are performed using an immersed boundary method (IBM) to quantify the effect of hydrodynamic forces on particle velocity fluctuations. The evolution of the second moment of particle velocity fluctuations is driven by the correlation...

Accurate simulation and control of nanoparticle aggregation in chemical reactors requires that population balance equations be solved by using realistic expressions for aggregation and breakage rate kernels. Obtaining such expressions requires that atomistic simulation approaches that can account for microscopic details of particle collisions be us...

Assemblies of granular materials behave differently when they are owing rapidly, from when they are slowly deforming. The behavior of rapidly owing granular materials, where the particle-particle interactions occur largely through binary collisions, is commonly related to the properties of the constituent particles through the kinetic theory of gra...

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate...

Simulations of gas-solid fluidized beds have been carried out using a hybrid simulation method, which couples the discrete element method (DEM) for particle dynamics with the ensemble-averaged two-fluid (TF) equations for the fluid phase. The coupling between the two phases is modeled using an interphase momentum transfer term. The results of the h...

The interphase transfer of turbulent kinetic energy (TKE) is an important term that affects the evolution of TKE in fluid and particle phases in particle-laden turbulent flow. This work shows that the interphase TKE transfer terms must obey a mathematical constraint, which in the limiting case of statistically homogeneous flow with zero mean veloci...

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kol...

We study the rise dynamics of a large particle in a granular bed under vertical vibration using molecular dynamics simulations. Systematic variation of the particle properties and external wall friction in the simulations shows that the large particle rising is very sensitive to external wall friction. The dynamical response of the granular bed wit...

Light-scattering data for the aggregation of colloidal nanoparticles shows that hybrid aggregates with two different fractal dimensions can be formed depending on the magnitude and duration of the applied shear (C. M. Sorensen's group, Kansas State University). Formation of such super-aggregate structures with Df = 2.55, and their reverting to Df =...

Force networks, formed by particles interacting with repulsive contact forces, are a salient feature of dense granular media, and play an important role in determining mechanical properties of granular media. We use a graph-theoretic approach based on the minimum spanning tree (MST) algorithm to analyze force networks in a dense granular bed under...

Hydrodynamically-induced particle clustering is observed in inertial suspensions of particle-laden flows. Second-order statistics like the pair correlation function are used to quantify the effect of clustering. The evolution equation for the second-order density contains a transport term involving the relative acceleration of a particle pair. In t...

In this study, we explore the effect of strong inhomogeneities in the initial number density on the evolution of a system of inelastically colliding hard spheres. The characteristic length scale of the inhomogeneity in number density (viz. n/(grad n) ) is varied compared to a characteristic length scale associated with the initially prescribed pair...

We perform Direct Numerical Simulations (DNS) of flow at moderate Reynolds numbers (based on mean flow velocity and particle diameter) through random arrangements of stationary spheres with varying levels of upstream turbulence. A pseudo-spectral implementation of the immersed boundary method is used to solve the Navier-Stokes equations with exact...