• Volume 40, Issue 3

May 2015,   pages  623-1048

• Editorial

• Foreword

• Level set method for computational multi-fluid dynamics: A review on developments, applications and analysis

Functions and conservation as well as subsidiary equations in Level Set Method (LSM) are presented. After the mathematical formulation, improvements in the numerical methodology for LSM are reviewed here for advection schemes, reinitialization methods, hybrid methods, adaptive-grid LSM, dual-resolution LSM, sharp-interface LSM, conservative LSM, parallel computing and extension from two to multi fluid/phase as well as to various types of two-phase flow. In the second part of this article, LSM method based Computational Multi-Fluid Dynamics (CMFD) applications and analysis are reviewed for four different types of multi-phase flow: separated and parallel internal flow, drop/bubble dynamics during jet break-up, drop impact dynamics on a solid or liquid surface and boiling. In the last twenty years, LSM has established itself as a method which is easy to program and is accurate as well as computationally-efficient.

• Liquid marbles: Physics and applications

Liquid marbles are formed by encapsulating microscale volume of liquid in a particulate sheath. The marble thus formed is robust and resists rupture if the particulate layer covers the entire volume of liquid and prevents contact between the liquid and the substrate. Liquid marbles have been objects of study over the past decade. Research has been focused on understanding their formation and properties – both static and dynamic. A range of particulate materials as well as liquids have been employed to make these objects. This paper summarizes the state of the art in this regard and discusses new developments that are being discussed. Finally, some directions are proposed based on lacunae observed in the community’s understanding – both in terms of the science as well as on the application front.

• A review on the thermal hydraulic characteristics of the air-cooled heat exchangers in forced convection

In this paper, a review is presented on the experimental investigations and the numerical simulations performed to analyze the thermal-hydraulic performance of the air-cooled heat exchangers. The air-cooled heat exchangers mostly consist of the finned-tube bundles. The primary role of the extended surfaces (fins) is to provide more heat transfer area to enhance the rate of heat transfer on the air side. The secondary role of the fins is to generate vortices, which help in enhancing the mixing and the heat transfer coefficient. In this study, the annular and plate fins are considered, the annular fins are further divided into four categories: (1) plane annular fins, (2) serrated fins, (3) crimped spiral fins, (4) perforated fins, and similarly for the plate fins, the fin types are: (1) plain plate fins, (2) wavy plate fins, (3) plate fins with DWP, and (4) slit and strip fins. In Section 4, the performance of the various types of fins is presented with respect to the parameters: (1) Reynolds number, (2) fin pitch, (3) fin height, (4) fin thickness, (5) tube diameter, (6) tube pitch, (7) tube type, (8) number of tube rows, and (9) effect of dehumidifying conditions. In Section 5, the conclusions and the recommendations for the future work have been given.

• Near field characteristics of buoyant helium plumes

Puffing and entrainment characteristics of helium plumes emanating out into ambient air from a circular orifice are investigated in the present study. Velocity and density fields are measured across a diametric plane using Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) respectively in phase resolved manner. Experiments are performed in Froude numbers range 0.2–0.4 and for Reynolds numbers 58–248. Puffing frequency measurements reveal that the plume puffing frequencies are insensitive to the plume exit conditions, since the instability is buoyancy driven. The frequencies obtained in the present case are in agreement with frequencies obtained by Cetegen &amp; Kasper (1996) for plumes originating from circular nozzles of various L/D ratios. Velocity and density measurements reveal that toroidal vortex formed during a puffing cycle entrains ambient air as it traverses downstream and this periodic engulfment governs the entrainment mechanism in pulsating plumes. The obtained velocity and density fields are used to calculate mass entrainment rates. It is revealed that though the flow is unsteady, the contribution of unsteady term in mass conservation to entrainment is negligible, and it becomes zero over a puff cycle. Finally, an empirical relation for variation of mass entrainment with height has been proposed, in which the non-dimensional mass entrainment is found to follow a power law with the non-dimensional height.

• Suppression of vortex shedding around a square cylinder using blowing

Direct numerical simulation (DNS) of flow past a square cylinder at a Reynolds number of 100 has been carried out to explore the effect of blowing in the form of jet(s) on vortex shedding. Higher order spatial as well as temporal discretization has been employed for the discretization of governing equations. The varying number of jets, jet velocity profiles and different blowing velocities are studied to investigate the characteristics of vortex shedding. The parabolic velocity profile has been found to be more effective in suppressing the vortex shedding as compared to the uniform velocity. Complete suppression of vortex shedding along with remarkable reduction in drag coefficient has been achieved for both jet velocity profiles but at different velocities. The corresponding values for uniform and parabolic jet profiles are 0.87 and 0.6, respectively at a mass flux of 0.120. The study also reveals that there is considerable effect of the number of jets on the vortex shedding phenomena.

• A numerical study on dynamics of spray jets

The study of flow characteristics of spray jets in an injector nozzle, solgel process is very critical for scientific studies. In this communication, we report results from a numerical modeling of spray jet dynamics and its breakup. The nature of instability depends on the density of the jet fluid and the ambient fluid and also on the velocity of the jet. The present work is motivated by the lack of quantitative measurement to explain the nature of instability of a vertically descending jet into a stagnant medium. In order to capture the sharp gradient between the interfaces, modified Volume of Fluid, using an extra compression term is used. The velocity profiles and spread angle are measured to quantitatively explain the mixing and growth of the instability in such complex multiphase flows.

• Experimental investigation of separated shear layer from a leading edge subjected to various angles of attack with tail flap deflections

Shear layer development over a thick flat plate with a semi-circular leading edge is investigated for a range of angles of attack under different pressure gradients for a Reynolds number of 2.44×105 (based on chord and free-stream velocity). The characteristics of the separated shear layer are very well documented through a combination of surface pressure measurement and smoke flow visualization. The instability of the separated layer occurs because of enhanced receptivity of perturbations leading to the development of significant unsteadiness and three-dimensional motions in the second-half of the bubble. The onset of separation, transition and the point of reattachment are identified for varying angles of attack and pressure gradients imposed by tail flap deflections. The data concerning bubble length, laminar portion and reattachment points agree well with the literature.

• Break-up of a non-Newtonian jet injected downwards in a Newtonian liquid

The present work on downward injection of non-Newtonian jet is an extension of our recent work (Lakdawala et al, Int. J. Multiphase Flow. 59: 206–220, 2014) on upward injection of Newtonian jet. The non-Newtonian rheology of the jet is described by a Carreau type generalized Newtonian fluid (GNF) model, which is a phenomenological constitutive equation that accounts for both rate-thinning and rate-thickening. Level set method based numerical study is done for Newtonian as well as various types of shear thinning and thickening jet fluid. Effect of average injection velocity ($V_{av,i}$) is studied at a constant Reynolds number Re = 14.15, Weber number W e = 1, Froude number F r = 0.25, density ratio $\chi$ = 0.001 and viscosity ratio $\eta$ = 0.01. CFD analysis of the temporal variation of interface and jet length ($L_{j}$) is done to propose different types of jet breakup regimes. At smaller, intermediate and larger values of $V_{av,i}$, the regimes found are periodic uniform drop (P-UD), quasi-periodic non-uniform drop (QP-NUD) and no breakup (NB) regimes for a shear thinning jet; and periodic along with Satellite Drop (P+S), jetting (J) and no breakup (NB) regimes for a shear thickening jet, respectively. This is presented as a drop-formation regime map. Shear thickening (thinning) is shown to produce long (short) jet length. Diameter of the primary drop increases and its frequency of release decreases, due to increase in stability of the jet for shear thickening as compared to thinning fluid.

• Mixed convection in a baffled grooved channel

In the present numerical work, flow structure and heat transfer characteristics are investigated in a baffled grooved channel, differentially heated from the sides. The baffle is placed vertically downward from the top wall of grooved channel geometry, with the motive of diverting outside forced flow towards the inside of the square cavity. In-house CFD code based on finite volume method has been used to solve the 2D equations of continuity, momentum and energy. The effect of change in baffle position and height is investigated in the range of Richardson numbers 0.1 to 10. For the present study, external flow from both left and right of the grooved channel are considered. A remarkable enhancement of heat transfer is observed in presence of baffle. The study has also pointed out that for optimal performance, the position and height of the baffle need to be adjusted depending on the direction of external flow.

• Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers

Conventionally, obtaining a converged solution for a MagnetoHydro-Dynamic problem entails a highly resolved Hartmann boundary layer, leading to excessive time and computational requirements. For high Hartmann number flows through electrically conducting channels, majority of the current loops close through the walls and the Hartmann layer contributes only a small fraction of the global current path. Hence, the effect on flow parameters due to coarsening the mesh of the Hartmann Layer was investigated using the ANSYS FLUENT code. Numerical simulations have been carried out in square and rectangular ducts with wall conductance ratio of 0.156 and 0.078 respectively. Magnetic field was varied from 1T to 4T to obtain solution for Hartmann numbers $(Ha = Ba \sqrt{\sigma/\mu})$ in the range of 260–1040 for the square duct, and 520–2080 for the rectangular duct. B, $\alpha$, $\mu$, and $\sigma$ are the strength of applied magnetic field, characteristic length of the channel, dynamic viscosity and electrical conductivity of the fluid respectively. The errors in estimating core and side layer peak velocity and fully developed pressure gradient were found to be low even for a grid system having 46% coarser grid than a well-resolved system. The analysis indicated that for high Hartmann number flows through thick, conducting ducts, coarsening the mesh in the Hartmann boundary layer reduced computational time, not compromising on the solution accuracy and appears to be a promising option for complex geometry MHD simulation.

• Numerical calculation of particle collection efficiency in an electrostatic precipitator

The present numerical study involves the finding of the collection efficiency of an electrostatic precipitator (ESP) using a finite volume (ANUPRAVAHA) solver for the Navier–Stokes and continuity equations, along with the Poisson’s equation for electric potential and current continuity. The particle movement is simulated using a Lagrangian approach to predict the trajectory of single particles in a fluid as the result of various forces acting on the particle. The ESP model consists of three wires and three collecting plates of combined length of L placed one after another. The calculations are carried out for a wire-to-plate spacing $H$ = 0.175 m, length of ESP $L$ = 2.210 m and wire-to-wire spacing of 0.725 m with radius of wire $R$wire = 10 mm and inlet air-particle velocity of 1.2 m/s. Different electrical potentials ($\varphi$ = 15–30 kV) are applied to the three discharge electrodes wires. It is seen that the particle collection efficiency of the ESP increases with increasing particle diameter, electrical potential and plate length for a given inlet velocity.

• Effect of coil embolization on blood flow through a saccular cerebral aneurysm

Coil embolization is a mildly invasive endovascular method for treatment of a cerebral aneurysm. The presence of a coil reduces fluid loading of the blood vessel and delays further deformation of the walls. Its effectiveness depends on the coil porosity and permeability apart from the nature of flow pulsations and its geometry. In the present work, a three dimensional numerical study of pulsatile flow of blood through an artery with saccular cerebral aneurysm is reported. The flow is unsteady but is taken to be laminar and incompressible. The coil is treated as homogeneous and isotropic porous medium. A comparative study has been carried out on aneurysms with and without a coil insert considering blood as a non-Newtonian fluid. The simulation is carried out for Reynolds numbers $Re$ = 500 and 1500. Results show that the velocity magnitude within the coil embolized aneurysm becomes negligible after coil insertion. The wall shear stress within the aneurysm decreases to a great extent for both Reynolds numbers. Pressure levels remain relatively unchanged. Overall, reduced wall loading with a coil stabilizes the growth of the aneurysm and thus provides an advantage.

• Foreword

• Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models

The motivation for this subject comes from physiology: Air-flow in the lungs, where flow limitation during forced expiration is a consequence of large-airway collapse, and wheezing, which is a manifestation of self-excited mechanical oscillations; Blood flow in veins, such as those of giraffes, in which the return of blood to the heart from the head must be accompanied by partial venous collapse, and in arteries, which exhibit self-excited oscillations (Korotkov sounds) when compressed by a blood-pressure cuff. Laboratory experiments are frequently conducted in a Starling resistor, a finite length of flexible tube, mounted between two rigid tubes and contained in a pressurised chamber. Steady conditions upstream and downstream give rise not only to steady flows, but also to a rich variety of self-excited oscillations, which theoreticians have been seeking to understand for at least five decades. Some of the observations have been reproduced in full Navier–Stokes computations for a two-dimensional model, but these do not provide physical understanding. We seek a self-consistent mathematical model for the oscillations. We concentrate first on 1D models, in which the key dependent variables are the cross-sectional area $A$ and the cross-sectionally averaged velocity $u$ and pressure $p$, all taken to be functions of longitudinal coordinate $x$ and time $t$. The governing equations are those of conservation of mass and momentum and a tube law representing the elastic properties of the vessel. In the momentum equation, the viscous resistance term is conventionally modelled either as a linear function of fluid velocity, accurate at low Reynolds number, or with an ad hoc representation of the energy loss at flow separation. Even with such crude approximations, the predictions of 1D models agree quite well both with observations in the giraffe and with some of the 2D computations and 3D experiments. For a more rational model, we examine a 2D model problem, in which part of one wall of a parallel sided channel is replaced by a membrane under tension. One approach, for large Reynolds-number flow, and a long membrane, is to consider small deflections of the membrane and use interactive boundary-layer theory. This leads to interesting predictions, such as the impossibility of simultaneously prescribing the flow rate and the upstream pressure, but not to oscillations, except in cases where wall inertia is important (flutter). Another approach is to assume a parabolic velocity profile everywhere, leading to a rational choice for the inertia and viscous terms in the 1D momentum equation. If, further, the undisturbed membrane is taken to be flat, by a suitable choice of external pressure distribution, the system leads to an oscillatory instability even without wall inertia. Whether these oscillations have the same physics as those computed numerically at lower Reynolds number remains to be seen.

• Experimental studies on the flow through soft tubes and channels

Experiments conducted in channels/tubes with height/diameter less than 1 mm with soft walls made of polymer gels show that the transition Reynolds number could be significantly lower than the corresponding value of 1200 for a rigid channel or 2100 for a rigid tube. Experiments conducted with very viscous fluids show that there could be an instability even at zero Reynolds number provided the surface is sufficiently soft. Linear stability studies show that the transition Reynolds number is linearly proportional to the wall shear modulus in the low Reynolds number limit, and it increases as the 1/2 and 3/4 power of the shear modulus for the ‘inviscid’ and ‘wall mode’ instabilities at high Reynolds number. While the inviscid instability is similar to that in the flow in a rigid channel, the mechanisms of the viscous and wall mode instabilities are qualitatively different. These involve the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The experimental results for the viscous instability mechanism are in quantitative agreement with theoretical predictions. At high Reynolds number, the instability mechanism has characteristics similar to the wall mode instability. The experimental transition Reynolds number is smaller, by a factor of about 10, than the theoretical prediction for the parabolic flow through rigid tubes and channels. However, if the modification in the tube shape due to the pressure gradient, and the consequent modification in the velocity profile and pressure gradient, are incorporated, there is quantitative agreement between theoretical predictions and experimental results. The transition has important practical consequences, since there is a significant enhancement of mixing after transition.

• Stability of fluid flow through deformable tubes and channels: An overview

The aim of this paper is to provide a systematic overview of the study of instabilities in flow past deformable solid surfaces, with particular emphasis on internal flows through tubes and channels. The subject is certainly more than five decades old, and arguably began with Kramer’s pioneering experiments on drag reduction by compliant surfaces. This was immediately followed by the theoretical studies of Benjamin and Landhal in the early 1960s. Most earlier theoretical studies were focused on stability of external flows such as boundary layers, and used relatively simple wall models composed of spring-backed plates. There has been a resurgence in the field since the mid-1980s, and more attention was focused on internal flows through deformable tubes and channels. The wall deformation was described by both phenomenological spring-backed plate models and continuum linear viscoelastic solid models. All these studies predict several types of instabilities in flow past deformable surfaces. This paper will attempt to place the various theoretical results in perspective, and to classify the instabilities predicted by various studies. Recent studies have also emphasized the importance of using a frame-invariant constitutive model, such as the neo-Hookean model, for the solid deformation. Until recently, however, the field has been dominated by theoretical and numerical studies, with very little experimental observations to corroborate the theoretical predictions. Recent experiments in flow through deformable tubes and channels indeed show instability at Reynolds number much lower than their rigid counterparts, and the experimental observations are in qualitative agreement with some of the theoretical predictions. There have also been a few studies on the non-linear aspects of the instability using the weakly non-linear formulation to determine the nature of the bifurcation at the linear instability. A brief discussion on weakly nonlinear analyses is also provided in this paper.

• Global instabilities and transient growth in Blasius boundary-layer flow over a compliant panel

We develop a hybrid of computational and theoretical approaches suited to study the fluid–structure interaction (FSI) of a compliant panel, flush between rigid upstream and downstream wall sections, with a Blasius boundary-layer flow. The ensuing linear-stability analysis is focused upon global instability and transient growth of disturbances. The flow solution is developed using a combination of vortex and source boundary-element sheets on a computational grid while the dynamics of a plate-spring compliant wall are couched in finite-difference form. The fully coupled FSI system is then written as an eigenvalue problem and the eigenvalues of the various flow- and wall-based instabilities are analysed. It is shown that coalescence or resonance of a structural eigenmode with either a flow-based Tollmien–Schlichting Wave (TSW) or wall-based travelling-wave flutter (TWF) modes can occur. This can render the nature of these well-known convective instabilities to become global for a finite compliant wall giving temporal growth of system disturbances. Finally, a non-modal analysis based on the linear superposition of the extracted temporal modes is presented. This reveals a high level of transient growth when the flow interacts with a compliant panel that has structural properties which render the FSI system prone to global instability. Thus, to design stable finite compliant panels for applications such as boundary-layer transition postponement, both global instabilities and transient growth must be taken into account.

• High Reynolds number liquid layer flow with flexible walls

The stability of liquid layer flow over an inclined flexible wall is studied using asymptotic methods based on the assumption that the Reynolds number is large. The flexible wall behaviour is described by a spring-plate model, and parameters chosen so that the wall flexibility affects the governing boundary layer problem. For the case of a rigid wall, the problem reverts to one studied by Gajjar. Asymptotic analysis of the governing equations leads to the triple-deck equations governing the interaction between the wall layer and the free-surface. The linearised and other solution properties of these set of equations are discussed.

• Effect of ultra-fast mixing in a microchannel due to a soft wall on the room temperature synthesis of gold nanoparticles

The room-temperature synthesis of mono-dispersed gold nanoparticles, by the reduction of chlorauric acid (HAuCl4) with tannic acid as the reducing and stabilizing agent, is carried out in a microchannel. The microchannel is fabricated with one soft wall, so that there is a spontaneous transition to turbulence, and thereby enhanced mixing, when the flow Reynolds number increases beyond a critical value. The objective of the study is to examine whether the nanoparticle size and polydispersity can be modified by enhancing the mixing in the microchannel device. The flow rates are varied in order to study nanoparticle formation both in laminar flow and in the chaotic flow after transition, and the molar ratio of the chlorauric acid to tannic acid is also varied to study the effect of molar ratio on nanoparticle size. The formation of gold nanoparticles is examined by UV-visual spectroscopy and the size distribution is determined using scanning electron microscopy. The synthesized nanoparticles size decreases from ≥6 nm to ≤4 nm when the molar ratio of chlorauric acid to tannic acid is increased from 1 to 20. It is found that there is no systematic variation of nanoparticle size with flow velocity, and the nanoparticle size is not altered when the flow changes from laminar to turbulent. However, the standard deviation of the size distribution decreases by about 30% after transition, indicating that the enhanced mixing results in uniformity of particle size.

• Role of viscoelasticity in instability in plane shear flow over a deformable solid

The stability of the flow of a viscoelastic fluid over a deformable elastic solid medium is reviewed focusing on the role played by the fluid elasticity on the earlier known instability modes for the Newtonian fluids. In particular, two classes of modes are emphasized: the viscous mode for the creeping flow, and the wall mode for high Reynolds number flow. The flow geometry is restricted to plane Couette flow of fluid supported on elastic substrate of finite thickness. The viscoelastic fluid is described using the Oldroyd-B model and the dynamics of the deformable solid continuum is described by either Hookean or neo-Hookean elastic model. In the limit of $Re \to 0$, the introduction of fluid elasticity delays the onset of instability and for sufficiently viscoelastic fluid with dilute polymer concentration, the instability is suppressed rendering the flow stable. For concentrated solution and polymer melt, the instability persists, but with higher value of critical shear rate than for the Newtonian fluid, indicating stabilizing role of fluid elasticity in creeping flow regime. However, for high Reynolds number flow of dilute polymer solution, the polymer addition plays a destabilizing role for wall modes, indicated by reduction in critical Reynolds number by an order of magnitude.

• Oscillatory and electrohydrodynamic instabilities in flow over a viscoelastic gel

The stability of oscillatory flows over compliant surfaces is studied analytically and numerically. The type of compliant surfaces studied is the incompressible viscoelastic gel model. The stability is determined using the Floquet analysis, where amplitude of perturbations at time intervals separated by one time period is examined to determine whether perturbations grow or decay. Oscillatory flows pas viscoelastic gels exhibit an instability in the limit of zero Reynolds number, and the transition amplitude of the oscillatory velocity increases with the frequency of oscillations. The transition amplitude has a minimum at a finite wavenumber for the viscoelastic gel model. The instability is found to depend strongly on the gel viscosity $\eta_{g}$, and the effect of oscillations on the continuation of viscous modes at intermediate Reynolds number shows a complicated dependence on the oscillation frequency. Experimental studies are carried out on the stability of an oscillatory flow past a viscoelastic gel at zero Reynolds number, and these confirm the theoretical predictions.

• Dynamics of a spreading thin film with gravitational counterflow using slip model

• Manipulation of interfacial instabilities by using a soft, deformable solid layer

Multilayer flows are oftensusceptible to interfacial instabilities caused due to jump in viscosity/elasticity across thefluid–fluid interface. It is frequently required to manipulate and control these interfacial instabilities in various applications such as coating processes or polymer coextrusion. We demonstrate here the possibility of using a deformable solid coating to control such interfacial instabilities for various flow configurations and for different fluid rheological behaviors. In particular, we show complete suppression of interfacial flow instabilities by making the walls sufficiently deformable when the configuration was otherwise unstable for the case of flow past a rigid surface. While these interfacial instabilities could be suppressed in certain parameter regimes, it is also possible to enhance the flow instabilities by tuning the shear modulus of the deformable solid coating for other ranges of parameters.