# Science-based research articles

25. A. Sharma, Rajaram Lakkaraju, and A. Atta, Insight into the particle laden turbulent flow statistics in sharply bent channels, Physics of Fluids 35, 095142 (2023) https://doi.org/10.1063/5.0169374

In canonical wall-bounded flows, point particle-laden turbulence exhibits a substantial interaction between scales with a variety of regimes, and the dynamics of the point particle-laden fluid are primarily identified by the Reynolds number. Such interactions are even more augmented in curved channels with variable curvature, and fixed Reynolds numbers demonstrate distinct flow behavior, as shown by Brethouwer [J. Fluid Mech. 931, A21 (2022)]. In this work, we demonstrate the characteristics of wall-bounded point particle-laden turbulent flows in sharply bent channels by evaluating the time-averaged velocity profiles at the straight section, at the bend, and in the inclined sections. The mean (time-averaged) normalized velocity profiles retain their well-known logarithmic features, with the von Karman and additive constants taking different values depending on the acute inclination of the bend. Near-wall fluctuations at the bend are found to be intensified due to the bend that leads to increased turbulent activity. On examining the friction Reynolds number along the bent channel walls in the streamwise direction, a modulated behavior with an abrupt change at the bend is observed. Budgets of turbulent kinetic energy (TKE) are delineated for various inclinations of the bend at different sections of the channel and are compared with the unladen sharply bent turbulent channel flows, which illustrate that TKE is modulated at the bend and there is an overall attenuation of TKE on loading the channel with point particles.

24. A. Basak, Rajaram Lakkaraju, and GPRS, Droplet in a shear flow, Journal of Fluid Mechanics--, -- (2023) https://doi.org/

23. A. Basak, Rajaram Lakkaraju, and GPRS, Droplet in a shear flow, Journal of Fluid Mechanics--, -- (2023) https://doi.org/

23. R. Roy, J. S. M. Quintero, Rajaram Lakkaraju, P. Waghmare, and S. Chakraborty, Droplet-on-chip electro-spectroscopy detects the ultra-short relaxation time of a dilute polymer solution, Soft Matter 19, 5345 (2023) DOI https://doi.org/10.1039/D3SM00608E

We report an electrode-embedded on-chip platform technology for the precise determination of ultra-short (of the order of a few nanoseconds) relaxation times of dilute polymer solutions, by deploying time-alternating electrical voltages. Our methodology delves into the sensitive dependence of the contact line dynamics of a droplet of the polymer solution atop a hydrophobic interface in response to the actuation voltage, resulting in a non-trivial interplay between the time-evolving electrical, capillary, and viscous forces. This culminates into a time-decaying dynamic response that mimics the features of a damped oscillator having its ‘stiﬀness’ mapped with the polymeric content of the droplet. The observed electro-spreading characteristics of the droplet are thus shown to correlate explicitly with the relaxation time of the polymer solution, drawing analogies with a damped electro-mechanical oscillator. By corroborating well with the reported values of the relaxation times as obtained from more elaborate and sophisticated laboratory set-ups. Our findings provide perspectives for a unique and simple approach towards electrically-modulated on-chip-spectroscopy for deriving ultra-short relaxation times of a broad class of viscoelastic fluids that could not be realized thus far.

22. R. Roy, J. S. M. Quintero, Rajaram Lakkaraju, P. Waghmare, and S. Chakraborty, Electro-wetting induced dynamic manipulation of symmetrically coalescing viscoelastic liquid bridges, Physics of Fluids 35, 052014 (2023) https://doi.org/10.1063/5.0151286

Merging of isolated liquid drops is a common phenomenon that may greatly be inﬂuenced by adding polymeric contents to the liquid. Here, we bring out an exclusive control on the dynamics of the intermediate liquid bridge, thus, formed via exploiting the interactions of an exciting electric ﬁeld with a trace amount of polymeric inclusions present in the intermingling drops. Our results unveil a unique competition of the elastic recovery and time-oscillatory forcing during the drop-uniﬁcation at early times. However, damped oscillations as a specific signature of the polymer concentration feature eventual stabilization of the bridge at later instants of time. We rationalize these experimental ﬁndings in light of a simple unified theory that holds its critical implications in droplet manipulation in a wide variety of applications encompassing digital microﬂuidics, chemical processing, and biomedical analytics.

21. R. Mundhra, Rajaram Lakkaraju, P. K. Das, M. A. Pakhomov, and P.D. Lobanov, Effect of wall proximity and surface tension on a single bubble

rising near a vertical wall, Water 15, 1567 (2023) https://doi.org/10.3390/w15081567

Path instability of a rising bubble is a complex phenomenon. In many industrial applications, bubbles encounter walls, and the interactions between the bubbles and the wall have a significant impact on flow physics. A single bubble rising near a vertical wall was experimentally observed to follow a bouncing trajectory. To investigate the near-wall dynamics of rising bubbles, 3D numerical simulations were performed based on the volume of fluid (VOF) method using the open source solver OpenFOAM. The effect of wall proximity and surface tension on the bubble trajectory was investigated. Previous studies have focused on the near-wall rising dynamics of bubbles for higher Eotvos numbers (Eo) and varied the Galilei number (Ga). The physical properties of the flow were chosen such that the free-rising bubble lies in the rectilinear regime. The Ga number was fixed and the Eo number was varied to analyze its effect on the bubble’s rising trajectory. It was found that the presence of the wall increases the drag experienced by the bubble and induces an early transition from rectilinear to a planar zigzagging regime. We identify the maximum wall distance and the critical Eo number for the bubble to follow a bouncing trajectory. The amplitude, frequency and wavelength of the bouncing motion are independent of the initial wall distance, but they decrease with decreasing surface tension.

20. A. Sharma, Rajaram Lakkaraju, and A. Atta, Influence of channel bend angle on the turbulent statistics in sharply bent channel flows, Physics of Fluids 35, 055102 (2023) https://doi.org/10.1063/5.0149086

Turbulence in wall-bounded flows shows a wide range of regimes, where interaction between scales significantly occur. Reynolds number is used to characterize the dynamics of fluid corresponding to single phase channel flows. Meanwhile, different flow behaviour exists in curved channels even at fixed Reynolds number, where curvature varies as shown by Geert Brethouwer (\textit{J. Fluid Mech.}, vol. 931, 2022, pp. A21) . In the present study, we show how wall-bounded turbulent flow behaves on sharply bending the channel by investigating the time averaged velocity profiles at the straight section, at the bend and in the inclined section. The well known logarithmic behaviour of the time averaged normalized velocity profile is retained, where the von K{\'a}rm{\'a}n and the additive constants assume altered values depending on the sharp bend inclination. The near wall fluctuations at the bend is enhanced, which is due to diffusion of counter rotating vortices leading to increased turbulent activity. In terms of spatial structure of the random fluctuating field, the two-point correlation statistics suggests that multiple high speed and low speed streak pairs are generated and there are multiple streamwise vortices of different sizes when bend inclination is increased. Budgets of turbulent kinetic energy are presented for various inclinations of the bend at different sections of the bend channel, which depicts that turbulent kinetic energy is modulated at the bend.

19. P. Kar, U. Chetan, A. Kumar, P. K. Das, and Rajaram Lakkaraju, Heat transport enhancement and flow transitions in partitioned thermal convection, Physical Review Fluids 8, 043501 (2023) https://doi.org/10.1103/PhysRevFluids.8.043501

Partitions are an essential part of industrial reactors and thermal management devices whose primary purpose is to increase transport rates by obstructing flow in one direction and promoting in the other via secondary and small-scale motions. Inspired by such applications, we have investigated thermal convection in a two-dimensional square enclosure heated at the bottom and cooled at the top, with four additional thin vertical partitions arranged parallel to facilitate organized plume motions in the range of Rayleigh numbers $10^6$ to $10^9$. The large-scale classical circulation observed in thermal convection breaks down into many roll configurations based on the constriction gap ($\mathcal{S}$) between the partitions and the conduction walls. Due to their arrangement, we observed increased plume ejection, impact, and shear near the conduction walls when the partitions disturb the thermal boundary layers. The plume ejection and impact on either end of the constriction gap sets a pressure-driven forced convection on the conduction wall, thus increasing overall heat transport by at least an order of magnitude. We found the maximum heat transport when $0.2\delta_{RB}<\mathcal{S}<0.4\delta_{RB}$, where $\delta_{RB}$ is the time-averaged thermal boundary layer thickness in classical thermal convection. Using both the numerical simulations and a simple control volume-based analysis, we have estimated that the heat transport increases as $\mathcal{S}^3$ for small constriction gaps and as an inverse power of $\mathcal{S}$ for the large gap limit. With the help of energy dissipation, we have concluded that increasing plume intensity near the conduction walls leads to the observed high heat transport.

18. P. Kar, U. Chetan, J. Mahto, T. Sahu, P.k. Das, Rajaram Lakkaraju, Heat flux enhancement by regular surface protrusion in partitioned thermal convection, Physics of Fluids 34, 127105 (2022) https://doi.org/10.1063/5.0123088

We performed two-dimensional numerical simulations in a square Rayleigh-B\'{e}nard (RB) convection enclosure with equally spaced protrusions in the top and bottom conduction plates, and equispaced partitions for the range of Rayleigh number $10^6$ to $10^8$ and at a fixed Prandtl number of $1$. The protrusions are in the form of a parallelepiped base and triangular top with vertex angle $90^o$, and the protrusion height varies from $10\%$ to $25\%$ of enclosure height. The tip of the triangular portion of the protrusion acts as an active plume emitting spot. We have inserted vertical adiabatic partition boards between two consecutive protrusions, and varied the partition board height from $20\%$ to $99.8\%$ of enclosure height to explore its effect on the flow pattern and heat transport. The partition boards are inserted with a gap between the conduction plate and the partition board. We observe a single large-scale elliptical roll with counter-rotating corner rolls for small partition board height. With an increase in partition board height, an elliptical large-scale roll breakdown into the number of large-scale rolls horizontally placed one beside the other. Finally, we observe multiple rolls stacked vertically when the partition boards almost touch the conduction walls. Heat flux enhancement strongly depends on the large-scale flow structures. We observe a maximum heat flux enhancement in protrusion with partitioned RB case approximately up to $4.7$ times classical square RB for an optimal gap between conduction plate and partition board. The maximum heat transport enhancement is due to the strong horizontal flow through the gap between the conduction plate and partition board, which locally reduces the thermal boundary layer's thickness. The interaction between the horizontal jets and the thermal boundary layers benefits heat transport enhancement.

17. T. Sahu, U. Chetan, J. Mahto, P. Kar, P.k. Das, Rajaram Lakkaraju, Formation and breakup of twisting ligaments in a viscous swirling liquid jet, Physics of Fluids 34, 112118 (2022) https://doi.org/10.1063/5.0122754

We analyze the successive steps of breakup morphology of a swirling liquid jet. Three-dimensional numerical simulations are carried out to find the physical mechanism behind the generation of twisting ligaments for axial Reynolds number of 50 and swirl numbers in the range of $0.50 \leq S \leq1 .55$. We present fundamental flow features of the swirling jet in terms of time-averaged axial and azimuthal velocity profiles. An azimuthal mode number of $m=4$ is observed for the considered range of Reynolds number and swirl number. We observed that viscous forces are the dominant forces in the flow which suppresses the rolling up of the shear layers. The results indicate that, corrugations in the form of tiny protrusions develop at the interface along each of the helical rims, which triggers centrifugally induced Rayleigh-Taylor instability. Subsequently, these tiny protrusions get stretched in the radially outward direction and transform into twisting ligaments that break into droplets. The mean diameter of the ligaments $d_l$ follows the scaling law $<d_l>=0.21\lambda_p$ where $\lambda_p$ is the distance between two protrusions developed along the helical rim.

16. A. Mishra, C. Bourquard, A. Roy, Rajaram Lakkaraju, O. Supponen, P. Ghosh, Flow-focusing from interacting cavitation, Physical Review Fluids 7, 110502 (2022), This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD), Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0038 (.pdf)

In most practical applications of cavitation, numerous tiny bubbles appear as clusters, filaments, and clouds of vapor. The dynamic behavior of the individual bubbles within the vapor cloud with mutual interactions is more complex than that of a single isolated bubble. We shed light on such interactions by reducing the problem to a growing and collapsing bubble pair and exploring their dynamics experimentally and numerically.

15. J. Mahato, D.K. Srivastava, D. K. Chandraker and Rajaram Lakkaraju, On offset placement of a compound droplet in a channel flow, Journal of Fluids Engineering, FE-21-1208 (2021) https:// https://doi.org/10.1115/1.4052052 (.pdf)

Investigations on flow dynamics of a compound droplet have been carried out in a two-dimensional fully-developed Poiseuille flow by solving the Navier Stokes equations with the evolution of the droplet using the volume of fluid method with interface compression. The outer droplet undergoes elongation similar to a simple droplet of same size placed under similar ambient condition in the flow direction, but, the inner droplet evolves in compressed form. The compound droplet is varied starting from the centerline towards the walls of the channel. The simulations showed that on applying an offset, asymmetric slipper-like shapes are observed as opposed to symmetric bullet-like shapes through the centerline. Temporal dynamics, deformation patterns, and droplet shell pinch-off mode vary with the offset, with induction of lateral migration. Also, investigations are done on the effect of various parameters like droplet size, Capillary number, and viscosity ratio on the deformation magnitude and lateral migration.

14. J. Mondal, Rajaram Lakkaraju, P. Ghosh, M. Ashokkumar, Acoustic cavitation‑induced shear: a mini‑review, Biophysical Reviews 13, 1229–1243 (2021) https://doi.org/10.1007/s12551-021-00896-5 (.pdf)

Acoustic cavitation (or the formation of bubbles using acoustic or ultrasound-based devices) has been extensively exploited for biological applications in the form of bio-processing and drug delivery/uptake. However, the governing parameters behind the several physical effects induced by cavitation are generally lacking in quantity in terms of suitable operating parameters of ultrasonic units. This review elaborates the current gaps in this realm and summarizes suitable investigative tools to explore the shear generated during cavitation. The underlying physics behind these events are also discussed. Furthermore, current advances of acoustic shear on biological specimens as well as future prospects of this cavitation-induced shear are also described.

13. J. Mondal, W. Li. A. R. Rezk, L. Y. Yeo, Rajaram Lakkaraju, P. Ghosh and M. Ashokkumar, Acoustic cavitation at low gas pressures in PZT- based ultrasonic systems, Ultrasonics Sonochemistry 73, 105493 (2021) https://doi.org/10.1016/j.ultsonch.2021.1054931 (.pdf)

The generation of cavitation-free radicals through evanescent electric field and bulk-streaming was reported when micro-volumes of a liquid were subjected to 10 MHz surface acoustic waves (SAW) on a piezoelectric substrate [Rezk et al., J. Phys. Chem. Lett. 2020, 11, 4655–4661; Rezk et al., Adv. Sci. 2021, 8, 2001983]. In the current study, we have tested a similar hypothesis with PZT-based ultrasonic units (760 kHz and 2 MHz) with varying dissolved gas concentrations, by sonochemiluminescence measurement and iodide dosimetry, to correlate radical generation with dissolved gas concentrations. The dissolved gas concentration was adjusted by controlling the over-head gas pressure. Our study reveals that there is a strong correlation between sonochemical activity and dissolved gas concentration, with negligible sonochemical activity at near-vacuum conditions. We therefore conclude that radical generation is dominated by acoustic cavitation in conventional PZT-based ultrasonic reactors, regardless of the excitation frequency.

12. P. Kar, Y. N. Kumar, P. K. Das and Rajaram Lakkaraju, Thermal convection in octagonal-shaped enclosures, Physical Review Fluids 5, 103501 (2020) https://doi.org/10.1103/PhysRevFluids.5.103501 (.pdf)

Flow reversal phenomena in a classical two-dimensional (2D) Rayleigh-B\'{e}nard convection, in a square enclosure, is usually explained through growth and merging of diagonally opposite counter-rotating corner rolls. To probe further on the corner roll growth dynamics, we have altered the square enclosure edges by additional slant conduction walls, so that the enclosure resembles an octagonal shape. We have performed a series of 2D numerical simulations by varying the slant wall inclination angle ($\alpha$) from $0^{\circ}$ to $45^{\circ}$, to construct a detailed flow map in thermal convection in a range $5\times10^5\le Ra\le 10^8$ and $0.8\le Pr\le 2.0$, where $Ra$ is the Rayleigh number, and $Pr$ is the Prandtl number. Depending on $Ra$, $Pr$ and $\alpha$, flow features in the octagonal enclosure can exist in the form of a uniform circulation, a two-roll, a mixed, a periodic, a quasi-periodic, or multiple flow states superimposed on each other. The flow reversals in the octagonal enclosure take place by several ways, for example, it is by the ejection of mushroom-shaped plumes alternatively from the opposite slant walls at low $Ra$ ($\approx 10^5$) and high $Pr$ ($\approx 2$), by the corner rolls growth at high $Ra$ ($\approx 10^8$) and low $Pr$ ($\approx 1.2$), and by the dipole at high $Ra$ ($\approx 10^8$) and high $Pr$ ($\approx 2$). Strikingly, the dimensionless flow reversal frequency scales linearly with an increase in $\alpha$, and the slope varies from $1.04$ at low $Ra=5\times 10^5$ to $0.328$ at high $Ra=10^8$. We have shown the flow reversals are a consequence of competition between the dipole (a two roll state where a cold roll sits above a hot roll) and the quadrupole (the four corner rolls) modes with the monopole mode. A uniform circulation with flow reversal results if the quadrupole mode wins, and a two-roll state with a reversal results, if the dipole wins. At high $Ra(\ge 10^8)$, the dipole strengthens, and the core bulk region shows hydrodynamic instabilities in the form of turbulent-like engulfments. We have uncovered the mechanism responsible for the observed engulfments due to the increase in turbulence production in the core bulk region by the buoyancy. As a result, we have observed total heat transport also increases up to $14\%$ when $\alpha$ is varied from $0^{\circ}$ to $45^{\circ}$.

11. R. Roy, S. Mukherjee, Rajaram Lakkaraju and S. Chakraborty, Streaming potential in bio-mimetic micro-vessels mediated by capillary glycocalyx, Microvascular Research 132, 104039 (2020) https://doi.org/10.1016/j.mvr.2020.104039 (.pdf)

Implantable medical devices and biosensors are pivotal in revolutionizing the field of medical technology by opening new dimensions in the field of disease detection and cure. These devices need to harness a bio-compatible and physiologically sustainable safe power source instead of relying on external stimuli, overcoming the constraints on their applicability in-vivo. Here, by appealing to the interplay of electromechanics and hydrodynamics in physiologically relevant microvessels, we bring out the role of charged endothelial glycocalyx layer (EGL) towards establishing a streaming potential across physiological fluidic conduits. We account for the complex rheology of blood-mimicking fluid by appealing to Newtonian fluid model representing the blood plasma and a viscoelastic fluid model representing the whole blood. We model the EGL as a poroelastic layer with volumetric charge distribution. Our results reveal that for physiologically relevant micro-flows, the streaming potential induced is typically of the order of 0.1 V/mm, which may turn out to be substantial towards energizing biosensors and implantable medical devices whose power requirements are typically in the range of micro to milliwatts. We also bring out the specific implications of the relevant physiological parameters towards establishment of the streaming potential, with a vision of augmenting the same within plausible functional limits. We further unveil that the dependence of streaming potential on EGL thickness might be one of the key aspects in unlocking the mystery behind the angiogenesis pattern. Our results may open up novel bio-sensing and actuating possibilities in medical diagnostics as well as may provide a possible alternative regarding the development of physiologically safe and biocompatible power sources within the human body.

10. O. Satbhai, S. Roy, S. Ghosh, S. Chakraborty and Rajaram Lakkaraju, Comparison of the quasi-steady-state heat transport in phase-change and classical Rayleigh-Bénard convection for a wide range of Stefan number and Rayleigh number, Physics of Fluids 31, 096605 (2019) https://doi.org/10.1063/1.5110295 (.pdf)

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height Raf is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters Raf (3.96 × 104 ≤ Raf ≤ 9.26 × 107 ) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102 ) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate Nuh vs Raf for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nuh increase with the increase in Ste and Raf . There are two distinct RB flow configurations at low Raf independent of Ste. At low and moderate Raf , the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection Nuh /NuRB is always greater than one. However, at higher Raf , the RB convection is turbulent, and Nuh /NuRB can be less than or greater than one depending on the value of Ste. The results may turnout to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

9. A. Senapati, G. Singh and Rajaram Lakkaraju, Direct numerical simulations of an in-line rising unequal sized bubble pair in a liquidcolumn, Chemical Engineering Science 208, 115159 (2019) https://doi.org/10.1016/j.ces.2019.115159 (.pdf)

We have studied the motion of a pair of unequal-sized in-line rising bubbles in a quiescent liquid column, using the Volume of Fluid (VOF) method based on direct numerical simulations. The simulations are performed for a wide range of Archimedes numbers ($400<Ar<4500$) to study the bubbles' shape, rise-velocity, induced flow topology, and the wake structure. The rise-velocity of leading bubble hardly changes, although the trailing bubble follows it. However, the trailing bubble always accelerates due to the negative pressure zone created by the leading bubble's wake. The trailing bubble rise-velocity increases with time as ${V_t}\propto t^{\zeta}V_L$, where $0<\zeta<2$. While bubbles rise, the surrounding liquid is subjected to intense agitation. The level of agitation is quantified using liquid kinetic energy and increases with $Ar$. We find that the agitation level in the vertical direction is nearly three times higher than in horizontal direction. Also, we have examined wake behaviour behind the bubbles using pressure distribution, streamwise vorticity, and the Q-criteria based vortex structures in detail. Our work has unveiled two dominant vortex structures in the wake: (1) a toroidal ring on the bubble surface near the maximum diameter plane which occasionally detaches, and (2) a set of hairpins near the rear stagnation point, which grows by diffusion. The hairpins grow with time and join to form flower-like ejections. However, the toroidal ring advects in the downstream direction and tries to mask the hairpins.

8. G. Singh and Rajaram Lakkaraju, Wall-mounted flexible plates in a two-dimensional channel trigger early flow instabilities, Physical Review E, 100, 023109 (2019) https://doi.org/10.1103/PhysRevE.100.023109 It is featured as a Kaleidoscope of the month (.pdf)

High level of mixing by passive means, is a desirable feature in microchannels for various applications, and use of flexible obstacles (or plates) is one of the prime choices in that regard. To get further insight, we have carried out two-dimensional numerical simulations for flow past one or two flexible plates anchored to a channel's opposite walls using fluid-structure interaction framework. On the inlet flow Reynolds number vs. the Strouhal number plane, we observed a sudden flow change from a laminar to a time-periodic vortex shedding state, when flexible plates are present in the channel. We found the critical Reynolds number as $Re_{cr}\approx 370$ when a single plate is anchored on the channel wall and $Re_{cr}\approx 290$ or even lower when two plates are anchored. With an increase in the inlet flow Reynolds number (up to 3200), we found vortices detach regularly at the plates' tips, which cause the flow to meander in the channel. In a two-plate anchored configuration, primary vortices generated at the first plate are constrained by the second plate, and result in an energetic secondary vortex generation in the downstream side. The overall flow features and the energy dissipation in the channel are mainly controlled by the separation gap between the plates. At high inlet flow Reynolds numbers ($\ge 1600$), the probability density function ($\mathcal{F}$) of the kinetic energy dissipation in a flexible plate configuration shows a stretched exponential shape in the form $\mathcal{F}(Z)\sim{\frac{1}{{\sqrt{Z}}}e^{-pZ^q}}$, where $Z$ is the normalized kinetic energy dissipation and the constants, $p=0.89$ and $q=0.86$. The observed increase in energy dissipation comes at the cost of an increase in pressure loss in the channel, and we found that the loss is inversely related to the plates' separation gap. From our simulations, we found that if high mixing levels are desired, then two flexible plates anchored to the channel walls is a better choice than a channel flow without obstacles or flow past a single plate. The two plate configuration with zero separation gap between the plates suits the best to achieve high mixing level.

7. Y. N. Kumar, S. Chakraborty, M. K. Verma and Rajaram Lakkaraju, On heat transport and energy partition in thermal convection with mixed boundary conditions, Physics of Fluids, 31, 066601 (2019) https://doi.org/10.1063/1.5095242 (.pdf)

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison to the classical Rayleigh-B\'{e}nard (RB) convection in the range of Rayleigh number $10^5\le Ra \le 10^9$. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represents the applied thermal conditions on the bottom wall, and the last two letters for the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number $Ra=10^8$ is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for the HCCH and HCHC as compared to the RB convection in a range $10^5\le Ra < 10^8$. The increase in heat transport is due to (1) increase in the background potential energy in case of HCCH, and (2) increase in the available potential energy in case of HCHC, and is confirmed by using the global energy budget.

6. S. A. Etha, A. Jena and Rajaram Lakkaraju, Clusterlike instabilities in bubble-plume-driven flows, Physical Review E, 99, 053101 (2019) https://doi.org/10.1103/PhysRevE.99.053101 (.pdf)

Continuous release of gas bubbles in large numbers from a localized source in a liquid column, popularly known as `bubble plumes', is very relevant in nature and industries. The bubble plumes morphologically consist of long continuous stem supporting a dispersed head. Through our direct numerical simulations using two-way coupled Euler-Lagrangian framework, we show that the bubble plume rising in a quiescent liquid column develops cluster-like instabilities for the Grashof numbers, $Gr>145$. For levels ($Gr<100$), the stem is continuous with small plume head, whereas at high buoyancy ($Gr>350$), the plume stem shows intermittently passing puffing instabilities in the form of bubble clusters. The clusters are a group of bubbles localized in space with high concentration and travel upward with speed $C_{ph}=0.45U_C$ and separated by a distance of $5L_0$, where $U_C$ is the characteristic velocity and $L_0$ is the characteristic length based on the injection conditions. The bubble rise Reynolds numbers in the steady state for both the plume head and the stem shows $Re\propto Gr^{0.45\pm 0.03}$, and the proportionality constant is ten times higher in the plume stem than in the plume head. In the plume core, the spatial acceleration due to the bubble motion generates the turbulent production, whereas, at the plume edge, the small-scale fluctuations generate the mean vorticity. At high $Gr$, the clusters evolve due to the lift forces acting on the bubbles as a result of increase in the mean vorticity. While rising, bubbles entrain the liquid from the surroundings, and we found the entrainment rate is not as strong as compared to the classical thermal plumes.

5. Rajaram Lakkaraju, F. Toschi and D. Lohse, Bubbling reduces intermittency in thermal convection, Journal of Fluid Mechanics, 745, 1-24 (2014) https://doi.org/10.1017/jfm.2014.33 It is featured as a Cover page of the Journal (.pdf)

Intermittency effects are numerically studied in turbulent bubbling Rayleigh-B\'{e}nard (RB) flow and compared to the standard RB case. The vapor bubbles are modelled with a Euler-Lagrangian scheme and are two-way coupled to the flow and temperature fields, both mechanically and thermally. To quantify the degree of intermittency we use probability density functions, structure functions, Extended Self Similarity (ESS) and Generalized Extended Self Similarity (GESS) for both temperature and velocity differences. For the standard RB case we reproduce scaling very close to the Obukhov-Corrsin values common for a passive scalar and the corresponding relatively strong intermittency for the temperature fluctuations, which are known to originate from sharp temperature fronts. These sharp fronts are smoothened by the vapor bubbles due to their heat capacity, leading to much less intermittency in the temperature but also in the velocity field in bubbling thermal convection.

4. Rajaram Lakkaraju, R. J. A. M. Stevens, P. Oresta, R. Verzicco, D. Lohse and A. Prosperetti, Heat transport in bubbling turbulent convection, Proceedings of the National Academy of Sciences of the United States of America (PNAS), 110 (23) 9237-9242 (2013) https://doi.org/10.1073/pnas.1217546110 (.pdf)

Boiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to several mechanisms many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubbles compounds with that of the liquid to give rise to a much enhanced natural convection. In this paper we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh-B\'{e}nard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping their difference constant we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between $2\times10^6$ and $5\times10^9$. We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh-B\'{e}nard convection.

3. Rajaram Lakkarajuu, R. J. A. M. Stevens, R. Verzicco, S. Grossman, A. Prosperetti, C. Sun and D. Lohse, Spatial distribution of heat flux and fluctuations in turbulent Rayleigh-Bénard convection, Physical Review E, 86, 056315 (2012) https://doi.org/10.1103/PhysRevE.86.056315 (.pdf)

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux $\overline{j}(r)$ in a cylindrical Rayleigh-B\'{e}nard cell with aspect ratio $\Gamma=1$ for Rayleigh numbers $Ra$ between $2 \times 10^6$ and $2\times 10^{9}$ at a fixed Prandtl number $Pr = 5.2$. The numerical results reveal that the heat flux close to the side wall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, $\overline{j}(r)\propto Ra^{\gamma_j(r)}$. The scaling exponent $\gamma_j(r)$ decreases monotonically from $0.43$ near the axis ($r \approx 0$) to $0.29$ close to the side walls ($r \approx D/2$). The effective exponents near the axis and the side wall agree well with the measurements of Shang et al. (Phys.\ Rev.\ Lett.\ \textbf{100}, 244503, 2008) and the predictions of Grossmann and Lohse (Phys.\ Fluids \textbf{16}, 1070, 2004). Extrapolating our results to large Rayleigh number would imply a crossover at $Ra\approx 10^{15}$, where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down, than in plume depleted regions.

2. Rajaram Lakkaraju, L. E. Schmidt, P. Oresta, F. Toschi, R. Verzicco, D. Lohse and A. Prosperetti, Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-Bénard convection, Physical Review E, 84, 036312 (2011) https://doi.org/10.1103/PhysRevE.84.036312 (.pdf)

Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudo-turbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

1. Rajaram Lakkaraju and M. Alam, Effects of Prandtl number and a new instability mode in a plane thermal plume, Journal of Fluid Mechanics, 592, 221-232 (2007) https://doi.org/10.1017/S0022112007008610 (.pdf)

The eﬀect of Prandtl number on the linear stability of a plane thermal plume is analysed under quasi-parallel approximation. At large Prandtl numbers (Pr > 100), we found that there is an additional unstable loop whose size increases with increasing Pr. The origin of this new instability mode is shown to be tied to the coupling of the momentum and thermal perturbation equations. Analyses of the perturbation kinetic energy and thermal energy suggest that the buoyancy force is the main source of perturbation energy at high Prandtl numbers that drives this instability.