Science-based research articles

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.

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.

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.

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.

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.

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.

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.

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. 

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. 

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.

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.

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.

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.