A computational study has been performed in order to characterize the free convection heat transfer around the thick tapered vertical tube (decreasing or increasing or uniform cross-section) with a ...constant inner surface temperature. Simulations are carried out by varying Rayleigh number (
Ra
) within the laminar range (10
4
≤
Ra
≤ 10
8
). Moreover, the geometrical and thermal parametric variations, namely, slant height to thickness ratio (5 ≤
L/B
≤ 20), diameter ratio (0.25 ≤
d
1
/d
2
≤ 1.75) and thermal conductivity of the tube material (
K
s
) are employed to obtain the pattern of the heat removal rate and flow field around thick pipe. Mass flow rate through the pipe is also estimated for different diameter ratio. Velocity vectors are shown to predict the flow behavior around the tapered pipe. It is found that the low value of velocity at core of the pipe for low
d
1
/d
2
in comparison to high
d
1
/d
2
. A correlation has been developed in order to predict the average Nusselt number in terms of geometrical and thermal parameters based on the computed data points which would be useful for the industrial purposes.
Efforts are made to elucidate a three-dimensional (3D) computational work on laminar free/natural convection flows around the isothermally heated inclined hollow cylinder immersed in the quiescent ...ambient air negligible wall thickness. The thermofluidic characterization is performed by solving three-dimensional governing differential equations i.e. continuity, momentum, and energy equations over the following ranges of pertinent parameters: Rayleigh number, 10
4
≤ Ra ≤ 10
8
; cylindrical aspect ratio, 1 ≤ L/D ≤ 20; tube inclination, 0°≤θ ≤ 90°. Detailed behaviors of thermal and flow fields are delineated with the help of visualization technique like temperature contours and velocity vectors in order to identify the regions of low/high temperature gradient and fluid velocity. The influence of Ra, L/D, and θ on the local and average Nusselt number is predicted and it is seen that the average Nusselt number on outer and inner surface increases and decreases, respectively with the reduction in tube inclination for a particular Ra and L/D. A couple of correlation has been developed for the average Nusselt number on outer and inner surface of the hollow cylinder as a function of Ra, L/D, and θ based on the computed data points which would be helpful for various academic and industrial purposes.
Efforts are made to delineate the free convection analysis numerically from a pair of vertically attached vertical hollow isothermally heated cylinders with negligible wall thickness immersed in the ...air within the laminar flow regimes. Thermofluidic behavior around the cylinders is characterized in detail by employing the influence of several relevant dimensionless parameters such as, Rayleigh number (10
3
≤
≤ 10
7
), spacing-to-length ratio
and upper to lower cylinder diameter ratio
Importantly, heat transfer and fluid flow patterns around the upper cylinder due to the presence of a lower cylinder are thoroughly elucidated, which is not fully understood in the existing literature. It is seen that the enhancement of heat transfer rate from the inner surface is greatly influenced at
for lower value of
and
A linear growth and non-linear reduction patterns against
are observed for Nusselt numbers for inner and outer walls, respectively, for fixed value of
and
Lastly, a suitable correlation has been proposed for net average Nusselt number as a function of relevant input dimensionless parameters. The correlation shows an excellent agreement with the computed data points within ±6%. This correlation is also expected to be helpful for the relevant engineering calculations and provide values for various academic and industrial purposes.
•A numerical work of head-on coalescence of binary drops onto a cylindrical target.•Temporal deformation factor is predicted during the entire droplet collision cycle.•Maximum deformation factor is ...estimated just after the collision of drops.•Ring drop is observed to be pinched off from the parent merged drop.•A correlation for maximum deformation factor is developed using computational data.
In this paper, a numerical exercise in understanding the binary head-on collision of equal-sized vertically aligned drops on the cylindrical substrate is reported. Subsequently, radial spreading of the liquid bridge, impact, and detachment of merged drop from the solid target. Different dimensionless relevant factors, namely Weber number (We), contact angle θ, Ohnesorge number (Oh), Bond number (Bo), and diameter ratio Dc/Do are used to characterize the coalescence, and subsequent impingement onto the cylindrical substrate. Temporal deformation factor βf is predicted throughout the entire droplet cycle, and the maximum deformation factor βf,max is obtained just after the collision of drops because of the significant radial expansion of merged drop. A larger value of βf,max is achieved at a higher We for a constant θ, Dc/Do, and Oh. Interestingly, the ring drop is pinched off from the parent merged drop when the value of Dc/Do is lower at a higher value of We. Again, the possibility of the appearance of the ring is significantly higher when the target surface becomes non-wetting. A correlation for the maximum deformation factor is developed using computational data points, which fits well with the simulated data within ± 6 %. Lastly, a theoretical framework is also predicted to determine the maximum deformation factor.
•A numerical work on collision and drainage of liquid droplet around sphere placed within a hollow cylinder.•Droplet undergoes several important stages.•Examined the behaviour of deformation factor ...across the course of the collision process.•The drainage process gets enhanced at a higher We compared to a lower W.•A correlation for deformation factor is developed using computational data.
It is attempted earnestly to elucidate the mechanism of collision and drainage of liquid mass around the spherical substrate suspended within the hollow cylinder using Gerris open-source code by employing Volume of Fluid (VOF) methodology. Various influencing parameters, namely, sphere-to-droplet diameter ratio (Ds/Do), Weber number(We), Ohnesorge number (Oh), and Bond number(Bo) are employed to observe the drainage mechanism through the constricted path. The pattern of the interfacial morphology of droplet collision and drainage mechanism is presented using numerical contours. It is important to mention herein that the droplet undergoes several important stages like collision, cap formation, engulfment, drainage, and pinch-off. The passage between the sphere and the cylinder is sufficiently wider at a lower value of Ds/Do due to which the liquid mass is drained out completely without any hindrance. The drainage process becomes considerably faster at a higher We compared to a lower We. In addition, the flow of liquid mass through the passage gets delayed at a greater Oh than a lower Oh assuming a given value of We and Ds/Do. The liquid drop requires less time to pass through the constricted path at lower Bo for a given value of Ds/Do and We. We have also attempted to quantify the drainage of liquid volume passes through the passage, which is denoted as (Q*=Q/Qo). One can notice the increasing pattern of Q/Qo with continuous progress of time stamp for all cases of Ds/Do for a fixed value of We.
Fluid entrainment is a complex and deeply attractive phenomenon that is frequently encountered in both industry and nature. In general, entrainment deals with the basic understanding of penetration ...one fluid into another which leads to occurrence of complex interfacial structure. The present article addresses a detailed description of the recent studies on entrainment dynamics caused by the external rotational flux across the interfaces is elaborated. Despite of considerable progress in understanding rotation induced entrainment, there are still several questions unanswered due to its difficulty, unpredictability, three-dimensional effects, and chaotic nature. Therefore, here we explained numerous numerical, experimental, and analytical investigations with their relevance in engineering applications wherein the increase of interfacial area causes enhancement of heat and mass transfer. The description also includes various patterns of entrained fluid entities due to rotations induced across the interface. Furthermore, the entrainment behaviors have been critically analyzed to draw out the distinct categorization of rollers relying on parameters such as submergence ratio with different gas–liquid pairs.
•We present the bubble-bubble interaction patterns when emerged from submerged orifices.•Three distinct patterns of bubble release dependent on mutual spacing of the orifices are ...reported.•Hydrodynamic reasons of different merging regimes are described using velocity vectors around the bubbles.•A map of different zones as a function of Mo, orifice diameter and spacing has been proposed.•Effect of van der Waals force has been established in connection of bridge thinning by virtue of gas inertia.
Present study reports numerical investigations on the bubble evolution at submerged orifices and their mutual interactions in quiescent liquid under constant inflow condition of air. In finite volume based 3D domain, breaking and making of interfaces are tracked using volume of fluid (VOF) solver. Binary interaction dynamics is studied for a wide range of fluid properties (3.85×10−11<Mo<4.645×10−6), orifice diameters (1, 1.5 and 2mm) and spacings (2–10mm). Apart from observed coalescence and non-coalescence, fusion of bubbles before and after pinch off from orifice mouth at different Mo are presented. Using velocity patterns inside the bubble, explanation of different merging pattern is proposed. A 3D map for distinct behaviour while merging, in terms of Mo, orifice diameter and spacing is also tried. Finally, effect of velocity of gaseous phase on merging between sister bubbles are assessed numerically.
