TRANSIENT ANALYSIS ON 3D DROPLET OVER HORIZONTAL SURFACE UNDER SHEAR FLOW WITH ADIABATIC BOUNDARY CONDITIONS BY USING FVM

International Journal of Advances in Engineering & Technology, June, 2017.
©IJAET ISSN: 22311963
373 Vol. 10, Issue 3, pp. 373-382
TRANSIENT ANALYSIS ON 3D DROPLET OVER HORIZONTAL
SURFACE UNDER SHEAR FLOW WITH ADIABATIC
BOUNDARY CONDITIONS BY USING FVM
R.Rajesh1
and B.Chandrasekhar2
1
PG Student Department of Mechanical Engineering,
ASR College of Engineering, Tanuku, India
2
Assistant Professor, Department of Mechanical Engineering,
ASR College of Engineering, Tanuku, India
ABSTRACT
In the present work, an investigation has been made about the shape change and movement
phenomena of liquid droplet over a horizontal solid surface under shear flow with adiabatic boundary
condition. Finite Volume Method (FVM) with 3D Volume of Fluid (VOF) model has been used to
formulate/simulate the complex interface in multiphase flow. The effect of important factors which govern
the drop dynamics on a solid surface (like fluid properties: density, surface tension, viscosity and the
surface characteristics: surface material, contact angle, roughness) have been studied extensively. Effects of
shear strength in terms of air inlet velocity and drop size have also been studied by varying the Reynolds
number of inlet air flow and drop volume respectively. Phase contours at different time instant have been
produced for each of the case study. Again, the velocity contours and velocity vectors have also been
generated for better understanding of the present phenomena. The acquired velocity by the droplet at
different time instants has been calculated and the variation of the acquired velocity with time instants is
plotted. Again it has been observed that depending upon various boundary conditions and external effects,
it may possible to move the drop in any desired direction as per the requirement in various engineering
applications like micro pumps, printers, coating devices etc.
KEYWORDS: Multiphase flow; Droplet; Interface; Volume of Fluid (VOF); Finite Volume Method (FVM);
Contact angle, Surface tension, Shear flow.
I. INTRODUCTION
Dynamics of liquid droplet is one of the most important areas of research not only for academic
reasons but also for various engineering applications. For example many industrial and material
processing operations require the regulation and control of movement of liquid drops on solid
surface. When a drop of liquid makes an impact on a flat solid surface, the movement and the final
shape obtained depends upon a large number of factors which mainly influence the drop dynamics.
As per various theories the shape and motion of a liquid droplet would be a function of surface
tension of the liquid pairs, material properties of the solid surface and liquids, homogeneity of
the materials, gravity effects, thermal gradient, surface wettability, surrounding medium, geometry
of the surface etc. The dynamics of a small liquid drop is a bit different than that of the bulk fluid
because the surface tension force dominates over the inertial and viscous forces. The movement of
the droplet is also influenced significantly by contact angle. The contact angle is conventionally
measured through the liquid, where liquid interface meets a solid surface. Contact angle
quantifies the wettability of a solid surface by a liquid which can be estimated by the Young’s
equations. The shape of the liquid interface is determined by Young-Laplace equation where the
contact angle plays the role of boundary condition via Young’s equation as shown in Figure. A solid
surface may be categorized as i) hydrophobic surface and ii) hydrophilic surface according to the

374 Vol. 10, Issue 3, pp. 373-382
contact angle of water on the given solid surface as shown in Figure 1.2. The solid surface is
said to be hydrophobic if the water contact angle is greater than 900 and if the water contact
angle is smaller than 900, the solid surface is treated as hydrophilic.
Fig 1.1: Schematic diagram for Young’s Equation Fig 1.2: Schematic diagram of hydrophobic and
hydrophilic surface.
II. APPLICATIONS OF CFD (FVM)
Several numerical methods of Computational Fluid Dynamics (CFD) are available to simulate
multiphase flow problem. The Volume of Fluid (VOF) model with 3D Finite Volume Method
(FVM) may be a very significant methodology to study and inspect the shape change and
movement phenomena of the liquid droplet under shear flow in a flat solid surface.
III. CASE STUDIES
Several studies have been undertaken in last few decades on the liquid droplet motion in a solid
surface. The motion of spherical or nearly spherical drops in a channel consisting of two
parallel walls has received attention by a variety of exact and approximate methods. The
parallel motion of a nearly spherical drop between two channel walls in a quiescent fluid was
considered by Shapira and Haber (1988) using the method of reflections. Approximate solutions
for the hydrodynamic drag force exerted on the droplet were obtained, which are accurate when the
drop-to-wall spacing is not small. Again Chen and Keh (2001) utilized a boundary-collocation
technique to examine the parallel motion of spherical drops moving near one plane wall and
between two parallel plates as a function of drop size and viscosity ratio. The motion of rigid
particles in Stokes flow between two planar walls has also been studied (Staben et al., 2003),
where a boundary-integral method was used to find the translational and rotational velocities of
spherical and ellipsoidal particles, as functions of particle size and location in the channel.
Also another related study to the problem is the motion of deformable drops through cylindrical
tubes, which has received considerable attention and is motivated by several applications in the
field of biomechanics. For example, the motion of red blood cells through veins or capillaries, as
well as the fate of gas bubbles in the blood stream, is of significant biological and clinical
interest. Olbricht and Kung (1992), For many years, the dynamics of drop impact and
spreading has been a challenging problem for physicists and engineers. The experimental
investigations of Sikalo et al. (2005a-c) with liquids of varying surface tension and viscosity
(e.g., isopropanol, water and glycerin) showed that the drop volume, the surface inclination and
impact velocity have a significant effect on the drop dynamics and the regimes of drop impact.
Besides the experimental investigations discussed above, several numerical studies on the

375 Vol. 10, Issue 3, pp. 373-382
dynamics of liquid droplet spreading over solid surfaces have been reported in the literature like
Fukai et al., 1995; Bussmann et al., 1999; Pasandideh-Fard et al., 2002; Gunjal et al., 2005,
Sikalo et al., 2005d. Different numerical methods are available for computations of flows with
moving interfaces, for example, the level set method (Osher and Sethian, 1988; Sussman and
Osher, 1994), the front tracking method (Unverdi and Tryggvason, 1992; Tryggvason et al., 2001)
and the lattice-Boltzmann method (Gunstensen et al., 1991; Grunau et al., 1993, Shan and Chen,
1993; Shan and Doolen, 1995; Nourgaliev et al., 2003) and the volume of fluid (VOF) method
(Hirt and Nichols, 1981). Gunjal et al., 2005; Sikalo et al., 2005d. Fukai et al. (1995) investigated
the effect of the surface wettability on the spreading behavior of a drop. They observed that the
impact velocity greatly influences the droplet spreading behavior. The incorporation of advancing
and receding angles in the numerical model with adaptive mesh refinement improved their
extrapolations. Pasandideh-Fard et al. (2002) studied the three- dimensional solidification of a
molten drop on horizontal and inclined surfaces with an interface tracking algorithm and a
continuum surface force (CSF) model. Gunjal et al. (2005) carried out an experimental and VOF
based numerical study of the drop impact over horizontal surfaces. Their predictions successfully
captured the spreading, splashing, rebounding and bouncing regimes of the drop dynamics over
horizontal surfaces of different states of wettability. Most of the numerical simulations of drop
spreading discussed above were carried for horizontal surfaces and using the Static Contact Angle
(SCA) model. Again several experimentations and investigations have been carried out by many
authors on dynamics of a liquid drop over an inclined surface with a wettability gradient. Thiele et
al. (2004) identified a reaction limited zone below the droplet moving over a gradient surface
and proposed that the change of reaction rate causes a different driving force for droplet movement.
Later, Pismen and Thiele (2006) developed an asymptotic solution for drop dynamics over a
gradient surface using lubrication theory. Subramanian et al. (2005) made some approximation of
the drop shape over a gradient surface by collection of over a horizontal surface. For the first time,
Huang et al. (2008) employed a numerical technique based on lattice Boltzmann method for the
investigation of wettability controlled planar movement of a liquid drop. Recently, Liao et al.
(2009) numerically simulated the equilibrium shape of a liquid drop on a surface having a surface
energy gradient applying a finite element method.
More recently, Das A.K. and Das P.K. (2010) investigated the motion of liquid drops over an
inclined gradient surface using a 3D computational technique. Simulation results reveal that drop
motion is dependent on the surface inclination, volume of the droplet and the strength of the
wettability gradient. It has been found that, depending on these parameters, a droplet can
experience downward or upward motion or can remain stationary on the inclined plane. Finally,
drop movement plots which give an idea about the regimes of uphill and downhill movement of a
drop over gradient surfaces have been proposed. In addition to above discussions as the formation,
growth and detachment of a drop are initial phenomena that take place during every process
involving drops, many investigations have been accomplished in this field. Regardless of being
critical to some industrial applications, the formation of a drop is a challenging, controversial free
boundary problem. Also, Loth (2008) reported various theoretical efforts in this field. These
investigations showed that the Weber number dominates the shape of the drops for a wide
surface tension, and determined different types of deformation dependent on the relevant
dimensionless numbers. In most of the theories, variations of important parameters which influence
the drop dynamics have been plotted with respect to dimensionless time.
IV. AIM AND OBJECTIVES
The main objective of the present work is to visualize the effects of key parameters on drop
formation, drop movement and to capture the drop dynamics on horizontal solid surface under
shear flow with adiabatic boundary condition. The shape change and movement of the liquid
droplet has been examined by varying the air inlet velocity and drop volume. The effects of
variation of contact angle and surface tension have also been studied on the above mentioned
phenomena.

376 Vol. 10, Issue 3, pp. 373-382
V. PROBLEM STATEMENT
5.1 Problem Descriptions
The shape change and movement phenomena of liquid droplet over a horizontal solid surface under
shear flow with adiabatic boundary condition have been studied in the present dissertation. Finite
Volume Method (FVM) with 3D Volume of Fluid (VOF) model has been used to
formulate/simulate the complex interface in multiphase flow.
For this study, a rectangular parallelepiped domain of air with dimension 40 mm × 40 mm × 20
mm has been chosen where the hemispherical water droplet (in terms of diameter) has been placed
in the bottom horizontal surface (40 mm × 40 mm) as shown in Figure 2.1. Velocity inlet boundary
condition has been used at the left plane of the rectangular parallelepiped. A uniform velocity
profile (u = uin, v = 0, w =0) is prescribed at the inlet. At the right plane Pressure outlet boundary
condition (p =patm) and at the top plane Pressure inlet boundary condition (p = patm) have
been considered. At the front, rear and bottom plane Wall boundary conditions (no slip and no
penetration boundary condition) have been used. The effects of key parameters on the present
phenomena have been studied by varying contact angle (angle of contact between the water
droplet and solid surface), and surface tension. Effects of shear strength in shear flow in terms
of air inlet velocity and drop size have also been studied by varying the Reynolds number of
inlet air flow and drop diameter respectively. For better understanding, six different cases have
been considered and studied about this dynamics of the droplet under the said boundary conditions.
Atmospheric pressure
Figure 5.1: Schematic representation of the selected problem.
Six different cases have been considered and studied successfully. They are mentioned below:
i. Dynamics of liquid droplet with diameter: 5 mm, contact angle: 90 degree and without
any shear flow.
ii. Dynamics of liquid droplet with diameter: 5 mm, contact angle: 90 degree and laminar
air flow (Re: 1500)
iii. Dynamics of liquid droplet with diameter: 5 mm, contact angle: 90 degree and
turbulent air flow (Re: 3000)
iv. Dynamics of liquid droplet with diameter: 10 mm, contact angle: 90 degree and
v. Dynamics of liquid droplet with diameter: 10 mm, contact angle: 150 degree and
vi. Dynamics of liquid metal (Hg) droplet with diameter: 5 mm, contact angle: 150
degree and turbulent air flow (Re: 3000)
VI. SOLUTION STRATEGY
Commercial CFD software Gambit and Fluent have been used to analyze the problem. The
rectangular parallelepiped domain of air has been modeled and meshed in Gambit with suitable
boundary conditions and Fluent has been used for hydrodynamic and heat transfer
calculation (numerically).
Liquid
Droplet
Flat
Plate
Uniformvelocity

377 Vol. 10, Issue 3, pp. 373-382

6.1 Numerical calculation
In the present work, the 3D Volume of Fluid (VOF) multiphase modeling with Finite Volume
Method (FVM) has been used to analyze the shape and movement of water droplet under shear
flow on a horizontal flat plate. Volume of Fluid (VOF) is a surface tracking technique used for
two or more immiscible fluids by solving a single set of momentum equation. Here, the VOF
technique with pressure-based solver in 3D version has been used to analyze such a complex,
non-linear, unsteady problem. Then Pressure Implicit solution by Split Operator (PISO) has been
used to simulate the complex interface. The pressure-based approach has been used where the
pressure field is extracted by solving a pressure or pressure correction equation which is
obtained by manipulating continuity and momentum equation. In addition, for turbulent modeling,
k-ε turbulent model is used.
6.1.1 Governing equations
The governing equations used to simulate this multi-phase flow problem are;
The Continuity Equation: As we know continuity equation is derived on the basis of principle of
conservation of mass, it is most important governing equation in any CFD problem. Moreover,
stability of the solution depends on this equation. The continuity equation in the vector form for
each the individual phase is given by;

.v0........................................................(6.1)
t
The Navier-Stroke’s Equation (Momentum equations): In VOF multiphase flow
modeling with pressure-based solver, a single set of mo equations has been used
throughout the domain. The Navier-stroke’s Equation which governs the flow field is given by;
(v) .vvp .v vT
g F.........................(6.2)
t  

Grid pattern employed
Figure 6.1: Modeling of parallelepiped domain with suitable mesh and boundary conditions.
It has been found that ‘Hex/Wedge’ element is the most suitable grid pattern for this
multiphase flow problem which can influence the accuracy of the solution. So the
‘Hex/Wedge’ elements with ‘Cooper’ type grid have been considered for meshing the
geometrical model as shown in Figure 6.1. Finally for the better shape and size of the
hemispherical water droplet a grid size of 0.000375 has been chosen through a grid
independent test.


378 Vol. 10, Issue 3, pp. 373-382
VII. RESULTS AND GRAPHS
Fig 7.1: Velocity contours at the vertical mid-
plane at different time instants (for droplet with
diameter: 5mm, contact angle: 90
0
and without
any shear flow)
Fig 7.3: Velocity contours at the vertical
mid-plane at different time instants (for
droplet with diameter: 5 mm, contact angle:
90
0
and with turbulent air flow, Re: 3000)
mid-plane at different time instants
(droplet diameter: 5 mm, contact angle: 90
degree and laminar air flow, Re: 1500)
mid-plane at different time instants (droplet
diameter: 10 mm, contact angle: 900 and
with turbulent air flow, Re:3000)

379 Vol. 10, Issue 3, pp. 373-382
Figure 7.5: Velocity contours at the vertical
mid-plane at different time instants (drop
diameter: 10 mm, contact angle: 1500
and with
turbulent air flow, Re: 3000)
Fig7.6: Velocity contours at the vertical mid-
plane at different time instants (mercury drop
diameter: 5 mm, contact angle: 900
with
turbulent air flow, Re: 3000)

380 Vol. 10, Issue 3, pp. 373-382
The velocity of the droplet under turbulent flow for different viscous liquids has been calculated
similarly at different time instants and is plotted against time instant as shown in Graph7.4 It
has been observed that the movement of mercury droplet is very slow as compared to water droplet
with the same pre-defined boundary conditions and key parameters (Re: 3000 and drop diameter: 5
mm). Again it has been observed that mercury droplet is approaching towards zero velocity
just after 0.5 seconds.

381 Vol. 10, Issue 3, pp. 373-382
VIII. CONCLUSION
From the extensive study on six different cases the important concluding remarks have been
made as mentioned below:
Simulation results without shear flow shows that the shape of the drop changes continuously before
reaching the final shape though it has no movement .Air inlet velocity basically influences the
movement phenomena of droplet .On shape change phenomena it has not so much influence. It has
been observed that for the same drop size, the velocity of movement of the droplet increases with
increasing the strength of the shear flow.
The velocity of movement of the drop strongly depends on its size. Shape change phenomena is also
significantly depends on drop size. Contact angle has not so much effect on drop movement
phenomena but in shape change phenomena it has a considerable effect. Movement and shape
change phenomena also depends strongly on the viscosity of the liquid.
IX. SCOPE FOR FUTURE WORK
Following studies may be entertained for the further study of this 3D drop dynamics problem;
 Dynamics of droplet with phase change process through conduction and convection.
 Investigation of drop dynamics for other viscous liquids (as only two viscous fluids have
been considered in this study).Dynamics of liquid droplet by varying contact angles within
the maximum possible range. Analysis of the problem by changing the atmospheric
conditions. i.e. at different density and temperature of the atmospheric air.
ACKNOWLEDGMENT
The Author would like to thank all the persons who helped in the completion of this design and
analysis work. Also thanks are extended to ASR College of Engineering, Tanuku, INDIA for support
throughout the execution of the design analysis work.
REFERENCES
[1]. Bussmann, M., Mostaghimi, J., Chandra, S., 1999. On a three-dimensional volume tracking.
Model of droplet impact. Physics of Fluids 11 (6), 1406–1417
[2]. Chen, K.H., Keh, P.Y., 2001. Slow motion of a droplet between two parallel walls Chem. Eng. Sci.
56, 6863 6871
[3]. Das, A.K., Das, P.K. “Motion of liquid drops over an inclined gradient surface using a 3D
computational technique” Langmuir 2010,26(12),9547-9555.
[4]. Fukai, J., Shiiba, Y., Yamamoto, T., Miyatake, O., Poulikakos, D., Megaridis, C.M., Zhao,Z.,1995.
Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and
modeling. Physics of Fluids 7 (2), 236– 247.
[5]. Ganatos, P., Pfeffer, R., Weinbaum, S., 1980. A strong interaction theory for the creeping
motion of a sphere between plane parallel boundaries. J. Fluid Mech. 99, 755–783.
[6]. Grunau, D., Chen, S., Eggert, K., 1993. A lattice-Boltzmann model for multiphase fluid flows.
Physics of Fluids A5, 2557–2562.
[7]. Gunjal, P.R., Ranade, V.V., Chaudhari, R.V., 2005. Dynamics of drop impact on solid surface:
experiments and VOF simulations. A.I.Ch.E Journal 51 (1), 64–83.
[8]. Gunstensen, A., Rothman, D., Zaleski, S., Zanetti, G., 1991. Lattice- Boltzmann model of
immiscible fluids. Physical Review A 43, 4320–4327.
[9]. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free
boundaries. Journal of Computational Physics 39,201–225.
[10]. Hodges, S.R., Jensen, O.E., Rallison, J.M., 2004. The motion of a viscous drop through. a
cylindrical tube. J. Fluid Mech. 501, 279–301
[11]. Martinez, M.J., Udell, K.S., 1990. Axisymmetric creeping motion of drops through circulartubes.
J. Fluid Mech. 210, 565–591
[12]. Šikalo, Š., Wilhelm, H.D., Roisman, I.V., Jakirlic, S., Tropea, C., 2005d. Dynamic contactangle
of spreading droplets: experiments and simulations. Physics of Fluids 17, 062103, 1–13.

382 Vol. 10, Issue 3, pp. abc-abc
[13]. Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallelplane
walls in low-Reynolds number Poiseuille flow. Phys. Fluids 15, 1711–1733 (Erratum: Phys. Fluids
16, 4204).
AUTHORS BIOGRAPHY
1
R Rajesh was born in Chebrolu, India, in Year 1992. He received the Bachelor’s degree
in Mechanical engineering from the Jawaharlal Nehru Technological University,
Kakinada, in Year 2013. He is currently pursuing the Master degree in Thermal
engineering from the University of Jawaharlal Nehru Technological University, Kakinada.
His research interests include Fluid Mechanics, heat pipes, Thermal Energy storage.
B Chandrasekhar graduated in Mechanical engineering from the Andhra University,
vishakapatnam, His research interests include Fluid Dynamics, Heat Exchangers, Thermal
Energy storage. Currently working on Water Dynamics in a PEM Fuel Cell.

TRANSIENT ANALYSIS ON 3D DROPLET OVER HORIZONTAL SURFACE UNDER SHEAR FLOW WITH ADIABATIC BOUNDARY CONDITIONS BY USING FVM

More Related Content

What's hot (20)

Similar to TRANSIENT ANALYSIS ON 3D DROPLET OVER HORIZONTAL SURFACE UNDER SHEAR FLOW WITH ADIABATIC BOUNDARY CONDITIONS BY USING FVM (20)

More from P singh (20)

Recently uploaded (20)

TRANSIENT ANALYSIS ON 3D DROPLET OVER HORIZONTAL SURFACE UNDER SHEAR FLOW WITH ADIABATIC BOUNDARY CONDITIONS BY USING FVM