On in-Flight Collision Behaviour of Droplets on a Spherical Particle
On in-flight collision behaviour of droplets on a spherical particle
1.0 Introduction:
In-depth understanding of droplet-particle collision phenomenon is essential for successful design and optimization of many significant industrial applications such as fluidized catalytic cracking, spouted bed coating etc. Typically, in these applications, droplets collide with the moving solid particles involving complex hydrodynamics which may result into deposition of droplets onto the particle surface or splashing leading to multiple secondary droplets or complete rebound [1]. Due to only few published studies reported in this area, the present study aims to provide further insight into the collision process specifically quantifying the oscillatory behaviour of droplet on the particle surface, liquid attachment and associated momentum transfer by examining the effects of both droplets and particle velocities on the collision process. Â
2.0 Experimental:
Experiments were carried out to investigate the in-flight collision behaviour between water droplets (300-550 μm) and glass ballotini particle (1.15±0.05 mm) at room temperature condition. Impact velocity and diameter of the droplets were changed by varying the impinging liquid jet flow rate while the particle impact velocity was varied by changing the height of fall a stationary particle utilizing a vacuum release system. The collision process was captured by high speed imaging technique and later analysed using in-house image processing MATLAB code.
3.0 Numerical modelling:
A two-phase 2D CFD model implementing volume of fluid (VOF) approach to capture the droplet interface and dynamic meshing for particle motion was adopted in the finite volume method based CFD solver ANSYS Fluent to simulate the single droplet particle collision process.
4.0 Results and discussions:
In the present study, collision interactions between multiple droplets and a particle at different impact velocities were investigated in the particle Reynolds number (Rep = dpupρg/μg) range of 17 to 45 and in the droplet Weber number (Wed = ddu2dρd/σ) range of 3.1 to 24.4.
4.1 Collision interaction outcomes:
At lower jet flow rate (lower Wed), less numbers of larger size droplets were produced which showed the oscillating behaviour after impingement on the particle surface. Conversely, at higher jet flow rate (higher Wed), more numbers of smaller-sized droplets were produced which after collision formed a thin liquid film over the surface due to coalescence (Fig.1).
Fig.1. Experimental images of droplet-particle collision at different Weber numbers a) Wed-3.1 b) Wed-7.0 c) Wed- 14.6 and d) Wed-24.4 at the same time instance.
4.1.1 Deposition behaviour of droplets:
In all the cases investigated, droplets were observed to undergo deposition on the particle surface without any occurrence of splashing and rebound. Deposition and splashing criterion was checked using Eq.1 [2]:
(1)
where Oh is Ohnesorge number and K is Mundo number which indicates that deposition occurs for K < 57.7 and splashing occurs above this value.
Rebound criterion was checked from Eq. 2 which predicts droplet rebound when excess energy (Eex) > 0 and deposition when Eex <0 [3]:
(2)
where θwis the static contact angle (55o) and ddmax is the maximum spread diameter which was determined from Eq. 3 [4],
(3)
Table 1 summarises the collision outcomes. In all cases, the values of K were found to be < 57.7 which indicates deposition. Also, Eexwas found to be negative in these cases which also confirmed the droplet deposition outcome.
4.1.2 Oscillatory behaviour of the colliding droplet:
At lower Wed, droplet after impingement on the particle surface, exhibited transient deformation behaviour (Fig.2). Such behaviour is attributed primarily to the interplay between inertia and surface tension force. During impingent, the momentum of the droplet normal to the surface causes a radial flow leading to spreading of the droplet into a disk shape structure on the particle surface.
Fig.2. Oscillatory deformation behaviour of the droplets depicted by β (ratio of max. spread diameter to initial droplet diameter) at two different locations on the particle surface (Wed-3.1).
At the maximum spreading state the droplet completely loses its kinetic energy and then a recoiling phase is initiated due to the restoring surface tension force [4]. The oscillatory behaviour, however, differs depending on the location of the impact (Fig.2). A parameter of interest here is the droplet oscillation period (Eq.4) which represents the dynamics of the collision process [4]:
(4)
Using Eq. 4, for the Wed-3.2 case the oscillation period was found to be 1.08 ms which was close to the experimentally observed oscillation period of the above two cases (1.96 ms for the top droplet and 1.17 ms for the bottom droplet).
Such transient deformation behaviour simulated by the CFD model is presented in Fig.3. Both the spreading and recoiling phase of the droplet were correctly predicted. A larger oscillation time of 2.8 ms, however, was obtained which could be attributed to the 2D nature of the model.
Fig.3. CFD simulation (coloured by volume fraction) indicating droplet deformation pattern during collision with the particle at different time instances.
4.1.3 Formation of liquid film on particle surface:
It was noted before that droplet-particle interaction at higher Wed resulted in formation of a thin film over the particle surface due to rapid collision and subsequent coalescence of the impinging droplets. Fig.4 presents a number of collisions measured when both Wed and Rep were increased.
In general, when Wedwas increased the number of collisions also increased. It could be noted that when the particle velocity (Rep) was increased then the relative velocity between the droplet and particle decreased which subsequently reduced the number collisions (Fig.4).
Fig.4 Number of collisions measured experimentally at different Wedand Rep.
Fig.5 presents the liquid film area over the particle surface. The 2D projection of the liquid film area was obtained using image processing by subtracting the surface area of the dry particle from all subsequent liquid-laden images. In all the cases studied the film thickness was found to vary in the range of 0.036-0.13mm.
Fig.5. Impact of Rep on the transient liquid film growth on the particle surface at Wed-24.4. Film thickness decreased in both cases when Rep was increased from 17 to 45.
It is also worth noticing that the film area first increased and then decreased in all Rep cases. Such variation in film area was attributed to the rotational motion during the collisions due to higher momentum transfer which caused out-of-plane orientation of the liquid laden particle.
4.2 Deposited film mass:
An image analysis-based method was utilized to determine the deposited film mass (Ml) based on average number of droplets (Nd) in the image field of view (FOV) using Eq.5.
Deposited film mass was observed generally to increase with higher Wed, however, it decreased with increasing Rep due to lesser interaction time (Fig. 6).
Fig.6. Impact of particle Reynolds number (Rep) on film mass on the particle surface at different droplet Weber numbers (Wed: 3.1 ? 24.4 and Rep: 17 to 45).
4.3 Angle of deflection:
For a hydrophilic surface the droplet-particle interaction process exhibits a pure inelastic collision. Some amount of energy is lost due to viscous dissipation occurring during droplet-particle collision. During collision, transfer of momentum occurs between droplets and particle and the resultant momentum changes the trajectory of the falling particle causing an angle of deflection (φ) (Fig.7). At higher Wed, more liquid mass accumulated on the particle surface which led to a higher angle of deflection due to larger momentum transfer. In general, this trend was observed in all the cases investigated. When the particle velocity is increased then less interaction time is available between the droplet and particle to exchange momentum. Hence, φ was observed to reduce at higher particle velocity.
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Fig.1. Experimental images of droplet-particle collision at different Weber numbers a) Wed-3.1 b) Wed-7.0 c) Wed- 14.6 and d) Wed-24.4 at the same time instance.
4.1.1 Deposition behaviour of droplets:
In all the cases investigated, droplets were observed to undergo deposition on the particle surface without any occurrence of splashing and rebound. Deposition and splashing criterion was checked using Eq.1 [2]:
(1)
where Oh is Ohnesorge number and K is Mundo number which indicates that deposition occurs for K < 57.7 and splashing occurs above this value.
Rebound criterion was checked from Eq. 2 which predicts droplet rebound when excess energy (Eex) > 0 and deposition when Eex <0 [3]:
(2)
where θwis the static contact angle (55o) and ddmax is the maximum spread diameter which was determined from Eq. 3 [4],
(3)
Table 1 summarises the collision outcomes. In all cases, the values of K were found to be < 57.7 which indicates deposition. Also, Eexwas found to be negative in these cases which also confirmed the droplet deposition outcome.
4.1.2 Oscillatory behaviour of the colliding droplet:
At lower Wed, droplet after impingement on the particle surface, exhibited transient deformation behaviour (Fig.2). Such behaviour is attributed primarily to the interplay between inertia and surface tension force. During impingent, the momentum of the droplet normal to the surface causes a radial flow leading to spreading of the droplet into a disk shape structure on the particle surface.
Fig.2. Oscillatory deformation behaviour of the droplets depicted by β (ratio of max. spread diameter to initial droplet diameter) at two different locations on the particle surface (Wed-3.1).
At the maximum spreading state the droplet completely loses its kinetic energy and then a recoiling phase is initiated due to the restoring surface tension force [4]. The oscillatory behaviour, however, differs depending on the location of the impact (Fig.2). A parameter of interest here is the droplet oscillation period (Eq.4) which represents the dynamics of the collision process [4]:
(4)
Using Eq. 4, for the Wed-3.2 case the oscillation period was found to be 1.08 ms which was close to the experimentally observed oscillation period of the above two cases (1.96 ms for the top droplet and 1.17 ms for the bottom droplet).
Such transient deformation behaviour simulated by the CFD model is presented in Fig.3. Both the spreading and recoiling phase of the droplet were correctly predicted. A larger oscillation time of 2.8 ms, however, was obtained which could be attributed to the 2D nature of the model.
Fig.3. CFD simulation (coloured by volume fraction) indicating droplet deformation pattern during collision with the particle at different time instances.
4.1.3 Formation of liquid film on particle surface:
It was noted before that droplet-particle interaction at higher Wed resulted in formation of a thin film over the particle surface due to rapid collision and subsequent coalescence of the impinging droplets. Fig.4 presents a number of collisions measured when both Wed and Rep were increased.
In general, when Wedwas increased the number of collisions also increased. It could be noted that when the particle velocity (Rep) was increased then the relative velocity between the droplet and particle decreased which subsequently reduced the number collisions (Fig.4).
Fig.4 Number of collisions measured experimentally at different Wedand Rep.
Fig.5 presents the liquid film area over the particle surface. The 2D projection of the liquid film area was obtained using image processing by subtracting the surface area of the dry particle from all subsequent liquid-laden images. In all the cases studied the film thickness was found to vary in the range of 0.036-0.13mm.
Fig.5. Impact of Rep on the transient liquid film growth on the particle surface at Wed-24.4. Film thickness decreased in both cases when Rep was increased from 17 to 45.
It is also worth noticing that the film area first increased and then decreased in all Rep cases. Such variation in film area was attributed to the rotational motion during the collisions due to higher momentum transfer which caused out-of-plane orientation of the liquid laden particle.
4.2 Deposited film mass:
An image analysis-based method was utilized to determine the deposited film mass (Ml) based on average number of droplets (Nd) in the image field of view (FOV) using Eq.5.
Deposited film mass was observed generally to increase with higher Wed, however, it decreased with increasing Rep due to lesser interaction time (Fig. 6).
Fig.6. Impact of particle Reynolds number (Rep) on film mass on the particle surface at different droplet Weber numbers (Wed: 3.1 ? 24.4 and Rep: 17 to 45).
4.3 Angle of deflection:
For a hydrophilic surface the droplet-particle interaction process exhibits a pure inelastic collision. Some amount of energy is lost due to viscous dissipation occurring during droplet-particle collision. During collision, transfer of momentum occurs between droplets and particle and the resultant momentum changes the trajectory of the falling particle causing an angle of deflection (φ) (Fig.7). At higher Wed, more liquid mass accumulated on the particle surface which led to a higher angle of deflection due to larger momentum transfer. In general, this trend was observed in all the cases investigated. When the particle velocity is increased then less interaction time is available between the droplet and particle to exchange momentum. Hence, φ was observed to reduce at higher particle velocity.
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Fig.7. Impact of particle Reynolds number (Rep) on angle of deflection at different droplet Weber numbers (Wed: 3.1 ? 24.4 and Rep: 17 to 45).
5.0 Future work: In continuation with this work, a collision model will be further developed to predict the number of collisions (Nc) and angle of deflection (φ) and compared with the present measurements. Additionally, the current 2D CFD model will be extended into 3D framework to simulate the single droplet-particle collision more accurately.
References:
1. Ge, Y., Fan, L-S. Droplet-particle collision mechanics with film boiling evaporation. J. Fluid Mech., 2007, 573 , pp. 311-337. 2. Mundo, C., Sommerfield, M., Tropea, C. Droplet-wall collisions: experimental studies of the deformation and breakup process. Int. Â J. Multiphase Flow, 1995, 21 (2), pp. 151-173. 3. Mao, T., Kuhn, C.S., Tran, H. Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE Journal, 1997, 43 (9), pp. 2169-2179. 4. Chandra, S., Avedisian, C.T. On the collision of droplet with solid surface. Proc. of Royal Soc. London A, 1991, vol. 432, pp. 13-41.