Sanjeev Chandra

On the collision of a droplet with a solid surface

The collision dynamics of a liquid droplet on a solid metallic surface were studied using a flash photographic method. The intent was to provide clear images of the droplet structure during the deformation process. The ambient pressure (0.101 MPa), surface material (polished stainless steel), initial droplet diameter (about 1.5 mm), liquid (n-heptane) and impact Weber number (43) were fixed. The primary parameter was the surface temperature, which ranged from 24°C to above the Leidenfrost temperature of the liquid. Experiments were also performed on a droplet impacting a surface on which there existed a liquid film created by deposition of a prior droplet. The evolution of wetted area and spreading rate, both of a droplet on a stainless steel surface and of a droplet spreading over a thin liquid film, were found to be independent of surface temperature during the early period of impact. This result was attributed to negligible surface tension and viscous effects, and in consequence the measurements made during the early period of the impact process were in good agreement with previously published analyses which neglected these effects. A single bubble was observed to form within the droplet during impact at low temperatures. As surface temperature was increased the population of bubbles within the droplet also increased because of progressive activation of nucleation sites on the stainless steel surface. At surface temperatures near to the boiling point of heptane, a spoke-like cellular structure in the liquid was created during the spreading process by coalescence of a ring of bubbles that had formed within the droplet. At higher temperatures, but below the Leidenfrost point, numerous bubbles appeared within the droplet, yet the overall droplet shape, particularly in the early stages of impact (< 0.8 ms), was unaffected by the presence of these bubbles. The maximum value of the diameter of liquid which spreads on the surface is shown to agree with predictions from a simplified model.

Capillary effects during droplet impact on a solid surface

Impact of water droplets on a flat, solid surface was studied using both experiments and numerical simulation. Liquid–solid contact angle was varied in experiments by adding traces of a surfactant to water. Impacting droplets were photographed and liquid–solid contact diameters and contact angles were measured from photographs. A numerical solution of the Navier–Stokes equation using a modified SOLA‐VOF method was used to modeldroplet deformation. Measured values of dynamic contact angles were used as a boundary condition for the numerical model. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces, after which they recoiled off the surface. Adding a surfactant did not affect droplet shape during the initial stages of impact, but did increase maximum spread diameter and reduce recoil height. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model modeled droplet shape evolution correctly. Accurate predictions were obtained for droplet contact diameter during spreading and at equilibrium. The model overpredicted droplet contact diameters during recoil. Assuming that dynamic surface tension of surfactant solutions is constant, equaling that of pure water, gave predicted droplet shapes that best agreed with experimental observations. When the contact angle was assumed constant in the model, equal to the measured equilibrium value, predictions were less accurate. A simple analytical model was developed to predict maximum droplet diameter after impact. Model predictions agreed well with experimental measurements reported in the literature. Capillary effects were shown to be negligible during droplet impact when We≫Re1/2.

On a three-dimensional volume tracking model of droplet impact

A three-dimensional model has been developed of droplet impact onto asymmetric surface geometries. The model is based on RIPPLE, and combines a fixed-grid control volume discretization of the flow equations with a volume tracking algorithm to track the droplet free surface. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at the contact line. The results of two scenarios are presented, of the oblique impact of a 2 mm water droplet at 1 m/sec onto a 45° incline, and of a similar impact of a droplet onto a sharp edge. Photographs are presented of such impacts, against which the numerical results are compared. The contact angle boundary condition is applied in one of two ways. For the impact onto an incline, the temporal variation of contact angles at the leading and trailing edges of the droplet was measured from photographs. This data is applied as a boundary condition to the simulation, and an interpolation scheme propos...

Modeling the splash of a droplet impacting a solid surface

A numerical model is used to simulate the fingering and splashing of a droplet impacting a solid surface. A methodology is presented for perturbing the velocity of fluid near the solid surface at a time shortly after impact. Simulation results are presented of the impact of molten tin, water, and heptane droplets, and compared with photographs of corresponding impacts. Agreement between simulation and experiment is good for a wide range of behaviors. An expression for a splashing threshold predicts the behavior of the molten tin. The results of water and especially heptane, however, suggest that the contact angle plays an important role, and that the expression may be applicable only to impacts characterized by a relatively low value of the Ohnesorge number. Various experimental data of the number of fingers about an impacting droplet agree well with predictions of a previously published correlation derived from application of Rayleigh–Taylor instability theory.

Impact, recoil and splashing of molten metal droplets

Abstract We studied the impact and solidification of molten tin droplets on a stainless steel surface. Droplet impact velocity was varied from 1.0 to 4.0 m/s and substrate temperature from 25 to 240°C (above the melting point of tin, 232°C). We photographed droplet impact and measured splat diameter and liquid–solid contact angle from these photographs. Substrate temperature under an impacting droplet was measured using a fast response thermocouple. Thermal contact resistance at the droplet–substrate interface was calculated by matching measured surface temperature variation with an analytical solution. A simple energy conservation model was used to predict the maximum spread of droplets during impact. Predictions agreed well with measured values. Instabilities were observed on the periphery of the droplet, which led to the formation of fingers. A model based on the Rayleigh–Taylor instability was used to predict the number of fingers around the periphery of the droplet.

A three-dimensional model of droplet impact and solidification

Abstract A three-dimensional model has been developed to simulate the fluid dynamics, heat transfer and phase-change that occur when a molten metal droplet falls onto a flat substrate. The model is an extension of one developed by Bussmann et al. [Phys. Fluids 11 (1999) 1406] and combines a fixed-grid control volume discretization of the fluid flow and energy equations with a volume-tracking algorithm to track the droplet free surface, and an improved fixed velocity method to track the solidification front. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at liquid–solid contact lines. The energy equations in both the liquid and solid portions of the droplet are solved using the Enthalpy method. Heat transfer within the substrate is by conduction alone. Thermal contact resistance at the droplet–substrate interface is included in the model. We studied the deposition of tin droplets on a stainless steel surface using both experiments and numerical simulations. The results of two different scenarios are presented: the normal impact of a 2.7 mm tin droplet at 1 m/s, and of the oblique impact of a 2.2 mm tin droplet at 2.35 m/s onto a surface inclined at 45° to the horizontal. Images obtained from numerical model were compared with experimental photographs and found to agree well.

Deposition of tin droplets on a steel plate: simulations and experiments

Abstract Impact and solidification of tin droplets on a flat stainless steel plate was studied using both experiments and numerical simulation. In the experiments, tin droplets (2.1 mm diameter) were formed and dropped onto a stainless steel surface whose temperature was varied from 25 to 240°C. Impact of droplets was photographed, and evolution of droplet spread diameter and liquid-solid contact angle measured from photographs. Substrate temperature variation under an impinging droplet was measured. A complete numerical solution of the Navier-Stokes and energy equations, based on a modified SOLA-VOF method, was used to model droplet deformation and solidification and heat transfer in the substrate. Measured values of liquid-solid contact angle were used as a boundary condition for the numerical model. The heat transfer coefficient at the droplet-substrate interface was estimated by matching numerical predictions of the variation of substrate temperature with measurements. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model correctly modelled droplet shape during impact as it simultaneously deformed and solidified. A simple analytical model was developed to predict the maximum spread diameter of a droplet freezing during impact.

Splat shapes in a thermal spray coating process: Simulations and experiments

We studied the deposition of nickel particles in a plasma spray on a stainless steel surface using both experiments and numerical simulations. We developed a three-dimensional computational model of free-surface fluid flow that includes heat transfer and solidification and used it to simulate the impact of nickel partcles. In our experiments, particles landing on a polished stainless steel surface at a temperature below 300 °C splashed and formed irregular splats, whereas those deposited on substrates heated above 400 °C formed round disk splats. Simulations showed that formation of fingers around the periphery of a spreading drop is caused by the presence of a solid layer. Droplets that spread completely before the onset of solidification will not splash. To sufficiently delay the instant at which solidification started in our simulations to obtain disk splats, we had to increase the thermal contact resistance between the droplet and the substrate by an order of magnitude. We measured the thickness of the oxide layer on the test surfaces used in our experiments and confirmed that heating them creates an oxide layer on the surface that increases the thermal contact resistance. We demonstrated that the numerical model could be used to simulate the deposition of multiple droplets on a surface to build up a coating.

Effect of liquid-solid contact angle on droplet evaporation

The effect of varying initial liquid-solid contact angle on the evaporation of single droplets of water deposited on a stainless steel surface is studied using both experiments and numerical modeling. Contact angle is controlled in experiments by adding varying amounts] (100 and 1000 ppm) of a surfactant to water. The evolution of contact angle and liquid-solid contact diameter is measured from a video record of droplet evaporation. The computer model is validated by comparison with the experimental results. Reducing the contact angle increases the contact area between the droplet and solid surface, and also reduces droplet thickness, enhancing heat conduction through the droplet. Both effects increase the droplet evaporation rate. Decreasing the initial contact angle from 90 to 20° reduces droplet evaporation time by approximately 50%. The computer model is used to calculate surface temperature and heat flux variation during droplet evaporation: adding 1000 ppm of surfactant to the droplet is shown to enhance surface cooling by up to 110%.

Cooling effectiveness of a water drop impinging on a hot surface

Abstract We studied, using both experiments and a numerical model, the impact of water droplets on a hot stainless steel surface. Initial substrate temperatures were varied from 50°C to 120°C (low enough to prevent boiling in the drop) and impact velocities from 0.5 to 4 m/s. Fluid mechanics and heat transfer during droplet impact were modelled using a “Volume-of-Fluid” (VOF) code. Numerical calculations of droplet shape and substrate temperature during impact agreed well with experimental results. Both simulations and experiments show that increasing impact velocity enhances heat flux from the substrate by only a small amount. The principal effect of raising droplet velocity is that it makes the droplet spread more during impact, increasing the wetted area across which heat transfer takes place. We also developed a simple model of heat transfer into the droplet by one-dimensional conduction across a thin boundary layer which gives estimates of droplet cooling effectiveness that agree well with results from the numerical model. The analytical model predicts that for fixed Reynolds number ( Re ) cooling effectiveness increases with Weber number ( We ). However, for large Weber numbers, when We ≫ Re 0.5 , cooling effectiveness is independent of droplet velocity or size and depends only on the Prandtl number.