Non-dimensionalisation parameters for predicting the cooling effectiveness of droplets impinging on moderate temperature solid surfaces (original) (raw)
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Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface
International Journal of Heat and Mass Transfer, 2008
Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet's free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120°C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet's evaporation rate is predicted using a model based on Fick's law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid-gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.
Cooling eectiveness of a water drop impinging on a hot surface
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 ¯ux from the substrate by only a small amount. The principal eect 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 eectiveness that agree well with results from the numerical model. The analytical model predicts that for ®xed Reynolds number (Re) cooling eectiveness increases with Weber number (We). However, for large Weber numbers, when We) Re 0:5 , cooling eectiveness is independent of droplet velocity or size and depends only on the Prandtl number.
Cooling effectiveness of droplets at low Weber numbers: Effect of temperature
International Journal of Thermal Sciences, 2013
The impact of water droplets onto a heated non-isothermal surface is studied numerically using the VOF methodology and assuming a 2D-axisymmetric computational domain. An adaptive grid refinement technique in both the fluid and the solid phases is used to solve the conjugate problem of fluid flow and heat transfer. Parametric studies examine the effect of initial solid surface temperature and initial droplet temperature, while all the other parameters which affect the temporal evolution of the phenomenon are kept constant; the wall temperatures examined are low enough to prevent the onset of nucleate boiling. It is proved that the variables describing the temporal evolution of the phenomenon evolve with the same way when they are non-dimensionalised with expressions arising from the transient heat conduction theory. Additionally, a formula for the maximum droplet spreading which accounts for the droplet heating during spreading is proposed, as also semi-analytical expressions which describe the thermal behaviour of the droplet Ó
Cooling effectiveness of a water drop impinging on a hot surface
International Journal of Heat and Fluid Flow, 2001
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¯ux from the substrate by only a small amount. The principal eect 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 eectiveness that agree well with results from the numerical model. The analytical model predicts that for ®xed Reynolds number (Re) cooling eectiveness increases with Weber number (We). However, for large Weber numbers, when We) Re 0:5 , cooling eectiveness is independent of droplet velocity or size and depends only on the Prandtl number.
Computational modelling of flow and conjugate heat transfer of a drop impacting onto a cold wall
International Journal of Heat and Mass Transfer, 2017
The flow and heat transfer in water drops impinging onto a dry cold surface has been computationally investigated. This situation pertains to aircraft icing or icing of power lines. The computational model solves the hydrodynamics using an algebraic implicit volume-of-fluid-based method for interface capturing with an extension for the simultaneous solution of the heat transfer within the drop and underlying substrate. The numerical solution is validated by computing a series of configurations of two-phase fluid flow and conjugate heat transfer for which experimental and analytical results are available in the literature. In a parametric study, the effect of the impact conditions and initial surface temperatures on the minimum liquid temperature reached and the heat transfer during drop impact are examined, representing the quantities relevant for nucleation and icing modelling. It is shown that these quantities do not depend on the impact conditions. However, the amount of heat transferred between the fluid and the wall is affected by the contact time and area available for heat transfer, which are determined by the impact conditions. Based on the numerical results, a semi-empirical model is developed, which accurately predicts the total heat transferred during a single impact event.
The evaporation of water droplets, impinging with low Weber number and gently depositing on heated surfaces of stainless steel is studied numerically using a combination of fluid flow and heat transfer models. The coupled problem of heat transfer between the surrounding air, the droplet and the wall together with the liquid vaporisation from the droplet's free surface is predicted using a modified VOF methodology accounting for phase-change and variable liquid properties. The surface cooling during droplet's evaporation is predicted by solving simultaneously with the fluid flow and heat transfer equations, the heat conduction equation within the solid wall. The droplet's evaporation rate is predicted using a model from the kinetic theory of gases coupled with the Spalding mass transfer model, for different initial contact angles and substrate's temperatures, which have been varied between 20-90°and 60-100°C, respectively. Additionally, results from a simplified and computationally less demanding simulation methodology, accounting only for the heat transfer and vaporisation processes using a time-dependent but pre-described droplet shape while neglecting fluid flow are compared with those from the full solution. The numerical results are compared against experiments for the droplet volume regression, life time and droplet shape change, showing a good agreement.
Experimental and numerical study on sensible heat transfer at droplet/wall interactions
Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems, 2017
The present study addresses a detailed experimental and numerical investigation on the impact of water dropletson smooth heated surfaces. High-speed infrared thermography is combined with high-speed imaging to couple the heat transfer and fluid dynamic processes occurring at droplet impact. Droplet spreading (e.g. spreading ratio) and detailed surface temperature fields are then evaluated in time and compared with the numerically predicted results. The numerical reproduction of the phenomena was conducted using an enhanced version of a VOF- based solver of OpenFOAM previously developed, which was further modified to account for conjugate heat transfer between the solid and fluid domains, focusing only on the sensible heat removed during droplet spreading. An excellent agreement is observed between the temporal evolution of the experimentally measured and the numerically predicted spreading factors (differences between the experimental and numerical values were always lower than 3.4...
International Journal of Heat and Mass Transfer, 2006
The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solidvapor/liquid-vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid-vapor and solid-vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet's initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.
Modeling of heat transfer through a liquid droplet
Heat and Mass Transfer
In dropwise condensation, the released latent heat passes through the static and sliding droplets to the condensing surface at a rate limited by various thermal resistances. In the present work, numerical simulation of heat transfer through a droplet is carried for one under static and sliding condition. 3-D governing equations with appropriate boundary conditions are solved for the surface, promoter layer and droplet included within the computational domain. Simulations are carried out using an in-house CFD solver. The simulation results are validated against the available data and are found in good agreement. The observations of the present work are: (a) heat transfer through the droplet achieves steady state over a timescale of micro-seconds, (b) the heat fluxes of deformed and equivalent spherical-cap droplet are found to be equal, (c) Marangoni convection is significant for Ma ≥ 2204, (d) convection is the dominant mode of heat transfer during drop slide-off (e) constriction resistance is insignificant for a copper surface of thickness ≤ 2 mm, (f) average heat flux increases with increasing contact angle, interfacial heat transfer coefficient, degree of subcooling and Reynolds number; however, it decreases with increasing Prandtl number of the liquid. These results are useful for sensitivity analysis of various thermal resistances in the mathematical modeling of dropwise condensation underneath inclined surfaces.
Sensible Heat Transfer during Droplet Cooling: Experimental and Numerical Analysis
Energies
This study presents the numerical reproduction of the entire surface temperature field resulting from a water droplet spreading on a heated surface, which is compared with experimental data. High-speed infrared thermography of the back side of the surface and high-speed images of the side view of the impinging droplet were used to infer on the solid surface temperature field and on droplet dynamics. Numerical reproduction of the phenomena was performed using OpenFOAM CFD toolbox. An enhanced volume of fluid (VOF) model was further modified for this purpose. The proposed modifications include the coupling of temperature fields between the fluid and the solid regions, to account for transient heat conduction within the solid. The results evidence an extremely good agreement between the temporal evolution of the measured and simulated spreading factors of the considered droplet impacts. The numerical and experimental dimensionless surface temperature profiles within the solid surface and along the droplet radius, were also in good agreement. Most of the differences were within the experimental measurements uncertainty. The numerical results allowed relating the solid surface temperature profiles with the fluid flow. During spreading, liquid recirculation within the rim, leads to the appearance of different regions of heat transfer that can be correlated with the vorticity field within the droplet.