The heat transfer of a single water droplet impacting on a heated hydrophobic surface is investigated numerically using a phase field method. The numerical results of the axisymmetric computations show good agreement with the dynamic spreading and subsequent bouncing of the drop observed in an experiment from literature. The influence of Weber number on heat transfer is studied by varying the drop impact velocity in the simulations. For large Weber numbers, good agreement with experimental values of the cooling effectiveness is obtained whereas for low Weber numbers no consistent trend can be identified in the simulations

Frohnapfel, B.

Marschall, H.

Samkhaniani, N.

Stroh, A.

Wörner, Martin

English

KITopen

Journal of Physics: Conference SeriesPAPER • OPEN ACCESSNumerical simulation of drop impingement andbouncing on a heated hydrophobic surfaceTo cite this article: N. Samkhaniani et al 2021 J. Phys.: Conf. Ser. 2116 012073 View the article online for updates and enhancements.You may also likeControlling Inkjet Fluid Kinematics toAchieve SOFC Cathode MicropatternsTheresa. Y. Hill, Thomas L. Reitz, MichaelA. Rottmayer et al.-Using arc voltage to locate the anodeattachment in plasma arc cuttingD J Osterhouse, J W Lindsay and J V RHeberlein-Effect of the liquid temperature on theinteraction behavior for single waterdroplet impacting on the immiscible liquidTiantian Wang,  , Changjian Wang et al.-This content was downloaded from IP address 129.13.72.196 on 13/12/2021 at 14:25Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd8th European Thermal Sciences Conference (EUROTHERM 2021)Journal of Physics: Conference Series 2116 (2021) 012073IOP Publishingdoi:10.1088/1742-6596/2116/1/0120731Numerical simulation of drop impingement andbouncing on a heated hydrophobic surfaceN. Samkhaniani1, H. Marschall2, A. Stroh1, B. Frohnapfel1,M. Wörner31 Karlsruhe Institute of Technology (KIT), Institute of Fluid Mechanics, Kaiserstr. 10, 76131Karlsruhe, Germany2 Computaional Multiphase Flow, Technische Universität Darmstadt, Alarich-Weiss Str. 10,64287 Darmstadt, Germany3 Karlsruhe Institute of Technology (KIT), Institute of Catalysis Research and Technology,Engesserstr. 20, 76131 Karlsruhe, GermanyE-mail: nima.samkhaniani@kit.eduAbstract. The heat transfer of a single water droplet impacting on a heated hydrophobicsurface is investigated numerically using a phase field method. The numerical results of theaxisymmetric computations show good agreement with the dynamic spreading and subsequentbouncing of the drop observed in an experiment from literature. The influence of Weber numberon heat transfer is studied by varying the drop impact velocity in the simulations. For largeWeber numbers, good agreement with experimental values of the cooling effectiveness is obtainedwhereas for low Weber numbers no consistent trend can be identified in the simulations.1. IntroductionHeat transfer on drop impact is important for various industrial applications such as spraycooling and fuel injection [1] or injection of urea-water solution sprays into automotive exhaustpipes for selective catalytic reduction [2].Various parameters such as drop diameter (d0), drop impact velocity (V0), gas-liquid surfacetension (σ), surface topology and wettability (static contact angle θe) determine the dropletbehaviour after impact on the hot surface. The main characteristic non-dimensional number isthe Weber number We = ρV02d0/σ. The outcome of drop impact can be deposition, reboundingor splash [3]. Also evaporation may occur during contact time based on solid (Ts) and droptemperature (Td). Surfaces in contact with the water droplet can be classified into hydrophilic(θe < 90) and hydrophobic (θe > 90). Surfaces which are fabricated with micro/nano texturescan become super-hydrophobic (θe > 130), see Fig. 1.Pasandideh-Fard et al. [4] studied the impact of a water droplet on a hot hydrophilic stainlesssteel surface using a VOF model and compared it with experiments. In another study withthe VOF method, Strotos et al. [5] investigate fluid flow and heat transfer during dropletimpingement. Their study proposed a simplified model to calculate the cooling effectivenesson droplet impact based on the exact analytical solution of two contacting semi-infinite media.Roisman [6] reported a similarity solution for spreading of the liquid film on a flat plate. Themethod was applied to estimate the heat transfer of impinging droplets yielding good agreementwith experiments [7].8th European Thermal Sciences Conference (EUROTHERM 2021)Journal of Physics: Conference Series 2116 (2021) 012073IOP Publishingdoi:10.1088/1742-6596/2116/1/0120732Figure 1. Smooth hydrophobic vs super-hydrophobic fabricated surface. Picture istaken from [8].Figure 2. Schematic representation ofcomputational set-up for drop impact onsolid surface.To the authors’ best knowledge, the heat transfer during the impact of a single droplet onhydrophobic walls has not been thoroughly investigated before. Therefore, the focus of thepresent study is simulating this phenomena with the in-house solver phaseFieldFoam extendedfor heat transfer, and validating it against experimental data of Guo et al. [8].2. Numerical methodThe present computations are performed by a phase field method with the coupled Cahn-Hillard-Navier-Stokes equations for two incompressible and immiscible phases being solvedby OpenFOAM-extend. For details on governing equations, numerical implementation andvalidation of the solver phaseFieldFoam the reader is referred to [9, 10]. In this study, the solverhas been extended by the energy equation∂T∂t+∇(uT ) = ∇ ·(kρCp∇T). (1)Here, u denotes the velocity field and T is temperature. The thermo-physical propertiesΘ ∈ [k, ρ, Cp] are taken from [8] and are calculated through arithmetic interpolation in theinterface regionΘ =1 + C2ΘL +1− C2ΘG. (2)Here, C is the order parameter bounded between −1, 1; the subscripts L and G represent theliquid and gas phase, respectively. As the inertia force is dominant in the present study, thevariation of surface tension with temperature is neglected and the surface tension is σ = 0.072N m−1. The drop properties are: ρL = 998 kg m−3, CpL = 4200 J kg−1 K−1, kL = 0.6 W m−1K−1 and for air: ρG = 1.29 kg m−3, CpG = 1006 J kg−1 K−1, kG = 0.026 W m−1 K−1.3. Result and discussion3.1. Problem definitionThe schematic of the problem is shown in Fig. 2. At the bottom wall, no slip condition, constanttemperature (Ts = Td + 40°C) and fixed contact angle θe = 120 are applied. At atmosphereboundary, the totalPressure with homogeneous Neumann boundary condition for velocity and8th European Thermal Sciences Conference (EUROTHERM 2021)Journal of Physics: Conference Series 2116 (2021) 012073IOP Publishingdoi:10.1088/1742-6596/2116/1/0120733Figure 3. Image sequence of bouncing droplet (d0 = 2.3 mm, We = 20, Td,0 = 20°C) on thesmooth hydrophobic surface (θe = 120, Ts = 60°C). Top: experiment [8], bottom: simulation.order parameter are used. The solver is capable of 3D simulations, but the drop behavior inour range of interest is axisymmetrical, so in order to reduce the computational cost, a 2Daxisymmetric computational domain is chosen. The grid is created with the OpenFOAM meshgenerator blockMesh. The domain size is 1.5d0 × 3d0, filled with uniform cells of width d0/200corresponding to Cahn number Cn = ε/d0 = 0.01 where ε is the interface thickness.3.2. ValidationIn Fig. 3, the sequence of drop impact (d0 = 2.3 mm, We = 20) on a smooth heated surfaceis compared with experimental data [8]. After impact, the drop spreads over the plate, thenumerical simulation resolves the capillary waves on interface at time t = 1.6 ms where the drophas a cupcake shape. The stretching continues until the drop reaches its maximum spreadingat t = 3.2 ms, then recoiling starts and the drop eventually bounces back from the surface.The spreading ratio (β = d/d0) is plotted in Fig. 4 For quantitative comparison. Fig. 5 showsthe effect of increased impact velocity (We number), for which the drop wets a larger area andreaches its maximum spreading ratio βmax in a smaller time interval tβmax. In contrast, thecontact time tc remains in the range t ∈ [14, 16] ms. Thus, a thinner liquid film layer forms forlarger impact velocities and a larger portion of the drop is in direct contact with the heatedsolid. In consequence, the mean droplet temperature Td increases rapidly during the spreadingstage as shown in Fig. 6. The drop mean temperature increases till the middle of recoiling stage.Afterwards, the drop cools down since a large part of the drop surface is in contact with thecool ambient air and the related heat loss outweighs the heat transfer from the hot solid.The overall cooling effectiveness is defined as χ = (Tdf − Td0)/(Tw − Td0), where Tdf refersto droplet temperature right before the second impact onto the surface. It represents the ratioof the actual heat transfer to the maximum heat that could be transferred to the droplet [4].The spreading ratio β and contact time tc defines the value of heat transferred to the drop. Thenumerical results compared with experimental data [8] are shown in Fig. 7 for We ∈ [5 − 40].It indicates the increase in drop impact velocity (We number) in general increases the coolingeffectiveness. But the non-linear profile is compatible via variation of drop spreading ratio βand contact time tc with We number in Fig. 5.8th European Thermal Sciences Conference (EUROTHERM 2021)Journal of Physics: Conference Series 2116 (2021) 012073IOP Publishingdoi:10.1088/1742-6596/2116/1/0120734Figure 4. Spreading ratio in experiment[8] and simulation (We = 20).Figure 5. Effect of We on maximumspreading ratio (βmax) for d0 = 2.3 mm.Figure 6. Effect of We for d0 = 2.3mm ontime evolution of mean drop temperature.Figure 7. Influence of We on coolingeffectiveness (experimental data from [8]).4. SummaryThe in-house solver phaseFieldFoam has been extended by the energy equation and is used tostudy heat transfer during drop impingement. The solver is validated by a comparison of thenumerical results with experimental literature data. While good agreement is found for higherWeber numbers, no consistent trend for cooling effectiveness can be identified for low Webernumbers. This deserves further investigations. The present study is limited to the smoothsurfaces with contact angle θe = 120. In future studies, we intend to investigate heat transferduring drop impingement on computationally resolved non-smooth surface structures.References[1] Liang G and Mudawar I 2017 Int. J. Heat Mass Transfer 106 103–126[2] Börnhorst M and Deutschmann O 2018 Int. J. Heat Fluid Flow 69 55 – 61[3] Rioboo R, Marengo M and Tropea C 2002 Exp. Fluids 33 112–124[4] Pasandideh-Fard M, Aziz S, Chandra S and Mostaghimi J 2001 Int. J. Heat Fluid Flow 22 201–210[5] Strotos G et al. 2011 Int. J. Thermal Sciences 50 698–711[6] Roisman I V 2010 J. Fluid Mech. 656 189–204[7] Batzdorf S et al. 2017 Int. J. Heat Mass Transfer 113 898–907[8] Guo C, Maynes D, Crockett J and Zhao D 2019 Int. J. Heat Mass Transfer 137 857–867[9] Cai X, Wörner M, Marschall H and Deutschmann O 2016 Catalysis Today 273 151–160[10] Cai X, Marschall H, Wörner M and Deutschmann O 2015 Chem. Eng. 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Numerical simulation of drop impingement and bouncing on a heated hydrophobic surface

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Numerical simulation of drop impingement and bouncing on a heated hydrophobic surface

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