Le gocce fanno spread, boing e splash: esperimenti, fenomeni e sfide Marengo Marco University of Bergamo, Italy Contents INDEX Introduction The main parameters Experimental studies Isothermal drop impacts Onto solid surfaces Roughness effects Wettability effects Inclined surfaces...on small targets Onto liquid layers in a deep pool on very thin film on liquid film Drop impact on hot surfaces Boiling regimes Secondary drop generation Multiple droplet impacts Numerical simulations Available methods (VOF, Level Set, BEM, etc) Isothermal simulations Energy equation and phase transition Perspectives
Industrial applications Spray Impingement in Internal Combustion Engines G. Popiołek, H. Boye, J. Schmidt, 2005 Institute of Fluid Dynamics and Thermodynamics Otto-von-Guericke-University Magdeburg, Germany mulda.avi Mitsubishi Web-site Industrial applications Spray cooling and quenching Typical hydrodynamic parameters (Choi and Yao, 1987) G = 0.3 20 kg/m 2 s U = 3-5 m/s d 10 0.5 mm Maximum heat transfer: 2 10 6 W/m 2 Metallurgical failures For G = 80 kg/m 2 s, dt/dt = 10 3 K/s
Industrial applications Agricultural sprays Decrease the overspray and avoid the aerosol Cosmetic sprays Small injection energy, small droplets, low velocities Spray in humidifiers and dryers High efficiency microspray Industrial applications Airplane icing solidification Cryogenic cooling evaporation
Industrial applications Fire suppression Progress in Energy and Combustion Science 26 (2000) 79-130 Fire suppression by water sprays G.Grant, J.Brenton, D.Drysdale Spray painting Non-newtonian fluids!!! Evaporative cooling tower Cleaner and sanitizers Etc... Impact parameters Impact dynamical parameters U, D, α, ρ, σ, µ,, g, t, h, R a, θ, λ,, E... Weber number We = ρ DU σ 2 Ca U = σ / µ Ohnesorge number Oh We = = Re µ ρσd La = µ 2 D ρσ Dimensionless film thickness δ = h D Strouhal number St = fd U Dimensionless roughness amplitude R = R D n d a U τ conv D t
Impact parameters Impact thermal parameters Saturation temperature T = Tw T sat Eckert number Ec = U c p 2 T Jakob number Ja = c T p h fg Effusivity ε = kρc p Nukijama temperature - CHF Leidenfrost temperature Isothermal drop impact Isothermal drop impacts
Isothermal drop impact Drop impact onto solid dry surfaces time scales D 1-4 mm Drop impact onto solid dry cold surfaces Drop impact evolution
Drop spreading on dry surfaces Drop impact evolution Rioboo R., C. Tropea, M. Marengo, "Outcome from a drop impact on solid surfaces", Atomization and Sprays Journal, Vol. 4, 2000 Roughness effects Roughness influence R a = 3µm R a = 120µm Silicon oil (µ=20 cst; σ=0.0206 N/m); V imp =3.16 m/s; D= 2.24 mm
Introduction Experimental studies Numerical simulations Perspectives Wettability effects Wettability influence on drop impact t = 0 ms t = 0.45 ms t = 1.31 ms t = 2.27 ms t = 6.02 ms t = 8.21 ms wax (D = 2.75 mm) t = 25.6 ms t = 34.2 ms t = 62.4 ms t = 72.2 ms t = 20.5 ms t = 14.0 ms t = 10.3 ms θrec =95 t = 82.8 ms Vi = 1.18 m/s Glass θrec =6 t = 0 ms t = 0.45 ms t = 8.23 ms Introduction (D = 3.04 mm) t = 2.27 ms t = 6.04 ms t = 20.5 ms t = 62.4 ms t = 1.31 ms t = 14.0 ms t = 10.3 ms Experimental studies Numerical simulations Perspectives Drop impact evolution Initial shock wave t 10ns Bowden, Lesser, Field, 1985-1988 Drop Shock wave Huygens principle of wave propagation Ve = U/tanβ Tri-supersonic point (a) Drop Shock wave z Liquid hap Cs sin β = U (b) Drop Shock wave r Liquid Shock separation Cs Jetting flow β re V Vjetting x (c) Jetting Cavitation
Drop impact evolution Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region HALLER, K. K. ; POULIKAKOS, D. ; VENTIKOS, Y. ; MONKEWITZ, P. Journal of Fluid Mechanics (2003) vol. 490, no. 1, pg. 1-14 Time between impact and shock detachment t sd C Mai D s = 1481 m/s U = 5 m/s 2 2 C s D = 3 mm t sd = 2 ns Drop impact evolution Edge propagation: kinetic phase From the geometry z = R R r z = Ut 2 2 z re = DUt U 2 t 2 t 0 r t e 1/ 2 if t << D/U U = 5 m/s D = 3 mm t << 600 µs U R Dimensionless form ~ re = τ τ 2 r e r
Drop impact evolution Edge propagation: kinetic phase Impact of a water drop on smooth PVC We = 88 50 Experimental data 40 Fitting edge propagation V = at b Fitting cinematic phase V = a exp(bt) t = 60 µs ; t < 250 µs Velocity [m/s] 30 20 r e DUt = 0.06t 0.5 10 Consider a water drop: D = 2.7 mm; U = 1.55 m/s There is a first phase where the impact is driven by the geometrical edge propagation 0 0 50 100 150 200 250 time [µs] A detailed study of the kinematic phase Drop impact onto liquid layers Splash on a dry and wetted surface Splash of a isopropanol drop We = 1020; Re = 3225; D = 3.26 mm (a) a dry glass surface (b) on a PVC surface covered by a liquid film of 0.1 mm thickness (c) on a PVC surface covered by a liquid film of 0.8 mm thickness.
Introduction Experimental studies Numerical simulations Perspectives Drop impact onto liquid layers Drop impact onto very thin films Liquid [σ (N/m); µ (Pa s); ρ (kg/m3 )] Range V (m/s) D (mm) H* We Oh Glycerol-water [0.067; 0.00513; 1100] min. max. min. max. min. max. min. max. 1.11 2.59 0.65 2.76 0.44 2.72 0.86 3.14 2.67 2.71 2.22 3.81 1.42 3.06 1.54 2.08 0.018 0.117 0.017 0.189 0.007 0.093 0.004 0.132 55 300 41 741 28 707 54 890 0.0114 0.0115 0.0159 0.0121 0.0195 0.0286 0.0474 0.0548 Hexadecane [0.0271; 0.00334; 730] PDMS5 [0.0197; 0.00459; 918] PDMS10 [0.0201; 0.00935; 930] 3500 splash 2500 K ( We.Oh -0.4 ) 3000 C-S limit (a) (c) 2000 (b) 1500 crown 1000 D-C limit 500 Dry 0 0,00 Liquid film 0,02 0,04 0,06 0,08 0,10 0,12 0,14 H* ( h/d ) Rioboo et al. (2003) Introduction Experimental studies Numerical simulations Perspectives Drop impact onto liquid layers Drop impact on liquid film We = 560; Oh = 2.e-3 K = 6730; t = 8.3 ms δ = 0.1 Perturbations Jet formation Secondary droplet formation Cossali G.E., A. Coghe, M. Marengo The impact of a sinlge drop on a wetted solid surface, Experiments in Fluids, Vol. 22, pp. 463-472, 1997
Wetted surfaces Crown evolution Important theoretical contributions from Prof. Ilia Roisman Wetted surfaces Crown height evolution η C = H D o η C,max = A 1 We n τ max = A 2 We n n = 0. 65 0. 75
Drop impact onto liquid layers Splash and jetting on a deep pool We~1 We > 60 with water only... Cascade of coalescences Oh~1 We > 84 Rein (1993) Splash and jetting on a deep pool Fr = U 2 /(gd) Hsiao et al. (1989)
Drop impact onto inclined surfaces Impact on inclined surfaces Examples of splashing a b t=3 ms Impact of a glycerin droplet (We=51, D=2.45) a b c d isotropic splash (water droplet D=2.7, We=390 on rough glass, α=45 splash in the forward direction (isopropanol droplet D=3.3, We=544 on smooth glass, α=45 ) a) with rebound from smooth glass (t 1 =0.0 ms, α=8 ) b) t 1 =7.32 ms, α=8 c) partial rebound (α=9 ) d) with deposition on wax (α=5 ) Dry inclined surfaces Influence of the impact angle Water on wax We = 90 Re = 4212 t = 3.67-3.99 ms
Dry inclined surfaces Sticking and slipping α = 5 We=390, Re=8875, d=2.7 mm contact contact t = 4.81 ms t = 4.81 ms Glass surface t = 10.38 ms Wax surface t = 10.38 ms Small targets Impacts onto small targets Radial flow Wetting Friction No Wetting No friction Dynamics of a liquid lamella resulting from the impact of a water drop on a small target, Rozhkov, A., Prunet-Foch, B., Vignes-Adler, M., Proc. Mathematical, Physical, Engineering Sciences (2004), 460, 2049, pp 2681-2704
Small targets Camera 1 Top view Camera 2 By courtesy M. Vignes-Adler Side view Small targets Camera 1 Camera 2 By courtesy M. Vignes-Adler
The splashing/deposition limit SPLASH/DEPOSITION THRESHOLD Influence of air pressure / drag The splashing/deposition limit Ethanol drop V = 3.74 m/s P 4 Repeat the experiment with other liquids and with a film Xu (2005)
The splashing/deposition limit Secondary droplet formation Crown splash High values of We, R nd and with wetted surfaces. With dry surfaces the crown has a lower angle respect to the solid surface Very high number of secondary droplets d sec = 0.05-0.7 D u = 0.1-0.9 V Conical jet break-up High and middle values of We, low wettable or wetted surfaces Low number of secondary droplets (<3) d sec = 0.5-0.8 D u < 0.6 V The splashing/deposition limit Secondary droplet formation Recoiling film break- up Very low wettable surface d sec (?) u = 0 Rebound High value of Weber and low wettable surfaces, small impact angle (?), hot surfaces d sec = D (?) u (?)
The splashing/deposition limit Secondary droplet formation Prompt splash a) b) Prompt splash High values of We, R nd and with wetted surfaces. Low liquid viscosity. Very high number of secondary droplets d sec < 0.2 D u = (?) Water drop impact ( D = 2.7 mm) on a glass surface a) Deterministic roughness R a = 6 µm, λ = 1mm b) R a = 3.5 µm, λ = 100 µm The splashing/deposition limit Crown splash threshold Number K K = We Oh 0.4 Depending on the impacting drop parameters Critical K number K > Kcr K < Kcr Generally Depending on impacted surface parameters Secondary droplets formation Deposition K cr = f n (R nd, θ, T, λ nd, δ) n = splash type
The splashing/deposition limit Crown splash threshold Dry high wettable surfaces K cr = 649 + 3.76/R nd 0.63 K = We Oh 0.4 3500 Mundo et al. (1995) Stow and Hadfield (1981) 3000 Coghe et al. (1995) 2500 2000 1500 1000 Splash limit K cr = 657 500 0 10-5 10-4 10-3 10-2 10-1 10 0 Dimensionless Surface Roughness R nd The splashing/deposition limit Crown splash threshold Wetted surfaces (δ < 1) Splash limit K cr = 2100 +5880 δ 1.44 Prompt splash limit K cr = 2100 + 760 δ 0.23
The splashing/deposition limit Crown splash threshold Influence of the wettability Critical Weber number as a function of the dimensionless surface roughness Aluminium;. Glas; * Plexiglas; + 3M Film (Range 1995) Drop Array Impacts Droplet array impact (T s = 80 ) z z x y Front and side view
NUMERICAL SIMULATIONS Numerical simulations Numerical methods Volume of fluid interface (VOF) LEVEL SET METHODS C.W. Hirt and B.D. Nichols, Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, J. Comp. Phys., 39, 201-225,1981 S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), pp. 1249 BOUNDARY ELEMENT METHODS
Definition of the VOF Method In a volume-of fluid method the motion of the interface itself is not tracked, but rather the volume of each material in each cell is evolved in time and the interface at the new time is reconstructed from the values of the volumes at this new time. For this reason VOF methods are sometimes referred to as volume tracking methods Numerical simulations Cij = Volume of «fluid» in cell ij Second-order accurate volume-of-fluid algorithms for tracking material interfaces James Edward Pilliod, Jr. and Elbridge Gerry Puckett Journal of Computational Physics, Volume 199, Issue 2, 20 September 2004, Pages 465-502 Numerical simulations where and x = y = h Advection equation If the fluid is incompressible Conservation law for the volume fraction function
Numerical simulations Interface reconstruction (c) is a first-order method of simple line interface calculation (SLIC) type (d) is a second-order method of piecewise... (PLIC) type Numerical simulations There are other methods, like Marker and Cell (MAC), Lagrangian Tracking, Integral Tracking and so on...
Numerical simulations LEVEL-SET Numerical simulations by courtesy of Daniele Di Pietro
Numerical simulations Numerical simulations LEVEL-SET 3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling Yang Ge, L.-S. Fan Int. J. Heat and Mass Transfer 49 (2006) 4231-4249
Introduction Experimental studies Numerical simulations Perspectives Numerical simulations Boundary element methods Introduction Experimental studies Numerical simulations Perspectives Numerical simulations VOF simulations and time accuracy Contact angle problem Numerical and experimental drop impact on solid dry surfaces W.I.Geldorp, R.Rioboo, SJ. A. Jakirlić, S. Muzaferija, C.Tropea, VIII Int. Conf. on Liquid Atomization and Spray Systems, Pasadena, USA, 2000
MOVIE Re = 1000, We = 8000 D = 6mm U = 6m/s 400 grid point in D 1 grid point = 15 microns by courtesy of Stephane Zaleski Numerical simulations Select a numerically «nice» case: Not too viscous (no splashing) Not too large Re (too unstable) A glycerine, 4 mm droplet falling at 2 m/s 256² Simulation ( 128 grid points/diameter ) Repeat at 128² : same result