Advertisement

Experiments in Fluids

, 59:55 | Cite as

From drop impact physics to spray cooling models: a critical review

  • Jan Breitenbach
  • Ilia V. RoismanEmail author
  • Cameron Tropea
Research Article

Abstract

Spray–wall interaction is an important process encountered in a large number of existing and emerging technologies and is the underlying phenomenon associated with spray cooling. Spray cooling is a very efficient technology, surpassing all other conventional cooling methods, especially those not involving phase change and not exploiting the latent heat of vaporization. However, the effectiveness of spray cooling is dependent on a large number of parameters, including spray characteristics like drop size, velocity and number density, the surface morphology, but also on the temperature range and thermal properties of the materials involved. Indeed, the temperature of the substrate can have significant influence on the hydrodynamics of drop and spray impact, an aspect which is seldom considered in model formulation. This process is extremely complex, thus most design rules to date are highly empirical in nature. On the other hand, significant theoretical progress has been made in recent years about the interaction of single drops with heated walls and improvements to the fundamentals of spray cooling can now be anticipated. The present review has the objective of summarizing some of these recent advances and to establish a framework for future development of more reliable and universal physics-based correlations to describe quantities involved in spray cooling.

Notes

Acknowledgements

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) in the framework of the SFB-TRR 75 Collaborative Research Center, subproject C4.

References

  1. Aamir M, Qiang L, Hong W, Xun Z, Wang J, Sajid M (2017) Transient heat transfer performance of stainless steel structured surfaces combined with air-water spray evaporative cooling at high temperature scenarios. Appl Thermal Eng 115:418–434CrossRefGoogle Scholar
  2. Abu-Zaid M (2004) An experimental study of the evaporation characteristics of emulsified liquid droplets. Heat Mass Transf 40(9):737–741Google Scholar
  3. Bai C, Gosman AD (1995) Development of methodology for spray impingement simulation. Technical Report 950283. SAE Technical PaperGoogle Scholar
  4. Bai C, Gosman AD (1996) Mathematical modelling of wall films formed by impinging sprays. Technical Report 960626. SAE Technical PaperGoogle Scholar
  5. Bar-Cohen A, Arik M, Ohadi M (2006) Direct liquid cooling of high flux micro and nano electronic components. Proc IEEE 94(8):1549–1570CrossRefGoogle Scholar
  6. Batzdorf S, Breitenbach J, Schlawitschek C, Roisman IV, Tropea C, Stephan P, Gambaryan-Roisman T (2017) Heat transfer during simultaneous impact of two drops onto a hot solid substrate. Int J Heat Mass Transf 113:898–907CrossRefGoogle Scholar
  7. Berberović E, van Hinsberg NP, Jakirlić S, Roisman IV, Tropea C (2009) Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys Rev E 79(3):036306MathSciNetCrossRefGoogle Scholar
  8. Berberović E, Roisman IV, Jakirlić S, Tropea C (2011) Inertia dominated flow and heat transfer in liquid drop spreading on a hot substrate. Int J Heat Fluid Flow 32(4):785–795zbMATHCrossRefGoogle Scholar
  9. Berenson PJ (1961) Film-boiling heat transfer from a horizontal surface. J Heat Transf 83(3):351–356CrossRefGoogle Scholar
  10. Bernardin JD, Mudawar I (1997) Film boiling heat transfer of droplet streams and sprays. Int J Heat Mass Transf 40(11):2579–2593CrossRefGoogle Scholar
  11. Bernardin JD, Mudawar I (1999) The Leidenfrost point: experimental study and assessment of existing models. J Heat Transf 121:894–903CrossRefGoogle Scholar
  12. Bernardin JD, Mudawar I (2004) A Leidenfrost point model for impinging droplets and sprays. J Heat Transf 126(2):272–278CrossRefGoogle Scholar
  13. Bernardin JD, Stebbins CJ, Mudawar I (1996) Effects of surface roughness on water droplet impact history and heat transfer regimes. Int J Heat Mass Transf 40(1):73–88CrossRefGoogle Scholar
  14. Bernardin JD, Stebbins CJ, Mudawar I (1997) Mapping of impact and heat transfer regimes of water drops impinging on a polished surface. Int J Heat Mass Transf 40(2):247–267CrossRefGoogle Scholar
  15. Bertola V (2015) An impact regime map for water drops impacting on heated surfaces. Int J Heat Mass Transf 85:430–437CrossRefGoogle Scholar
  16. Biance AL, Pirat C, Ybert C (2011) Drop fragmentation due to hole formation during Leidenfrost impact. Phys Fluids 23(2):022104CrossRefGoogle Scholar
  17. Bird JC, Tsai SS, Stone HA (2009) Inclined to splash: triggering and inhibiting a splash with tangential velocity. New J Phys 11(6):063017CrossRefGoogle Scholar
  18. Bisighini A, Cossali GE, Tropea C, Roisman IV (2010) Crater evolution after the impact of a drop onto a semi-infinite liquid target. Phys Rev E 82(3):036319CrossRefGoogle Scholar
  19. Bolle L, Moureau JC (1982) Spray cooling of hot surfaces. Multiphase Sci Technol 1(1–4)Google Scholar
  20. Breitenbach J, Roisman IV, Tropea C (2017) Drop collision with a hot, dry solid substrate: Heat transfer during nucleate boiling. Phys Rev Fluids 2(7):074301CrossRefGoogle Scholar
  21. Breitenbach J, Roisman IV, Tropea C (2017) Heat transfer in the film boiling regime: single drop impact and spray cooling. Int J Heat Mass Transf 110:34–42CrossRefGoogle Scholar
  22. Brutin D (ed) (2015) Droplet wetting and evaporation: from pure to complex fluids. Academic Press, LondonGoogle Scholar
  23. Buchmüller I (2014) Influence of pressure on Leidenfrost effect. Ph.D. thesis. TU Darmstadt. DarmstadtGoogle Scholar
  24. Butt HJ, Roisman IV, Brinkmann M, Papadopoulos P, Vollmer D, Semprebon C (2014) Characterization of super liquid-repellent surfaces. Curr Opin Colloid Interface Sci 19(4):343–354CrossRefGoogle Scholar
  25. Carey VP (1992) Liquid-vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment. Series in Chemical and Mechanical Engineering. Taylor & Francis, BristolGoogle Scholar
  26. Castanet G, Caballina O, Lemoine F (2015) Drop spreading at the impact in the Leidenfrost boiling. Phys Fluids 27(6):063302CrossRefGoogle Scholar
  27. Cazabat AM, Guena G (2010) Evaporation of macroscopic sessile droplets. Soft Matter 6(12):2591–2612CrossRefGoogle Scholar
  28. Celata GP, Cumo M, Mariani A, Zummo G (2006) Visualization of the impact of water drops on a hot surface: effect of drop velocity and surface inclination. Heat Mass Transf 42(10):885–890CrossRefGoogle Scholar
  29. Chandra S, Avedisian CT (1991) On the collision of a droplet with a solid surface. Proc R Soc Lond A Math Phys Sci 432(1884):13–41CrossRefGoogle Scholar
  30. Chaze W, Caballina O, Castanet G, Lemoine F (2016) The saturation of the fluorescence and its consequences for laser-induced fluorescence thermometry in liquid flows. Exp Fluids 57(4):58CrossRefGoogle Scholar
  31. Chaze W, Caballina O, Castanet G, Lemoine F (2017) Spatially and temporally resolved measurements of the temperature inside droplets impinging on a hot solid surface. Exp Fluids 58(8):96CrossRefGoogle Scholar
  32. Chen RH, Chow LC, Navedo JE (2002) Effects of spray characteristics on critical heat flux in subcooled water spray cooling. Int J Heat Mass Transf 45(19):4033–4043CrossRefGoogle Scholar
  33. Chen SJ, Tseng AA (1992) Spray and jet cooling in steel rolling. Int J Heat Mass Transf 13(4):358–369Google Scholar
  34. Cheng L (1977) Dynamic spreading of drops impacting onto a solid surface. Ind Eng Chem Process Des Dev 16(2):192–197CrossRefGoogle Scholar
  35. Cheng WL, Zhang WW, Chen H, Hu L (2016) Spray cooling and flash evaporation cooling: the current development and application. Renew Sust Energ Rev 55:614–628CrossRefGoogle Scholar
  36. Cho J, Goodson KE (2015) Thermal transport: cool electronics. Nat Mater 14:136–137CrossRefGoogle Scholar
  37. Choi K, Yao S (1987) Mechanisms of film boiling heat transfer of normally impacting spray. Int J Heat Mass Transf 30(2):311–318CrossRefGoogle Scholar
  38. Clanet C, Béguin C, Richard D, Quéré D (2004) Maximal deformation of an impacting drop. J Fluid Mech 517:199zbMATHCrossRefGoogle Scholar
  39. Collings EW, Markworth JK, McCoy JK, Saunders JH (1990) Splat-quench solidification of freely falling liquid-metal drops by impact on a planar substrate. J Mater Sci 25:3677–3682CrossRefGoogle Scholar
  40. Cossali GE, Coghe A, Marengo M (1997) The impact of a single drop on a wetted surface. Exp Fluids 22:463–472CrossRefGoogle Scholar
  41. Cossali GE, Marengo M, Coghe A, Zhdanov S (2004) The role of time in single drop splash on thin film. Exp Fluids 36(6):888–900CrossRefGoogle Scholar
  42. Cossali GE, Marengo M, Santini M (2005) Single-drop empirical models for spray impact on solid walls: a review. Atom Sprays 15:699–736CrossRefGoogle Scholar
  43. van Dam DB, Clerc CL (2004) Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys Fluids 16(9):3403–3414zbMATHCrossRefGoogle Scholar
  44. Datrice N, Ramirez-San-Juan J, Zhang R, Meshkinpour A, Aguilar G, Nelson JS, Kelly KM (2006) Cutaneous effects of cryogen spray cooling on in vivo human skin. Dermatol Surg 32(8):1007–1012Google Scholar
  45. Deng W, Gomez A (2011) Electrospray cooling for microelectronics. Int J Heat Mass Transf 54(11):2270–2275CrossRefGoogle Scholar
  46. Elston LJ, Yerkes KL, Thomas SK, McQuillen J (2009) Cooling performance of a 16-Nozzle array in variable gravity. J Thermophys Heat Transf 23(3):571CrossRefGoogle Scholar
  47. Erbil HY (2012) Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv Colloid Interface Sci 170(1–2):67–86CrossRefGoogle Scholar
  48. Estes KA, Mudawar I (1995) Correlation of Sauter mean diameter and critical heat flux for spray cooling of small surfaces. Int J Heat Mass Transf 38(16):2985–2996CrossRefGoogle Scholar
  49. Fabbri M, Jiang S, Dhir VK (2005) A comparative study of cooling of high power density electronics using sprays and microjets. J Heat Transf 127(1):38–48CrossRefGoogle Scholar
  50. Fedorchenko AI, Wang AB (2004) On some common features of drop impact on liquid surfaces. Phys Fluids 16(5):1349–1365MathSciNetzbMATHCrossRefGoogle Scholar
  51. Forster HK, Zuber N (1954) Growth of a vapor bubble in a superheated liquid. J Appl Phys 25(4):474–478MathSciNetzbMATHCrossRefGoogle Scholar
  52. Foucart H, Habchi C, Le Coz JF, Baritaud T (1998) Development of a three dimensional model of wall fuel liquid film for internal combustion engines. Technical Report 980133. SAE Technical PaperGoogle Scholar
  53. Fukai J, Shiiba Y, Yamamoto T, Miyatake O, Poulikakos D, Megaridis CM, Zhao Z (1995) Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling. Phys Fluids 7:236–247CrossRefGoogle Scholar
  54. Ghodbane M, Holman J (1991) Experimental study of spray cooling with Freon-113. Int J Heat Mass Transf 34(4):1163–1174CrossRefGoogle Scholar
  55. Griffith P (1958) Bubble growth rates in boiling. J Heat Transf 80:721–726Google Scholar
  56. Gross KA, Berndt CC (1998) Thermal processing of hydroxyapatite for coating production. J Biomed Mater Res 39(4):580–587CrossRefGoogle Scholar
  57. Hall DD, Mudawar I (1995) Experimental and numerical study of quenching complex-shaped metallic alloys with multiple, overlapping sprays. Int J Heat Mass Transf 38(7):1201–1216CrossRefGoogle Scholar
  58. Herbert S, Fischer S, Gambaryan-Roisman T, Stephan P (2013) Local heat transfer and phase change phenomena during single drop impingement on a hot surface. Int J Heat Mass Transf 61:605–614CrossRefGoogle Scholar
  59. van Hinsberg NP, Budakli M, Göhler S, Berberović E, Roisman IV, Gambaryan-Roisman T, Tropea C, Stephan P (2010) Dynamics of the cavity and the surface film for impingements of single drops on liquid films of various thicknesses. J Colloid Interface Sci 350(1):336–343CrossRefGoogle Scholar
  60. Holman J, Kendall C (1993) Extended studies of spray cooling with Freon-113. Int J Heat Mass Transf 36(8):2239–2241CrossRefGoogle Scholar
  61. Hong K, Lee SH, Ryou HS (2001) Modelling of wall films formed by impinging diesel sprays. Technical Report 2001-01-3228. SAE Technical PaperGoogle Scholar
  62. Hsieh CC, Yao SC (2006) Evaporative heat transfer characteristics of a water spray on micro-structured silicon surfaces. Int J Heat Mass Transf 49(5):962–974CrossRefGoogle Scholar
  63. Hsieh SS, Fan TC, Tsai HH (2004) Spray cooling characteristics of water and R-134a. Part I: nucleate boiling. Int J Heat Mass Transf 47(26):5703–5712CrossRefGoogle Scholar
  64. Hsieh SS, Hsu YF, Wang ML (2014) A microspray-based cooling system for high powered LEDs. Energy Convers Manag 78:338–346CrossRefGoogle Scholar
  65. Huddle JJ, Chow LC, Lei S, Marcos A, Rini D, Lindauer S, Bass M, Delfyett P (2000) Thermal management of diode laser arrays. In 16th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2000. IEEE. (pp 154–160)Google Scholar
  66. Itaru M, Kunihide M (1978) Heat transfer characteristics of evaporation of a liquid droplet on heated surfaces. Int J Heat Mass Transf 21(5):605–613CrossRefGoogle Scholar
  67. Josserand C, Thoroddsen ST (2016) Drop impact on a solid surface. Annu Rev Fluid Mech 48(1):365–391MathSciNetzbMATHCrossRefGoogle Scholar
  68. Karbalaei A, Kumar R, Cho HJ (2016) Thermocapillarity in microfluidics: a review. Micromachines 7(1):13CrossRefGoogle Scholar
  69. Karl A, Anders K, Rieber M, Frohn A (1996) Deformation of liquid droplets during collisions with hot walls: experimental and numerical results. Part Part Syst Charact 13(3):186–191CrossRefGoogle Scholar
  70. Karwa N, Kale SR, Subbarao P (2007) Experimental study of non-boiling heat transfer from a horizontal surface by water sprays. Exp Therm Fluid Sci 32(2):571–579CrossRefGoogle Scholar
  71. Kato M, Abe Y, Mori YH, Nagashima A (1995) Spray cooling characteristics under reduced gravity. J Thermophys Heat Transf 9(2):378–380CrossRefGoogle Scholar
  72. Kelly KM, Nelson JS, Lask GP, Geronemus RG, Bernstein LJ (1999) Cryogen spray cooling in combination with nonablative laser treatment of facial rhytides. Arch Dermatol 135(6):691–694CrossRefGoogle Scholar
  73. Khavari M, Sun C, Lohse D, Tran T (2015) Fingering patterns during droplet impact on heated surfaces. Soft Matter 11(17):32983303CrossRefGoogle Scholar
  74. Kim J (2007) Spray cooling heat transfer: the state of the art. Int J Heat Fluid Flow 28(4):753–767CrossRefGoogle Scholar
  75. Kim J, You S, Choi SU (2004) Evaporative spray cooling of plain and microporous coated surfaces. Int J Heat Mass Transf 47(14):3307–3315CrossRefGoogle Scholar
  76. Klinzing WP, Rozzi JC, Mudawar I (1992) Film and transition boiling correlations for quenching of hot surfaces with water sprays. J Heat Treat 9(2):91–103CrossRefGoogle Scholar
  77. Kovalchuk NM, Trybala A, Starov VM (2014) Evaporation of sessile droplets. Curr Opin Colloid Interface Sci 19(4):336–342CrossRefGoogle Scholar
  78. Kunkelmann C, Ibrahem K, Schweizer N, Herbert S, Stephan P, Gambaryan-Roisman T (2012) The effect of three-phase contact line speed on local evaporative heat transfer: experimental and numerical investigations. Int J Heat Mass Transf 55(7):1896–1904CrossRefGoogle Scholar
  79. Kyriopoulos ON (2010) Gravity effect on liquid film hydrodynamics and spray cooling. Ph.d. thesis. Technische Universität Darmstadt. Darmstadt, GermanyGoogle Scholar
  80. Labergue A, Gradeck M, Lemoine F (2015) Comparative study of the cooling of a hot temperature surface using sprays and liquid jets. Int J Heat Mass Transf 81(Supplement C):889–900CrossRefGoogle Scholar
  81. Lagubeau G, Fontelos MA, Josserand C, Maurel A, Pagneux V, Petitjeans P (2012) Spreading dynamics of drop impacts. J Fluid Mech 713:5060zbMATHCrossRefGoogle Scholar
  82. Leidenfrost JG (1756) De aquae Communis Nonnullis Qualitatibus Tractatus. Ovenius, Duisburg ad Rhenum. See the translation in Int J Heat Mass Transf 9:1153–1166 (1966)Google Scholar
  83. Lembach AN, Tan HB, Roisman IV, Gambaryan-Roisman T, Zhang Y, Tropea C, Yarin AL (2010) Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats. Langmuir 26(12):9516–9523CrossRefGoogle Scholar
  84. Liang G, Mudawar I (2017a) Review of drop impact on heated walls. Int J Heat Mass Transf 106:103–126CrossRefGoogle Scholar
  85. Liang G, Mudawar I (2017) Review of spray cooling – Part 1: single-phase and nucleate boiling regimes, and critical heat flux. Int J Heat Mass Transf 115(Part A):1174–1205CrossRefGoogle Scholar
  86. Liang G, Mudawar I (2017) Review of spray cooling – Part 2: high temperature boiling regimes and quenching applications. Int J Heat Mass Transf 115(Part A):1206–1222CrossRefGoogle Scholar
  87. Lin L, Ponnappan R (2003) Heat transfer characteristics of spray cooling in a closed loop. Int J Heat Mass Transf 46(20):3737–3746CrossRefGoogle Scholar
  88. Liu H, Lee CF (2014) Numerical study on wall film formation and evaporation. Technical Report 2014-01-1112. SAE Technical PaperGoogle Scholar
  89. Lopes MC, Bonaccurso E, Gambaryan-Roisman T, Stephan P (2013) Influence of the substrate thermal properties on sessile droplet evaporation: effect of transient heat transport. Colloids and Surf A: Physicochem Eng Aspects 432:64–70CrossRefGoogle Scholar
  90. Manzello SL, Yang JC (2002) On the collision dynamics of a water droplet containing an additive on a heated solid surface. Proc R Soc Lond A Math Phys Sci 458(2026):2417–2444CrossRefGoogle Scholar
  91. Marengo M, Antonini C, Roisman IV, Tropea C (2011) Drop collisions with simple and complex surfaces. Curr Opin Colloid Interface Sci 16(4):292–302CrossRefGoogle Scholar
  92. Marmanis H, Thoroddsen ST (1996) Scaling of the fingering pattern of an impacting drop. Phys Fluids 8(6):1344–1346CrossRefGoogle Scholar
  93. Mathur P, Apelian D, Lawley A (1989) Analysis of the spray deposition process. Acta Metall 37(2):429–443CrossRefGoogle Scholar
  94. Michalak TE, Yerkes KL, Thomas SK, McQuillen JB (2010) Acceleration effects on the cooling performance of a partially confined FC-72 spray. J Thermophys Heat Transf 24(3):463–479CrossRefGoogle Scholar
  95. Mikic BB, Rohsenow WM (1969) Bubble growth rates in non-uniform temperature field. Prog Heat Mass Transf 2:283–292Google Scholar
  96. Moita AS, Moreira AL (2012) Scaling the effects of surface topography in the secondary atomization resulting from droplet/wall interactions. Exp Fluids 52(3):679–695CrossRefGoogle Scholar
  97. Moreira A, Moita A, Panao M (2010) Advances and challenges in explaining fuel spray impingement: how much of single droplet impact research is useful? Prog Energy Combust Sci 36(5):554–580CrossRefGoogle Scholar
  98. Mudawar I, Deiters TA (1994) A universal approach to predicting temperature response of metallic parts to spray quenching. Int J Heat Mass Transf 37(3):347–362CrossRefGoogle Scholar
  99. Mudawar I, Valentine WS (1989) Determination of the local quench curve for spray-cooled metallic surfaces. J Heat Treat 7(2):107–121CrossRefGoogle Scholar
  100. Mühlbauer M (2010) Modelling wall interactions of a high-pressure, hollow cone spray. Ph.D. thesis. Technische Universität Darmstadt. Darmstadt, GermanyGoogle Scholar
  101. Mundo C, Sommerfeld M, Tropea C (1995) Droplet-wall collisions: experimental studies of the deformation and breakup process. Int J Multiph Flow 21(2):151–173zbMATHCrossRefGoogle Scholar
  102. Nelson JS, Milner TE, Anvari B, Tanenbaum BS, Kimel S, Svaasand LO, Jacques SL (1995) Dynamic epidermal cooling during pulsed laser treatment of port-wine stain: a new methodology with preliminary clinical evaluation. Arch Dermatol 131(6):695–700CrossRefGoogle Scholar
  103. Nishio S, Kim YC (1998) Heat transfer of dilute spray impinging on hot surface (simple model focusing on rebound motion and sensible heat of droplets). Int J Heat Mass Transf 41(24):4113–4119zbMATHCrossRefGoogle Scholar
  104. Ohtake H, Koizumi Y (2004) Study on propagative collapse of a vapor film in film boiling (mechanism of vapor-film collapse at wall temperature above the thermodynamic limit of liquid superheat). Int J Heat Mass Transf 47(8):1965–1977CrossRefGoogle Scholar
  105. Oliphant K, Webb B, McQuay M (1998) An experimental comparison of liquid jet array and spray impingement cooling in the non-boiling regime. Exp Therm Fluid Sci 18(1):1–10CrossRefGoogle Scholar
  106. Opfer L (2014) Controlling Liquid Atomization using Dilute Emulsions: Mitigation of Pesticide Spray Drift. Ph.D. thesis. Technische Universität Darmstadt. Darmstadt, GermanyGoogle Scholar
  107. O’Rourke PJ, Amsden A (2000) A spray/wall interaction submodel for the KIVA-3 wall film model. Technical Report 2000-01-0271. SAE Technical PaperGoogle Scholar
  108. Pais MR, Chow LC, Mahefkey ET (1992) Surface roughness and its effects on the heat transfer mechanism in spray cooling. J Heat Transf 114(1):211–219CrossRefGoogle Scholar
  109. Palacios J, Hernández J, Gómez P, Zanzi C, López J (2013) Experimental study of splashing patterns and the splashing/deposition threshold in drop impacts onto dry smooth solid surfaces. Exp Therm Fluid Sci 44:571–582CrossRefGoogle Scholar
  110. Pan KL, Tseng KC, Wang CH (2010) Breakup of a droplet at high velocity impacting a solid surface. Exp Fluids 48(1):143–156CrossRefGoogle Scholar
  111. Pasandideh-Fard M, Qiao YM, Chandra S, Mostaghimi J (1996) Capillary effects during droplet impact on a solid surface. Phys Fluids 8:650–659CrossRefGoogle Scholar
  112. Puschmann F (2003) Experimentelle Untersuchung der Spraykühlung zur Qualitätsverbesserung durch definierte Einstellung des Wärmeübergangs. Ph.D. thesis. Otto-von-Guericke-Universität Magdeburg, UniversitätsbibliothekGoogle Scholar
  113. Quere D (2013) Leidenfrost dynamics. Annu Rev Fluid Mech 45:197–215MathSciNetzbMATHCrossRefGoogle Scholar
  114. Rieber M, Frohn A (1999) A numerical study on the mechanism of splashing. Int J Heat Fluid Flow 20(5):455–461CrossRefGoogle Scholar
  115. Rini DP, Chen RH, Chow LC (2002) Bubble behavior and nucleate boiling heat transfer in saturated FC-72 spray cooling. ASME J Heat Transf 124(1):63–72CrossRefGoogle Scholar
  116. Rioboo R, Marengo M, Tropea C (2001) Outcomes from a drop impact on solid surfaces. Atom Sprays 11:155–165Google Scholar
  117. Rioboo R, Voué M, Vaillant A, De Coninck J (2008) Drop impact on porous superhydrophobic polymer surfaces. Langmuir 24(24):14074–14077CrossRefGoogle Scholar
  118. Roisman IV (2009) Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys Fluids 21(5):052104zbMATHCrossRefGoogle Scholar
  119. Roisman IV (2010) Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition. J Fluid Mech 656:189–204MathSciNetzbMATHCrossRefGoogle Scholar
  120. Roisman IV, Berberović E, Tropea C (2009) Inertia dominated drop collisions. I: on the universal flow in the lamella. Phys Fluids 21(5):052103zbMATHCrossRefGoogle Scholar
  121. Roisman IV, Breitenbach J, Tropea C (2017) Thermal atomisation of a liquid drop after impact onto a hot substrate. J Fluid Mech (accepted)Google Scholar
  122. Roisman IV, van Hinsberg NP, Tropea C (2008) Propagation of a kinematic instability in a liquid layer: capillary and gravity effects. Phys Rev E 77(4):046305CrossRefGoogle Scholar
  123. Roisman IV, Horvat K, Tropea C (2006) Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys Fluids 18:102–104MathSciNetzbMATHCrossRefGoogle Scholar
  124. Roisman IV, Lembach A, Tropea C (2015) Drop splashing induced by target roughness and porosity: the size plays no role. Adv Colloid Interface Sci 222:615–621CrossRefGoogle Scholar
  125. Roisman IV, Rioboo R, Tropea C (2002) Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc R Soc Lond A Math Phys Sci 458(2022):1411–1430zbMATHCrossRefGoogle Scholar
  126. Roisman IV, Tropea C (2005) Fluctuating flow in a liquid layer and secondary spray created by an impacting spray. Int J Multiph Flow 31(2):179–200zbMATHCrossRefGoogle Scholar
  127. Rybicki JR, Mudawar I (2006) Single-phase and two-phase cooling characteristics of upward-facing and downward-facing sprays. Int J Heat Mass Transf 49(1):5–16CrossRefGoogle Scholar
  128. Saski K, Sugitani Y, Kawasaki M (1979) Heat transfer in spray cooling on hot surface. Tetsu-to-Hagane 65(1):90–96CrossRefGoogle Scholar
  129. Sawan ME, Carbon MW (1975) Spray-cooling and bottom-flooding work for LWR cores. Nucl Eng Des 32(2):191–207CrossRefGoogle Scholar
  130. Scheller BL, Bousfield DW (1995) Newtonian drop impact with a solid surface. AIChE J 41(6):1357–1367CrossRefGoogle Scholar
  131. Schmehl R, Rosskamp H, Willmann M, Wittig S (1999) CFD analysis of spray propagation and evaporation including wall film formation and spray/film interactions. Int J Heat Fluid Flow 20(5):520–529CrossRefGoogle Scholar
  132. Schremb M, Borchert S, Berberovic E, Jakirlic S, Roisman IV, Tropea C (2017) Computational modelling of flow and conjugate heat transfer of a drop impacting onto a cold wall. Int J Heat Mass Transf 109:971–980CrossRefGoogle Scholar
  133. Sehmbey MS, Chow LC, Hahn OJ, Pais MR (1995) Spray cooling of power electronics at cryogenic temperatures. J Thermophys Heat Transf 9(1):123–128CrossRefGoogle Scholar
  134. Senda J, Kanda T, Al-Roub M, Farrell PV, Fukami T, Fujimoto H (1997) Modeling spray impingement considering fuel film formation on the wall. Technical Report 970047. SAE Technical PaperGoogle Scholar
  135. Senda J, Yamada K, Fujimoto H, Miki H (1988) The heat-transfer characteristics of a small droplet impinging upon a hot surface. JSME Int J II 31(1):105–111Google Scholar
  136. Shedd TA (2007) Next generation spray cooling: high heat flux management in compact spaces. Heat Transf Eng 28(2):87–92CrossRefGoogle Scholar
  137. Shirota M, van Limbeek MAJ, Sun C, Prosperetti A, Lohse D (2016) Dynamic Leidenfrost effect: relevant time and length scales. Phys Rev Lett 116:064501CrossRefGoogle Scholar
  138. Siemons N, Bruining H, Castelijns H, Wolf KH (2006) Pressure dependence of the contact angle in a CO2–H2O-coal system. J Colloid Interface Sci 297(2):755–761CrossRefGoogle Scholar
  139. Silk EA, Kim J, Kiger K (2006) Spray cooling of enhanced surfaces: impact of structured surface geometry and spray axis inclination. Int J Heat Mass Transf 49(25):4910–4920CrossRefGoogle Scholar
  140. Sinha-Ray S, Yarin AL (2014) Drop impact cooling enhancement on nano-textured surfaces. Part I: theory and results of the ground (1g) experiments. Int J Heat Mass Transf 70:1095–1106CrossRefGoogle Scholar
  141. Sivakumar D, Tropea C (2002) Splashing impact of a spray onto a liquid film. Phys Fluids 14(12):L85–L88zbMATHCrossRefGoogle Scholar
  142. Sodtke C, Stephan P (2007) Spray cooling on micro structured surfaces. Int J Heat Mass Transf 50(19):4089–4097CrossRefGoogle Scholar
  143. Srikar R, Gambaryan-Roisman T, Steffes C, Stephan P, Tropea C, Yarin A (2009) Nanofiber coating of surfaces for intensification of drop or spray impact cooling. Int J Heat Mass Transf 52(25):5814–5826zbMATHCrossRefGoogle Scholar
  144. Staat HJJ, Tran T, Geerdink B, Sun C, Gordillo JM, Lohse D (2015) Phase diagram for droplet impact on superheated surfaces. J Fluid Mech 779:R3CrossRefGoogle Scholar
  145. Stanton DW, Rutland CJ (1996) Modeling fuel film formation and wall interaction in diesel engines. Technical Report 960628. SAE Technical PaperGoogle Scholar
  146. Stanton DW, Rutland CJ (1998) Multi-dimensional modeling of heat and mass transfer of fuel films resulting from impinging sprays. Technical Report 980132. SAE Technical PaperGoogle Scholar
  147. Tartarini P, Lorenzini G, Randi MR (1999) Experimental study of water droplet boiling on hot, non-porous surfaces. Heat Mass Transf 34(6):437–447CrossRefGoogle Scholar
  148. Taylor GI (1959) The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc R Soc Lond A Math Phys Sci 253(1274):296–312MathSciNetzbMATHCrossRefGoogle Scholar
  149. Testa P, Nicotra L (1986) Influence of pressure on the Leidenfrost temperature and on extracted heat fluxes in the transient mode and low pressure. J Heat Transf 108(4):916–921CrossRefGoogle Scholar
  150. Tilton DE, Kearns DA, Tilton CL (1994) Liquid nitrogen spray cooling of a simulated electronic chip. In Advances in cryogenic engineering. Springer, Boston, pp 1779–1786Google Scholar
  151. Tran T, Staat HJJ, Prosperetti A, Sun C, Lohse D (2012) Drop impact on superheated surfaces. Phys Rev Lett 108(3):036101CrossRefGoogle Scholar
  152. Tropea C, Roisman IV (2000) Modelling of spray impact on solid surfaces. Atom Sprays 10:387–408CrossRefGoogle Scholar
  153. Tsui YC, Clyne TW (1997) An analytical model for predicting residual stresses in progressively deposited coatings. 1. Planar geometry. Thin Solid Films 306(1):23–33CrossRefGoogle Scholar
  154. Ukiwe C, Kwok DY (2005) On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21:666–673CrossRefGoogle Scholar
  155. Vander Wal RL, Berger GM, Mozes SD (2006) The splash/non-splash boundary upon a dry surface and thin fluid film. Exp Fluids 40(1):53–59CrossRefGoogle Scholar
  156. Visaria M, Mudawar I (2008a) Effects of high subcooling on two-phase spray cooling and critical heat flux. Int J Heat Mass Transf 51(21):5269–5278zbMATHCrossRefGoogle Scholar
  157. Visaria M, Mudawar I (2008b) Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux. Int J Heat Mass Transf 51(9):2398–2410zbMATHCrossRefGoogle Scholar
  158. Visser CW, Frommhold PE, Wildeman S, Mettin R, Lohse D, Sun C (2015) Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matter 11(9):1708–1722CrossRefGoogle Scholar
  159. Walzel P (1980) Zerteilgrenze beim tropfenprall. Chemie Ingenieur Technik 52(4):338–339CrossRefGoogle Scholar
  160. Wang H, Wu J, Yang Q, Zhu X, Liao Q (2016) Heat transfer enhancement of ammonia spray cooling by surface modification. Int J Heat Mass Transf 101:60–68CrossRefGoogle Scholar
  161. Wang Y, Liu M, Liu D, Xu K, Chen Y (2010) Experimental study on the effects of spray inclination on water spray cooling performance in non-boiling regime. Exp Therm Fluid Sci 34(7):933–942CrossRefGoogle Scholar
  162. Weickgenannt CM, Zhang Y, Lembach AN, Roisman IV, Gambaryan-Roisman T, Yarin AL, Tropea C (2011) Nonisothermal drop impact and evaporation on polymer nanofiber mats. Phys Rev E 83(3):036305CrossRefGoogle Scholar
  163. Weiss C (2005) The liquid deposition fraction of sprays impinging vertical walls and flowing films. Int J Multiph Flow 31(1):115–140zbMATHCrossRefMathSciNetGoogle Scholar
  164. Wendelstorf J, Spitzer KH, Wendelstorf R (2008a) Spray water cooling heat transfer at high temperatures and liquid mass fluxes. Int J Heat Mass Transf 51(19):4902–4910zbMATHCrossRefGoogle Scholar
  165. Wendelstorf R, Spitzer KH, Wendelstorf J (2008b) Effect of oxide layers on spray water cooling heat transfer at high surface temperatures. Int J Heat Mass Transf 51(19):4892–4901zbMATHCrossRefGoogle Scholar
  166. Wildeman S, Visser CW, Sun C, Lohse D (2016) On the spreading of impacting drops. J Fluid Mech 805:636655MathSciNetCrossRefGoogle Scholar
  167. Worthington AM (1876) On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc Lond 25(171–178):261–272CrossRefGoogle Scholar
  168. Worthington AM (1895) The splash of a drop. S.P.C.K, LondonGoogle Scholar
  169. Worthington AM, Cole RS (1897) Impact with a liquid surface, studied by the aid of instantaneous photography. Phil Trans R Soc Lond A 189:137–148zbMATHCrossRefGoogle Scholar
  170. Xie JL, Tan YB, Duan F, Ranjith K, Wong TN, Toh KC, Choo KF, Chan PK (2013) Study of heat transfer enhancement for structured surfaces in spray cooling. Appl Thermal Eng 59(1):464–472CrossRefGoogle Scholar
  171. Xu L, Zhang WW, Nagel SR (2005) Drop splashing on a dry smooth surface. Phys Rev Lett 94(18):184505CrossRefGoogle Scholar
  172. Yamanouc A (1968) Effect of core spray cooling in transient state after loss of coolant accident. J Nucl Sci Technol 5(11):547–558CrossRefGoogle Scholar
  173. Yang J, Chow LC, Pais MR (1996) Nucleate boiling heat transfer in spray cooling. ASME J Heat Transf 118(3):668–671CrossRefGoogle Scholar
  174. Yao S, Choit K (1987) Heat transfer experiments of mono-dispersed vertically impacting sprays. Int J Multiph Flow 13(5):639–648CrossRefGoogle Scholar
  175. Yao SC, Cai KY (1988) The dynamics and Leidenfrost temperature of drops impacting on a hot surface at small angles. Exp Therm Fluid Sci 1(4):363–371CrossRefGoogle Scholar
  176. Yao SC, Cox TL (2002) A general heat transfer correlation for impacting water sprays on high-temperature surfaces. Exp Heat Transf 15(4):207–219CrossRefGoogle Scholar
  177. Yao SC, Henry RE (1978) An investigation of the minimum film boiling temperature on horizontal surfaces. J Heat Transf 100(2):260–267CrossRefGoogle Scholar
  178. Yarin AL (2006) Drop impact dynamics: splashing, spreading, receding, bouncing. Annu Rev Fluid Mech 38:159–192MathSciNetzbMATHCrossRefGoogle Scholar
  179. Yarin AL, Roisman IV, Tropea C (2017) Collision phenomena in liquids and solids. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  180. Yarin AL, Weiss DA (1995) Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J Fluid Mech 283:141–173CrossRefGoogle Scholar
  181. Zenzie HH, Altshuler GB, Smirnov MZ, Anderson RR (2000) Evaluation of cooling methods for laser dermatology. Lasers Surg Med 26(2):130–144CrossRefGoogle Scholar
  182. Zhang Y, Jia M, Liu H, Xie M (2016) Development of an improved liquid film model for spray/wall interaction under engine-relevant conditions. Int J Multiph Flow 79:74–87MathSciNetCrossRefGoogle Scholar
  183. Zhang Z, Jiang PX, Ouyang XL, Chen JN, Christopher DM (2014) Experimental investigation of spray cooling on smooth and micro-structured surfaces. Int J Heat Mass Transf 76:366–375CrossRefGoogle Scholar
  184. Zhang Z, Li J, Jiang PX (2013) Experimental investigation of spray cooling on flat and enhanced surfaces. Appl Therm Eng 51(1):102–111CrossRefGoogle Scholar
  185. Zhong L, Guo Z (2017) Effect of surface topography and wettability on the Leidenfrost effect. Nanoscale 9(19):6219–6236CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Fluid Mechanics and AerodynamicsTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations