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Experimental and modelling investigation of the deformation, drag and break-up of drizzle droplets subjected to strong aerodynamics forces in relation to SLD aircraft icing

By Geoffrey Luxford

Abstract

The distortion, drag and break-up of drizzle droplets subjected to strong aerodynamic forces was investigated to understand the pre-impact behaviour of droplets in aircraft icing from supercooled freezing drizzle. The objective was to obtain a formulation and data for the drag properties of droplets distorted by the aerodynamic forces, which were beyond the scope of available experimental and modelling methods. A practical and efficient semi-empirical computer model was developed for small water droplets in air, 100μm < D < 500μm, at moderate Reynolds numbers, 350 < Re < 1500, and high Weber numbers 3 < We < 20. This used available experimental terminal velocity data for free-falling droplets, extrapolated to higher Weber numbers, and the numerical solution for sessile droplets on a horizontal unwettable surface, with corrections for the Reynolds number. A theory for bag break-up was developed based on the Rayleigh-Taylor instability of the windward droplet surface. The critical Bond number was 13.7, with a critical diameter of 10.1mm for free-falling water droplets, compared to the experimental value of 10mm diameter. The equivalent Weber number was 14.2 for free falling water droplets. Aerodynamic interaction between the closely-spaced droplets from a vibrating nozzle droplet generator resulted in irregular spacing and coalescence of droplets. In an alternative design a laminar jet impinged on a rotating slotted disk to achieve the necessary droplet spacing, but the significant size variability of the droplets degraded the experimental measurements. High-speed videos, to 50,000pps, and photographs were obtained of droplet distortion, break-up, coalescence and splashes using a high-intensity LED strobe flash. A specially-designed convergent wind tunnel was developed for experimental measurements, to validated the drag model and provide data for droplets distorted by aerodynamic forces. The convergent profile produced a rapidly-increasing Weber number at a sufficiently slow rate to avoid transients or droplet vibrations. A special instrument was developed, with three equispaced parallel laser beams and photo detectors, to determine the droplet velocity and acceleration. Droplet drag characteristics were measured up to Weber numbers of 16. Good agreement was obtained between droplet drag model and experimental results. The greatest discrepancy was about 20% at a Weber number of about 8

Publisher: School of Engineering
Year: 2005
OAI identifier: oai:dspace.lib.cranfield.ac.uk:1826/945
Provided by: Cranfield CERES

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Citations

  1. 0.1787 Bo 0.8209) This is plotted in Figure 95 as the red curve. It can be seen that this curve also encompasses many of the experimental points, particularly at higher Bond numbers.
  2. (2002). 196 86. T** Jan 02 Frank Schmelz, “Tropfenzerfall in beshleunigten Gasströmungen”, Dissertation D290,
  3. (2002). A more sophisticated option was Direct Numerical Simulation, allowing the free movement of the droplet surface within CFD modelling. These methods were improving and still being developed (Schmehl
  4. (1995). A photographic study of the break-up of high-speed vaporizing drops”, Proc Int Conf on Liquids Atomization and Spray Systems, ILASS Toy,
  5. (1982). A Similarity Analysis of the Droplet Trajectory Equation”, AIAA82-4285, v 20, n 12, doi
  6. (1972). A theoretical and experiment. study of the internal circulation in water drops falling …. in air”, doi
  7. A Vertical Wind Tunnel”, Suffield
  8. Aerodynamic drag of droplets in turbulent flow doi
  9. (1992). Aerodynamics drag of droplets in turbulent flow fields
  10. (1997). AGARD, “Ice Accretion Simulation”, AGARD-AR-344 199.
  11. (1996). Aircraft Icing”, From Engineering Outlook,
  12. Also because the X axis covers such a large range this could result in difficulties with the curve fitting in Excel. For the pressure tapping at 20mm from the exit this gave; Chapter 11: Calibration of Convergent Droplet Tunnel Page 161 y =
  13. (1982). An Album of Fluid Motion”, doi
  14. (1997). An analysis of the distortion and break-up mechanisms of high-speed liquid drops”, doi
  15. (1986). An experimental investigation of drop deformation and break-up in steady 2D linear flows”,
  16. (2003). An experimental study of droplet break-up using a wind tunnel”, doi
  17. (2000). An experimental study of the effect of density on the distortion and break-up .. of drops in … gas stream”,
  18. (1986). An Experimental Study on the Mechanism of Jet Break-up”, Proc on sprays and their applications, Dep Energetica-Politecnico 353.
  19. (1999). An issue was that for low Reynolds numbers, 200 < Re < 300, the various data for the disk drag coefficient data differed by as much as 40% to 50% (Nakayama and Boucher,
  20. (1959). and Ingebo
  21. (2002). Anemometry (PDA) The PDA method works by determining the Doppler frequency as the droplet intercepts two intersecting laser beams (Lacoste et al,
  22. (1978). Apart from the Maybank & Briosi data (1961), considered later, there was a variability of about 10% between the different sources. The preferred sphere drag formulation was that given in Table 2, from Clift, Grace and Weber
  23. (1987). Approximate Theory of a Single Droplet Vaporization in a Convective Field: Effects of Variable Properties, Stefan Flow and Transient Liquid Heating”,
  24. (1989). Atomization and Sprays”, Hemisphere Publishing Corp, ISBN: 0891166033, 327.
  25. Automated comparison of ice accretion shapes”, AIAA-99-0625 155. **
  26. (1998). Bibliography and Literature Page 199 175. **
  27. (1963). Bibliography and Literature Page 208 458. **
  28. (1962). C.A. Sleicher, “Maximum drop size in turbulent flow”, doi
  29. (1984). Calculation of Water Droplet Trajectories about an Aerofoil in Steady Two-Dimensional Compressible Flow”, RAE TR 84060 367. *
  30. (1998). CFD investigation into the influence of simplifying predicted ice-shapes-BAe contribution the 3E’s icing harmonisation programme, Task 5”, Tech report, BAe Airbus, Systems Eng Rep SDF/B81/A/108/4299_01.
  31. (1978). Chapter 1: Distortion, Drag and Break-up of Droplets Page 35 The benefit of the sessile droplet was that it allowed the evaluation of the distorted shapes which were well beyond what could be obtained for free-falling droplets. Clift, Grace and Weber
  32. (2002). Chapter 10: Air Flow Calculation for Convergent Droplet Tunnel Page 148 Various CFD results were obtained for convergent tunnels, such as shown for the Cranfield 5m tall vertical tunnel in Figure
  33. Chapter 11: Calibration of Convergent Droplet Tunnel Page 158 Comparison between Nozzle theory, CFX analysis and measured results for mini wind tunnel
  34. Computations of Droplet Distributions in the NASA Icing Research Tunnel”, AIAA 2000-0101 131. * doi
  35. (1988). Computer Simulation of Drop Deformation and Drop Break-up”, AIAA 24 th Joint Propulsion Conf, doi
  36. Deformation and secondary break-up of drops”, AIAA 93-0814, 31 st Aerospace Sciences Meeting, Jan 93, Reno NV 262. **
  37. Design of a Vertical Tunnel for Large Droplet Dynamic Studies”, Nat Inst for Aviation Research report for Cranfield University 75. **
  38. (1992). Determination of Air Velocity The air velocity at the pressure tappings was determined with the following equation,
  39. (1978). Determining Droplet Shape With the first approach the shape of the droplet could be determined from measurements of photographic images and it would seem that various researchers had done this
  40. (1974). Dimensional analysis for engineers”, doi
  41. (1956). Drag Coefficient for Droplets and Solid Spheres in Clouds Accelerating in Airstreams”. NACA TN3762,
  42. (1988). Drop break-up in a turbulent flow – Conception and modelling considerations”, Chem Eng Sci, v43, n3, p617-679 341. ** Sep 87 ESDU, “Performance Improvements of Axial Diffusers for Incompressible Flow”, ESDU data sheet 87015 342.
  43. (1981). Droplet break-up regimes and criteria for their existence”,
  44. (1999). Droplet interaction with shear-driven liquid films: analysis of deposition and 2 ndary droplet characteristics”, doi
  45. (1989). Droplet Valorisation Model for Spray Combustion Calculations”,
  46. (1994). Dynamics of drop deformation and break-up in viscous fluids”, Ann Rev Fluid Mech, doi
  47. Effect of Velocity doi
  48. (1999). Evaluation of AIRUNS2D for high Re flows”, Tech rep, BAe Airbus Wing Engr (B61) report B61R/R&D/991002 170.
  49. (1981). Evaluation of Turbulence Reduction Devices for the Langley 8-Foot Transonic Pressure Tunnel”,
  50. (1952). Evaporation from drops”, Chem Eng Prog,
  51. Experimental Facilities for New Hybrid Ice/Spray Flow Tunnel with Laser Based Drop. Meas.”, AIAA 2002-2867 84. *T May 02 Anni Vuorenski, (Cranfield Univ), Simulation of fuel droplet behaviour in and intake manifold. (MSc thesis ) 85. jt
  52. (2000). Experimental Study of Evaporating Full-Cone Spray by Determining Droplet Temperature with Rainbow Refractometry
  53. (1992). Experimental study of time-varying aerodynamics break-up of liquid drops …..”, Fluid Mech Res,
  54. (1986). Experimental study of water droplets at high speeds and low incidence”, RAE report C2450/FR 359.
  55. (1997). FAA, “FAA In-flight Aircraft Icing Plan”, doi
  56. (1964). Factors affecting the application of low-volume sprays”,
  57. (1959). Fall of liquid drop in water, drag coefficients, peak velocities and maximum drop sizes.”, doi
  58. Figure 103: Large deflection of water interface Stability of limit inverted water interface suported by air pressure and stabilised by surface tension
  59. (1958). Figure 144: Displacement of droplets due to airflow along the droplet stream. The reason for this was that the upwind droplet reduced the aerodynamic force on the adjacent downwind droplet. Figure 145 shows the interaction between two disks, or cylinders,
  60. (2004). Figure 165 also shows results for similar conditions to those in
  61. Figure 48: Sphere Drag Data, from Massey 1989, 6 th Ed. Figure 49: Comparison of various Sphere drag data.
  62. (1958). Figure 52: Test disk for drag measurement Chapter 3: Drag Model for Distorted Droplets from Published Data Page 66 Hoerner
  63. (2000). Figure 54: Drag correction derived from Kennedy and Roberts Chapter 3: Drag Model for Distorted Droplets from Published Data Page 68 O’Donnell and Helenbrook
  64. (1964). Figure 58: Extrapolation of data for free-falling water droplet in ambient air Chapter 3: Drag Model for Distorted Droplets from Published Data Page 73 This procedure was also applied to the Gunn and Kinzer data from Scott
  65. (1985). Fluid Mechanics”, McGraw-Hill (Fig 6.11, drag coeffs for spheres and circular disks) 363. B
  66. (1978). For free-falling droplets Clift et al
  67. (2000). For Re < 1: Cd = 24 / Re: For Re <= doi
  68. (1956). For spherical droplets and particles Ingebo
  69. Given the assumption of a constant drag coefficient, Cd, in stagnant air and no compressibility effects, the equation of motion and force balance is given by; m.dU/dt +
  70. (2002). Handbook of Applied Surface Colloidal Chemistry, Vol 2”, Wiley, Chap 12 measuring Dynamic Surface Tensions 100. **
  71. (1982). Heat and Mass Transfer from Single Spheres in Low Reynolds Number Flow.”, doi
  72. (1996). Heat transfer on fluid dynamics during the collision of a liquid droplet on a substrate ...”, doi
  73. (2004). http://www.ceic.unsw.edu.au/users/peter_neal/downloads/research/nom_dimlessnos.pdf 40. T** Apr 04 Lars Reichelt, “Aerodynamisher Tropfenzerfall bei dieselmortorischen Umgebungsbedingungen”, Dissertation, D82(Diss. RWTH Aachen) 41. **
  74. Ice accretion prediction on multi-element airfoils”, AIAA 97-0177, 35 th A.S.M. Reno NV 188. **
  75. (1999). Ice and water film growth from incoming supercooled droplets”, Int J Heat Transfer, v42, p2233-2242 165. ** doi
  76. (1994). Ice Evaluation of Three Scaling Laws”, doi
  77. Icing at the McKinley Climate Laboratory: An update of the new icing capability project (end of FY03)”,
  78. (2000). Icing Scaling with Surface Film Thickness Similarity, for High LWC Conditions” AE/PRO/4420/184/INTA/00, Técnica Aerospatiale, Oct References, Bibliography and Literature Page 198 146. **
  79. (2003). In his publication “Scaling of Icing Tests – A Review of Recent Progress”, doi
  80. (1999). In the Reynolds number range of 125 to 500 there would seem to be appreciable uncertainty about the drag on a flat circular disk, with differences of up to 50% for Re
  81. (1981). indicated that droplets could remain intact for Weber numbers in excess of 20.
  82. (1999). Introduction to Fluid Mechanics”, doi
  83. (1961). It was later discovered that the Maybank and Briosi drag data for spheres with turbulent Drag correction for high Weber numbers Maybank
  84. (1993). Lewice droplet trajectory calculations on a parallel computer”, AIAA-1993-0172 (available at Cranfield) 277. doi
  85. (1997). Mapping of impact and heat transfer regimes of water drops impinging on a polished surface”, doi
  86. Mass Flux Imaging in Sprays”, LaVision GmbH, Göttingen, Germany, Info@LaVision.de 46. ** Oct 03 R Schmehl, “Droplet deformation and break-up in technical mixture preparation process”,
  87. (1993). Mathematical modelling of heat and mass transfer in transpiration cooling of water droplets ….”, doi
  88. (2002). Measuring Dynamic Surface Tensions”, doi
  89. (1959). Mechanism and speed of break-up of drops”,
  90. Mechanism of atomization of liquids”, doi
  91. (1987). Mechanisms of atomization processes in high-pressure vaporizing sprays”,
  92. Modelling droplet impact on dry and wet walls”, doi
  93. (1999). Modelling fluid-particle flows: Current status and future directions”, AIAA 99-3690, 30 th Fluid Dynamics Conf, doi
  94. (1993). Modelling the effects of drop drag and break-up on fuel sprays”, doi
  95. (1980). Monodispersed atomizers for agricultural aviation applications”,
  96. (1992). Near-limit deformation and secondary break-up.”,
  97. (1971). Non-Linear Response of Deforming Drops”, Nature Physical Science , v 233, 13 doi
  98. (1992). Nonlinear Oscillations of Viscous Liquid Drops”, doi
  99. (1992). Numerical simulation of droplet deformation in convective flows”, doi
  100. (1991). Numerical Simulation of Non-spherical Droplet Evaporation in Convective Flows”, doi
  101. Observation of drizzle at temperatures below -20C”, AIAA 2002-0678 89. ** doi
  102. (1914). On physically similar systems; illustrations of the use of dimensional equations.”, doi
  103. (1974). On the mechanism of break-up of large bubbles in liquids in three-phase fluidized beds.”, doi
  104. (1996). On the separation of droplets from a liquid jet”, Fluid Dynamics Res, doi
  105. (1964). Particle drag and heat transfer in rocket nozzles”, doi
  106. Performance of 560mm Flakt fan at 2898rpm,
  107. (2004). Phase Doppler anemometry measurements of a diesel spray”. School of Eng.,
  108. (1991). Predicting droplet impingement of yawed doi
  109. Properties of Air with Altitude for
  110. (1986). Quadratic resonance in the three-dimensional oscillations of Inviscid drops with surface tension.”, doi
  111. (2004). r Previous drag correction (Luxford
  112. Relative Normlsd Relative Normlsd Relative Normlsd Time/us Signal Time/us Signal Time/us
  113. (1989). Relaxation and break-up of an initially extended drop in an otherwise quiescent fluid”, doi
  114. (1969). SAE Aerospace Applied Thermodynamics Manual”, 2nd Ed, By SAE Committee AC-9, Aircraft Environmental Systems. From Soc of Automotive Eng,
  115. Scaling of Icing Tests – A Review of Recent Progress”, AIAA 2003-1216 50. ** doi
  116. Sessile drop Equation Sessile drop estimate Chapter 6: Droplet Distortion Modelling. Page 110 Distortion of free-falling droplets Sessile droplet, linear fit y =
  117. (1980). Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stress – theory.”, doi
  118. (1992). Stochastic Particle Dispersion Modelling and the Tracer-Particle Limit”, Phys Fluids A, doi
  119. Stochastic spectral relaxation model of drops break-up in liquid spray computations”, doi
  120. Table 10: Average Experimental Results Fan rpm Air Vel Relative Velocity Droplet Acceleration Reynolds number Weber number Bond number 1200
  121. Table 11: Tunnel condition 20mm from exit Rev/S Vacuum Std Dev Variance x U /
  122. (2002). Table 2; Sphere drag formulation; from
  123. (1961). Table 3: Drag coefficient formulation for a flat disk, data from Nakayama
  124. (1989). Table 4: Formulation for drag coefficient of a flat disk, from Massey,
  125. (1961). Table 5: Terminal Velocities for free-falling Drops
  126. (1964). Table 6: Terminal free-fall velocity of water droplets, from Scott
  127. (1978). Techniques and Facilities at ONERA Modane Centre for Icing Tests”, Appendix to Paper No. 6 in AGARD Advisory Report No.
  128. (1997). Temporal properties of drop break-up in the shear break-up regime”, doi
  129. (1986). th order Runge-Kutta solution method The 4 th order Runge-Kutta is a single step method, which computes the parameter changes over an interval h. For this; doi
  130. (2002). The accuracy and sophistication of CFD airflow modelling could, however, be of little value if the modelling of the droplet motion dynamics was substantially in error due to the spherical droplet assumption normally made,
  131. (1969). The collision of drops with dry and wet surfaces in air atmosphere”, Proc Inst Mech Eng (Lond), v184, paper 23, p1969-432. **
  132. (1949). The data in Table 6 was originally obtained by Gunn and Kinzer,
  133. (1995). The dev. and application of a diesel ignition and combustion model for multidimensional engine simultn”, SAE 872089 231. T
  134. The distorted aspect ratio of the droplet is then calculated from the Bond number, as discussed in Chapter 6. This can either be from data for free-falling droplets
  135. (1940). The drag characteristics for spheres was adequately determined by Lapple and Shepherd
  136. (1953). The Dynamics and Thermodynamics of Compressible Fluid Flow”, doi
  137. (1974). The dynamics of colliding and oscillating drops.”,
  138. The equations used for this evaluation were obtained from &quot;Engineering Thermodynamics Work and Heat Transfer&quot;,
  139. (1951). The evaporation and thermal relaxation of freely falling water drops”, doi
  140. (1922). The Flow of Air behind and Inclined Flat Plate of Infinite Span”, Proc Roy Soc, v116, n773, p170, www.jstor.org 503.
  141. (1957). The fluid flow associated with the impact of liquid drops with solid surfaces”, Proc Heat Transfer Mech Inst,
  142. The green curve is the equation given by Clift et al,
  143. (1998). The Handbook of Fluid Dynamics”, doi
  144. (2005). The influence of Viscous Effects on Ice Accretion Prediction and Aerofoil Performance Predictions”, AIAA-05-1373 3. * doi
  145. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their planes”, doi
  146. (1989). The losses in a circular diffuser are shown in Figure 111
  147. (1956). The mechanics of drops and bubbles”, doi
  148. The Motion and Shattering of Burning and Non-Burning Propellant Droplets”, Rocketdyne report R-1503.
  149. (1982). The motion of particles inside a droplet.”, doi
  150. (1959). The oscillations of a viscous liquid globe.”, doi
  151. (2002). The results of Hinze could not, however, be correct, as the drag coefficient increases as the droplet velocity increases, due to its distortion. The maximum measured terminal free-fall droplet velocity was 9.24m/s (Schmehl
  152. The shape and acceleration of a drop in a high-speed airstream”, The Scientific Paper of
  153. (1967). The splash of a liquid drop”, doi
  154. (1958). Theoretical Distribution of Laminar-Boundary-Layer Thickness, Boundary-Layer Reynolds Number and Stability Limit, and Roughness Reynolds Number for a Sphere and Disk in Incompressible Flow”,
  155. (1959). Theory of Wing Sections”, Dover Publications 471. B*
  156. (2004). Time 12:20 Data file '04062214':Inverted detector 40rps,35m from exit ta =
  157. (2004). Time 22:47 Data file '04070660':Inverted N=20rps X=40mm from exit T=23C Pa=1009.2 Trig Ch 1 slotted disk drop generator ta =
  158. (1966). Time-dependant characteristics of the heterogeneous nucleation of ice”,
  159. (2002). Time.11:03 Distance Dev length Offset Offset Size Angle (mm) (mm) (mm) (mm) (mm) (deg) doi
  160. (1994). Transient deformation and evaporation of droplets at intermediate Re numbers”, doi
  161. (2004). Transient heat transfer of deforming droplets at high Reynolds numbers”, doi
  162. (1999). Tryggvason, “Secondary break-up of axisymmetric liquid drops: I Acceleration by constant body force”, doi
  163. (2001). Two-dimensional angular light-scattering in aqueous NaCl single aerosol particles during deliquescence and efflorescence”, V8, N6, Optics Express, p314, 12 doi
  164. (2004). Typical results for this are shown in Figure 62, together with the drag correction from Figure 61 (Luxford
  165. (1973). Ultrasonic atomization – a photographic study of the mechanism of disintegration”, doi
  166. (1991). Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity”, doi
  167. (1999). v20, p462 162. T**
  168. (1904). v50, p 323-338, 519-534 (early drag data for spheres) 509. 1879 Rayleigh, “On the capillary phenomena of jets.”,
  169. (1974). Viscous effects in Rayleigh-Taylor instability.”, doi
  170. (1949). When the resulting Bond number was evaluated for distilled water and standard ambient conditions, the resulting critical spherical diameter was 10.07mm. Hinze
  171. (1930). Wind Tunnel Experiments with Circular Discs”, report no. 1334, Air Ministry HMSO.

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