Arnold Frohn

A numerical study on the mechanism of splashing

Abstract The impact of a single drop on a liquid film is studied numerically by solving the Navier–Stokes equations for incompressible fluids in three dimensions. The extension dynamics of the splashing lamella is analyzed and compared with theoretical results from the literature. Physically reasonable numerical results for the disintegration of the splashing lamella are obtained by applying disturbances to the liquid film and to the drop. It is shown that for the conditions considered here the Rayleigh instability is a possible driving mechanism for the formation of cusps at the free rim of the splashing lamella.

A new light-scattering technique to measure the diameter of periodically generated moving droplets

Abstract A new sensitive light-scattering technique for measuring the diameter of transparent droplets is described. In contrast to the usual method of average intensity measurements here the pattern of scattered light is used to determine the droplet size. The intensity distribution is recorded in the forward scattering region over an angle of approximately ten degrees using a linear CCD-array. The evaluation of scattered light, based on the theory of ray optics, is done on-line by a microcomputer. With this technique it is possible to determine the droplet diameter with an accuracy of approximately 2%. In the present paper the technique is used to measure the size of moving droplets. With a vibrating orifice droplet generator monodisperse droplets can be produced in a diameter range from 10 to 300 μm. For a constant excitation frequency all droplets have exactly the same size; therefore a quasi-stationary scattering pattern is obtained. It is shown that the new light-scattering technique can be used to measure droplet evaporation rates as a function of Reynolds number and Knudsen number.

Refractive-index measurements for the correction of particle sizing methods

For many optical methods in liquid particle sizing the refractive index of the liquid must be known. There is no problem if the data are available in the literature. If the liquid is unknown or if the refractive index changes because of a heating process or chemical reactions, the refractive index must be measured to achieve accurate sizing. A method is presented to determine the real part of the refractive index of droplets using the shift in the position of the first rainbow. Results from the application of this method to burning droplet streams are presented.

The velocity change of ethanol droplets during collision with a wall analysed by image processing

Monodisperse droplet streams are used to study the droplet wall interaction of ethanol droplets in the micrometer range. Qualitative results are given for different regimes of droplet wall interaction. The phenomena observed range from complete wetting to almost elastic reflection of the droplets. Complete wetting is observed for low wall temperatures, whereas reflection occurs for wall temperatures above the Leidenfrost temperature. For high impact velocities and high wall temperatures above the Leidenfrost temperature the formation of secondary droplets can be observed. Image processing is used to obtain quantitative results for the loss of momentum during wall interaction for cases of droplet reflection without formation of secondary droplets.

Collision and merging of two equal droplets of propanol

Equally spaced and uniform droplets are produced by a vibrating orifice and move away in a straight line. They intersect with an exactly equal string of droplets and collide one by one. With stroboscopic lighting and multiple exposures, they are photographed. Thus successive stages of the collision process are shown on a single photo. The droplets can be made to collide with or without angular momentum by adjusting the aim of the emitting orifices. The impacting speeds can be varied from 2.8 to 11.7 m/s. Droplet sizes from 70 to 200 μm are employed. Motions of the coalesced drop after the merging are bizarre and well-displayed. The results are important for spray modeling. When the streams of droplets merge at higher speeds, they may distort to the extent that the two streams of droplets merge to a single continuous sinuous stream.

Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method

A special sizing technique is applied to measuring the diameter of monosized droplet streams that are used for investigation of fuel droplets in enginelike conditions. For these experiments the droplet diameter must be known precisely. The sizing technique used is based on the evaluation of the fringe spacing of scattered light in the forward direction. This technique is independent of the intensity of the incident light. No absolute intensities need to be measured. The droplets are exposed to a focused laser beam. Therefore the frequently used assumption of plane wave fronts is not fulfilled. Elaborate experiments have been carried out to study the influence of a Gaussian intensity distribution of the laser beam on the accuracy of the sizing technique. It has been shown that the droplet diameter can be measured to an accuracy of better than 2% even if the droplet is illuminated by a Gaussian beam for a droplet diameter that is smaller than the beam diameter.

ION DENSITY PROFILES BEHIND SHOCK WAVES IN AIR.

Experimental results are reported for the ionization rate behind shock waves of Mach numbers between 7.2 and 9.2. The results were obtained using a hollow, total collector probe in combination with a 38-mm-diam, stainless steel shock tube designed to minimize the impurity level in the test gas. Good agreement was obtained with a theoretical result based on Lin and Teares rate equations. Equilibrium ion densities in good agreement with theory were measured behind shocks of Mach number 7.2-12.8, with initial pressures between 0.5 and 40-mm Hg. The effects on the measurements of deviations from ideal shock tube flow were determined to be small. Ion densities measured range from 108 to 10 12 cm~3. At the higher ion densities there are large space charge effects inside the probe. Under these circumstances, proper operation of the probe still could be obtained provided the collector potential was not made too high. This implies that the mobility of the NO ions collected must be rather large. ON density profiles behind shock waves in air have been the subject of various recent investigations. Lin, Neal, and Fyfe1 made measurements in a low-density shock tube using microwave techniques and a magnetic induction device, in the range of shock Mach numbers Ms between 14 and 20. A theoretical analysis of their results based on chemical rate equations was given by Lin and Teare.2 Experimental results for even higher shock Mach numbers were reported by Wilson,3 who found that for shock Mach numbers above 27, electron densities become high enough so that electron impact reactions become dominant. At the lower temperature end experimental data have been obtained by Thompson, 4 who used a low-density shock tube in combination with microwave techniques, with infrared emission measurements, and with a hollow, total collector probe described by de Boer.5 The present investigation was undertaken in order to extend the range of measured profiles to still lower temperatures. At these temperatures, both the ion density and the ionization relaxation rate become much smaller, and it is impractical to use a low-density shock tube because the test time required is too long. A 38-mm-diam shock tube was used in combination with the hollow, total collector probe of Ref. 5. This probe has a very high sensitivity and can be used without difficulty in the regime of interest. The main problem to be overcome was the influence of impurities on the ionization rates. This problem could be solved by using great care in the experimental procedures.

New technique for investigating phase transition processes of optically levitated droplets consisting of water and sulfuric acid

Experimental techniques for studying supercooled or frozen droplets will be presented. Single particles consisting of water or of water contaminated with sulfuric acid have been levitated optically and stabilized in a vertical laser beam by radiation pressure forces. In the experiments the levitated droplet has been observed in a chamber, in which temperatures down to -60°C can be reached, in order to simulate conditions in contrails. After introduction into the chamber the droplet is supercooled rapidly. Depending on temperature and vapor pressure in the chamber, the droplet will grow or evaporate until it disappears. During this process the droplet is observed by a video camera. Furthermore the scattered laser light is evaluated at scattering angles of approximately 45° to characterize the droplet and to determine the droplet size. Simultaneously with the size, the position of the droplet along the axis of the laser beam is determined. The droplet oscillates for a fixed laser power along the axis of the laser beam, when the droplet radius changes with time. These oscillations are due to oscillations of the radiation pressure forces during monotonic decrease or increase of the radius, i.e., for evaporation or condensation. With this new technique it is possible to associate directly the frequency of these oscillations with the radius change rate. Typical experimental results for size and for the radius change rate are shown.

Structure of fully dispersed waves in dusty gases

The structure of one-dimensional fully dispersed waves in dusty gases is investigated using the Navier-Stokes equations for the gas phase and for the particle phase. The resulting system of six ordinary nonlinear differential equations is reduced to a system of four autonomous nonlinear differential equations which is solved analytically in phase space by expanding the variables of state in power series.ZusammenfassungDie Struktur eindimensionaler voll dispergierter Wellen in staubhaltigen Gasen wird untersucht indem die Navier-Stokesschen Gleichungen auf die Gas-Phase und auf die Partikel-Phase angewendet werden. Das sich ergebende System von sechs gewöhnlichen nichtlineren Differentialgleichungen wird auf ein System von vier autonomen nichtlinearen Differentialgleichungen zurückgeführt. Dieses System wird durch Reihenentwicklung der Zustandsgrößen im Phasenraum analytisch gelöst.

Heat conduction in binary gas mixtures between concentric cylinders

The heat conduction in binary gas mixtures of monatomic gases between concentric cylinders is investigated theoretically using Maxwells moment method. By using Maxwells force law, analytical results are obtained for small temperature differences. The heat conduction coefficient obtained in the present analysis for the continuum region agrees with the Chapman‐Enskog well known result for binary mixtures. In order to check the theoretical results, the heat loss from a fine wire in investigated experimentally for different He‐Ar and He‐Kr mixtures. The measured heat conduction agrees well with the results of the present analysis.