Stuart W. Churchill

Representation of the Angular Distribution of Radiation Scattered by a Spherical Particle

Exact expressions have been derived from the Mie equations for the angular distribution coefficients, an, in the equation, f(θ)=14π+14π∑n=1∞anPnu2009(cosθ),proposed by Hartel for the fraction of randomly polarized radiation scattered by a spherical particle into a unit solid angle in the direction θ. The coefficients are functions of the wavelength, particle diameter, and physical properties, and Pn (cosθ) are the Legendre polynomials. This equation is shown to be more convenient in form for tabulation of the scattering properties and for application than the intensity functions used by Mie and most subsequent investigators. Approximate methods for evaluating the coefficients were found to be inaccurate or inconvenient. The exact expressions, although detailed, are suitable for straightforward computation.

Angular Distribution Coefficients for Radiation Scattered by a Spherical Particle

The fraction of randomly polarized radiation scattered by a spherical particle into a unit solid angle in the direction θ can be represented by the equation f(θ)=14π+14π∑n=1∞anPn(cosθ),where Pn(cosθ) are the Legendre polynomials. Values of the angular distribution coefficients, an, are presented for nonabsorbing spheres with an index of refraction of 1.33 at a series of values of the ratio of circumference to wavelength of 1, 2, 3, 4, 5, 6, 8, 10, 15, 20, 25, and 30. Application of the results is illustrated.

Rayleigh-Benard oscillatory natural convection of liquid gallium heated from below

Abstract The average rate of heat transfer as well as the oscillatory span-widths of the Nusselt number and the Rayleigh number were measured for natural convection in a layer of liquid gallium (Prxa0=xa00.023) heated from below electrically and cooled from above with running water. These quantities were determined by measuring the instantaneous temperature difference between the upper and lower horizontal copper plates. The time-averaged Nusselt number agreed well with the previous data of Rossby for mercury (Prxa0=xa00.025), at comparable values of the Rayleigh number. The oscillations are a consequence of reduced viscous damping for a fluid with low Prandtl number.

Scattering of Electromagnetic Radiation by Infinitely Long, Hollow, and Coated Cylinders

The scattering efficiency and backward component of the scattered flux have been calculated for infinitely long, hollow cylinders with real indices of refraction of 1.5, 2.0, and 2.5; ratios of inner diameter to outer diameter of 0.0, 0.01, 0.10, 0.50, 0.90, and 0.99; and outer circumference to wavelength ratios of 0.12(0.02) 6.00. Values were obtained for the cases of incident radiation parallel polarized and perpendicularly polarized. A generalized computer subroutine has been made available for the calculation of the amplitude functions, as well as the above functions, for any arbitrary values of the parameters.

Removal of drops from liquid--liquid dispersions upon flow through screens

Abstract Fibre-packed coalescers are widely employed to remove drops from liquid—liquid dispersions. This work has as its objective a quantitative correlation of drop removal with filtration variables. Photo-etched screens, which were positioned perpendicular to the flow, served as geometrically defined representations of fibrous media. Forward-angle light scattering was employed to measure the extent of drop removal for a variety of screen geometries, flow rates and physical properties of oil-in-water dispersions. The dispersions, which were prepared by homogenisation, had a narrow range of drop sizes whose average was approximately three microns. The measurements indicate that drop interception, screen geometry, viscous shear and drop-filament adhesion are the main factors which govern drop removal. The redispersion of the drop phase which had accumulated on the filaments was generally not observed. The data for the removal of uniform drops by screens with fixed surface energy were correlated with the product of interstitial velocity, continuous phase viscosity and the projected width of the filament in the plane of the screen.

Scattering and Absorption of Electromagnetic Radiation by Infinite Cylinders

Expressions suitable for machine computation are presented for the scattering and absorbing properties of infinitely long, dielectric, and conducting cylinders. These properties include the amplitude functions, the angular distribution of scattered light, and the scattering and absorbing cross sections for both parallel and perpendicular polarized light. Illustrative calculations were carried out for real indices of refraction of 1.5, 2.0, and 2.5 at circumference to wavelength ratios of 0.5, 1.0, 1.5, 2.0, 3.0, and 4.0.

The characteristics of a heat-recirculating ceramic burner

Abstract An experimental burner of the heat-recirculating-type was constructed and its thermal characteristics were investigated for methane–air fuel-lean combustion. Temperature distributions of air and burned gas flowing in the passes of the burner were determined by means of both experimental measurements and numerical simulations. Using the fractional heat recirculation rate as a criterion for thermal performance, the optimal design of the burner was examined in terms of a chemical parameter (the equivalence ratio), a fluid–mechanical parameter (the Reynolds number) and two geometrical parameters (the aspect ratio and the number of passes).

Spectroscopic Measurements of High Emissivity Materials Using Two-Dimensional Two-Color Thermometry

Radiative heat transfer characteristics from the surface of a substance coated with a high-emissivity material have been examined from the measured two-dimensional (2D) temperature distribution using two-color thermometry principle. The technique utilized a charge coupled device camera and optical filters having either wide or narrow wavelength bandpass filters. The results obtained were compared to evaluate the accuracy of the temperature measurements. The 2D emissivity distributions were also derived from the measured 2D temperature distributions. The results indicate that the substrate coated with high-emissivity material exhibit high emission of radiation, resulting in effective cooling. The enhanced emissivity of materials also results in improved radiative heat transfer in heating furnaces and other high-temperature applications. The emissivity measured with the wide-bandpass filters increased with temperature. Atmospheric absorption, mainly due to humidity, made a negligible contribution to the total spectral intensity and to the temperature measurements. The small discrepancies are attributed to the dependence of emissivity on wavelength. Thus, the use of narrow-bandpass filters in thermometry is advantageous over the wide-bandpass ones.

Two-Dimensional Temperature Distributions of the Surface of Heated Materials by Spectroscopic Measurements

In order to investigate the characteristics of the surface of substrates without destroying and touching them, two-dimensional (2D) surface brightness distributions have been measured with a CCD camera equipped with optical filter (700-800 nm). The images measured with each wavelength gave 2D temperature distributions by two-color thermometry. In addition 2D emissivity distributions were also derived from the derived 2D temperature distribution and the measured images. We demonstrate the convenience and usefulness of this method for heated materials with different surface roughness or with and without coasting of high emissivity material. Subject headings: 2D-temperature distribution, two color method, high temperature, emissivity

Elimination of Optical Discontinuity between Two Immiscible Fluids

The indices of refraction of heptane and of aqueous solutions of glycol were measured over a range of temperature. It is shown that the indices of this pair of fluids can be matched exactly and hence that the optical discontinuity at the interface of the two phases can be eliminated over a range of temperature by varying the composition of the solution. The utilization of this matched pair of fluids for light transmission measurements through dispersions is discussed.