Accounting for laser sheet extinction in applying PLLIF to sprays

Abstract

A method is presented herein to correct for laser sheet extinction effects in performing Planar Liquid Laser Induced Fluorescence (PLLIF) in dense sprays. The method involves sequential illumination of the spray by counterpropagating laser sheets, and assumes only that extinction occurs according to Beer's law. Spray symmetry is not jired. The method is experimentally evaluated us ig a hollow cone spray and a flat fan spray. Introduction For non-fluorescing fluids, a means of achieving Planar Liquid Laser Induced Fluorescence (PLLIF), is to dissolve a fluorescent dye in the fluid to be sprayed. When later illuminated as a spray with a laser sheet, the fluorescence intensity distribution can be related to the mass distribution in the plane of the sheet. This can then be used as an alternative to more intrusive mechanical patternation techniques. In dense sprays, however, secondary scattering can introduce three primary sources of error: (a) extinction of the laser sheet; (b) illumination of particles outside the plane of the sheet by the scattered light and subsequent additional fluorescence from them; and (c) extinction of the fluorescence signal by particles in the path of the detector. A method is presented to correct for the first of these by making quantitative PLLIF measurements independent of laser sheet intensity. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Outline of the approach To a first approximation, the gray level G registered by a pixel in a CCD array by the PLLIF technique can be related to the laser sheet intensity and the total spray mass per unit volume by the following derivation. Neglecting noise, the gray level in a given pixel will be proportional to the total number of photons received from some small solid angle in the optical field. Ideally, these photons will originate only from the region defined by the intersection of the finite thickness laser sheet with the small solid angle. This intersection defines a small volume element, SV, which can be approximated as the product of a cylinder of length h and cross sectional area 5A, i.e., SV = h6A. The total number of photons emitted from this volume is assumed to be proportional to the camera exposure time (or laser pulse period if that is exposure determining) At, the laser sheet intensity, /, and the average number of fluorescing molecules in 8V during the exposure period. If the dye concentration is constant and uniform (this implies that there is no vaporization), the latter quantity is proportional to the total average amount of liquid mass present at any time, m. An average measure of liquid mass concentration (mass per unit volume) can be defined as ~pm = Sm/SV. If A is sufficiently small and the statistical sample is sufficiently representative of the spray, then p>OT will approximate the true local liquid mass per unit volume, or dispersed phase density, p(x5ty,z), which is related to droplet statistics through the equation pm = p(x,y,z) = $ (1) where D is the droplet diameter, p, is the density of the pure liquid, and n(D\x,y,z) is the droplet size distribution, that is, n(D\x,y,z)dD is the number of droplets per unit volume with diameters between D and D + dD, as a function of position (x,y,z). However, the laser sheet intensity is rarely uniform over the thickness of the sheet. The more usual case is a Gaussian distribution if the original beam is Gaussian. It is then necessary to take into account an intensity distribution I(z), where z is the distance perpendicular to the sheet. Thus, when all of the above factors are considered, the gray level registered by a pixel element can be estimated from