Abstract:
An apparatus and procedure is described for the characterization of sprays composed by spherical particles, by means of a laser source (1) generating a collimated laser beam (2) that is passed through the spray to be characterized. The laser beam is made to coincide with the x-axis of a cartesian coordinate system (3) contained in a measurement plane perpendicular to the spray axis. A scattering collection means (5) is disposed to obtain the 90° scattering activity produced by the spray material in a small probe volume formed at the intersection of the laser beam and the object volume of the scattering collection means. Additional collection means (14) are included to obtain the attenuation of the laser beam passing trough the measurement plane. The optical systems (5 and 14) are coupled to photodetectors (10 and 18) and signal processing units (10&#39; and 18&#39;) able to generate electrical signals proportional to the received light intensities. A transverse means is also disposed to move the spray along the laser beam direction and perpendicular to it as to sequentially obtain a tomographic record of the scattering and attenuation activity in points of the spray forming a Cartesian grid within the measurement plane. Concentration measuring means (21) are coupled to the attenuation and scattering electrical signals output to extract the information related to the number density of the spray in the nodes of the tomographic grid system.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a procedure for characterizing a spray composed of spherical particles, by determining information related to its number density (particles per unit volume) in points located within a measurement plane intersected by the spray. The characterization is based on the scattering of a laser light beam by the particles contained in the spray, when the particle size is large enough for the Mie scattering theory to apply. The invention includes also the apparatus to materialize the procedure. 
     There are a number of techniques which, working in the Mie regime, exploit the scattering of laser light by a spray of particles to extract information related to the spray number density. 
     A technique known as laser diffraction particle sizing determines the spatial number size distribution of the spray material intersected by a laser beam by measuring the forward scattering pattern through a set of photodetectors located in the focal plane of a receiving lens. The application of this technique for characterizing sprays is used in the apparatus developed by the British company Malvern Instruments, where the photodetectors are ring-shaped photodiodes. Diffraction is the dominant scattering mode in the collection angles sensed by the photodiodes. Since the far field diffraction pattern for spherical particles is a well known function of the particle size and the laser wavelength, the technique obtains the size distribution by matching the measured diffraction pattern to that obtained from a collection of particles distributed in a finite number of size classes. In addition, the attenuated laser intensity is measured with a photodiode located in the receiving lens axis. Knowing the attenuation of the laser beam and the spray size distribution allows the technique to infer the spray number density. Since the technique is an on-axis method, the laser diffraction technique can only give a measure of the spray number density averaged along the volume intercepted by the spray and the laser beam. 
     Another family of methods developed to obtain information related to the spray number density is based on counting techniques initially used for fluid anemometry purposes. The optical arrangement is similar to that of the dual beam laser Doppler velocimetry system (LDV). The interference pattern formed at the intersection of two coherent laser beams modulates the light scattered by particles passing through the probe volume. A set of photodetectors is placed to detect the off-axis particle scattering activity. The velocity of the particles can be obtained by recording the Doppler frequency of the scattering light produced by the particles intersecting the probe volume. The size of the particles can be inferred either from a measurement of the visibility of the Doppler signal (technique disclosed in U.S. Pat. No. 4,329,054), or from the phase difference of the Doppler signal detected in spatially separated photodetectors (technique disclosed, under different hardware implementations, in International Patent WO 84/04592 and in U.S. Pat. No. 4,540,283). A critical aspect of the obtained size distribution is that it is biased towards the large particle sizes, since the laser beams have a gaussian intensity decay from their axis, and the large particles scatter more light intensity than the smaller ones. As a consequence, the characteristic probe volume of the large particles is greater than that of the smaller ones. A deconvolution based on the statistics of the transit time and velocity of the particles can be applied to eliminate this bias. The velocity of the particles also biases the number-size distribution but, since this velocity is known, a transformation can be introduced to obtain the unbiased spatial number-size distribution. The number density information can be obtained by knowing the cross-stream area of the formed probe volume and the number of particles passing through it during a known measurement time. Being based on off-axis scattering analysis, these counting techniques can perform highly spatially resolved number density measurement. Determination of the probe volume cross-stream area and of the effective measurement time encounters, however, severe difficulties when characterizing sprays subjected to high optical attenuation levels and/or flowing in directions other than that perpendicular to the laser beams bisector. 
     The invention disclosed hereinafter performs spatially resolved measurements of a quantity proportional to the spray number density in a measurement plane intersected by the spray and characterized by arbitrarily large optical attenuation levels, and arbitrary spray trajectory angles. In addition, the technique of the invention can be combined with independently obtained measurement of the spray number-size histogram and of the velocity-size correlation to explicitly infer the spray number density and volume flux without knowledge of the probe volume cross-stream area or of the effective measurement time. 
     SUMMARY OF THE INVENTION 
     An apparatus and procedure is described to obtain information related to the concentration of a polydispersed spray of spheres (referred hereinafter as particles), having optical attenuation levels arbitrary large but lower than 100%. Specifically, the apparatus and procedure is able to determine spatially resolved information proportional to the spray number density (particles per unit volume) in a measurement plane intersecting the spray. In addition, and combining this result with an independent measurement of the spray spatial diameter and velocity distribution, the apparatus and procedure can be used to generate tomographic maps of the spray volume flux (volume of particles per unit time per unit surface). The apparatus and procedure principle of operation is based on the analysis of light scattered by the particles. The procedure includes means to extract the number density related information in sprays characterized by arbitrary, lower than 100%, optical attenuation levels along directions embedded in the measurement plane. A laser generating means is provided to generate a collimated light source. The laser beam is passed through the measurement plane. A scattering collection means is disposed to obtain the 90° scattering activity produced by the spray material in a small probe volume formed at the intersection of the laser beam and the object volume of the scattering collection means. An additional collection means is included to obtain the attenuation of the laser beam passing trough the measurement plane. The scattering and attenuation collection means are directed to photodetectors and signal processing means to obtain electrical signals proportional to the scattered and attenuated light intensities. A transverse means is disposed to move the spray along the laser beam direction and perpendicular to it as to sequentially obtain a tomographic record of the scattering and attenuation activity in points of the spray forming a cartesian grid within the measurement plane. Concentration measuring means are coupled to the tomographic attenuation and scattering electrical signals to extract the information related to the number density of the spray in the nodes of the tomographic grid system. 
    
    
     DESCRIPTION OF DRAWINGS 
     The invention will be discussed making reference to a set of figures attached at the end of the document, in which: 
     FIG. 1 schematically describes the preferred physical embodiment of the invention. 
     FIG. 2 schematically presents the scattering signal processing means. 
     FIG. 3 schematically presents the attenuation signal processing means. 
     FIG. 4 displays the light intensity received by the scattering collection means for arbitrary, spherical particles located in the probe volume. 
     FIG. 5 schematically presents the preferred physical embodiment used in the tomographic measurements. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An apparatus and procedure to extract information related to the particle number density of polydispersed sprays using laser scattering techniques operating in the Mie regime is presented. The apparatus and procedure are able to generate the number density information corresponding to a spray composed by spherical particles in points located within a plane intersected by the spray. FIG. 1 displays the physical arrangement of the optical parts used in the apparatus. 
     A laser head 1 generates a collimated, visible laser beam 2, which is directed (by means, for example, of an optical element 1&#39;) through the axis of a cartesian measurement system 3 (x 0 , y 0 ). This system is affixed to the optical elements to facilitate the geometrical description of the optical arrangement. A beam expander unit 4 ensures an output beam with a characteristic diameter much greater than the maximum size of the particles to be characterized. The plane formed by the cartesian coordinate system 3 will be referred to as the measurement plane. The laser beam propagates along the x 0  direction of the optics coordinate system 3, and is linearly polarized along the x 0  -z 0  plane, with z 0  being aligned along the measurement plane normal direction. A scattering activity collection means 5 is located with its optical axis at 90° of the laser propagation direction. The y 0  axis coincides with the optical axis of scattering activity collection means. The scattering activity collection means are composed by a small depth of field, moderate f number entrance optics, 6, and a rectangular pinhole 7 located in the image plane of the entrance optics. The rectangular pinhole images a probe volume 8 centered at the origin of the coordinate system 3. The geometry of the scattering pinhole 7 is such that the probe volume dimensions along the x 0  and z 0  directions are much larger than the maximum particle size to be characterized, but smaller than the characteristic diameter of the laser beam 2. The light passing through the scattering pinhole 7 is collimated by an output lens 9 and directed to a photodetector 10. The electrical current generated by the photodetector is then handled by scattering signal processing means 10&#39;, shown in FIG. 2. The scattering signal processing means amplifies the scattering current produced by photodetector 10 through a low-pass filtered input amplifier 11 and a variable gain output amplifier 12 with zeroing output capability. A variable high voltage power supply unit 13 controls the sensitivity of the scattering photodetector 10. The laser beam intensity that is not attenuated by the spray material intersecting the x 0  -y 0  plane is directed to attenuation collection means 14 (FIG. 1). The axis of the attenuation collection means is coincident with the x 0  axis of the coordinate system 3. The laser radiation reaching the attenuation collection means 14 passes through an entrance aperture 15 whose diameter is similar to the laser beam characteristic diameter, and is focused by a high f number receiving lens system 16. A small, circular pinhole 17 is located in the focal plane of the attenuation collection means receiving lens system 16. The receiving lens/pinhole combination 16-17 is such as to reject optical radiation whose propagation direction differs more than an angle of the order of 1 mrad from the attenuation collection means axis. The radiation passing through the attenuation collection means pinhole 17 is directed to a photodetector 18. The electrical current generated by the photodetector is then handled by attenuation signal processing means 18&#39;, shown in FIG. 3. The attenuation processing means amplify the electrical current produced by photodetector 18 through a variable gain, low-pass filter input amplifier 19, and a variable gain output amplifier 20 with zeroing output capability. 
     Finally, the electrical signals related to the scattering and attenuation activity are converted, by post-processing means 21 in a measure of the spray particle density times the square of the spray mean quadratic diameter that is present in each point of the measurement grid. 
     The measurement principle of the apparatus schematically shown in FIG. 1 is based on the fact that, under proper conditions, the scattering radiation sensed by sensor 10 is proportional to the number density N D  (particles per unit volume) multiplied by the square of the spray mean quadratic diameter D 20  characterizing the material located in the probe volume: 
     
         w.sub.sc ×N.sub.D D.sub.20.sup.2 =N.sub.D ∫n.sub.s (D)D.sup.2 dD.                                                       (1) 
    
     where w sc  and D 20  denote the light power scattered by the particles intersecting the probe volume 8 which propagates towards photodetector 10, and the spray average diameter constructed from the second moment of the spatial number-size probability density function n s  (D) respectively. Expression (1) assumes that the particles are illuminated by plane wave light radiation with uniform intensity along distances of the order of the particle sizes D. The error incurred when using expression (1) can be estimated by using the generalized Lorenz-Mie theory of scattering. Use of it allows one to obtain the light radiation scattered by spheres of given index of refraction and that is collected within a solid angle similar to that subtended by the scattering collection means 5. 
     The result of applying the Lorenz-Mie theory to a single sphere is shown in FIG. 4, which displays the scattered light power for individual particles of given diameter and refraction index m=1.33, and after filtering out the original data on size bins with a 5 μm width. The results presented in FIG. 4 correspond to an incident laser radiation characterized by a power density of 10 3  W/m 2  and a λ=0.51 μm wavelength, matching the blue line of an Argon-Ion laser. FIG. 4 shows the size to size large scattering power variations that are obtained when considering particles of fixed diameter. These power excursions are due to superficial wave interference effects. However, when the average power corresponding to a given, 5 μm wide, size interval is obtained, the excursions are highly damped. In this case, proportionality of the scattered power to the square of the diameter located at the center of the size interval is obtained within a given accuracy for particles satisfying the geometrical optics condition: ##EQU1## with Re(m) being the real part of the index of refraction m. Thus, for 5 μm size width families, the points in the smoothed curve of FIG. 4 separate less than 2% from a fitting parabola for q&gt;20 (i.e. D&gt;5 μm). 
     When a polydispersed spray is considered, and if independent scattering conditions apply, the power scattered from the probe volume must be multiplied by the number of particles embedded on it, i.e., by the spray number density times the volume of the probe region. Thus, expression (1) is recovered. The condition under which independent scattering occurs is that the particles are separated more than 2 diameters. This restriction establishes a limit for which expression (1) still holds: 
     
         N.sub.D ≦0.01D.sub.10.sup.-3,                       (3) 
    
     with D 10  being the spray average diameter constructed from the first moment of the spatial probability density function. Condition (3) is satisfied except for extremely high particles packing. 
     The procedure to extract the information related to the spray number density makes use of FIG. 5, which schematically displays the arrangement of the apparatus presented in FIG. 1. The coordinate system 22, (x,y), is parallel to the optics related coordinate system 3, (x 0 , y 0 ), and is fixed to the spray produced by injector 23. The two-axis transverse 24, rigidly attached to the spray nozzle 23, is used to move around coordinate system 22 with respect to coordinate system 3. The spray nozzle 23 is located at some distance z N  from the measurement plane formed by the coordinate system 3. The apparatus of FIG. 1 with the set-up presented in FIG. 5 is used to record the scattering activity of the particles created by the spray nozzle 23 as they intersect the measurement plane formed by coordinate system 3. The characterization proceeds by using the two-axis transverse 24 to sequentially position a set of points (x i ,y j ), related to the spray coordinate system 22, at the probe volume location 8, and recording the signals produced by the attenuation and scattering collection means. It will be assumed for simplicity that the grid system formed by the set (x i ,y j ) has constant separation Δx, Δy in the two cartesian coordinate directions, and covers a rectangular domain composed by N x , N y  lines in the x, y direction. Extension of the procedure for non-uniform grid spacing is straightforward. 
     Denoting (x i , y j ) as an arbitrary point of the spray grid that is positioned at the probe volume location 8, and (x j ,y k ) as an arbitrary point of the spray which, in these measurement conditions, is located along the axis of the scattering collection means, use will be made of the following notation: 
     w 1  (x i ,y j ): Laser power available at the probe volume 8 which is sensed by the attenuation collection means. 
     w 2  (x i ,y j ): Laser power available at the probe volume 8 which is sensed by the scattering collection means. 
     w sc  (x i ,y j ,y k ), which will be ultimately sensed by the scattering collection means. 
     Making use of this notation, the undisturbed laser power in characterization line j is w 1  (1,y j ); the power laser measured by the attenuation collection means is w 1  (N x ,y j ); and the scattering activity measured by the scattering collection means is w sc  (x i ,y j ,N y ). 
     The following set of difference equations is used to describe the evolution of the quantities introduced above: ##EQU2## 
     The above set implies: 
     a) The particle scattering process can be evaluated by the geometrical optics approximation. 
     b) The attenuation sensor senses only the attenuated radiation. It rejects the forward diffraction lobe and the large angle portions of the spray scattering. 
     c) The scattering sensor senses the original attenuated radiation and the portion of the scattering included in the forward diffraction lobe. 
     d) The radiation reaching the scattering sensor means is a fraction of the large angle scattering by the particles present in the probe volume. 
     Constraint (2) and the polydispersed character of the sprays being evaluated support assumption a). Assumptions b) and c) can be supported, to given accuracy, by proper design of the attenuation and scattering collection means. Finally, assumption d) reverts to expression (1) by establishing the proportionality between the reduction in w 2  and the cause creating such reduction, i.e., the large angle scattering. 
     Manipulation of equations (4.1) to (4.4) leads to: ##EQU3## 
     The scattering proportionality constant K can be obtained from the attenuation level and scattering profile recorded at an arbitrary, j=constant line, y=y j  : ##EQU4## where the quantity w 1  (x Nx ,y j )/w 10  represents the signal registered by the attenuation collection means with spray being present divided by the signal registered when no spray is present along the laser propagation path. In the limit expressed by inequality (2), the constant K j  should be independent of the characterization line j. 
     The light intensities w sc  (x i ,y j ,y j ) must be related to the ones registered by the scattering collection means w sc  (x i ,y j ,y Ny ) by an additional difference evolution equation: ##EQU5## with L sc  being related to the scattering collection means depth of field. Expression (7) establishes that the radiation scattered at the probe volume its attenuated only by the large angle scattering mechanism as it travels towards the scattering collection means 5. This assertion can be supported to given accuracy by proper design of the scattering collection means. Using equation (7) it is possible to establish a relationship between w sc  (x i ,y j ,y j ) and w sc  (x i ,y j ,y Ny ): ##EQU6## where the reception correction coefficient C RX  (x i ,y j ) is given by: ##EQU7## 
     Determination of the coefficient C RX  (x i ,y j ) requires, therefore, knowledge of N D  D 20   2  along the lines y k ,y k  &gt;y j . 
     A procedure can then be constructed to obtain the measurement of N D  D 20   2  along a discrete grid system of points (x i  y j ) distributed in the measurement plane: 
     1) Guess a value of the scattering constant by averaging expression (6) over a set of y j  lines in a spray region where the light power measured by the scattering collection means w sc  (x i ,y j ,y Ny ) does not differ substantially from the one that would be measured if no spray was intercepting the propagation of light scattered at the probe volume until it reaches the scattering collection means: ##EQU8## where the averaging process is applied to N k  number of y-constant lines. 
     2) Obtain an estimate of the N D  D 20 (x.sbsb.i.sub.,y.sbsb.j.sub.) 2  surface. Resolve the tomographic problem by advancing backwards through the y j  lines, starting from y Ny . Use expression (8.2) to obtain first the set of C RX  (x i ,y j ) coefficients in the line y j . Obtain then w sc  (x i ,y j ,y j )/w 10  from the signal recorded by the scattering sensor means w sc  (x i ,y j ,y Ny )/w 10  by using expression (8.1). Determine then N D  D 20 (x.sbsb.i.sub.,y.sbsb.j.sub.) 2  from expression (5). Proceed afterwards to the line y j-1  until the total tomography is resolved. 
     3) Determine an updated, more accurate value of the average scattering constant K, by inserting in expression (6) the non-dimensional powers w sc  (x i ,y j ,y j )/w 10  as obtained in the previous step: ##EQU9## 4) Repeat steps 2) and 3) until the updated value of K does not change by a prescribed percentage. 
     Once that the tomographic measurement N D  D 20 (x.sbsb.i.sub.,y.sbsb.j.sub.) 2  is completed, the volume flux produced by the spray nozzle which intercepts the measurement plane can be obtained if a tomographic measurement of the spatial number-size distribution histogram n s  (D k ) and of the size-velocity correlation u(D k ) are determined by some independent technique. In these quantities, D k  denotes the particle diameter characterizing an arbitrary size bin k in which the particles of the polydispersed spray are classified, whereas u(D k ) is the mean velocity in the direction normal to the measurement plane of the particles contained in size bin k. These two statistical spray magnitudes can be used to obtain a tomographic map of the following velocity-size moment: ##EQU10## 
     The volume flux at point (x i ,y j ) can then be obtained combining the above given velocity-size moment and the N D  D 20 (x.sbsb.i,y.sbsb.j.sub.) 2  measurement: ##EQU11## 
     The apparatus and procedure to obtain a tomographic measurement of the quantity N D  D 20   2  (number density times square of the average diameter based on the second order moment of the spatial probability density function) and of the volume flux for a spray of particles intersecting a measurement plane with an arbitrary large but lower than 100% attenuation level has been described.