摘要:

Particle Sizing by Interference Fringes and Signal Coherence in Doppler Velocimetry A. R. JONES,M. J. R. SCHWAR BY R. M. FRISTROM," 1-AND F. J. WEINBERG Imperial College London S.W.7. Received 15th January 1973 To supplement another paperf presented at this Symposium (which deals with sizing suspended particles by light scattering) a new optical method is proposed for sizes larger than a few wavelengths. To this end conditions under which the alternating light signal generated by a particle traversing a fringe pattern falls to zero are examined with a view to measuring such particle sizes by varying fringe spacing. The a.c. frequency is a measure of the particle velocity and can be expressed with identical results either as a beat note caused by Doppler shift or in terms of the varying illumination of the particle due to its movement across the light grid.The theory giving the a.c. amplitude for two infinitesimal particles moving with a common velocity as a function of their separation is extended to a variable number of particles moving together. This provides the basis not only for an assessment of how the signal legibility in Doppler velocimetry falls off as the number of scatterers increases but also for the integration which treats particles of finite size as the sum of their infinitesimal elements. A variety of optical systems are proposed for measuring the size of particles droplets fibres etc. under different conditions. For some purposes fringe systems of non-uniform spacing may be advantageous and the use of a dark field schlieren image which shows the particle as a thin circumferential line-in place of the illuminated area produced by normal imaging-is often valuable.Such a schlieren system is used in a simple experimental test of the method ; the results accurately conform to the theoretical predictions. This study was initiated as a potential method for sizing droplets and particles appreciably larger than the wavelength of light during Prof. Weinberg's visit to the Applied Physics Laboratory of the Johns Hopkins University and pursued further in a wider context at Imperial College. The light scattered by a particle depends on the local illumination and when this is in the form of a field of interference fringes which the particle is. traversing an ax.signal will result except under certain conditions which are the subject of this paper. When there are two small particles travelling with a common velocity the signal produced by a photodetector receiving light from both will depend on their separation. Fur certain separations the amplitude of the a.c. signal falls to zero. A similar succession of zeros occurs as the size of one particle increases in relation to the fringe separation or more practically when the fringe separation is decreased in relation to the size of the particle. All this applies to any field of stratified illumination whether produced interfero- metrically or e.g. by projecting the image of a grid. The convenience of interference fringes lies in the ease and precision of varying their separation by changing the angle between the interfering beams.This becomes particularly easy when the light source * Applied Physics Lab. The Johns Hopkins Univ. Silver Spring Maryland U.S.A. 7 now at Paint Research Association Teddington Middx. $ M. D. Carabine and A. P. Moore "A light scattering instrument for kinetic measurements in aerosols with changing particle size distributions". 183 PARTICLE SIZING IN DOPPLER VELOCIMETRY is a laser which is especially suitable for producing interferometrically a fine light grid over a small test area at a very high level of illumination. The frequency of the a.c. signal is a direct measure of the particle velocity which can be described either in terms of traversing a fringe pattern or of the heat note between two frequencies which have experienced a differential Doppler shift due to the interaction of one or both of them with the moving particle.The two descrip- tions are mathematically equivalent both where a fringe pattern moves across a point detector in the image plane and for a fringe pattern in the test space (“ fringe anemometry ”). * The concept is thus relevant to two quite different practical applications. One is a new method of particle sizing based on the disappearance of the a.c. signal at given fringe spacings. The other is the limitation to Doppler velocimetry due to multiple scatterers in the test space. GEN€RAL PRINCIPLES A wide range of optical systems suitable for implementing the various appli- cations of this principle will be discussed.However it will be convenient to consider general properties in terms of the simplest underlyingschem asshownin fig. 1 in which two plane waves are incident at symmetric angles 8 with respect to the x-axis and form a set of interference fringes in the y-z plane. Observation is made of the light scattered into the direction 4 by a particle moving with velocity at an angle a to the y-axis. We shall not concern ourselves with the polar distribution of the scattered light but deal in terms of a constant fractionfof the illumination of the particle. The a.c. frequency is independent of angle at least so long as velocities do not approach the speed of light and for small particlesf is almost independent of angle. This means that light can be collected over a range of angles without affecting the result.The distribution of illumination in the y z plane is given by r = 210(1 +cos (2ky sin O)]. With k* = 27r/rZ* where A* = A/2 sin 8 is the fringe spacing r = 24(1 +cos k*y). ‘t FIG.1 .-Co-ordinate system for scattering of two plane waves by a moving panicle. FRISTROM JONES SCHWAR AND WEINBERG Thus the light scattered at the angle 4 by a point particle situated at Y may be represented by I,, = 2ZOf(+){ 1 +cos k* Y>. (1) Now the particle is moving along the y-axis with speed u = dY/dt = u cos a Thus as the particle moves the scattered intensity flucwates with a frequency vb given by vb = (u cos .)/A*. (2) An alternative approach is based on the Doppler shift.The apparent frequencies of the two waves as seen by the particle are vp,l = tp +; cos (;-a-o)] vp,2 = v[I+-cos -a+8 , c >I Likewise the frequency scattered by the particle as seen by an observer looking along 4is uo = up[ 1-5 cos (;-LY-4)] for both waves. The observer sees a beat frequency v; = I~0,2-~0,1l or V; = 2u cu -cosccsin8 [1-cos(;-LY-cj)] (3) If u/c is small then eqn (3) reduces to eqn (2). Alternatively since the particle is considered as a source emitting at frequency v, in the derivation of eqn (2) if the motion of the particle relative to the observer is taken into account the result is vb = vb 1-sin (a+411 [: which is identical to eqn (3). So both approaches give the same answer. To find the scattered intensity the incident amplitudes of the light wave may be set out as follows Eo,l = E,-,exp(ikYsinO); Eo,2 = E,exp(-ik YsinO).The scattered waves are then ELI = Eo ,/"exp (-ik Y sin 4); Es,2= Eo.2Jfexp (-ik Y sin 4) where k and k2 are the Doppler shifted wave numbers. We have assumed that f(O+ 4) N fC0-4)which is reasonable for small particles. Adding the amplitudes the scattered intensity is I,, = 21,f(l+cos[2kYsin O+(kZ-kl)Ysin 4]}. I86 PARTICLE SlZING IN DOPPLER VELOCIMETRY Now k2-kl 21 (2kuy/c) sin 0 so that Is, N 2Iof( 1 +cos [2k Y sin O( 1+uY/csin 4)]}. (4) For (u,/c)< 1 this equation is identical with eqn (1). Thus the two approaches yield identical results for small u/c. This approximation is inherent in the Doppler equation used i.e.the full relativistic treatment has not been considered. Inclusion of a second particle separated from the first by a distance d gives the scattered intensity as I,, = 2IOf(2+cos ~*Y+cos k*(Y+d)} (5) provided that the detector aperture is sufficiently large for incoherent addition to be used.3 A large aperture integrating over a range of angles can be used sincef for small particles and Vb are almost independent of 4. Eqn (5) can be derived either from eqn (1) or (4) with small u,,/c i.e. either by adding illuminations in two parts of the fringe system or by combining two beat frequencies with a phase difference between them. The beat frequency observed is the same as for one particle and since Is, = 4Iof(1 +COS k*( Y+d/2) cos (k*d/2)} the signal falls to zero whenever d = (2n+ 1)L*/2.In the most general case we may consider N particles having the same velocity < so that their respective separations are constant in time but randomly distributed. If thejth particle is at a distance yj from the first which is situated at Y one may expand eqn (5) into the form N I,, = 210f N+COS k*Y+ C cos k*(Y+yj) I j=2 since y1 = 0. The probable intensity (Isca)is the ensemble average over the cloud of N particles. Since the particles are randomly distributed the probability of yj having any particular value is a constant. Further if the width of the particle cloud is w (less than or equal to the beam width) then -w<yJ<w. Consequently. lW -w j’” ***Sw -w -W Iscady,dy,*.*dy 9 <IsJ = j-w j-w .,.j-w dY2 dY -dY -w -w -w or (Isca) = 210f(N+cos k*Y[l+(N-l)(sin k*w)/k”w]).This is the probable intensity observed at any one time or value of Y. As Y varies the signal varies and the visibility of the observed as. signal is (1sca)max -(Isca>min (1sca)max +(IsJmin’ which gives finally 1 N-1 sin k*w v = -+ -A N Ic*w FRISTROM JONES SCHWAR AND WEINBERCi I87 We note some of the properties of this function. Clearly for N = 1 V = 1 as expected. Also where sin k*w = 0 (i.e. the width of the cloud is a whole number of fringes) or for an infinitely wide cloud V = 1/N. However in general for a large number of particles as N+m V+(sin k*w)/k*w. That this is not zero is explained by the fact that the fringe pattern is repetitive.For every whole fringe the scattered intensity integrates to zero. If there is a fraction of a fringe left over only the effect due to those particles in this section is seen as over a fraction of a fringe the scattered intensity does not integrate to zero. The physical implication is that legibility of the a.c. signal can be assured only in the case of a single scatterer. For any greater number it is always possible that zero a.c. signal will result if the particle distribution is unfavourable. On the other hand it is quite likely that a residual a.c. signal will be obtained for the reasons discussed above even for a large cloud of particles-a result which explains observa- tions in many practical studies when naturally occurring scatterers are used.This applies purely to the a.c. component i.e. under conditions where the detector is not saturated by the d.c. signal which increases with number of scatterers. So far we have considered particles much smaller than the fringe spacing. The relevance to size measurement for which the fringe spacing must be made at least equal to the particle dimensions is by way of regarding infinitesimal particles as elements of a larger particle. We may then take the next step on a model of inte- grating across all the elements illuminated by a sinusoidal fringe pattern or of adding those locating the periphery depending on the optical system used. Consider first a strip of length 21 and width dZ situated with its centre at Y,as seen in fig.2. Taking an elementary area of length dY the element of the scattered intensity from the strip is dZ,, Y+I = 21~fJ (1 +cos k*~) dY dZ Y-1 or wherefis now the scattering efficiency factor. It remains to integrate over 2. We -m Y FIG.2.-Scheme for integration of illumination across a strip situated in an interference pattern. I88 PARTICLE SIZING IN DOPPLER VELOCIMETRY first note that for a longstrip e.g. a fibre or wire parallel to the fringes 1isiodependent of 2 and I,, = 41 fLi(1 +cos k*Y(sin k*l)/k*l) (7) where L is the length of the strip and 21its width. The a.c. component is zero when- ever 21 = nP i.e. no beat frequency will be observed if the strip has a width exactly equal to a whole number of fringes.This is obvious physically since the test object is then exposed to a total illumination which does not vary with change in position and it was this concept which first suggested the method. For a particle with a circular cross-section I = (R2-Z2)' where R is the radius of the particle. Thus Isce= 81,/s1 ((R2-Z2)*+-1 cos k*Y sin (k*JR2-Z2) dZ. 0 k -1 Substituting 2 = R cos # yields Using nJ,(Z) = 2 sin (2 sin 4)sin 4 d# Jal gives where Jl(k*R) is a Bessel function of order one which has zeros at k*R = 3.832 7.016 etc. The a.c. component thus falls to zero for 2R = 1.22 A* 2.24 A* etc. The theory as it stands is restricted to particles large enough for geometrical optics to be applicable i.e. the total flux of radiation extinguished by a particle is proportional to its cross-sectional area.For very smalf particles the scattering efficiency is an oscillatory function of particle size.5 However for transparent particles with size to wavelength ratio D/A;Z60 and for absorbing particles with D/A2 15 the oscillations are effectively damped out. For smaller particles the above concept must be examined in terms of wave theory. Scattering by infinite cylinders parallel to a system of interference fringes has been investigated by Jones.6 It is found that for quite small particles the discrepancy between the zeros as predicted by wave theory and geometrical optics is remarkably small. This is illustrated in fig. 3 which indicates for which particle sizes the two theories agree to within 10 % as a function of refractive index.It should be noted that the wave theory is rigorous and gives the positions of the zeros exactly. A second condition imposed on the above theory is that the detector aperture must be made large enough for the assumption of incoherent superposition to be FRISTROM JONES SCHWAR AND WEINBERG applicable. In fact since large transparent objects scatter very strongly forward it would be advisable to collect as much forward scattered light as possible. The resulting variation would then be expected to be similar to that for the total scattering. The wave theory has shown god agreement between the zeros in the total scattering and in the total forward scattering efficiencies for sizes as low as than 10% L I I I I I c 0 0:2 0.4 0;6 0;8 1.0 1IP FIG.3.4urve approximately indicating particle sizes (D/h)as a function of refractive index p for rigorous wave theory and geometrical optics to agree within 10 % in predicting the position of the first zero of the ax.amplitude (D/A*-l) for cylinders. p = co corresponds to a perfectly conducting cylinder. DliL-2. For small metal particles the scattering is mainly backward which suggests obvious modifications to the optical systems discussed in the next section e.g. a mirror to collect and reflect the backward scattered light. With the exception of fibres and droplets particles are not generally cylindrical or spherical. It is therefore of interest to compare the width deduced with that of the area-mean (since this particular optical system is based on illumination of the entire area-but see below).The correspondence is exact for any shape whose width varies linearly with height. For circular discs the area-mean width is nR2/2R which for the first zero differs from the above value by approximately 5 %. The discrepancy increases for higher-order zeros and though it is calculated easily it may be simplest to use only the first zero in circumstances when mixed shapes are likely to occur. In practice it is convenient to collect only a fraction of the light scattered by the particle into a certain range of solid angles. Moreover the circumstance that the direct light from the source must be cut-off if the photodetector is not to be saturated by an overhwelming d.c.contribution makes any light scattered about the optic axis unavailable. The use of a schlieren system to select a suitable range of scattering angles is not only simple (see fig. 4) but also allows a simpler and more convenient form of the theory to be used. PARTICLE SIZING IN DOPPLER VELOCIMETRY The principle is obvious if we consider the image. Here the luminous regions correspond to those parts of the test objects in which the particular deflections originate which are selected by the schlieren aperture used and which in the absence of refrac- tion are occasioned by diffraction alone.' When this system is applied to transparent lmaginq Leiis -Scattering ScNinen StOD Tat Sdrliercn Space LUIS FIG.4.-Schematic showing basic Schlieren system for the observation of scattered light.droplets it is better to use an opaque dye to avoid complications due to internally refracted rays. The range of angles so defined can be varied by limiting the outer as well as the inner boundary of the schlieren aperture using e.g. circular or double slits of various dimensions. Now the regions around the boundary from which the diffracted light comes are narrowly confined so that except for the very smallest of particles the above theory may be modified as follows. The photodetector is effectively only seeing the edges of the scattering particle crossing the field of fringes. For a cylinder these are two narrow line sources parallel to the fringes separated by the diameter of the cylinder.Eqn (5) can be applied directly giving zeros for 21 = (2n+ l)L*]2. The same result can be arranged for particles of circular cross-section if a strip schlieren stop is used of a width just sufficient to give an image consisting of two points coming from the ends of a diameter. This is the simplest and most direct measurement of width providing enough light is available. For a large number of particles in such a system one has effectively N pairs of particles of fixed separation d. Then eqn (6)takes the form 1 N-1 sin k*w d -+----} cos k* z. N N k"w If a circular schlieren stop is used with a sufficiently large particle of circular cross-section the image takes the form of a ring of radius R. If we take an element d1 of such a ring situated at the angle 8 we have d1 = Rd8 and if 6R is the width of the ring I,, = 4106Rf (1+COS k*y)R d6; s since y = Y+R cos 8 the centre of the ring being at Y then I,, = 410R6Rf [1 +cos k*y cos (k*R cos 8)-sin k*y sin (k*R cos O)] do, f or I,, = 4nR6R10f [1+ Jo(k*R)cos k"~].FRISTROM JONES SCHWAR AND WEINBERG Jo(k*R) is a Bessel function of order zero with zeros at k*R = 2.405 5.520 etc. Hence the a.c. component has zeros for diameters. 2R = 0.766A* 1.757 A* etc. The limitations regarding very small particle sizes which were detailed above for illumination of the whole area also become less serious for the schlieren type of optical system. The dark-field schlieren image when using a strip stop consists of two slivers of illumination at its extremities.These differ from being infinitesimal only to the extent to which the diffracted light derives from regions other than the edge and to the effect on the light pattern of diffraction elsewhere in the system^.^ However since this marking is symmetrical about the particle and since the fringe separation corresponds to the width of the whole particle-at feast for the first extinction-the approximation is a good one provided the schlieren stop is small and the numerical aperture of the optical system is large. In the simplest case of only one imaging lens the detailed structure of the schlieren image depends on the open aperture the stop and the boundaries of the lens (see e.g. Speak and Walters,lo). If this aperture were infinite in extent a point object would be imaged as a point.When a very small schlieren stop is used-and the parallelism of laser beams makes this feasible-the uncertainty in the schlieren edge is in practice limited only by the lens aperture. The dark-field schlieren system is also particularly suitable for very large particles for which the total illumination method is dominated by backward reflection from a three-dimensional body. Although here again the light can be reflected forward and extinction conditions precisely calculated for any known shape the schlieren method can be used directly without modification either to the optical system or to the method of data analysis-irrespective of shape size or reflectivity of the test object. SOME OPTICAL SYSTEMS Several configurations suitable for particular purposes are shown in fig.5. The method was originally intended to select particles of abnormal size (diseased cells) and this exemplifies probably the simplest application possible. Such particles can be held eg on a microscope slide driven at a known velocity or conveyed in a stream of liquid along capillary tubing. If the fringe spacing is set at a value giving zero (or minimum) a.c. amplitude for the standard size any particle of abnormal size will signal its presence by its ax. component. Since the particle velocity can be arranged independently in such applications suitable filter circuits could be used for the known ax. frequency. Under these conditions it would not even be necessary to have only one particle passing through the test space at a time although it would be desirable not to have more than one abnormal particle there.Under less controllable conditions however it is necessary to collect light from only one particle at a time into the photomultiplier otherwise the sizes will "add up " in a manner depending on their separation. This requirement is similar to that though more stringent than in velocimetry (see above) and in a cloud of particles can be arranged most readily by making the area of the fringe field smaller than the minimum particle separation. Using a focused laser beam in a system such as that shown in fig. 5a (similar to the " velocimeter " of Rudd 11) would be suitable for quite dense clouds. In the case of velocimetry there would be no merit in having the separation between the two slits or two apertures adjustable.For present purposes however the two apertures can be mounted on a micrometer screw or pair of callipers which may PARTICLE SIZING IN DOPPLER VELOCIMETRY Lens Lens Schlieren Oetect or slits Beamsplitter \ - - r Detector Space 1 Detector en Oiff 1)sing Screen (4) FIG.5.-Various possible optical systems for the observation of light scattered from particles sub-jected to modulated illumination. FRISTROM JONES SCHWAR AND WEINBERG then be adjusted to the disappearance of the a.c. signal when the particle size can be expressed directly in terms of the separation so measured. The particle velocity may be deduced for each slit separation (other than that giving zero a.c.signal) during this adjustment thereby improving the accuracy of velocimetry. The accuracy of both measurements is limited by the aperture widths which also define the depth of the sampling zone along the optic axis. This system would be well-suited to size determination in monodisperse clouds whether or not the particles move with a uniform velocity component perpendicular to the fringes so that the adjustment of fringe spacing can be carried out during the passage of a succession of individual particles-in which case the velocity of each particle as well as the common size can be deduced. For tenuous clouds extending over appreciable areas a system such as that shown in fig. 5b may be preferable in order to reduce the delays which would occur between successive signals for a small test area.To increase the angle between the beams and decrease fringe spacing conventional interferometers may be used e.g. fig. 5c though the limitations on minimum particle size discussed above still apply and there may be little point in reducing fringe separation to its theoretical minimum of A/2. All the optical systems not using diffused light in fig. 5 are based on schlieren imaging for convenience. If that is not desired it would be advisable to move the photodetector off axis (e.g. in the position shown dotted in 5c) to avoid saturation by light which has not interacted with particles. (b) FIG.6.-(a) Grid of variable spacing for particle sizing.(b)Signal due to a particle traversing the grid. Particle size corresponds to central grid spacing. Many other optical systems may be useful for particular purposes. Probably the simplest method of achieving interference with laser light uses the front and rear reflections from a piece of glass (almost any optical quality if a sufficiently small area is used).12 Fringe spacing can then be varied by varying magnification (fig. 54. The same method of varying spacing can be used when projecting a grid within the test region in which case neither a laser nor indeed monochromatic light s7-7 PARTICLE SIZING IN DOPPLER VELOCIMETRY is required (fig. 5c). As regards this system the " Doppler theory " gives cancellation in pairs at each wavelength when the correct separation is reached.The major difficulty which arises when particles are all of different size is the need to carry out the adjustment in fringe spacing during the passage of each particle unless a spectrum analysis can be carried out on a large number of records. Such adjustment could be carried out mechanically only for particles travelling very slowly and being widely dispersed so that the " null point '' for one could be deter- mined before another entered the test space. An attractive alternative is the use of a grid or fringe system the spacing of which is arranged to vary across the test space. Fig. 6a shows such a grid while fig. 6b shows the signal expected from a particle travelling across it at constant speed whose diameter corresponds to the centre of the range.This system can be contrived by interfering wavefronts the angle between which varies across the field e.g. planar and spherical or by projecting the image of an actual grid made in this form. The use for this purpose of an optical system such as that shown in fig. 5c would allow the overall grid magnification to be varied as well so that a large range of particle sizes could be accommodated. EXPERIMENTAL TESTS The variation of the signal with ratio of fringe spacing to particle size should be much the same whichever optical system is used except that those based on varying magnification also vary the overall illumination level. This however is a trivial point and it was considered that the simplest convenient arrangement could be used for comparison of the signals with the above theory.Preliminary work at the Applied Physics Laboratory was based on an arrangement similar to that shown in GRAT I NGS 50cm. BLIND 87 Line mm? Focal Length (4 I L T s P (61 FIG.7.-Apparatus for particle sizing. (a) Production of the two effective point sources ; (b) the schlieren optics. PLATE1.-Image of wire traversing interference pattern. [Toface page 194 A* =d PLATE2.-Typical photomultiplier output produced by wire traversing a variable interference pattern. FRISTROM JONES SCHWAR AND WEINBERG fig. 54largely because a shadow interferometer based on front and rear reflections at a glass slab had just been set up for fire research.13 These experiments were cursory owing to shortage of time.The work at Imperial College was based on a system similar to fig. 5b and is illustrated in fig. 7a. Fig. 5b is a special case of the system in fig. 7a as there the two sources S1 and S2 are effectively at infinity. The narrowly confined test space of fig. 5b was not required for a test in which the object could be precisely located. In practice the problem is one of being able to adjust the separation of S1 and S2 conveniently and precisely. To achieve this a collimated laser beam passed through a pair of identical gratings having 87 lines mm-l (see fig. 7b). The diffracted beams were then brought to a focus using a 50-cm focal length lens. When both gratings were accurately aligned with respect to each other the diffracted orders coincided exactly.Rotation of one grating in its own plane rotated one set of diffracted orders about their common central maximum. A blind placed in the focal plane selected only one order from each grating so as to produce two point sources corresponding to S and S2 in fig. 7a. The separation of the point images depended only on the relative rotation of the two gratings. The separation of the sources was therefore easily and precisely adjustable and therefore the fringe spacing was readily varied. TABLEFRINGE SPACINGS CORRESPONDING TO MAXIMA AND MINIMA IN THE DOPPLER BEAT FREQUENCY SIGNAL FOR A SINGLE PARTICLE SIZE grating setting min. max. order no. n 1In fringe spacing 1.50 0.5 2.000 0.0730 3.30 1.o 1.ooo 0.0394 5.00 1.5 0.667 0.0275 6.80 2.0 0.500 0.0208 8.80 2.5 0.400 0.0168 The dimensions of the optical system beyond S and S were S2T = 77.0 cm ; TL = 26.2 cm ;LS = 15.0cm ; and SP = 20 cm (see fig.7a). A single stop 2.5 mm wide was used to block off the direct beams. The aperture in front of the photo- multiplier was 3.0 mm long and 0.3 mm wide. The fringe spacing was continuously variable from effectively infinity down to 170pm. The test object was a thin moving wire the average diameter of which was measured with a micrometer as 0.0399+0.0001 cm. It was attached to a fly wheel and driven through the test region by a constant speed electric motor with its axis parallel to the fringes as is illustrated in plate 1. Each time the wire crossed the fringe system the periodic signal picked up by the photomultiplier was displayed on a oscilloscope.Starting with an infinite fringe spacing the oscilloscope traces were observed as the fringe spacing was decreased. A series of readings were made of the grating settings corresponding to the minimum and maximum amplitude in Doppler beat frequency traces. Three examples of the traces recorded are shown in plate 2 and the complete set of data is given in table 1. The grating settings were calibrated by measuring the associated fringe spacings with a travelling microscope. As discussed in the previous section we expect that for this system minima in a.c. amplitude occur when A* = D/(n+3) n = 0,1,2 3.. . s7-7 * PARTICLE SIZING IN DOPPLER VELOCIMETRY Similarly maxima occur whenever A* = Din n = 1,2,3... One interesting result of the experimental test is that the minima in a.c. amplitude approach but never quite reach zero. This is due to the Gaussian modulation of the fringe amplitudes across the field and becomes obvious by reference to fig. 8 which I A t (c) FIG.8.-Effect of adding two unbalanced out of phase a.c. signals. (a) signal produced by leading edge of object ; (b)signal produced by trailing edge of object ; (c)net signal from detector the sum of (a)and (6). 1In FIG.9.-Linear least-squaresfit to the points listed in table 1. FRISTROM JONES SCHWAR AND WEINBERG also explains the shape of the observed traces. The schlieren images of the leading and trailing edges derive from somewhat different regions and the two intensities are therefore never fully matched.Should this become a practical limitation to accuracy it would be necessary to use a wider field of fringes in relation to the width to be measured or to avoid a Gaussian distribution altogether (see fig. 5c). To illustrate the deduction of D and assess variation in individual readings as compared with the mean a graph of A* against n-l was plotted. This is shown in fig. 9 where a linear least-squares fit has been made to the points. Taking all points into account the slope gives d = 0.0377 cm a 5.5 % difference from the micrometer reading. However the error in locating the first minimum is much greater than for the other points.If this first point is omitted one obtains d = 0.0404 which is only 1 % different from the directly measured value. Since the form of the records and analysis is independent of the optical system and of the nature of the test object there seemed little point in extending the experi- mental tests to other configurations. It is concluded that the results conform accurately to the theroretical predictions. M. J. R. Schwar and F. J. Weinberg Proc. Roy. Soc. A 1969,311,469. F. Durst and J. H. Whitelaw Proc. Roy. Soc. A 1971 324 157. L. E. Drain J. Phys. D. Appl. Phys. 1972 5,481. A. ErdClyi Higher Transcendental Functions (McGraw-Hill New York 1955). G. N. Plass Appl. Optics 1966 5 279. A. R. Jones J. Phys. D. Appl. Phys. 1973,6 417. ’F. J. Weinberg Optics of Flames (Butterworths London 1963).M. D. Fox and F. J. Weinberg Brit. J. Appl. Phys. 1960 11 269. K. G. Birch Optica Acta 1968 15 113. lo G. S. Speak and D. J. Walters Aero. Res. Council,Rep. Mem. 1954 2859. M. J. Rudd J. Phys. E. Sci. Instr. 1968 1 723. l2 A. K. Oppenheim P. A. Urtiew and F. J. Weinberg Proc. Roy. SOC. A 1966 291 279. l3 J. E. Creeden R. M. Fristrom C. Grunfelder and F. J. Weinberg J. Phys. D.,Appl. Phys. 1972 5 1063.

ISSN:0301-5696    

DOI:10.1039/FS9730700183

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Processes Sources and Particle Size Distributions BY J. R.BROCK Dept. of Chemical Engineering University of Texas Austin Texas 78712 U.S.A. Received 28th March 1973 Rational control policies for particulate air pollutants ultimately must consider the particle size distribution. This point is illustrated by a simple example of the inadequacy of regulations based on limitation of total particulate mass emissions from primary sources. A general model for the evolu- tion of the atmospheric aerosol size distribution is discussed for the particular case of an urban area. Conservation equations for particulate matter and nucleating vapour are developed. An important element in the development of the general model is knowledge of the particle size distribution associ- ated with various primary sources of particulate matter.Such primary sources are classified according to the basic aerosol generation process of homogeneous and heterogeneous nucleation and com- minution. Aerosols from primary sources in which particle generation occurs by homogeneous nucleation are considered to be well aged aerosols which by virtue of coagulation have reached asymptotic limit or " self preserving " distributions. As a practical matter however randomization will alter the asymptotic limit distributions from primary sources. Inherent complications in attempts to characterize the particle size distributions of aerosols formed by heterogeneous nucleation are discussed. Aerosols generated by comminution are known to approach asymptotic limit distributions which in certain cases have the log normal form although randomization again will alter such asymptotic forms.1. INTRODUCTION The pollution of the atmosphere with aerosols is a topic of current concern. Adverse health effects have been traced to exposure of urban populations to high ambient levels of particulate matter and sulphur oxides. Reduction in visibility is an obvious consequence of an increase in the amount of atmospheric aerosol. Consider-able speculation continues as to the possible role of pollutant aerosol in inadvertent modification of weather and even the global energy balance. In many of these instances the unfavourable effects are related not solely to the total quantity of suspended particulate matter but in a detailed manner to the aerosol size distribution.Therefore it would appear that formulation of a rational policy for control of pollutant aerosol must consider the size distribution. As an illustration of this point consider a single elementary example. Controls on emissions of particulate matter from sources have been directed primarily toward reduction of total mass emissions. From a regional or international standpoint this may not be sufficient. Consider that the rate of change of total suspended particulate mass m owing to a primary source emission is a function of the primary source emission rate a and the residence time b-l of the aerosols from that source. As we shall discuss later these simple assumptions are not generally correct but they will serve for the purposes of this simple illustrative example.The functional relationship described above may be expressed in the form dm -= a-bm dt 198 J. R. BROCK 199 where b-l is a function of particle size which for a particular source category will be chosen as the residence time of the mass median diameter. For short time periods dm -0 = a-bm dt N so that rn = a/b gives the total mass of atmospheric aerosol at any time owing to a particular source category. Table 1 presents some comparisons for several source categories in the U.S.A. In these examples the largest tonnage sources of particulate emissions are not the largest contributors to the inventory of suspended particulate matter. There is of course no pretension that the data in table 1 are accurate but they do serve to illustrate the point that total mass emissions may not be a reliable guide to assessment of atmospheric degradation by primary sources.TABLE l.-M~ss OF AEROSOL IN ATMOSPHERE OWING TO INDICATED PRIMARY SOURCES primary source (uncontrolled) mass median diam./pm(uncontrolled)ref. (I) inverse particle residence time/yr-1 ref. (2)b source mass emission rate/ton yr-1 U.S.A. ref. (1) a mass of particulate matter of atmosphereU.S.A. alb 1. automobile 0.4 20 4~ 105 2~ 104 2. coal-fired 10 625 3x lo6 5x lo3 electric utility pulverized sand gravel FFC units 3. crushed stone 4. petroleum 20 0.5 1250 30 5x lo6 4.5~105 4~ 103 i.5~104 In general rational control policy for particulate matter requires detailed answers to such questions as What are the sources of aerosols in the atmosphere? What are the processes producing changes in the aerosol size distribution in the atmosphere? How are particles removed from the atmosphere ? Detailed answers to these questions would imply a knowledge of the evolution of the aerosol particle size distribution in the atmosphere.The purpose of this paper is to develop an analytical framework for the examina- tion of some of these questions. We begin with the formulation of a model for the evolution of the atmospheric aerosol size distribution. Consequences and approxi- mations of the model are discussed. As an important element of the general model examination is made of the particle size distributions arising from basic aerosol generation processes and associated with primary sources of particulate matter.2. MODEL OF THE ATMOSPHERIC AEROSOL In this section an analytical model for the atmospheric aerosol is discussed. While the general model is not necessarily limited the direction of the discussion is toward the evolution of the particle size distribution in the atmospheric boundary layer of urban areas. A major element in the evolution of the particle size distribu- tion and the essential feature of the hydromechanical description of the atmospheric boundary layer is the presence of turbulence. These facts make difficult a rigorous derivation of an evolution equation for the atmospheric aerosol. The nature of these difficulties in the development of aerosol dynamics in a turbulent medium has been outlined in ref.(3). In the development of this model a first assumption is that the 200 PROCESSES SOURCES AND PARTICLE SIZE DISTRIBUTIONS velocity of the suspending gas is not altered by the presence of particles. While this assumption may be valid for the ambient urban aerosol it clearly excludes detailed consideration of aerosol dynamics in such systems as dense or hygroscopic plumes fogs clouds etc. A second assumption is that aerosol particles and gaseous contami- nants diffuse similarly in the presence of atmospheric turbulence. Justification for this assumption is given in ref. (3) and (4). Brownian diffusive transport of individual particles is considered to be negligible compared with turbulent diffusive transport.With this discussion in view the following relation is assumed to describe the evolution of the density function n(p X t) for the atmospheric aerosol an 6(p-p' p') + ~(,d)n(p-p') dp' -1.1 b(p',p)n(p')dp' + at a"2 a __ [cc(,u)n]-[P(p)n]+ G(p) Vn+ ip+ vN (2.1) aP2 3P P N where n(p X t) dp is the number of aerosol particles haveing masses in the range p dp at a poiiit in space X at time t. co is the fluid velocity. The first two terms on the right hand side of the equation represent the change in n owing to coagulation. The third and fourth terms describe the change in n owing to condensation of trace gaseous substances. The change in n owing to gravitational settling is given by the fifth term in which G(p)is the gravitational settling velocity of a particle of mass p.Lp(p,X t) is the rate of input at X t of particles of mass p from primary source P,and the summation is extended over all primary sources which may be treated as point line or area sources. Similarly j2Ni(p X t)represents the rate of production of particles of mass p at X t by homogeneous nucleation of the ith chemical species. It should be noted that heterogeneous nucleation of condensable species is accounted for by the condensation terms three and four. It should be noted that the coagulation coefficient b(p p') and condensation coefficients a@) p(p) may be very complicated functions if refinements such as particle shape composition and other physico-chemical properties are included. Coupled to eqn (2.1) are conservation equations for those substance undergoing heterogeneous and homogeneous nucleation as co -+G VS = 1Sjr+cSjp-csjrl-s (s, p)n(p)dp at r P r' 0 Sj is the mass concentration of the jth chemical species undergoing heterogeneous nucleation.Sjr represents the rate of production of this species by the vth chemical reaction and sj the rate of production by the Pth primary source. Similarly Sjr' is the rate of removal ofj by the rth chemical reaction. The last term on the right hand side of eqn (2.2) is the rate of removal of speciesj by condensation onto the existing aerosol; the function y(Sj,p) will in general be a complex function of the physico- chemical properties of the particles. The first three terms on the right hand side of eqn (2.3) are analogous respectively to those in eqn (2.2).The last term is the rate of removal of i by homogeneous nucleation as defined in eqn (2.1). Eqn (2.1) (2.2) and (2.3) are of course coupled closely to the energy and momen- tum balance equations for the atmosphere.' We shall discuss this coupling shortly. J. R. BROCK 20 1 However consider now the first two moments of n 03 N =lon(P)dP N being the total number of particles per unit volume and M the total mass. Through performing the indicated integrations one obtains the following moment equations from eqn (2.1) The details of the integration of eqn (2.1) to obtain eqn (2.6) and (2.7) are well .. known and are therefore omitted here. Np,APlvand jlp,A?Nrepresent respectively total number and mass of particles contributed by both primary sources and homo- geneous nucleation.It is clear from eqn (2.6) and (2.7) that N is unaffected by condensation processes but is altered by coagulation whereas the reverse is the case for M. Hence the two moment eqn (2.6) and (2.7) provide complementary information on these two important processes shaping the size distribution. For a turbulent fluid eqn (2.1) (2.2) and (2.3) are not in a useful form. By analogy with the usual procedure for turbulent dispersion of non-reactive gases we can express quantities in these equations in terms of time averaged quantities with an overbar and fluctuating components. For example v =V+V’ sj=sj+s; n =E+n‘ hi=hi+hi where by definition V’ =0 etc. Unfortunately eqn (2.1) (2.2) and (2.3) are non-linear in n Sj and hi so that the usual procedure of introducing Prandtl’s mixing length hypothesis is not sufficient.This is a familiar problem occurring in the analysis of non-linear chemical reactions in turbulent fluids. It has recently been discussed for atmospheric chemical reactions.6 Unfortunately there is no simple resolution. For example if one seeks to ignore a product such as relative to E2 it is necessary that characteristic coagulation times l/bn and temporal variations in 5 be much greater than the Lagrangian time scale of the turbulence. In addition the spatial variation of ii must be large compared with the length scales of the turbulence. These conditions may not always be met ;and if they are not we do not have a convenient hypothesis such as Prandtl’s to relate quantities such as n-and ii2.More detailed study of these questions appears to be essential for further development of the present theory. We proceed then under the restrictions indicated above and neglect terms such as nT relative to EE etc. With the introduction of Prandtl’s mixing length hypothesis eqn (2.1),(2.2) and (2.3) become 202 PROCESSES SOURCES AND PARTICLE SIZE DISTRIBUTIONS cop -+V a hi Vhi = V KVgi+xzjy+xHjp-I gjq,-s &(p) dp (2.11) at 4 q‘ 0 where K is the so-called eddy diffusivity. The difficulties in the concept of eddy diffusivity applied to atmospheric dispersion are well known and extensively re~iewed.~ We restrict our discussion here to urban particulate pollution.In order to apply these equations in the descriptions in the description of the aerosol concentration in an urban area it is clear that detailed knowledge of chemical reaction rates nucleation rates and physico-chemical alterations of the particulate matter is necessary. In addition meterological data in the form of mean winds atmospheric stability conditions relative humidity tempera- ture and radiative flux are essential. The boundary and initial conditions will depend also in part on this meteorological information. A discussion of the solution of eqn (2.9) (2.10) and (2.11) is beyond the scope of this paper. It is possible however to indicate the relative importance of some of the terms in these equations which will serve to provide a framework for later investiga- tions.With the restriction of the discussion to pollution by aerosols of an urban area various characteristic time scales may be introduced as scale factors in eqn (2.9) (2.10) and (2.11). For an urban area a characteristic residence time tRES may be introduced as the ratio of the crosswind diameter D of the area to the mean wind velocity U-that is tREs -D/U. Obviously a problem occurs in this definition if winds are light and variable as occurs during inversion conditions. This point will be touched on later. There are also characteristic diffusion times for longitudinal ?LONG and vertical tVERT dispersion tLoNG N L2/KL and where L is the longitudinal distance perpendicular to a line in the mean wind direction through a point of observation His the vertical distance above the surface.K,and KH are the corresponding eddy diffusivities. For particulate systems the characteristic particle gravitational settling time tCRAV -H/ Vg(,u),must be considered along with ~VERT-There are also characteristic times for the aerosol growth processes. For coagulation 1 tCOAG -____ b(p p‘)’‘’’ J. R. BROCK 203 where for the collision pair n(,u) > n(,u'). For condensation where ACj is the difference between the number density of jin the gas and just at the surface of the particle. iij is the molecular mean speed of j. /z(r) is a function of particle radius r and Knudsen number Kn such that for Kn -+0 h(r) -r. In addition to these characteristic times there are times associated with the gas phase reactions homogeneous nucleation processes flux rates of particulate matter to boundary surfaces etc.If one is interested solely in the evolution of the aerosol distribution in urban areas it is clear that only those processes with characteristic times within the period tREs need be considered. The assumption here of course is that upwind outside the urban area the aerosol concentration is low and plays no important role in the evolution processes occuring in the urban area. By way of example for an urban area with a cross wind diameter of 30 km and a mean wind speed of 2 m/s tREs-4 h. Consequently for KL -8 x 106cm2fs primary sources located longitudinally more than approximately 3 km from the line in the direction of the mean wind speed through a reference or monitoring point need not be considered in interpreting observations at that monitoring station.In the same manner one can conclude that coagulation between two particles both with radii greater than 0.1 ,urn can be neglected in eqn (2.9) inasmuch as for such coagulating pairs of particles at known urban concentrations tCoAG230 h. Also in photo- chemical smog reactions the induction period for formation of ozone which appears to be one of the reactants producing particles by nucleation is of the order of 4 h so that for the conditions of this particular example such processes cannot be neglected in eqn (2.9). From this one can infer that it is not generally necessary to consider all the complication inherent in eqn (2.9) (2.10) and (2.11) in that some of the terms may be of negligible order for certain meteorological and boundary conditions.A difficulty arises with these arguments under inversion conditions where the mean wind speed is very small and highly variable in direction. In these circum- stances the ground surface and inversion base suggest the applicability for the urban raea of a so-called '' box model " in which unfortunately much detail is lost. It is assumed that the urban region closed at the top by the inversion base corresponds to a well-mixed container. If eqn (2.9) is integrated over this defined volume and the volume integrals are converted where applicable to surface integrals the following result is readily obtained where (n) is the volume-averaged density function.~(p)represents the inverse residence time of particles of mass p in the volume and is a function for the conditions specified above of the mean wind dispersion coefficients and surface removal processes. zifi(p) represents the rate of input of particles from primary or homo- geneous nucleation source i with density mi@) and characteristic time zt '. This model has been applied' in the discussion of the evolution of the size spectrum for particle radii greater than 0.1 ,urn. As noted above coagulation of pairs of particles found in this portion of the atmospheric size spectrum can be 204 PROCESSES? SOURCES AND PARTICLE SIZE DISTRIBUTIONS neglected over reasonably long time periods.Hence for radii greater than 0.1 pm eqn (2.12) becomes (2.13) where the small nuclei below 0.1 pm may be considered as participants in the conden- sation process on the large particles ; the new coefficients a' and p' include this con- sideration. If primary source inputs are neglected it is easy to show ** that as a result of condensation eqn (2.13) leads to certain characteristic forms for the particle size distribution for particles greater than 0.1 pm radius. Of course primary sources in many urban areas may be dominant. Therefore in such circumstances if generalizations concerning urban particle size distributions are to be found one must look at charac- teristics of the particle size distributions of typical dominant primary sources. Consideration is given to this topic in the next section.3. PROCESSES AND SIZE DISTRIBUTIONS The necessity for consideration of the particle size distribution of primary sources has been noted above. Primary sources as defined by the relations developed in Section 2 include all those sources injecting particles as such directly into the atmosphere. Particles from a given primary source may be generated by the processes of nucleation comminution or by combinations of these processes. Nucleation may be homogeneous or heterogeneous. The term homogeneous nuckation embodies all those processes in which vapour molecules interact physically or chemically to form particles ;the particle growth process begins from particle sizes of molecular order and may proceed by coagulation condensation or a combination of these.In heterogeneousnucleation,new particles are not formed ;vapour molecules condense physically or chemically onto existing particles and primarily one is dealing with a condensational growth process. Particle generation by comminution involves successive usually mechanical sub- divisions of liquids or solids to the fine particle state. Aerosol generation at the air- sea interface and dust rise by wind action at the air-land interface are important examples of natural primary sources of particles formed by comminution. These sources in fact are estimated lo to constitute the two largest contributors of aerosol mass on a world wide basis. With these definitions characteristics of the particle size distribution produced by the particle generation processes of nucleation and comminution will now be examined.HOMOGENEOUS NUCLEATION Automobile exhaust represents perhaps one of the important examples of an anthropogenic primary source in which particles are apparently generated principally by homogeneous nucleation as defined here. The residence time of the aerosol before injection and subsequent fairly rapid dilution in the atmosphere in this and other important industrial combustion sources is usually of the order 0.1 -1 s. Therefore the particulate emissions from such sources are comparatively well-aged aerosols for which the particle size distribution has had sufficient time to reach a "self-preserving "form by coagulation.' ' The term "self-preserving "refers to the tendency of aerosols coagulating with the same collision parameter b(p p') to achieve similar particle size distributions after sufficient time of coagulation.Also J. R. BROCK 205 a simple calculation is sufficient to show that usually aerosols formed by homogeneous nucleation will in the time period 0.1 -1 s have an average size which is in the sub- micrometre range. If A$’ is the total mass concentration of condensed material formed by nucleation the order of the mean radius of the coagulated aerosol should be r -[3 Jzl( 1+bNot)/47EpN0]+ (3.1) where No is the initial embryo concentration and p is the particle density. Eqn (3.1) becomes for No t % 1 r -(3Abt/4np)+ (3.2) and the order of the mean radius becomes independent of No.As an example for an automobile using leaded gasoline the undiluted exhaust has a total particulate mass concentration A%’,of -lO-’-lO-* g/cm3. Eqn (3.2) indicates as do measurements,12 that most of the aerosol is certainly in the submicrometre range. For anthropogenic primary sources of aerosol formed principally by homogeneous nucleation and in which subsequent particulate growth is by coagulation one might infer that particle size distributions from all such sources should have the same functional form and should differ only in the parameters of the “self preserving ” form. The inference is the same if simultaneous condensation occurs. Published studies l1 of the numerical solution of the coagulation equation in the free molecule and continuum regimes support the foregoing conclusion.However experimental measurements of coagulating aerosols reveal that generally the aerosol is more polydisperse than predicted by the self-preserving functional form. The explanation for this behaviour is a very familiar one to statistician^.'^ The aerosol measured in the coagulation experiments does not represent a single population but instead a mixture usually in random proportion of a heterogeneous population. In other words the aerosol actually measured is a composite of many different aerosol populations each with a different history. Thus the particle distribution function realized in an experiment G(X)is where the pi are random weights attached to the various members of the heterogeneous population each with distribution function Fi(X).For an infinitely composite population G(X) = 1F(X a) dU(a). (3.4) In experimental realizations of coagulation not only systematic spatial or time variations or random experimental error serve to create a composite population but for dilute systems unavoidable random fluctuations also contribute. As a result of the effect of heterogeneity of population the aerosol formed by homogeneous nucleation from a given primary source will always be more poly- disperse than predicted by the “self-preserving” theory. Unfortunately the extent of this increase in polydispersity for a given primary source will probably depend on the details of that source such as geometry flow dynamics etc. As a result it remains to be determined whether or not for various primary sources of this type generaliza- tions axe possible.Certainly the fact of the “ self-preserving ” form provides a useful base from which to proceed in the inquiry. S7-8 206 PROCESSES SOURCES AND PARTICLE SIZE DISTRIBUTIONS HETEROGENEOUS NUCLEATION The dense hygroscopic plumes emitted from various industrial processes are examples of aerosols formed by heterogeneous nucleation. In these instances water vapour has condensed on an existing hygroscopic aerosol which may itself in turn have been generated by homogeneous nucleation or comminution. For the simple process of condensation of a pure substance on an aerosol of some given initial density function no(r)dr of particle radius r it is a simple matter to examine the development in time of n(r t).In this case the evolution of n(r t) is dn a -+-[f(r)n]at ar =0 (3.5) wheref(r) is the growth law for a particle of radius Y. For example in the continuum region Kn +0 neglecting the Kelvin effect f(r) =a/r where a is a con~tant.~ Similarly in the free molecule region f(r) =a a constant if the Kelvin effect is neglected. Eqn (3.5) is a first order equation for which solutions may readily be found for arbitrary initial conditions. However perhaps the most interesting feature of the pure condensation process is the tendency of condensation to produce a less poly- disperse aerosol in the continuum region when the Kelvin effect can be neglected. In this case it is a simple matter to show that the ratio of the standard deviation CT to the mean radius yl approaches zero with increasing time d -60 Y1 (Yl.0 +24+ where the subscript designates initial conditions.Similarly in the free molecule regime (3.7) No being the initial total particle concentration. This characteristic of pure conden- sational growth has been utilized for the production of approximately monodisperse aerosols in variations of the original Sinclair-La Mer aerosol generat~r.~ If as in the previous examples the concentration of condensing vapour is held fixed but the Kelvin effect is included in the termf(r) it can be shown that a/yl -,0 as a result of condensation. However if the quantity of condensing vapour is limited one finds that in an initially polydisperse aerosol after condensation has proceeded the smaller particles will begin to evaporate while the larger ones continue to grow.Also additional complication beyond the scope of this discussion arises in con- sideration of a hygroscopic aerosol which grows at humidities below the critical supersaturation of some of the particles. In such cases n(r)can become bimodal and very polydisperse. More general condensation processes including stochastic effects have been examined elsewhere (see also Section 2). Such processes as well as randomization indicated in eqn (3.3) and (3.4),usually act to increase the polydispersity ofan aerosol. Additional complication can be introduced by considering as well simultaneous coagulation and condensation. When the deterministic condensational growth described by eqn (3.5) is the only process altering the aerosol size distribution the final distribution clearly will be J.R. BROCK 207 determined by the initial size distribution. This initial size distribution will be that owing either to homogeneous nucleation or comminution or both. When the condensation process is stochastic and/or randomization occurs the final particle size distribution resulting from condensational growth will become asymptotically independent of the initial distribution the equivalent of the “ self-preserving ” behaviour for a coagulating aerosol. However in general it is much more difficult to draw conclusions concerning the nature of the particle size distribution resulting from condensation in these cases than for coagulation.Unlike the coagulation equation the condensational growth equation is coupled to the conservation equation of the condensing vapour; the state of the suspending gas usually plays a secondary role in the coagulation of fine particles. Furthermore the ability of particles to grow by condensation depends in detail on particle composition or surface properties ;such characteristics are usually not considered to be of great importance in coagulation. Therefore for sources in which particle generation by heterogeneous nucleation plays an important role detailed examination of the process dynamics will be necessary to characterize the particle size distribution. COMMINUTION Important natural sources of aerosol particles generated by comminution have been cited at the beginning of this section.Anthropogenic sources of aerosol generated by comminution are also of common occurrence and include emissions from industrial operations such as mineral rock and gravel processing sand blasting cement manufacture etc. as well as inadvertent emissions resulting from farming operations etc. The process of comminution begins with a body of macroscopic size and by successive subdivisions or splittings liquid or solid particles capable of aerosolization are formed. It is therefore the inverse operation to homogeneous nucleation and subsequent coagulation. The evolution equation for comminution may be represented by the relation = Ja c(p/p’)n(p‘jdp’-c(p)n(p) at P where c(p/p’)dt is the probability that a particle of mass p’ will split in time dt to form 1,2,3...particles of mass p and c(p)dt is the probability that in the same time a particle of mass p undergoes splitting.The basic assumption of eqn (3.8) is that each particle splits with a probability independent of the presence of other particles. Clearly additional detail can be introduced. It is possible to show that the splitting process approaches asymptotically a limit distribution,l which for certain assumptions concerning the splitting probabilities can be approximated by the log normal distribution. Just as the coagulation process has for certain assumptions concerning collisions an asymptotic limit distribution so too does the process of comminution. A common assumption in the discussion of the splitting process l6 is that the probability of splitting is proportional to some power of the mass of a particle.Clearly if a comminution process is carried out so that a particle of say 1000pm is split with unit probability a particle of 1 pm radius will be split with a probability orders of magnitude less in fact if splitting is directly proportional to particle mass for particles of unit density). For this reason many large sources of particles produced by comminution such as those cited above will produce particles in the range of larger particle sizes. 208 PROCESSES SOURCES AND PARTICLE SIZE DISTRIBUTIONS Although asymptotic limit distributions may exist for a given comminution process randomization can be expected to be important owing to the comparatively small number of particles per unit volume in typical comminution processes.How-ever very large particles are not important in the consideration of sources of air pollution so that the distribution produced by a comminution process can be truncated at the order of 100pm radius. Therefore the particle size variation of interest will generally be over only one or two orders of magnitude of particle radius. As a result the range of polydispersity which might arise from randomization is restricted. 4. CONCLUSION While the model described in Section 2 for the evolution of the atmospheric aerosol appears to be very complex it is nevertheless suggested that owing to the important role of the particle distribution in many of the detrimental effects of air pollution this complexity eventually must be faced.Characterization of the primary sources of pollutant aerosol is one of the necessary first steps. It is recognized of course that primary sources of particulate matter will not generally fit into the separate categories discussed here. The aim here has been to examine the basic aerosol generation processes and to inquire into the characteristics of the resultant particle size distributions. Further progress along these lines will require adequate field data which are at present insufficient. This work was supported in part by a research grant from the Division of Chemistry and Physics National Environmental Research Center E.P.A. The author also wished to thank Prof.J. Bricard of the University of Paris for many helpful discussions. Particulate Pollutant System Study MRI Contract No. CPA 2269104 (EPA 1971). N. Esmen and M. Corn Atmospheric Environment 1971 5 571. G. Hidy and J. R. Brock The Dynamics of Aerocolloidal Systems (Pergamon Oxford 1970). N. Fuchs The Mechanics of Aerosols (Pergamon Oxford 1964). R. Bird W. Stewart and E. Lightfoot Transport Phenomena (Wiley NY 1960). R. Lamb Atmospheric Environment 1972 6 257. F. Pasquill Quart. J. Roy. Met. Soc. 1971 97 369. J. R. Brock Atmospheric Environment 1971 5 833. J. R. Brock J. Coll. Interface Sci. 1972 39 32. lo G. Hidy and J. R. Brock,Proceedings 2nd IUAPPA Clean Air Congress (Academic Press New York 1971). l1 R. Drake in Topics in Current Aerosol Research (Pergamon Oxford 1972).l2 R. Lee et al Atmospheric Environment 1971 5 225. l3 J. Pich S. Friedlander and F. Lai Aerosol Sci. 1970 1 115. l4 M. Girault Calcul des Probabilities (Dunod Paris 1972). l5 J. R. Brock to appear. l6 A. Kolmogorov Akad. Nauk SSSR 1941 31,99.

ISSN:0301-5696    

DOI:10.1039/FS9730700198

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

A Field Study of Radiation Fog BY W. T. ROACH,? R. J. ADAMS,? AND P. GOLDSMITH? J. A. GARLAND$ Received 3rd January 1973 A survey of the history of theoretical and practical studies of the basic physics of fog formation in the atmosphere is followed by an account of some preliminary results of field investigations into fog. 1. INTRODUCTION A supersaturated atmosphere in which fog droplets may grow may be produced by cooling or by mixing of two damp (but not necessarily saturated) masses of air at different temperatures (due allowance being made for any consequential release of latent heat by condensation). However unlike the situation in many industrial processes involving fogs and smokes the conditions under which these processes may occur are uncontrolled and highly variable.Stewart 1v has said “. . . the inter- actions between the different processes lead to such complexities that there has been little success in calculating the important features of the final state on a foggy night from observable initial conditions ”. This situation has changed little in recent years. A deeper understanding of the physical processes of fog formation maintenance and dissipation is a necessary condition for assessing future prospects of improving methods of fog modification and forecasting. This paper consists of a brief summary of past investigations followed by an account of some preliminary results of the current Meteorological Office field investigations of radiation fog. 2. PAST INVESTIGATIONS (a) Taylor made a study of radiation fogs at Kew and noted that clear skies light winds and high relative humidities were conducive to fog formation but that fog actually occurred on about half the occasions when it was expected.He observed the cooling and drying-out of the atmosphere near the ground on a clear night and realized that the initial formation of fog appeared to depend upon a balance between these two processes. As he put it ‘‘ . . .if the dryness caused by the deposition of dew on the ground diffuses upwards at a greater rate than the coldness is conducted up- wards fog is less likely to form than if reverse conditions hold ”. He attributed the “conduction ” to turbulent diffusion and also suggested that “ . . .it is possible that the cooling due to radiation from the fog particles after a fog has started may have the effect of making it thicker ”.He discounted the effect of radiation before fog formation a view we now know to be wrong. However he laid the foundations for our understanding of the formation of radiation fog. (b) The next practical studies were made by Stewart who realized the need to measure simultaneously as many as possible of the parameters likely to be significant t Meteorological Office Bracknell Berks $ Atomic Energy Research Establishment Hanvell 209 FIELD STUDY OF RADIATION FOG in fog formation. From his observations he drew the following main conclusions. (i) Direct cooling of the lowest km of atmosphere by radiation and by convection (turbulent diffusion) were comparable.(ii) The surface deposition of water was comparable to that lost from the air by cooling. (iii) The lowest layers of atmosphere often reached and remained at saturation for up to a few hours before fog actually formed. Before saturation was reached however large fluctuations in relative humidity (not reflected in temperature observations) were usually observed. (iv) Once fog formed it usually did so within a few minutes. Subsequently its depth tended to increase in steps. Stewart also developed Taylor’s suggestion that fog droplets could produce their own contribution to radiative cooling. (c) Many investigations of the atmosphere near the ground have been made in conditions favourable for fog formation but with other objectives in view. Monteith noted that the rate of dew deposition decreased abruptly when the wind speed dropped below about 0.5 ms-’ at 2m above ground.The implication is that turbulent diffusion virtually ceased thus removing the primary mechanism for dew deposition. He also noted that “ saturation (within the grass cover below about 1 cm) was always followed by the formation of fog ”. This appears to conflict with Stewart’s observa- tion (iii) above and may reflect some significance of the state of the ground in fog formation. Rider and Robinson noted that “the change of temperature in the lowest layers of air is normally the small resultant of much larger tendencies due to changes in radiative and convective fluxes acting in opposite directions ”. They also noted a quasi-periodic oscillation of period of about 10min in temperature in the lowest 0.5 m on some radiation nights once at about the time of fog formation.In summary the occurrence of radiation fog depends upon a fine balance between the drying and cooling of the atmosphere near the ground. The drying-out is caused by dew deposition which generates a water-vapour gradient down which turbulent diffusion drives a flux of water vapour. The cooling is caused by a combination of radiation and turbulent diffusion. The strength of the turbulent diffusion is con- trolled by the wind field which is always a fluctuating quantity. These however are essentially qualitative conclusions which do not tell us why fog forms when it does nor what its evolution and structure will be given initial meteorological and aerosol information nor does it give any precise quantitative information on heat and water budgets and the role of latent heat release in these.3. THE METEOROLOGICAL OFFICE PROJECT This investigation is a collaborative field project between the Cloud Physics and the Boundary Layer Research Departments of the Meteorological Office and the Aerosol Group of the Health Physics Department A.E.R.E. Harwell. The first exercise was carried out at Cardington Beds. late in 1971 when the following para- meters were measured. CLOUD PHYSICS DEPARTMENT METEOROLOGICAL OFFICE (i) Net radiative fluxes at 2 9 and 37 m above ground using Funk net flux radio- meters (F2, F,,F3,). (ii) Downward flux of radiation at 1 m using a Linke-Feussner (directional) radiometer (&).(iii) Fog top detector and thermistor (for temperature profile up to 300m) on 700ft3 balloon. (iv) Continuous record of temperature at surface and 2 m (To,Tz). (v) Continuous record of dew-point at 2 m. (vi) Spatial and size distribution of fog droplets using holography at 1 m. W. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 211 BOUNDARY LAYER RESEARCH UNIT METEOROLOGICAL OFFICE (vii) Wind speed measurements at 2 4 8 16m (Uz, U,,W,,UI6).(viii) Wind direction measurements at 16m. (ix) Soil flux measurements at depths of 6 and 15 cm. (x) Deposition of moisture at surface using a lysimeter (So). (xi) Tempera-ture measurements at 4 8 16 m at 2-min intervals (T4, T8,T16). (xii) Tethered balloon ascents at 6-h intervals giving temperature dew-point and wind speed to 1 km.HEALTH PHYSICS DEPARTMENT A.E.R.E. HARWELL (xiii) Visibility at Im (Vl) with a transmissometer and at 5m (Vs)with a nephelo-meter. (xiv) Liquid water content using an impinger. (xv) A cloud condensation nucleus counter. (xvi) A cascade impactor for drop size distribution. (xvii) Air chemistry sampling equipment. The meteorological instrumentation used to make these measurements is in general well established. Special arrangements had to be made to keep the polythene domes protecting the detector surfaces of the radiometers free from moisture. The construction and operation of the radiometers is described by Funk.6 The aerosol instrumentation included some relatively novel features particularly the use of holographic techniques for obtaining 3-dimensional " snapshots " of the spatial distribution and size of fog droplets (above about 5 pm radius) within a volume of about 500cm3.A description of this technique has been published by Pavitt Jackson Adams and Bartlett.7 Drop-size distributions down to about 1 pm were also obtained by impacting fog droplets on thin plastic foils coated with gelatin as described by Garland.8 The fog top detector consisted essentially of a hot-wire detector which evaporated fog droplets in an air-stream drawn over it by a pump. The resulting change of resistance in the detector element is converted to frequency change and transmitted to a ground receiver using standard electronic techniques.The instrument was mounted on a tethered balloon which was moved up and down through the fog top. The cloud condensation nucleus counter was developed at Harwell from a thermal diffusion cloud chamber and maintained supersaturations of up to I % in an airflow of 10 cm3 s-l. Droplets formed on cloud nuclei in the chamber scatter light from a narrow collimated beam to a photomultiplier and the resulting pulses are counted automatically by a specially designed electronic counter. The transmissometer consisted of a collimated receiver and projector separated by about 30 m. The integrating nephelometer consists essentially of a photomultiplier which detects the amount of light scattered in a small volume of the atmosphere illuminated by a flash lamp. The chemical sampling of the atmospheric aerosol was obtained by drawing air at about 0.3m3 min-l (but 0.01 m3min-l for gaseous sampling) through an area of a filter paper tape.The paper tape is moved forward once per hour. Further details of the samplers and analytical techniques are described in Eggleton and Atkins." 4. RESULTS One good case study was obtained on 7 Dee. 1971 and some account of this is given here as it illustrates the wealth of information which can be obtained from a project of this type and it has in our view served to bring some ofthe main problems into sharper focus. FIELD STUDY OF RADIATION FOG (a) THE RADIATION FOG OF 7 DEC. 1971 A sheet of stratocumulus cloud covered the observing site until 0330 GMT when a complete clearance of cloud occurred.Fog began to form soon after 0400 soon thickened and persisted until its rapid dispersal at 1030. Its depth never exceeded 40 m and for most of its duration was 15-25 m deep. Wind speeds within the fog were l.Ok0.5 m s-I until shortly before dispersal when there was a steady increase to 2-3 m s-l. The “ life ” of the fog appeared to consist of two major phases-an “ optically thin ” phase (phase I) followed by an “ optically thick ” phase (phase 11). The main phases can be subdivided into further identifiable phases. The transition between each phase usually lasted a few minutes. Table 1 gives a survey of the development of the fog. The ‘‘ optical thickness ” refers to the infra-red transmission properties of the fog in a vertical direction.TABLE 1.-HISTORYOFFOG DEVELOPMENT phase period remarks Ia 0400-0430 Layer of ground mist 1-2 m deep. Surface inversion begins to develop. I Ib 0430-0645 Visibility at 1 m fluctuates between 100 and 200 m until shortly before 0600 optically when it decreases to 50-100 m. Depth thin fog of fog fluctuates between 10 and 40 m. Surface inversion about 10 m deep by end of period. I1 a 0700-0845 Inversion lifts off ground and settles near 20 m taking the fog top with it. Sunrise at 0755. I1 b 0900-1000 Inversion and fog top lifted a further [ optically 5-10 m. thick fog I1 c 1000-1030 Dispersal phase. Gradual thinning followed by rapid dispersal. Freshening surface winds. (b) TEMPERATURE AND DEW-POINT Fig.la shows a temperature-time cross-section for the lowest 60 m of atmosphere based on 20-min means from (iii) (iv) and (xi) of the list of measurements. The vertical scale is linear in Jheight in order to offset undue cramping of isotherms near the ground. There are three main cooling events the first was associated with the sky clearance and onset of phase I; the second was associated with the transition from phase I to phase I1 when the surface inversion lifted off the ground; and the third was associated with the transition from phase IIa to phase 116. The major heating event occurred during the dispersal phase (IIc). There were also lesser but marked heating and cooling events during the fog period e.g. the heating in the lowest metre at the onset of phase 11.The atmosphere at 2 m became saturated at about 0400 and remained saturated during the rest of the period. Balloon measurements made at 0505 suggested that the atmosphere was saturated up to at least 100 m during this period. w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 213 (C) WJND Fig. lb shows a wind speed-time cross-section for the 2-16m layer of atmosphere also based on 20-min means. The wind direction at 16m is also shown. There is a significant association between wind minima and cooling events. There is also some (b) 0400 0600 0800 1000 time (GMT) FIG.1.-(u) Temperature-time cross-section based upon 20 min means of To,T2 T4 Ts,T16and observations of temperature up to 60 m made at irregular intervals with a balloon-borne thermistor.The ordinate is linear in ,/height. Full lines are isotherms at intervals of 1°C. Dotted lines are approximate isopleths of local heating and cooling rates at intervals of 2"C/h. Observations of fog top height H maximum heating zone ; C maximum cooling zone. (b)Time cross-section of wind speed based upon 20-min means of wind speed at 2,4,8,16 m. The ordinate is linear in log (height). Full lines are isotachs at intervals of 0.2m s-I. Uniform separation of isotachs in the vertical indicate regions of log-linear wind profile. The dotted lines indicate the approximate field of gradient Richardson number between 2 and 16m. tendency for wind minima to be associated with wind veer. It follows that wind minima also occurred during the periods of fog development (transitions from phase I to 11 and IIa to IIb).The shape of the wind profile does not in general conform to a log-linear shape although there is (except for short periods) a general increase of wind with height. Wind speed averaged about 0.8 m s-l at 2 m increasing to 1.3 m s-l at 16 m. (d) TURBULENCE The wind and temperature structure of the atmosphere near the ground when averaged over about an hour is a function of and can therefore be used to give FIELD STUDY OF RADIATION FOG approximate information on the statistical properties of the turbulent field. For instance it should be possible to infer the magnitudes of the turbulent fluxes of heat water vapour and momentum. In the lowest 50-100m it is usually found (and assumed) that these fluxes are constant with height and would not therefore change the quantity of heat momentum and water vapour contained in a given layer.This is usually known as the " constant flux "layer. However in the case under discussion when light winds and very stable conditions are prevalent the turbulent field becomes very weak and may in fact become intermittent. The profiles of wind and temperature (particularly wind) become so irregular and variable that it is no longer possible to fit them to any existing model of low level turbulence. Direct observations of turbulent fluxes are difficult if not impossible to make and so the exchange coefficient can only be estimated from indirect methods. In fig. Ib isopleths of the gradient Richardson number is shown.Basically this represents the ratio of buoyancy forces (which inhibit vertical displacements of the atmosphere) and inertial forces (which tend to overturn the air through wind shear). When this number is less than about 4,turbulence will be generally prevalent; when it is greater than about unity turbulence has probably ceased throughout most of the volume and is confined to intermittent patches. Also over half the total wind change with height is confined below 2 m which is probably the depth of the " constant flux " layer on this occasion. The order of magnitude of the exchange coefficient can be obtained using scale analysis based on Fickian diffusion law e.g. AT/At = KAT/(Az)~ (4.1) where AT/At is a characteristic heating rate (with the radiative contribution removed) Az is the characteristic vertical dimension over which AT is observed to occur e.g.AT/Atx3°C h-l. A change of AT of 3°C is observed typically over a depth of 3-10 m which gives KNN m2 s-l. This gives a value on which to base numerical model- ling of the case. (e) FOG STRUCTURE Fig. 2a shows the approximate time variation of the visibility at heights of 1 m (solid line) and 5 m (dashed line) above the ground. This evidence taken together with the fog top and the radiation observations (Fig. la) suggest that in phase I the opacity of the fog decreased rapidly with height and the top was ill-defined and var- iable in height. In phase 11 the fog top became well-defined and identified with the radiation inversion.No obvious correlation between visibility and other meteoro- logical parameters has been found. The radiation observations show that radiative cooling (HR in fig. 3) was generally small in phase I but became large in phase 11. Hence the terms " optically thin " and " optically thick ". During the latter phase the fog top lay between the upper two radiometers and HRin this layer (the " upper layer ") remained high throughout the phase. In phase IIb the layer appeared to be in radiative equilibrium (HRx0) suggesting that the fog above this layer had become optically opaque thus shielding the lou7er layer from ftirther cooling. The drop-size distribution (fig. 2b) shows the development of a secondary peak in droplet sizes in the radius range 5-10 pm during phase 11 and is mainly responsible for the increase in liquid water concentration to about 0.2 g m-3 in this phase.Both the liquid water concentration and the optical extinction coefficient can be explained in terms of the observed droplet population. The number of cloud condensation nuclei (30-100 ~m-~) observed at 0.8 % supersaturation was of the same w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 215 order as the total number of droplets in the large droplet peak. The infra-red extinction coefficient in a vertical direction could be approximately inferred from the radiation observations. In phase Ira this agreed roughly with that expected if the drop size distribution and liquid water concentration observed near ground level persisted throughout the depth of the fog.The holography results are summarized in fig. 4. The co-ordinates of each identifiable drop within a volume of 10cm3 was tabulated and for each drop the distance of its nearest neighbour was obtained and a histogram constructed. Two of the histograms shown are taken from the fog sampled a third from hill cloud on a mountain in Wales and the fourth represents the results of a Monte-Carlo-type \ I i-, ,I' j -nephelometer(5m.l loo 50 t I I I 0400 0600 0800 1000 time (GMT) FIG.2.44 Time plots of transmissometer(Vl)and nephelometer (Vs). Vlis taken from a contin- uous trace. Vs is taken from spot observations at variable intervals. (6)The histograms are drop- size distributions with the equivalent total liquid water content and time of observation written on each histogram.A 2 .................. ."a" t2 u 80 -2 --A -0400 0600 0800 1000 time (GMT) FIG.3.-Observed heating rates averaged over upper (9-37 m) and lower (2-9 m) layers. -total heating rate HT ; --,radiative heating rate HR ; ..... non-radiative heating rate HN. FIELD STUDY OF RADIATION FOG numerical experiment which simulated the “nearest neighbour ” computation shown above except that the space co-ordinates of each droplet was chosen at random. The difference between the random experiments and the observations is large with discrepancies amounting to an order of magnitude for drop separation less than about 0.5 mm. In fact on one sample of 600 drops two droplet pairs separated by 50-100 pm was observed.The probability of this occurring at random appears to be of the -I I 0.2 0.4 0.2 distance /cm FIG.4.-Histograms of distance to nearest neighbour (a)radiation fog sample at 0500 GMT 609 drops ; (b)radiationfog sample at 0647 GMT 536 drops ; (c) hill cloud sample 639 drops ; (d)mean of 10 random samples of 609 drops each in volume identical to (a). This histogram is also super- imposed on (a)as a dashed line. order of 1 in lo9. The implications of this clustering of droplets for fog investigations in particular and cloud microphysics in general cannot at present be assessed. It seems possible however that this represents some aspects of the interaction of turbu-lence with droplet growth on scales at which dissipation of turbulent kinetic energy by viscosity becomes important.(f) CHEMICAL SAMPLING This was done at a site some 800 m from the main investigation site and was mostly out of fog. The results are summarized in fig. 5. The ion concentrations showed a more or less steady decrease during the period of the fog particularly the nitrate ion. This was followed by an abrupt increase in all concentrations following the dispersal of the fog. There was also a temporary increase at 0700 to 0800 just after the transi- tion to phase 11. The large chloride concentration so far inland suggests an industrial source. The anion-cation balance shows roughly 30 % excess anions throughout (except for 0600-0700) indicating the presence of moderate amounts of some cation other than ammonium.The sulphur dioxide concentration dropped prior to fog formation fluctuated about an ill-defined minimum during the fog period and increased again after fog dispersal. These changes probably reff ect changes in vertical mixing which appears to be a minimum during the fog period although it may also w. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 217 reflect the scavenging action of fog droplet deposition to some degree. No chemical analysis of fog water was undertaken on this exercise. (9)HEAT AND WATER BUDGET The net flux of radiation was measured at levels of 2 9 and 37 m. These levels defined two layers an upper and a lower layer. The measured radiative heating HR and observed total heating rate HT of these layers are shown in fig.3. The difference ... . .........-.... .. . ...... . .-. . . . . . ,. ......... All negative ions NH so;-0.3 c1-~ 0.1 -NO; I I I I (HR-HT) = HN,where HNmust be attributed to convergence of eddy heat flux or to latent heat release or to both. The principal feature of fig. 3 is the overall tendency for the radiative cooling to be greater than the observed cooling (HNpositive)-an observation also reported by Rider and Robinson. The cooling of the lowest 50 m or so of an initially-saturated atmosphere during the period of interest implies a removal of an amount of water vapour by condensation which can be directly estimated by using the Clausius-Clapeyron relationship and is compared with the lysimeter data in table 2 below.While the overall totals of condensed water are roughly in agreement the totals over shorter periods are not. The liquid water content of the fog accounts for only a few per cent of the total. The rate of water deposition on the surface is normally taken as a measure of the FIELD STUDY OF RADIATION FOG latent heat fluat the surface. This assumption cannot be made in fog as much of the water may be condensed as fog droplets (thus releasing its latent heat directly to the atmosphere) and then water is transferred to the ground by some mechanism other TABLE 2.-ESTIMATES OF CONDENSED WATER condensed watcrlg m-2 paid (approx.) cooling lysirneter oQoeo630 50 20 06304730 20 10 0730-0830 small 25 0830-1OOO 5 10 - - 75 65 than dew deposition-particularly in the period after 0730.The observed deposition velocity (defined here as the rate of deposition of water/liquid water concentration at 1 m) is about 2 cm s-l. Gravitational settling can only account for 0.5-1 cm s-* of this. (h) QUA SI -PER I0 D I C 0sCI LLA TI0N S Another unexpected result was the observation of intermittent periods of marked oscillations of 10-12 min period in several of the meteorological parameters measured notably wind speed surface temperature and downward radiation intensity (from directional radiometer). Similar oscillations appeared occasionally in temperature at high levels apparently when these levels were lying in the radiation inversion. The traces of these elements are shown in fig.6. A possible interpretation of these fluctuations gives some account of the observed phase relationships. The oscillations are attributed to gravity wave propagation and the phenomenon can be regarded as a demonstration of the varying balance between radiation and turbulence-the latter being controlled by the wind speed oscillations while the former is influenced by a sympathetic oscillation of the fog depth. DISCUSSION The principal results requiring explanation are (i) the observed radiative cooling was in general greater than the observed total cooling in the lowest 40 m of atmos- phere. (ii) Lulls in wind were accompanied by maxima in cooling while major lulls coincided with periods of significant fog onset and development. (iii) The water condensed on cooling appears to have been mainly deposited on the ground.The water content of the fog was always a small fraction of the total water condensed out. (iv) The presence of quasi-periodic oscillations. (v) The clustering of droplets in space. Some of these features have been reported by earlier workers. They all point to the fundamental role played by turbulence and show that the lack of a satisfactory account of the water budget remains a central problem for on this rests an account of the heat budget and the role that microphysics plays in fog development. The probIem may be examined by considering the conventional one-dimensional equations for the heat and water budget. These are Heat w. T. ROACH R. J. ADAMS J.A. GARLAND P. GOLDSMITH 219 Water vapour Liquid water = +-)+c, a aw at aZ az (5.3) Where t = time z = vertical co-ordinate T = temperature p = air density c = specific heat at constant pressure F = net flux of radiation K = exchange coefficient (assumed the same for heat water vapour and momentum) L = latent heat of vapor-ization of water C = rate of condensation per unit mass of air x = humidity mixing ratio 11’ time (GMT) FIG.6.-Time plots for selected periods of the following parameters To,Tz,T4,Ts,T16, FLFbased on spot readings at 1-min intervals. U,,U4,Us,U169 D16 based on 2-min runs of wind. Eqn (3.1) represents local rare or cnange or temperature aue to raaiative neating turbulent diffusion and condensation. Eqn (5.2) and (5.3) represent local changes in the gaseous and liquid phases of water due to turbulent diffusion and condensation.Gravitational settling is ignored. First one may try and establish a condition whereby the atmosphere is maintained exactly at saturation with no liquid water present and then to study deviations from this. We do this by assuming the condensation term to be zero and eqn (5.3) also FIELD STUDY OF RADIATION FOG becomes identically zero. In this case x( = x, the saturation mixing ratio) is a function of T only through the Clausius-Clapeyron relationship hence axslat = xaT/at; ax,/az = xaT/az (5.4) where X = dx,/dT. Substituting eqn (5.4) into (5.2) and combining with (5.1) leads to where represents radiative heating rate. Eqn (5.5) can only be balanced when 9is positive since the terms on the right-hand side are essentially positive.But ,%? is observed to be negative; physically this means that because the mixing ratio has been taken as a monotonic function of temperature an eddy flux convergence of sensible heat is incompatible with an eddy flux divergence of water vapour. Thus the condensation and latent heat terms have to be re-introduced and condensation rates of the order of 1 g m-3 h-l are needed to balance the equations for typical values of the relevant parameters. Since the liquid water content of the fog is never greater than about 0.2 g IT^-^ this implies that the " life " of an individual droplet is of around 10 min before arriving at the surface. While the surface inversion is on the ground this balance can reasonably be accomplished by dew deposition but in phase 11 this seems to be no longer possible since the mechanism for dew deposition is removed.Further cooling should there- fore condense water directly into the atmosphere and produce a very dense fog. There is some indirect evidence that this occurred at the top of the fog in phase 1Ib as discussed in §3(e). This still leaves unexplained the increased rate of water deposition on the surface during phase 11. Some ideas may be worth investigating. (i) During this phase 11 surface moisture was in the form of frost. Above the surface the atmosphere satur- ated with respect to water would be supersaturated with respect to ice so that it is possible that a gradient of water vapour in the lowest metre may have been induced which was sufficient to maintain the observed deposition rate in the form of frost.(ii) Impaction of fog droplets on grass blades. Both these methods would quickly dry out the lowest few metres of atmosphere so that local replenishment is required. This may be provided by radiative cooling. It may be significant that the rate of deposition dropped sIowly after transition from phase IIa to phase IIb ; in phase IIa the radiative cooling was about 4"C/h but dropped to zero in phase 116. Thus it is not possible to state what determines the total liquid water content of the fog or why it develops when it does without considering the role of microphysics. The balance required to keep the atmosphere within 0.1 % of 100 % relative humidity corresponds to a temperature-dew point difference not exceeding about 0.02"C-a change which will take place in about 20 s with normally observed rates of heating or cooling in the lowest few metres of the atmosphere under these conditions.This balance seems to be too fine in view of the considerable fluctuations in wind and therefore of turbulent diffusion which take place and it seems likely that an already- present droplet population may exert the main control on the relative humidity by release or absorption of latent heat as required. W. T. ROACH R. J. ADAMS J. A. GARLAND P. GOLDSMITH 221 (a) ROLE OF ADVECTION The approach both in designing the observational programme and in the discussion has been deliberately one-dimensional.However this is not to deny the existence of horizontal inhomogeneities which must be considered in relation to the scale on which the relevant processes operate. It is a common observation that radiation fog forms more or less simultaneously over an area of mesoscale dimensions (say up to 100 km) implying that the vertical structure of the atmosphere is the main factor in the development of fog. On the scale of hundreds of metres to km,on the other hand there are always considerable spatial fluctuations of fog structure for which variations in the nature and slope of the local terrain are at least partly responsible and will produce mesoscale circulations which are likely to control temporal fluctuations in parameters observed at a fixed point over time intervals of up to a few minutes.In the absence of two-dimensional measurements it becomes increasingly likely that observed changes are due to advection rather than development the shorter the period over which the change takes place. A useful time scale is defined by D/U,where D is the depth of the fog and U is the mean wind speed in the fog. (In this case-study this is about 30 s). Providing a change takes place over a time t$ D/U,then it is reasonable to ascribe it to development. 6. CONCLUSIONS The development of fog is roughly controlled by a balance between radiation which encourages fog and turbulence which appears to inhibit it while fine control is exerted by a balance between the humidity and the droplet population.Quantitative details of these balances must await further resolution of the details of the water balance. One result which may prove useful in assessing future prospects of local forecasting or modification of fog is that given a saturated atmosphere and radiative cooling rapid development of fog is likely to occur if the wind speed drops below about 0.5 m s-I at 2 m above ground. Any conclusions which are based on one case study must be tentative but these results do demonstrate the complexity of the competing and interacting physical processes which result in meteorological fogs. Field Projects of this type involve a large number of participants and we grate- fully acknowledge the support of all our colleagues. This paper is published by permission of the Director General of the Meteorological Office.K. H. Stewart Air Ministry Met. Res. Cttee (1955) paper 912 43 pp. K. H. Stewart Air Ministry Met. Res. Cttee (1957) paper 1074 26 pp. G. I. Taylor Quart. J. Roy. Met. SOC.,1917 43 241. J. L. Monteith Quart. J. Roy. Met. Soc. 1957 83 p. 322. N. E. Rider and G. D. Robinson Quart. J. Roy. Met. Soc. 1951 77 375. J. P. Funk Quart. J. Roy. Met. Soc. 1962 88 233. 'K. W. Pavitt M. C. Jackson R. J. Adams and J. T Bartlett J. Phys. E 1970 3 971. J. A. Garland Quart. J. Roy. Met. Soc. 1971 97 483. J. A. Garland and J. B. Rae J. Phys. E 1970 3 275. lo A. E. J. Eggleton and D. M. F. Atkins A.E.R.E. R 6983 (1972).

ISSN:0301-5696    

DOI:10.1039/FS9730700209

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Predicting the Concentration of Effluent Material within a Plume Emitted from a Tall Chimney BYD. J. MOORE Central Electricity Research Laboratories Leatherhead Surrey Received 23rd November 1972 The rates of formation of aerosols and the visual appearance of chimney plumes (including the effects of condensation of water vapour) both depend upon the dilution of the effluent gases. This dilution differs from that predicted by conventional dispersion formulae in that these latter refer to time mean concentrations whereas what is required is the dilution at any given instant in time as the plume travels downwind. The instantaneous dilution near the source depends on the turbulence induced by the plume’s movement through the atmosphere rather than the dispersive properties of the surrounding atmos- phere at the plume level.A theoreticallempirical model which has been developed to predict the trajectory of hot chimney plumes also predicts this instantaneous dilution. Dilutions calculated by this method in different conditions of wind speed and atmospheric stability for various plant emission characteristics are tabulated and compared with values obtained from field measurements. 1. INTRODUCTION If one is concerned with the concentration of material at ground level resulting from the emission from a source which is some distance away the normal practice is to sample the material over a period of time. It is then possible with the aid of various hypotheses about the nature of the dispersion of the material and possibly the rise of the plume material above the discharge point due to its buoyancy and initial vertical momentum to come to a reasonably satisfactory understanding in physical terms of the observed concentration.There are however certain aspects of plume behaviour including the rise of the plume the visibility of the plume and rates of chemical reactions within the plume which depend not on the time-averaged concentrations but on the concentration within the plume at various distances downwind at an instant in time. The time- averaged plume dimensions are the result of the meanderings of the instantaneous plume due to the large scale turbulence in the atmosphere and may bear little relation to the instantaneous dimensions. Furthermore the dilution of any large emission of material certainly within the first few hundred metres of its leaving the source is almost entirely due to its motion relative to the atmosphere and the intense mixing produced by this relative motion.Thus any information which is based on observa- tion of the dispersion of small releases of material over extended periods of time such as the Porton work reported by Sutton is irrelevant to the problems enumerated above. In the various attempts to explain the observed trajectories of buoyant plumes over the first kilometre or so of their path observations of the instantaneous dimen- sions have been made either from photographs or from lidar 3s traverses of the plume. These have in general shown that the plume diameter in so far as it can be determined from the irregular shape of the plume elements is on a given occasion 222 D.J. MOORE 223 proportional to the height of rise above the source. For a plume with substantial heat emission (i.e. several MW or more) this relation appears to hold for hundreds of metres and perhaps even to over 1 km on some occasions.2 This sort of behaviour is consistent with the assumption that the rate of entrain- ment of ambient air into the plume elements is equal to the product of the surface area of plume element exposed to the ambient air times the velocity of the plume relative to the ambient air. That is in general to the vertical velocity of the element. The constant of proportionality implicit in the above relationship is in fact a constant for a given plume element only; its value changes from element to element in a way which is not fully understood but appears to be determined by such factors as the angle of attack of the wind at the stack top the ratio of the wind speed to the effiux velocity and the initial buoyancy and its relation to wind forces on the emerging plume.Despite the complexity of the problem a number of investigators have developed models which give a very fair representation of the plume trajectories over distances out to 1 km or more. The principal differences between the models concern the idealised geometrical forms assumed for the plume elements e.g. bent-over chains of spherical puffs 8p and the expression for the relative velocity which some- times includes additions to the vertical velocity with various weighting factors.'O* '' The other source of difference is the assumptions made about the way in which the atmospheric turbulence eventually assumes the major role in the dispersion when the plume elements have become so diffuse that their physical properties (i.e.turbulence and density) are no longer distinguishable from those of the surrounding air. A comprehensive test of a trajectory equation based on the recombining plume model has been shown to give mean errors of around 10-15 % in determining plume heights over a wide range of meterological conditions distances downwind and plant capacities. In this short paper it is not intended to explore in any depth the difference between the various plume models.They are sufficiently similar for the differences between them to be relatively small compared with the differences between concentrations calculated from their basic assumptions and concentrations calculated for an inert plume model. Here we shall show where the use of such a model which assumes that the plume behaves as though it were no different from the surrounding atmosphere as far as dispersive properties are concerned will lead to serious over estimates of " in-plume " concentrations. 2. THE INERT PLUME We consider the dimensions at any instant in its time of travel of an element of the plume which contains material which has been emitted into the atmosphere without in any way changing its dispersive properties. For an emission of any size this is clearly impossible and furthermore if we consider a true point source with a finite emission the concentration at the source is infinite.In practice stack emissions are usuaIly diluted with air or at least nitrogen so that the material is apparently emanating from a point source some distance upstream of the actual source. The familiar gaussian distribution of material is in fact due mainly to the meander- ings of the plume axis over the period during which the effluent is being sampled. Most truly instantaneous traverses of the plume e.g. by laser rangefinder indicate a "top-hat " distribution of material but then the traversed plumes have not been inert. Some attempts to calculate instantaneous dimensions from smoke puff photographs (e.g.by Gifford 12) have made assumptions about the distribution of material in the plume. EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES If we consider that the instantaneous plume has a " top hat " distribution of material that the axis of the time-average plumes remains within the instantaneous plume for most of a given sampling period but points removed vertically or in the cross wind direction are out of the plume for an increasing proportion of the period as one moves away from the axis then one could represent the instantaneous concen- tration by the axial concentration of the meandering time-average plume. This would give an underestimate of the instantaneous plume concentration because the time-average axis would occasionally be out of the plume.However for purposes of comparison with the self-diluting plume models it will be assumed that the axial concentration in the time-average plume for sampling times of several minutes is a reasonable estimate of the average concentration within the plume elements. Such concentrations as functions of distance from the source or time of travel through the atmosphere may be readily estimated from the data presented e.g. by Pasquill l3 and reproduced in convenient graphical form as in " Meterology and Atomic Energy ". Following Pasquill we write an expression for this axial concentration C1 = Q(xf' q)/(27cxp+qU0,aYl) where C1 is the axial concentration (units m-3) at distance x/m downwind. Q is the rate of emission of the material considered (units r1).x1 is the distance down- wind at which the vertical and cross wind concentration distributions have standard deviations crzl and crY1 respectively (m).0 is the mean wind speed (m s-I). p and q are numerical constants whose values lie between 0.5 and 1.0. If we wish to sub-stitute time of travel t in place of distance x then we replace x by Ot in eqn (2.1). Eqn (2.1) may be written in the form where B = 2nazl~,,,/(x~f4) and may be regarded as a constant on any given occasion but whose value will vary with meterological conditions. Qh = the rate of heat emission in MW. Expressing the concentration in the form given by eqn (2.2) is convenient for comparison with the concentrations deduced for buoyant plumes which follow in section 3 below. 3.BUOYANT PLUME For the sake of simplicity we consider a plume of material with the same density at ambient temperature and pressure as the ambient air emitted into an atmosphere in which the potential density (i.e. the density referred to a standard pressure) is not changing with height. The simpler plume models then indicate that the concentration of material within a plume element is given by where C2 is the concentration in a plume element which has risen a height z above the source. rn is a numerical constant with a value between 2 and 3 depending on the assumed nature of the plume elements (i.e. 2 if they are conical or cylindrical 3 if they are spherical or any other closed configuration). A may be a constant if the heat content of a plume element is assumed to remain invariant with distance from the source or may be a function of distance if the heat content of the element is changing with distance.Its dimensions are mz-m. It may be a function of the D. J. MOORE wind speed. The various expressions forplume rise in the above assumed meterological conditions are of the form l8 z = AIQLxs//U (3.2) if one ignores the initial momentum of the plume and assumes that the rate of entrain-ment is proportional to the vertical velocity. Here Y is a numerical constant equal to $ for the two dimensional (conical etc.) models and + for the 3-dimensional (spherical etc.,) models. s is a numerical constant with values between 3 and $-and Al is a parameter equal to (g/p,CpO)'A2where g is the acceleration of gravity (m s-~),Cpis the specific heat at constant pressure of the effluent (MJ kg-l K-l) pe is the density of the ambient air (kg m-3) 8 is the absolute temperature of the ambient air reduced to standard pressure (K) A2 is a parameter of dimensions (m ~-~)-(~'-')m(~-('+~)) which represents the effect of such factors as the initial length of plume material within a plume element and the dependence of the rate of entrainment factor on the wind speed etc.Substituting for z in eqn (3.1) from eqn (3.2)we arrive at c2= (Q/Q~)Q;-~~/(A~x~~D~ (3.3) -") where A = AAY. The buoyant plume model used above would estimate the maximum dilution due to relative motion at a given distance downwind. If the atmosphere were stably stratified (i.e.the potential density were decreasing with height) then the plume would rise less rapidly than eqn (3.2) indicates the difference becoming more marked as the distance from the source increased. For practical purposes it would be sufficient to assume that the plume followed eqn (3.2) out to some distance xT where X is proportional to the stability parameter ((g/p,D2) I (dpe/&) 1 )* and is roughly equal to 120 U m for isothermal conditions in light winds. If one is concerned with a plume of gas with a density at ambient temperature and pressure which differs appreciably from that of air then Qhin eqn (3.1) (3.2) and (3.3) may be replaced by the term (VApCJI),where is the total volume rate of emission of the effluent (m3 s-l) (i.e. of all the gases being emitted from the stack not just the material being considered) Ap is the difference in density between the ambient air and the effluent (kg m-3).4. COMPARISON OF INERT AND BUOYANT PLUME MODELS The ratio of the plume concentrations calculated from the inert and buoyant plume models mentioned above may be obtained from eqn (2.2) and (3.3) and is equal to C1/C2 = QcrA3/(Bx(~+~ -ms)Um). (4.1) If we wish to use the dilution given by the buoyant plume model out to a distance xEwhere the value of C1/C2is equal to 1 and the inert plume dilution beyond this distance then xEis given by xE = Q~mr/(P+q-ms))(A31B)(l/(P+q-ms))/V(m/(P +4-ms)). (4.2) The equivalent time of travel to xE,tE,will be tE = xE/u= Q~~r/(p+q-ms))(A3/B)(l/(p+q-ms))/~(m(l -s) +~+dl(p+q-ms).(4.3) EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES Eqn (4.2) and (4.3) are valid only if A3 is not a function of distance from the source and/or wind speed. In some of the models e.g. the recombining plume model A3 is in fact assumed to be proportional to D and inversely proportional to x. In this case t = (A,lB)4Q~D-9 where A3 = A,D/x. Although expressions like (4.3) appear rather complicated their interpretation is fairly straightforward. All the models indicate that the term in the denominator of the exponents is small ie. ms is only slightly smaller than pfq (or (1+p+q) in the case of the recombining plume model). The term mr is however a fairly large fraction and the numerator of the exponent of is about 2. This means that tE varies rapidly (i.e.as the third or fourth power) of Qhand even more rapidly (i.e. as the ninth or greater power) of l/o. Hence for practical purposes there are wide ranges of low wind speeds and high heat emissions where the buoyant plume model is valid for calculating concentrations while the dispersion or inert plume model may be used in strong winds for most sources and in all but the lightest winds for very small sources. Since by the same reasoning eqn (4.1) indicates that C1/C2is a very slowly varying function of distance from the source (or time of travel) it follows that in border-line cases either model may be used over a considerable range of time or distance without serious error. The precise values of plume concentrations for given values of 0 and Qh will depend on the values chosen for A3 or A4 and B and the parameters p q rn r and s i.e.on the plume rise and dispersion models used. Table 1 shows some values of the concentrations calculated from eqn (2.2) using values of p+q and B consistent with plume dimensions at seueral kilometres from the sources and from eqn (3.3) using the plume rise equation of Briggs C2(BR) and Lucas l6 C2(LU) (see Pasquill 15) modified to take account of distance down- wind but not of stability or atmospheric turbulence.'* The plume rise model has relatively little effect on the calculated concentrations but the dilutions in light winds are very much greater than with the inert plume model when one is considering the large heat sources even though the dispersion parameters used are appropriate to unstable meteorological conditions.In very stable conditions the buoyant plume dilutions would remain effectively constant after something like 120 m or so of travel (i.e. 120 s in a 1 m s-I wind). Even so the plumes are much more diffuse than the inert plumes; consequently serious errors could be made both in estimates of plume visibility and in chemical reaction rates in plumes if the inert models were used in these sort of conditions. Taking 1 m s-I as the worst condition concentrations at 120 m downwind would be 1652 and 1181 p.p.h.m. for the C2(BR) and C,(LU) models respectively. Atmos-pheric dilution might be considered negligible in these conditions and the plumes would then drift downwind with little further dilution.Size of source would have comparatively little effect since eqn (3.3) shows C,varies as a small power of Qh but the concentration is directly proportional to the S02/MJratio. 5. COMPARISON WITH EXPERIMENTAL DATA Comprehensive data on peak concentrations of SO2 at several km from the Keystone Power Plant are available. The ratio of S02/MJ was about 0.8 times that assumed in table 1 and the plant was emitting heat at an average rate of 100 MW D. J. MOORE during the period of the measurement (1967-69).20 C2(BR) and C2(LU)would be about 0.8(+)* and 0.8($)* times the concentration at the same time of travel for the 300 MW source in table 1 i.e. 916 and 717 p.p.h.m. for 120s travel at 1 ms-'. With these emission conditions the highest concentration observed in the plume was in fact 767 p.p.h.m.at 4.8 km downwind on 30th October 1967. At 10 km the con- centration peak was 352 p.p.h.m. Winds as light as 0.6 m s-l were recorded by pilot balloon ascent on that day. Pasquill Category F would give a concentration of 1940p.p.h.m. and Category E about 850 p.p.h.m. at 4.8 km and 707 p.p.h.m. and 296 p.p.h.m. respectively at 10 km. It appears therefore either that Category F type of dispersion is never observed from an elevated plume (or observed so seldom that several years' measurements TABLE1.-CONCENTRATION (p.p.h.m.) vol/vol SO2 FROM A SOURCE EMITTING 0.008 m3 (KEDUCED TO s.T.P.) OF SO2PER MJ OF HEAT EMITTED time CdUS) Oh CABR)'' 300 MW; CZ(LU)+ 0 1 m S-* CdST) 250 3342 621 472 954 930 500 1181 246 198 244 850 750 643 143 119 119 740 lo00 418 98 83 77 320 2000 148 39 35 25 610 u= 7ms-1 timc CI C2(BR) C2(LU) 250 352 324 290 500 125 129 122 750 68 75 73 lo00 44 51 51 2000 16 20 21 Qh= low* g= Ims-1 time CdUS) c*(BR); CZ(LU)+ CdST) 250 158 200 201 31 830 500 56 79 85 8 160 750 30 46 51 3 991 lo00 20 31 36 2 577 2000 854 C2values are calculated from the buoyant plume model using the following numerical values C2(BR) corresponds to the two-dimensional bent over cone type of plume model advocated by Briggs and others C2(LU)corresponds to the Priestley l7 type model of Lucas l6 and the recombining plume model of Moore 8s C2(BR) = Q/((0.426~)~nV), where z = 3.1 Qgx%/owhich with the assumed relation between SO2 and heat emission gives C2(BR) = 146 014Qh*0-f.t-3 C2(LU) = 3 ex/(16(0.3 13~)~n~') where z = 2.4Q4d/U which gives C2(LU) = 112 635Qtu-*t-* p.p.h.m.Taking Bxt = 2n(0.O8L*(7/U)*),l9C1was equal to 556 921 Qh/(t*u2j2L*)in unstable (US) conditions with L = 160 m for the large source; and L = 80 m for the small source.19 The Pasquill Category F values of a,,and cZwere used in stable (ST) condition^.'^ * The values of C,(BR) and C2(LU) at 120 m downwind in a 1 m s-l (i.e after 120 s travel) would be 1652 1181 532 and 503 p.p.h.m. in columns 3,4 10 and 11 respectively. These conditions would represent the minimum dilution at greater distances in the most stable conditions. EFFLUENT MATERIAL WITHIN CHIMNEY PLUMES fail to detect it) or that the extra dispersion caused by the relative motion has the effect of making the minimum observed dilution comparable with Category E at distances of around 5-10 km downwind of large sources.Unfortunately there do not appear to be any comprehensive " in-plume '' measurements made closer to the stack but the dimensions of the plume recorded by the various techniques described in section 1 above indicate that the concentra- tions predicted in table 1 by the buoyant plume models are more likely to be correct than the much higher concentrations predicted by dispersion models. 6. CONCLUSIONS The calculations indicate that for large heat source the dilution of buoyant plumes in light winds is much more rapid than the classical formulae would indicate.The effect is most noticeable in the early stages of the plume's travel because the plume's motion relative to the surrounding air is then at its greatest and the dilution effected by this relative motion far exceeds the diluting effect of the turbulence in the surrounding air. In very stable conditions most of the dilution probably occurs within a 100 m or so of the stack because the plume rise is completed in this distance. Further dilution will proceed at a very slow rate so that for practical purposes in-plume concentrations may be considered constant for several km after this initial rapid dilution. Even so concentrations at all distances out to 10 km would be less than those indicated by a simple application of the Pasquill Category F curves.In unstable conditions the dilution produced by relative motion is also greater than that produced by atmospheric turbulence in light winds close to the stack for large heat sources but the atmospheric diluting mechanism will become important at a much earlier stage than it does in stable conditions. When it is windy both models (atmospheric dilution and buoyant plume) give roughly the same dilutions out to several km from the source. The work was carried out at the Central Electricity Research Laboratories and the paper is published by permission of the Central Electricity Generating Board. The author is grateful to Dr. K. W. James and Mr. D. H. Lucas for helpful criticism. 0.G. Sutton Atmospheric Turbulence (Methuen London 1949). Tennessee Valley Authority Report Full Scale Study of Plume Rise at Large Electric Generating Stations (T.V. A. Muscle Shoals Alabama 1968). P. M. Hamilton Phil. Trans. A 1969 265 153. P. M. Hamilton Atmospheric Environment 1967 1 370. C. H. Bosanquet J. Inst. Fuel. 1957 30 322. R. S. Scorer Int. J. Air Pollution 1959 1 198. 'G. A. Briggs Plume Rise (U.S.A.E.C. Critical Review Series 1969). D. J. Moore Int. J. Air and Water Polution 1966 10 411. D. J. Moore Atmospheric Environment 1968 2 247. lo D. P. Hoult J. A. Fay and L. J. Forney J. Air Polution Control Assoc. 1969 19 585. G. Ooms Atmospheric Environment 1972 6 899. l2 F. Gifford J. Meteorology 1957 14 410. l3 F. Pasquill Meterological Mag. 1961 90 33. l4 Meteorology and Atomic Energy ed. D. Slade (U.S.A.E.C.1968). l5 F. Pasquill Quart. J. Roy. Meteorological Soc. 1972 97 369. l6 D. H. Lucas Atmospheric Environment 1967 1,421. C. H. B. Priestly Quart. J. Roy. Meteorological SOC.,1956 82 165. D. J. Moore Atmospheric Environment 1974 8 131. l9 D. J. Moore Adv. Geophysics-Turbulent Diflusion in Atmospheric Pollution ed. F. N. Frenkiel and R. E. Munn (1974). 2o Tennessee Valley Authority Large Power Plane Effluent Study Vol. 1 1967 and 1969 Vol. 2 1968 (U.S. Dept. of Health Education and Welfare 1970).

ISSN:0301-5696    

DOI:10.1039/FS9730700222

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. A. Arrowsmith (University of Birmingham) said In the experimental work on particle deposition Williams has measured particle sizes and concentrations after sampling with a probe of 1 cm diam in the 10 cm diam. duct. At the entrance to the probe the gas/particle flow will be influenced by the flow in the duct which will have component eddies of larger diameter than the probe. Also assuming isokinetic sampling the Reynolds number of the probe flow would be an order of magnitude less than that in the duct. Under such conditions for what lengths of the probe is the flow affected by the duct flow and thereafter it is possible that deposition may take place in the probe through mechanisms which are of a different nature or at least intensity to those which are the object of study.Dr. Ian Williams (Shell Res. Ltd. Chester) (communicated) In reply to Arrow- smith the measurements of interest in this experiment were the radial distribution of polydisperse droplets as a function of several parameters including the axial position in the duct. It has been shown that particle deposition is strongly dependent upon the Reynolds number of the flow and the particle size. For the two values of Re. no. considered the corresponding values in the probe were an order of magnitude less than in the duct ; this factor together with the short residence time of a droplet within the probe is effective in reducing deposition in the probe. Except near the duct wall the ratio of the fluid eddy diameter to the probe diameter is 1 this probably results in near laminar flow within the probe and subsequent low droplet deposition.A correction factor was obtained experimentally to take into account deposition within the probe. Twelve sampling probes each of 1.0cm i.d. and 0.5 crn id. respectively were used to sample an aerosol source of a known constant size distribution and concentration under similar dynamic conditions to those existing in the duct. A deposition factor was obtained as a function of droplet size fluid Re. no. probe diameter and probe length. This factor was applied to all subsequent experimental measurements. Alternatively it was possible to extrapolate the effect of the sampling probe to zero length and thus eliminate the effect of droplet deposition in the probe as a result.Prof. C. S. Kiang (Clark College Atlanta Ga.) said Is it possible to apply the experimental technique of Carabine and Moore to study the initial aerosol formation of aqueous sulphuric acid droplets (via the heteromolecular nucleation and hetero- molecular condensation) ? Dr. M. D. Carabine (Imperial College) said In reply to Kiang the angular varia- tion of scattered light intensity would not be sufficient if clusters of a few tens of molecules are being observed. We have indicated in the paper an approximate lower limit of 0.06 pm using He-Ne radiation. Prof. M. Kerker (Clarkson Coll. Tech. Potsdam N.Y.) said Does Carabine have some experimental results to check the efficacy of his instrument? Our exper- ience with inverting light-scattering data for distributions as broad as oo = 0.50 and a = 0.40 pm has been far less successful than he reported.Indeed for this size we find that the results become multivalued when ao>0.20. In studying the rate of 229 230 GENERAL DISCUSSION growth of sulphuric acid aerosols in a humidified atmosphere,’ we found it necessary to start with nearly 100 % H,SO in order to obtain concentrated sulphuric acid aerosols by the condensation technique. Dr. A. Moore (Imperial College) said In reply to Kerker theoretical light scatter- ing data were generated for 15 angles for the size distributions characterized by I I1 rII IV V VI VII VIII IX dM (pm) 0.1 0.1 0.3 0.4 0.4 0.6 0.8 1.0 1.o 00 0.2 0.6 0.4 0.1 0.6 0.2 0.4 0.05 0.4 The inversion programme was then tested using the following input data (a) theoretical (b) theoretical 23 % random fluctuation (c) theoretical 5 % random fluctuation.Three different starting points were used for each search. The results were as follows (a) correct answers to 3 significant figures in all cases ; (b) answers to within 10 % in all cases except for V and IX at one starting point only. Consider-ably better than 10 % accuracy was achieved in most cases; (c) Answers to within 10 % in all cases except V where there was a 25 % error in dM and VII where all starting points gave answers dM = 0.55 and o0 = 0.52. Details of the procedure will be published soon together with error contour diagrams. These should show that there is one global minimum and possibly other “ shallow areas ” which the present programme interprets as minima.It is hoped to rectify this by further sophistication of the programme. Dr. M. D. Carabine (Imperial College) said In reply to Kerker we have not yet completed our experiments to check the light scattering instrument using polymer latex suspensions of size less than 1 pm. Troublesome back reflections in simple cylindrical vessels have justified the use of the light-trap described in the paper. Moore has commented in this discussion on tests of our strategy in the angular scanning using hypothetical particle size distributions. Mr. J. Maddock (Imperial College) said We have been using a Rapaport-Weinstock Generator to produce sulphuric acid aerosols.2 This relies on mechanical atomization to disperse the aerosol into an air-stream and must therefore produce an aerosol of the same composition as the stock liquid unless the carrier gas contains water vapour.We have been using nitrogen from cylinders containing up to 15 p.p.m. water vapour. This is sufficient to dilute the droplets considerably and there- fore the gas was dried by passing it through phosphorus pentoxide. Our suppliers inform us that helium from cylinders is also likely to contain water vapour. Can Kerker state whether or not and if so how his gas supply was dried? Dr. G. H. Walker (Clark College Atlanta Ga.) said Carabine and Moore have described a potentially useful instrument which can give us valuable information about growth processes in aerosols.However there may be difficulties in this scheme at the low concentration levels which are characteristic of many aerosols (typically 105-106particles ~rn-~) unless suitable restrictions are imposed upon the size of the scattering volume and upon the concentration. These problems arise because the number of particles in a given volume fluctuate and these fluctuations (which decay L. Coutarel E. Matijevic and M. Kerker J. Colloid Interface Sci. 1967 24 338. E.Rapaport and S. Weinstock Experienfia,1955 11 363. GENERAL DISCUSSION 231 very slowly) can influence the measured size distribution. These effects have been studied theoretically first by Smoluchowski and later by Chandrasekhar and experimentally by Schaefer and Berne in optical homodyne experiments using dilute suspensions of polystyrene spheres in water.To gain some estimate of the mean lifetimes of particle number fluctuations in an aerosol we consider spheroids of 1 pm radius suspended in a carrier gas (nitrogen) at 25°C. Using the Einstein-Stokes equation we find the diffusion constant to be roughly 12 x cm2/s. If n(t) is the number of particles in a given volume at time t? then the particle number correlation function (n(O)n(t)) decays in a time z which can be estimated by z-L2/24D where L is a typical dimension of the scattering volume. For L-1 mm (say) Z-3000 s. Even for very small particles (-0.1 pm) z N 300 s. Thus one must observe the scattering volume for relatively long times in order to average out the effects of particle number fluctuations.Since one is interested in making measurements of time-dependent phenomena in an aerosol which is changing much more rapidly than the relaxation of density fluctuations time averaging is not feasible. There are several ways to avoid this problem. For a given concentration one can either increase the scattering volume or else use a flowing carrier gas system (as has been done in recent experiments where optical homodyning has been applied to aerosol measurements. 3 Disregarding the last possibility it is of interest to estimate the size of the volume needed so that the number fluctuations may be safely ignored while keeping in mind that one would like as small a scattering volume as possible to minimize the effects of scattering angle variation.First we consider a monodisperse aerosol with a number density c. The particles are statistically independent and are described by the Poisson distribution. Thus the root-mean-square number density fluctuation is given by = ,/- cY where V is the scattering volume. We can treat the fluctuations in particle number as noise and if a maximum of 4 % noise is tolerable then we must have cY2625. For a typical volume defined by an unexpanded laser beam V'2:0.03cm3 and c>,2 x lo4 particles CM-~in order not to exceed the permissable noise level. For a polydisperse aerosol the situation is similar. Suppose that we try to measure the size distribution by counting the particles in a number of different radial classes and plotting the resultant histogram.In a class with a low frequency of occurrence the effects of fluctuations can be quite significant. For example suppose we have an aerosol with a total concentration of lo5 particles ~m-~ and we use ten radial classes. Then at least one of the classes must contain less than 10 % of the particles in the scattering volume and the concentration of this particular class is less than lo4 particles ~m-~. Applying the method used before we find that V20.0625 cm3 which is substantially greater than one might ordinarily use. Obviously increas- ing the number of radial classes used (or increasing the resolution) necessitates a corresponding increase in the scattering volume. One sees that fluctuations will not present a problem in most cases provided that the scattering volume is made large enough.Only in cases of low concentration and high resolution could the scattering volume become uncomfortably large. Prof. M. Kerker (Clarkson Coll. Tech. Potsdam N.Y.) said Can Brock say anything about the forms of the size distribution of an aerosol formed in a generator which functions by cooling of a mixture of heterogeneous nuclei and vapour. With l Reu. Mod. Phys. 1943 15. Phys. Rev. Letters 1972 28. W. Hinds and P. C.Reist Aerosol Sci. 1972,3. GENERAL DISCUSSION regard to the self-preserving size distribution my understanding is that the semantics originates in the terminology for the spectral distribution of turbulence. What are the physical assumptions relevant to aerosols which are the basis of the mathematical approximations in the self-preserving size theory ? Some astrophysicists estimate that 1000 tons of interplanetary dust enter the earth's atmosphere each day.Would this be a significant factor in the global aerosol economy? Prof. J. R. Brock (Uniu. Texas at Austin U.S.A.)said In reply to Kerker ifthe conditions of growth of the heterogeneous nuclei in the vapour are known precisely it is possible in principle to determine the resultant size distribution by integration of eqn (3.5) or suitable generalizations thereof. As indicated in the paper under unrestricted pure condensational growth an initially polydisperse aerosol will become less polydisperse with time. Such behaviour provided the basis of the original Sinclair-La Mer aerosol generator.In any practical experimental situation one will have imperfect knowledge of the temporal and spatial variations of the physical parameters governing condensation. This would introduce a "randomization " whose effect is generally an increase in measured polydispersity over that predicted from the calculation based on imperfect knowledge. The term "self-preserving " size distribution has been perhaps the source of some confusion. A " self-preserving " size distribution is one found through solution of a coagulation equation using the similarity transformation as proposed originally by Friedlander and colleagues. However an asymptotic limit distribution may exist for a particular coagulation process for which the similarity transformation or " self-preserving " hypothesis may not be valid.The physical assumptions pertinent to " self-preserving " size theory require extensive discussion such as that provided in ref. (1 1). Various estimates tend to show that the contribution of extraterrestrial dust to the global aerosol economy is of negligible order providing less than 0.01 % of the total mass inventory on a world-wide basis. Dr. E. R. Buckle (Shefield University)said With regard to the paper by Brock the coagulation process as usually modelled leads to theoretical distributions in an aged aerosol that are independent of the initial populations of particles. In a spontane- ously condensed aerosol of the kind I described the growth of particles by vapour condensation eventually becomes so slow even when the vapour is still appreciably supersaturated that coagulation becomes the only mechanism of further enlargement.This will not occur while the particles remain small and volatile for under such conditions the particle sizes are governed by much faster processes of growth and decay. While these processes are continuing to dominate the growth kinetics the initial state (i.e. the state of the vapour before the spontaneous process began) is kept in sight in the sense that the aerosol is evolving towards a final state thermo- dynamically related to the initial state. The so-called '' Kelvin effect " in aerosols viz. the tendency for the large particles to grow at the expense of the small arises in the need of the system to attain the final stable distribution by the indefinite enlarge- ment of fewer and fewer growing centres.According to the kinetic theory this effect will slow down in a homogeneous aerosol while the particles are still very small but because of the thermodynamic requirements coagulation processes will not be able to disturb the size distribution while the particles remain sufficiently volatile. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said The paper by Roach Adams Garland and Goldsmith should prove invaluable in fog studies. One point GENERAL DISCUSSION of note was the sudden increase in depth of fog which occurred between phases IIa and IIb. I have always thought that sudden changes in depth were largely associated with drift fog zones of greater or less depth being presented to the observation point as they are carried by the wind.Thus depth change should be associated with wind. Yet in the transition between phases IIa and IIb there was a sudden increase in depth of 5-10 m associated with a minimum in the wind. Is this attributed to the formation of fog in previously clear air or is there some other explanation? Dr. T. W. Roach (Meteorological Oflice Bracknell) (communicated) When observations are made from one site it is not possible to determine the relative contributions of drift and local development to an observed change in a parameter such as fog depth. It is however reasonable to suppose that changes in a shallow radiation fog which occur within a period of a few minutes are more likely to be due to drift while those changes taking place over 15 min or longer are more likely to be due to local development.The ‘‘ sudden ”change in fog depth referred to by Picknett in fact took about 20min so that we consider this to be more likely to be due to development than due to drift particularly as the wind dropped. Our main thesis was that if the wind dropped turbulent diffusion weakened or even ceased thus allowing radiative cooling to predominate. Dr. M. B. Green (British Gas Corp. London) said An application of chimney dispersal models which is particularly relevant to the symposium is their use in the prediction of the size of visible plumes found by condensing effluents. The essential feature of the analysis is to use the temperature and concentration profiles obtained from the dispersal formulae to compute via vapour pressure considerations the local levels of saturation of the effluent/air mixture.The volume bounded by the surface corresponding to a supersaturation of unity is to a first approximation the region in which condensation of the products is likely to occur. Wessel and Wisse have used this approach in conjunction with the Pasquill dispersal model to develop nomograms for the prediction of the size of cooling tower plumes. In view of the statements made in this paper about the differences between instantaneous and time averaged values of plume dispersal does Moore believe that a true estimate of the saturation region can be obtained with the classical dispersion formulae ? Dr.D. J. Moore (Central Elect. Gen. Board Leatherhead) said In reply to Green the paper by Wessel and Wisse does not take account of the effect of relative motion on plume growth or of plume rise on the plume temperature. These effects will tend to some extent to be self-cancelling with regard to condensation in the plume but Wessel and Wisse’s model should be regarded as a first attempt to solve this problem. It could be seriously in error in the meteorological conditions for some sources but one would need to put numbers in the plume trajectory and rise equations to find out when this would happen. Dr. D. J. Moore (Central Elect. Gen. Board Leatherhead) said I agree with Brock that gas washed plumes can have negative buoyancy especially if they contain liquid water on emission and this subsequently evaporates.It is possible that such plumes could produce higher ground level concentrations of a pollutant which had been partly removed by washing than the corresponding unwashed plume emitted with Atm. Em. 1971,5 751. Atm. Em. 1971,5,743. GENERAL DISCUSSION normal buoyancy (at around 100°C above ambient temperature). Re-heating the washed plume would overcome this problem but might be difficult to achieve on existing plant. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said Can Moore give more information about the formulae he quotes for a plume with a density at ambient temperature and pressure which differs from that of air? Dr. D. J.Moore (Central Elect. Gen. Board Leatherhead) said :In reply to Picknett the plume rise and dilution are really a function of the buoyancy flux vpb.For plumes which have the same density at ambient temperature and pressure as air where 0; = temperature excess of effluent = 6*-0 and p; = density difference between ambient air and effluent = pe-po = Ap. Since Qh = V6hp,Cp it follows that Tip; may be replaced by Qh/Cp6for plumes of hot air. The general expression for plume rise would therefore be one using the term V’;Cp6 rather than Qh,and this expression would apply to an emission of any density. (The term CpO occurs because of the presence of a similar term in the denominator of the parameter Al).

ISSN:0301-5696    

DOI:10.1039/FS9730700229

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

AUTHOR INDEX* Adams R. J. 209. Lecomte F. 57. Arrowsmith A. 229. Maddock J. 230. Brock J. R. 161 198,232. Moore A. P.,176 230. Buckle E. R.,17,42,45,46,48,49,50,72,76,77 Moore D. J. 222,233 234. 78 99 232. Mozzanega H. 57. Carabine M. D. 176 229 230. Murley R. D. 63. Cox R. A. 51. Nicolaon G. A. 133. Davies C. N. 34 52 53 157 160. Picknett R. G. 52 55 232 234. Dunning W. J. 7 42 45 46 47 48 49 50 74. Place E. R. 63 74 75 76. Fristrom R. M. 183. Pointon K. C.,78 97 99. Fuchs N. A. 143. Roach W. R. 209,233. Garland J. A. 209. Rosner E. 53 55. George A. P. 63. Schwar M. J. R. 183. Goldsmith P. 209. Stauffer D. 26,45 49 51 52 74. Green M. B. 233. Stechkina I. B. 143. Graham S. C. 75 85,97 99 100 102. Teichner S. J. 57 72 73 74. Hedley A. B. 162. Tesner P. A. 104. Homer J. B. 85. Thevenet A. 57. Howard J. B. 109 157. Vergnon P. 57. Jones A. R. 183. Waldie B. 73. Juillet F. 57. Walker G. H. 161 230. Kerker M. 44,50 55 75,98 102,133 157 161 Weinberg F. J. 120 183. 229 231. Wersborg B. L. 109 157. Kiang C. S.,26 42 45 47 51 76 229. Williams G. C. 109. Kirsch A. A. 143. Williams I. 162 229. * The references in heavy type indicate papers submitted for discussion. 235

ISSN:0301-5696    

DOI:10.1039/FS9730700235

出版商:RSC    

年代:1973

数据来源: RSC