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5. pp. 1033-1035. 1984 ooo4-6981184 13.00 + 0.00 8 1984 Peqamon Press Ltd. SHORT COMMUNICATION A COMPARISON BETWEEN MODELS FOR PREDICTING THE PERFORMANCES OF BLUNT DUST SAMPLERS (First receioed 10 October 1983 and received for publication 19 January 1984) Abstract-A need is recognized for greater understanding of the factors which govern the performances of blunt dust sampling devices. This paper compares theoretical models developed from constrasting approaches, the one involving detailed calculation of particle trajectories in well-defined flow fields and the other involving particle transport in flow fields whose shapes are more-loosely defined in terms of the positions of aerodynamic stagnation on the sampler body. It is shown that, over wide ranges of conditions, good agreement can IX achieved between the two models. Key word index: Samplers, dust, blunt. 1. INTRODUCTION Dust samplers are widely used in workplace and ambient atmospheres to enable portions of dust-laden air to be aspirated, collected onto a filter, and assessed so that the concentration of the airborne dust in the atmosphere in question can be determined. In such devices, aspiration takes place (with the aid of a pump) by drawing air through one or more orifices in the solid casing which houses the filter. All are blunt samplers, since their physical presence inevitably impose some obstruction to the movement of the surround- ing air. The familiar sharp-edged isokinetic probe is merely a limiting case of that family of samplers. Much of dust sampling is carried out with regard to potential health effects. There is, therefore, a need that the performances of samplers should reflect the aerodynamic processes which take place inside and outside the body during the inhalation of airborne particles. Thus it follows that, in order to develop and use new practical sampling systems, a quantitative physical description of the factors which in- fluence sampling performance should be available. Although such a description has been given for sharp-edged isokinetic probes (for example Badzioch, 195% Sehmel, 1967; Belyaev and Levin, 1974, Jayasekera and Davies, 1980; Davies and Subari, 1982 and many others), substantially less progress has been made with respect to the more general blunt sampler case. Two contrasting approaches to blunt sampler theory have been suggested, with attention being focused in the first instance on samplers of simple symmetrical shape with single sampling orifices facing the wind. Ingham (1981) has analysed the trajectories of particles in potential flow about a two- dimensional cylindrical sampler with a slot intake. We (Vincent and Mark, 1982, Vincent et al., 1982) have adopted an alternative approach, working from the shape of the limiting streamsurface which separates the sampled air from that which is not sampled (particularly as indicated by the positions on the sampler body of points or lines of aerody- namic stagnation) and using ideas for particle motion exten- ded from those contained in simple sharp-edged sampler theory. This short paper sets out to compare the results obtained by each of these two approaches, and to consider how future progress might be made. 2. CALCULATIONS OF ASPIRATION EFFICIENCY From our model described in the papers cited above, calculation of aspiration efficiency (A, the ratio between the concentration of dust in the air entering the sampler and that in the ambient air) for an idealized, infinitely-long, two- dimensional blunt sampler with a slot entry facing the wind (see Fig. 1 for cylindrical version) can bc reduced to appli- cation of the following set of equations: St = d&y* U/18q S with y* = 10 kg me3 (1) $ = &?/DU (2) R = 6/D (3) S = Bt#2D (4) St, = RSr(S/D)- (3 St, = t#~ St (S/D)- (6) QI = 1 -{l/(1 +g1 Sb,) (7) a2 = f - {l/(1 + hSb)J (8) A, = l+a,{(S/D#)-1) (9) A,= l+a,{(RD/S)-l} (10) A = A,A2, (11) where d, is the aerodynamic diameter of the particles in question, Lr the wind speed, B the mean entry velocity of the sampled air, 6 the width of the sampling slot, D the width of the sampler body, and B its bluntness (which depends on its aerodynamic profile). The dependent quantity S is the width of the region at the sampler surface enclosed by the limiting streamsurface. A similar set of equations can be written down for a corresponding sampler with axial symmetry (e.g. disc- shaped), where Equations (2), (4). (6), (9) and (10) are replaced by 4 = S%/D2U (12) S = Bc#J~D (13) T D 1 Fig. 1. Air flow pattern in the vicinity of an idealised, infinitely-long, cylindrical blunt dust sampler facing the wind. 1033 1034 Short communication Sf, = cpsr (s/D)-2 (14) Al = 1+a,{(S2/D2f$)-1) (15) A, = 1+a2((RD/S)2-1). (16) Terms identitied by the subscript 1 refer to particle motion in the flow at some distance from the sampler entry, dominated by the divergence produced by the presence of the sampler body. Terms identified by the subscript 2 refer to particle motion in the flow close to the sampler entry, dominated by the convergence produced by the sampling air flow. Most of the quantities needed in order to compute A using the above equations are defined, independent properties of the system. The exceptions are R, g, and gs. Of the latter, B may be determined mathematically for simple systems from potential flow theoretical considerations, and by experiment for more complicated ones. Thus for a flat-nosed, two-dimensional blunt sampler we have R = 0.80 and for a cylindrical one R = 0.56. For a disc-shaped axisymmetric sampler, B + 1. The remaining quantities g, and g2 are numerical coefficients appearing in the empirical expressions for a, and aa which in turn represent the efficiencies with which particles impact onto theenclosed stagnation region (width S)and the sampler entry (width a), respectively. In the first part of his model, Ingham (1981) determined the aspiration efficiency for a cylindrical blunt sampler where it was assumed that all particles arriving at the surface of the sampler within a region enclosed by the limiting streamsur- face eventually enter the sampling orifice. This is equivalent to A, in our model. Noting that the inertial parameter employed by lngham (say, St,,,) is related to our own (St) by St,,, = 2 R St, (16) we can compare results obtained from each of the two models (using R = 0.56). The comparison (on the basis of Ai plotted as a function of St,,,, consistent with Inghams original presentation) is shown in Fig. 2, where we have chosen gi = 0.15 empirically. Agreement is good for the ranges of Q, and R indicated. It&am next proceeded to calculate the aspiration ef- ficiency for the same sampler, assuming now that only particles entering the sampling slot directly are considered as having been sampled. This is now equivalent to A in our model where, having already empirically chosen g, , it remains to select a corresponding value for g2. The results for the two models (this time plotting A as a function of St,,,) are compared in Fig. 3, for both g2 = 1.5 and g, = 5.0. For the range StlNG > 0.3 and for the ranges of 4 and R indicated, agreement is good (especially for g2 = 5.0). For St,,, -C 0.3 however, our calculated values of A lie substantially below those of Ingham. The reasons for the apparent discrepancy between the two models at low values of St,,, may be examined in terms of Al 0 I I I 10-2 lti lo St,NG lo 1 102 Fig. 2. A, for cylindrical blunt sampler as a function of StlNG for various I+--- from Ingham (1981) 0 our model (with gi = 0.15). A -i0-* lo4 100 10 102 St ING Fig. 3. A for cylindrical blunt sampler as a function StlNG forvariousdandR.-from Ingham (1981)0, q ,Aour model (with gi = 0.15, g2 = 1.5) l , m ,A our mode1 (with gi = 0.15, ga = 5.0). the main assumptions underlying each of them. Inghams theory is based on the important assumption that the presence of a sampling slot of finite width does not affect the shape of the flow pattern near the sampler. While this is reasonable at a distance from the sampler, it will be less satisfactory for the region close to the entry slot. This is the region for which, in our model, particle motion is described by A,, and is therefore the main source of the overall dis- crepancy. By contrast our model is built on a set of assumptions aimed at eliminating the need to express mathe- matically the air flow pattern everywhere in the vicinity of the sampler. Unfortunately, experimental data for two- dimensional blunt samplers against which to test these models are not yet available, and so the questions of detail raised in the above comparison cannot yet be satisfactorily answered. Rigorous calculation of aspiration eficiency for axisym- metric blunt samplers has not ken carried out because of the difficulty in obtaining closed-form expressions for the poten- tial flow in such cases. Therefore, although we can calculate A for these using our own simpler model, we cannot compare models. However we do have some limited wind tunnel experimental data for a disc-shaped axisymmetric blunt sampler facing the wind. These were obtained as part of a larger study into turbulence effects (to be published sep- arately) and are for fixed sampler and flow parameters (a =4mm, D=4Omm, U = Zms- and 6= 12.6ms-i), using monodisperse spheres of human serum albumen (HSA) and wax (d, = 10, 20 and 40 pm) and narrowly-graded aloxite dusts (effective d,, = 8, 15 and 40 pm). The results for A as a function of St,,, are shown in Fig. 4, together with curves obtained using our model with g, = 0.15 and g2 = 1.5 and 5.0. Allowing for the inevitable scatter in the experimental data, agreement is seen to be quite good (especially for g2 = 1.5). Relating this back to the earlier discussion relating to the two-dimensional sampler, the experimental results are therefore seen to support the trend at low St,,, (< 0.3) predicted by our model. Short communication 1035 A s 0 I I 1O-2 to- 16 St ING Fig. 4. A for disc-shaped bhmt sampler as a function of St,,, theory compared with experiment. - our model (et = 0.15 with 8s = 1.5 and 5.0) o,e Data points obtained from wind tunnel experiments (arithmetic means from numbers of runs given in brackets, error bars indicate standard deviations). 3. DISCUSSION If all that can be achieved from blunt sampler theory is to predict the performances of highly-idealised systems like those described, then it is of little practical value. Rather, the aim of such theoretical exercises should be to provide a framework from which to begin to understand the perform- ances of reet dust samplers like those used for motoring dusts in workplaces and in the ambient atmospheric environ- ment. Mathematical analyses dependent on detailed knowl- edge of the flow field are difficult for such complicated systems. It was originally hoped that our approach (much simpler, but still embodying the essential physical picture) would provide such a basis. This paper confirms its potential, if not always to accurately enable calculation of the quantitat- ive performance of sampling systems then at least to reflect their functional behaviour. To achieve even the latter can be of considerable practical value. By extension of these ideas we have, for example, been able to explain the shape of the inhalability curve which relates to the dust sampling efficiency of the human head during breathing, to design inhalable dust samplers having appropriate entry characteristics, and to account for changes in the performances of personal and static samplers when their designs are modified (Vincent and Mark, 1981). Blunt sampler theory is still at a very rudiments stage. To make further progress and to extend it more fully to applications in practical dust sampling, further experimental research is called for. Some such work is in progress in our laboratories and wiil be reported in due course. Physics Branch J. H. VINCENT l~t~tate qf Occupational Medicine 8 Ruxburgh Place Edinburgh EH8 9SV, U.K. REFERRN~~ Badxioch S. (1959) Collection of gasborne dust particles by means of an aspirated ~mpling nozzle. Br. J. appl. Pkys. 10, 26-32. Belyaev S. P. and Levin L. M. (1974) Techniques for collection of representative aerosol samples. J. Aerosol Sci. 5, 325-338. Davies C. N. and Subari M. (1982) Aspiration above wind velocity of aerosols with thin-walled nozzles facing and at right angles to the wind direction. J. Aerosol Sci. X3,59-71. Ingham D. B. (1981) The entrance of airborne particles into a blunt sampling head. J. Aerosol Sci. 12, 541-549. Javasekera P. N. and Davies C. N. 119801 Asoiration below wind velocity of aerosols with sh&p-edgednoxzles f&ing the wind. J. Aerosol Sci. 11, 535-547. Sehmel G. A, (1967) Errors in the subisokinetic sampling of an air stream. Ann occup. Hyg. 10, 73-82. Vincent J. H. and Mark D. (1982) Appliitions of blunt sampler theory to the definition and measurement of inhalable dust. In: Inhaled Particles Y (edited by Walton W. H.), Ann. occup. Hyg. 26.3-19. Vincent J. H., Hutson Dand Mark D. (1982)~e~tureofair flow near the inlets of blunt dust sampling probes. Atmospheric Environment 16, 1243-1249. Vincent J. H. and Mark D. (1981) The basis of dust sampling in ~u~tionai hygiene: a critical review. Ann. occup. Hyg. 24375-390.