Particle transmission efficiency through the nozzle of the API Aerosizer (TM)

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PII: S0021-8502(98)00789-7

PARTICLE TRANSMISSION EFFICIENCY

THROUGH THE NOZZLE OF THE API AEROSIZER

2+

Chuen-Jinn Tsai,*R Wu-Song Yang,R Wladyslaw W. SzymanskiS and Hung-Min CheinA

R Institute of Environmental Engineering, National Chiao Tung University, No. 75 Poai St., Hsin Chu, Taiwan S Institute of Experimental Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria

A_{Center for Industrial Safety and Health Technology, Industrial Technology Research Institute, Hsin Chu, Taiwan}

(First received 30 May 1998; and in ,nal form 1 December 1998)

Abstract*This study has investigated the particle transmission e$ciency through the nozzle of the API Aerosizer2+ numerically. Two-dimensional#ow "eld in the nozzle was "rst simulated. Particle trajectories for both liquid and solid particles were then calculated to obtain the particle trans-mission e$ciency under various conditions. This study shows that particle aerodynamic diameter, particle materials, particle density and laser beam diameter in#uence the transmission e$ciency. The transmission e$ciency is found to increase with increasing particle diameter when the particle aerodynamic diameter is less than several micrometers. The e$ciency for liquid particles drops signi"cantly when particle aerodynamic diameter increases from several micrometers because of particle impaction loss in the nozzle. For solid particles, the relationship of the e$ciency with particle diameter is found to be more complicated. For particles less than several micrometers in aerodynamic diameter, solid particles behave similarly to the liquid particles. However, as particles are greater than several micrometers, the e!ect of solid particle bounce is to increase the trans-mission e$ciency with increasing aerodynamic diameter until particles become large enough so that plastic deformation occurs in the particles. Then the transmission e$ciency will decrease with increasing particle aerodynamic diameter. 1999 Elsevier Science Ltd. All rights reserved

I N T R O DU C T I O N

The API Aerosizer2+ (Amherst Process Instruments Inc., Amherst, MA, USA) is an aerosol spectrometer used to measure size distributions of airborne particles in real time. Its design is based on the research of Dahneke (1973), Dahneke and Padliya (1977), Dahneke and Cheng (1979), and Cheng and Dahneke (1979). The Aerosizer is claimed to be capable of measuring particles of diameters between 0.2 and 700km, determining up to 10,000 particles per second with 5% accuracy, and discriminating between two particles di!ering in diameter by less than 10% (API, Inc., 1992). Its claimed wide range of measurement in real time surpasses other aerosol instruments and the instrument has been used in many aerosol measurement applications (Terzieva et al., 1996; Bohan, 1996; Etzler and Deanne, 1997; de Juan and Fernandez de la Mora, 1997; Ulevicius et al., 1997; Grinshpun et al., 1997).

However, some limitations and problems of API Aerosizer have been found recently by researchers. Comparison of the Aerosizer with other aerosol measurement devices shows that this instrument is not suitable for airborne particles of diameter below 0.5km at normal atmospheric pressure (Grinshpun et al., 1995; Qian et al., 1995). The Aerosizer signi"cantly underestimates aerosol concentrations and a!ects the accuracy of aerodynam-ic partaerodynam-icle size at reduced pressures (Cheng et al., 1993; Grinshpun et al., 1997). The instrument's response depends on ambient conditions and calibration is suggested at di!erent ambient pressure other than standard atmospheric pressure (Cheng et al., 1993). Theoretical time-of-#ights of particles calculated from one dimensional #ow "eld and incorrect drag coe$cients underestimate the experimental data (Tsai et al., 1998). Particle density and dynamic shape factor in#uence sizing accuracy of aerosols (Marshall and Mitchell, 1992; Cheng et al., 1993; Tsai et al., 1998). Particle diameter, particle

* Author to whom correspondence should be addressed.

concentration, photomultiplier tube (PMT) voltage, and model type also in#uence Aeorosizer's counting accuracy (Mitchell and Nagel, 1996; Thornburg et al., 1999). For liquid oleic acid particles less than 8km in diameter, the counting e$ciency was shown to increase with increasing particle diameter. However, there are no data available for larger liquid particles and no data for solid particles except some PSL data obtained by Cheng (1998).

The basic principle of the Aerosizer is similar to that of the TSI Aerodynamic Particle Sizer (APS). Both measure time-of-#ight of particles. APS has been studied extensively (Baron et al., 1993). It was found that the counting e$ciency of the APS nozzle is low due to impaction loss of liquid particles in the nozzle (Kinney and Pui, 1995). For solid particles, there are almost no data available for the APS, although it was indicated in a preliminary study that counting e$ciency is considerably higher than that of liquid particles (Blackford

et al., 1988). Similar impaction loss is expected to occur in the nozzle of the API Aerosizer

and it is worth investigating.

To understand the particle transmission e$ciency of the Aerosizer, a numerical method was developed in this study. The transmission e$ciency of the nozzle is de"ned as the fraction of particles entering the nozzle that is detected by the laser beams downstream of the nozzle. The #ow "eld in the nozzle was obtained from the previous study by Tsai et al. (1998) and the particle trajectories of both liquid and solid particles were then calculated. E!ect of particle density and laser beam diameter on the transmission e$ciency was also investigated. In this study, three di!erent laser beam diameters, 300, 600 and 800km were assumed. The simulation for the 800km beam diameter is the most relevant to the performance of the API Aerosizer LD, since its nominal beam width under the nozzle is 900km (allowable range: 800}1000km). For simplicity, it is assumed that when a particle is intercepted by both laser beams, it is regarded as being detected. Scattered light intensity for a particle passing through the laser beam at di!erent radial location is assumed to be the same. Also the transmission e$ciency problems due to di!erent settings of signal threshold and di!erent methods of signal processing are not considered in this study.

N U M E R I C A L M E T H OD

Numerical modeling for -ow ,eld

Simulation of #ow "eld in the nozzle and jet regime has been described in details in Tsai

et al. (1998). The air #ow in the Aerosizer is assumed inviscid, isentropic, and compressible.

Two-dimensional Euler equations are converted into the non-dimensional form for the axisymmetric coordinate system as

*; *t# *E *z# *G *r#H"0, (1) where ;"

















The unknown variables, o, u, v and e, in the above equations are designated the gas density, velocity components in z (axial) and r (radial) directions and total energy per unit volume, respectively. Air was assumed to behave as a perfect gas, and the pressure P is de"ned as

P"(c!1)



2(u#v)



The total air #ow rate is 5.3 l p m\ with sheath#ow at 3.2 l p m\ and aerosol#ow at 2.0 l p m\. Ambient temperature is 203C and pressure is 1 atm. For the Aerosizer in this study, the tip of the nozzle is 750km in diameter and half angle is 153. The "rst and second laser beams are located at 1 and 2 mm downstream of the nozzle exit, respectively.

The complete calculation algorithm and stimulation of the #ow "eld were fully described by Tsai et al. (1998). The previously calculated #ow "eld is adopted here for particle trajectory calculation.

Calculation of particle trajectory

It is assumed that the #ow "eld is not in#uenced by particles with low concentrations. The calculation involves integrating particle equations of motion by means of the fourth Runge}Kutta method, applying an empirical drag law for the ultra-Stokesian regime, and neglecting the gravitational force of spherical particles. The dimensionless equations of motion of a particle in r (radial) and z (axial) directions under consideration are

dr

dt"CRe24 (u!dr/dt)q , (4)

dz

dt"CRe.24 (uX!dz/dt)q , (5)

where q is the particle relaxation time de"ned as q"odC/18k (o: particle density,

d: particle diameter, C: the Cunningham slip correction factor, and k: air dynamic

viscosity), Re is the particle Reynolds number and C is the empirical drag coe$cient. Also,

u and uX are local #ow velocities in the radial and axial directions, respectively.

The dimensionless particle equations of motion are integrated through the region of interest. The initial velocity is given equal to the local #ow velocity, and the initial position is set at the entrance of the nozzle. The new particle position and velocity after a small increment of time is calculated by numerical integration. The procedure is repeated until the particle passes the second laser beam.

The empirical drag coe$cient, C, originally developed by Henderson (1976), is adopted for a wide range of #ow conditions taking into account particle Mach number, M. In the subsonic #ow regime, C is given by the following expression:

C"24





1#0.353 ¹/¹





\

#exp

(Re



#0.1M#0.2M



#



Re



And in the supersonic regime at Mach numbers equal to or greater than 1.75, the form of

C is

C"0.9#(0.34/MR)#1.86 (M/Re) [2#(2/S)#1.058/S(¹/¹ )!1/S]

1#1.86 (M/Re) .

(7) When the Mach number at the transition region between 1.0 and 1.75, C is the linear interpolation of equations (6) and (7).

In the above equations, S is the molecular speed ratio equal to M(c/2; M is the particle Mach number determined by the relative velocity between the particle and air #ow; ¹ is

the temperature of the particle; ¹ is the air temperature. The subscript, R, denotes free stream conditions.

Particles in the sampling #ow would impinge on the nozzle wall when unable to follow the curving streamline near the wall because of their inertia. Solid particles that bounce back into the sampling #ow may exit the nozzle, whereas liquid particles stick on the nozzle wall. When the center of a solid particle approaches the solid wall within a distance equal to its radius, the particle is considered impacted. Trajectories of rebounding particles are then simulated. The particle transmission e$ciency through the nozzle is calculated by the ratio of the number of particles detected by the two laser beams to the total number of particles entering the nozzle. Only the particle that passes through both laser beams is considered to be counted.

The model developed by Xu et al. (1993), and Xu and Willeke (1993), which considered elastic and plastic deformation and rotation of solid particles during impact process, was adopted to calculate the rebound velocity of particles. Particle bounce may occur when its incident velocity is greater than the critical velocity. The rebound velocity and the critical velocity were found to be strongly dependent on the incident impact angle and velocity.

In this model, the kinetic energy of a impacting particle, E , is divided into normal and tangential components, E , and E . In the normal direction of impact, a particle may experience primary and secondary elastic deformations, and plastic and elastically de-formed plastic deformations. In the tangential direction, only particle rotation was con-sidered. The normal component of impact kinetic energy equals the sum of rebound, surface adhesion, elastic and plastic deformation energies as

E "E#E#E#E, (8)

where E is energy stored in primary elastic deformation, E is energy stored in elastically deformed plastic deformation, E is energy stored in secondary elastic deformation, and

E is energy loss due to plastic deformation.

The rebound kinetic energy, E, is less than the impact kinetic energy because of loss of surface adhesive energies in tangential and normal directions (E  and E ) and plastic energy, E. The relationship from energy balance is

E "E#E #E #E. (9)

The rebound velocity is calculated from the rebound kinetic energy when the impact kinetic energy overcomes the energy loss during the impact process, as follows:

<"



m , (10)

where < is the initial velocity and m is the particle mass.

The critical velocity, <, is the maximum impact velocity when no rebound occurs. That is

<"(2(E #E #E)/m . (11)

Brach and Dunn (1992, 1995) have developed another bounce model. This model takes advantage of the simplicity of algebraic solutions for collisions of particles on surfaces. It applies several coe$cients to describe dynamics of particle bounce. These coe$cients are acquired by experimental data. After the coe$cients are determined, whether particle rebound or captured can be predicted.

A kinetic coe$cient of restitution, R, representing internal energy dissipation in the sphere is de"ned as

where P0" and P" are the impulses of force due to deformation of the particle in rebound (superscript &&R'') and approach (superscript &&A'') phases, respectively. The ratio of a tangen-tial impulse component, P, to the corresponding normal impulse component, P, over approach and rebound phases is calledk, which is calculated as

P"kP. (13)

The ratio of the adhesion impulse, P0, to the body impulse P0", during rebound is called o, which is calculated as

P0"!oP0". (14)

Once coe$cients R, k and o are obtained experimentally, the particle rebound velocity is then calculated algebraically. The particle rebound velocity in the normal and tangential directions, < and <, are

<"!R(1!o) v, (15)

<"vR!k[1#R(1!o)]v, (16)

where v and v are initial normal and tangential velocities of the particle. R E S U L T S A N D D I S C U S S I O N

Particle trajectoy

Particle trajectories for particle aerodynamic diameter ranging from 0.1 to 150km were simulated. Ambient air condition is assumed to be 203C and 1 atm (101.33 kPa). Some typical trajectories are presented here for illustrative purposes.

Figure 1 illustrates the behavior of small 0.5km PSL particles. Small particles having less inertia tend to follow air streamlines. They do not impact on the wall and eventually will exit the nozzle. However, it is seen that some particles that follow the expanding jet will likely miss the laser beams. In addition, interception e$ciency of small particles by laser beams is low because of their small radii. It is therefore expected that transmission e$ciency of small particles is low but increases with increasing particle diameter. From light scattering point of view, smaller particles scatter less light than larger particles which may result in less counting e$ciency for smaller particles. However, this e!ect is not considered here.

Large liquid particles will likely stick to the nozzle wall upon impact. An example of the behavior of liquid particles of 50km in diameter (o"1.05 g cm\) is shown in Fig. 2. The

Fig. 2. Particle trajectories for liquid particles of 50km, density"1.05 g cm\.

Fig. 3. Particle trajectories for PSL particles of 50km, density"1.05 g cm\.

downstream laser beams cannot detect the majority of liquid particles that impact on the wall. Only a small fraction of particles near the centerline of the nozzle are likely to be detected. It is expected when impaction loss of large liquid particles becomes important, particle transmission e$ciency declines with increasing particle diameter. Clogging of nozzle by large liquid particles is also expected to be severe.

In comparison, large solid particles rebound from the wall upon impact, and are likely to be detected depending on the rebound trajectory. Figure 3 shows that some large 50km particles may bounce into the two laser beams upon impact with the nozzle wall. Hence, its expected transmission e$ciency for large solid particles is higher than that of liquid particles.

¹ransmission e.ciency

The transmission e$ciency for liquid particle (assumingo"1.05 g cm\) is shown in Fig. 4. When particle aerodynamic diameter is less than 2.5, 1.7, and 0.9km for laser beam of 300, 600 and 800km in diameter, transmission e$ciency increases with increasing particle diameter. This is because that larger particles do not follow expanding jet very well

Fig. 4. Transmission e$ciency for liquid particles of 1.05 g cm\ in density.

and are intercepted by the laser beam more easily than smaller particles. Laser beam diameter is seen to a!ect particle transmission e$ciency signi"cantly. For example, when the aerodynamic diameter is 1.0km, transmission e$ciency is 17.5, 65.6, and 99.9% for the laser beam of 300, 600 and 800km in diameter, respectively. Laser beam with larger diameter intercepts more particles resulting in higher transmission e$ciency.

Increase in counting e$ciency with increasing particle diameter was also found in the preliminary study by Cheng (1998). The unpublished data for the counting e$ciency of PSL particles are: 0.594, 4.24 and 26.96% for 0.77, 0.97 and 2.76km particles in aerodynamic diameter, respectively.

When impaction loss occurs for particles larger than several micrometers, transmission e$ciency starts to drop with increasing particle aerodynamic diameter as shown in Fig. 4. Transmission e$ciency becomes less than 10% when aerodynamic diameter is greater than 100km. Particle density also in#uences transmission e$ciency to a great extent due to modi"cation of the drag coe$cient caused by ultra-Stokesian motion (Tsai et al., 1998) as indicated in Fig. 5 for liquid particles with density equal to 10.5 g cm\. Transmission e$ciency for small particles is seen to be higher than the case of smaller particle density, 1.05 g cm\, given all other conditions"xed. Now the transmission e$ciency for 1.0km particle is 36, 100, and 100% for the laser beam of 300, 600 and 800km in diameter, respectively.

While large liquid particles have low transmission e$ciency, bounce of large solid particles leads to the improvement of transmission e$ciency. The transmission e$ciency for solid PSL particles (o"1.05 g cm\) through steel nozzle is presented in Fig. 6 using the bounce model of Xu et al. (1993), and Xu and Willeke (1993). For small particles, impaction loss does not occur, transmission e$ciency is the same as that of liquid particles. For particles larger than several micrometers in aerodynamic diameter, it is seen that now the transmission e$ciency for solid particles is much higher than the case of liquid particles, Fig. 4. The improvement is more obvious when the laser beam diameter is larger. For example, when the laser beam diameter is 300km, particle bounce does not increase transmission e$ciency until particle is greater than about 10km in aerodynamic diameter.

Fig. 5. Transmission e$ciency for liquid particles of 10.5 g cm\ in density.

Fig. 6. Transmission e$ciency for PSL particles through steel nozzle.

In contrast, for a laser beam of 800 mm in diameter, particle bounce increases the transmission e$ciency dramatically. The e$ciency is nearly 100% for particles of 1}70km in aerodynamic diameter. As particles become too large, particles acquire large enough velocity in the nozzle so that plastic deformation may occur which reduces particle rebound

velocity. In this case, transmission e$ciency drops again with increasing aerodynamic diameter.

Another simulation of harder #yash particles (o"1.8 g cm\) through steel nozzle was also made. It was shown that there is very little di!erence for the transmission e$ciency compared to the case of softer PSL particles (Fig. 6) except the density e!ect, which increases the transmission e$ciency slightly. Other material properties, such as hardness and surface energy, do not seem to in#uence transmission e$ciency too much. Previous results were obtained using particle bounce model of Xu et al. (1993), and Xu and Willeke (1993). Simulations using newer bounce model of Brach and Dunn (1992, 1995) have obtained almost identical results for both PSL and #yash particles.

One advantage of the bounce model of Brach and Dunn (1992, 1995) over that of Xu et al. (1993) is that the former has more empirical constants for di!erent materials than the latter. For example, for the transmission of silver-coated glass particles (o"2.6 g cm\) through stainless steel nozzle, empirical constants are readily available only in the bounce model of Brach and Dunn (1992, 1995). For these materials, a separate calculation shows that the transmission e$ciency curves are similar to Fig. 6 except that it remains high for particles greater 100km in aerodynamic diameter. This is presumably due to the di!erence in material properties.

C ON C L U S I O N S A N D R E C OM M E N DA T I O N S

It is important to know the transmission e$ciency versus particle aerodynamic diameter for the API Aerosizer as the instrument has been used widely to measure size distribution of aerosols. If the transmission e$ciency is low or the transmission e$ciency depends on particle diameter, then the interpretation of particle size distribution is di$cult and may be erroneous. This study has investigated theoretically the e!ect of particle aerodynamic diameter, particle materials, particle density and laser beam diameter on the transmission e$ciency of the API Aerosizer. In this study, it is assumed that particles exiting the nozzle and intercepted by the laser beams are detected. The transmission e$ciency is calculated as the percentage of particles entering the nozzle that are detected by both two laser beams. Small particles less than several micrometers have low transmission e$ciency because laser beams intercept small particles less e$ciently and particles that follow expanding jet miss the laser beams. For particles less than several micrometers, transmission e$ciency increases with increasing aerodynamic diameter. When liquid particles are too large, impaction occurs to the wall of the nozzle which reduces transmission e$ciency dramati-cally. The transmission e$ciency continues to decrease with increasing aerodynamic diameter. The optimum transmission e$ciency of liquid particles lies within the range from 1 to 10km in aerodynamic diameter when the particle density is 1.05 g cm\.

The transmission e$ciency of solid particles improves a lot when particles are greater than about 10km because particles may rebound into the laser beams. Transmission e$ciency remains the same as that of liquid particles for smaller particles which do not bounce.

Laser beam diameter has an important e!ect on the transmission e$ciency. In this study laser beams having larger diameter are shown to provide more e$cient particle detection than smaller diameter beams.

There are not enough experimental data available in the literature to validate the present theoretical study. It is recommend that careful experiments be conducted to determine the transmission e$ciency of the API Aerosizer. Besides what have been treated here, many other factors that may in#uence the transmission e$ciency of the API Aerosizer have to be considered. Finally, in view of the low transmission e$ciency and its dependence on the particle properties (size, density, etc.) of the Aerosizer, improvement of the transmission e$ciency of this instrument is critical and worthwhile.

Acknowledgements*The authors would like to thank the Taiwan National Science Council of the Republic of

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