Modeling particle deposition from fully developed turbulent flow in

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Atmospheric Environment 40 (2006) 457–466 www.elsevier.com/locate/atmosenv

Modeling particle deposition from fully developed turbulent flow in ventilation duct Bin Zhao, Jun Wu Department of Building Science, School of Architecture, Tsinghua University, Beijing 100084, PR China Received 8 June 2005; received in revised form 12 September 2005; accepted 23 September 2005

Abstract This paper proposes an improved Eulerian model to predict particle deposition velocity in fully developed turbulent duct flow. The model is modified based on the three-layer model by Lai and Nazaroff (Journal of Aerosol Science, 31, 463–476, 2000), accounting for turbophoresis as well as Brownian diffusion, turbulent diffusion and gravitational settling. An expression relating the turbophoretic velocity to particle relaxation time, friction velocity and the normal distance to the wall surface is presented to model the turbophoresis. Similar with previous one by Lai and Nazaroff, the model only needs to input friction velocity, which makes it easy to apply. The predicted results agree well with measurement data for floor and vertical walls. And then deposition velocity of airborne particles to smooth walls in straight steel ducts is predicted by the modified model. The results agree with the published measured data, especially for floor and vertical walls of ventilation duct. Thus it is expected to be applied for predicting particle deposition in ventilation duct for indoor air quality control or evaluation. Furthermore, the condition to ignore turbophoresis for particle deposition is discussed by comparing the results of the improved model and that of Lai and Nazaroff. r 2005 Elsevier Ltd. All rights reserved. Keywords: Aerosol; Particle; Deposition; Ventilation duct; Indoor air quality (IAQ)

1. Introduction It is useful to know particle deposition in ventilation ducts when evaluating human exposure to particles within buildings and predicting particle accumulation rates in ducts. As air flows through duct, deposition onto duct surfaces may alter particle size distributions and therefore affect exposures of building occupants. Furthermore, the Corresponding author. Tel.: +86 10 62779995; fax: +86 10 62773461. E-mail address: [email protected] (B. Zhao).

1352-2310/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2005.09.043

deposited particles in ventilation duct may resuspend and be taken by supply air if there are enough particles accumulated in the duct and energy of air flow, thus it would pollute indoor environment and cause adverse effect on human health. Investigation of National Institute for Occupational Safety and Health (NIOSH) of US indicates that a number of problems associated with human health of heating, ventilation and air conditioning (HVAC) systems are caused by the pollution of ventilation ducts (NIOSH, 1991). Waking up to the situation, China government issued the cleaning code for air duct system in

ARTICLE IN PRESS 458

B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

HVAC systems, and began to put into practice since 30 June 2003 (General Administration of Quality Supervision, 2003). Thus it is important to predict particle deposition in ventilation duct rightly when evaluate or control indoor air quality. Authors have tried to simulate particle deposition from fully turbulent flow in ventilation ducts by combining Lai and Nazaroff’s three-layer model (2000) with computational fluid dynamics (CFD) method (Zhao and Chen, 2005). The predicted deposition velocity onto floor agrees with measured data by Sippola and Nazaroff (2003), but the simulated results of particle deposition to vertical wall and ceiling depart far away the experiment. Therefore, maybe other transport mechanism of particle deposition needs to be considered to get reasonable results. Reviewing the work by Lai and Nazaroff (2000), it could be found that one important mechanism of particle deposition, turbophoresis, is not incorporated in their particle deposition model owing to the estimated small effect for the situations considered by those authors. In turbulence that is inhomogeneous, the gradient in turbulent fluctuating velocity components (turbulent velocity intensity) gives rise to turbophoresis, which is regarded as a particle transport mechanism distinct from Brownian diffusion. It is known that near wall turbulence is highly inhomogeneous due to sharp decay of turbulent velocity fluctuations, thus it is essential to consider turbophoresis when predicting particle deposition onto walls in ventilation ducts, where the dominant inhomogeneous turbulence near the surfaces does exist. If the particle inertia is large enough, turbophoresis would become dominant and it should be considered carefully. Actually, some previous particle deposition models had taken turbophoresis into account (Caporaloni et al., 1975; Reeks, 1983; Johansen, 1991; Guha, 1997; Young and Leeming, 1997). However, some of them present a complicated expression of turbophoretic velocity (Caporaloni et al., 1975; Reeks, 1983; Johansen, 1991), which is related with particle mean and fluctuating velocity components, and thus hard to analyze. The others even need to solve a series of partial differential equations of particle phase (Guha, 1997; Young and Leeming, 1997), which is time consuming and thus not practical. On the other hand, Lai and Nazaroff’s particle deposition model is easy to use as the only required input parameter is friction velocity. It analyzes particle deposition from turbulent flow by

examining the turbulent structure zone by zone and formulates transport equations for each zone. Thus the model is logical and practical to use. The main purpose of this paper, therefore, is to modify the three-layer model for particle deposition by taking turbophoresis into account to improve the model performance for predicting particle deposition in ventilation ducts, without adding other input parameters. The model presented in this paper calculates the turbophoretic velocity as a function of particle relaxation time, friction velocity and normal distance to the wall. After validation with measured data by Liu and Agarwal (1974), the improved model is applied to predict particle deposition velocity in real ventilation ducts, comparing with the measured data by Sippola and Nazaroff (2004). The condition to ignore turbophoresis when predicting particle deposition velocity is further discussed. 2. Model development 2.1. Brief review of the three-layer model Lai and Nazaroff (2000) proposed their threelayer particle deposition model by considering three particle transport mechanisms: Brownian diffusion; turbulent diffusion; and gravitational settling. This Eulerian model is based on the understanding that there is a very thin particle concentration boundary layer within the turbulent boundary layer, and through the concentration boundary layer the particle flux, J, is constant, which could be described by a modified form of Fick’s law: J ¼
ðep þ DÞ

qC
ivs C, qy

(1)

where D is the Brownian diffusivity of the particle, ep is the particle eddy diffusivity in the boundary layer, which is regarded as equal to the fluid turbulent viscosity, ut , in Lai and Nazaroff’s work, due to small dimensionless particle relaxation time they encountered, and it may be described according to DNS results (Kim et al., 1987). C is the (mean) particle concentration, y is the normal distance to the surface, vs is the settling velocity, and i is used to characterize the orientation of the surface, i.e., for an upward facing horizontal surface (floor), i ¼ 1; for a downward facing horizontal surface(ceiling), i ¼
1; for a vertical surface, i ¼ 0. By rewriting Eq. (1) in dimensionless format, and introducing the DNS results of Kim et al. (1987) for

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

ut , Lai and Nazaroff analyze the equation zone by zone in the three zones of particle concentration boundary layer, and then formulate transport equations for each zone of particle deposition. The detail could be found in Lai and Nazaroff (2000). The following is focused on the simulation of turbophoresis. 2.2. Modeling turbophoresis as an improvement for particle deposition model To model the turbophoresis as a mechanism of particle deposition, the particle flux should be modified as J ¼
ðep þ DÞ

qC
ivs C þ V t C, qy

(2)

where Vt is the turbophoretic velocity. Caporaloni et al. (1975) were the first to recognize turbophoresis phenomenon of particle transport and they calculated the turbophoretic velocity to be ______

V t ¼
tp

d v0 2py dy

,

(3)

where tp is the particle relaxation time and calculated by tp ¼

C c rp d 2p , 18m

(4)

where m is the molecular dynamic viscosity of air, rp and dp are particle density and diameter, respectively, Cc is Cunningham coefficient caused by slippage (Hinds, 1982):

 l dp Cc ¼ 1 þ 2:514 þ 0:8  exp
0:55 , (5) dp l l is the mean free length of the air molecule and it is equal to 0.066 mm at a temperature of 20 1C and atmospheric pressure (Hinds, 1982). Substituting Eq. (3) into Eq. (2), we get the particle mass flux as J ¼
ðep þ DÞ ______ v0 2py

qC
iV s C
tp qy

______ d v0 2py

dy

C.

(6)

is the particle wall normal fluctuating velocity intensity, which could be approximately estimated according to Johansen (1991) to be  ______ ______
tp
1 2 2 , (7) v0 py ¼ v0 y 1 þ tL

459

______ v0 2y

is the air wall normal fluctuating where velocity intensity, and tL is the Lagrangian timescale of the fluid (air). In fact Eq. (7) has its criterion and Johansen (1991) has discussed this issue in detail. According to the typical value of Lagrangian timescale in the buffer layer, the maximum value of air fluctuating velocities and typical thickness of buffer layer, this reference presented the criterion of Eq. (7), that is, dimensionless particle relaxation time should be much less than 138 (Eq. (20) in p. 360 of the reference). For the cases in this study, most particles (small sizes) meet this criterion and, for larger particles (dimensionless particle relaxation time larger than 10), the accurate representation of particle fluctuating velocity would play only a limited role in deposition according to this reference (Johansen, 1991). Thus it is reasonable to use Eq. (7) in this work, which could help to keep the governing equation (Eq. (32)) in simple format and still get reasonable results (see below). For relatively larger particles, which could be usually found in ventilation duct, it is not reasonable to treat the particle eddy diffusivity, ep , as equal to air turbulent viscosity, ut . Here we use the relation by Hinze (1975) to express the particle eddy diffusivity ep to be
 ep tp
1 ¼ 1þ . (8) ut tL Letting C 1 be the particle concentration outside the concentration boundary layer, the particle deposition velocity, vd, is defined as vd ¼

Jðy ¼ 0Þ . C1

(9)

To normalize Eq. (6) for convenience in model development, the following dimensionless parameters are defined: Cþ ¼

C , C1

(10)

yþ ¼

yu , u

(11)

vþ d ¼

vd , u

(12)

tþ ¼ tp ______þ 2 v0 py

u2 , u

¼

______ v0 2py , u2

(13)

(14)

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460 ______þ 2 v0 y

¼

______ v0 2y , u2

(15)

The fitted equation of ut by Lai and Nazaroff is repeated here to ensure the integrity of the improved model:

Sc ¼

u , D

(16)

ut =u ¼ 7:669  10
4 ðyþ Þ3 ; ut =u ¼ 1:00  10
3 ðyþ Þ2:8214 ;

0pyþ p4:3; 4:3pyþ p12:5;

uþ t ¼

ut , u

(17)

ut =u ¼ 1:07  10
2 ðyþ Þ1:8895 ;

12:5pyþ p30:

where u is the friction velocity, u is molecular kinematic viscosity of air. Using Eqs. (7)–(17), Eq. (6) could be rewritten as 
  þ tL dC þ
1 vþ ¼ Sc þ þ ivþ uþ t s C d tp þ tL dyþ    ______þ d tL =ðtp þ tL Þ v0 2y þ tþ Cþ ð18Þ dyþ The Lagrangian timescale of the fluid (air), tL , is given as (Johansen, 1991): ut tL ¼ ______ . (19) v0 2y For smooth surfaces, the boundary conditions for Eq. (18) are: yþ ¼ r þ ; yþ ¼ 30;

C þ ¼ 0; C þ ¼ 1:

(20)

Here r+ is rþ ¼

ðd p =2Þu . u

(21)

Eq. (18) is the improved model for predicting particle deposition velocity considering turbophoreris. One can solve Eq. (18) in case he gets the expression for air turbulent kinematic viscosity, ut , and wall normal air fluctuating velocity intensity, ______ v0 2y , as a function of normal distance to wall. Thus this model is somewhat universal if one knows the structure or characteristic of the boundary layer in concerned problems. 2.3. Solution of the model based on the three-layer model Here we adopt the fitted equations by Lai and Nazaroff (2000) based on the DNS results of ut by Kim et al. (1987), and distribution of wall normal ______ air fluctuating velocity intensity, v0 2y , in boundary layer by the fitted equation by Guha (1997) to solve the model Eq. (18).

(22) The dimensionless air wall normal fluctuating ______þ

velocity intensity v0 2y are expressed as function of the dimensionless normal distance to the wall (y+) as given by Guha (1997):
2 ______þ 0:005yþ2 2 v0 y ¼ . (23) 1 þ 0:002923yþ2:128 In Eq. (16), Brownian diffusion coefficient, D, is calculated by D¼

kB TC c , 3pmd p

(24)

where kB is the Boltzmann’s constant and it is equal to 1.38  10
23 J K
1, T is the absolute temperature. The settling velocity of particle, vs, is derived by equaling the fluid drag force on the particle with the gravitational force. It can be expressed as
1=2 4 g  d p ðrp
rÞ jvs j ¼ C c  , (25) 3 CD r where CD is the drag coefficient, r is the density of the air and g is the gravitational acceleration. The drag coefficient is either derived by Stokes equation (Reo1) or a revised equation (1oReo1000) (Hinds, 1982): 24 Rep 24 CD ¼ ð1 þ 0:15Re2=3 p Þ Rep

CD ¼

Reo1 (26) 1oReo1000;

where Rep is the Reynolds number according to the settling velocity and particle diameter: vs d p . (27) u For air flow in ventilation duct, u* could be calculated by pffiffiffiffiffiffiffiffi u ¼ U 1 f =2, (28)

Rep ¼

where U 1 is the average air speed in axial direction and f is the Fanning friction factor. For fully developed turbulent flow in ducts, f could be

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

calculated by following equation presented by White (1986): "
1:11 # 1 6:9 k pffiffiffi ¼
3:6 log þ , (29) Re 3:7Dh f where k is the mean microscale roughness height of the rough wall, and it is zero for smooth walls studied in this paper, and Re is the Reynolds number for the duct flow: Dh U 1 , (30) u Dh is the duct hydraulic diameter, defined by

Re ¼

4Ac , (31) P where Ac is the cross-sectional area of the duct, P is the perimeter of the duct normal to the flow direction. Eq. (18) could be rearranged as  8 ______þ 9 > > > > d ðtL =ðtp þ tL ÞÞ v0 2y = dC þ < þ þ þ iv þ t s > dyþ dyþ > > > ; :

Dh ¼


 
1 tL
1  Sc þ Cþ uþ tp þ tL t 
 
1 tL
1 ¼ vþ Sc þ . uþ d tp þ tL t

ð32Þ

Solution of Eq. (32) is as follows (Kreyszig, 1999): R yþ þ þ þ þA þ F ðy Þgðy Þ dy þ C ¼ r , (33) þ F ðy Þ where Z

þ

!

yþ þ

F ðy Þ ¼ exp

pðy Þ dy

þ

,

(34a)

rþ

pðyþ Þ ¼

8 > > < > > :

þ ivþ s þt

 ______þ 9 > > d ðtL =ðtp þ tL ÞÞ v0 2y = dyþ


 
1 tL  Sc
1 þ , uþ ðtp þ tL Þ t þ

gðy Þ ¼

vþ d

 Sc


1

 
1 tL þ . uþ ðtp þ tL Þ t

> > ; ð34bÞ




(34c)

A is a constant, which can be obtained by the boundary conditions shown as Eq. (20).

461

Substituting the boundary conditions, we get A ¼ 0 and vþ d ¼R 30 rþ

F ð30Þ . h  i
1 þ L þ F ðyþ Þ Sc
1 þ tptþt dy u t L

(35)

Consequently, by using the expression of ut ______þ

(Eq. (22)) and v0 2y (Eq. (23)), vþ d could be solved numerically because of the complexity of the exponent function involved. However, it is easy to be solved and much computational time can be saved compared with those models that need to solve partial differential equation. In this work, compound trapezoid formula is used to evaluate the R 30 approximate value of rþ F ðyþ Þgðyþ Þ dyþ and Clenshaw–Curtis quadrature is used to evaluate the approximate value of F ðyþ Þ. Compared with previous work (Caporaloni et al., 1975; Reeks, 1983; Johansen, 1991; Guha, 1997; Young and Leeming, 1997), this model only employs a combination of dimensionless normal distance in boundary layer to the duct walls and necessary particle parameters (relaxation time) to calculate turbophoretic velocity (the third term on the right hand side of Eq. (18)), without solving additional equations. The only input parameter is the friction velocity, u , and necessary particle parameters such as diameter. 3. Results analysis 3.1. Validation of the improved model The measured data by Liu and Agarwal (1974) is adopted to validate the improved model, which is widely used to validate particle deposition models. Fig. 1 shows the comparison of the predicted results by the improved model and the model of Lai and Nazaroff (2000) with data collected by Liu and Agarwal (1974). The agreement of the improved model with experiment is seen to be much better than that of the model of Lai and Nazaroff (2000). Specially, the ‘‘S-shaped’’ deposition curve is produced by the improved model, which correctly models the three different zones according to particle relaxation time. That is, the turbulent diffusion regime, where tþ o0:1; the turbulent diffusion-eddy impaction regime where 0:1otþ o10 (particles follow turbulent air fluctuations less faithfully and may shoot ahead of or lag behind eddies near the wall, that is, there exist

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

462

Table 1 Cases from Sippola and Nazaroff (2004)

Liu & Agarwal(1974) Present model: turbophoresis excluded our model 100 dimensionless deposition velocity,Vd+

u*=0.75m/s 10-1

u* (m s
1)

2.2 5.3 9.0

0.12 0.27 0.45

rp=920kg/m3

10-2 10-3 10-4 10-5 10-3

U 1 (m s
1)

10-2

10-1

100

101

dimensionless relaxation time,

102

103

τ+

Fig. 1. Comparison of predicted results with data collected by Liu and Agarwal (1974).

interaction between particle inertia and turbulent eddies); and particle inertia moderated regime where tþ 410 (particles are too large to respond to the rapid fluctuations of near wall eddies and transport to the wall by turbulent diffusion is very weak). This ‘‘S-shaped’’ curve has been validated by many researchers’ experiments and it is regarded as the benchmark for particle deposition from fully developed turbulent flow onto surfaces. However, the model by Lai and Nazaroof (2000), which dose not account for the turbophoresis, could not get this result. 3.2. Predicting particle deposition in real ventilation ducts The cases of particle deposition in real ventilation ducts are selected fully following those by Sippola and Nazaroff (2004), thus the measured data could be used to validate the improved model. Only steel duct cases are studied, whose inner walls could be treated as smooth surfaces. In China, most of the ventilation ducts are of steel and externally insulated, therefore we focus on smooth walls in this study. As mentioned above, we only need to input friction velocity to model particle deposition velocity when applying the improved model. Thus the cases studied are summarized in Table 1. Fig. 2 shows the comparison of the simulated results by the improved model with data collected by Sippola and Nazaroff (2004) for three different

friction velocities. The calculated dimensionless deposition velocity onto floor (upward facing walls in ventilation ducts) agrees very well with the experiment for all the cases of different friction velocities. The previous study (Zhao and Chen, 2005) also shows that the model without turbophoresis also generates good agreement with measurements for upward horizontal surfaces in ventilation ducts. The present model still predicts this well. The agreement for vertical walls differs under different friction velocities. When the friction velocity grows bigger, the predicted dimensionless deposition velocity onto vertical wall agrees better with measured data. In general, the particle deposition velocity onto floor is two or more orders larger that of vertical walls, which could be rightly modeled by the improved model. However, the particle deposition velocity onto the ceiling tells a different story. The big discrepancy needs to be further explored. Fig. 3 shows the dimensionless deposition velocity onto the vertical wall vs. particle diameter under the three friction velocities. It indicates when particle diameter is less than 1 mm, the dimensionless velocity seems to be equal at different friction velocities. The reason is that the effect of turbophoresis on particle deposition is far less than that of Brownian and turbulent diffusion in this range of particle diameters. The particle eddy diffusivity in this case can be regarded as equal to the fluid turbulent viscosity, ut , according to Eq. (8), which is only related to the dimensionless normal distance to the wall (see Eq. (22)). Brownian diffusion is only related to the particle diameter for this isothermal case which is right for airflow in ventilation ducts (see Eq. (24)). Consequently, the particle deposition velocity keeps the same when particle diameter is small enough for different friction velocities. Furthermore, the effect of Brownian diffusion decreases as the particle diameter increases, leading to the decrease of the dimensionless velocity. However, the dimensionless deposition velocity increases as the friction velocity increases when the particle diameter is larger. This is mainly because

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

100

10-2 10-3

ceiling wall floor ceiling wall floor

dimensionless deposition + velocity,Vd

+

velocity, Vd

dimensionless deposition

100 10-1

10-4 10-5

10-1 10-2

(a)

u*=0.27m/s u*=0.45m/s

10-4 10-5 10-6 -1 10

10-3 10-2 10-1 100 dimensionless relaxation time, τ+

u*=0.12m/s

10-3

10-6 10-4

463

101

100 101 particle diameter, dp (µm)

102

Fig. 3. Comparison of the dimensionless deposition velocity onto vertical wall at three friction velocities.

+

10-1 velocity, Vd

dimensionless deposition

100

10-2

ceiling wall floor ceiling wall floor

10-3 10-4 10-5 10-6 10-4

(b)

10-3 10-2 10-1 100 101 dimensionless relaxation time, τ+

102

+

10-1

velocity, Vd

dimensionless deposition

100

10-2 10-3

could be regarded as  ______þ  2 d ðtL  u =uÞ v0 2y dyþ

10-4 10-5 10-6 10-3

(c)

ceiling wall floor ceiling wall floor

the dimensionless relaxation time will increase when the friction velocity grows larger, thus the effect of turbophoresis becomes stronger, which makes the dimensionless deposition velocity larger, and when the particle diameter is large enough (about 100 mm), the dimensionless deposition velocity seems to be a constant. In this range of particle diameters, the effect of turbophoresis is far larger than that of Brown and turbulent diffusion. When the particle diameter is large enough, the dimensionless particle relaxation time is corresponding large enough, thus the value of tp =ðtp þ tL Þ is nearly equal to 1. In this case, the turbophoretic velocity,  ______þ  d ðtL =ðtp þ tL ÞÞ v0 2y tþ dyþ

10-2 10-1 101 100 dimensionless relaxation time, τ+

102

Fig. 2. Comparison of predicted results with data collected by Sippola and Nazaroff (2004) in real ventilation ducts. (a) v ¼ 0:12 m s
1 , (b) v ¼ 0:27 m s
1 , (c) v ¼ 0:45 m s
1 .

;

þ which has the same value with duþ t =dy due to Eqs. þ (15), (17) and (19). The value of dut =dyþ is only related to the dimensionless normal distance to the wall. Consequently, the dimensionless deposition velocity becomes a constant when the particle diameter is large enough. Fig. 4 further shows the predicted dimensionless deposition velocity onto floor vs. particle diameter at three friction velocities. General speaking, the dimensionless deposition velocity decreases as particle diameter increase first, and then grows bigger when the particle diameter increases, which is similar with that of vertical wall as shown in

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

464

100 10-1

Present model: our model u*=0.12m/s

u*=0.12m/s u*=0.27m/s

u*=0.27m/s

u*=0.45m/s

u*=0.45m/s

10-2

10-4 10-5 -1 10

turbophoresis excluded u*=0.12m/s u*=0.27m/s u*=0.45m/s

100

10-3

100 101 particle diameter, dp (µm)

102

Fig. 4. Comparison of the dimensionless deposition velocity onto floor at three friction velocities.

Fig. 3. The reason is that the effect of Brownian diffusion controls particle deposition mainly when the particle diameter is small enough (1 mm for vertical wall and 0.1 mm for floor), while the turbophoresis and gravitational settling play very less role. As discussed above, the particle eddy diffusivity in this range of particle diameters could be regarded as equal to the fluid turbulent viscosity, ut , which is only related to the dimensionless normal distance to the wall and Brownian diffusion is only related to the particle diameter, which decreases as particle diameter increases. When the particle diameter is large enough (this range differs for different friction velocities), the turbophoresis and gravitational settling grow stronger as the particle diameter increases, which control the particle deposition much more than Brown and turbulent diffusion. Consequently, the dimensionless deposition velocity increases with the particle diameter. On the other hand, the dimensionless deposition velocity differs less under different friction velocity for floor. As friction velocity increases, the dimensionless settling velocity grows smaller while the turbophoretic velocity grows bigger, thus the dimensionless deposition velocity onto floor varies less vs. friction velocity than that of vertical wall. 3.3. Comparison with the model without turbophoresis Fig. 5 shows the comparison of dimensionless deposition velocity onto vertical wall calculated by the improved model and the model without turbophoresis (Lai and Nazaroff, 2000) at three friction velocities. When the particle diameter is

dimensionless deposition + velocity,Vd

dimensionless deposition + velocity,Vd

101

10-1 10-2 10-3 10-4 10-5 10-6 -1 10

100 101 particle diameter, dp (µm)

102

Fig. 5. Comparison of dimensionless deposition velocity onto vertical wall calculated by the improved model and the model without turbophoresis (Lai and Nazaroff, 2000) at three friction velocities.

small enough, the dimensionless deposition velocities calculated by the improved model and the model without turbophoresis are nearly the same, indicating that the turbophoresis could be ignored in this case. The range of particle diameter where the turbophoresis could be ignored differs according to friction velocity. It could be larger when friction velocity is smaller, which is because the effect of turbophoresis is less dominant under smaller friction velocity. Thus the difference between the results calculated by the improved model with turbophoresis and the model without turbophoresis is less. When the particle diameter is smaller than 1 mm, the dimensionless deposition velocity by the improved model and the model without turbophoresis could be regarded as the same in ventilation ducts, where the friction velocities is usually in the range of the three friction velocities studied. That is, the turbophoresis could be ignored to predict particle deposition velocity for simplicity in this case. 4. Discussion This study focuses on particle deposition from fully developed turbulence flow in ventilation duct.

ARTICLE IN PRESS B. Zhao, J. Wu / Atmospheric Environment 40 (2006) 457–466

The developing turbulent flow at connectors and duct bends in ventilation ducts is hard to simulate by theoretical method. One has to use empirical equations based on experiment (Sippola and Nazaroff, 2003; Sippola and Nazaroff, 2005). For the purpose of studying the particle deposition in ventilation duct by theoretical method, knowledge on developing turbulent duct flow and its boundary layer structure need to be further investigated. Furthermore, this study only considers the steel duct, which is treated as smooth surface duct. Most HVAC systems adopt steel ducts and externally insulates in China, thus the reported study is applicable for many cases. However, the presented model is also applicable for particle deposition onto rough surfaces, so far as one can know the boundary layer structure, getting the distribution of air turbulent kinematic viscosity and air velocity fluctuation intensity in the boundary layer, with adjustment of the boundary conditions of Eq. (20) to meet the rough wall cases. This needs to be developed in the future to meet wide range of applications, and it may appear in a later report of our study. 5. Conclusions This study proposes an improved Eulerian model, which considers particle turbophoresis to predict the particle deposition velocity from fully turbulent flow onto smooth surfaces in ventilation ducts. The results are compared with published measured data and the model without turbophoresis. The conclusions could be drawn as follows: (1) The improved model is practical to use, as the only required input parameter is friction velocity. The model results agree well with the widely used measured data by Liu and Agarwal (1974), and the agreement between simulated results and experimental data is acceptable for vertical wall and very well for the floor in real ventilation ducts, but the results for ceiling need further study. (2) When the particle diameter increases, the dimensionless deposition velocity becomes smaller first due to Brownian diffusion, and then gets larger due to turbophoresis. The dimensionless deposition velocity onto vertical wall would become a constant when the particle diameter is large enough, as turbophoresis keeps nearly a

465

constant and far stronger than Brown and turbulent diffusion. (3) When the particle diameter is smaller than 1 mm, the results of the improved model with turbophoresis and the model without turbophoresis are nearly the same, which implies that the effect of turbophoresis on particle deposition could be ignored for simplicity. Acknowledgement This study is supported by the Fundamental Research Foundation of Tsinghua University (Grant No. Jcqn 2005002).

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