CFD study of human respiratory dose to indoor particular contaminants.
The upper conducting airways of human lung (Figure 1a) contains the trachea and bronchi that form a tree structure with millions of branching tubes. The computational domain of this study contains the trachea and the first bronchial bifurcation (Figure 1b) following the description of a physiologically realistic bifurcation lung model proposed by Heistracher and Hofmann (1995), and Phillips (1997).
[FIGURE 1 OMITTED]
Figure 2 displays the computational grid. Unstructured tetrahedral elements of dimension 1mm (0.039 in.) are used in the fully developed core region. Near the wall, a highly refined boundary layer of hexahedron elements is employed, which evolves from a cell dimension of 0.05 mm (0.002 in.) to the airflow core with a growth factor of 1.2. Grid independency is conducted and verified.
[FIGURE 2 OMITTED]
AIR FLOW FIELD
Mild, moderate and intensive breathing conditions are considered in this study. Table 1 lists the flow field properties corresponding to different breathing conditions.
Table 1. Flow Field Properties under Different Breathing Conditions Breathing Pattern Volume Rate [L/min] ([cfm]) Reynolds Number Light 15 (0.53) 1400 Moderate 37 (1.31) 3450 Intensive 60 (2.12) 5600
For the flow field, the continuity equation is given as:
[[[partial derivative][u.sub.i]]/[[partial derivative][x.sub.i]]] = 0 (1)
Here [u.sub.i] is the instantaneous velocity and [x.sub.i] is the position vector. The momentum equation for flow in laminar regime is given as:
[u.sub.j] [[[partial derivative][u.sub.i]]/[[partial derivative][x.sub.j]]] = - [1/[rho]][[[partial derivative]p]/[[partial derivative][x.sub.i]]] + v[[[[partial derivative].sup.2][u.sub.i]]/[[partial derivative][x.sub.j][partial derivative][x.sub.j]]] (2)
Here p is the pressure, and v is the kinetic viscosity of the fluid. For turbulence flow the Reynolds-averaged Navier-Stokes equation is given as:
[U.sub.j][[[partial derivative][U.sub.i]]/[[partial derivative][x.sub.j]]] = - [1/[rho]] [[[partial derivative]P]/[[partial derivative][x.sub.i]]] + v[[[[partial derivative].sup.2][U.sub.i]]/[[partial derivative][x.sub.j][partial derivative][x.sub.j]]] - [[partial derivative]/[[partial derivative][x.sub.j]]] [R.sub.ij] (3)
where [R.sub.ij] is the Reynolds stress tensor, and it is directly solved with Reynolds stress transport model that is of the following form:
[U.sub.k][[partial derivative]/[[partial derivative][x.sub.j]]][R.sub.ij] = [[partial derivative]/[[partial derivative][x.sub.k]]]([[v.sub.T]/[[sigma].sup.k]] [[partial derivative]/[[partial derivative][x.sub.k]]] [R.sub.ij]) - [bar.[u'.sub.k][u'.sub.k]][[[partial derivative][U.sub.j]]/[[partial derivative][x.sub.k]]] + [bar.[u'.sub.i][u'.sub.k]][[[partial derivative][U.sub.i]]/[[partial derivative][x.sub.k]]] - [C.sub.1][[epsilon]/k][[R.sub.ij] - [2/3][[delta].sub.ij]k] - [C.sub.2][[epsilon]/k]([P.sub.ij] - [2/3][[delta].sub.ij]P) - [2/3][[delta].sub.ij][epsilon] (4)
In Equation (4), [P.sub.ij] is the turbulence production, P = [P.sub.ii]/2. The values of the standard values of the standard values of constants are: [[sigma].sup.k] = 1.0, [C.sub.1] = 1.8, [C.sub.2] = 0.6 (Launder 1975). These values of constant leads to the proper values of [[bar.u'].sub.1.sup.2], but over estimates [[bar.u'].sub.2.sup.2]. He and Ahmadi (1999) suggested using [C.sub.1] = 1.5, [C.sub.2] = 0.1 for proper estimation of [[bar.u'].sub.2.sup.2]. In addition to the Reynolds stress transport equation, Equation (5) is used to model turbulence dissipation rate [epsilon]:
[d[epsilon]/dt] = [[partial derivative]/[[partial derivative][x.sub.j]]]([[v.sub.T]/[[sigma].sub.[epsilon]]] [[[partial derivative][epsilon]]/[[partial derivative][x.sub.j]]]) + [c.sub.[epsilon]1][v.sub.T][[epsilon]/k]([[[partial derivative][[bar.u].sub.i]]/[[partial derivative][x.sub.j]]] + [[[partial derivative][[bar.u].sub.j]]/[[partial derivative][x.sub.i]]]) [[[partial derivative][[bar.u].sub.i]]/[[partial derivative][x.sub.j]]] - [c.sub.[epsilon]2][[[epsilon].sup.2]/k] (5)
Here, [v.sub.T] = [c.sub.[mu][k.sup.2]/[epsilon], is the eddy viscosity, and k = [[bar.u'].sub.1][[bar.u'].sub.1]/2 is the turbulence kinetic energy. [[bar.u].sub.i]is the mean velocity. The standard values of the constants are: [c.sub.[mu]] = 0.09, [c.sub.[epsilon]1] = 1.45, [c.sub.[epsilon]2] = 1.9, [[sigma].sub.k] = 1, [[sigma].sub.[epsilon]]= 1.3 (Jones and Launder 1973).
PARTICLE TRANSPORT MODEL
In this study, it is assumed that concentration is sufficiently dilute that the airflow field is not affected by the presence of particles. The governing equation of particle motion is given by:
[[d[u.sub.i.sup.P]]/dt] = [1/[tau]] [[[C.sub.D][Re.sub.p]]/24]([u.sub.i] - [u.sub.i.sup.P]) + [F.sub.i.sup.L] + [g.sub.i] + [n.sub.i](t) (6)
Here [u.sub.i.sup.p] = [dx.sub.i]/dt is the particle velocity, [F.sub.i.sup.L] is the lift force, [g.sub.i] is acceleration of gravity, [n.sub.i](t) is the Brownian force per unit mass, and [tau] is the particle relaxation time. In Equation (6) [C.sub.D] is the drag coefficient (Hinds 1982), and [Re.sub.p] is the particle Reynolds number.
FLOW FIELD SIMULATION
By nature human breathing contains periodic inhalation and exhalation, however, it is assumed that the particle deposition mainly occur during the inhalation process. Therefore, steady-state inhalation is considered in the simulation. Corresponding to the light, moderate and intense breathing conditions, uniform air velocity of 0.265 m/s (0.87 ft/s), 1.6 m/s (5.25 ft/s), and 3.2 m/s (10.5 ft/s) are specified at the trachea inlet. The flow is driven by pressure gradient in main flow direction and a standard no slip boundary condition is applied at the wall. Because of the uncertainty in the flow regime, laminar flow is considered for light and moderate breathing conditions, while turbulence modeling is performed for all of the breathing conditions. A turbulent intensity of 2% at the trachea inlet to simulate the larynx jet is assumed for all turbulent condition. The air properties are: temperature = 288 K (518 R), dynamic viscosity [micro] = 1.84 x [10.sup.-5] Ns/[m.sup.2] (3.84 x [10.sup.-7] lb-s/[ft.sup.2]), and density [rho] = 1.125 kg/[m.sup.3] (2.18 x [10.sup.-3] slug/[ft.sup.3]).
The transport and deposition of spherical particles of size 0.01 [micro]m, 1 [micro]m, and 30 [micro]m are numerical simulated in the trachea and the main bronchus of human respiratory system. Typically 10,000 particles are released uniformly from the trachea inlet. Statistical consistency on the deposition rate is observed for lower ensemble of population. It is worth to note that particles of size 30 [micro]m will not pass the nasal passage, however, they might be inhaled to human trachea bronchial tree via mouth breathing.
Figure 3 displays the particle deposition pattern in the bifurcation model. Moderate cardiac load of 37 L/min (1.31 cfm) is assumed in these simulations, and the laminar flow model is used. Diesel-oil-liquid droplets of diameter 0.01 [micro]m, 1 [micro]m, and 30 [micro]m are included in these analyses. Figure 3 shows that the deposition rates and deposition patterns vary significantly with particle size. For example, Figures 3b shows that no 1 [micro]m particles are deposited for the sample size used, while highly localized deposition is observed for the 30 [micro]m particles. Figure 3 also shows that there is no particle deposition in the trachea region for all of the cases studied with the laminar flow assumption. For the ultrafine particles with d = 0.01 [micro]m, deposition occurs uniformly.
[FIGURE 3 OMITTED]
Figure 4 displays the results for the moderate breathing condition with the turbulence assumption. A Reynolds stress transport model was used for the airflow simulation and the turbulence fluctuations are included by incorporating stochastic "discrete random walk" (DRW) model. Comparing Figures 4 with 3, it shows significant enhancement of the particle deposition because of the effect of turbulence dispersion. The deposition patterns are also altered. Figures 4a shows that the 30 [micro]m particles have highest deposition rate, and the deposition sites are more uniformly distributed across the entire bifurcation model. The deposition on the trachea is markedly increased. All of these changes are due to the additional dispersion effects introduced by the turbulence fluctuating velocity field. For the 0.01 [micro]m particles, the turbulence effect increases the trachea and overall deposition. The deposition pattern is roughly uniformly across the entire bifurcation model. Figures 4b shows that some 1[micro]m particles are deposited under the turbulent flow condition. The deposition rate of this particle size, however, is still the lowest.
[FIGURE 4 OMITTED]
From the results shown in Figure 3 and 4, it is deduced that the turbulence dispersion mechanism plays an important role in the transport and deposition processes of the inhaled particles in the upper human respiratory system. Turbulence fluctuation velocity enhances mixing and provides random dispersion of particles.
Figure 5 and 6 displays the comparison of the simulated particle deposition efficiency in the trachea and the bronchus at moderate and light breathing conditions with that of the experiment measurements. Of the experimental studies, inertial range of 0.9 [micro]m < d < 30 [micro]m polystyrene latex particles were used by Zhou and Cheng (2005). Ultrafine [.sup.212]Pb particles attached to the silver particles in the range of 1.7 nm < d < 200 nm were used by Smith et al. (2001). In addition, the experimental data of Chan and Lippmann (1980), and Schlesinger et al. (1977) by using ferric oxide particles are included as well. Of all these experiments, human tracheobronchial casts were used and steady-state inhalation airflow rate of 15 (0.53), 30 (1.06), and 60 (2.12) L/min (cfm) were considered.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Both turbulent and laminar airflow are considered in the simulation. Particles in the range of 0.01 [micro]m to 30 [micro]m are included in this study. It is shown that the predicted deposition efficiency by using CFD with turbulence assumption agrees well with the experiments. However, the simulation results with laminar airflow assumption underestimates the particle deposition efficiency, especially in the trachea and for fine particles in the range from 0.1 to 10 [micro]m. Three distinctive particle deposition characteristics are displayed in Figure 5 and 6. For particle smaller than 0.1 [micro]m the deposition rate decreases with the size. This implies that the Brownian motion is an important factor governing the motion of the particle. However for particle larger than 10 [micro]m the deposition rate increases with the size, implying a different driving transport mechanism--particle inertia. For particles in between 0.1 and 10 [micro]m, the deposition rate is the minimum and no distinct deposition characteristics can be identified. It is also shown in Figure 5 that turbulence diffusion affects particle deposition significantly in the trachea over the entire range. Without turbulence diffusion, as indicated by the laminar simulation, the deposition rate is lower than the experiments. For particle around 1 [micro]m, no deposition is detected. It should also be pointed out that the simulation result is slightly higher than the experimental measurement in this region due to the solution sensitivity to the computational grid. Similar results are obtained in the first bifurcation (Figure 6) though turbulence diffusion have less effect in the Brownian and ineria regions.
Evaluating the fate of particles of size 0.01 [micro]m, 1 [micro]m, and 30 [micro]m, 1 [micro]m particles have the lowest deposition in upper respiratory systems and pose the highest risk. For 30 [micro]m particles, they are more likely to be caught by the airway surfaces before they penetrate to deeper airways. The risk of dose for 0.01 [micro]m particles is in between that of the 1 [micro]m and 30 [micro]m particles.
Human exposure risk to particles of size 0.01 [micro]m, 1 [micro]m, and 30 [micro]m is evaluated by performing CFD study of the transport of these particles once inhaled. Based on the study, following observations are made:
* Particle of 1 [micro]m poses the highest risk to human respiratory health as it is more likely to penetrate into deeper lung.
* Of the three sizes, particle of 30 [micro]m are more likely to be caught by upper respiratory airways.
* Airflow patterns in the trachea and bronchi were affected more by the airway geometry (larynx) than the breathing intensity. Turbulence occurs at mild breathing condition.
* Turbulence significantly affects the particle transport and dispersion in the human respiratory system.
[C.sub.D] = particle drag coefficient
d = particle diameter
[F.sub.t.sup.L] = lift force
[g.sub.t] = acceleration of gravity
k = turbulence kinetic energy
[n.sub.t] = Brownian force vector
p = pressure of the fluid
P = Turbulence production
[Re.sub.p] = Particle Reynolds number
[R.sub.ij] = Reynolds stress tensor of the fluid
t = time
[[bar.u].sub.i], [u.sub.i], [u'.sub.i] = mean, instantaneous and fluctuation velocity vector of the fluid
[u.sub.i.sup.p] = velocity vector of particle
[x.sub.i] = position vector, i = 1, 2, 3 for stream wise, lateral and span wise direction
[rho] = mass density of the fluid
[v.sub.T] = eddy viscosity of the fluid
[epsilon] = turbulence dissipation rate
[tau] = particle relaxation time
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Schlesinger, R.B., D.E. Bohning, T.L. Chan, and M. Lippmann. 1977. Particle deposition in a hollow cast of human tracheobronchial tree. Journal of Aerosol Science, 8, pp. 429-445.
Smith, S., Y.S. Cheng, and H.C. Yeh. 2001. Deposition of ul-trafine particles in human tracheobronchial airways of adults and children, Aerosol Science and Technology, 35, pp. 697-709.
Tian, L. and G. Ahmadi. 2007. Particle deposition in turbulent duct flows--Comparisons of different model predictions. Journal of Aerosol Science, 38, pp. 377-397.
Zhou, Y. and Y.S. Cheng. 2005. Particle deposition in a cast of human tracheobronchial airways. Aerosol Science and Technology, 39, pp. 492-500.
Lin Tian is assistant professor in the Department of Science and Engineering Technology, State University of New York, Canton, NY. Goodarz Ahmadi is professor in the Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY Philip K. Hopke is professor in the Department of Chemical Engineering, Clarkson University, Potsdam, NY. Yung-Sung Cheng is senior scientist and research director at Lovelace Respiratory Research Institute, Albuqerque, NM.
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|Author:||Tian, Lin; Ahmadi, Goodarz; Hopke, Philip K.; Cheng, Yung-Sung|
|Date:||Jan 1, 2010|
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