Validation is an important part of any modeling study. In the case of simulating aerosol particle transport in the alveolated airways, such validation has been scarce in the past. The current study used a scaled-up in vitro model to validate the CFD predictions with PIV and PTV experimental data. While this is still an in vitro model, such data provided some valuable information regarding the accuracy of numerical simulations of fluid flow and particle transport in small airways and of low Reynolds number flow in general. Oldham (2006)
recently summarized some of the issues related to validating CFD-derived inhaled aerosol deposition predictions, such as lack of a consensus for what is a validated CFD model, difficulties in creating the exact desired airway geometry, and difficulties in controlling and modeling all important physical factors involved in particle deposition such as particle charge, etc. Although the issues were discussed in the context of large airways, it is also applicable to cases in alveolated airways. In the current study we have restricted our efforts to comparing CFD predicted velocity profiles and particle trajectories with those measured from experiments in an identical geometrical model.
The fast re-establishment of parabolic velocity profile after a disturbance (bifurcation) is consistent with a typical low Reynolds number viscous flow, and support the use of flat velocity profile at the model entrance. Indeed, for laminar flow in a straight tube, the entrance length LE
, which is a measure of the distance required by the flow to be fully developed, is expressed by (Munson et al., 2006
where D is the lumen diameter and Re is the flow Reynolds’ number at the entrance. At the inlet of the model in this study, LE
/D is 0.0078 and LE
is 0.156 mm. Thus velocity profile will be fully developed 0.156 mm from the inlet. Therefore, it is unlikely that the use of any other velocity profiles such as a parabolic profile at the entrance of the model will lead to different results. The independence on initial particle velocity showed that the system had a very short response time and that the particles reached final equilibrium velocity quickly after being released into the flow field. This is consistent with the very short relaxation time (5.5e-4 second for 1.2 mm bead and 9.5e-5 second for 0.5 mm bead) of these beads in the experiments.
To obtain the velocity profiles at the twelve cross sections (), a uniform distribution of 80 sampling points along the cross section were used, thus the distance between sampling points was equal. To obtain the flow field values at these arbitrarily selected points, a linear interpolation based on the values at nearby CFD mesh cell centers were used. At some points the slope of the velocity-radial distance curve was larger than those at nearby points. Therefore, the equal distance of sampling points in space did not resulted in equal distance on the velocity-distance curve, creating visual discontinuities in some velocity profiles. Such discontinuities did not have any physical significance but rather were due to the discrete nature of the data.
The particle sizes used in this study were chosen based on practical experimental limitations, such as availability of materials. Nevertheless, the interpretation of these experimental data and the corresponding CFD simulations, and the extrapolation to the in vivo system are not necessarily restricted to the assumptions made in designing the experiments. Previous analysis (Theunissen et al., 2006
) showed that it is hard to match both Stokes number and velocity ratio (particle settling velocity to mean flow velocity) between in vivo and in vitro systems. In the current study the in vitro particle sizes were selected based on similarity of particle Reynolds number and velocity ratio. By these criteria, the corresponding in vivo aerosol size is 14.6 μm for 1.2 mm bead and 6.1 μm for 0.5 mm bead. Aerosol particle of 14.6 μm is very unlikely to occur in the pulmonary region due to impaction and sedimentation in the conducting airways. Including this size in the current study is mainly for validation purposes, and although the current study was designed in the context of pulmonary aerosol transport, the data themselves may not necessarily be restricted to this specific field.
By considering the Stokes number the current data may also be interpreted differently. In the experimental system the Stokes number (St = ρpdp2U/(18μD), U is mean flow velocity, and D is tube diameter) is about 2.2e-4 for the 1.2 mm bead, and 3.8e-5 for the 0.5 mm bead. Using data based on the 20th generation of the Weibel model, the Stokes numbers for 14.6 μm and 6.1 μm aerosol particles are 0.02 and 3.5e-3, respectively, which are two orders of magnitude larger than those of the beads. For the same Stokes numbers, the in vivo aerosol sizes are 1.7 μm and 0.7 μm, respectively. Therefore, although the in vitro particle sizes were initially selected based on similarity of particle Reynolds number and velocity ratio, by Stokes number similarity the corresponding in vivo aerosol sizes are smaller and fall within the size of interests for respiratory aerosols. According to the Stokes-Einstein relation, the diffusion coefficient (Ddf = KbT/(3πμdp), Kb is Boltzmann’s constant, T is absolute temperature) for 0.5 and 1.2 mm beads in silicone oil were 8.8e-19 and 3.7e-19 m2s−1, respectively. Therefore, diffusion was negligible for these beads and was not considered in CFD simulations.
Kim et al. (1998)
studied the motion of a freely moving sphere injected into an initially stationary or oscillating fluid for particle Reynolds number ranging between 2 and 150 and particle to fluid density ratio ranging between 5 and 200. Results showed that the relative magnitude of the forces acting on the sphere depends strongly on the particle to fluid density ratio. When the density ratio is much larger than one, the total drag force can be well approximated by the steady viscous drag force; however, when the density ratio is small (e.g. 5), the particle history force and force due to initial velocity difference between the particle and the carrier fluid become important so that the total drag force differs slightly from the steady viscous drag force in both magnitude and phase. In the current study the history force and the force due to initial velocity difference were ignored, although the particle to fluid density ratio (7800/970 = 8.04) is much smaller than that for realistic aerosol (around 1000). Since the flow Reynolds number (<0.13) and particle Reynolds number (<0.008) in the current study were significantly smaller than those in the study of Kim et al. (1998)
, and based on the observation that the particle trajectory was insensitive to initial particle velocity, it seems that these ignored forces did not significantly affect the particle trajectory in this study.
Almost all previous experimental validation studies of particle deposition in the large human airways compared the total or averaged deposition efficiency using a large amount of particles. In contract, the current study has tried to directly validate the trajectory of each individual particle. The current study was designed to evaluate the accuracy of using CFD to simulate airflow and aerosol transport in pulmonary region of the human lung, using an in vitro model by dynamic similarity principle. The data in this study showed that CFD simulations can provide reasonably accurate predictions of flow field and particle trajectory for predominantly viscous flows in the in vitro model. It is expected that comparable accuracy can be obtained for CFD simulations in realistic models of the human alveolated airways using similar numerical techniques.