Micron Particle Deposition in the Nasal Cavity Using the v2 -f Model

8/6/2019 Micron Particle Deposition in the Nasal Cavity Using the v2 -f Model

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Micron Particle Deposition in the Nasal CavityUsing the v 2-f Model

Kiao Inthavong, Jiyuan Tu, Christian Heschl

Abstract From a health perspective inhaled particles can lead to many respiratory

ailments. In terms of modelling, the introduction of particles involves a secondary

phase (usually solid or liquid) to be present within the primary phase (usually gas

or liquid). The influence of the fluid flow regime, whether it is laminar or turbu-

lent plays a significant role on micron particle dispersion. RANS (Reynolds Av-

eraged Navier-Stokes) based turbulence models provide simpler and quicker mod-

elling over the more computationally expensive Large Eddy Simulations. However

this comes at an expense in that the RANS models fails to resolve the near wall tur-

bulence fluctuating quantities due to the turbulent isotropic assumption. This error

further propagates to the Lagrangian particle dispersion. Using the v2-f the normal

to the wall turbulent fluctuation, can be solved and used on the particle dispersion

model directly in order to overcome the isotropic properties of RANS turbulence

models. This technique is first validated against experimental pipe flow for a 90o-

bend and then applied to particle disperion in a human nasal cavity using Ansys-

Fluent. The results arising from the nasal cavity application will increase the un-

derstanding of particle deposition in the respiratory airway. Greater knowledge of particle dynamics may lead to safer guidelines in the context of exposure limits to

toxic and polluted air.

Kiao Inthavong

RMIT University, Bundoora, Australia e-mail: [email protected]

Jiyuan Tu

RMIT University, Bundoora, Australia e-mail: [email protected]

Christian HeschlFachhochschulstudiengange Burgenland - University of Applied Science, Pinkafeld, Austria e-

mail: [email protected]

1



2 Kiao Inthavong, Jiyuan Tu, Christian Heschl

1 Introduction

Studies of gas-particle flows in the human nasal cavity have generated a lot of in-

terest recently as computational modelling offers a complementary alternative to

experimental methods. In particular the inhalability of particles has been studiedwhich showed aspiration efficiencies of 60-80% [3] and 50-95% [2] for micron par-

ticles between 1-40µ m. In terms of modelling, the introduction of particles involves

a secondary phase (usually solid or liquid) to be present in conjunction with the pri-

mary phase (usually gas or liquid), leading into the field of multiphase flows. The

dispersed phase can be modelled under two different approaches, i.e. Lagrangian or

Eulerian. Both approaches have their own advantages in computational modelling,

however this paper is limited to the Lagrangian approach only. Micron particles

are dominated by its inertial property which lead to inertial impaction upon sud-

den changes in the airflow streamlines. When the flow field is turbulent, turbulent

dispersion of the particles has to be addressed. Reynolds Averaged Navier Stokes

(RANS) based turbulence models are often used to resolve the flow field, as it pro-

vides simpler and quicker modeling over the more computationally intensive Large

Eddy Simulations. However this comes at an expense in that the RANS models fails

to resolve the turbulence dissipation and anisotropy in the near wall regions (i.e.

fixed stationary surfaces or boundaries). The turbulence fluctuating quantities are

overpredicted by RANS models and this error propagates to the particle dispersion.

In this paper, the v2-f and the k-ε turbulence model are used to solve the fluid flow,

while a dispersed phase model (Lagrangian reference) is used to track the individ-

ual particles. Turbulent dispersion of particles is modeled by the so-called Discrete

Random Walk found in Ansys Fluent. The turbulent particle tracking scheme is

evaluated and the requirements for the models to account for the anisotropic flow

behavior in the near wall region is discussed. Successful modelling of micron par-

ticles will allow more flexibility in simulations of gas-particle flows for inhalation

toxicology, and drug delivery studies through the human respiratory system.

2 Model Description

The 90o curvatures in the nasal cavity are located just after the nostril entrance, and

at the nasopharynx region (Fig. 1). These two bends act as a naturally occurring filter

system that traps high inertial particles as they travel through the airway. A simpler

test case for evaluation of the CFD modeling is to use a 90 o-bend pipe based on

experimental [5] and Large Eddy Simulation [1] data (Fig. 1). The computational

pipe (0.6million cells) has a diameter of 0.02, radius of curvature Rb = 0.056, a

curvature ratio of Ro = 5.6, Re=10,000 and De=4225. The nasal cavity (3.5million

cells) is subjected to a Re=2498 at the outlet which corresponds to a flow rate of

20L/min.The realizable k-ε turbulence model with enhanced wall function is applied

through Ansys-Fluent and its model equations are provided in Ansys-Fluent (An-



Micron Particle Deposition in the Nasal Cavity Using the v2-f Model 3

Fig. 1 (a)Lateral view of the nasal cavity model showing the left cavity side. Two 90o curvature

bends are present; one at the nostril inlet and the other at the nasopharynx region. (b)Lateral view

of the 90o bend pipe.

sys 2009). The The v2-f model was implemented in Fluent via user-defined scalar

interface (UDS). The segregated solver in Fluent is used to solve the additional

transport equations for v2 and f , and therefore the code friendly v2-f version by

Lien and Kalitzin [4] is applied to improve convergency. For the Discrete PhaseModel (DPM) the Lagrangian approach is used. The normal (perpendicular to the

wall) fluctuation component, (v) in the near wall region (y+ ≈ 0-30) is significantly

damped in comparison to the corresponding fluctuating components, u and w. With

the v2-f model, the turbulent fluctuation component perpendicular to the wall is re-

solved which can then be applied to the DRW model in the near wall region. The

modified DRW model applied to regions where y+ < 30 is then reformulated as

v = ζ

v20.5

. The number of droplets tracked was checked for statistical indepen-

dence since the turbulent dispersion is modelled based on a stochastic process. Inde-

pendence was achieved for 40,000 droplets since an increase of droplets to 60,000

droplets yielded a difference of 0.1% in the inhalation efficiency. To achieve the uni-

form droplet concentration assumption, droplets were released at the same velocity

as the freestream.

3 Results and Discussion

Velocity contours at the 45o and 90o deflection are shown in Fig. 2. It can be seen

that the high velocity region moves from the inner wall to the outer wall (from the

45o deflection to the 90o deflection). A larger region of slower velocity is found at

the inner wall region as the secondary flow effects progress with the flow moving

through the bend from 45o to 90o. In addition the streamlines highlight the move-

ment of the fluid from the core towards the outer pipe wall with two resultant vor-

tices near the inner wall region. The secondary flow features are captured well with

the LES model by [1]. The v2-f model was also able to capture some of the sec-

ondary flow effects although at a reduced level. The region of slow moving fluid is

much smaller than that of the LES data especially at the 45o deflection. Even worse




Fig. 2 v2-f and k-ε simulation

results compared with LES

data by Berrouk and Laurence

(2008). The angled deflections

indicate the pipe curvature lo-

cation. The inside wall of the

pipe is on the left side and the

outer wall of the pipe is on

the right indicated by I and O

respectively.

performing is the k-ε model which does not capture the slow moving region at all

at the 45o deflection. Furthermore, the streamlines in the core flow, moving towards

the outer wall are distorted at the 90o deflection which is not reproduced by the two

RANS turbulence models.

Fig. 3 a) RMS of velocity fluctuations for v’. The CFD simulations for the v2− f and k −ε simulations had a Reτ =267 while the DNS data from Abe et al. (2001) is shown for Reτ =395. b)

Particle deposition in a pipe bend for Re=10000.

The normal fluctuating velocity component (v’) taken at the pipe bend entrance

is chosen for comparison with DNS data because this is the component that is

overpredicted by the DRW models when a RANS-based turbulence model is ap-

plied. In the DRW model, the particle takes the fluctating velocity component as

v = u = w=

2k /3. Fig. 3 shows that when this occurs the v’ component is

overpredicted in both the v2-f and the k-ε model. Because the v2-f model provides

directly the v2 profile near the wall, the v2 can be defined directly into the DRW



Micron Particle Deposition in the Nasal Cavity Using the v2-f Model 5

model. Its profile is shown in Fig. 3 by the dashed line and denoted as v2-f(v2)

which shows a better improvement in the near wall region. Therefore the proposed

modification of the DRW model is expected to improve the turbulent particle dis-

persion. The predicted deposition of 1-30 µ m particles in a 90o bend pipe compared

with the experimental data of Pui et al. [5] is shown in Fig. 3b, where the particleStokes number is based on the pipe inlet conditions. The deposition efficiency for

the DRW model taking the default isotropic fluctuating component from k (turbulent

kinetic energy) shows an overprediction in the deposition for St < 0.1 (square sym-

bols in Fig. 3b). The overprediction becomes greater, away from the experimental

data as the St decreases further. When the DRW model is modified and the normal

fluctuating component takes on the v2 profile, the deposition efficiency for St < 0.1

is improved.

Fig. 4 Flow field and parti-

cle deposition patterns taken

at cross-sectional slices A-D

as depicted in Fig. 1. The

contours show axial velocity

magnitudes while the surface

streamlines represent the sec-

ondary flow. Particles passing

through the slices are coloured

by velocity magnitude. The

percentage of 1µ m and 15µ mparticles passing through each

cross-section is given beloweach slice.

Particle tracking analysis using the DRW-mod-v2-f model is performed and the

coordinates of the particles as they move through specified slice planes in the ge-

ometry are recorded. This can give an indication of how the particles are moving

through the nasal cavity, and also how many are passing through. Three cross-

sectional slices are created (Fig.1) which are viewed from the front of the nose. Slice

A exhibits the highest maximum velocity, with streamlines directed toward the inner

nasal septum wall. At this slice, only 77% of 15µ m particles pass through, mean-

ing that ≈23% has deposited already in the anterior nasal cavity (nasal vestibule)

region. The particles are concentrated close to the ceiling of the passageways with

high velocities. The streamlines in Slice A tell us that the secondary flow will pushthe particles both upwards and downwards. This results in the 1µ m particle dispers-

ing more evenly through Slice B whereas the 15µ m particles remain close to the




top of the slice because of its high inertial property. All particles are mainly passing

through the inner side of the passageway (the nasal septum wall side). For the 15µ mparticles there is a large drop in the number of particles passing through from Slice

A to Slice B ( 61%), meaning that this is the main section of deposition for the parti-

cles. Interestingly this is also the main deposition region for the 1µ m particles witha percentage deposition of 3.3%. At Slice C, the airflow between the left and right

nasal cavity chambers have merged. Here we see complex secondary flow patterns,

exhibiting two vortices and two peak axial velocity regions each of which are almost

symmetrical to each other. The streamlines from the left and right sides converge in

the middle of the slice and are directed towards the inner curvature wall side of the

slice. Nearly all the particles moving from Slice B to Slice C have passed through

the passageway which has now expanded in cross-sectional area. The main cluster

of particles for the 15µ m particles is still found in the superior regions of the slice,

which is now the outer curvature wall side. These flow patterns provide a predictive

tool as to where the particles may travel. The particle tracking model can be used to

determine the localised regions of high particle deposition.

4 Conclusion

The Discrete Random Walk (DRW) model used in Ansys-Fluent was used to simu-

late dispersed particles through a wall-bounded geometry such as the human nasal

cavity. A breathing rate of 20L/min was used and a RANS based turbulence models

in the form of the k-ε and the v2-f model was applied. It was shown that by applying

the small modification of v=

√v2 directly the DRW can take on a more realistic

turbulent dispersion in the near wall region. A 90o pipe bend was used to validate the

model which showed an improvements to the particle deposition. The nasal cavity

was then used as an application which also showed that the modified DRW model

improved the deposition efficiency for smaller inertial particles.

References

1. Abdallah S. Berrouk and Dominique Laurence. Stochastic modelling of aerosol deposition for

les of 90◦ bend turbulent flow. International Journal of Heat and Fluid Flow, 29(4):1010–1028,

2008.2. Nola J. Kennedy and William C. Hinds. Inhalability of large solid particles. Journal of Aerosol

Science, 33:237–255, 2002.3. Camby Mei King Se, Kiao Inthavong, and Jiyuan Tu. Inhalability of micron particles through

the nose and mouth. Inhalation Toxicology, 22(4):287–300, NaN.4. F. Lien and G. Kalitzin. Computations of transonic flow with the v2-f turbulence model. Inter-

national Journal of Heat and Fluid Flow, 22:53–56, 2001.

5. David Y. H. Pui, Francisc Romay-Novas, and Benjamin Y. H. Liu. Experimental study of particle deposition in bends of circular cross section. Aerosol Science and Technology, 7(3):301

– 315, 1987.

Micron Particle Deposition in the Nasal Cavity Using the v2 -f Model

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