Nomenclaturec : propagation velocity of number density

distribution of bubbles [mm/s] v : advection velocity of bubbles [mm/s] t : time [s] Re : Reynolds number [-] R : Radius of bubble [mm] Fr : Froude number [-] U : cross-sectional average flow velocity [mm/s] L : height of gas-liquid interface [mm] l : hight of the suspension [mm] g : gravitational acceleration [m/s2] Greek letters

: normalized number density of bubbles [-] : angle of inclined wall [-] : viscosity [mPa s] : density [kg/m3] : void fraction [-] : Ensemble average of time variation

of intensity [mm/s]

Subscriptsx : x direction y : y direction T.–S. : Tollmien-Schlichting wave K.–H. : Kelvin-Helmholtz wave [1] Lee, W. T., McKechnie, J. S. and Devereux, M.

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[16] Jordinson, R., The Flat Plate Boundary Layer. Part 1. Numerical Integration of the Orr-Sommerfeld Equation, Journal of Fluid Mechanics, Vol. 43, 801-811 (1970).

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* 2017.11.9 ** 036-8561 TEL: (0173)39-3662 E-mail: mshirota@hirosaki-u. ac.jp *** †

Numerical Simulation of Particle Deposition in an Upper Respiratory Tract

*** FUJII Sayaka SHIROTA Minori KASAMATSU Yuki TANABE Tsubasa

† INAMURA Takao OKABE Takahiro TASAKA Sadatomo

Abstract Inhaled drug delivery is the most common treatment for respiratory disease today. The inhaled particles deposit mostly in upper respiratory even if they are aim to deposit in lower regions such as lung. Many previous studies have revealed that the Stokes number, which is the ratio of a characteristic time of the flow field Tf to the relaxation time of the particle Tp, well describes the deposition in upper respiratory tracts. However, most of the previous studies defined Tf as the ratio of the inlet diameter to the inlet velocity. This assumption oversimplifies a realistic flow field in an upper respiratory where the characteristic length and velocity greatly depends on the region. Here we propose a Stokes number, Stwall, in which Tf employs the inverse velocity gradient on the respiratory tract surface. As a result of our numerical simulation studies, we revealed that we can estimate the local deposition position with Stwall which can be calculated with the CFD of the airflows only. We also found that even the deposition fraction by the inertial impaction of particles of sinusoidal inflow rates can be well described with the impaction factor if it is weighted with the air inflow rate.

Keywords: Particle deposition, Respiratory airway, Stokes number, Inertial impaction, LES

1.

[1 5][6-20]

CT[6 11]

Japanese J. Multiphase Flow Vol. 32 No. 1（2018）132

- 4 -

[12 14] Aerosol Research Laboratory of Alberta

10 CT

[15,16]

[12,17 19]

RANS LES DNSDNS[11,12]

RANS RANS k- [18,19] k-[7,13,16]

[8,10,20]RANS

EIM Eddy interaction modelEIM

3.2 LES

SGS Smagorinsky [15,17] Smagorinsky-Lilly [6,14]

[8-10,20]

St St

St

[5]L U

[2]

Nicolaou et al.

[12]

StSt

St

2.

1

1 m ~ 10 m s

混相流 32 巻 １号（2018） 133

[12 14] Aerosol Research Laboratory of Alberta

10 CT

[15,16]

[12,17 19]

RANS LES DNSDNS[11,12]

RANS RANS k- [18,19] k-[7,13,16]

[8,10,20]RANS

EIM Eddy interaction modelEIM

3.2 LES

SGS Smagorinsky [15,17] Smagorinsky-Lilly [6,14]

[8-10,20]

St St

St

[5]L U

[2]

Nicolaou et al.

[12]

StSt

St

2.

1

1 m ~ 10 m s

Japanese J. Multiphase Flow Vol. 32 No. 1（2018）134

混相流 32 巻 １号（2018） 135

Japanese J. Multiphase Flow Vol. 32 No. 1（2018）136

LES 3

(Impaction Parameter)(Impaction

Parameter) [13]

1Fig.8

QFig.9

Fig.10 (a)2 (b)

3

(100 500 s) (5 20 s)

(1s)

t

5.

Stwall

(1) Stwall

Stwall

25 (2)

Nomenclature

: Stokes number : Characteristic length : Characteristic velocity : Particle diameter

: Air inflow rate : Characteristic time scale of the flow : Particle response time

: Air velocity parallel to the wall : Distance from the wall

: Dimensionless distance from the wall Greek letters

: wall shear stress : Density of particle : Viscosity of air

[1 ] Grgic, B., Finlay, W. H. and Heenan, A. F., Regional Aerosol Deposition and Flow Measurements in an Idealized Mouth and Throat, J. Aerosol Sci., Vol. 35(1), 21–32 (2004).

[2] Grgic, B., Finlay, W. H., Burnell, P. K. P. and Heenan, A. F., In Vitro Intersubject and Intrasubject Deposition Measurements in Realistic Mouth-Throat Geometries, J. Aerosol Sci., Vol. 35(8), 1025–1040 (2004).

[3] Grgic, B., Martin, A. R. and Finlay, W. H., The Effect of Unsteady Flow Rate Increase on in Vitro Mouth-Throat Deposition of Inhaled Boluses, J. Aerosol Sci., Vol. 37(10), 1222–1233 (2006).

[4] Sun, K. and Lu, L., Particle Flow Behavior of Distribution and Deposition Throughout 90° Bends: Analysis of Influencing Factors, J. Aerosol Sci., Vol. 65, 26–41 (2013).

[5] Cheng, Y. S., Zhou, Y. and Su, W.-C., Deposition

混相流 32 巻 １号（2018） 137

LES 3

(Impaction Parameter)(Impaction

Parameter) [13]

1Fig.8

QFig.9

Fig.10 (a)2 (b)

3

(100 500 s) (5 20 s)

(1s)

t

5.

Stwall

(1) Stwall

Stwall

25 (2)

Nomenclature

: Stokes number : Characteristic length : Characteristic velocity : Particle diameter

: Air inflow rate : Characteristic time scale of the flow : Particle response time

: Air velocity parallel to the wall : Distance from the wall

: Dimensionless distance from the wall Greek letters

: wall shear stress : Density of particle : Viscosity of air

[1 ] Grgic, B., Finlay, W. H. and Heenan, A. F., Regional Aerosol Deposition and Flow Measurements in an Idealized Mouth and Throat, J. Aerosol Sci., Vol. 35(1), 21–32 (2004).

[2] Grgic, B., Finlay, W. H., Burnell, P. K. P. and Heenan, A. F., In Vitro Intersubject and Intrasubject Deposition Measurements in Realistic Mouth-Throat Geometries, J. Aerosol Sci., Vol. 35(8), 1025–1040 (2004).

[3] Grgic, B., Martin, A. R. and Finlay, W. H., The Effect of Unsteady Flow Rate Increase on in Vitro Mouth-Throat Deposition of Inhaled Boluses, J. Aerosol Sci., Vol. 37(10), 1222–1233 (2006).

[4] Sun, K. and Lu, L., Particle Flow Behavior of Distribution and Deposition Throughout 90° Bends: Analysis of Influencing Factors, J. Aerosol Sci., Vol. 65, 26–41 (2013).

[5] Cheng, Y. S., Zhou, Y. and Su, W.-C., Deposition

Japanese J. Multiphase Flow Vol. 32 No. 1（2018）138

of Particles in Human Mouth–Throat Replicas and a USP Induction Port, J. Aerosol Med. Pulm. Drug Deliv., Vol. 28(3), 147–155 (2015).

[6] Koullapis, P. G., Kassinos, S. C., Bivolarova, M. and Melikov, A. K., Particle Deposition in a Realistic Geometry of the Human Conducting Airways: Effects of Inlet Velocity Profile, Inhalation Flowrate and Electrostatic Charge, J. Biomech., Vol. 49(11), 2201-2212 (2016).

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[8] Takano, H., Nishida, N., Itoh, M., Hyo, N. and Majima, Y., Inhaled Particle Deposition in Unsteady-State Respiratory Flow at a Numerically Constructed Model of the Human Larynx, J. Aerosol Med., Vol 19, 314–28 (2006).

[9] Naseri, A., Shaghaghian, S., Abouali, O. and Ahmadi, G., Numerical Investigation of Transient Transport and Deposition of Microparticles Under Unsteady Inspiratory Flow in Human Upper Airways, Respir. Physiol. Neurobiol., Vol. 244, 56–72 (2017).

[10] Se, C., Inthavong, K. and Tu, J., Unsteady Particle Deposition in a Human Nasal Cavity during Inhalation, J. Comput. Multiph. Flows, Vol. 2(4), 207–218 (2010).

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[13] Yousefi, M., Inthavong, K. and Tu, J., Microparticle Transport and Deposition in the

Human Oral Airway: Toward the Smart Spacer, Aerosol Sci. Technol., Vol. 49(11), 1109–1120 (2015).

[14] Agnihotri, V., Ghorbaniasl, G., Verbanck, S. and Lacor, C., On the Multiple LES Frozen Field Approach for the Prediction of Particle Deposition in the Human Upper Respiratory Tract, J. Aerosol Sci., Vol. 68, 58–72 (2014).

[15] Jin, H. H., Fan, J. R., Zeng, M. J. and Cen, K. F., Large Eddy Simulation of Inhaled Particle Deposition Within the Human Upper Respiratory Tract, J. Aerosol Sci., Vol 38(3), 257–268 (2007).

[16] Matida, E. A., Finlay, W. H., Lange, C. F. and Grgic, B., Improved Numerical Simulation of Aerosol Deposition in an Idealized Mouth-Throat, J. Aerosol Sci., Vol. 35(1), 1–19 (2004).

[17] Berrouk, A. S. and Laurence, D., Stochastic Modelling of Aerosol Deposition for LES of 90° Bend Turbulent Flow, Int. J. Heat Fluid Flow, Vol. 29(4), 1010–1028 (2008).

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