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==Key Fluid Physics and Deposition Mechanisms==
==Key Fluid Physics and Deposition Mechanisms==
Airflow in the human upper airways transitions to turbulence due to geometric effects,
Airflow in the human upper airways transitions to turbulence due to geometric effects,
such as the bent in the oropharyngeal region and the constriction at the glottis. The bent
such as the bend in the oropharyngeal region and the constriction at the glottis. The bend
in the oropharynx causes substantial filtering of inhaled aerosols due to inertial impaction
in the oropharynx causes substantial filtering of inhaled aerosols due to inertial impaction
on the airway walls. Filtering in the extrathoracic airways increases as the particle size
on the airway walls. Filtering in the extrathoracic airways increases as the particle size
and inhalation flowrate increase.
and inhalation flowrate increase.
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the air travels through a larger total cross-sectional area. As a result, airflow relaminarizes
the air travels through a larger total cross-sectional area. As a result, airflow relaminarizes
in the first generations. At the flowrate examined in the present AC, the main deposition
in the first generations. At the flowrate examined in the present AC, the main deposition
mechanism in this region is inertial impaction, with significant deposition at the bents and
mechanism in this region is inertial impaction, with significant deposition at the bends and
the bifurcations. At lower flowrates, deposition can also be influenced by gravitational
the bifurcations. At lower flowrates, deposition can also be influenced by gravitational
sedimentation because the residence times of the particles in the bronchial airways is
sedimentation because the residence times of the particles in the bronchial airways is
longer.
longer.
==Application Uncertainties==
==Application Uncertainties==
The differences between measurements and simulations can result from several uncertainties
The differences between measurements and simulations can result from several uncertainties
Line 73: Line 74:
tracking. Recommended values for the parameters involved in mesh generation (initial cell
tracking. Recommended values for the parameters involved in mesh generation (initial cell
height, average expansion ratio, number of near-wall prism layers, average cell volume in
height, average expansion ratio, number of near-wall prism layers, average cell volume in
the domain, number of computational cells etc.) can be found in Table 5.
the domain, number of computational cells etc.) can be found in
[[CFD_Simulations_AC7-01#table5|Table 5]].
 
==Physical Modelling==
==Physical Modelling==
===Turbulence models===
===Turbulence models===
In the LES simulations, the dynamic version of the Smagorinsky-Lilly subgrid scale model
In the LES simulations, the dynamic version of the Smagorinsky-Lilly subgrid scale model
(Lilly, 1992) is adopted in order to examine the unsteady flow in the realistic airway
([[Best_Practice_Advice_AC7-01#lilly1992|Lilly, 1992]])
is adopted in order to examine the unsteady flow in the realistic airway
geometries. Previous studies have shown that this model performs well in transitional
geometries. Previous studies have shown that this model performs well in transitional
flows in the human airways (Radhakrishnan & Kassinos, 2009; Koullapis ''et al.'', 2016).
flows in the human airways
([[Best_Practice_Advice_AC7-01#radhakrishnan2009|Radhakrishnan & Kassinos, 2009]];
[[Best_Practice_Advice_AC7-01#koullapis2016|Koullapis ''et al.'', 2016]]).


For the RANS simulations, the standard k-ω SST turbulence model is used due to
For the RANS simulations, the standard ''k-ω'' SST turbulence model is used due to
its good prediction of such wall—bounded flow (i.e. using a blending between wall and
its good prediction of such wall-bounded flow (i.e. using a blending between wall and
free-stream region) and low computational cost. Other turbulence models have not been
free-stream region) and low computational cost. Other turbulence models have not been
considered but based on prior experince they are exprected to perform worse.
considered but based on prior experince they are exprected to perform worse.
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===Lagrangian particle tracking===
===Lagrangian particle tracking===
Lagrangian particle tracking has been adopted in the present application. Although there
Lagrangian particle tracking has been adopted in the present application. Although there
is a number of forces acting on the particles (Drag, buoyancy, Basset (or history), pressure
is a number of forces acting on the particles (drag, buoyancy, Basset (or history), pressure
gradient force, lift due to shear and rotation and Brownian forces), only few of them
gradient force, lift due to shear and rotation and Brownian forces), only few of them
are important when considering the transport of micron—sized particles in the human
are important when considering the transport of micron-sized particles in the human
airways. This is mainly because the particle density is much greater than the density of
airways. This is mainly because the particle density is much greater than the density of
the air (''&rho;<sub>p</sub>''&nbsp;/&nbsp;''&rho;<sub>f</sub>''&nbsp;&ge;&nbsp;1000).
the air
<math>{(\rho_p/\rho_f\ge 1000)}</math>.
Furthermore, in numerical simulations the particles are assumed
Furthermore, in numerical simulations the particles are assumed
spherical and, as a result, the important forces that need to be taken into account in lung
spherical and, as a result, the important forces that need to be taken into account in lung
deposition studies are drag, gravity and Brownian motion force. However, Lift force due
deposition studies are drag, gravity and Brownian motion force. However, lift force due
to shear can also be important as particle size increases. This is evident in figure 21, that
to shear can also be important as particle size increases. This is evident in figure 21, that
plots deposition fraction in the mouth—throat / trachea (segments 1&2) of the benchmark
plots deposition fraction in the mouth-throat / trachea (segments 1&2) of the benchmark
geometry for three particle sizes (1, 4.3 and 10&mu;m) at a flowrate of 60 L / min (LES results).
geometry for three particle sizes (1, 4.3 and 10<math>{\mu m}</math>) at a flowrate of
In this case, the expression for the shear lift is obtained by Saflman (1965), Saflman (1968)
60 L / min (LES results).
and Mei (1992). It is observed that the Saflman lift force results in an increase in the
In this case, the expression for the shear lift is obtained by
deposition of 10&mu;m particles by approximately 5%.
[[Best_Practice_Advice_AC7-01#saffman1965|Saffman&nbsp;(1965)]],
[[Best_Practice_Advice_AC7-01#saffman1968|Saffman&nbsp;(1968)]]
and [[Best_Practice_Advice_AC7-01#mei1992|Mei&nbsp;(1992)]].
It is observed that the Saffman lift force results in an increase in the
deposition of 10<math>{\mu m}</math> particles by approximately 5%.




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|align="center"|[[Image:AC7-01_fig21.png|650px]]
|align="center"|[[Image:AC7-01_fig21.png|650px]]
|-
|-
|align="left"|'''Figure 21:''' LES predictions of Deposition fraction in the mouth—throat / trachea (segments 1&2) of the benchmark geometry for three particle sizes (1, 4.3 and 100<math>{\mu}</math>m) at a flowrate of 60 L/min.
|align="left" width=650|'''Figure 21:''' LES predictions of Deposition fraction in the mouth-throat / trachea (segments 1&2) of the benchmark geometry for three particle sizes (1, 4.3 and 10<math>{\mu}</math>m) at a flowrate of 60 L/min.
|}
|}


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In our LES the grid size is larger than the Kolmogorov scale and thus this
In our LES the grid size is larger than the Kolmogorov scale and thus this
condition is satisfied. Specifically, the minimum ratio of resolved scales (mesh size near
condition is satisfied. Specifically, the minimum ratio of resolved scales (mesh size near
the wall) to the particle size is 40 for 1&mu;m particles and 4 for 10&mu;m.
the wall) to the particle size is 40 for 1<math>{\mu m}</math> particles and
4 for 10<math>{\mu m}</math>.


In point-particle LES, the resolved velocities are used in the calculation of the forces
In point-particle LES, the resolved velocities are used in the calculation of the forces
Line 137: Line 149:
deposition in the airways has not been investigated.
deposition in the airways has not been investigated.


Armenio ''et&nbsp;al.'' (1999) examined the effects of small-scale velocity fluctuations on the
[[Best_Practice_Advice_AC7-01#armenio1999|Armenio&nbsp;''et&nbsp;al.''&nbsp;(1999)]]
examined the effects of small-scale velocity fluctuations on the
motion of tracer and inertial particles in a turbulent channel flow at
motion of tracer and inertial particles in a turbulent channel flow at
Re<sub>&tau;</sub>&nbsp;=&nbsp;175.
<math>{Re_\tau=175}</math>.
They concluded that well-resolved LES with an adequate LES model can provide fairly accurate
They concluded that well-resolved LES with an adequate LES model can provide fairly accurate
particle statistics for moderate Reynolds number flows. They also observed that errors in
particle statistics for moderate Reynolds number flows. They also observed that errors in
Line 145: Line 158:
errors. Specifically, good agreement in dispersion statistics was found between DNS and
errors. Specifically, good agreement in dispersion statistics was found between DNS and
well-resolved LES with the dynamic model (differences less than 8%) whereas rather higher
well-resolved LES with the dynamic model (differences less than 8%) whereas rather higher
errors were recorded for the coarser meshes. The study of Armenio ''et&nbsp;al.'' (1999) provides
errors were recorded for the coarser meshes. The study of
[[Best_Practice_Advice_AC7-01#armenio1999|Armenio&nbsp;''et&nbsp;al.''&nbsp;(1999)]] provides
conservative estimates of the accuracy of LES in the prediction of particle-laden flow since
conservative estimates of the accuracy of LES in the prediction of particle-laden flow since
tracer particles were used, which are the most sensitive to the small-scale fluctuations, In
tracer particles were used, which are the most sensitive to the small-scale fluctuations, In
Line 160: Line 174:


In the RANS simulations, the minimum ratio of resolved scales (mesh size near the
In the RANS simulations, the minimum ratio of resolved scales (mesh size near the
wall) to the particle size is 30 for 1&mu;m particles and 3 for 10&mu;m and therefore the particles
wall) to the particle size is 30 for 1<math>{\mu m}</math> particles and 3 for
10<math>{\mu m}</math> and therefore the particles
can be considered as point-particles and Lagrangian simulations can be performed. For
can be considered as point-particles and Lagrangian simulations can be performed. For
particle tracking in RANS simulations, the generation of the fluid fluctuating velocity
particle tracking in RANS simulations, the generation of the fluid fluctuating velocity
Line 190: Line 205:
in the human airways is influenced when two- and four-way coupling effects are present.
in the human airways is influenced when two- and four-way coupling effects are present.
==Acknowledgements==
==Acknowledgements==
This Application Challenge is based upon work from COST Action MP1404 SimInhale 'Simulation and pharmaceutical technologies for advanced patient-tailored inhaled medicines', supported by COST (European Cooperation in Science and Technology). http://www.siminhale-cost.eu ; http://www.cost.eu
<!--
The present application challenge is based upon work from COST Action MP1404 SimInhale
The present application challenge is based upon work from COST Action MP1404 SimInhale
&lsquo;Simulation and pharmaceutical technologies for advanced patient-tailored inhaled
&lsquo;Simulation and pharmaceutical technologies for advanced patient-tailored inhaled
medicines&rsquo;, supported by COST (European Cooperation in Science and
medicines&rsquo;, supported by COST (European Cooperation in Science and
Technology&nbsp;—&nbsp;www.cost.eu).
Technology&nbsp;—&nbsp;[https://www.cost.eu www.cost.eu]).
-->
 
==References==
==References==
Armenio, V., Piomelli, U. & Fiorotto, V. 1999 Effect of the subgrid scales on particle
<div id="armenio1999"></div>
motion. ''Physics of Fluids'' '''11''' (10), 3030&nbsp;&ndash;&nbsp;3042.
Armenio, V., Piomelli, U. & Fiorotto, V. 1999
:Effect of the subgrid scales on particle motion. ''Physics of Fluids'' '''11''' (10), 3030&nbsp;&ndash;&nbsp;3042.




Line 218: Line 238:
:''The Mechanics of Inhaled Pharmaceutical Aerosols''. Academic Press, New York.
:''The Mechanics of Inhaled Pharmaceutical Aerosols''. Academic Press, New York.


Jasak, H. 1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Department of Mechanical Engineering, Imperial
 
College of Science, Technology and Medicine, London, UK.
<div id="jasak1996"></div>
Jasak, H. 1996
:Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, London, UK.




Line 275: Line 297:
Mei, R. 1992
Mei, R. 1992
:An approximate expression for the shear lift force on a spherical particle at finite reynolds number. ''International Journal of Multiphase Flow'' '''18''' (1), 145&nbsp;&ndash;&nbsp;147.
:An approximate expression for the shear lift force on a spherical particle at finite reynolds number. ''International Journal of Multiphase Flow'' '''18''' (1), 145&nbsp;&ndash;&nbsp;147.
<div id="nesterov2009"></div>
Nesterov SV, Han CL, Maki M, ''et al.'' 2009
:Myocardial perfusion quantitation with (15)O-labelled water PET: high reproducibility of the new cardiac analysis software (Carimas (TM)). ''Eur&nbsp;J&nbsp;Nucl&nbsp;Med&nbsp;Mol&nbsp;I&nbsp;2009''; '''36''': 1594&nbsp;&ndash;&nbsp;1602.




Line 286: Line 313:
:The lift on a small sphere in a slow shear flow. ''Journal of Fluid Mechanics'' '''22''' (2), 385&nbsp;&ndash;&nbsp;400.
:The lift on a small sphere in a slow shear flow. ''Journal of Fluid Mechanics'' '''22''' (2), 385&nbsp;&ndash;&nbsp;400.


Saffman, P. G. 1968 The lift on a small sphere in a slow shear flow corrigendum. Journal
 
of Fluid Mechanics 31 (3), 6247624.
<div id="saffman1968"></div>
Saffman, P. G. 1968
:The lift on a small sphere in a slow shear flow &ndash; corrigendum. ''Journal of Fluid Mechanics'' '''31''' (3), 624&nbsp;&ndash;&nbsp;624.
 
 
<div id="saha2010"></div>
Saha GB.
:''Basics of PET imaging physics, chemistry, and regulations.'' 2nd ed. New York; London: Springer, 2010.




Line 297: Line 331:
<div id="schmidt2004"></div>
<div id="schmidt2004"></div>
Schmidt, Andreas, Zidowitz, Stephan, Kriete, Andres, Denhard, Thorsten, Krass, Stefan
Schmidt, Andreas, Zidowitz, Stephan, Kriete, Andres, Denhard, Thorsten, Krass, Stefan
& Peitgen, Heinz—Otto 2004
& Peitgen, Heinz-Otto 2004
:A digital reference model of the human bronchial tree. ''Computerized Medical Imaging and Graphics'' '''28''' (4), 203&nbsp;&ndash;&nbsp;211.
:A digital reference model of the human bronchial tree. ''Computerized Medical Imaging and Graphics'' '''28''' (4), 203&nbsp;&ndash;&nbsp;211.


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{{ACContribs
|authors=***
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|number=01
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Latest revision as of 08:42, 21 October 2019

Front Page

Description

Test Data

CFD Simulations

Evaluation

Best Practice Advice

Aerosol deposition in the human upper airways

Application Challenge AC7-01   © copyright ERCOFTAC 2019

Best Practice Advice

Key Fluid Physics and Deposition Mechanisms

Airflow in the human upper airways transitions to turbulence due to geometric effects, such as the bend in the oropharyngeal region and the constriction at the glottis. The bend in the oropharynx causes substantial filtering of inhaled aerosols due to inertial impaction on the airway walls. Filtering in the extrathoracic airways increases as the particle size and inhalation flowrate increase.

As we move in the tracheobronchial airways, the Reynolds number is reduced because the air travels through a larger total cross-sectional area. As a result, airflow relaminarizes in the first generations. At the flowrate examined in the present AC, the main deposition mechanism in this region is inertial impaction, with significant deposition at the bends and the bifurcations. At lower flowrates, deposition can also be influenced by gravitational sedimentation because the residence times of the particles in the bronchial airways is longer.

Application Uncertainties

The differences between measurements and simulations can result from several uncertainties involved in the tests. A first source of uncertainty are the in vitro inlet conditions, which might be different from the velocity and particle profiles assumed in the CFD simulations. In the experimental setup, various devices were placed upstream of the mouth inlet (see figure 5) and these devices are expected to alter the inlet flow and particle conditions from what is prescribed in the simulations.

Another source of uncertainty between the experiment and the simulations is the size of the particles. Monodisperse particles have been assumed in the simulations whereas the aerosols generated in the experiments had a standard geometric deviation of size smaller than .

Computational Domain and Boundary Conditions

The geometry of the extrathoracic airways must be included because turbulence is generated in this region and alters transport and deposition of particles in the distal airways. In addition, significant filtering occurs in the mouth and throat, which affects the amount of inhaled aerosols that will eventually reach the desirable lung generations. In the present AC, in both LES and RANS tests the inlet at the mouth of the model was extruded in order to generate turbulent velocity conditions. This strategy was adopted due to the absence of a more realistic inlet velocity profile.

Concerning the boundary conditions, the inlet velocity profile and the particle distribution are important determinants of particle deposition and thus realistic inlet conditions should be used. At the outlets, it is important to apply correct pressures such that the ventilation of the airway tree is realistic. Otherwise, both the air and particle distribution in the trachea will not be predicted accurately.

In the LES simulations, the volumetric flowrates at the 10 terminal outlets are prescribed based on the values measured in vitro (Table 3). These outlet conditions result in high asymmetry in the ventilation of the two lungs: the left lung receives 29% of the inhaled air whereas the right lung receives 71%.

In the RANS calculations, a simplified boundary condition setup was applied. Instead of applying prescribed flowrates at the outlets of the system similarly to the experiments, a simpler strategy of applying the flowrate at the inlet and zero pressure at the outlets was used. Using these boundary conditions, an overall good agreement with the experimental data was observed with small differences on the ventilation distribution after the third branching level. This approach may be used to obtain preliminary results, however, the correct application of the flow field for all the outlets is recommended in future works to better predict the flow in the further downstream located sections of the system.

Discretisation and Grid Resolution

Since it is not possible to generate a structured hexahedral grid for the present geometry due to its complexity, a higher refinement ratio should be applied to avoid numerical diffusion. In addition to that, layers of prismatic elements should be added near the wall boundaries for a better prediction of this region, not only with regard to flow properties itself, but the flow conditions seen by the particles, i.e. mean velocity and turbulence properties. Despite the application of interpolated properties for the particle positions, a better agreement was observed when a refinement was applied to the wall layers. Hence, a finer grid in the vicinity of the wall is recommended for allowing more accurate particle tracking. Recommended values for the parameters involved in mesh generation (initial cell height, average expansion ratio, number of near-wall prism layers, average cell volume in the domain, number of computational cells etc.) can be found in Table 5.

Physical Modelling

Turbulence models

In the LES simulations, the dynamic version of the Smagorinsky-Lilly subgrid scale model (Lilly, 1992) is adopted in order to examine the unsteady flow in the realistic airway geometries. Previous studies have shown that this model performs well in transitional flows in the human airways (Radhakrishnan & Kassinos, 2009; Koullapis et al., 2016).

For the RANS simulations, the standard k-ω SST turbulence model is used due to its good prediction of such wall-bounded flow (i.e. using a blending between wall and free-stream region) and low computational cost. Other turbulence models have not been considered but based on prior experince they are exprected to perform worse.

In order to better validate the numerical predictions of LES and RANS, a second application challenge will follow that will focus on airflow characteristics in the same geometry. Moreover, in this second AC, numerical predictions will be compared against PIV measurements.

Lagrangian particle tracking

Lagrangian particle tracking has been adopted in the present application. Although there is a number of forces acting on the particles (drag, buoyancy, Basset (or history), pressure gradient force, lift due to shear and rotation and Brownian forces), only few of them are important when considering the transport of micron-sized particles in the human airways. This is mainly because the particle density is much greater than the density of the air . Furthermore, in numerical simulations the particles are assumed spherical and, as a result, the important forces that need to be taken into account in lung deposition studies are drag, gravity and Brownian motion force. However, lift force due to shear can also be important as particle size increases. This is evident in figure 21, that plots deposition fraction in the mouth-throat / trachea (segments 1&2) of the benchmark geometry for three particle sizes (1, 4.3 and 10) at a flowrate of 60 L / min (LES results). In this case, the expression for the shear lift is obtained by Saffman (1965), Saffman (1968) and Mei (1992). It is observed that the Saffman lift force results in an increase in the deposition of 10 particles by approximately 5%.


AC7-01 fig21.png
Figure 21: LES predictions of Deposition fraction in the mouth-throat / trachea (segments 1&2) of the benchmark geometry for three particle sizes (1, 4.3 and 10m) at a flowrate of 60 L/min.


As described in the discrete phase modelling, the time step of the particle tracking calculation should automatically and independently be adapted along the trajectories by considering all relevant time scales, which are also changing throughout the flow field. This allows for numerically eflicient particle tracking. If such an approach is not possible, a verification of the relevant time scales should be calculated by using averaged values in order to apply a correct time step for the simulations.

Modelling of unresolved flow velocities

In Lagrangian point-particle methods the particle size must be smaller that the Kolmogorov scale. In our LES the grid size is larger than the Kolmogorov scale and thus this condition is satisfied. Specifically, the minimum ratio of resolved scales (mesh size near the wall) to the particle size is 40 for 1 particles and 4 for 10.

In point-particle LES, the resolved velocities are used in the calculation of the forces acting on the particles whereas the unresolved part of the air velocities is lost due to the filtering procedure. Thus, the effect of the small-scale (unresolved) motion on particle dispersion and deposition must be either modelled separately, or neglected. In the present LES calculations, the effect of the unresolved scales of the continuous phase on particle deposition in the airways has not been investigated.

Armenio et al. (1999) examined the effects of small-scale velocity fluctuations on the motion of tracer and inertial particles in a turbulent channel flow at . They concluded that well-resolved LES with an adequate LES model can provide fairly accurate particle statistics for moderate Reynolds number flows. They also observed that errors in LES are mainly attributed to the LES filtering operation rather than to sub-grid modelling errors. Specifically, good agreement in dispersion statistics was found between DNS and well-resolved LES with the dynamic model (differences less than 8%) whereas rather higher errors were recorded for the coarser meshes. The study of Armenio et al. (1999) provides conservative estimates of the accuracy of LES in the prediction of particle-laden flow since tracer particles were used, which are the most sensitive to the small-scale fluctuations, In the case of particles with inertia, the errors are expected to be smaller.

In the present application challenge, airflow Reynolds numbers are low to moderate in the extrathoracic airways and the motion of inertial particles is simulated. Therefore, it is expected that if sufficient mesh resolution is employed then a model for accounting the effect of the unresolved scales on particle motion is not necessary. However, there are cases where the inhalation flowrate and thus the Reynolds number is higher, such as the inhalation from low-resistance inhalers, coughing etc. Therefore, further studies are needed to determine the conditions under which a model accounting for the effect of the unresolved scales on particle motion is required.

In the RANS simulations, the minimum ratio of resolved scales (mesh size near the wall) to the particle size is 30 for 1 particles and 3 for 10 and therefore the particles can be considered as point-particles and Lagrangian simulations can be performed. For particle tracking in RANS simulations, the generation of the fluid fluctuating velocity acting on the particle is an essential step, which in this study has been done assuming isotropic turbulence. Moreover, the relevant turbulent time and length scales have been determined based on this assumption. Nevertheless, a spurious drift may occur driving fine particles to the wall and unrealistically enhancing deposition. This spurious drift has to be corrected appropriately.

Recommendations for Future Work

The present application challenge focuses on aerosol deposition and the airflow in the geometry has not been studied. In order to better validate the numerical predictions of LES and RANS, a second application challenge will follow that will focus on airflow characteristics in the same geometry. Moreover, in this second AC, numerical predictions will be compared against PIV measurements.

Concerning the dispersed phase, it is known that forces due to collision between particles become important in the case of dense aerosol suspensions. In other words, as the volume fraction of the particle phase increases, collisions between particles influence the simulation results. In addition, the flow is affected by the presence of the particles and thus particle force source terms must be included in the momentum equations of the fluid phase. This case is known as four-way coupling. If the particle volume fraction is sufficiently low, the particles do not collide with each other and also the flow remains unaffected by their presence. This is known as one-way coupling. In an intermediate state, named two-way coupling, the flow is affected by the particles, but particle collisions do not have significant impact and therefore collision effects can be discarded in the simulation. The limits of validity of the coupling regimes are reported by Elghobashi (1994). In the present study, we have assumed one-way coupling, however, it is important to examine how deposition in the human airways is influenced when two- and four-way coupling effects are present.

Acknowledgements

This Application Challenge is based upon work from COST Action MP1404 SimInhale 'Simulation and pharmaceutical technologies for advanced patient-tailored inhaled medicines', supported by COST (European Cooperation in Science and Technology). http://www.siminhale-cost.eu ; http://www.cost.eu

References

Armenio, V., Piomelli, U. & Fiorotto, V. 1999

Effect of the subgrid scales on particle motion. Physics of Fluids 11 (10), 3030 – 3042.


Baker, T. J. 2003

Interpolation from a cloud of points. pp. 55 – 63. Santa Fe, New Mexico.


Chan, Tai & Lippmann, Morton 1980

Experimental measurements and empirical modelling of the regional deposition of inhaled particles in humans. American Industrial Hygiene Association Journal 41 (6), 399 – 409.


Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2012

Multiphase flows with droplets and particles. CRC Press.


Finlay, W. H. 2001

The Mechanics of Inhaled Pharmaceutical Aerosols. Academic Press, New York.


Jasak, H. 1996

Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, London, UK.


Von Karman, T. & Horwarth, L., ed. 1938

On the statistical theory of isotropic turbulence, vol. A164. Proc. Royal Society London.


Koullapis, P., Kassinos, S. C., Muela, J., Perez-Segarra, C., Rigola, J., Lehmkuhl, 0., Cui, Y., Sommerfeld, M., Elcner, J., Jicha, M., Saveljic, I., Filipovic, N., Lizal, F. & Nicolaou, L. 2018

Regional aerosol deposition in the human airways: The siminhale benchmark case and a critical assessment of in silico methods. European Journal of Pharmaceutical Sciences 113, 77 – 94.


Koullapis, P. G., Kassinos, S.C., Bivolarova, M. P. & Melikov, A. K. 2016

Particle deposition in a realistic geometry of the human conducting airways: Effects of inlet velocity profile, inhalation flowrate and electrostatic charge. Journal of Biomechanics 49, 2201 – 2212.


Legg, B. J. & Raupach, M.R,. 1982

Markov-chain simulations of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient eulerian velocity variance. Boundary-Layer Meteorology 24 (3 – 13).


Li, A. & Ahmadi, G. 1992

Dispersion and deposition of spherical particles from point sources in a turbulent channel flow. Aerosol Science and Technology 16, 2097226.


Lilly, D. K. 1992

A proposed modification of the Germano subgrid-scale closure method. Physics of Fluids A 4 (3), 6337635.


Lizal, Frantisek, Belka, Miloslav, Adam, Jan, Jedelsky, Jan & Jicha, Miroslav 2015

A method for in vitro regional aerosol deposition measurement in a model of the human tracheobronchial tree by the positron emission tomography. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 229 (10),750 – 757.


Lizal, Frantisek, Elcner, Jakub, Hopke, Philip K, Jedelsky, Jan & Jicha, Miroslav 2012

Development of a realistic human airway model. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 226 (3), 197 – 207.


Macpherson, G. B., Nordin, N. & Weller, G. 2009

Particle tracking in unstructured, arbitrary polyhedral meshes for use in CFD and molecular dynamics. Communications in Numerical Methods in Engineering 25 (3), 263 – 273.


Matida, E. A., Finlay, W. H., Lange, C. F. & Grgic, B. 2004

Improved numerical simulation of aerosol deposition in an idealized mouth-throat. Aerosol Science 35, 1 – 19.


Mei, R. 1992

An approximate expression for the shear lift force on a spherical particle at finite reynolds number. International Journal of Multiphase Flow 18 (1), 145 – 147.


Nesterov SV, Han CL, Maki M, et al. 2009

Myocardial perfusion quantitation with (15)O-labelled water PET: high reproducibility of the new cardiac analysis software (Carimas (TM)). Eur J Nucl Med Mol I 2009; 36: 1594 – 1602.


Radhakrishnan, H. & Kassinos, S. 2009

CFD modeling of turbulent flow and particle deposition in human lungs. 31st Annual International Conference of the IEEE EMBS, Mineapolis, Minnesota, USA pp. 2867 – 2870.


Saffman, P. G. 1965

The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics 22 (2), 385 – 400.


Saffman, P. G. 1968

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