Airflow in the human upper airways

Application Challenge AC7-02 © copyright ERCOFTAC 2020

Best Practice Advice

Key Fluid Physics

In the present AC, experiments and simulations were conducted at a flowrate of 60 L/min through an upper airway geometry. At this flow conditions, the Reynolds number for air in the trachea is 4920, which is well within the turbulent regime. Geometric effects, such as the bent in the oropharyngeal region and the constriction at the laryngeal glottis (just upstream of the trachea, see figure 25 ) enhance turbulence levels as the air moves from the inlet to the region of the trachea. Turbulent kinetic energy levels reach a peak in the shear layer formed between the high speed laryngeal jet and the surrounding (low speed) air (see figure 25). The characteristics of the laryngeal jet formation bear a resemblance to the flow through a constricted pipe, which can be classified as a free shear flow where the wall serves to confine the spreading of the jet rather than producing turbulence (Tawhai & Lin, 2011). High turbulence levels persist in the region of the first bifurcation (stations H1-H2 & J1-J2 in figure 12(b)).

Application Uncertainties

The differences between measurements and simulations can result from several uncertainties involved in the tests. A first source of uncertainty are the inlet conditions, which are not perfectly matched between the measurements and the computations. In the experiments, the lung model was placed in an open liquid tank with a piston diaphragm pump attached to a linear actuator to achieve a quasi-stationary inspiratory flow. The stroke of the piston followed a cyclic triangular function with an adjustable falling constant slope and thus constant velocity to match different flow rates during inspiration. The measured mean velocity at the inlet of the model, shown in Fig. 7, is asymmetric, probably due to the action of the piston diaphragm pump. In the computations, instead of reproducing the measured inlet conditions, either uniform or turbulent inlet velocity profiles were prescribed. Due to a leakage flow between the upper and lower part of the model in the experiments, the achieved flowrate within the main bifurcation and bronchi region was about 10% lower than in the upper part of the model. As a result, a maximum flowrate of $Q_{w/g}$ = 28.56 L/min could be achieved in the measurements. This value is slightly lower than $Q_{w/g}$ = 31.75 L/min, which is the target value for an equivalent air flowrate of 60L/min through the model. Although the flow is well within the turbulent regime, the theoretical maximum Reynolds number decreases from 4921 to 4286.

Computational Domain and Boundary Conditions

The geometry of the extrathoracic airways must be included because turbulence is generated in this region that propagates in the first airway generations. Concerning the boundary conditions, the inlet velocity profile is important 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 physiologically realistic (Yin et al., 2010). In the present AC, in order to simplify the experimental setup and be able to perform the flow measurements, uniform pressures were prescribed at all outlets.

Concerning the inlet conditions for the turbulent variables in RANS calculations, the application of a turbulence intensity of 5% for the k-ω SST model at the extended inlet (10xDinlet) yielded higher turbulent kinetic energy values close to the inlet of the model compared to the mapped inlet condition (Inlet 1). The k-ε models were found to provide overall higher turbulence levels than the k-ω SST model, especially at the near-wall regions.

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. Airflow through the glottis constriction at the larynx, illustrated in fig. 25, bears a resemblance to flow through a constricted pipe. This type of flow may be classified as a free shear flow in which the wall serves to confine the spreading of the jet rather than producing turbulence. In this case, turbulence is most active at the interface between two free streams (high and low speed) and along the jet core and therefore, fine mesh resolution should be placed accordingly to capture strong turbulence activities. Use of a strict y+ = 1 condition in the generation of the near-wall mesh but extremely coarse mesh in the core region of the airway model is conceptually wrong (Tawhai & Lin, 2011). 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 Tables 4,5 (LES) and 6 (RANS).

LES were found to give similar results independent of the discretisation method used (Finite Volume or Finite Element).

Figure 25: Laryngeal jet formed at the glottis constriction. (a) Isosurfaces of

|<u>|

= 6.7m/s ; (b) Mean velocity contours; (c) Turbulent kinetic energy contours.

Turbulence Models

The ability of four LES subgrid-scale models was assessed by comparing their predictions to the PIV data. These models were the WALE, the Smagorinsky, the variational multiscale (VMS) WALE and the QR eddy-viscosity model from Verstappen. All the models were found to provide very similar results. It is concluded that the influence of the subgrid scales on the airflow in the human upper airways is small, and the choice of subgrid-scale turbulence model is not as important as in cases with higher Reynolds numbers.

In general the RANS prediction for the velocity magnitude follow trends similar to those of the measured data. RANS however show poor performance at locations with shear layers, recirculation and flow separation. Moreover, RANS simulations consistently underestimate turbulent kinetic energy levels compared to PIV and LES data. This is a direct consequence of discarding many of the elements of the underlying turbulence physics when solving only for the mean flow (see discussion in section 4). The k-ε models provides overall higher turbulence levels than the k-ω SST turbulence model.

Results presented in AC7-01 showed that the deposition fractions obtained with RANS models achieved a quite good agreement with LES and measurements. This might seem surprising given the tendency of RANS to under-predict turbulence intensities at several station downstream of the glottis constriction. This apparent paradox probably relates to the fact that the dominant deposition mechanism in the upper airways is inertial impaction. While inertial impaction tends to be dominated by mean flow effects, turbulent dispersion still plays an important role, especially in regions where there is significant large-scale anisotropy in the turbulence. Hence, it is known that using only the time-averaged air velocity field for deposition studies (this is the case in RANS) leads to deposition overpredictions (Matida et al., 2004). Still, RANS deposition predictions can be improved when they are used together with a turbulent dispersion model, as was done in AC7-01. When using a a turbulent dispersion model, individual particles are allowed to interact successively with discrete eddies, each eddy having length, velocity and lifetime characteristic scales obtained from the primary flow calculation results. It is therefore important to correctly select the turbulent dispersion model and it’s parameters for accurate deposition predictions. LES on the other hand, since they resolve the large scale eddies, do not need a model to account for these in particle-laden flows. The study of Armenio et al. (1999) has shown that the motion of inertial particles in low to moderate Reynolds number flows, is not influenced from the unresolved sub-grid scales in LES.

In conclusion, LES are more capable than RANS in predictions of airflow in the human upper airways, since they can account better for the physics of the turbulent flow

Recommendations for Future Work

The present application challenge focuses on the airflow that develops in the human upper airways. The airway geometry has been considered rigid. In reality, the lung expands and contracts and the airway walls deform during inhalation and exhalation (Mead-Hunter et al., 2013). In addition, there is periodic movement of the glottal aperture during tidal breathing that regulates the respiratory airflow dynamics (Xi et al., 2018). It is therefore important to assess the effect of wall deformation on the developed flow features inside the airways.

The higher temperature and humidity of the human body compared to the inhaled ambient air results in heat and water vapor transfer as the air is transported in the airways (Wu et al., 2014). During inhalation, air is heated and humidified by the airway walls until it reaches the body temperature and approximately 100% relative humidity. Such effects can play a role in air and inhaled aerosols transport inside the airways and should be further examined in the future studies.

Acknowledgements

The present 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 - www.cost.eu).

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Contributed by: P. Koullapis^a, J. Muela^b, O. Lehmkuhl^c, F. Lizal^d, J. Jedelsky^d, M. Jicha^d, T. Janke^e, K. Bauer^e, M. Sommerfeld^f, S. C. Kassinos^a —
^aDepartment of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
^bHeat and Mass Transfer Technological Centre, Universitat Politècnica de Catalunya, Terrassa, Spain
^cBarcelona Supercomputing center, Barcelona, Spain
^dFaculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic
^eInstitute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany
^fInstitute Process Engineering, Otto von Guericke University, Halle (Saale), Germany