Numerical Study of High-Frequency Oscillatory Air Flow and Convective Mixing in a CT-Based Human Airway Model
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DOI: 10.1007/s10439-010-0110-7
- Cite this article as:
- Choi, J., Xia, G., Tawhai, M.H. et al. Ann Biomed Eng (2010) 38: 3550. doi:10.1007/s10439-010-0110-7
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Abstract
High-frequency oscillatory ventilation (HFOV) is considered an efficient and safe respiratory technique to ventilate neonates and patients with acute respiratory distress syndrome. HFOV has very different characteristics from normal breathing physiology, with a much smaller tidal volume and a higher breathing frequency. In this study, the high-frequency oscillatory flow is studied using a computational fluid dynamics analysis in three different geometrical models with increasing complexity: a straight tube, a single-bifurcation tube model, and a computed tomography (CT)-based human airway model of up to seven generations. We aim to understand the counter-flow phenomenon at flow reversal and its role in convective mixing in these models using sinusoidal waveforms of different frequencies and Reynolds (Re) numbers. Mixing is quantified by the stretch rate analysis. In the straight-tube model, coaxial counter flow with opposing fluid streams is formed around flow reversal, agreeing with an analytical Womersley solution. However, counter flow yields no net convective mixing at end cycle. In the single-bifurcation model, counter flow at high Re is intervened with secondary vortices in the parent (child) branch at end expiration (inspiration), resulting in an irreversible mixing process. For the CT-based airway model three cases are considered, consisting of the normal breathing case, the high-frequency-normal-Re (HFNR) case, and the HFOV case. The counter-flow structure is more evident in the HFNR case than the HFOV case. The instantaneous and time-averaged stretch rates at the end of two breathing cycles and in the vicinity of flow reversal are computed. It is found that counter flow contributes about 20% to mixing in HFOV.
Keywords
High-frequency oscillatory ventilationCT-based human airwayCFDSecondary flowStretch rateMixingIntroduction
Ventilatory support via invasive mechanical ventilation is often necessary for patients in an intensive care unit. Conventionally, the tidal volume of normal mechanical ventilation is approximately 75–150% of the patient’s natural respiration volume26 based on the prediction that gas exchange volume has to exceed the anatomical dead space (the volume of conducting airways) of the lung to achieve adequate alveolar ventilation. However, this large tidal volume can cause volutrauma (over-stretch of lung tissue) and other ventilator-induced lung injuries including oxygen toxicity (the effect of over-rich levels of oxygen on lung tissue), and hemodynamic compromises.7,37 To avoid lung injuries due to volutrauma, high-frequency ventilation (HFV) with smaller tidal volume has been used on patients with acute lung injury, acute respiratory distress syndrome, and neonates. HFV is a fast and shallow ventilation mode which is postulated to minimize the lung injuries associated with cyclic opening and closing of alveolar units in conventional ventilation mode.15 HFV includes high-frequency positive pressure ventilation, high-frequency jet ventilation, and high-frequency oscillatory ventilation (HFOV).
Lunkenheimer et al.21 proposed the use of oscillating pumps for HFOV. This reciprocating process produces both active inspiration and expiration processes, eliminating gas entrainment and decompression of gas jets in the conducting airways. With active expiration, the lung volume can be controlled to avoid over-extension of the lung tissue, reducing the risks of lung injuries. HFOV has been used extensively both on neonates25 and adults.2,6,27,28 HFV has attracted much research interest; a comprehensive review of this area of study can be found in Chang.3 Fluid dynamics studies include Tanaka et al.,34 who used laser Doppler anemometer (LDA) to examine the secondary flow intensities and its influence on gas mixing in HFOV in a 3-generation Horsfield13 model. Lieber and Zhao17 also applied LDA to interrogate oscillatory flow in a symmetric single-bifurcation tube model, and found that the flow exhibits quasi-steady behaviors for only about 50% of the oscillatory cycle. Zhang and Kleinstreuer44 used a finite-volume code (CFX4.3) to study oscillatory flow in a symmetric triple-bifurcation tube model representing generations 3 to 6 of the human airways under normal breathing and HFV. They found that the oscillatory inspiratory flow is quite different from the equivalent steady-state case even at peak flow. Adler and Brücker1 studied high-frequency oscillatory flow using particle image velocimetry (PIV) in a 6-generation airway model, and observed mass exchange between child branches at end inspiration or expiration known as Pendelluft. Nagels and Cater29 used large-eddy simulation (LES) (CFX 11.0) to study high-frequency oscillatory flow in a 2-generation asymmetric tube model. They observed reverse flow near the walls when the driving velocity is small. Heraty et al.11 carried out PIV experiments to measure velocity fields and secondary flows in both idealized and realistic single airway bifurcations under HFOV conditions. They observed the coaxial counter-flow feature, which the flow in the core region of the airway lumen lags behind the flow in the near-wall peripheral region at flow reversal during change of the respiratory phase. They reported that the counter-flow feature persisted for a significant time period. The coaxial counter flow at flow reversal is characteristic of the Womersley solution noted in the classic high-frequency oscillatory straight pipe flow.40 This flow feature, however, is neither evident nor reported in Tanaka et al.34 It suggests that airway geometry (morphological structure) may also play a role in determining flow characteristics (in association with lung function, e.g., gas transport and mixing for ventilation) under HFOV conditions.
This leads to the current work which aims to provide insight into the structure–function (geometry-flow) relationship of the human lung under different flow conditions using computational fluid dynamics (CFD); in particular, to understand the coaxial counter-flow feature in HFOV and quantify the efficiency of convective mixing under different flow conditions. From a kinematical point of view, fluid mixing involves stretching and folding of material lines, and is determined by the fluid velocity field.23,30–32 Mixing of this viewpoint is referred to as convective5,12 or kinematic10 mixing. We consider three geometries with increasing complexity: a straight tube, a symmetric single-bifurcation tube system, and a computed tomography (CT)-based airway model including the upper airways and the intra-thoracic airways of up to seven generations. For the complete airway model, three flow conditions are considered to examine the effects of unsteadiness (oscillation) and convection (inertia). Mixing efficiencies are quantified by the stretch rate analysis.23,30–32 The rest of this article is laid out as follows. The mathematical formulations for the CFD analysis and the stretch rate analysis are described in the “Methods” section. In the “Results” section, oscillatory flows in a straight tube and a single bifurcation are first presented to demonstrate the features of coaxial counter flow and secondary flows. The stretch rates are used to quantify convective mixing in both cases. We then compare the characteristics of flows under three flow conditions in the complete airway model and quantify their stretch rates at the end of cycles and in the vicinity of flow reversal. In the “Discussion” section, the counter-flow features and mixing efficiencies are discussed in conjunction with existing literatures. Concluding remarks are drawn in the last section.
Methods
Fluid Solver
The fractional four-step method is applied to solve Eqs. (1) and (2). The continuity equation is enforced by solving a pressure-Poisson equation. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations, being of second-order accuracy in time and space.18 The SGS model of Vreman39 is adopted for calculation of the eddy viscosity ν_{T} to capture both turbulent and transitional flows. The solver has been validated for flows under various conditions.4,16,19,41 A validation case against LDV measurements will be presented later.
CT Image-Based Central Airway Model and 1D Centerline Model
Breathing Conditions for the CT-Based Airway Model
Flow parameters for the three CT-based airway cases
Case | Period T (s) | Frequency f (Hz) | Peak Re | Tidal volume V_{T} (mL) | Description |
---|---|---|---|---|---|
NORM | 4.8 | 0.20 | 1288 | 500 | Normal breathing |
HFNR | 0.16 | 6.28 | 1288 | 16.58 | Same frequency as HFOV and same peak Re as NORM |
HFOV | 0.16 | 6.28 | 3656 | 47 | HFOV |
The CFD mesh for the CT-based airway model consists of 899,465 points and 4,644,447 tetrahedral elements. We tested a series of consecutively finer meshes of I—1,305,429 elements, II—2,573,085, and III—4,644,447 tetrahedral elements. The kinetic energies based on the radial velocity component of the secondary flow at station C in Fig. 1a in the trachea are compared for these meshes at peak inspiration. The differences of secondary flow energies between meshes I and II is 8.3% and it is 2.4% between meshes II and III, indicating the results are mesh-insensitive. The mesh III is chosen for study.
Stretch Rate Analysis
Flow Regimes
To study the characteristics of oscillatory secondary flow in a tubal branching network, it is important to know about the expected flow features in terms of key dimensionless parameters. Jan et al.14 categorized the oscillatory flow in a model bifurcation into three regimes according to two dimensionless parameters. One parameter is the dimensionless frequency α^{2}, where \( \alpha = a\sqrt {\omega /\nu } \) is the Womersley parameter. ω = 2π/T = 2πf (T, period in seconds; f, frequency in Hz) is the angular frequency and a is the average radius of an airway segment (or a tube). The other parameter is the local dimensionless stroke length L/a, where L = v_{t}/A (v_{t} is the local tidal volume, and A = πa^{2} is the average cross-sectional area of an airway segment). The Reynolds number is given by Re = α^{2}(L/a) if the breathing waveform is a sinusoidal function.
Also exhibited in Fig. 2 are the conditions computed with the 1D centerline model using the parameters averaged by generation for the three cases (open symbols). Each open symbol represents the average flow condition for each generation of the entire airway tree beginning from the trachea to terminal bronchioles (distributing from right to left in the figure). For HFOV, the distribution curve is shifted downwards to the right and the effects of convection penetrate deeper into the lungs (note that the curve intersects Re = 30 at the seventh generation in both NORM and HFNR, but at the ninth generation in HFOV). Overall, the characteristics of HFOV are more turbulent in the central airways and more convective in the smaller airways. For HFNR, due to its smallest L/a and high α^{2}, the flow in the range of α^{2} > 10 (denoted by “IIIb-CONVECTIVE” in Fig. 2) may behave more similar to the Womersley solution.
Results
Model Validation
The dimension of the symmetric bifurcating tube model is illustrated in Fig. 3a. The formula used to generate the model and stations 2, 4, 10, and 15 are given in Zhao and Lieber.45 An enlarged view of the model is shown in Fig. 3b, where station S12.5 is located midway between stations S10 and S15. The child-branch angle of 70° falls within the range of those at generations 3 and 4 (see Fig. 1b). The diameter ratio between child and parent branches is \( 1/\sqrt 2 \approx 0.7, \) which also agrees with the current CT data (Fig. 1c). A sinusoidal flow waveform with the Womersley velocity profile is imposed at the boundary face of the parent branch. The mesh consists of 141,403 nodal points and 747,344 tetrahedral elements. The fluid properties and flow conditions used by Lieber and Zhao17 are adopted. The instantaneous velocity profiles (solid lines) at stations S2, S10, and S15 at t/T = 0.2 (inspiration) and 0.7 (expiration) in the bifurcation and transverse planes are plotted against the measurement data (solid squares) of Lieber and Zhao.17 The bifurcation plane is co-planar with the centerlines of the three branches, whereas the transverse plane for each of the three branches is perpendicular to the bifurcation plane and co-planar with the centerline of an individual branch. Overall, they are in good agreement. It is noted that the CFD solution is more symmetric with respective to r/R = 0 than the measurement data. For instance, in the range of r/R < 0 in Fig. 3f, the current data over-predict (under-predict) the experimental data at S2 (S15), but they agree with the CFD data of Zhang and Kleinstreuer.44
Womersley Solution and Flow in a Straight Tube
With the imposition of the flow condition at point B which has the same frequency as A, but a higher Re than A, the CFD-simulated velocity profiles at various times during a cycle (data not shown) exhibit the same shapes as those of Fig. 4c, but have different magnitudes. This is in agreement with the Womersley solution equation (6) that the shape of velocity profile depends on frequency (cf. Figs. 4a and 4b), with a given frequency an increase in velocity amplitude increases Re. Thus, in spite of an increase in Re for point B which places it in the convective IIIb regime, the straight and axisymmetric features of the tube constrain the flow motion only in the axial direction. As a result, the convective terms in the Navier–Stokes equations are zero, yielding the linear Womersley solution.
Flow in a Bifurcating Tube Model
Flow in the CT-Based Airway Model
Flow parameters for the two bifurcations in the CT-based airway model
Generation | L/a | α | α^{2} | Peak Re | Local tidal volume (mL) |
---|---|---|---|---|---|
A bifurcation between second and third generations enclosed by a dot-dashed box in Fig. 1a | |||||
NORM | 163.4 | 1.45 | 2.10 | 343 | 73.1 |
HFNR | 5.42 | 7.96 | 63.31 | 343 | 2.42 |
HFOV | 15.36 | 7.96 | 63.31 | 972 | 6.87 |
A bifurcation between third and fourth generations enclosed by a dotted box in Fig. 1a | |||||
NORM | 746 | 0.61 | 0.37 | 277 | 24.8 |
HFNR | 24.7 | 3.35 | 11.2 | 277 | 0.82 |
HFOV | 70.1 | 3.35 | 11.2 | 785 | 2.33 |
Stretch Rate Analysis
Next, we apply the stretch rate analysis to a particle released in the middle of the above tracer. The time histories of the three orientation components m_{i} of a line element calculated by Eq. (3) are shown in Fig. 12b. The initial vector (m_{1}, m_{2}, m_{3}) = (0, 1, 0) is in parallel to the radial direction of the tube. As time progresses, m_{3} remains unchanged in the absence of shear. The line element experiences rotation with increasing m_{1} and decreasing m_{2} due to positive shear of the flow before reaching peak inspiration at t/T = 0.25 as in Fig. 12a. At expiration t/T = 0.6, the orientation of the line element is first reversed back to (0, 1, 0), and then m_{1} is changed to −1 due to negative shear in response to the change of flow direction. At the end of one cycle, the line element recovers its initial orientation. In one cycle, the line element experiences stretching in opposite directions and is restored to its initial orientation twice. The instantaneous (s_{I}) and time-averaged (s_{T}) stretch rates for this line element are displayed in Fig. 12c, and the enlarged view of s_{T} is plotted in Fig. 12b. The time history of the instantaneous stretch rate shows alternating positive and negative stretches twice, corresponding to the twice-stretched tracer illustrated above. As a result, at the end of one cycle, the time-averaged stretch rate s_{T} is zero, e.g., t/T = 1 and 2, signifying a reversible process. The relatively high s_{T} at initial time is due to small time t in the denominator of Eq. (5). The stretch rate analysis shows that there is no net convective mixing at the end of one cycle in spite of the existence of counter flow and phase lag in the straight-tube system that sustains the Womersley solution.
For the single-bifurcation cases shown in Figs. 5 and 6 for Re = 100 and 740, about 1700 particles are released in the parent branch at a distance of 0.88D and 6.5D from the bifurcation for Re = 100 and 740, respectively. The ratio of the particle release distances for Re = 100 and 740 is the ratio of the stroke lengths for the two cases so that the spreads of particles with respect to the bifurcation for both cases are dynamically similar. Application of the stretch rate analysis to two cycles of data yields the maximum-instantaneous and time-averaged stretch rates of 13.2 and 1.49 (29.2 and 10.9) s^{−1}, respectively, for Re = 100 (740). The stretch rates are no longer zero due to the formation of secondary vortical motions. The ratio of the time-averaged stretch rates for both cases is close to the ratio of Re.
Next we shall consider the stretch rates at end inspiration and early expiration t/T ~ 1.5. The distributions of the stretch rates for the three cases are qualitatively similar to those at t/T ~ 1. Overall, the stretch rates at t/T ~ 1.5 are smaller than those at t/T ~ 1. The maximum instantaneous stretch rates s_{I,max} for NORM, HFNR, and HFOV are 26, 36, and 138 s^{−1}, respectively, and the time-averaged stretch rates s_{T} are 0.46, 2.4, and 6.7 s^{−1}, respectively. The s_{I,max} ratio is ~1:1.4:5.3, and the s_{T} ratio is ~1:5.2:14.6. It is noteworthy that in the single-bifurcation model shown in Fig. 7, at end inspiration t/T ~ 1.5 a pair of secondary vortices is formed in the child branches, whereas at end expiration t/T ~ 1 two pairs of secondary vortices are formed in the parent branch. More vortices formed at end expiration yield greater stretch rates and more effective convective mixing.
Discussion
Counter Flow
Heraty et al.11 investigated the spatial flow structures under HFOV in both idealized and anatomically realistic bifurcation models using PIV. One of the important findings of their study was that the inspiratory and expiratory fluid streams co-exist (known as coaxial counter flow) in the airways for significant periods around flow reversal for both idealized and realistic models. Shear layers were formed between the opposing fluid streams, and persisted for slightly longer in the wider left child branch than in the right child branch. Vortical structures were resulted from the roll-up of shear layers in both models. More specifically, in their Fig. 3 with Re = 740 and α = 7 (the same flow parameters as point B in Fig. 2), counter flow and shear layers were found further away from flow reversal at early inspiration t/T = 0.057 and 0.115, at end inspiration t/T = 0.452, and at early expiration t/T = 0.623.
Contrary to their work, the current single-bifurcation case with the same flow parameters (Re = 740 and α = 7) shows that these structures are completely absent further away from flow reversal at t/T = 1.06 (or 0.06) and t/T = 0.56 (see Figs. 6d and 6h). That is, the time period for the existence of counter flow and shear layers around flow reversal reported in Heraty et al.11 is about twice longer than that of this study. To investigate the potential effect of an imposed velocity profile on the counter-flow period, a uniform velocity profile (to mimic the blunt feature of the Womersley velocity profile) with the same sinusoidal flow waveform as before is imposed in the single-bifurcation model. The result shows that the uniform profile rapidly adjusts to the Womersley profile in the parent branch. To investigate the effect of the shape of breathing flow waveform, we impose a triangular waveform that increases the flow rate linearly from zero to the same peak inspiratory flow rate as the sinusoidal waveform, reduces it linearly to zero at end inspiration and then repeats it for the expiratory phase. The triangular waveform has the same frequency as the sinusoidal waveform, but has ~50% lower flow rate at t/T ~ ±0.06 and ±0.56 than the sinusoidal one. The result shows that the flow characteristics are qualitatively the same as before, but having a smaller velocity magnitude. Lastly, we design a case with a sinusoidal waveform only for the inspiratory phase. After end inspiration t/T = 0.5 when the flow rate is zero, the inlet boundary velocity is set to zero, maintaining a zero flow rate for t/T > 0.5. The results show that the counter-flow structures similar to Figs. 6f and 7g persist within the time window of t/T = 0.5–1.0, but with decaying velocity magnitude and shrinking thickness of the inspiratory flow region. At t/T = 0.5, the thickness of the inspiratory flow in the parent branch is approximately constant, similar to the red region in Fig. 7g. With increasing time, the thickness of the red zone at a distance of ~0.5D to the bifurcation point shrinks at a rate faster than other regions. At the center point of that location, the velocity magnitudes at t/T = (0.5, 0.6, 0.7, 0.8, 0.9, 1.0) are (0.47, 0.42, 0.32, 0.19, 0.11, 0.07), and the thicknesses normalized by the parent-branch diameter are (0.65, 0.42, 0.26, 0.21, 0.21, 0.23). Thus, the velocity magnitude drops by 32% (85%) from t/T = 0.5 to 0.7 (1.0). The pattern of the narrowing inspiratory flow ahead of the bifurcation resembles that shown in Fig. 3 at t/T = 0.623 of Heraty et al.11 Thus, the “significant” periods around flow reversal reported in their observations can only be reproduced in this study with a significantly low flow rate over a non-negligible period around flow reversal.
While the flow structures at flow reversal found in the current single-bifurcation model bear some resemblances to those observed by Heraty et al.,11 they exhibit differences as well. For example, we do not observe the roll-up of shear layers due to shear instability and the subsequent vortices formed at the interface between opposing fluid streams at flow reversal under the same flow condition of Re = 740. The only vortical structures observed in the current single-bifurcation model are the secondary rotational motions, namely Dean vortices, due to centrifugal instability associated with the curvature of the bifurcation.4,33 At end expiration t/T = 0.97 and early inspiration t/T = 1.03, two pairs of strong counter-rotating vortices are formed in the parent branch (see Figs. 7e and 7f), whereas at end inspiration t/T = 0.47 and early expiration t/T = 0.53 a pair of counter-rotating vortices is formed in the child branch (see Figs. 7g and 7h). The primary difference between these vortices (found at flow reversal) and those found in a typical breathing condition (evident at peak flow rate rather than at flow reversal) is the spiral pattern of the current vortices that exhibit alternating positive and negative axial velocities, as indicated by the blue and red colors in the figure, along the spiral stream-traces of the vortices.
The branching angle and the diameter of the airways shall also affect the counter-flow structures. Heraty et al.11 reported the persistence of quasi-axisymmetric counter flow and shear layers to a greater extent of t/T = 0.115 at early inspiration and in the “wider” left child branch of the realistic model as shown in their Fig. 3. In contrast, in this study Fig. 7f shows that at t/T = 1.03 (or 0.03) the counter flow exists in the child branch, but is skewed toward the inner wall of the bifurcation. As illustrated in the straight-tube and single-bifurcation cases, deviation from axisymmetric counter flow to skewed counter flow is due to the inertia effect augmented in the flow through a curved tube. A close inspection of their idealized and realistic single-bifurcation models shows two major geometric differences between them. Both geometries’ features happen to yield the same effect of sustaining axisymmetric counter flow. The two features are the ratio of child-branch diameter to parent-branch diameter and the angle between the two child branches. In their idealized model the ratio is ~0.84 and the angle is ~63°, whereas in their realistic model the ratio is ~0.68 (0.64) for the left (right) child branch and the angle is 44°. In the current single-bifurcation model (Fig. 3a), the ratio is 0.7 and the angle is 70°, which fall within the ranges of the CT-based airways shown in Fig. 1 with an average ratio of 0.75 and an average angle of 70°. Their models have either a large diameter ratio (thus, yielding a smaller Re in the child branch) or a small angle (thus, a smaller curvature). Both reduce the effect of inertia, resulting in more apparent Womersley-like flow features. It is noted that their realistic model is based on a cadaver, while ours is based on in vivo imaging.
Convective Mixing
Convective mixing is quantified by instantaneous and time-averaged stretch rates. Lagrangian particles act like micro-sensors that are advected along with the flow and measure the degree of stretching by local flow structures. Coaxial counter flow alone (and associate shear layers) does not contribute to convective mixing as demonstrated in Fig. 12 because the Womersley solution is a linear solution such that passive tracers are reversed back to their original states at the end of one cycle or multiple cycles. With the presence of a bifurcation, at low Re = 100 coaxial counter flows are observed in both parent and child branches, and secondary vortices are present but weak, contributing little to mixing. Effective mixing takes place at Re = 740 in the single-bifurcation model when strong secondary vortices are induced. The flow becomes irreversible in that strong vortices are formed in the “parent” branch at end expiration and early inspiration, whereas they are formed in the “child” branch at end inspiration and early expiration. Unlike the Womersley solution where the velocity profiles at t/T are mirror images of those at t/T + 0.5 (Fig. 4a) and thus they are reversible, secondary vortices at t/T are no longer reverse processes of those at t/T + 0.5 due to inertia. Besides, regardless of axial flow direction, vortices on inspiration rotate in the same direction as those on expiration, which depends on the curvature of the bifurcation, contributing to irreversibility and mixing as well.
For the CT-based airway model, three breathing conditions are considered. They are the normal breathing case NORM, HFNR, and HFOV cases. Although HFNR is clinically impractical, it facilitates the investigation of the respective effects of unsteadiness (oscillation) and convection (inertia). Due to the long stroke length in NORM, we first compare the stretch rates for HFNR and HFOV for two cycles and then compare the stretch rates for the three cases in the vicinity of flow reversal. The results show that flow structures at flow reversal are not as effective as those at peak flow rate in mixing, but they contribute non-negligibly (~20%) to the total of time-averaged stretch rates in both HFNR and HFOV cases (based on the division that the flow structures within ±0.06 around t/T = 0.5 and 1 are regarded as counter-flow-related structures). A comparison of time-averaged stretch rates at the end of two cycles shows that mixing in HFOV is about three to four times more effective than HFNR, which is slightly greater than the ratio of Re for both cases.
Considering the flow structures at flow reversal near the first bifurcation within the time duration of ±0.06t/T, the stretch rate analysis shows that an increase in frequency by 30-fold increases the peak instantaneous stretch rate (time-averaged stretch rate) by 1.9 (8.4)-fold, whereas an increase in Re by threefold increases the peak instantaneous stretch rate (time-averaged stretch rate) by 2.6 (2)-fold. Contrary to HFNR and HFOV, the instantaneous stretch rate at flow reversal in NORM is nearly zero and the time-averaged stretch rate is much smaller than HFNR and HFOV. This demonstrates the unsteady features of the high-frequency oscillatory flow at flow reversal that is characterized by the interplay among counter flow, secondary vortices, and turbulence. Nonetheless, according to the flow visualization at small airways (see Fig. 11) and the flow regime (see Fig. 2), these unsteady flow features are only evident and significant in convective mixing up to the bifurcations between the third and fourth generations of the airways.
Conclusions
In this study, high-frequency oscillatory flow was studied using CFD in three models with increasing geometrical complexity, including a straight tube, a symmetric single-bifurcation tube model, and a CT-based trachea-bronchial airway model. The focus of the study is placed on the counter-flow phenomenon at flow reversal and its contribution to mixing. While in the straight-tube case the Womersley velocity profiles are produced, in the single-bifurcation case coaxial counter flow is altered by secondary vortices especially at high Re, resulting in convective mixing. It is also found that counter flow can sustain over a significant time period when the flow rate is set to zero. For the CT-based airway case, three flow conditions were considered to examine the effects of unsteadiness and inertia. It is found that in the normal breathing case the flow structures at flow reversal contribute little to mixing, whereas in the HFOV case the interplay among counter flow, secondary vortices, and turbulence enhances mixing at flow reversal.
Acknowledgments
This study was supported in part by NIH Grants R01-HL094315, R01-HL064368, R01-EB005823, and S10-RR022421. The authors are grateful to Youbing Yin and Haribalan Kumar for generating meshes and CT images of the airway model and assisting with stretch rate analysis. We thank Drs. C. Kleinstreuer and Z. Zhang for assisting with generation of a single-bifurcation geometrical model. We also thank the Texas Advanced Computing Center (TACC) and TeraGrid sponsored by the National Science Foundation for the computer time.