Large Eddy Simulation and Reynolds-Averaged Navier–Stokes modeling of flow in a realistic pharyngeal airway model: An investigation of obstructive sleep apnea
Introduction
Obstructive sleep apnea (OSA) is a disorder characterized by recurrent episodes of pharyngeal airway collapse and obstruction during sleep, resulting in airflow cessation, oxygen desaturation, and sleep disruption (Malhotra and White, 2002). Although both airway narrowing (Arens et al., 2003) and airway collapsibility are believed to play a role in the pathogenesis of OSA, the exact mechanisms are not clear. The accurate knowledge of the abnormal flow behavior associated with OSA in the upper airway will be an important step in understanding the interaction between airway anatomy and airway collapsibility in the pathophysiology of OSA. Performing a detailed flow characterization in the upper airway using experimental techniques is expensive and difficult to achieve due to the intrusive character of such methods. By using non-intrusive flow-modeling techniques, such as computational fluid dynamics (CFD), one can capture the flow features in the airway and obtain quantitative and qualitative information about flow variables, such as the distribution of the wall pressures.
Several researchers highlighted the use of CFD for analyzing the flow characteristics through simplified airway models (Kleinstreuer and Zhang, 2003; Matida et al., 2006; Nithiarasu et al., 2007). Collins et al. (2007) discussed the importance of considering models that are geometrically correct in representing the airway anatomy. Indeed, biological systems such the human upper airway, have complex geometries that are highly asymmetric and show variable cross-sectional shape and size from the nostrils to the bronchi. Recently, CFD has been applied to analyze the flow in exact upper airway models reconstructed from magnetic resonance (MR) or computed tomography (CT) imaging data of patients with OSA (Xu et al., 2006; Sung et al., 2006; Vos et al., 2007; Jeong et al., 2007). In all this studies the CFD analysis was based on Reynolds-Averaged Navier–Stokes (RANS) solvers using two-equation turbulence models. The RANS approach is based on a time averaging of the flow field. The two equation models necessitate solving two differential-transport equations. Commonly one equation is a transport equation for the turbulent kinetic energy (k). The second equation describes the transport of another turbulent quantity such as the dissipation rate of turbulent kinetic energy (ε) or the specific turbulent kinetic energy dissipation rate (ω). These models offer relatively accurate results for simple flow situations and require low computational costs in comparison with other, more complex (but more accurate) turbulence models. However, their ability to accurately predict anisotropic flows that develop adverse pressure gradients, secondary flow regions, or curved streamlines such as in the airway, is limited (Wilcox, 1993). Since only information about the local mean flow is computed, RANS cannot describe the flow field unsteadiness that is particularly important in case of flow separation or when vortical structures develop in the flow. In some situations it is possible to use simplified airway models to describe features of the flow by using RANS that incorporates the renormalization group k–ε model, but such model should be carefully tuned (Zhang et al., 2002; Jeong et al., 2007).
Any attempt to fully understand the physics of the transitional/turbulent flow through the airway needs to employ time accurate tools and Eddy resolving techniques that can capture the present unsteady phenomena. Such a technique is Large Eddy Simulation (LES) approach (Pope, 2000). It is characterized by a division of the flow field into large and small scales by a filtering procedure. Unlike RANS where the averaged results are provided by modeling all the turbulent scales, LES can directly solve the equations that describe the evolution of a large range of turbulence scales. Only the smallest scales are modeled by LES using Sub-Grid-Scale (SGS) models. An additional LES advantage over the computationally simpler RANS formulation is the increased level of detail and accuracy it can deliver for unsteady, separated or vortical turbulent flows, LES being able to resolve the evolution of turbulent flow structures and to predict the flow dynamics. A large number of engineering-related problems (Mahesh et al., 2004; Tokyay and Constantinescu, 2006; Boudier et al., 2007; Mongia, 2008) and a few biomedical flow studies showed good agreement of LES data with experimental measurements in contrast with RANS results (Luo et al., 2004; Matida et al., 2006; Jin et al., 2007; Varghese et al., 2008). Therefore, this more accurate numerical technique for flows in a complex geometry, such as the upper airway, was employed here and compared with two typical steady RANS formulations.
The present work describes the prediction of flow in a three-dimensional pharyngeal airway model using both RANS and LES approaches. In the steady RANS modeling framework two distinct turbulence models were used, namely, k–ε and k–ω. The airway model was reconstructed from cross-sectional MR scans of a patient with OSA and it is characterized by a maximum narrowing at the site of retropalatal pharynx. The differences between the LES solution and the flow predictions from RANS simulations are addressed.
Section snippets
MR imaging data acquisition and analysis
MR imaging was performed in the Department of Radiology at Cincinnati Children's Hospital on a 1.5 T MRI scanner. The patient was a 17.9 years old female that had a height of 1.57 m, a weight of 129.6 kg, and a body mass index of 53.94. Nine transverse MR sequences (Axial T1) with 5 mm thickness and zero spacing between them were acquired to cover the entire length of the pharyngeal airway extending from the roof of the nasopharynx to the lower mandibular plane as shown in Fig. 1a. The pixel
Results
The influence of the grid spatial resolution on the numerical solution was evaluated by repeating the solution with a sequence of different refined meshes (Grid1, Grid2, and Grid3). Fig. 2 shows details of the computational grids used. An important issue, especially for LES, is the estimation of Taylor micro-scale (λT) that is a measure for the computational cell size. Assuming the integral length scale as one order of magnitude smaller than geometrical characteristic length scale (l=0.07Deq)
Discussion and conclusions
The present study compares LES and steady RANS solutions of flow through a pharyngeal airway model. The airway model was reconstructed from MR scans of a patient with OSA. In the RANS modeling framework both k–ε and k–ω turbulence models have been used.
The largest differences between the results were found in terms of axial velocity distributions downstream of the maximum narrowing. This flow region is characterized initially by an acceleration of the flow and then by a deceleration due to
Conflict of interest statement
None of the authors have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.
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