Elsevier

Journal of Biomechanics

Volume 43, Issue 6, 19 April 2010, Pages 1081-1085
Journal of Biomechanics

On the assumption of steadiness of nasal cavity flow

https://doi.org/10.1016/j.jbiomech.2009.12.008Get rights and content

Abstract

The unsteady flow through a model of the human nasal cavity is analyzed at a Strouhal number of Sr=0.791 for the complete respiration cycle. A comparison of the essential flow structures in the model geometry and a real nasal cavity shows the relevance of the model data. The analysis of the steady and unsteady solutions indicate that at Reynolds numbers Re1500 the differences of the solutions of the unsteady and steady flow field can be neglegted. To be more precise, the comparison of the total pressure loss distribution as a function of mass flux for the steady state and unsteady solutions shows the major differences to occur at increasing mass flux. At transition from inspiration to expiration the unsteady results differ the most from the steady state solutions. At high mass fluxes the total pressure loss of the nasal cavity flow almost matches that of the steady state solutions. The comparison with rhinomanometry measurements confirms the present numerical findings.

Introduction

The most obvious functions of the human nose are related to respiration and the sense of smell. Nonetheless important, the human nasal cavity combines a variety of other functions like moistening, tempering, and cleaning the air. All these do strongly depend on the flow field inside the nasal cavity. Due to a very low Strouhal number at normal breathing conditions the overall respiratory flow is usually considered quasi steady. The question arises whether or not this assumption is independent from the mass flux or, in other words, from the Reynolds number.

Many publications are based on this steady state condition for the respiratory flow. For a survey of these studies see (Hörschler et al., 2006a). The unsteady respiration cycle in various two-dimensional transverse cross sections is investigated in Naftali et al. (1998), where the average flow rate is about 125 ml/s and the study focuses on the air-conditioning characteristics in terms of humidification and warming of the respirated air. Note, in Naftali et al. (1998) no study on the impact of the unsteadiness compared to a steady state flow is performed. In another two papers (Naftali et al., 2005, Elad et al., 2006) an unsteady three-dimensional simulation of a sinusoidal pulse-like inspiration has been performed. The characteristic unsteady dynamics combining inspiration and expiration is not considered, which makes a comparison with the results of this study not useful, since the transition between inspiration and expiration characterized by a vanishing mass flux was not analyzed in the aforementioned references. Recent reviews (Elad et al., 2008, Doorly et al., 2008) confirm the complete unsteady cycle including the aforementioned transition to be not sufficiently studied, yet. The same holds for the investigations in Lindemann et al. (2005), Chung et al. (2006), Ishikawa et al. (2006), i.e., no analysis of the impact of the unsteadiness compared to a steady state flow is undertaken. In Lindemann et al. (2005) the unsteady inspiration phase is numerically simulated by the commercial code Fluent to analyze air-conditioning aspects of the human nose. An investigation based on particle-image velocimetry measurements of the unsteady nasal cavity flow is discussed in Chung et al. (2006). In Ishikawa et al. (2006) a complete respiration cycle with 5.2 s cycle duration including a 0.1 s zero-mass-flux period between inspiration and expiration, which is called resting phase, is simulated using Fluent. Especially the resting phase is numerically questionable since it does suppress unsteady flow phenomena caused by the changed flow direction between inspiration and expiration. In Ishikawa et al. (2009) both the inspiratory and the expiratory phase is simulated as well as the flow during sniffling. No comparison between the phenomena in the unsteady and steady flow fields has been taken such that the validity of a steady-flow assumption has not been substantiated. In Shi et al. (2006) inspiration and expiration are treated separately, i.e., the transition phase is not considered. Using a tidal volume of 250 ml and a respiration period of 3 s the overall unsteady development and the characteristic dynamic vortex behavior at transition from inspiration to expiration match the numerical findings discussed at length in Hörschler et al. (2006a).

To closer examine the dependence of the unsteady behavior of the nose flow on the phase of the respiration period, the complete respiration cycle of the flow through a model nasal cavity is numerically analyzed in this study. To show the relationship beween the flow of the model geometry and that of a real human nose configuration the major flow structures at inspiration and expiration are briefly compared. Despite this comparison physiological implications are not addressed as they are beyond the scope of this study. The investigation emphasizes concisely the differences between steady and unsteady flow solutions at low Reynolds number flows and the good agreement between steady and unsteady flows at high Reynolds numbers. The discussion focusses on the distribution of the total ressure loss vs. mass flux to show the steady flow condition to be a valid assumption especially in the high Reynolds number range.

Considering the Reynolds number which is in the range of Re2900 it can be concluded that the flow in the nasal cavity is neither clearly laminar nor turbulent. The flow structure differs dramatically in various areas of the nasal cavity, i.e., in some areas the flow will be laminar and in others transitional. Since such a flow field cannot be successfully described by classical turbulence modeling approaches based on the Reynolds averaged Navier–Stokes (RANS) equations the flow is computed pursuing another ansatz. The conservation laws are solved without any turbulence model using a high resolution to determine the fundamental time-dependent flow which is dominated by vortical structures especially at transition from inspiration to expiration and vice versa. In this transition phase, which is of primary interest in the context of the analysis of the time dependent flow behavior, the Reynolds number is small and as such the aforementioned computational concept without any RANS based turbulence modeling is well suited to resolve the details of the flow field.

First, the nasal cavity geometry and the grid generation are described followed by a compact presentation of the method of solution and the boundary conditions. Next, a set of steady state boundary conditions is given. To simulate the complete respiration cycle and hence, to compare steady and unsteady flow features unsteady boundary conditions are developed extending the basic principle of the steady state boundary conditions. In Section 3 the flow is analyzed by comparing the pressure loss over mass flux of the unsteady flow calculations with the equivalent steady state results. The final conclusions are drawn in Section 4.

Section snippets

Geometry and mesh description

From the data by Masing (1967), Brücker and Park (1999) an anatomically correct replica model with inferior and middle turbinate is constructed. As the superior turbinate is often vestigial in the average human nasal passage it is neglected in this study. That is, we will refer to the anatomical middle turbinate as upper turbinate and the inferior turbinate will be denoted as lower turbinate. The geometry of the nasal cavity model includes besides lower and upper turbinate also cartilage spurs.

Results

The analysis is divided into three parts. First, the main parameters of the steady and unsteady flows are introduced. Second, a comparison of the essential flow structures at inspiration and expiration of the model and the real nasal cavity configuration is given to emphasize the relevancy of the findings of the model flow for the real nasal cavity flow. Third, the distribution of the total pressure loss as a function of the mass flux is discussed for steady state and unsteady nasal cavity

Conclusion

An analysis of the unsteady respiration cycle through a model of the human nasal cavity was performed at Sr=0.791. The comparison of the flow structures in a model and a real geometry indicated the relevance of the model based solutions. The discussion of the total pressure loss vs. mass flux for the steady state and unsteady solutions showed a clear hysteresis and the major differences to occur at increasing mass flux. At decreasing mass flux smaller discrepancies between the steady and

Conflict of interest statement

To the best of our knowledge there is no conflict of interest.

Acknowledgments

This research has been conducted under research Grant WE 2186/5. The financial support by the German Research Foundation (DFG) is gratefully acknowledged.

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