Fundamentals of Fluid Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 123

models exhibit turbulence characteristics such as formation of eddies, cross-currents,
and mixing (Churchill et al. 2004). Further downstream, the flow becomes turbulent
in the laryngeal region before becoming laminar deep in the bronchial airway tree.
In order to capture as much of the flow physics in the different flow regimes but still
use accessible computing resources, a suitable LRN turbulence model may be used.
This may be achieved through RANS-based models such as the LRN- k-ε and LRN-
k-ω models. However, it has been suggested that the LRN k- ε model fails to simulate
the transition to turbulent flow while the k-ω showed better ability in reproducing the
behaviour of all flow regimes in the airways (Zhang and Kleinstreuer 2003). The LES
model is also capable in capturing all flow regimes; however, the mesh requirements
and temporal resolution must be sufficiently refined to capture the relevant turbulent
flow features, and therefore this model is computationally restrictive. It is anticipated
that future trends in the choice of turbulence models will slowly shift from RANS to
LES or a hybrid RANS-LES model (such as the Detached Eddy Simulation model),
as computational power increases and access to such resources become more widely
available. The main drawback of RANS models is in the requirement to decompose
the flow into a mean and fluctuating component that contains large and small scale
turbulence. Thus, a RANS model cannot capture the large scale transient structure of
turbulence that may be needed for many research applications. The DNS approach
for respiratory flows remains out of reach at the present time due the rather complex
shape of the airway passages.

5.3.5 Near-Wall Modelling

Airflow through the respiratory passages is confined by the surrounding walls and
can be broadly classified as internal flows or wall bounded flows. In terms of fluid
dynamics, the near-wall regions are primary sources of vorticity and turbulence as
they are the regions with a sharp velocity gradient where the moving fluid rapidly
decreases to a velocity of zero at the wall surface. In describing the near-wall velocity
profile, dimensionless variables with respect to the local conditions at the wall are
typically used. If we let y be the normal distance from the wall and u be the time-
averaged velocity parallel to the wall, then the dimensionless velocity u +

and wall

distance y + can be appropriately described in the form as u + = u/u τ and y + = yu τ /ν ,

respectively. Within these dimensionless parameters, the wall friction (shear) velocity
u τ is related to the wall shear stress τ w as u τ = √ τ w /ρ .
The velocity profiles in Fig. 5.12 show a thinner profile for turbulent flows, which
consist of three regions based on the distance from the wall. The layer closest to
the wall is the viscous sublayer which is very thin and is dominated by molecular
viscosity (i.e. viscous laminar-like profile and negligible turbulence effects). In this
region viscous damping reduces the tangential velocity fluctuations, leading to tur-
bulent dissipation. Its profile is nearly linear and can be described by the equation
known as the law of the wall :

u + = y + for y + < 5 .