Fundamentals of Fluid Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 128

Whichever model is chosen, the user needs to take on the necessary task of carrying
out careful validation and verification to ensure confidence in the solution in order
to fully justify the application of the turbulence model chosen to solve the particular
problem. For more strategies on turbulence modelling and simulations, the reader is
encouraged to refer to the work of Nallasamy (1987), Spalart (2000), and Wilcox
(1993).

Creating the Mesh After determining the feasibility of converting a physical model
into a CFD model, the modelling procedure can begin. This involves the construction
of a suitable mesh that will increase the likelihood of attaining a converged and stable
solution. Mesh construction involves the subdivision of the computational domain
into a number of smaller mesh or grid cells overlaying the entire domain geometry.
For internal turbulent flows and any non-moving surfaces, proper resolution of the
boundary layer is imperative. Wall functions can be used to relieve the high compu-
tational demands, where the particular physics related to the boundary layer is not as
important as the flow field far away from the boundary walls. There are many wall
functions each of which can model up to different sublayers of the boundary layer.
The use of wall functions is to relate flow variables within the sublayers up to
the first computational mesh point, thereby removing the requirement to resolve the
actual structures in between the boundary wall and the y + of the first nodal point.
This point must be carefully placed so that it does not fall into the region actually
being modelled. As an example, let us consider a wall function that models up to
the transtional sublayer (i.e. this includes the viscous sublayer). The mesh should
then be arranged so that the values of y + at all the wall-adjacent integration points
are considered around the sublayer limit of y + = 30. It should be noted that, for non-
uniform geometries, there will be inevitable variations of y + across the wall surface
due to the different flow conditions. This means that besides checking the lower limit
of y + , it is also important to ensure that the upper limit of y + is not too far from the

sublayer limit (e.g. y + > > 30).
Let us also assume that the boundary layer extends up to y + between 300 and 500.
If the first integration point is placed at a value of y + = 100, then this will certainly
yield an inadequate solution due to insufficient resolution for the region. Adequate
boundary layer resolution generally requires at least ten nodal points in the layer,
and it is recommended that a post-analysis of the CFD solution be undertaken by
measuring the y + plus values across the surface walls to determine whether the degree
of resolution is achieved.
Wall functions may not be applicable in all cases, as discussed earlier; in this case,
the LRN turbulence model approach is used. This involves resolving the flow through
to the wall, requiring a higher demand on computational resources to produce the
near-wall mesh. Typically the mesh is of an order of magnitude greater than when
wall functions are used. In order to resolve the viscous sublayer inside the turbulent
boundary layer, y + at the first node adjacent to the wall should be set to as close to 1
as possible. Nevertheless, a higher y + is acceptable so long as it is still well within
the viscous sublayer ( y + < 5). Depending on the Reynolds number and in order to
properly resolve the mean velocity and turbulent quantities, the user should ensure