Numerical Methods and Its Solution - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 223

way of directly comparing numerical data with experimentally measured values
(e.g. Fig. 7.34 a). Also, logarithmic scales allow the identification of important flow
effects occurring especially in the vicinity of solid boundaries. Furthermore they are
common in representing line profiles of velocity and for plots of surface quantities
such as pressure and skin-friction coefficient.
Vector Plots A vector plot displays a vector quantity at discrete points (usually ve-
locity) with an arrow whose orientation indicates direction and whose size indicates
magnitude. It generally presents a perspective view of the flow field in two dimen-
sions. In a three-dimensional flow field, different slices of two-dimensional planes
containing the vector quantities can be generated in different orientations to better
scrutinize the global flow phenomena (see Fig. 7.34 b). If the mesh density is con-
siderably high, the CFD user can either interpolate or reduce the numbers of output
locations to prevent the clustering of these arrows “obliterating” the graphical plot.
Contour Plots In contrast to X-Y plots, contour plots provide a global description
of the fluid flow encapsulated in one view, a feature found in vector plots (e.g.
Fig. 7.34 a). Generally, contours are plotted such that the difference between the
numerical value of the dependent transport variable from one contour line to an
adjacent contour line is held constant. The use of contour plots is not usually targeted
for precise evaluation of numerical values between contour lines but rather to give a
qualitative perspective. A contour line (also known as isoline ) can be described as a
line indicative of some property that is constant in space. Its equivalent representation
in three-dimensions is an isosurface. In practice, the contours are usually linearly
scaled. However, to better capture the hidden details in some small regions within the
flow field, the reader may be required to employ a finer scaling choice to reveal these
isolated flow behaviors. For the contour plots where the isoline interval values are
the same, then clustering of these lines indicates rapid changes in the flow quantities.
Particle Trajectory and Deposition Plots When a Lagrangian method is used, par-
ticle trajectories can be plotted. In more complex flow problems such as multiphase
flows that involve the transport of solid particles, particle tracks associated with
the discrete particles of a certain diameter and mass being injected inside the bulk
fluid fall in this same category. Here, important information on the particle residence
time, particle velocity magnitude and other properties can be duly extracted. When
a particle hits a surface wall, the particle tracking can be terminated and the parti-
cle's impaction onto the wall can be recorded. By plotting these coordinates onto the
computational geometry, a deposition plot can be achieved. Figure 7.35 shows the
deposition sites of particles after it has travelled through the nasal cavity and finally
deposited onto the nasal walls. Some things to note for this case include the assump-
tion that there is no mass or momentum transfer from the particle to the surface wall
and the particle does not bounce/rebound or splatter upon impact. Furthermore when
producing a particle deposition plot, there are limitations on the number of particles
that can be displayed on the computer screen based on the graphical processing
ability of the computer being used. Typically 10,000 particles on today's standard
desktop computers will be the limit (based on 1 Gb graphics card).