Fundamentals of Fluid Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 112

terms, imagine the problem concerning the fluid flowing in a pipe (Fig. 5.7 ) whose
walls are now heated. If the surrounding fluid velocity is very low, the surrounding
fluid temperature within the pipe increases due to the heat flowing from the pipe
surface into the bulk fluid—this corresponds to the case that the heat conduction
dominates the local convection of the fluid. However, if the surrounding fluid velocity
is high, the heat of the fluid is carried away by the relatively cooler fluid. The high
temperatures are only found near the hot surface of the pipe walls—this corresponds
to the case that the local convection dominating the heat diffusion .

5.3 Turbulent Flow

5.3.1 What is Turbulence?

Fluid flow can be classified into one of two main regimes, namely laminar flow
and turbulent flow. Laminar flows are characterised by smooth fluid layers passing
over each other without mixing. The viscosity of the fluid plays a significant role
in holding the fluid together in its layered formation; thus, if a fluid particle was
tracked throughout the flow, its path could be predicted. Turbulent flows on the other
hand are characterised by the random fluctuations, irregular and chaotic motion, and
high level of vortices. The fluctuation velocities of the fluid play a significant role in
transporting and dispersing the fluid across different regions, thus, breaking down
the layered motion that is present in laminar flows. If a fluid particle was tracked
throughout the flow, it would have an irregular path with no discernable pattern. The
presence of turbulence significantly increases dispersion, mixing, energy dissipation,
and heat, mass and momentum transfer. Many flows found in nature and in industrial
applications are in a turbulent regime, such as rivers, wind flows, and smoke rising
from a cigarette (Fig. 5.10 ).
If you have looked over the ocean from above you may have noticed the water
flow is chaotic and random, with little pockets of vortices. The smoke rising from
a cigarette begins with a smooth plume (laminar flow) before it becomes disturbed
and breaks out into random fluctuating smoke streaks (turbulent flow). Disturbances
originate from the free stream of the cigarette smoke, amplify and lead to formation
of turbulent flow. However, these disturbances can be induced by surface roughness
in internal flows as well, where they may be amplified in the direction of the flow,
in which case turbulence will occur. The onset of turbulence depends on the ratio
of the inertia force to viscous force, which is indicated by the Reynolds number, as
described earlier in Eq. (5.15). For internal pipe flows,

• the flow is laminar for Re < 2,000,

• the flow is transitional between 2,000 < Re < 4,000 and

• the flow is turbulent for Re > 4,000.