Fundamentals of Fluid Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 114

Fig. 5.12 Velocity profiles in a 2D pipe flow showing the difference between a laminar and a
turbulent velocity profile. (In fluid mechanics the flow of fluid through a pipe of uniform cross-
section is known as Hagen-Poiseuille flow
components. Random, irregular fluctuations in the flow are characteristic features of
turbulent flows.
Velocity Profiles One important flow feature of laminar and turbulent flows is the
influence of the viscosity and its mixing effect. Under a laminar flow the velocity
profile is parabolic in shape. Let us imagine fluid passing over a pipe surface as layers
of molecules. The molecules are transported mainly by the flow in the streamwise
direction ( y -direction in Fig. 5.12 ), but they also exhibit random motion due to the
molecular state which causes them to momentarily move vertically into adjacent
layers of molecules. This process is called molecular diffusion . At the wall surface,
the air molecules stick to the surface and the velocity is zero. The adjacent layer of
air molecules immediately above are slowed down as they collide with the molecules
that have stuck to the surface. In turn, these molecules slow down the flow in the layer
just above it, and this continues until far from the surface where the slowing effects
(or viscosity effects) from the stationary wall are weak. This creates a thin layer of
fluid, called the boundary layer, near the surface in which the velocity changes from
zero at the surface to the free stream value far away from the surface. Under a laminar
flow, the slowing down process due to molecular diffusion of the molecules from
one 'layer' to its adjacent layer above occurs gradually, since the molecules mainly
travel in an orderly path through the pipe.
For turbulent flows the velocity is no longer orderly, and there are no discernable
layering motions of the fluid but rather the fluid elements swirling and fluctuating
randomly within the boundary layer. It has been suggested that turbulence is a col-
lection of eddies, which are parcels of rotating fluids. These eddies have a spectrum
of vorticities and provide a high level of mixing in the fluid. Turbulence eddies carry
and rapidly disperse momentum, mass and heat in the transverse direction. This leads
to greater momentum and heat transfer in turbulent flows, and, thus, significantly
higher values of friction and heat transfer coefficients, in comparison to laminar
flows.