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Turbulent flow by UKM JKKP Students Set 2 (2021/2022), image, fmmmm, fq,…
Turbulent flow
by UKM JKKP Students Set 2 (2021/2022)
POWER LAW VELOCITY PROFILE
• boundary layer flow on a flat plate can be expressed as a power law:
• use n = 7 but the value of n depends on the
Reynolds number
• If n = 7 then Blasius
skin friction in pipes
•Turbulent skin
friction on flat plate
APPLICATION
to accelerate chemical reaction rates in liquids and gases or in liquid gas mixtures
To mix and homogenize fluid mixtures. Example: mixer
oil transport in pipelines
Examples of operational unit
Bioreactor
Fermenter
Boussineq Theory of Turbulence
Comparison between viscous and Reynold shear stresses in shear layer in terms of order in magnitude
Types of turbulent flow
Wall (shear) layer turbulence
flow in pipes, channels & boundary layers
Free Shear Layer
Turbulent flow free from effects of walls
Homogeneous
for ex: decaying turbulence behind the grid in wind tunnels
Turbulent Boundary Layer
In laminar flow (Re x < 2 x 10^5 ) a simple polynomial to represent the similarity velocity profile can be used in the von Karman integral momentum equation
In turbulent flow (Re x >3 x 10^6 ), velocity near wall depends on shear stress and NO single function represent velocity profile
To use the von Karman integral momentum equation, a simple velocity profile is assumed and the Blasius correlation for the shear stress is used
Von Karman momentum integral,
has bigger mean velocity, momentum and
energy
-At same Re, turbulent boundary layer is thicker, turbulent boundary layer is preferred in engineering application because it resists separation. Turbulent boundary layer has bigger mean velocity, momentum and energy
Reynolds Averaging
Velocity can be presented as the sum of a mean velocity & a velocity deviation
Velocity varying with time around a mean velocity
The mean of the deviation is zero by definition
Likewise for y and z velocity components
Other properties like pressure presented in the same way
Characterization
Caused by formation of eddies during flow & not by complex geometry or time variation.
Characterized by semi-random, stochastic property changes
Occurs at high Reynolds number , Re ≥ 4000
Diffusion causes rapid mixing & enhance heat, mass & momentum transfer
Dissipative by viscous shear work converting turbulent kinetic energy into internal energy
UNIVERSAL VELOCITY DISTRIBUTION
Reynolds Equation of Motion
TURBULENT FLOW BY JABATAN KEJURUTERAAN KIMIA DAN PEMPROSESAN (UKM) SET 2 (2020/2021)
