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JORDANIAN GERMAN WINTER ACCADMEY. Lecture of : the Reynolds equations of turbulent motions. Prepared by: Eng. Mohammad Hamasha Jordan University of Science & Technology . Most of the research on turbulent –flow analysis is the past century has used the concept of time averaging.
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Eng. Mohammad Hamasha
Jordan University of Science & Technology
So any variable is resolve into mean value plus
Lets assume the turbulent flow is incompressible flow with constant transport properties with significant fluctuations in velocity, pressure and temperature.
( compressible fluid ).
the turbulent inertia tensor .
source of our analytic difficulties.
properties but also to local flow conditions (velocity,
geometry, surface roughness, and upstream history).
though rather thinly formulated from nonrigorous postulates.
rearranged to display the turbulent inertia terms as if they
total stress on the system were composed of the Newtonian
Viscous Stresses plus an additional or apparent turbulent-
stress tensor .
Now consider the energy equation (first law of thermodynamics)
for incompressible flow with constant properties
have collected conduction and turbulent convection terms into a
sort of total-heat-flux vector qi which includes molecular flux plus
the turbulent flux .
case. In two-dimensional turbulent-boundary-layer flow (the most
common situation), the dissipation reduces approximately to
empirical modeling ideas
Many attempts have been made to add "turbulence conservation“
relations to the time-averaged continuity, momentum, and energy
turbulence kinetic energy K of the fluctuations, defined by
A conservation relation for K can be derived by forming the mechanical energy
equation, i.e., the clot product of u; and the ith momentum equation. then, we
subtract the instantaneous mechanical energy equation from its time-averaged
value. The result is the turbulence kinetic-energy relation for an incompressible
Here the roman numerals denote (I) rate of change of Reynolds stress,
(II) generation of stress, (III) dissipation, (IV) pressure strain effects,
and (V) diffusion of Reynolds stress.