In practical transport problems, we are mostly interested in transfer across a system boundary, or in the case of pipe flow, to the wall. Empirical transfer coefficients provide proportionality factors between the flux at the boundary and a driving force:
The most common method of accounting for the effects of turbulence on momentum transfer in piping systems is through the use of friction factors. These represent the ratio of the shear stress at the wall of a conduit to the kinetic energy (velocity head) of the flow, and thus measure the frictional losses in a system.
Correlations for determining the friction factor will be discussed later in the course. Friction factor methods apply to both laminar and turbulent flow, as long as it is incompressible and fully developed.
Turbulent eddies transport heat and mass as well as momentum. Analogies relating the three modes enable prediction of heat and mass transfer based on momentum transfer and allow the approximations developed for turbulent flow to be extended.
The simplest analogy is to say that the eddie diffusivities are the same for all modes of transport, that is: ET = EH = EM.
Two other analogies will be mentioned. First is the "Reynolds Analogy", which relates the Fanning friction factor for fluid flow to heat transport:
Note that one-half the friction factor is equivalent to the ratio of the overall momentum transported to the wall to the inertial effects in the mainstream. The Stanton number represents the ratio of the overall heat transport to the wall to the convective effects in the mainstream. The Reynolds analogy says that these ratios are equal for mass and momentum transport.
The Reynolds analogy postulates direct interaction between the turbulent core of the flow and the walls. If a laminar sublayer is included between these, the Prandtl-Taylor analogy applies:
References:
R.M. Price
Original: 5/99
Revised: 7/22/99; 10/6/99; 10/15/99
Copyright 1999 by R.M. Price -- All Rights Reserved