Handbook of Turbomachinery Second Edition Revised - Ventech!

point in the flow as the fraction of time in which the flow is turbulent at that
point. Where the flow is all laminar g is 0 and where it is fully turbulent g is
1.
As turbulent spots in the boundary layer move down stream and
coalesce into full turbulence, intermittancy can be used to scale (or weight)
the values of quantities of interest through transition. The non-dimensional
heat transfer coefficient, St, may be given in this manner. If the momentum
thickness Reynolds number (Re y) of 162 is used as the start of transition
(Kays and Crawford [11]), and intermittancy is expressed by Emmon’s
relationship
Where
gðxÞ ¼1 exp½ nsðRex RextÞ 2 Š ð1Þ
Rext is the x (surface distance) Reynolds number at the start of
transition.
n and s are experimentally determined parameters.
Then we can write the heat-transfer coefficient as
StðxÞ ¼ð1 gÞStlam þ gStturb ð2Þ
In other words, the Stanton number in the transition zone is a linear
combination of the fully laminar and fully turbulent heat-transfer
coefficients at the same surface distance.
While this approach serves well to estimate how the heat transfer and
other quantities change through the transition zone, designers must still find
a method to predict the intermittancy values from transition onset to finish.
Clark et al. [12] is an example of this approach.
LOW-SPEED, LARGE-SCALE EXPERIMENTS
Virtually all of the turbine experimental heat-transfer studies through the
mid-1970s were done either in flat-plate wind tunnels or in cascades of vanes
or blades. The study of three-dimensional flow in a turbine cascade by
Langston et al. [13] is typical of many similar investigations.
The flow in these facilities could be compressible but more often was
not because of the expense involved. Further, earlier experiments were most
often steady and run at relatively low temperature differences between the
wall and mainstream gas. The large scale of these facilities allowed matching
of the Reynolds numbers in the experiments to the design Reynolds
numbers of actual machines. But, as mentioned, Mach numbers could rarely
Copyright © 2003 Marcel Dekker, Inc.