Handbook of Turbomachinery Second Edition Revised - Ventech!

nondimensional heat transfer coefficient:
St ¼ q 00 w = ropUðTw T?Þ ¼ kðqT=qyÞ w = ropUðT? TwÞ
also St ¼ Nu=RePr
The heat transfer is a function of Reynolds number and Prandtl number and
is directly proportional in the case of turbulent boundary layer to the skin
friction Cf ¼ 0:058ðReÞ 1=5 ; Nu ¼ Cf=2ðRePr 1=3 Þ,orNu¼ 0:029 Re 4=3 Pr 1=3 .
A thin boundary layer (smaller resistance) permits a greater heat
transfer. The case of zero boundary-layer thickness (as in stagnation point)
has the maximum heat transfer. The thickness of thermal and velocity
boundary layers is about the same for air, and the velocity and temperature
ðTw T?Þ profiles are similar for a flat plate (zero pressure gradient).
In a turbulent boundary layer, the turbulent heat flux can be treated
much the same way as the Reynolds stress. The velocity temperature
correlation is assumed to be proportional to the temperature gradient in the
y direction (normal to wall). Hence, the heat flux due to turbulent
fluctuations can be written as
q 00
t
¼ rcpehqT=qy
where eh is the eddy thermal diffusivity.
The similarities between the exchanges of heat and momentum by
turbulence fluctuations should be emphasized in the presence of velocity
gradient. There is a close coupling between heat transfer and momentum
transfer, which translates into a close coupling between heat flux and
shearstress. Since the major concern here is the heat transfer between fluid
and solid, the shear stress at the wall plays a key role. The dimensionless
turbulent Prandtl number Prh ¼ em=eh provides a relation between closely
coupled momentum and heat transfer.
Role of Similarity in Experimental Emulation of a Turbine
Airfoil Heat and Mass Transfer
One of the most critical measures affecting turbine blade and nozzle vane
life is their metal temperature. A 20–30 8F (12–18 8C) underprediction in
metal temperature may easily result in a 50% reduction in blade creeprupture
life. Accurate prediction of this temperature is often based on highquality
experimental simulation of the component heat transfer representing
actual engine conditions. This is particularly important for a cooled turbine
airfoil where both external and internal convective heat transfer have to be
considered as boundary conditions for the conduction heat transfer in the
Copyright © 2003 Marcel Dekker, Inc.