Handbook of Turbomachinery Second Edition Revised - Ventech!

in heat transfer as the Reynolds number is increased. The converse is true as
the Mach number is increased. This follows the classical trends for flat-plate
boundary layers, and the only difference in the present case is the effect of
curvature and pressure gradient which modify the onset and length of
transition. The effects of turbulence are well catalogued by a number of
authors, for example by Arts et al. [29] and Consigny et al. [30]. Their
studies show (Fig. 12) that as inlet turbulence is increased, the location of
transition moves upstream and generally leads to an increase in the heat
transfer to the suction side of the airfoil.
Curvature
It has been established that the aerodynamics on the pressure side is mainly
two-dimensional. Therefore, the heat transfer on the pressure side is also
mainly two-dimensional and can be predicted, in most cases, using twodimensional
boundary-layer computer programs. It has been observed that
the presence of Goertler vortex on concave surfaces [[31] and [32]] (Volino et
al., Dring et al.) can increase the heat transfer to turbine pressure sides
particularly at low inlet turbulence intensity. However, experiments on
actual turbine vanes and blades that exhibit high inlet free-stream
turbulence (Tu > 5%) do not appear to confirm such phenomena. It may
also be that the convex to concave curvature transition near the leading edge
in real engine airfoils (test cascades and engine vanes) eliminates or destroys
the growth of the Goertler vortex, which is quite sensitive to curvature
effects and inlet turbulence.
The effect of streamwise surface curvature is to stabilize the boundary
layer on a convex surface and to destabilize the boundary layer on a concave
surface. The destabilizing effect of centrifugal forces on the concave wall
induces an instability, which results in Goertler vortices with axes in the
same direction as the main-stream flow. It has been shown that the heat
transfer on a concave wall is increased with surface curvature and that for a
convex wall the heat transfer is decreased. Turbulence intensities in the
boundary layer are significantly reduced on a convex wall and enhanced on
a concave wall. The results of some studies also suggest that the effect of
surface curvature is nonlinear, being very strong at small curvature values
but increasing less than proportionately as curvature increases.
Vane suction surfaces are more influenced by secondary flows. It has
been shown that the end-wall boundary layers migrate across the suction
surface of the vane. In case of a blade, the tip section has a more intensive
secondary flow resulting from the radial pressure gradient (tip to hub) that
tends to push more fluid along the airfoil suction side. The secondary flows
affect the heat transfer close to the tip and hub sections of the nozzle.
Copyright © 2003 Marcel Dekker, Inc.