Optimization and Computational Fluid Dynamics - Department of ...

158 René A. Van den Braembussche
(a) (b)
Fig. 6.7 Definition of (a) leanand(b) rake in radial impellers
gal stresses. The parameters of primary importance in controlling the blade
bending due to the static and dynamic load in an axial compressor or turbine
blade are: minimum and maximum moment of inertia (Imin) and(Imax) of
the cross sections and the direction κ of its maximum value.
PMach is the penalty for a non-optimum Mach number distribution. Analyzing
the Mach number distribution may help to rank blades that have
nearly the same loss coefficient. NS solvers are not always reliable in terms
of transition modeling and erroneous penalty function may occur when the
transition point is incorrectly located. Transition criteria based on the Mach
number distribution may help to relieve this uncertainty.
One is also not interested in designing blades that have very good performance
at design point but for which the flow is likely to separate (with
large increase in losses) at slightly off-design conditions. A rigorous way of
verifying the operating range is discussed in Sect. 6.5. A simpler approach
accounts for the changes in the Mach number distribution that can be expected
at off-design. It increases the chances for good performance of the
blade over a wide range of operating conditions without the cost of extra NS
computations.
The Mach number penalties that have been formulated for turbine blade
optimizations are presented in Sect. 6.4. They tend to achieve a continuous
flow acceleration with minimum deceleration. Mach number penalties for
radial compressor impellers are presented in Sect. 6.6.
Pdischarge can be used to penalize the spanwise distortion of the flow at the
exit. It results from the idea that a more uniform exit flow has a favorable
effect on the downstream diffuser or blade row and hence, on the stage effi-