Handbook of Turbomachinery Second Edition Revised - Ventech!

Optimization Problem
For the design optimization problem considered, a wide range of design
objectives can be addressed even with the coupling between two disciplines.
In the results described below, the average and maximum temperatures at
each spanwise section are used as objective functions. The trailing-edge
thickness is held constant during the optimization, and the ratio of
maximum thickness to chord for each section is constrained to within 10%
of the reference value, which results in better aerodynamic characteristics for
the blade.
The results discussed below are for a simplified optimization problem
involving two design objectives per section since the main purpose here is
the demonstration of the optimization procedure. The two objectives are
minimum average temperature and minimum peak temperatures in each
blade section. A more detailed optimization problem with more design
objectives is given in Ref. [17]. The constraints are
Where
ttr4ttr ref
ttr5ttr ref
tmax
C 41:1 tmax ref
Cref
tmax
C 50:9 tmax ref
Cref
Xlower;i4XðiÞ4Xupper;i; i ¼ 1; ...; NDV ð10Þ
ttr is the trailing-edge thickness.
tmax is maximum blade thickness.
C is the blade chord. The subscript ‘‘ref separate’’ stands for
reference value.
XðiÞ is the vector of design variables, which includes the ycoordinate
of the Bezier control points of each section, end
locations of each internal coolant passage in each section, and
the location of the film-cooling ports (centers) along the blade.
For all the sections combined, there are 24 objective functions, 48
constraints, and 384 design variables [17] in the optimization problem.
Sensitivity Analysis
The sensitivities of the objective function and constraints with respect to the
design variables (required for the optimization procedure) are evaluated
Copyright © 2003 Marcel Dekker, Inc.