<DOC>
<DOCNO>
869
</DOCNO>
<TITLE>
the calculation of transient temperature in turbine
blades and tapered discs using biot's variational method .
</TITLE>
<AUTHOR>
howe,p.w.h.
</AUTHOR>
<BIBLIO>
arc cp.617, 1961.
</BIBLIO>
<TEXT>
  transient temperatures in aerofoil
sections and tapered discs are
calculated taking advantage of simplifications
in heat flow analysis
achieved in biot's variational method .
cross-sections are represented by
a line of adjacent squares of various
sizes suitable for the local dimensions,
e.g. small squares near the leading
and trailing edges .  the potential,
dissipation and surface dissipation
functions of biot's method are
set up, and the lagrange equations lead,
by automatic procedures, to an
eigenvalue formulation in matrix form for
the temperatures and their first
time derivatives .  solutions are sums
of exponentials in time, and are
evaluated by digital computer, requiring
about five minutes for each crosssection
and heat transfer coefficient .
transient temperatures in a particular
aerofoil section for variation
of heat transfer coefficient and for
external temperature depending exponentially
on time agree with results
obtained on an analogue computer .
maximum transient temperature differences
are evaluated for tapered discs
by a simple electrical analogue) with
variation of edge radius and heat
transfer coefficient .  peculiarities
in the solution for cyclic temperature
external to an aerofoil over
a range of frequencies indicate limitations
in the mathematical formulation .
a successful solution for cyclic
external temperature might enable
eigenvalues to be separated out in
experimental measurements using
electronic equipment, and this might be
extended to exponential external
temperature if a relationship between
cyclic and exponential external
temperature could be established .  eigenvalues
and eigenvectors as discrete
values arise fictitiously from the
sub-division into squares and the
possibility of an integral formulation
is mentioned .  there is a possible,
but not immediate, extension to
cooled blades, whose cross-sections
are multiply-connected regions .
transient stresses due to creep, and
viscoelasticity might be included .
</TEXT>
</DOC>
