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8.4 Computer Program STP 257
To calculate the location of the onset of transition it is usually sufficient
to perform neutral stability calculations at four x-locations so that four fre-
quencies can be computed and amplification rates determined on four curves
with constant dimensional frequencies. While STP is general and can be used
for external flows with suction and injection as well as free shear flows such as
jets and wakes, changes are required to accommodate boundary conditions and
provide better estimates of initial eigenvalues where required. STP can also be
used for flows with heat transfer as discussed in [3].
STP consists of MAIN and four subroutines - VELPRO, CSAVE, NEWTON
and NEWTONI - and are described in the following subsections.
8.4.1 M A I N
In MAIN the total number of x-stations (NXT) and the x-station where the
stability calculations begin (NXO) are identified together with the requirement
of neutral stability (IXT = 0) or transition. In the latter case, it is necessary to
specify the number of frequencies, and this is done by setting IXT to 1, 2, or
any number other than zero but less than twenty so that, for example, 1 will
lead to transition calculations for one frequency and 2 for two frequencies, etc.
To calculate the neutral stability curves, the dimensionless external velocity
UE(I) (= Ue/uoo) is required as a function of surface distance S(I) (= s/L), to-
gether with Reynolds number Ri (= u^L/v), a reference length L and velocity
UINF (= i^oo)- The stability Reynolds number REY(I) (= R) is then calculated
from Eq. (8.1.7) with R x given by
Rx = u e ( | ) R L (8.4.5)
The calculation of the eigenvalues a and UJ at NX = NXO (s = SQ) also requires
the specification of their initial estimates at the Reynolds number corresponding
to its value at SQ. For Blasius flow, they can be obtained from the already
constructed stability diagrams, such as those given by Fig. 8.1. When other
figures are used, care should be taken to ensure that the estimated eigenvalues
have the same length and velocity scales as those used in STP.
The velocity profiles u and u" needed in the stability equation are obtained
by calling VELPRO, and the calculations for neutral stability are performed
by calling NEWTON and for amplification rates ai and n-factor by calling
NEWTONI.
8.4.2 Subroutine VELPRO
The velocity profiles for STP can be generated by any boundary-layer method.
Here we assume that they are provided by BLP of Section 7.4. The read-in
values of KX and NP in this subroutine refer to the NX-station and the j-points