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8.5 Applications of STP 259

n
CLOGA corresponding to the exponent n in the e -method, can be written as

8.5 Applications of STP

8.5.1 Stability Diagrams for Blasius Flow
The stability diagrams for Falkner-Skan flows, similar to those given in Fig.
8.1, can be constructed by using BLP and STP. For a given external velocity
distribution (constant for Blasius flow), BLP generates the laminar velocity pro-
files so that ETA(J), U(J,2) and V(J,2), J = 1,..., NP, can be printed from the
MAIN program in a format compatible with the READ statement of subroutine
VELPRO.
For the neutral stability diagrams, the calculations can be performed at a
sufficiently high Reynolds number by specifying initial estimates of a r and UJ.
Once a solution is obtained at one Reynolds number, the calculations for other
Reynolds numbers can be obtained with the procedure of subsection 8.2.2. The
same procedure can also be used for lower Reynolds numbers provided da r/dR
is small. When this is not the case, a r is incremented by small specified values
and UJ and R are computed to satisfy Eq. (8.2.11). The program of Section 8.4
is written for the case of small da r/dR and needs to be changed when da r/dR
becomes large.
To demonstrate the use of STP, in this section we consider the Blasius
flow and calculate the eigenvalues a r and UJ at four x-locations. We take u e =
6
160 ft/sec, RL = 5 x 10 , L = 5 ft and initiate the calculations at x 0 = 0.54 ft
for ai = 0. This corresponds to a Reynolds number of R(= y/R^) = 735 which
is sufficiently high for da r/dR to be small, see Fig. 8.1a. Initial estimates of a r
and UJ follow from Fig. 8.1, and are 0.084 and 0.025 respectively, on the lower
branch of the neutral stability curve at R = 800.
Figure 8.5 shows the computed eigenvalues a r and UJ along the surface dis-
tance x for values of c^ equal to 0 and —0.004. The calculations for c^ = —0.004
are essentially the same as those for the neutral stability curve, ai = 0. The ini-
tial estimates of a r and UJ can be obtained from those corresponding to ai = 0
provided that Aai is small. If this is not the case, then it is best to divide the
increment in Aai to small values and perform the stability calculations for each
value of ai until the desired value of ai is reached.

8.5.2 Transition Prediction for Flat Plate Flow
n
To demonstrate the prediction of the onset of transition location with the e -
method, we first apply STP to a zero-pressure gradient flow which is identical