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CHAPTER 12
12.1 Define the following dimensionless variables:
where the subscript zero denotes reservoir conditions. The governing equations are Eqs. (12.5) –
(12.9). Replacing p by RT in Eq. (12.6) and e by cvT in Eq. (12.7), and noting that ao =
RTo
, the transformed equations in terms of the dimensionless variables are:
‘
n A
‘
u
‘
‘
t = x/(u +
T‘
)
Notes on setting up a computer solution:
1. Although the first grid point I = 1 will be at a finite area ratio, A/A* = 6, assume that
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3. All flowfield variables at the last grid point can be obtained by linear extrapolation
from the internal points, i.e., if there are 31 grid points, 31 = 230 – 29, etc.
4. The flowfield variables at the internal grid points, I = 2 to 30, are calculated from the
MacCormack predictor-corrector scheme as discussed in Section 12.1.
5. The initial conditions for , u and T at t = 0 are assumed to be linear variations with
x connecting the entrance and exit values (which are picked from Table I).
A FORTRAN IV computer program for this problem is listed below, followed by
selected tables and graphs of the results.
