26-05-2012, 04:27 PM
A NUMERICAL PROCEDURE FOR THE PARAMETRIC OPTIMIZATION OF THREE DIMENSIONAL SCRAMJET NOZZLES
A NUMERICAL PROCEDURE FOR THE PARAMETRIC.pdf (Size: 1.62 MB / Downloads: 73)
INTRODUCTION
This report describes a numerical procedure permitting the rapid determination
of the internal performance of a class of scramjet nozzle configurations. The
geometric complexity of these configurations rules out attempts to employ conventional
nozzle design procedures1, wherein properties at the nozzle exit
plane are specified and wave cancellation techniques are then employed to design
the wall surfaces. It is not feasible to stipulate exit conditions
a priori and wave cancellation techniques employing three dimensional characteristics
are beyond the current state of the art.
The approach developed is based on the construction of quasi two dimensional
simple wave networks, wherein lateral expansion effects are incorporated via
one dimensional approximations, as first suggested by Dr. Antonio Ferri 2. A
numerical procedure following this approach has been developed and results
obtained are highly comparable to those obtained employing a characteristic
procedure.
The numerical program developed permits the parametric variation of cowl length,
turning angles on the cowl and vehicle undersurface and lateral expansion and
is subject to fixed constraints such as the vehicle length and nozzle exit
height. The program requires uniform initial conditions at the burner exit
station and yields the location of all predominant wave zones, accounting for
lateral expansion effects. In addition, the program yields the detailed pressure
distribution on the cowl and vehicle undersurface and calculates the nozzle
thrust, lift and pitching moment.
NUMERICAL PROCEDURES
Consider a typical nozzle configuration as depicted in Figure (1), where the
lateral expansion distribution Z(x) may result from a combination of several
nozzles merging into a single nozzle. It is assumed in this preliminary
analysis that the jets after merging are bounded by sidewalls which extend
downstream of the merged section. The initial flow (at the burner exit) is
represented as an average uniform flow. The assessment of nonuniformities
at the entrance station may be obtained applying the numerical procedures described
in Reference (3).
For this configuration, the total amount of expansion from entrance conditions
is known (based on two dimensional considerations) at the grid points labeled
Vl, C1, A, B1 C, D, V3, C3, E2, E3, F and G and can be readily obtained at
points V2, C2, E1 and E4 . The numerical procedure predicts the location of
these grid points based on three dimensional flow considerations and effectively
distributes the waves on the cowl and vehicle undersurface to assess
the pressure distribution. It should be noted that a significant amount of
the logical procedures in the numerical program are employed to distinguish
the varying types of wave situations that may be encountered. In the configurations
shown the expansion waves emanating from the cowl (at C1) and the
vehicle (at V1) are both only partially captured on the undersurface and cowl
respectively. Tv denotes the portion of the cowl expansion wave Avc captured
on the vehicle undersurface while c denotes that portion of the vehicle expansion
wave Avv captured on the cowl. In other situations, these waves may
be totally captured or not captured at all, hence all these various situations
must be distinguishable and treated discretely.
DETERMINATION OF NOZZLE FLOW FIELDS
A nozzle calculation is performed subject to the following constraints:
1. The initial profile is uniform. For the frozen flow (constant
y) calculation this requires specification of the pressure
Pi. flow deflection angle ei, Mach number Mi, and specific
heat ratio y. For the equilibrium calculation one must
specify Pi ei, Mi, the temperature Ti and the fuel-air
equivalence ratio i'"
2. The initial turning at the vehicle undersurface (LAvv) and cowl
(AVc ) occur via sharp corners as depicted in Figure (1).
3. The wall segments downstream of these sharp corners remain
straight until the expansion waves emanating from the cowl
and vehicle undersurface reach the walls (points V3 and C3 of
Figure 1).