A Discussion of Two-Dimensional Turbulent Base Flows - aerade

3.2. The Nature of the Flow.
The nature of the supersonic base flow is now reasonably well understood and there is little dispute
among the theoreticians as to the gross features of the flow model which forms the basis of analytical
treatments of the problem. Indeed, schematic diagrams similar to Fig. 9 are to be found in scores of pub-
lished papers.
The boundary layer which has developed on the surface of the body approaches the trailing edge
and separates there to form a free-mixing layer. Since the base pressure is usually lower than the pressure
on the afterbody an expansion fan springs from the corner and the shear layer is deflected away from
the external flow. Some distance downstream of the base the free shear layer either reattaches to a solid
wall or coalesces with a second shear layer and continues downstream. The reattachment of confluence
occurs in a region of abrupt pressure rise, in contrast to the region closer to the base in which the pressure
gradients are small. In the case of the flow past a step the position of the reattachment line can easily be
found by the use of a surface oil technique or by some other means which senses the surface shear (the
reattachment point is a point of zero surface shear). The reattachment point is found to lie part of the
way up the abrupt pressure rise. Presumably the equivalent is true of the flow in the wake of an isolated
aerofoil section.
The mixing layer induces a recirculating flow immediately downstream of the base but (unless there is
bleed into the cavity) the mass flux of the recirculating flow must be conserved, and the theoretical flow
models posit the existence of a mean dividing streamline joining the separation point of the point of con-
fluence (or reattachment point). If there is bleed the streamline springing from the separation point is
taken to be distinct from that which passes through the point of confluence and the mass flux between
them to be equal to the bleed mass flux.
, These considerations concerning the streamline pattern in the separated region have a meaning only
in the context of the assumption that the flow is steady (although turbulent flow is accommodated).
That the flow in the wake is steady is an assumption and must be weighed against the evidence that
exists pointing to periodic effects (in the downstream part of the wake) even at high supersonic speeds a2.
Nevertheless the assumption is a sensible one and there has been no suggestion that the periodic effects
play any significant part in the determination of the pressure field as, of course, they do at subsonic speeds.
For the case of the flow past a step there is even more likelihood that a steady-flow model will be physically
realistic, and the fact that a well-defined reattachment line can be observed offers strong support to this
view (see, for example, Ref. 30).
3.3. General Features of the Theories.
A common feature of the theoretical methods for predicting base pressure is the assumption that the
base pressure.depends on the pressure recovery which can be sustained by the wake, or by the reattaching
boundary layer. The final recovery pressure far downstream is assumed known; frequently it is either
equal to, or can be approximated by, free-stream static pressure. The base pressure is then found by
subtraction from this known pressure the computed pressure rise occurring between the base and infinity
downstream.
The pressure recovery downstream of the base is estimated by an analysis of the development of the
wake, or the reattaching boundary layer, and its interaction with the external supersonic stream. In their
method of analysis the theories can be divided into two groups : those which depend on the dissection of
the base flow into a number of discrete parts and those which employ integral techniques. The two groups
will now be discussed in turn.
3.4. The 'analytic" approach.
This class of theories owes its inspiration to the original thoughts of Chapman a4, Korst a5 and Kirk a 6
but the degree of sophistication tias increased considerably since the early days. The theories assume that
the flow can be dissected into a niamber of parts which can be analysed separately:
(a) The flow approaching the separation point.
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