• Version
• 155 Downloads
• 1.66 MB File Size
• 1 File Count
• January 17, 2017 Create Date
• January 17, 2017 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - Reflection of Weak Shock Wave from a Boundary Layer Along a Flat Plate - II - Interaction of Oblique Shock Wave with a Laminar Boundary Layer Analyzed by Differential Equation Method

By analogy with the boundary-layer concept, the flow produced by
the interaction between a shock wave and a laminar boundary layer is
subdivided into a viscous layer and a potential field. The assumptions
that the compressibility effect in the inner layer is negligible and
that the original flow in the outer layer is uniform lead to simple
analytic solutions for the perturbed flow. The Joining conditions at
the interface between the layers determine an eigenvalue which gives
the rate of decay and the character of the disturbances both upstream
and downstream of the point of incidence. The final conclusions are
in agreement with experiments.

The present investigation is an independent study of the inter-
action of an oblique shock with a laminar boundary layer in a compress—
ible supersonic stream. In reference 1, where interaction of weak shock
waves with both laminar and turbulent boundary layers was treated, the
integrated momentum across the boundary layer was considered, rather
than the balance among various dynamic effects at each point. This
momentum-integral method is simple and, in certain respects, powerful
and capable of yielding useful qualitative information such as the
upstream pressure influence, pressure distribution, and the growth of
boundary-layer thickness due to the presence of a shock, but it fails
in regard to what actually happens inside the boundary layer. In the
present report a different approach has been adopted, with the inten-
tion of filling the gap left by the previous investigation. The pur—
pose will, on the whole, be complementary, so as to provide a physical
picture for the understanding of this complex phenomenon.

Contrary to reference 1, the differential-equation method is E
employed here. According to available experimental observation, when
an oblique shock is incident upon a laminar boundary layer the result— _
ant flow bears no resemblance to the flow predicted by potential theory.
For if the viscous flow is absent the flow ahead of the shock will not
be affected. Because of the presence of the boundary layer in which
there is a subsonic layer, however, a sudden decrease of pressure at a
point will immediately be transmitted forward by the inability of the
subsonic layer to support an excess pressure rise. When the pressure
is transmitted, the flow in the boundary layer will be retarded and the
streamlines distorted. Since the outer field is supersonic, this change
occurring in the viscous layer will affect the whole potential field.
This is actually observed. For stronger shocks, the flow in the bound-
ary layer generally will separate and will have backflow under the
influence of an adverse pressure gradient.