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National Advisory Committee for Aeronautics, Technical Notes - Method for Evaluating from Shadow or Schelieren Photographs the Pressure Drag in Two Dimensional or Axially Symmetrical Flow Phenomena with Detached Shock

A method has been developed for evaluating from shadow or schlieren
photographs the pressure drag of axially symmetrical bodies at zero
angle of attack or of two—dimensional bodies producing detached shock.
The method consists in the determination of the flow properties along
a characteristic line and the application of the momentum.theorem to a
stream tube around the body. The method can be applied to the determina—
tion of external drag of supersonic inlets with subsonic flow at the
entrance of the inlet.

The system of characteristics permits the pressure drag and the
shape of the shock for axially symmetrical and two—dimensional flow
phenomena having everywhere supersonic speed to be determined directly
from the boundary conditions. In this case if viscous effects are
neglected, the value of the pressure drag can be determined analytically,
and no experimental measurement is necessary. The determination of the
shape of the shock can be useful in making a comparison between experi—
mental and theoretical results and permits an evaluation of the displace—
ment thickness of the wake and of the boundary layer along the body.

The characteristic system does not permit, however, direct determination
of the pressure drag when the shock is detached from the body, because it
cannot be applied to the subsonic part of the flow.

The determination of the pressure drag of bodies producing
detached shocks is important in many problems; for example, the bodies
of revolution used in practical applications often have round noses and,
in supersonic inlets, conditions exist in which the flow at the entrance
of the inlet is subsonic. The experimental measurement of the pressure
drag for these cases usually requires complicated experimental equipment;
therefore, the determination of drag from shadow or schlieren photographs
of the phenomena can be very useful for practical applications.

A method is presented herein that permits determination of the pressure
drag directly from shadow or schlieren photographs. This system can be
especially useful in all cases in which the experimental technique uses
the principle of moving models (shooting ranges, whirling arms, etc.)
and in emeriments of supersonic inlets in which also the internal flow
produces forces and in which it is, therefore, difficult to measure the
external drag independently of the internal drag. [the method gives the
value of the pressure drag due to the subsonic and supersonic regions of
the flow and permits also the determination of pressure and velocity
distribution of the supersonic region, from which the shape and thickness
of the wake can be obtained.