Air flow separation at high speed

Abstract

The resistance coefficient of a body moving in a fluid depends on Reynolds Number R, Mach Number M and the parameter gL U 2 , which is customarily neglected in view of small weight of the air. Here L denotes a characteristic length; U denotes the body's speed of translation. The author points that dimensional deduction of this parameter does not limit it to the acceleration of gravity, and that the resistance coefficient is affected by the general acceleration to which the air is subjected. Evaluation of the acceleration of the air flowing about spheres puts this parameter in the form L R , where the characteristic length L is interpreted as the mean free molecular path. Large and small spheres were found to have widely different values of the pressure coefficient Δp q for the same Reynolds Number or Mach Number. Here Δp denotes the difference in pressure between front stagnation point and the rear portion of the sphere, and q denotes the dynamic pressure. The plot of Δp q against the parameter L R removes this confusion. The low values of Δp q are found to be associated with L R below a certain critical value, and high values of Δp q with L R above the critical value, which apparently indicates the condition under which the flow separation takes place. Attention is called to the effect of air pressure on the separation as shown by the parameter L R , and its possible bearing on the drag in high altitude flying.