Curvature Radius Of Surface Research Articles

Surface and Volume Sound from Boundary Layers

It is made plausible for turbulent boundary layers that surface, dipole sound is in general very much less than volume, quadrupole sound. This is so for two reasons. Firstly, the relative volume sound is increased by several orders of magnitude because of shear-flow enhancement within the boundary layer. Secondly, through the use of an image argument similar to that used in the discussion of flat layers, it is indicated that the dipole sound is reduced by a factor of (L/R)2, where L is the boundary layer thickness and R is the surface radius of curvature. A discussion of irregular, surface bumps shows that such imperfections may be the source of significantly large dipole sound. A calculation is given of low-Mach-number surface and volume sound from a rotating cylinder.

Effect of Surface Curvature on Boundary-Layer Noise

It has been previously remarked that inviscid turbulent boundary layers over a flat plate produce no dipole sound. The plane acts merely to reflect the volume-generated quadrupole sound. An image argument is used to examine the effect of a slight surface curvature on the dipole-generated sound. It is found that, if R is a surface radius of curvature and L the thickness of the boundary layer, then the amplitude of the farfield dipole sound is reduced by a factor of L/R. Thus, if L/R<(Mach number), the dipole sound can be neglected in order of magnitude estimates. The surface merely reflects and diffracts the volume-produced sound. The result of this analysis is that, for many practical situations involving boundary layers, the sound intensity will be proportional to the 8th power of the Mach number. The amount of dipole sound produced by bumps on the surface is also discussed.

An optical device for the measurement of the radius of curvature

The present paper describes the construction and principle of a new and original optical instrument based on the optical section principle and designed for the control of objects whose surface radius of curvature is small.