Paper 7: An Investigation of Steady Compressible Flow through Thick Orifices

Abstract

A thick orifice of a given diameter is one in which the length-diameter ratio exceeds that of a British Standard sharp-edge orifice of the same diameter. Thick orifices are important technically but little systematic work appears to have been performed on them. Sharp-edge orifices are treated as limiting cases of thick orifices. This paper describes a carefully controlled investigation into the behaviour of the steady flow of air through thirty-eight orifices ranging in diameter from 3/32 to 1/2 in and of length-diameter ratios, l/d, of 2.0, 1.0, and 0.5 and of sharp-edge orifices. These orifices have been calibrated against a range of sharp-edge orifices according to the British Standards code. The maximum possible instrument error over the experimental range (maximum pressure 150 lb/in2 absolute, maximum temperature 940°R) is estimated to be less than 0.1 per cent. The greater part of the overall error is attributed to the use of the code and may be as high as 1.6 per cent in some cases. About seven hundred experimental measurements have been made during the course of this investigation from which new relationships between the geometrical and physical parameters have been derived. The existence of a hysteresis phenomenon in a compressible flow through an orifice has also been measured for the first time. The main conclusions are: (1) When the ratio of the orifice diameter, d, to that of the cylinder cross-section is small the air expands from a state of virtual stagnation at a distance of one orifice-diameter from the plane of entry to the orifice. The ambient pressure is attained at the plane of exit only in the case of orifices for which l/d ≥ 2. (2) In the range of Reynolds numbers between 104 and 105 the dimensionless mass flow, G = m( T0)1/2 /d2 po, and the coefficient of discharge, Cd, are independent of the Reynolds number. (3) For a given l/d ratio G, or Cd, is a function only of the overall pressure ratio. (4) The l/d ratio is an important parameter in thick orifices because of the possibility of jet attachment. The observed behaviour of thick orifices may be explained on this basis. (5) For l/d = 0.5 there is a clearly delineated hysteresis in the flow near the threshold of choking, the lower branch corresponding roughly to the behaviour of a sharp-edge orifice and the upper branch attaining a value of Cd of nearly 0.9 for the choked regime. (6) Within the limits of accuracy of measurement, eccentric location of the orifice has no effect upon either G or Cd. Finally, the experimental results are compared with published theoretical and experimental work on compressible steady flow through orifices.