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.

Measurement and Prediction of Discharge Coefficients in Highly Compressible Pulsating Flows to Improve EGR Flow Estimation and Modeling of Engine Flows

“…For the current work, the ratio of upstream to downstream density for the engine data ranged between 1.08 and 1.91. On the other hand, many researchers have investigated highly compressible (critical) but non-pulsating flows (Grace and Lapple, 1951;Jackson, 1963;Kastner et al, 1964;Deckker and Chang, 1965;Rohde et al, 1969;Brain and Reid, 1975;Ward-Smith, 1979).…”

Launch Vehicle Cavity Venting: Modeling Concepts & Validatio

“…The next natural question that comes to mind is whether sonic conditions in the vent can produce a similar effect, since after all one would expect the sonic line to eliminate the downstream pressure fields ability to send acoustic signals to the upstream flow field and alter its expansion. The data in the figure below from the experimental data of Deckker and Chang's, 3 Calligan and Bowden's, 2 and this author's analytical steady RANS CFD simulations show that as the pressure ratio across the vent is increased past sonic or choke flow conditions, that the length to diameter effects are generally eliminated. One note of caution, as the length to diameter of the orifice becomes very large (>> 1), significant venting efficiency losses are realized through out the entire pressure ratio regime due to the momentum losses associated with boundary layer growth.…”

Discharge Coefficients of Ports with Stepped Inlets

“…A water flow rig has been used for most measurements in which a single row of multiple ports is fed by an annular crossflow and the jets issue into a crossflow, as in a combustor, this also allows for a bleed flow stream, where the port only receives a fraction of the approaching cross flow. Flow through the ports are at supercritical jet Reynolds numbers above which it is found that there is little variation in C d , quoted in various works to be between 1.8 × 10 4 and 3.5 × 10 4 [13,14]. Reynolds number variation in C d has been tested in this work in the range 5 × 10 4 to 2 × 10 5 , which has agreed with these previous works and all results presented are for jet Reynolds numbers above 5 × 10 4 .…”