Simple orifices have an edge

Paul A. Baillio
Bird Precision
Waltham, Mass.

Changes in flow rate through a scuba oxygen analyzer can prove dangerous, even deadly to a diver. That's why a maker of the equipment traded an adjustable needle valve for a ruby precision orifice that meters flow at a fixed, predictable rate.

In many cases, orifice-flow repeatability is an essential design requirement because equipment that uses the devices may be only as precise as the orifices themselves. And repeatability, or lack of it, originates in the orifice manufacturing process.

Essentially, precision orifices flow a certain amount of gas or liquid depending on their hole diameter, hole-entrance geometry, and the pressure differential across them. A key metric in orifice design is the coefficient of discharge, C_d, because efficiency and hence flow rate directly depend on it.

In critical, choke-flow conditions where a vacuum is being pulled through the orifice, C_d to a large extent controls repeatability of the flow rate. When a gas is pushed through an orifice, gas compression controls flow rate, though at constant pressure C_d still determines repeatability. In many instrument applications, pressure is set to a known value, which requires a consistent orifice flow rate for calibration.

It turns out C_d is especially sensitive to hole-entrance geometry. For example, an orifice with a sharp-edged entrance has a C_d of about 0.60. Adding a chamfered edge to the entrance boosts C_d to about 0.9, while a radius ups it to about 0.98.

But a high C_d is not necessarily desirable because chamfers or radiuses introduce additional variables in production that can hurt repeatability. Making repeatable sharp-edged orifices is a challenge as well, especially in small hole sizes. Drills, for example, leave behind spiral marks and burrs. And drill wobble can make holes out-of-round or elliptical. Chamfering removes burrs but obviously changes discharge coefficient. Secondary procedures such as electropolishing help remove some but not all irregularities from drilling. For these reasons, drilled orifices are often individually flow-checked before they leave the factory, a labor-intensive and costly procedure.

Additional inaccuracies may creep in when orifices enter service. For example, an instrument that was initially calibrated to a certain flow rate may read low when an orifice edge begins to wear or become damaged in use. This is especially true in high-pressure applications that tend to quickly dull orifice entrance edges. For example, a water-jet cutter operating at about 40,000 psi would immediately dull a sharp-edged carbide orifice. Diamond orifices in the same application last about 1,500 hr though they tend to be expensive.

Synthetic ruby or sapphire orifices cost substantially less than those made of diamond and have about five times the abrasion resistance of carbide units. Such orifices last about 20 to 40 hr in the water-jet cutter application described above.

Single crystals of either ruby or sapphire grow from alumina powder melted at high temperature. Ruby has a red color because of the addition of chromium (0.05%) dopant. Clear sapphire contains no dopant. Both materials are about chemically inert and 9 on the Mohs hardness scale. For reference, diamond is 10 on the Mohs scale.

Such extreme hardness makes ruby and sapphire difficult to mechanically drill so Bird Precision uses a laser instead. Lasers are able to quickly pierce the material and leave a fairly clean and round hole. In fact, sharp-edged orifices sized 0.0016-in. diameter and smaller can be made net shape to tolerances of +0.0002, -0.0000 in.

Larger-diameter ruby orifices go through a three-step process of laser piercing, wire lapping, and surface lapping. Pierced blanks are strung thousands at a time on long, precision-sized tapered wires that then have slurry applied to them. The wires connect to large spools that slowly advance the taper in an oscillating motion to hone bores to proper size and finish. Bore surface finish is 2-µin. or better and diameter tolerance within a lot is less than 0.0001 in., while overall tolerances of 0.0002 in. are typical. The final finishing operation face laps both sides of an orifice to adjust throat length and impart the desired sharp edges. Faces also have a 2-µin. finish.

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Measuring orifice flow

Gas flow through an orifice or nozzle depends on the pressure differential across the device, to a certain point. Holding upstream pressure constant and lowering discharge pressure raises flow rate to a critical value, beyond which further drops in downstream pressure cause no further flow increase. Critical or choked flow is a function of the velocity of sound in the gas which, in turn. depends on its molecular weight, ratio of specific heats, and temperature. Typically, critical flow happens when upstream pressure is about two or more times downstream pressure.

Critical flow through an orifice can be calculated by:

where q = mass rate of flow of the gas; C_d = discharge coefficient, A = cross-sectional area of the nozzle throat, p = gas upstream static pressure, K = dimensional coefficient involving the gas constant, M = gas-molecular weight, and T = gas absolute-temperature upstream. U = a constant that is characteristic of the gas and equal to:

where k = ratio of specific heats (C_p/C_v) and s = (k + 1)/(k - 1).

For air, the orifice-flow equation becomes:

where q = flow rate (lb/sec), p = pressure (psia), T = absolute temperature (°R), and A = orifice bore area (in.²).

For example, a nozzle with a 0.005-in.-diameter throat has a critical flow of about 150 cc/min. Here, a 3-cc/min flow change corresponds to about a 0.0001-in. change in orifice diameter, or roughly 3%. Experiments on small orifices like those used in propane hand torches (0.006-in. bore) show a critical flow of about 132 standard cc/min, constant to ±1% for downstream pressures from 1/2 to 1/10th atmosphere. Theoretical flow based on area through such a nozzle is 216 cc/min so C_d = 132/216, or 0.61.