Bulk Modulus Cell

Harwood Engineering Company, Inc.

Bulk Modulus Cell

by Donald Newhall and Leonard Abbot

Donald H. Newhall has B.S.E., 1934, and M.S.E., University of Michigan, 1935. His experience includes Capt. Ordnance department, United States Army, The Foxboro Company, and Harwood Engineering Company (1948 to date). He is a member ASME, ISA, Fellow British Inst. Mech. Eng., Chartered Eng. UK. He established the Harwood Engineering Company, incorporated in 1950. Harwood, of which Mr. Newhall is president, manufactures high-pressure apparatus. Pressures of nearly 1,500,000 PSI (10¹⁰ N/m²) have been developed at Harwood on a laboratory scale.

Leonard H. Abbot has B.S., Worcester Polytechnic Institute; graduate course, Harvard University. His experience includes work at Astrophysical Observatory, Smithsonian Institution; Standardizing and General Engineering Laboratories, General Electric Company; Physics Laboratory (assistant to P.W. Bridgman) Harvard University; physicist for Harwood Engineering Company. Member ASME.

The Bulk Modulus Cell (Figure 1) consists essentially of a hollow cylindrical steel probe, closed at its inner end, introduced into a thick-walled steel cylinder (the cell body) which is connected hydraulically to the high-pressure system. The probe is held in place by a threaded retainer which also serves to compress a conventional packing between shoulders on the cell body and on the probe. A stem projects from the inner end, one inch beyond the outer end of the probe proper. A clearance of 1/64" (4 mm) between the stem and the wall of the probe assures freedom of motion.

When the active part of the probe (from the shoulder inward) is subjected to the hydrostatic pressure of the system, it contracts isotropically. Its contraction is measured by the motion of the stem (unrestrained except at its two ends) with respect to the outer end of the probe.

To a first approximation, the active part of the probe can be treated as an isotropic solid. The longitudinal direction is amplified by virtue of the hole containing the stem. The linear motion of the stem is large enough to be measured in any of several ways — pneumatic transmitter (1) and electrical (strain gage) (Figure 2), for instance.

Pneumatic Transmitter

A pneumatic transmitter (developed by the Foxboro Company) is used in conjunction with a Foxboro pneumatic receiver (Figure 3).

The beam of the transmitter is a cantilever held in equilibrium by the downward-acting restraint of the block flexure (made of spring steel), and by the upward force exerted by the stem, the bellows, and the air jet from the relay pilot nozzle. Since the pressure within the air jet is but a fraction of that within the bellows, and the cross-sectional area of the bellows is a hundred or more times larger, the effect of the jet on the beam is negligible. The transmitter operates on an air supply at 20 PSIG (140 kP) which is modulated to deliver 3-15 PSI (21-105 kP).

As pressure is applied to the probe, it contracts, and the stem moves upward, causing the beam to pivot at the block flexure and compress the bellows. The deflection of the beam also restricts the air space above the relay pilot nozzle; this raises the air pressure within the bellows until equilibrium is established again. The change in the bellows pressure is proportional to the system pressure felt by the probe. Calibration is accomplished by loosening the nuts and moving the bellows along the beam, increasing the moment arm in order to reduce the transmitted air pressure.

The receivers are standard instruments, widely used to measure flow, temperature, liquid level, pressure and humidity.

Electrical Transmitter

The stem operates on a cantilever beam in the electrical transmitter (Figure 2). Strain gages are bonded to the upper and lower surfaces near the inner end of the reduced section. As the stem moves upward it deflects the end of the beam. The gages are placed nearly at the point of maximum strain. They are connected to constitute a full bridge, temperature compensated, and the proportions of the beam and the constants of the gages are selected so as to give an output of 1 millivolt/volt input. A wide range of electric or electronic instrumentation is currently available for this output, including digital, indicating, recording or controlling instruments.

Applications

The bulk-modulus cell finds its most important applications where comparatively rapid pressure changes or viscous media are unfavorable to manganin cells or to the small bores of Bourdon gages, as in the cases of slurries or other viscous process materials which may tend to cake or solidify, and for pressures in the ranges to 200,000 psi (1400 MP), where moderate accuracy and rather fast instrument response are desired.

The pneumatic transmitter and strain gage are both remote reading. However, in the former, it is advantageous to make the transmission line short. The bulk-modulus cell is superior to the conventional Bourdon and (to a lesser degree) to the strain gage and long helical in the matter of hazard. The probe, being subjected to hydrostatic compression only, is not subject at rated pressure to fatigue which would result from repeated excessive strains, and the transmitting air pressure is completely innocuous. The cell body has no limitations on its proportions imposed by the functioning of the probe, and hence can be built to maximum strength and fatigue resistance. This is in marked contrast to those operating elements whose signal depends on internal pressure and where large strain is required for the signal: this is necessarily achieved at the expense of strength of the gage element, and hence fatigue becomes a serious consideration.

There are distinct advantages, also, in pneumatic transmission. In an explosive atmosphere, it presents no danger sparks, and the signal is not subject to the disturbing influence of stray magnetic fields. The manganin gage will be the subject of a detailed feature article in the next issue of M&D.

Reprinted from Measurements & Data, March-April 1970...

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