Coriolis flowmeter design uses a Ushaped tube that redirects the fluid flow back to the center of rotation. The curved end of the flexible U-tube is forced to shake back and forth by an electromagnetic force coil (like the force coil on an audio speaker) while the tube ends anchor to a stationary manifold:
If ﬂuid inside the tube is stagnant (no ﬂow), the tube will simply vibrate back and forth with the applied force. However, if ﬂuid ﬂows through the tube, the moving ﬂuid molecules will experience acceleration as they travel from the anchored base to the tube’s rounded end, then experience deceleration as they travel back to the anchored base. This continual acceleration and subsequent deceleration of new mass generates a Coriolis force altering the tube’s motion.
This Coriolis force causes the U-tube assembly to twist. The tube portion carrying ﬂuid from the anchored base to the end tends to lag in motion because the ﬂuid molecules in that section of the tube are being accelerated to a greater lateral velocity. The tube portion carrying ﬂuid from the end back to the anchored base tends to lead in motion because those molecules are being decelerated back to zero lateral velocity. As mass ﬂow rate through the tube increases, so does the degree of twisting. By monitoring the severity of this twisting motion, we may infer the mass ﬂow rate of the ﬂuid passing through the tube:
In order to reduce the amount of vibration generated by a Coriolis ﬂowmeter, and more importantly to reduce the eﬀect any external vibrations may have on the ﬂowmeter, two identical Utubes are built next to each other and shaken in complementary fashion (always moving in opposite directions). Tube twist is measured as relative motion from one tube to the next, not as motion between the tube and the stationary housing of the ﬂowmeter. This (ideally) eliminates the eﬀect of any common-mode vibrations on the inferred ﬂow measurement:
Viewed from the end, the complimentary shaking and twisting of the tubes looks like this:
Great care is taken by the manufacturer to ensure the two tubes are as close to identical as possible: not only are their physical characteristics precisely matched, but the ﬂuid ﬂow is split very evenly between the tubes so their respective Coriolis forces should be identical in magnitude.
A photograph of a Rosemount (Micro-Motion) U-tube Coriolis ﬂowmeter demonstration unit shows the U-shaped tubes (one tube is directly above the other in this picture, so you cannot tell there are actually two U-tubes):
A closer inspection of this ﬂowmeter shows that there are actually two U-tubes, one positioned directly above the other, shaken in complementary directions by a common electromagnetic force coil:
The force coil works on the same principle as an audio speaker: AC electric current passed through a wire coil generates an oscillating magnetic ﬁeld, which acts against a permanent magnet’s ﬁeld to produce an oscillating force. In the case of an audio speaker, this force causes a lightweight cone to move, which then creates sound waves through the air. In the case of the Coriolis meter assembly, the force pushes and pulls between the two metal tubes, causing them to alternately separate and come together (shake in opposite directions).
Two magnetic displacement sensors monitor the relative motions of the tubes and transmit signals to an electronics module for digital processing. One of those sensor coils may be seen in the previous photograph. Both the force coil and the sensor coil are nothing more than permanent magnets surrounded by movable copper wire coils. The main diﬀerence between the force coil and the sensor coil is that the force coil is powered by an AC electric current to impart a vibratory force to the tubes, whereas the sensor coils are both unpowered so they can detect tube motion by generating AC voltage signals to be sensed by the electronics module. The force coil is shown in the left-hand photograph, while one of the two sensor coils appears in the right-hand photograph:
The two AC signals generated by the sensor coils provide data from which the electronics package may interpret ﬂuid density and mass ﬂow rate. The frequency of the two coils’ signals is inversely related to ﬂuid density, because a denser ﬂuid will cause the tubes to have greater mass and therefore vibrate at a lower frequency (Note 1). The phase shift of the two coils’ signals is directly related to mass ﬂow rate, because a greater mass ﬂow rate will cause the tubes to twist to a greater degree, causing the sensors’ signals to shift further out of phase with each other.
Note 1 : The force coil is powered by an electronic ampliﬁer circuit, which receives feedback from the sensor coils. Like any ampliﬁer circuit given positive (regenerative) feedback, it will begin to oscillate at a frequency determined by the feedback network. In this case, the feedback “network” consists of the force coil, tubes, and sensor coils. The tubes, having both resilience and mass, naturally possess their own resonant frequency. This mechanical resonance dominates the feedback characteristic of the ampliﬁer loop, causing the ampliﬁer circuit to oscillate at that same frequency.
Advances in sensor technology and signal processing have allowed the construction of Coriolis ﬂowmeters employing straighter tubes than the U-tube unit previously illustrated and photographed. Straighter tubes are advantageous for reasons of reduced plugging potential and the ability to easily drain all liquids out of the ﬂowmeter when needed. In straight-tube Coriolis ﬂowmeters, we still ﬁnd the same general design of a force coil ﬂanked by matching sensor coils measuring vibration frequency (for density measurement) and phase shift (for mass ﬂow measurement).