Mass flow measurement is the basis of many key elements throughout industry, including most recipe formulations, material balance determinations, and billing and custody transfer operations. With these being the most critical flow measurements in a processing plant, the reliability and accuracy of mass flow detection is very important.
A (Brief) History of Mass Flow Measurement
In the past, mass flow was often calculated from the outputs of a volumetric flow meter and a densitometer. Density changes were either directly measured or were calculated using the outputs of process temperature and pressure transmitters. Ultimately, because the relationship between process pressure or temperature and density are not always precisely known, these were not very accurate measurements.
One of the early designs of self-contained mass flow meters operated using angular momentum – it had a motor-driven impeller that imparted angular momentum (rotary motion) by accelerating the fluid to a constant angular velocity. The higher the density, the more angular momentum was required to obtain this angular velocity. Downstream of the driven impeller, a spring-held stationary turbine was exposed to this angular momentum. The resulting torque (spring torsion) was an indication of mass flow. However, with complex mechanical designs and high maintenance costs, these types of meters have been largely replaced by more robust and less maintenance-demanding designs.
One such design is the Coriolis mass flow meter, which is widely considered the most accurate type of mass flow meter and is widely used in industrial applications for accurate measurement. Coriolis flow meters feature instrumentation that function on the working principle of mass flow meter effect – a notable (and strange) phenomenon whereby a mass moving in a rotating system experiences a force acting perpendicular to the direction of motion and to the axis of rotation. The first industrial Coriolis patents date back to the 1950s and the first Coriolis mass flow meters were built in the 1970s.
The coriolis flow meter working principle
It was G.G. Coriolis, a French engineer, who first noted that all bodies moving on the surface of the Earth tend to drift sideways because of the eastward rotation of the planet. In the Northern Hemisphere, the deflection is to the right of the motion; in the Southern Hemisphere, the deflection is to the left. This drift plays a principal role in both the tidal activity of the oceans and the weather of the planet. Because a point on the equator traces out a larger circle per day than a point nearer the poles, a body traveling towards either pole will bear eastward because it retains its higher (eastward) rotational speed as it passes over the more slowly rotating surface of the Earth. This drift is defined as the Coriolis force.
When a fluid is flowing in a pipe and it is subjected to Coriolis acceleration through the mechanical introduction of apparent rotation into the pipe, the amount of deflecting force generated by the Coriolis inertial effect will be a function of the mass flow rate of the fluid. If a pipe is rotated around a point while liquid is flowing through it (toward or away from the center of rotation), that fluid will generate an inertial force (acting on the pipe) that will be at right angles to the direction of the flow.
With reference to Figure 1, a particle (dm) travels at a velocity (V) inside a tube (T). The tube is rotating about a fixed point (P), and the particle is at a distance of one radius (R) from the fixed point. The particle moves with angular velocity (w) under two components of acceleration, a centripetal acceleration directed toward P and a Coriolis acceleration acting at right angle to ar:
ar (centripetal) = w2r
at (Coriolis) = 2wv
In order to impart the Coriolis meter acceleration (at) to the fluid particle, a force of at (dm) has to be generated by the tube. The fluid particle reacts to this force with an equal and opposite Coriolis force:
Fc = at(dm) = 2wv(dm)
Then, if the process fluid has density (D) and is flowing at constant speed inside a rotating tube of cross-sectional area A, a segment of the tube of length X will experience a Coriolis force of magnitude:
Fc = 2wvDAx
Because the mass flowrate is dm = DvA, the Coriolis force Fc = 2w(dm)x and, finally:
Mass Flow = Fc / (2wx)
This is how measurement of the Coriolis force exerted by the flowing fluid on the rotating tube can provide an indication of mass flowrate. While rotating a tube is not necessarily practical standard operating procedure when building a commercial flow meter, oscillating or vibrating the tube – which is practical – can achieve the same effect.