Coriolis Flow Meter Technology
What Is A Coriolis Meter?
The Coriolis Effect is a natural phenomenon that causes objects to appear to “curve” as they move across the surface of the Earth. Coriolis flow meters, also called Coriolis meters, are mass flow meters that make use of the Coriolis Effect to directly measure the mass flow rate of a process.
Compared to other flow meter technologies, Coriolis flow meters are relatively new, not finding widespread use in industrial applications until the 1980s. Modern Coriolis meters are available in a number of different designs, with most configurations consisting of one or two essentially U-shaped flow tubes with inlets on one side and outlets on the other. These tubes are enclosed in a sensor housing that is connected to an electronic unit.
More recent variations of the “standard” Coriolis meter design include double-looped single tubes and straight-through tubes intended for use with dirty and/or abrasive liquids that could clog a U-shaped tube.
How Do Coriolis Flow Meters Work?
SmartMeasurement’s Coriolis meters artificially introduce positive and negative Coriolis acceleration into the metering process. As illustrated in the diagram above, the fluid media is split and redirected through two curved tubes. An oscillating excitation force is applied to the tubes via miniature velocity transducers or electric coils, causing vibration that is measured by magnetic sensors. Coriolis flow meters vibrate at a very small amplitude, usually less than 0.1” (2.5 mm). This frequency is near the natural frequency of the device, which is usually roughly 80 Hz.
When no flow is present, the tubes vibrate and the sine wave outputs of each hall-effect transducer are in phase. When flow is initiated, the fluid flowing through the tubes induces a rotation or twist to the tube due to acceleration of the Coriolis Effect, which operates in opposite directions on either side of the applied force.
For example, when the flow meter tube is moving upward during the first half of a cycle, the fluid flowing into the meter resists being forced up and pushes down on the tube. Conversely, liquid flowing out of the meter resists having its vertical motion decreased by pushing up on the tube. This action causes the flow meter tube to twist. When moving downward during the second half of the vibration cycle, the tube twists in the opposite direction. This twist results in a phase difference (time lag) between the inlet and outlet sides, and this phase difference is directly affected by the mass passing through the tube.
See below for additional information on how these liquid flow meters work.
Benefits of Using A Coriolis Meter
One key benefit of Coriolis flow meters is their ability to perform multiple measurements. In addition to measuring mass flow directly, Coriolis meters also measure the density of the process by monitoring the duration of the tube’s vibration and characterizing it as a density. Advanced digital signal processors enable Coriolis meter transmitters to calculate the concentrations of two component mixtures and net volumes.
Another advantage of Coriolis meters is their ability to measure the mass flow rate directly, which eliminates the need to compensate for changing temperature, viscosity, and pressure conditions.
Additional benefits include:
- Greater accuracy than most other flow meter technologies
- Can be used in a wide range of liquid flow conditions
- Capable of measuring both hot (e.g. molten sulfur) and cold (e.g. liquid nitrogen) fluid flow
- Low pressure drop
- Suitable for bi-directional flow
Common specifications for commercially-available Coriolis flow meters are as follows:
Suppose that fluid is flowing into the Coriolis meter’s U-shaped tube at velocity V and the tube is vibrating at angular velocity Ω. Consider a small section of the fluid that is on the inlet side, away from the point of flexure at distance r.
Operating Principles of Coriolis Meters
Note that the amplitudes of vibration and twist are extremely small compared to the size of the U-shaped tube. The above graphics are intentionally exaggerated for illustrative purposes.
The Coriolis Effect on the small fluid section ∂ m is
During the cycle, the tube applies an upward resisting force to the fluid, or the fluid pushes the tube down. On the outlet side, the Coriolis force acts in the opposite direction.
To simplify the problem, we assume that the tube has a perfect “U” shape, with a cross section area of A. The length and width are l and d, respectively. The Coriolis Effect, acting in opposite directions on the inlet and outlet sides, results in a twisting moment, or Tc.
A K factor can be introduced to compensate for the more generalized “U” shape, where Qm = ρAV is the mass flow rate.
The equation governing this twisting is
Where Iu is the inertia of the U-shaped tube, Cu is the damping coefficient, Ku is the stiffness, θ is the twist angle, and t is time.
Knowing that Coriolis flow meters vibrate the U-shaped to generate rotation, the real angular velocity Ω is a function of vibrating frequency ω.
Assuming that the damping term Cu is negligible, the equation of twisting becomes
The particular solution (steady-state solution) of the twist angle is
Furthermore, the velocity of the turning corners of the U-shaped tube is Ωl, and the displacement between these two corners is θ d/2. Therefore, the time lag Ƭ between the two corners is
By measuring the time lag Ƭ, the mass flow rate can be obtained
In vibration analysis, it is customary to use the natural frequency as a basis and normalize frequency terms against it. The natural frequency of the U-shaped tube system is
Note that Iu includes the mass of the fluid in the tube.
The mass flow rate then becomes