In the past, mass flow was often calculated from the outputs of a volumetric flow meter and a densitometer. Density was either directly measured (Figure 5-1A), or was calculated using the outputs of process temperature and pressure transmitters. These measurements were not very accurate because the relationship between process pressure or temperature and density are not always precisely known--each sensor adds its own separate error to the overall measurement error, and the speed of response of such calculations is usually not sufficient to detect step changes in flow.
One of the early designs of self-contained mass flow meters operated using angular momentum (Figure 5-1B). 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.
These meters all had moving parts and complex mechanical designs. First developed for the measurement of aircraft fuel, some are still in use. However, because of their complex nature and high maintenance costs, they are gradually being replaced by more robust and less maintenance-demanding designs.
Mass flow also can be measured by batch weighing or by combining an accurate level sensor with a densitometer. Another method is to mount two d/p transmitters on the lower part of an atmospheric tank at different elevations. In this case, the output of the top d/p cell will vary with the level in the tank, while the lower one will measure the hydrostatic head over a fixed elevational distance. This pressure differential yields the density of the material in the tank. Such systems have been used to measure the total mass flow of slurries.
The effect of the Coriolis force on the vibrating tube is small. Full-scale flow might cause a deflection of only 0.001 inch. To obtain a flow rangeability of 100:1, sensors must be able to detect deflections to an accuracy of 0.000001 inch in industrial environments where the process pressure, temperature, and fluid density are all changing, and where pipe vibration interferes with measurement.
The elasticity of metal tubes changes with temperature; they become more elastic as they get warmer. To eliminate the corresponding measurement error, the tube temperature is continuously measured by an RTD element and is used to continuously compensate for variations in tube elasticity.
Coriolis mass flow meters usually are calibrated on water, because the constants are valid for all other liquids. Calibration for density is usually done by filling the tubes with two or more (stagnant) calibration fluids of known densities.
Accuracy & Rangeability
Coriolis meters provide 0.1-2% of rate inaccuracy over a mass flow range of up to 100:1. In general, curved tube designs provide wider rangeability (100:1 to 200:1), while straight-tube meters are limited to 30:1 to 50:1 and their accuracy is lower. Overall meter error is the sum of base inaccuracy and zero-shift error, the error attributable to the irregular output signal generated at zero flow conditions. Zero-shift error becomes the dominant portion of total error at the lower end of the flow range, where the error is between 1% and 2% of rate. Some manufacturers state the overall accuracy as a percentage of rate for the upper portion of the flow range and as a percentage of span for the lower portion, while others state it as a percentage of rate plus a zero-shift error. There is a fair amount of "specmanship," and one must read sales literature carefully when comparing different devices.
When used for density measurement, the typical error range of a Coriolis measurement is 0.002-0.0005 g/cc.
Errors are caused by air or gas pockets in the process fluid. In the case of homogeneously dispersed small bubbles, more power is required to vibrate the tubes, whereas, if the gas phase separates from the liquid, a damping effect on tube vibration (and, consequently, error) develops. Small voids also cause noise because of the sloshing of the process liquid in the tubes. Larger voids will raise the energy required to vibrate the tubes to excessive levels and may cause complete failure. Because the flowtube is subjected to axial, bending, and torsional forces during meter operation, if process or ambient temperature and pressure fluctuations alter these forces, performance may be affected and re-zeroing of the meter may be required.
Variations in the density of the process fluid can affect the frequency transfer function of mechanical systems, necessitating the re-zeroing of older designs to protect them from degraded performance. Because of their tube configurations, newer designs are unaffected by density changes over wide ranges of specific gravity variations.
Sizing & Pressure Drop
Because of the wide rangeability of Coriolis flow meters (30:1 to as high as 200:1), the same flow can be measured by two or three different sized flow tubes. By using the smallest possible meter, one will lower the initial cost and reduce coating build-up, but will increase erosion/corrosion rates and head loss, increasing pumping and operating costs.
Downsizing (using a meter that is smaller than the pipe) is acceptable when the pipe is oversized, and the process fluid is clean with a low viscosity. On corrosive, viscous, or abrasive slurry services, downsizing is not recommended. A list of acceptable flow tube sizes and corresponding pressure drops, inaccuracies, and flow velocities can be obtained from software provided by the manufacturer.
Different Coriolis meters incur different pressure drops, but in general, they require more than traditional volumetric meters, which usually operate at less than 10 psid. (The yearly electricity cost of pumping 1 GPM across a differential of 10 psid is about $5 U.S.). This higher head loss is due to the reduced tubing diameter and the circuitous path of flow. Besides pumping costs, head loss can be of concern if the meter is installed in a low-pressure system, or if there is a potential for cavitation or flashing, or if the fluid viscosity is very high.
The viscosity of non-Newtonian fluids is a function of their flowing velocity. Dilettante fluids, for example, increase their apparent viscosity (resistance to flow) as their velocity is increased. This apparent viscosity can be drastically higher than their viscosity when stagnant. In order to provide suppliers with data on the flowing viscosity in a particular pipe, head loss per foot of pipe (used in pump sizing calculations) can be used as an approximation.