Coriolis mass flow rate meters for low flows


Mehendale, Aditya (2008) Coriolis mass flow rate meters for low flows. thesis.

open access
Abstract:The accurate and quick measurement of small mass flow rates (~10 mg/s) of fluids is considered an "enabling technology" in semiconductor, fine-chemical, and food & drugs industries. Flowmeters based on the Coriolis effect offer the most direct sensing of the mass flow rate, and for this reason do not need complicated translation or linearization tables to compensate for other physical parameters (e.g. density, state, temperature, heat capacity, viscosity, etc.) of the medium that they measure. This also makes Coriolis meters versatile – the same instrument can, without need for factory calibration, measure diverse fluid media – liquids as well as gases. Additionally, Coriolis meters have a quick response, and can principally afford an all-metal-no-sliding-parts fluid interface. A Coriolis force is a pseudo-force that is generated when a mass is forced to travel along a straight path in a rotating system. This is apparent in a hurricane on the earth (a rotating system): when air flows towards a low-pressure region from surrounding areas, instead of following a straight path, it “swirls” (in a {towards + sideways} motion). The sideways motion component of the swirl may be attributed to the Coriolis (pseudo)force. To harness this force for the purpose of measurement, a rotating tube may be used. The measurand (mass flow rate) is forced through this tube. The Coriolis force will then be observed as a sideways force (counteracting the swirl) acting upon this tube in presence of mass-flows. The Coriolis mass flow meter tube may thus be viewed as an active measurement – a "modulator" where the output (Coriolis force) is proportional to the product of the excitation (angular velocity of the tube) and the measurand (mass flow rate). From a constructional viewpoint, the Coriolis force in a Coriolis meter is generated in an oscillating (rather than a continuously rotating) meter-tube that carries the measurand fluid. In such a system (typically oscillating at a chosen eigenfrequency of the tube-construction), besides the Coriolis force, there are also inertial, dissipative and spring-forces that act upon the meter tube. As the instrument is scaled down, these other forces become significantly
larger than the generated Coriolis force. Several "tricks" can be implemented to isolate these constructional forces from the Coriolis force, based on orthogonality – in the time domain, in eigenmodes and in terms of position (unobservable & uncontrollable modes, symmetry, etc.). Being an active measurement, the design of Coriolis flowmeters involves multidisciplinary elements - fluid dynamics, fine-mechanical construction principles, mechanical design of the oscillating tube and surroundings, sensor and actuator design, electronics for driving, sensing and processing and software for data manipulation & control. This nature lends itself well to a mechatronic system-design approach. Such an approach, combined with a "V-model" system development cycle, aids in the realization of a Coriolis meter for low flows. Novel concepts and proven design principles are assessed and consciously chosen for
implementation for this “active measurement”. These include:
- shape and form of the meter-tube
- a statically determined affixation of the tube
- contactless pure-torque actuator for exciting the tube
- contactless position-sensing for observing the (effect of) Coriolis force
- strategic positioning of the sensor & actuator to minimize actuator crosstalk and to
maximize the position sensor ratio-gain
- ratiometric measurement of the (effect of) the Coriolis force to identify the measurand
(i.e. the mass flow rate)
- multi-sensor pickoff and processing based solely on time measurement – this is
tolerant to component gain mismatch and any drift thereof
- measurement of temperature and correction for its effect of tube-stiffness

The combined effect of these and other choices is the realization of a fully working prototype.
Such prototype devices are presented as a test case in this thesis to assess the effectiveness
of these choices.
A “V-model” system-development cycle involves the critical definition of requirements at the
beginning and a detailed evaluation at the end to verify that these are met. To reduce
ambiguity of intent, several test methods are defined right at the beginning with this model in
mind. These end-tests complete the “cycle” – a loop that began with the concepts and with
the definition of requirements. However, a V-model also entails shorter iterative cycles that
help refine concepts and components during the intermediate design phases. Such “inner
loops” are also presented to illustrate design at subsystem and component levels.
A Coriolis flowmeter prototype with an all-steel fluid-interface is demonstrated, that has a
specified full-scale (“FS”) mass flow rate of 200 g/h (~55 mg/s) of water. This instrument has
a long-term zero-stability better than 0.1% FS and sensitivity stability better than 0.1%,
density independence of sensitivity (within 0.2% for liquids), negligible temperature effect on
drift & sensitivity, and a 98% settling time of less than 0.1 seconds. For higher and/or
negative pressure drops, these instruments have been seen to operate from –50×FS to
+50×FS (i.e. from –10 kg/h to +10 kg/h) without performance degradation – particularly
important in order to tolerate flow-pulsations in dosing applications.
Finally, the results of the present work are discussed, and recommendations are made for
possible future research that would add to it. Two important recommendations are made - about the possibility to seek, by means of an automated optimization algorithm, an improved tube shape for sensing the flow, and about constructional improvements to make the measuring instrument more robust against external vibrations.
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