Structure of volumetric flowmeter
Published on:2014-12-25 9:15:08 Hits:

Weizhong Lei Department of Mechanics, Peking University, Beijing 100871


Mass flow meter is now favored by the users, is because it can directly measure the mass flow rate of the fluid in the pipeline, rather than as in the past, were used to measure the volumetric flow rate and density of the fluid to be measured, then calculable. In addition, its high accuracy and stability, turndown ratio is relatively large, but its high cost performance. For manufacturers, this is a lucrative product, so this product development, trial production and marketing, has been positive.


Coriolis mass flowmeter principle, the essence is the use of an elastic body resonance characteristics: teammate fluid flow and vibration-free fluid flow (in the vicinity of the resonance region) metal pipe elements, measured dynamic response characteristics, obtained this resonance system phase (time difference) between the relationship between the mass flow rate. The dynamic response characteristics of the metal pipe element fluid flow resonances, and no difference in the dynamic response characteristics of fluid flow between the metal pipe, is due to Coriolis effects. The so-called Coriolis effect, means that when the particle at a rotating frame of reference for the relative motion, centrifugal force will produce a different from the usual inertial force acting on the particle. Its size and direction available 2mvXw (formula) to represent. This is the Coriolis French scientists first discovered. Flowmeter elastic element constituted by the above principle, also known as the Coriolis mass flowmeter. So to the theoretical analysis, the development of a mass flow meter, which is essentially a difficulty to calculate the dynamic elastic metal pipe resonance characteristics. This is mainly rely on the theory of solid mechanics elastomer for vibration analysis to determine. Existing literature A flexible tube is dynamic response analysis.

1. Dynamic response analysis of a flexible tube

Analysis of (i) a flexible curved tube

Hemp and Sultan (Cranfield Institute of Technology, England) with Euler beam theory, the dynamic response of flexible curved pipe resonance been analyzed, and combined U- shaped tube made specific calculations.

a. Equation (Oscillating tube of cruved part)


For different geometries, the above-described general formula and the boundary conditions can also be further simplified. For example, on the straight portion of the resilient metal tube, you can make a tends to infinity.

b. the boundary conditions


On the endpoint, there is a connecting point between pipe sections of different shapes, have

c. the numerical solution and the calculation results


The authors calculate that the U- type elements fundamental frequency and its vibration modes (displacement mode and bending mode), as well as the relationship, the theoretical and experimental values and the traffic between the phase resonance good agreement.

Analysis (ii) a flexible straight tube

Raszillier and Durst (University of Erlangen, Germany) using the Euler beam theory, consider the fluid is moving string, the dynamic response of a one-dimensional flexible straight pipe resonance analyzes

a. Equation (Oscillating tube of staight part)


b. the boundary conditions


On the endpoint,

c. the numerical solution and the calculation results

The authors used a rather complicated solution process, calculate the fluid flow and fluid flow without the fundamental frequency and the resonant vibration mode of the displacement of the straight tube, and calculating from the relationship between the phase difference and the flow rate.

2. Dynamic response analysis of rigid straight pipe

Cascetla assumed intuitive rigid, to avoid calculating the fundamental frequency of the elastic tube and the resonant vibration modes of displacement, which can further simplify the calculation, the last root simple result can be obtained: the relationship between the vibration displacement and flow.

Practical design issues

Analysis of the dynamic response of the resonance, although very detailed but collegial. Engineers are most concerned about the strength of the stress distribution and fatigue resistance and airway wall to guide the resonance frequency of the elastic tube is adequate. The easiest way is to use structural analysis software package SAP, or ANSYS analysis and calculation.

Selecting the elastic element

From the mechanical point of view, mass flow meter design, first select the appropriate time to feel elements to maximize the Coriolis effect once the element. This includes feelings of selecting the best shape of elements, as well as the best material elastic metal pipe and wall thickness options. Shape elements can be broadly grouped into four categories, namely: elbow-shaped and straight tube; single tube-shaped and multi-tubular (twin tube). In the election form, its main principle is to balance performance, range and cost of the best elements of a selected these three factors. Generally speaking, the more complex the shape selected, the Coriolis effect is higher, but the more complex production processes and technologies, and thus the higher the cost. Usually the primary element is always attributable to the above four categories in the form of binding: If combined elbow and double tubular shape.

At present, the Coriolis force as the principles, and the mass flowmeter primary element with a variety of geometric shapes, such as:

Double U-shaped or triangular

Double S

Double w type

Double K type


Single tube polycyclic

Single J-

Single straight tube

Dual straight tube

Currently in urgent need of some mechanical problem solving

1. Theoretically, precision Coriolis mass flowmeter is not measured fluid affect working conditions, but the actual situation is indeed subject to a variety of working conditions affect fluids (although this has little effect), because Charles also sometimes unclear. The authors estimate that is attached by a secondary vortex effect 加柯's primary element within the pipeline caused caused.

Because the north by the viscous fluid is always, so the velocity profile in the pipe cross-section is approximately parabolic (large viscous case) and the power of type (small viscosity circumstances), rather than a uniform velocity profile. The flow rate of the pipe wall at zero, while the maximum flow rate of the center line, so that, at different radial positions on the cross section is not the same Coriolis accelerations. Thus, the non-uniform Coriolis effect will produce secondary vortex, its direction of rotation and vibration tube vector direction is perpendicular to each other. Fluid under different working conditions, the flow pattern inside the meter tube is not the feel similar, resulting attached 加柯's effects, which vary in size. This allows the accuracy of the flow meter changes, as well as beyond the range of values given by manufacturers.

2. The mass flow meter can measure two-phase principle, but in practice the measurement error is large, so that the industry can not accept applications in this field, is also being further study the issue. The authors estimate that cause these problems, ibid.

3. In addition, due to a vibrating element, so it is subject to interference from outside vibrations greater impact this issue has attracted the attention of manufacturers, the ongoing research. The author believes that the problem should be designed anti-vibration components and circuitry to proceed, but it should first analyze the frequency shift and frequency-locked clear phenomena, and then to find the right anti-vibration measures.

Material issue

Because of a metal tube vibration sensor, so the pipe can withstand fatigue to consider in a variety of environmental impacts as well as the ability to withstand corrosion. As we all know, the increased resistance to fatigue damage, one is to reduce the vibration amplitude of the metal tube, the second is to increase the thickness of the tube vibration and the third is to select the appropriate metal materials. At present, most of 316L stainless steel, metal material is more desirable Hastelloy (Hastelloy alloy), namely NiCrMo alloy, its ability to fatigue damage is stronger than 316L, especially chloride corrosion practical situations. ? Titanium best, but the latter too expensive.


Coriolis mass flowmeter is particularly suitable for flow measurement applied to large viscosity of non-Newtonian fluid, which are particularly suitable for measuring the flow of viscous even difficult media such as:

All kinds of things latex mixed pulp slurry

Paint vitamin syrup

Pulp heavy

Polymers and other polymer slurry. . . .

Therefore, the West has already Coriolis mass flowmeter application into various industries: such as chemical and pharmaceutical industries, food and beverage, refrigeration, energy, petrochemicals and so on. In the industry, the majority of the ingredients used in the control of the mixing process. In addition, also used in the car and wear in the handling of the spine.

Accuracy problems

Currently Western manufacturers have declared precision Coriolis mass flow meter can reach 0.5%, 0.2% or even 0.1%. But the actual use to be especially careful, accuracy at low flow range is generally not meet the above-precision values. In addition, secondary instrument zero drift, especially after a period of time, up to a value less than a given manufacturer.

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