Coriolis flow measuring principle

In many sectors of industry, it is mass flow measurement rather than volume flow that has to be measured. In food processing, for example, products such as pastes, pulps and yogurt are generally batched by weight, not volume. Therefore, the label on the packaging tells the consumer the weight of the product instead of the volume. One reason for this is that the volume of most fluids can vary widely under physical influences such as pressure, temperature and density. The mass of a fluid is not affected by these influences – so mass flow measurement has some advantages that volumetric measurement simply cannot match. This is an aspect of particular importance for fiscal metering in batching and metering fluids.

The mass of a body is generally determined by weighing. From the engineering point of view, however, there are major difficulties to be overcome when directly weighing a mass that is flowing continuously through a piping system. This is the reason why recent decades have seen the emergence of a measuring principle that enables mass flow in pipes to be measured directly and continuously – namely mass flow measurement by the Coriolis principle. In some applications it makes more sense to apply this Coriolis principle than to determine mass indirectly by measuring volume flow and density (volume × density = mass).

The earliest description of this principle is generally attributed to the French physicist and mathematician whose name it now bears, Gaspard-Gustave de Coriolis (1792 – 1843).

The effect occurs only in rotating systems, for example on fairground merry-go-rounds or on our rotating planet, but it should not be confused with centrifugal force. Despite the fact that the term “Coriolis force” is in widespread use, it is frequently difficult to describe the force, much less explain it. Its occurrence is always to be observed when straight movement and rotary action are superimposed in a system.

A practical example is illustrated in Figure 1: A person standing still on a rotating turntable has only to lean slightly inward to counteract centrifugal force (left). A person moving from the center of rotation toward the edge of the turntable, however, encounters steadily increasing rotational speed and, as inertia comes into play, has to overcome a force known as the Coriolis force. This Coriolis force acts to deflect the person from the shortest route across the turntable (straight along the radius). The heavier the person, the faster the speed of rotation, and the faster the person walks toward the circumference (“mass flow”), the more inertia is perceptible and the more powerful is the effect of the Coriolis force.

In mathematical terms, the Coriolis force (F_C) is therefore proportional to the moving mass (_m^· ), speed of rotation (ω) and radial velocity (v_r) in the rotating system:

F_c = 2 ⋅ m ⋅ ω ⋅ v_r

Coriolis forces are always present when linear movement and rotary action are superimposed within a system (Fig. 1, right). In the absence of linear movement (Fig. 1, left, person standing still), only centrifugal forces occur.

In a Coriolis mass flowmeter (see Fig. 2), the individual mass particles are influenced in the same way as the body of the person on the turntable in the above illustration. The rotary motion described above that generates the Coriolis force is replaced in the flowmeter by exciting the measuring tube to oscillate at its resonance frequency.

a  =  Zero flow: oscillation state of the measuring tubes at zero flow
b  =  Flow → oscillation state of the measuring tubes at time interval 1
c  =  Flow → oscillation state of the measuring tubes at time interval 2

At zero flow, when the fluid is at a standstill, there is no linear movement (a). Consequently, no Coriolis forces occur. Once the mass is flowing, the movement induced by oscillation (= rotation) in the measuring tube superimposes itself on the linear movement of the flowing fluid. The Coriolis force causes the measuring tubes to “twist” (b, c). Sensors (A, B) at the inflow and outflow register the difference in time in this movement, in other words, they register the phase difference. The higher the mass flow, the larger the phase difference (see Fig. 3).

When the fluid is flowing, the mass particles move through the measuring tube and are subjected to superimposed lateral acceleration by the Coriolis forces (F_C ). As they enter the tube, the mass particles (m) drift away from the center of rotation (Z₁), and return toward the center (Z₂ ) as they approach the outlet end. Consequently, the Coriolis forces act in opposed directions at inlet and outlet and the measuring tube starts to “twist”. This change in the measuring tube’s oscillation-induced geometry is registered as a phase difference by sensors (A, B) at each end of the measuring tube. This phase difference (∆ϕ) is directly proportional to the mass of the fluid and to the flow velocity (v), and therefore also to mass flow.

The nominal diameter range currently available extends from DN 1 to 300. Usage can therefore range from the dosing of very small amounts in pharmaceutical applications up to the loading and discharge of ship cargoes. The choice of designs is correspondingly wide.

The measuring tubes are continuously excited at their resonance frequency. As soon as the fluid density changes, and consequently the mass of the oscillating system (measuring tube plus fluid), the excitation frequency is adjusted accordingly. Thus, the resonance frequency is a function of fluid density and can be used as an additional output signal.

The temperature of the measuring tubes is determined in order to calculate the compensation factor due to temperature effects. This signal corresponds to the process temperature and is also available as an output signal.

Single, dual and four measuring tube designs in a vast array of shapes and bending radii are available to optimally serve differing applications found in industry.

In most dual-tube meters, the measuring tubes are excited so as to oscillate in counterphase, an arrangement that effectively decouples the entire flowmeter from the influences of external vibrations. There are various types of dual-tube meters. As far as geometric properties are concerned, the measuring tubes vary from manufacturer to manufacturer, and straight, looped or slightly bowed designs can all be found. The straight or slightly bowed tubes used by Endress+Hauser enable the construction of compact, space-saving sensors.

Single-tube measuring systems have a number of advantages over their dual-tube counterparts:

• Easier to clean
• Pressure losses significantly lower
• Less imposed stress on the fluid because there is no need for a splitter to divide the flow between two measuring tubes

The advantage of this design – namely that there is only one oscillating measuring tube – inevitably means that decoupling, which is a feature of dual-tube meters, is not automatically realized. Care therefore has to be taken at the development stage to build in characteristics that will effectively decouple the system from external influences.

The “Torsion Mode Balancing system”:
Endress+Hauser accomplishes this decoupling by combining the characteristically high resonance frequency with its patented Torsion Mode Balancing System (TMB). In the case of the Proline Promass I single-tube sensor, the system balance needed for correct measurement is achieved by means of a counter-oscillating pendulum mass arranged eccentrically on the measuring tube (torsional action) (Fig. 5). Because of this built-in system balance, Promass I is just as easy to install as the dual-tube meter. There is no need for special vibration-inhibiting mounts upstream or downstream of the flowmeter.

With the Promass I measuring system, even the viscosity can be determined “in-line” as a further process parameter.

ω = Angular velocity
m₁ = Measuring tube and fluid mass
m₂ = Pendulum mass
v₁ = Velocity of m₁
v₂ = Velocity of m₂
p = Impulse

Four-tube measuring systems have similarity to dual-tube systems in that they incorporate counterphase oscillation which effectively decouples the flowmeter from the installation environment. Additionally, they have the benefit of allowing comparatively higher flow turndown and higher throughput with lower pressure drop as compared to similar nominal sized dual-tube meters. This is especially valuable for pipeline and loading applications.

The advantages of Coriolis mass flow measurement are clear: This measuring principle is not affected by physical factors such as conductivity, pressure, temperature, density and viscosity. Straight inlet and outlet runs are unnecessary, a fact that can be extremely advantageous when space is at a premium. It is not surprising, therefore, that Coriolis flowmeters are to be found in widely differing applications and sectors of industry, particularly in chemicals and pharmaceuticals.

Virtually every fluid can be measured: detergents and solvents, heating oil and fuels, vegetable oils, animal fats, latex, silicone oils, toluene, benzene, alcohol, methane, fruit juices, toothpaste, cooking oils, vinegar, ketchup, mayonnaise, gases, liquified gases (butane, propane, natural gas), etc.

Coriolis flowmeters register simultaneously the fluid density as well as mass flow, and with the aid of temperature sensors they can also monitor the fluid temperature. Consequently, this measurement type can truly be designated “multivariable metering”. The primary measured variables, namely mass flow, fluid density and temperature, can be used to compute and display other variables such as volume flow, entrained solids content, concentration or derivative density values (e.g., standard density, °Brix, °Baumé, °API, °Balling, °Plato). Modern measuring systems are equipped to calculate and output these secondary measured variables directly via the transmitter.

The outstanding characteristics of these Coriolis devices make them an excellent match for a wide array of applications:

• Mixing and batching of various raw materials
• Controlling processes
• Measuring of fluids with quickly changing density
• Control and monitoring of product quality
• Custody transfer of liquids and gases

These are some of the reasons why the Coriolis principle has become established as a proven measuring technique within the last 25 years. Coriolis flowmeters are frequently used in chemical processes, primarily on account of the following:

• Direct method of measuring mass with a high accuracy (typically ±0.1 %)
• Highly versatile because of wide range of measuring tube materials

Many applications are encountered in the food industry, e.g., for dosing minimal quantities of ingredients and for filling (Fig. 6). Coriolis meters are also becoming more and more widespread in low-pressure and high-pressure gas metering applications (Fig. 7), e.g., with compressed natural gas (CNG). Meters suitable for custody transfer are also available on the market for numerous applications.

For some time now, the advantages outlined earlier have been consistently opening new fields for flowmeters based on the Coriolis principle. Consequently, there is every indication that the market for Coriolis meters will continue to grow at the present rate or even expand further in the coming years.

The features of Coriolis measurement are particularly attractive and promising for applications which, in the past, were fulfilled by “traditional” metering techniques. Cost of ownership is one of the many factors that come into play in this respect. It comprises not only the initial cost of acquisition, but also the outlay and overheads incurred over the entire life cycle of the device. Coriolis meters show surprisingly low life cycle costs because they are relatively maintenance-free and have a high level of flexibility under widely varying process conditions.

In the application depicted in Figure 7, ethylene is being measured with a pressure between 75 to 95 bar and a flow of 10 to 40 t/h. In spite of pipeline vibration, the Promass flowmeter requires absolutely no additional means of support or attachment.

• Universally applicable principle for measuring the flow of liquids and gases
• Direct measurement of mass flow (no need for pressure and temperature compensation)
• Measuring principle is independent of fluid density and viscosity
• Very high measuring accuracy (typically ±0.1 % o.r.)
• Multivariable sensor concept: simultaneous measurement of mass flow, density and temperature
• Not affected by the flow profile
• No inlet and outlet runs necessary
• No moving parts inside the measuring tube
• No need for filters
• No need for separate density measurement

• Relatively high initial investment
• Most designs introduce some pressure drop
• Restricted usability if the gas content of the fluid is high, and in the case of multiphase fluids