Vortex flow measuring principle

This measuring principle is based on the fact that vortices are formed downstream of an obstacle in a fluid flow, either in a closed pipe or in an open channel. This phenomenon can be observed by looking at the eddies (“vortex street”) formed downstream of a bridge pillar, for example (Fig. 1). The frequency of vortex shedding down each side of the pillar (bluff body) is proportional to the mean flow velocity and therefore to the volume flow. As early as 1513, Leonardo da Vinci had sketched stationary vortices downstream of obstacles shedding flow.

In 1878, Strouhal was attempting to describe in scientific form the eddies that form behind bluff bodies. His studies revealed that a wire stretched tight in a jet of air will oscillate. He found that the frequency of this oscillation is proportional to the velocity of the air jet. This phenomenon can be observed in a car or house: the whistling tone of the wind is caused by vortex shedding and rises or falls as velocity changes. This is called the “aeolian tones”.

The Strouhal number used in this context describes the relationship between the vortex shedding frequency, the velocity of flow and the diameter of the bluff body (see Fig. 2):

St: Strouhal number
f: Vortex shedding frequency
d: Diameter of the bluff body
v: Flow velocity

The physicist Theodore von Kármán laid down more of the theoretical groundwork for flow measurement with vortex meters in 1912, when he described what has become known as the “vortex street”. His analysis of the double row of vortices behind a bluff body in a fluid flow revealed a fixed ratio between their transverse spacing (d) and longitudinal spacing (L). If the bluff body is cylindrical, this ratio is 0.281, for example. With a uniform pipe diameter, the volume of the individual vortices is therefore constant. Presuming that the vortices are of the same size despite differences in operating conditions, flow can therefore be derived directly from the number of vortices per unit of time.

The flow reaches its maximum velocity at the widest part of the bluff body and subsequently loses some of this speed. Figure 3 shows that the flow tries to break away (a) from the contour of the bluff body, instead of continuing to follow it. This causes localized low pressure, producing backflows and, ultimately, vortices (b). These vortices shed alternately down each side of the bluff body and are carried away by the fluid.

Bluff bodies vary in shape from manufacturer to manufacturer. They can be rectangular, triangular, round, delta-shaped or one of several proprietary and patented designs. The design must be such that the Strouhal number remains constant over the entire measuring range, in other words, the vortex frequency is independent of pressure, temperature and density. It is this constant range (Re > 10.000) that is utilized for measuring volume flow with vortex meters (see Fig. 4). Delta-shaped bluff bodies exhibit almost ideal linearity and have proved particularly reliable. NASA engineers have subjected these bluff-body designs to exhaustive studies. Measuring accuracy can be ±0.75% o.r., and reproducibility is around 0.1%.

It is usual to define the characteristics of vortex flowmeters in terms of the “K factor”. This factor represents the number of vortices in unit time (pulses per unit of volume). The manufacturer obtains this K factor by calibration and includes this information on the instrument name plate. It is dependent on bluff body shape and pipe size.

A vortex flowmeter (DN 50/2") has a K factor of 10 pulses per liter, so each vortex pulse generated corresponds to a volume of 0.1 liter, irrespective of whether the fluid being measured is water, steam or any other fluid.

Vortex flowmeters are used in numerous branches of industry to measure the volume flow of steam, liquids and gas. Vortex meters are becoming more and more common in applications that were formerly the preserve of differential pressure flowmeters such as orifice plates. This trend is ongoing, for the simple reasons that vortex meters are easier to install and have a wider range of turndown. Figure 5 shows an example of such a case.

Ever since the nineteen-eighties, vortex meters have become particularly popular in all sectors of industry for metering steam. Vortex meters measure only volume flow, but steam systems are generally rated by mass or energy content, so these meters are frequently used in combination with either integrated or separately installed pressure and temperature sensors.

In contrast to electromagnetic flowmeters (also known as magmeters), vortex meters can be used to determine the flow of non-conductive or only very slightly conductive liquids such as hydrocarbons, demineralized water, condensate or boiler feedwater. They can also be used at elevated pressures and much higher temperatures than electromagnetic flowmeters.

In applications of this nature, vortex meters find widespread use in the metering of compressed air, natural gas, or individual components of the air such as nitrogen, oxygen, carbon dioxide, hydrocarbon, etc.

The focus of end customers has evolved from purely volumetric measurement to compensated mass measurement. This development makes it possible to draw up precise balance sheets. By taking pressure and temperature into account, accurate mass measurements can be achieved, which is essential for accurate balancing, process control and optimization.

Furthermore, special wet steam measurement (dryness fraction/steam quality) can help operators to understand the quality of their steam and detect potential accumulation of wetness online. This way, safety and efficiency can be improved reliably. Best accuracy results become possible in saturated/wet steam environments enabling customers to close potential gaps in their mass balances.

The Proline Prowirl flowmeters from Endress+Hauser combine the measurement of flow, pressure and temperature in a single instrument, resulting in a significant increase in efficiency and accuracy.

• Accuracy: By recording pressure and temperature simultaneously, accurate flow measurements can be determined that are independent of fluctuations in operating conditions, hence ideally suited for mass balancing of gas and steam.
• Efficiency: The integration of multiple parameters in one device significantly reduces installation effort and maintenance costs.
• Reliability: Prowirl flowmeters are robust and durable, ensuring reliable performance even in demanding conditions.