sensors Article Analysis of the Influence of the Vortex Shedder Shape on the Metrological Properties of the Vortex Flow Meter Mariusz R. Rzasa 1,* and Beata Czapla-Nielacna 2 1 Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Proszkowska 76 Street, 45-758 Opole, Poland 2 Faculty of Mechanical Engineering, Opole University of Technology, Mikolajczyka 5 Street, 45-271 Opole, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-602-345-162 Abstract: Vortex flow meters are used to measure the flow of gases and liquids. The flow meters of this type measure the frequency of vortices that arise behind an obstacle set in the path of the flowing fluid. The frequency is a function of the speed of the flowing fluid. This obstacle is called the vortex shedder bar. The advantage of this solution is that the frequency of vortices does not viscose on the rheological properties of the fluid, such as viscosity or density. As a result, the indications of the vortex flowmeter do not depend on the temperature and type of fluid. The work includes numerical and experimental studies of the effect of changing the shape of a vortex generator on the stability of vortex generation in a vortex flowmeter. The article presents a numerical analysis of the influence of selected surfaces of the vortex shedder on the parameters of the vortex flowmeter. In order to determine the influence of the shape of the vortex shedder on the type of generated vortices, simulations were carried out for various flow velocities. Numerical calculations were experimentally verified for a cylinder-shaped vortex shedder. The experimental tests consist in determining the Citation: Rzasa, M.R.; velocity field behind the vortex shedder. For this purpose, a proprietary method of determining local Czapla-Nielacna, B. Analysis of the liquid velocities and the visualization of local vortices were used. On the basis of the conducted Influence of the Vortex Shedder Shape research, the influence of the shape of the vortex shedder on the width of the von Karman vortex on the Metrological Properties of the street was determined and the optimal longitudinal distance from the shedder was determined in Vortex Flow Meter. Sensors 2021, 21, which it is most useful to measure the frequency of the vortices. This place ensures the stability of the 4697. https://doi.org/10.3390/ frequency of the generated vortices. s21144697 Keywords: vortex flow meter; flow visualization; flow measurement; flow visualization Academic Editor: Giovanni Betta Received: 10 June 2021 Accepted: 7 July 2021 1. Introduction Published: 9 July 2021 One of the solutions used to measure the velocity of liquids are vortex flow meters. These flow meters are used to measure the velocity of liquids of various densities and Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in viscosities. Their advantage is that the measurement result is not significantly influenced by published maps and institutional affil- solid particles carried with the liquid. They can therefore be used to measure contaminated iations. liquids. A second advantage is the very low pressure drop across the measuring device. Their disadvantage is the relatively small measuring range [1]. The principle of operation of the vortex flowmeter is to create regular vortices behind the generator placed in the flowing liquid. The frequency of the vortices is a function of the flow velocity. The vortex generator can have different shapes. This shape has a direct Copyright: © 2021 by the authors. impact on the sensitivity and measuring range of the flowmeter. The frequency of the Licensee MDPI, Basel, Switzerland. This article is an open access article resulting vortices is a measure of the flow velocity, which is expressed by the Strouhal distributed under the terms and number [2]: f ·d conditions of the Creative Commons St = , (1) Attribution (CC BY) license (https:// v creativecommons.org/licenses/by/ where: St—Strouhal number, f —frequency of vortices, d—characteristic dimension, v— 4.0/). flow velocity. Sensors 2021, 21, 4697. https://doi.org/10.3390/s21144697 https://www.mdpi.com/journal/sensors Sensors 2021, 21, x FOR PEER REVIEW 2 of 22 Sensors 2021, 21, 4697 2 of 20 where: St—Strouhal number, f—frequency of vortices, d—characteristic dimension, v— flow velocity. The Strouhal number is constant regardless of the velocity of the liquid that passes The Strouhal number is constant regardless of the velocity of the liquid that passes the vortex generator. The advantage of this solution is that the frequency of the generated the vortex generator. The advantage of this solution is that the frequency of the generated von Karman vortices does not depend on the rheological properties of the fluid, such as von Karman vortices does not depend on the rheological properties of the fluid, such as viscosity or density. As a result, the indications of the vortex flowmeter do not depend on viscosity or density. As a result, the indications of the vortex flowmeter do not depend on the temperature and type of fluid. the temperature and type of fluid. It should be noted, however, that the von Karman vortex path arises for the turbulen It should be noted, however, that the von Karman vortex path arises for the turbulen flow. Thus, the Reynolds number should be greater than 5000 [3]. Therefore, the size of flow. Thus, the Reynolds number should be greater than 5000 [3]. Therefore, the size of the vortex shedder bar should be adapted to the rheological properties of the liquid and the vortex shedder bar should be adapted to the rheological properties of the liquid and the measuring range. The rheological properties of the fluid depend on the type of fluid, the measuringtemperature range. and The its physicochemical rheological properties composition. of the fluid Moreover, depend the on presence the type of of a significantfluid, temperatureamount and of solid its physicochemical particles in a liquid composition. significantly Moreover, changes the itspresence rheological of a significant properties [4]. amountWhen of solid selecting particles the diameterin a liquid of significantly the vortex shedder, changes the its valuerheological of the properties Reynolds [4]. number Whencalculated selecting fromthe diameter the formula of the should vortex be considered.shedder, the value of the Reynolds number calculated from the formula should be considered. v·dr Re =⋅ , (2) = , (2) m where:where: ρ—densityr—density of the of fluid, the fluid, μ—dynamicm—dynamic viscosity viscosity of the of fluid. the fluid. In thisIn work, this work, tests tests were were carried carried out out for for pure pure water water at at a a temperature temperature of 2020 ◦°CCin in the the speed speedrange range from from 0.5 0.5 to to 2 2 m/s. m/s. Assuming Assuming a a vo vortexrtex generator generator size size of of 20 20 mm, mm, Reynolds Reynolds num- numbers bers areare between between 10,000 10,000 and and 40,000. 40,000. Thus, Thus, this this is is sufficient sufficient to to produce produce a avon von Karman Karman street. street. FigureFigure 1 shows1 shows a typical a typical design design of a flowmeter of a flowmeter [5]. It [ 5consists]. It consists of a vortex of a vortex generator, generator, whichwhich is mounted is mounted in the inflow the space. flow It space. causes It vortices causes to vortices form behind to form it, behindcreating it, the creating char- the acteristiccharacteristic von Karman von vortex Karman path. vortex In order path. to In measure order to the measure frequency the frequency of the vortices of the that vortices arise,that a pressure arise, adetector pressure is detectormounted isat mounteda certain distance. at a certain The distance. simplest solution The simplest is a pres- solution sure sensoris a pressure with high sensor measurement with high measurementdynamics. The dynamics. frequency Theof the frequency vortices is of measured the vortices is electronically.measured electronically. Vortex detector Shedder bar FigureFigure 1. Vortex 1. Vortex flowmeter. flowmeter. The shapeThe shape of the of vortex the vortex sheder sheder has a has signifi a significantcant impact impact on the on theparameters parameters and and met- metro- rologicallogical properties properties of the of theflow flow meter meter [6]. [Its6]. shape Its shape should should ensure ensure the formation the formation of regular of regular vorticesvortices in the in largest the largest possible possible measuring measuring range. range. The most The mostcommon common shape shape is a cylinder. is a cylinder. ThereThere are many are many works works on this on subject this subject in the in lit theerature literature [1,7]. [Classic1,7]. Classic designs designs of vortex of vortex flow flow metersmeters are also are used also usedin two-phase in two-phase flows flows [8]. [The8]. Theresearch research in this in this paper paper will will be becompared compared to to a cylinder-shapeda cylinder-shaped shedder shedder bar. bar. The The main main di disadvantagesadvantage of of the the cylindrical cylindrical shape shape is its very very narrow measuring rangerange [[9].9]. Therefore,Therefore, therethere is is a a need need to to look look for for other other solutions solutions [2 [2].]. There Thereare are many many works works in in the the literatureliterature whichwhich describedescribe cylindricalcylindrical shedder bar [1,7,10]. [1,7,10]. In In this this paper,paper, this shape willwill bebe usedused as as a a reference reference in in the the assessment assessment of theof the influence influence of selected of selectedshedder shedder surfaces surfaces on the on vonthe Karmanvon Karman vortex vortex path. path. The mainThe main disadvantage disadvantage of the of cylindrical the cylindricalshape shape is its narrow is its narrow measuring measuring range rang duee to due the to stability the stability of the of generated the generated vortices vor- [7].