Uncertainty evaluation for velocity–area methods

Velocity–area methods are used for flow rate calculation in various industries. Applied within a fully turbulent flow regime, modest uncertainties can be expected. If the flow profile cannot be described as “log-like”, the recommended measurement positions and integration techniques exhibit larger errors. To reduce these errors, an adapted measurement scheme is proposed. The velocity field inside a Venturi contour is simulated using computational fluid dynamics and validated using laser Doppler anemometry. An analytical formulation for the Reynolds number dependence of the profile is derived. By assuming an analytical velocity profile, an uncertainty evaluation for the flow rate calculation is performed according to the “Guide to the expression of uncertainty in measurement”. The overall uncertainty of the flow rate inside the Venturi contour is determined to be 0.5 % compared to 0.67 % for a fully developed turbulent flow

Simulation-based determination of systematic errors of flow meters due to uncertain inflow conditions

Computational fluid dynamics (CFD) provides well-established tools for the prediction of the velocity profiles in turbulent pipe flows. As far as industrial pipe and district heating systems are concerned, combinations of elbows are the most common pipe assemblies. Among the different pipe combinations, double elbows out-of-plane are of special interest, since they introduce strong disturbances into the flow profile and have a strong influence on many common types of flow meters. In front of a double elbow there is often another flow-disturbing installation. As a result the upstream conditions are unknown and an investigation of the resulting systematic bias on the measurement of the flow rate and the associated contribution to its measurement uncertainty is necessary. We demonstrate here that this can be achieved by a variation of the inlet profile in terms of swirls and asymmetry components. In particular, an ultrasonic and an electromagnetic flow meter are modeled in order to quantify the systematic errors stemming from uncertain inflow conditions. For this purpose, a generalized non-intrusive polynomial chaos method has been used in conjunction with a commercial CFD code. As the most influential parameters on the measured volume flow, the distance between the double elbow and the flow meter as well as the orientation of the flow meter are considered as random variables in the polynomial chaos approach. This approach allowed us to obtain accurate prediction of the systematic error for the ultrasonic and electromagnetic meter as functions of the distance to the double elbow. The resulting bias in the flow rate has been found to be in the range of 1.5–4.5% (0.1–0.5%) with a systematic uncertainty contribution of 2–2.4% (0.6–0.7%) for the ultrasonic (electromagnetic) flow meter if the distance to the double elbow is smaller than 40 pipe diameters. Moreover, it is demonstrated that placing the flow meters in a Venturi constriction leads to substantial decrease of the bias and the contribution to the measurement uncertainty stemming from the uncertain inflow condition

Simulationsbasierte Unsicherheitsanalyse von Durchflussmessungen

Flow meters are usually calibrated in ideal flow conditions. In consequence, flow rate measurements in non-ideal, so-called disturbed conditions are defective. These disturbances are caused by non-straight pipe geometries and are characterized by asymmetrical axial velocity profiles, enhanced turbulence and cross flow components. These flow structures slowly decay in a long straight pipe. In most piping networks elbow configurations are the most common pipe installations, long straight pieces are rarely found. This thesis deals with uncertainty estimation of flow rate prediction in non-ideal flow conditions using numerical methods. Therefore, different measurement principles are applied to simulated flow fields. In contrast to the most other studies of this kind, particular pipe geometries are not studied separately, but rather a class of disturbances is examined by using random inflow conditions from several elbows in a row with variable distances. It is demonstrated that simulation results from a steady state eddy viscosity model are sensitive to their inflow conditions. To analyze the effect of each inflow condition a separate time consuming flow simulation is necessary. Therefore, different effective methods for uncertainty quantification are evaluated. To save additional computation time, a simulation with ideal inflow conditions can be used. To assess the effect of random inflow conditions, the azimuthal orientation of the calculated flow field is set to random. Based on these assumptions uncertainties are quantified downstream several combinations of elbows for - simulated velocity profiles, - velocity-area measurements in a Venturi nozzle, - ultrasonic and electromagnetic flow meters with and without a Venturi/rectangular nozzle as flow conditioner, - single-beam ultrasonic flow meters with different reflecting path configurations, including two suggested new designs, - flow rate prediction with LDV single-path measurements including the LDV-bias error and - a combined laser-optical and numerical method for on-site calibration of flow meters.Die Genauigkeit einer Durchflussmessung ist in der Regel abhängig von den vorherrschenden Strömungsbedingungen. Da Messgeräte normalerweise bei idealen Strömungsbedingungen kalibriert werden, sind bei nicht idealen Bedingungen fehlerbehaftete Messwerte zu erwarten. Solche gestörten Strömungsbedingungen werden von nicht geraden Rohrinstallationen verursacht und sind geprägt von asymmetrischen axialen Geschwindigkeitsprofilen, einer erhöhten Turbulenz und Sekundärströmungen. In den meisten Rohrleitungssystemen sind vor allem Krümmer installiert, lange gerade Rohrstrecken sind nur selten zu finden. Diese Dissertation beschäftigt sich mit der Bestimmung von Unsicherheiten verschiedener Durchflussmessverfahren bei nicht idealen Strömungsbedingungen mit numerischer Simulation. Dafür werden verschiedene Messprinzipien modelliert und auf simulierte Strömungen angewandt. Im Gegensatz zu anderen Studien werden hier nicht bestimmte Rohrgeometrien separat voneinander untersucht, sondern eine Klasse von Störungen mit zufälligen Zuströmbedingungen hinter mehreren Krümmern mit variablem Abstand. Es wird gezeigt, dass die Resultate von zeitlich stationären Simulationen mit Wirbelviskositätsmodellen sensitiv gegenüber den Zuströmbedingungen sind. Da jede Zuströmrandbedingung eine neue rechenintensive numerische Strömungssimulation erfordert, werden verschiedene effektive Methoden zur Unsicherheitsquantifizierung verglichen. Zur vereinfachten Abbildung der Sensitivität der Strömung gegenüber verschiedenen Einlassrandbedingungen kann eine Simulation mit idealen Zuströmbedingungen ausgewertet werden bei der die azimutale Orientierung der resultierenden Strömung als zufällig angenommen wird. Durch diese Vereinfachung kann Rechenzeit gespart werden. Basierend auf diesen Annahmen werden die Unsicherheiten hinter verschiedenen Kombinationen von Krümmern quantifiziert von - simulierten Strömungsprofilen, - Netzmessungen in einer Venturi-Düse, - Ultraschall- und magnetisch-induktiven Durchflussmessgeräten sowohl mit, als auch ohne Strömungskonditionierung durch eine Venturi- und Rechteck-Einziehung, - verschiedenen Ein-Strahl-Reflektionsanordnungen eines Ultraschall-Durchflussmessgeräts, inklusive zwei neu vorgeschlagener Designs, - einem laseroptischen Ein-Pfad-Verfahren zur Durchflussmessung inklusive LDV-Bias und - einem kombinierten laseroptischen und numerischen Verfahren zur Vor-Ort-Kalibrierung von Durchflussmessgeräten.BMWi, 03ET1204, EnEff: Wärme, On-site calibration of flow meters in district heatin

Simulation Uncertainty for a Virtual Ultrasonic Flow Meter

Ultrasonic clamp-on meters have become an established technology for non-invasive flow measurements. Under disturbed flow conditions, their measurement values must be adjusted with corresponding fluid mechanical calibration factors. Due to the variety of flow disturbances and installation positions, the experimental determination of these factors often needs to be complemented by computational fluid dynamics (CFD) simulations. From a metrological perspective, substituting experiments with simulation results raises the question of how confidence in a so-called virtual measurement can be ensured. While there are well-established methods to estimate errors in CFD predictions in general, strategies to meet metrological requirements for CFD-based virtual meters have yet to be developed. In this paper, a framework for assessing the overall uncertainty of a virtual flow meter is proposed. In analogy to the evaluation of measurement uncertainty, the approach is based on the utilization of an expanded simulation uncertainty representing the entirety of the computational domain. The study was conducted using the example of an ultrasonic clamp-on meter downstream of a double bend out-of-plane. Nevertheless, the proposed method applies to other flow disturbances and different types of virtual meters. The comparison between laboratory experiments and simulation results with different turbulence modeling approaches demonstrates a clear superiority of hybrid RANS-LES models over the industry standard RANS. With an expanded simulation uncertainty of 1.44 × 10−2, the virtual measurement obtained with a hybrid model allows for a continuous determination of calibration factors applicable to the relevant mounting positions of a real meter at a satisfactory level of confidence

Simulation Uncertainty for a Virtual Ultrasonic Flow Meter

Ultrasonic clamp-on meters have become an established technology for non-invasive flow measurements. Under disturbed flow conditions, their measurement values must be adjusted with corresponding fluid mechanical calibration factors. Due to the variety of flow disturbances and installation positions, the experimental determination of these factors often needs to be complemented by computational fluid dynamics (CFD) simulations. From a metrological perspective, substituting experiments with simulation results raises the question of how confidence in a so-called virtual measurement can be ensured. While there are well-established methods to estimate errors in CFD predictions in general, strategies to meet metrological requirements for CFD-based virtual meters have yet to be developed. In this paper, a framework for assessing the overall uncertainty of a virtual flow meter is proposed. In analogy to the evaluation of measurement uncertainty, the approach is based on the utilization of an expanded simulation uncertainty representing the entirety of the computational domain. The study was conducted using the example of an ultrasonic clamp-on meter downstream of a double bend out-of-plane. Nevertheless, the proposed method applies to other flow disturbances and different types of virtual meters. The comparison between laboratory experiments and simulation results with different turbulence modeling approaches demonstrates a clear superiority of hybrid RANS-LES models over the industry standard RANS. With an expanded simulation uncertainty of 1.44 × 10−2, the virtual measurement obtained with a hybrid model allows for a continuous determination of calibration factors applicable to the relevant mounting positions of a real meter at a satisfactory level of confidence