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

Sensitivity analysis of threshold parameters in slug detection algorithms

Slug flow is a common flow pattern in pipelines that is often accompanied by undesirable effects like vibrations, pressure loss, and corrosion. Since these effects correlate with slug frequency, various attempts to predict this parameter by empirical or semi-empirical methods have been undertaken in the past. However, significant mismatches between these predictions can be observed. In this work, different slug frequency calculation methods have been applied to simulation data to investigate the sensitivity of threshold parameters that are often used in slug detection algorithms. The findings reveal that the detection of slugs from liquid holdup data is highly sensitive to these thresholds. Aeration of the liquid phase causes the gas-liquid interface to be less distinct and requires an adaption of the thresholds to the degree of aeration. In contrast, slug detection algorithms based on frequency analysis are robust to small deviations of the liquid level but fail to properly discriminate between slugs and waves. Our investigations show that slug frequency strongly depends on the method chosen for the determination of the liquid level. We propose new approaches that are less susceptible to aeration and approximate the liquid level very close to the authors’ human judgment

Implementation of turbulence damping in the OpenFOAM multiphase flow solver interFoam

In the presented work Egorov’s approach (adding a source term to the ω-equation in the k-ω model, which mimics the damping of turbulence close to a solid wall) was implemented in on the subclass of shear stress transport models. Hence, turbulence damping is available for all shear stress transport type models, including hybrid models that are based on the ω-equation. It is shown that turbulence damping improves the prediction of the axial velocity profile not only for Reynolds-averaged Navier–Stokes simulation but also for detached eddy simulation and delayed detached eddy simulation models. Furthermore, it leads to a more realistic estimation of the pressure drop and, hence, to a more correct prediction of the liquid level. In this paper, simulation results for four different turbulence models are presented and validated by comparison with experimental data. Furthermore, the influence of the magnitude of the damping factor on the pressure drop in the channel is investigated for a variety of different gas-to-liquid flow rate ratios. These investigations show that higher gas-to-liquid flow rate ratios require higher damping factors to correctly predict the pressure drop. In the end, advice is formulated on how an appropriate damping factor can be determined for a specific test case

A3.1.2 Suitable modeling approaches for the most important influences of real gas effects in high-pressure hydrogen flows

<p>This report reviews different modeling approaches to account for the most relevant real gas effects in high-pressure hydrogen flows with the special focus on critical nozzle flow. It summarizes the important physical properties that are affected by real gas effects, presents several real gas modeling approaches, and compares them with ideal gas models. Furthermore, this report highlights the importance of a time-efficient as well as accurate implementation of real gas models when used in CFD software.</p&gt

A3.1.3 Suitable turbulence models for high-pressure hydrogen flows through critical nozzles

<p>This report reviews several turbulence modeling approaches in the context of simulating high-pressure hydrogen flows through critical nozzles. It summarizes the relevant flow effects that need to be captured by the turbulence model, presents several modeling approaches from the literature, and reviews them.</p&gt

Derivation and validation of a reference data-based real gas model for hydrogen

<p>Hydrogen plays an important role for the decarbonization of the energy sector. In its gaseous form, it is stored at pressures of up to 1000 bar at which real gas effects become relevant. To capture these effects in numerical simulations, accurate real gas models are required. In this work, new correlation equations for relevant hydrogen properties are developed based on the Reference Fluid Thermodynamic and Transport Properties Database (REFPROP). Within the regarded temperature (150-400 K) and pressure (0.1-1000 bar) range, this approach yields a substantially improved accuracy compared to other databased correlations. Furthermore, the developed equations are validated in a numerical simulation of a critical flow Venturi nozzle. The results are in much better accordance with experimental data compared to a cubic equation of state model. In addition, the simulation is even slightly faster.</p&gt

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