Velocity profile effects represent one of the possible installation effects in flowmeters. They are perceived as variations in a flowmeter characteristic arising from different inlet velocity profiles that may be classed as: (1) developed - i.e. fully developed velocity profiles that depend on Reynolds number and are present after long straight inlet pipe sections - and (2) disturbed - i.e. disturbed velocity profiles (e.g. asymmetric or swirling flows) that result from perturbation elements, such as upstream elbows, double elbows, reducers etc. The aim of this paper is to discuss velocity profile effects in Coriolis flowmeters. The new-generation devices try to achieve accuracies better then +- 0.1 percent, and this has to be considered when evaluating the significance of particular influences on their characteristics. Although the velocity profile effect is generally not considered as problematic as, for instance, some dynamic effects (flow pulsations, mechanical vibrations, two-phase flows, etc.), some accessible experimental studies give an indication of its magnitude. For example, three commercial Coriolis flowmeters showed 'no' or in one case 'just detectable' measurement errors under disturbed flow conditions in [1] (a relatively high threshold of 0.25 percent was used for reporting a significant effect), but the output of a commercial shell-type Coriolis flowmeter was affected by up to a few percent in [2] (testing with pressurized gas). Such results are in agreement with the common findings of theoretical studies, which are the subject of this paper (see the review of references in Section 2). It has been already confirmed that velocity profile effects are expected to be negligible (but not zero) in many configurations. However, this cannot be taken as a rule for all flowmeters that work on the Coriolis measuring principle, because their sensitivity to velocity profiles depends on many constructional and operational parameters of the flowmeter. The effect of certain of these parameters will be considered for the first time in this paper. Section 2 of this paper describes some modelling concepts, which are applicable for predictions and analyses of velocity profile effects in fluid-structure interacting systems like Coriolis flowmeters. We can classify them into analytical and numerical models that are respectively based on: (1) the weight vector theory (Section 2.1) and (2) CFD simulations of fluid flow in the vibrating tube (Sections 2.2 and 2.3). Section 3 uses the weight vector approach to analyse velocity profile effects in beam-mode Coriolis flowmeters with a straight and slender measuring tube. The study is limited to fully developed flows at the inlet and discusses the influence on velocity profile effect of Reynolds number, aspect ratio of the tube, axial working mode, positions of the motion sensors and boundary conditions at the tube ends.
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