Accuracy Analysis of the Numerically Calculated Discharge Characteristics of Flow-Measuring Weirs and Flumes
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Vol. 54, No. 3, September, 2020
ACCURACY ANALYSIS OF THE NUMERICALLY CALCULATED DISCHARGE CHARACTERISTICS OF FLOW-MEASURING WEIRS AND FLUMES A. M. Kusher1 Translated from Gidrotekhnicheskoe Stroitel’stvo, No. 4, April 2020, pp. 12 – 17.
A comparative analysis of the empirical and numerically found discharge characteristics of the most common flow-measuring structures was performed. The results of testing the developed technical solutions by comparison with known experimental and theoretical dependencies are presented. Keywords: computational fluid dynamics; flow-measuring structure; discharge characteristic; thin-plate weir; broad-crested weir; crest with a sloping front wall; critical-depth flume; Crump weir.
In this research, a comparative analysis of the empirical and numerically found discharge characteristics of the most common flow-measuring structures is performed. The results of testing the developed technical solutions by comparison with known experimental and theoretical dependencies are presented.
The flow of water through a flow-measuring structure has a complex three-dimensional character. The discharge characteristics of such structures depend both on the individual size and shape and on the flow structure in the approach canal. The discharge characteristics of almost all flow-measuring structures are obtained on the basis of experimental studies. The range of application and reliability of the existing empirical discharge dependences are limited by the accuracy and amount of experimental studies, on the basis of which these dependences are constructed. For example, the values of water discharge through a thin-plate weir, calculated using known formulas, can differ by up to 5%. The presence of the approach velocity coefficient Cv in modern empirical formulas, which is a function of the ratio of the total and geometric heads, does not ensure that the influence of the approach flow velocity profile is taken into account, which is essential for structures with a low headrace backwater. The known theoretical methods for calculating the flow, that are based on the solution of the St. Venant’s system of hyperbolic differential equations, are inapplicable for flowmeasuring structures due to the presence of supercritical flow mode with the Froude code Fr > 1. The known numerical solutions based on the Navier – Stokes equations without taking into account the flow history have insufficient accuracy of determining the flow discharge for water metering. For example, in published studies, the error in calculating the flow discharge in the Parshall flume is 4 – 16% [5, 6]. 1
MATERIALS AND METHODS The numerical calculation of the discharge characteristics of flow-measuring structures was carried out using the software and computing complex DisCo4 [1 – 3]. The operating principle of the complex is based on the numerical solution of the motion equations (Navier – Stokes) and preservation in a three-dimensional formulation by the finite volume method. The operations scope is standard: generation of a three-dimens
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