Fast and accurate modelling of frictional transient pipe flow. Issue 5 (2nd February 2018)

• Record Type: Journal Article
• Authors: Urbanowicz, Kamil
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 5(2018)
• Page Start: 802
• Page End: 823
• Publication Date: 2018-02-02
• Subjects: cavitation -- convolution integral -- hydraulic resistance -- transient pipe flow -- weighting function; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600246
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: This paper is devoted to the one‐dimensional (1D) modelling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is present in the form of a convolution of liquid acceleration with a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In the original model of Zielke (1968), computation of the convolution integral had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing efficient models for estimation of unsteady hydraulic resistance (with nearly linear growth of computational time). In the present paper, a correction to the erratic recursive formula by Schohl (1993), being used to calculate the unsteady wall shear stresses during transient flow, is presented. The simulation results obtained with the corrected Schohl's recursive formula are consistent with the classic but computationally inefficient formula proposed recently by Vardy and Brown (2010). The accuracy of the efficient weighting function obtained in wall shear stress models is verified. The results of pressure pulsation obtained when taking into account cavitating flow, or not, are surprising in the sense that the weighting function does not need to be built by a lengthy sum of exponential terms to accurately simulate the transient event. Abstract : This paper is devoted to the one‐dimensional (1D) modelling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is present in the form of a convolution of liquid acceleration with a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In the original model of Zielke (1968), computation of the convolution integral had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing efficient models for estimation of unsteady hydraulic resistance (with nearly linear growth of computational time). In the present paper, a correction to the erratic recursive formula by Schohl (1993), being used to calculate the unsteady wall shear stresses during transient flow, is presented. The simulation results obtained with the corrected Schohl's recursive formula are consistent with the classic but computationally inefficient formula proposed recently by Vardy and Brown (2010). The accuracy of the efficient weighting function obtained in wall shear stress models is verified. The results of pressure pulsation obtained when taking into account cavitating flow, or not, are surprising in the sense that the weighting function does not need to be built by a lengthy sum of exponential terms to accurately simulate the transient event.