CONVOLUTION INTEGRAL IN TRANSIENT PIPE FLOW

Abstract

This paper is devoted to the modeling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is presented in the form of a convolution integral of liquid acceleration and a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In its first revision (Zielke W 1968 J. ASME 90 109) it had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing the so-called efficient models for correct estimation of hydraulic resistance with simultaneous linear loading of the computer’s operating memory was needed. The work compared the methods of numerical solving of the convolution integral known from the literature (classic by Zielke W 1968 J. ASME 90 109 and Vardy A E and Brown J M B 2010 J. Hydraul. Eng. 136 (7) 453 and efficient by Trikha A K 1975 J. Fluids Eng. p. 97, Kagawa T et al. 1983 Trans. Jpn. Soc. Mech. Eng. 49 (447) 2638 and Schohl G A 1993 J. Fluids Eng. 115 420). The comparison highlighted the level of usefulness of the analyzed models in simulating the water hammer and revealed the demand for further research for the improvement of efficiency of the solutions.