A precursor in waterhammer analysis : rediscovering Johannes von Kries

In 1883 Johannes von Kries published the theory of waterhammer in a study of blood flow in arteries. He derived the “Joukowsky formula ” before Joukowsky (1898) and Frizell (1898) did. He considered skin friction in unsteady laminar flow and thus derived formulas for wave attenuation and line pack. The theory was confirmed by experimental results obtained in rubber hoses. In 1892 he published the first textbook describing “classical ” waterhammer. It presents formulas for phase-velocity and damping that are frequency-dependent because of skin friction, and in this sense it is the first contribution to the – these days popular – subject of unsteady friction

A. Isebree Moens and D.J. Korteweg: on the speed of propagation of waves in elastic tubes

The Moens-Korteweg formula for the speed of propagation of pressure waves dates back to 1878 and was used by Kries in haemodynamics and Frizell, Joukowsky, Allievi and others in waterhammer to calculate the pressure variations in unsteady pipe flows. This paper describes the life and work of Dutchmen Isebree Moens and Korteweg. Their doctoral dissertations (in Dutch) are partly translated, reviewed and compared with their key publications (in German). Korteweg gave Moens’ semi-empirical wavespeed a mathematical basis and he made the first contributions toward the study of fluid-structure interaction and unsteady friction. Their work is placed in historical context, in terms of both their predecessors and contemporaries, and also how it was subsequently built on by their successors in different disciplines

Thomas Young's research on fluid transients : 200 years on

Thomas Young published in 1808 his famous paper (1) in which he derived the pressure wave speed in an incompressible liquid contained in an elastic tube. Unfortunately, Young's analysis was obscure and the wave speed was not explicitly formulated, so his achievement passed unnoticed until it was rediscovered nearly half a century later by the German brothers Weber. This paper briefly reviews Young's life and work, and concentrates on his achievements in the area of hydraulics and waterhammer. Young's 1808 paper is "translated" into modern terminology. Young's discoveries, though difficult for modern readers to identify, appear to include most if not all of the key elements which would subsequently be combined into the pressure rise equation of Joukowsky

Experimental and numerical analysis of water hammer in a large-scale PVC pipeline apparatus

This paper investigates the effects of the pipe-wall viscoelasticity on water-hammer pressures. A large-scale pipeline apparatus made of polyvinyl chloride (PVC) at Deltares, Delft, The Netherlands, has been used to carry out waterhammer experiments. Tests have been conducted in a reservoir-pipe-valve system with a 275.2 m long DN250 PVC pipeline. Rapid closure of a manually operated ball valve at the downstream end generated water hammer. Computed results are compared with experimental runs. Calibrated creep functions have been obtained using optimization in conjunction with an inverse hydraulic transient solver and these are used in the simulations. It is shown that the incorporation of both unsteady skin friction and viscoelastic pipe wall mechanical behaviour in the hydraulic transient model contributes to a favourable fitting between numerical results and observed data. Keywords: Water hammer, Unsteady Skin Friction, Viscoelasticity, Pipeline Apparatus, PVC Pipe

Experimental and numerical analysis of water hammer in a large-scale PVC pipeline apparatus

This paper investigates the effects of the pipe-wall viscoelasticity on water-hammer pressures. A large-scale pipeline apparatus made of polyvinyl chloride (PVC) at Deltares, Delft, The Netherlands, has been used to carry out waterhammer experiments. Tests have been conducted in a reservoir-pipe-valve system with a 275.2 m long DN250 PVC pipeline. Rapid closure of a manually operated ball valve at the downstream end generated water hammer. Computed results are compared with experimental runs. Calibrated creep functions have been obtained using optimization in conjunction with an inverse hydraulic transient solver and these are used in the simulations. It is shown that the incorporation of both unsteady skin friction and viscoelastic pipe wall mechanical behaviour in the hydraulic transient model contributes to a favourable fitting between numerical results and observed data. Keywords: Water hammer, Unsteady Skin Friction, Viscoelasticity, Pipeline Apparatus, PVC Pipe

Simulating water hammer with corrective smoothed particle method

The corrective smoothed particle method (CSPM) is used to simulate water hammer. The spatial derivatives in the water-hammer equations are approximated by a corrective kernel estimate. For the temporal derivatives, the Euler-forward time integration algorithm is employed. The CSPM results are in good agreement with solutions obtained by the method of characteristics (MOC). A parametric study gives insight in the e¿ects of particle distribution, smoothing length and kernel function. Three typical water-hammer problems are solved. CSPM will not beat MOC in classical water-hammer, but it has potential for water-hammer problems with free surfaces as seen in column separation and slug impact

Analysis of beat phenomena during transients in pipelines with a trapped air pocket

Trapped gas pockets may cause severe operational problems in liquid piping systems. The severity of the resulting transients depends on the size and position of the trapped air pocket. Previous numerical simulations by the authors have indicated that a beat is possible to develop for ‘medium’ size air pockets. This paper investigates the beat phenomenon in detail, both theoretically and experimentally. Trapped air pockets are incorporated as boundary conditions (discrete gas cavities) into two distinct numerical solution schemes: (1) the method of characteristic scheme (MOC) and (2) a conservative solution scheme (CSS). The classical discrete gas cavity model (DGCM) allows gas cavities to form at computational sections in the MOC. A discrete gas cavity is governed by the water hammer compatibility equations, the continuity equation for the gas cavity volume, and the equation of state of an ideal gas. A novel CSS-based DGCM solves the system of unsteady pipe flow equations and respective state equations for four dependent variables (pressure, density, cross-sectional area, flow velocity) rather than two variables (pressure, flow velocity) in the classical MOC approach. In the MOC-based DGCM, the Courant number is equal to unity. This condition is difficult to fulfil (without using interpolations) in complex pipe networks without modification of wave speeds and/or pipe lengths. The CSS-based DGCM offers flexibility in the selection of computational time and space steps, however, the numerical weighting coefficients in the scheme should be carefully selected. Both models incorporate a convolution-based unsteady friction model. Experimental investigations of beat phenomena have been carried out in the University of Adelaide laboratory apparatus (reservoirpipeline- valve system). A trapped air pocket is captured at the midpoint of the pipeline in a specially designed device. The transient event is initiated by rapid closure of a side-discharge solenoid valve. Predicted and measured results are compared and discussed. It is shown that the fully-developed beat is strongly attenuated by unsteady friction and not so by steady friction