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1

Improved lumping friction model for liquid pipe flow

Urbanowicz K., Zarzycki Z.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 2

295--305

EN

Normally, during one-dimensional pipe flow, the friction terms are calculated with the use of a numerical method (for example MOC – method of characteristics) at every computational node along the pipe and at every time step. This procedure tends to increase the computational effort greatly. A considerable increase in computational speed can be archived by calculating the frequency-dependent friction at the end of the pipe only. To avoid possible problems (no damping at closed walls, underestimate damping on high impedance components) the frequency-dependent friction term is calculated from the flow waves. The lumping friction model in this work is based on a modificated Schohl convolution integral solution. In addition, the work examined the impact of using of simplified effective weighting function on the obtained results of numerical simulations. The modified method in conjunction with the use of simplified weighting function allow determination of real-time estimate of the basic parameters representing the fluid flow in complex hydraulic systems, water supply, etc.

2

A numerical approach to the standard model of water hammer with fluid-structure interaction

Henclik S.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

543--555

EN

In the classic water hammer (WH) theory, 1D liquid flow in a quasi-rigid pipe is assumed. When the pipe is flexible or is fixed to the foundation with elastic supports, the dynamic fluid structure interaction (FSI) should be taken into account for more accurate modelling of the system behaviour. The standard model of WH-FSI for a straight pipe reach is governed by fourteen hyperbolic partial differential equations of the first order, two for 1D liquid flow and twelve for 3D motion of the pipe. This model is presented in the paper and an algorithm for its numerical solution based of the method of characteristics is proposed. Basic boundary conditions (BC) are shortly discussed. The important condition at the junction of two subpipes fixed to the foundation with a viscoelastic support is presented in details and a general method of its solution is proposed.

3

Universal weighting function in modeling transient cavitating pipe flow

Urbanowicz K., Zarzycki Z., Kudźma S.

Journal of Theoretical and Applied Mechanics

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2012

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Vol. 50 nr 4

889-902

EN

This work concerns modeling of time-varying resistance during transient cavitating liquid pipe flow. The wall shear stress is presented in the way introduced by Zielke as the integral convolution of liquid local velocity changes and a weighting function. A new procedure for determination, so-called, a universal laminar-turbulent weighting function, which combines functions of Zielke and Vardy and Brown or Zielke and Zarzycki, is presented. Based on these weighting functions, the method of simulation transients in the pressure lines in a wide range of Reynolds numbers is presented. It eliminates numerical problems associated with the change of laminar flow into turbulent and vice versa. An example application of this method for simulation of water hammer is presented. The calculation results are compared against experiments presented by Bergant and Simpson, and good agreement is found.

PL

Praca dotyczy modelowania zmiennych w czasie oporów podczas nieustalonego przepływu cieczy w przewodach ciśnieniowych. Naprężenie styczne na ściance przewodu przedstawione zostało w klasyczny sposób (wg. Zielke) jako całka splotowa z przyśpieszenia cieczy i pewnej funkcji wagowej. Przedstawiono procedury wyznaczania dwóch uniwersalnych funkcji wagowych laminarnoturbulentnych (wg. Zielke i Vardy-Browna oraz wg. Zielke i Zarzyckiego).W oparciu o te funkcje przedstawiono metodę modelowania (symulacji) przebiegów przejściowych w przewodach ciśnieniowych w szerokim zakresie liczb Reynoldsa. Eliminuje on problemy natury numerycznej związane z przechodzeniem min. z przepływu laminarnego w turbulentny i odwrotnie. Podano przykład zastosowania opracowanej metody do symulacji uderzenia hydraulicznego. Wyniki obliczeń porównano z wynikami eksperymentalnymi wg. Berganta i Simpsona, otrzymując dobrą zgodność.

4

Mathematical model and numerical computations of transient pipe flows with fluid-structure interaction

Henclik S.

Transactions of the Institute of Fluid-Flow Machinery

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2010

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nr 122

77-94

EN

Transient flows in closed conduits are of interest from over a century, but the dynamic interaction between the fluid and the pipe is taken into consideration more thoroughly just from a few decades. A standard model of the phenomenon consists of fourteen first order partial differential equations (PDE), two for a one-dimensional (1D) liquid flow and twelve for 3D pipe motion. In many practical cases however, a simpler four equations (4E) model can be used, where 1D longitudinal pipe movement is assumed. A short description of waterhammer event with fluidstructure interaction taken into account is presented in the article. The 4E mathematical model is presented in detail with the assumptions and main algorithms of computer program that has been developed. Two phase flow is assumed not to take place, but the friction between the liquid and the pipe wall are taken into consideration. A method of characteristics (MOC) with time marching procedure is employed for finding the solutions, but instead of direct solving the resulting finite difference equations (FDE) the “wave method” is proposed. Some other important elements of the algorithm are presented and selected results of numerical computations as well.