IMPROVED LUMPING FRICTION MODEL FOR LIQUID PIPE FLOW

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.

[1]  W. Zielke.  Frequency dependent friction in transient pipe flow , 1968 .

[2]  D. Seiler.  Fluid Flow and Rotating EquipmEnt Special RepoRt , 2007 .

[3]  Z. Zarzycki.  Hydraulic resistance of unsteady turbulent liquid flow in pipes , 1997 .

[4]  Adam Adamkowski,et al.  A New Method for Numerical Prediction of Liquid Column Separation Accompanying Hydraulic Transients in Pipelines , 2007 .

[5]  Jim Brown,et al.  Evaluation of Unsteady Wall Shear Stress by Zielke’s Method , 2010 .

[6]  Angus R. Simpson,et al.  Large water-hammer pressure for column separation in pipelines , 1991 .

[7]  Adam Adamkowski,et al.  Investigation of Hydraulic Transients in a Pipeline with Column Separation , 2012 .

[8]  C F Colebrook,et al.  TURBULENT FLOW IN PIPES, WITH PARTICULAR REFERENCE TO THE TRANSITION REGION BETWEEN THE SMOOTH AND ROUGH PIPE LAWS. , 1939 .

[9]  G. A. Schohl,et al.  Improved approximate method for simulating frequency-dependent friction in transient laminar flow , 1993 .

[10]  F. T. Brown,et al.  The Transient Response of Fluid Lines , 1962 .

[11]  D. Nigel Johnston.  Efficient Methods for Numerical Modelling of Laminar Friction in Fluid Lines , 2004 .

[12]  A. Vardy,et al.  Transient turbulent friction in fully rough pipe flows , 2004 .

[13]  A. K. Trikha,et al.  An Efficient Method for Simulating Frequency-Dependent Friction in Transient Liquid Flow , 1975 .

[14]  D N Johnston.  Efficient Methods for Numerical Modeling of Laminar Friction in Fluid Lines , 2004 .

[15]  Adam Adamkowski,et al.  Experimental Examination of Unsteady Friction Models for Transient Pipe Flow Simulation , 2006 .

[16]  K. Urbanowicz,et al.  Convolution integral in transient pipe flow , 2012 .

[17]  A. Vardy,et al.  TRANSIENT TURBULENT FRICTION IN SMOOTH PIPE FLOWS , 2003 .