Modeling of unsteady friction and viscoelastic damping in piping systems

In real systems, the phenomena, such as pipe-wall viscoelasticity, unsteady friction or fluid structure interaction induce additional damping and dispersion of transient pressure waves than that defined by classical waterhammer. In this paper, unsteady friction models and viscoelastic damping models will be presented and a theoretical formulation of the viscoelastic damping in piping systems without cavitation will be developed. Firstly, the friction factor will be presented as the sum of the quasi-steady part and the unsteady part related to the instantaneous local acceleration and instantaneous convective acceleration. This unsteady friction model has been incorporated into the method of characteristic algorithm (MOC). Secondly, the damping will be defined in terms of viscoelastic effect attributed to a second viscosity µ’. This model is solved using the Finite Difference Method. Finally, numerical results from the unsteady friction and viscoelastic models are compared with results of laboratory measurements for waterhammer cases with low Reynolds number turbulent flows. This comparison validates the new viscoelastic model.

[1]  Alan Vardy,et al.  A characteristics model of transient friction in pipes , 1991 .

[2]  Ivan Stoianov,et al.  Water hammer in pressurized polyethylene pipes: conceptual model and experimental analysis , 2004 .

[3]  Angus R. Simpson,et al.  Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines , 2006 .

[4]  E. Benjamin Wylie,et al.  Fluid Transients in Systems , 1993 .

[5]  Mohamed Salah Ghidaoui,et al.  Discussion of "Extended Thermodynamics Derivation of Energy Dissipation in Unsteady Pipe Flow" , 2001 .

[6]  Giuseppe Pezzinga,et al.  Unsteady flow in hydraulic networks with polymeric additional pipe , 2002 .

[7]  Christophe Nicolet,et al.  Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems , 2007 .

[8]  Huan-Feng Duan,et al.  Relevance of Unsteady Friction to Pipe Size and Length in Pipe Fluid Transients , 2012 .

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

[10]  A. Vardy,et al.  Transient, turbulent, smooth pipe friction , 1995 .

[11]  J. Vítkovský,et al.  Developments in unsteady pipe flow friction modelling , 2001 .

[12]  Cedo Maksimovic,et al.  The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II—model development, calibration and verification , 2005 .

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

[14]  Giuseppe Pezzinga,et al.  EVALUATION OF UNSTEADY FLOW RESISTANCES BY QUASI-2D OR 1D MODELS. TECHNICAL NOTE , 2000 .

[15]  Mohamed Salah Ghidaoui,et al.  Efficient Treatment of the Vardy–Brown Unsteady Shear in Pipe Transients , 2002 .

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