Numerical errors in discharge measurements using the KDP method

The kinetic differential pressure (KDP) method for measuring unsteady discharge in pressurized fluid conduits is introduced. The method utilizes two pressure measurements to estimate the unsteady discharge at the sampling rate of the pressure sensors. The technique is based on the linear approximation of the one-dimensional governing equations for transient flow. The application of the method is affected by two sources of error: the numerical error due to linear approximation of the one-dimensional governing equation and the modelling error representing the inability of the one-dimensional model to replicate the real transient behaviour. This research provides a first step in the verification of the KDP method by investigating the numerical error caused by the linear approximation. The numerical error is quantified as a function of the measurement location, system and signal characteristics. The method exhibits minor numerical errors if the system resonance is avoided.

[1]  Luisa Fernanda Ribeiro Reis,et al.  Analysis of PVC Pipe-Wall Viscoelasticity during Water Hammer , 2008 .

[2]  M.H. Sherif,et al.  An introduction to the analysis and processing of signals , 1985, Proceedings of the IEEE.

[3]  M. Pereira.  Flow meters: Part 1 , 2009, IEEE Instrumentation & Measurement Magazine.

[4]  Andrea Catania,et al.  Development and assessment of a new operating principle for the measurement of unsteady flow rates in high-pressure pipelines , 2009 .

[5]  Giuseppe Pezzinga.  Local Balance Unsteady Friction Model , 2009 .

[6]  H. S. Costa Mattos,et al.  Modelling of pipeline integrity taking into account the fluid–structure interaction , 1998 .

[7]  Angus R. Simpson,et al.  LEAK DETECTION IN PIPELINES USING THE DAMPING OF FLUID TRANSIENTS , 2002 .

[8]  R. S. Wick.  Applied Hydraulic Transients , 1981 .

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

[10]  M. Lambert,et al.  Detection and Location of a Partial Blockage in a Pipeline Using Damping of Fluid Transients , 2005 .

[11]  Silvia Meniconi,et al.  Experimental Evidence of Hysteresis in the Head-Discharge Relationship for a Leak in a Polyethylene Pipe , 2011 .

[12]  Angus R. Simpson,et al.  Leak location using the pattern of the frequency response diagram in pipelines: a numerical study , 2005 .

[13]  Kazuo Nakano,et al.  An Unsteady Flow Rate Measurement Method Utilizing Dynamic Characteristics between Pressure and Flow Rate along a Pipeline. A Method Using Pressures at Two Separated Points. , 1992 .

[14]  Pedro Lee,et al.  Quantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method , 2010 .

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

[16]  Miguel Dias Pereira.  Flow Meters: Part 1 Part 18 in a series of tutorials in instrumentation and measurement , 2009 .

[17]  Ichiro Asano,et al.  Analysis of pulsating flow measurement of engine exhaust by a Pitot tube flowmeter , 2005 .

[18]  H. Schock,et al.  An indirect technique for determining instantaneous flow rate from centerline velocity in unsteady duct flows , 2008 .

[19]  Xia Shuang,et al.  Flowmeter for large-scale pipes , 2009 .

[20]  K. Vairavamoorthy,et al.  Analysis of transient flow in pipelines with fluid–structure interaction using method of lines , 2005 .

[21]  Dimosthenis Trimis,et al.  Measurement of instantaneous flow rates in periodically operating injection systems , 1996 .

[22]  Satoshi Takahashi,et al.  Measurement of Transiently Changing Flow Rates in Oil Hydraulic Column Separation , 1996 .