Correction Factors for the Use of 1D Solution Methods for Dynamic Laminar Liquid Flow through Curved Tubes

The modeling of transient flows of liquids through tubes is required for studies in water hammer, switched inertance hydraulic converters, and noise reduction in hydraulic equipment. While 3D gridded computational fluid dynamics (CFD) methods exist for the prediction of dynamic flows and pressures in these applications, they are computationally costly, and it is more common to use 1D methods such as the method of characteristics (MOC), transmission line method (TLM), or frequency domain methods. These 1D methods give good approximations of results but require many orders of magnitude less computation time. While these tubes are typically curved or coiled in practical applications, existing 1D solution methods assume straight tubes, often with unknown deviation from the curved tube solution. This paper uses CFD simulations to determine the correction factors that can be used for existing 1D methods with curved tubes. The paper also presents information that can be used to help evaluate the expected errors resulting from this approximation.