Numerical methods for compressible flows in compliant tubes

Among the numerical schemes, the Method of Characteristics is the preferred method by Engineers for the resolution of transient fluid flows in pipes. Only in the last years, the availability of very efficient and robust numerical schemes for the complete system of equations, such as recent Finite Volume Methods (FVM), has encouraged the adoption of different numerical schemes also in these contexts. This choice allows for a better representation of the physics of the phenomena without neglecting the contribution of the convective terms. A wide and critical comparison of the capability of Method of Characteristics (MOC), Explicit Path-Conservative (DOT solver) FVM and Semi-Implicit (SI) staggered FVM, for the resolution of hydraulic transients in flexible tubes, is presented and discussed in the event of a water hammer in a high density polyethylene (HDPE) pipe. The viscoelastic mechanical behaviour of the tube material is taken into account through a Standard Linear Solid rheological Model. Results are shown in terms of accuracy, against experimental data, and in terms of efficiency. All the numerical methods show a good agreement with the reference data and a high efficiency of the MOC is observed. Moreover, three Riemann Problems (RP), for which a quasi-exact solution is available if considering only an elastic wall behaviour, were chosen and run to stress the numerical methods, taking into account cross-sectional changes, more flexible materials (e.g. rubber) and a cavitation case. In these demanding scenarios, the weak spots of the classical formulation of the Method of Characteristics are depicted, suggesting a less robustness of this method in comparison to the other two FVM analysed. To obtain adequate solutions for more complex configurations, indeed, it is not possible to apply the MOC in its simplest form: the code needs to be rearranged for the specific request and, even so, in the event of cavitation, the MOC presents difficulties in the correct capture of the discontinuities inherent in the Riemann problem.