Godunov-Type Solutions for Transient Pipe Flow Implicitly Incorporating Brunone Unsteady Friction

An approach combining the Brunone unsteady friction model and first- and second-order Godunov-type scheme (GTS) is developed to simulate transient pipe flow. The exact solution to the Riemann problem calculates the mass and momentum fluxes while implicitly considering the Brunone unsteady friction factor. The boundary cells can either be computed by applying the Rankine–Hugoniot condition or through virtual boundary cells adapted to achieve a uniform solution for both interior and boundary cells. Predictions of the proposed model are compared both with experimental data and with method of characteristics (MOC) predictions. Results show the first-order GTS and MOC scheme have identical accuracy, but both approaches sometimes produce severe attenuation when used with small Courant numbers. The presented second-order GTS numerical model is more accurate, stable, and efficient, even for Courant numbers less than one, a particularly important attribute for unsteady-friction simulations, which inevitably create numerical dissipation in both the MOC and proposed first-order Godunov-type schemes. In fact, even with a coarse discretization, the new second-order GTS Brunone model accurately reproduces the entire experimental pressure oscillations including their physical damping in all transient flows considered here.