Best-estimate water hammer simulations to avoid the calculation of unrealistically high loads or unphysical pressure and force peaks

Abstract

For safety-related systems fluid loads due to fluid transients have to be quantified for subsequent structural analyses to ensure their integrity or function, as required. Usually transient fluid loads in pipe systems are determined with one-dimensional water hammer software. For single-phase liquid flow, the method of characteristics (MOC) is often used that gives in this case appropriate results. For the consideration of local vapor bubbles, the MOC is combined with the discrete vapor cavity model (DVC). The DVC model may generate unrealistic pressure spikes due to the calculation of the collapse of multi-cavities in scenarios, where only one vapor bubble should actually occur. The application of a two-phase code may improve the calculation results. One requirement for the latter codes is the ability to calculate the propagation of steep gradients without suffering from numerical diffusion to exclude the underestimation of fluid loads. This is commonly attained by applying higher-order numerical schemes. However, the application of a numerical method of pure 2nd order leads to the calculation of unphysical oscillations at steep gradients causing severe problems during the solution. To exclude this, numerical methods with flux limiters can be used. With their application, the calculation of unrealistically high loads due to numerical deficiencies can be minimized. In addition, the consideration of further physical effects, that lead to the reduction of loads during transient flow processes, allows for a more realistic calculation of the loads. These are unsteady friction, widening of the pipe caused by pressure increase, fluid-structure interaction at junctions and due to friction, degassing of gas that is initially dissolved physically in a liquid and thermodynamic non-equilibrium during vapor bubble collapse. The in-house code DYVRO applies a second-order accurate scheme with flux limiters based on the Godunov method and can account for the above-described physical phenomena. It is shown by comparison of calculation results obtained by DYVRO with experimental data from literature that with modeling of these physical effects the loads can be calculated more realistically. Generally, these loads are lower than the results calculated by simplified models, which do not account for these effects. Considering that these loads are applied in subsequent structural analyses, cost-intensive oversizing of pipes and their supports can be avoided, by ensuring the necessary safety.