Simulating unsteady conduit flows with smoothed particle hydrodynamics

Pipelines are widely used for transport and cooling in industries such as oil and gas, chemical, water supply and sewerage, and hydro, fossil-fuel and nuclear power plants. Unsteady pipe flows with large pressure variations may cause a range of problems such as pipe rapture, support failure, pipe movement, vibration and noise. The unsteady flow is generally caused by flow velocity changes due to valve or pump operation. Water hammer is the best known and extensively studied phenomenon in this respect. Fast transient may also occur in rapid pipe filling and emptying processes. Due to high driving heads, the advancing liquid column may achieve a high velocity. When this high-velocity column is blocked or restricted in its flow, high water-hammer pressures may result. Another scenario is that of slug flow, which arguably is the most dangerous type of two-phase pipe flow. Heavy isolated liquid slugs travelling at high speed behave like cannonballs. Damage is likely to happen when these slugs impact on barriers such as pumps, bends and partially closed valves. Advancing liquid columns occurring in rapid pipe filling and emptying can be seen as a special case of isolated slugs. In this thesis, we present a Lagrangian particle method for solving the Euler equations with application to water hammer, rapid pipe filling and emptying, and isolated slugs travelling in an empty pipeline. As a meshfree method, the smoothed particle hydrodynamics (SPH) used herein is suitable for problems encompassing moving boundaries and impact events, which are the common features of the concerned topics. We first present the kernel and particle approximation concepts, which are two essential steps in SPH. Based on numerical approximation rules, the SPH discrete form of the Euler and Navier-Stokes equations are derived. To treat various boundary conditions, we apply several types of image particles that are particularly designed to complete the kernels truncated by system boundaries. The global conservation of mass and linear momentum is then demonstrated. The SPH errors in the integral approximation and summation approximation are analyzed based on given particle distribution patterns. Several other problems such as particle clustering, tensile instability, particle boundary layer and lacking of polynomial reproducing abilities (incompleteness) are also discussed together with possible remedies. Before applying the implemented particle solver to the thesis topics, we first thoroughly test it against a selection of two-dimensionale benchmarks, which have close relationship with the concerned problems. They include dam-break, jet impinging onto an inclined plane, emerging jet under gravity, free overfall and flow separation at bends. Good agreements with analytical and numerical solutions in literature are found. The convergence rate of SPH is shown to be of first order, which is consistent with the theoretical analysis. For the rapid pipe filling problem, we apply the 1D SPH solver to the experiment of Liou & Hunt [114]. The velocity head at the inlet has to be taken into account to obtain a good agreement with the experiment. Water elasticity does not play a role and the friction formulation for steady state flows can be used. Head transition analysis provides deeper insight into the hydrodynamic behaviour in the filling process. As a special case of pipe filling, water hammer due to liquid impact at partially and fully closed valves is studied. The results agree well with standard MOC solutions. Similar observations are made for the rapid emptying process. For the isolated slug travelling in a voided pipeline and impacting on a bend, we apply the 1D and 2D SPH solvers to the experiments of Bozkus [24]. To obtain the arrival velocity of the slug at the elbow, a 1D model including mass loss at the slug tail is used. In the slug impact, flow separation at the bend plays a vital role, which is typical 2D flow behaviour at a geometrical discontinuity. With the flow contraction coefficient obtained from 2D SPH solutions, the improved 1D model gives good results for the reaction force, not only in magnitude but also its duration and shape. Finally, to study the evolutions of air/water interface and its possible effect on filling and emptying processes, a new experimental study is performed in a large-scale pipeline. It is found that in filling the water front tends to split into two fronts propagating with different velocities. This results in air intrusion on top of a water platform. In emptying, flow stratification occurs at the water tail. Consequently, the validated assumption of vertical air/water interfaces for small-scale system with high driving head may not be applicable to large-scale systems. The interface evolution does not play an important role in pipe filling, the overall behaviour of which can be well predicted with 1D SPH solutions. However, flow stratification largely affects the overall draining process.