Simulating unsteady conduit flows with smoothed particle hydrodynamics Citation for published version (APA): Hou, Q. (2012). Simulating unsteady conduit flows with smoothed particle hydrodynamics. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR733420 DOI: 10.6100/IR733420 Document status and date: Published: 01/01/2012 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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A catalogue record is available from the Eindhoven University of Technology Library Proefschrift. - ISBN: 978-90-386-3167-7 NUR 919 Subject headings: initial boundary value problems; moving boundaries; channel flows; two-phase flows; waterhammer; pipe filling and emptying; isolated slug; smoothed particle hydrodynamics 2010 Mathematics Subject Classification: 65D07, 65D10, 65N15, 65N35, 76B10, 76D05, 76D50, 76M28, 76T10 The work described in this thesis has been financially supported by the China Scholarship Council (CSC). Simulating Unsteady Conduit Flows with Smoothed Particle Hydrodynamics PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op maandag 25 juni 2012 om 16.00 uur door Qingzhi Hou geboren te Shandong, China Dit proefschrift is goedgekeurd door de promotor: prof.dr. R.M.M. Mattheij Copromotor: dr.ir. A.S. Tijsseling Summary 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 rupture, support failure, pipe movement, vibra- tion 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 exten- sively studied phenomenon in this respect. Fast transients may also occur in rapid pipe filling and emptying processes. Due to high driving heads, the ad- vancing liquid column may achieve a high velocity. When this high-velocity col- umn 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 be- have 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 equa- tions with application to water hammer, rapid pipe filling and emptying, and iso- lated slugs travelling in an empty pipeline. As a meshfree method, the smoothed particle hydrodynamics (SPH) used herein is suitable for problems encompass- ing 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 dis- crete form of the Euler and Navier-Stokes equations are derived. To treat var- ious 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 analysed based on given particle distribution patterns. Other problems such as particle clustering, tensile instability, particle boundary layer and lacking of poly- nomial reproducing abilities (incompleteness) are also discussed together with possible remedies. vi Summary Before applying the implemented particle solver to the thesis topics, we first thor- oughly test it against a selection of two-dimensionale benchmarks, which have a close relationship with the concerned problems. They include dam-break, jet im- pinging 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 laboratory experiment of Liou & Hunt [116]. 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 of 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 laboratory 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 a 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 evolution of air/water interfaces and its possible effect on fill- ing 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 1D assumption of vertical air/water interfaces for small-scale systems with relatively high driving head may not be applicable to large-scale systems. The interface evolution does not play an important role in filling, the overall behaviour of which can be well predicted with 1D SPH solu- tions. However, flow stratification largely prolongs the overall draining process. Samenvatting Pijpleidingen worden gebruikt voor transport en koeling in de olie- en gasin- dustrie, in de chemische industrie, voor watervoorziening en riolering, en in en- ergiecentrales werkende op waterkracht, fossiele brandstof of kernreacties. In- stationaire buisstromingen met grote drukvariaties kunnen een scala aan prob- lemen veroorzaken, zoals lei-dingbreuk, schade aan verankering en ophanging, verplaatsing van buizen, trillingen en lawaai. De instationaire stroming wordt meestal veroorzaakt door veranderingen van de vloeistofsnelheid ten gevolge van het manipuleren van kleppen of pompen. Waterslag is het bekendste en meest bestudeerde verschijnsel op dit gebied. Waterslag kan ook optreden bij het snel vullen en legen van leidingen. Bij een hoge aandrij-vende druk kan de bewegende vloeistofmassa een grote snelheid bereiken. Wanneer zo’n hoge- snelheidsmassa botst op een blokkade of lokale weerstand, kan dit resulteren in waterslag en de bijbehorende hoge drukvariaties. Een ander scenario is dat van propstroming, mogelijk de meest gevaarlijke vorm van twee-fasenstroming. De zware vloeistofproppen die zich verplaatsen met hoge snelheid zijn te vergeli- jken met kanons-kogels. Schade is bijna onvermijdelijk wanneer een dergelijke prop botst op een pomp, een bochtstuk of een gedeeltelijk gesloten kleplichaam. De bewegende vloeistofmassa’s bij het vullen en ledigen van leidingen mogen beschouwd worden als een speciaal geval van de ge¨ısoleerde prop. Dit proefschrift beschrijft een Lagrangiaanse deeltjesmethode voor het oplossen van de Euler vergelijkingen met toepassing op het gebied van waterslag, het snel vullen en legen van leidingen en de beweging van ge¨ısoleerde vloeistofproppen in een verder lege buis.