Dr. Carsten Thorenz (BAW), Dr. Peter VollmÃ¶ller (BAW), Dr. Jürgen Stamm (BAW)

As a basis for further work serves the existing flow solver NaSt3DGPF, a CFD package which is developed at the Institute of Numerical Simulation. Please refer to the NaSt3DGP homepage for details of the basic flow solver and information about NaSt3DGP, the free version of NaSt3DGPF. The basic solver NaSt3DGP has been extended by a level-set method for the simulation of two- and multiphase flows. Surface tension effects are taken into account by the Continuum Surface Force Method. Also NaSt3DGPF is able to handle complicated geometries, which is a prerequisite for applications resulting from hydraulic engineering problems.

As already mentioned in the introduction, most real-life flows around hydraulic constructions or watercrafts, especially the propulsion unit, are turbulent. Since the Direct Numerical Simulation (DNS) of turbulent phenomena still is not feasible due to the lack of compute power, a turbulence model is the only way to include such effects into a flow solver. We have chosen to implement a model based on Large-Eddy Simulation (LES), where, in contrast to classical more or less statistical approaches like Reynolds-Averaged Navier-Stokes (RANS), turbulent structures up to a specified scale are resolved directly, and only for smaller flow features on the so-called subgrid-scale, a model is used to describe their effects on the flow field. One major objective is to adapt the turbulence model based on the Smagorinsky approach to a two-phase flow model which is described by the level-set method. Here, special attention has to be turned on the behaviour of turbulent quantities near the free surface, where large jumps in material parameters occur.

To avoid too fine mesh resolutions near the boundaries of the domain, which could lead to numerical costs similar to that of a DNS, the turbulence model has to be accompanied by appropriate wall-functions. The wall-laws which are under investigation in this project should also offer the possibility to include different wall roughnesses, e.g. to model various materials on the slopes of waterways.

The datasets arising from parallel, three-dimensional time-dependent simulation runs are often too large for interactive visualization in the postprocessing stage. Therefore efficent strategies for adaptive handling of huge datasets during post-processing have to be applied.

Due to the aforementioned large jump in the material constants density and viscosity, which adversely affects the condition of the matrix arising from the discretization of the pressure Poisson equation, preconditioning is a basic requirement for the efficient solution of this linear system of equations. The current version of NaSt3DGPF employs a BiCGStab solver preconditioned by a block-Jacobi method. Further development plans include the application of a robust and efficient algebraic multigrid solver for the pressure Poisson equation.

Further project-related research topics include fluid-structure interaction between hydraulic constructions, floating bodies or propulsion units and the flow field. Also bidirectional coupling with various transport models for the simulation of sedimentary deposition is relevant to this project.

The above photograph shows a section of a simple sluice geometry. The CAD geometry data has been translated into input suitable for our flow solver NaSt3DGPF and first numerical studies have been performed on this test case. The figure shows a top-down view on the mesh of the simulated region, which is the inner section of the sluice between the two floodgates (marked by the red lines). As initial condition for the simulation of a filling process of the sluice a water column with the height of 2.25 meters at the upper floodgate and an inflow velocity of 3 meters per second were prescribed.

The above pictures show the free surface as well as the velocity field behind the upper floodgate after 10.5 seconds of physical time, the following figures show isolines of the velocity field in the main flow direction and the vertical flow direction , respectively, at the same time.

**Example 2:**

In this projekt the underlying geometry represents another more complex sluice building. After this rather complex CAD geometry data has been translated into the appropiate NaSt3DGPF readable file format, the computational grid generation itself was completed in a couple of minutes and allowed for a direct start of the simulation on a massive parallel computer without further manual domain decomposition treatments. Furthermore the two-phase flow model has recently been coupled with a large eddy turbulence model proposed by Smagorinsky.

The picture above shows a physical experiment with a scaled model of the sluice in Untertürkheim (taken from [4]). The pictures below show the converted geometry of a similar sluice on the left hand side and the free surface of the two phase (water/air) flow at the center and the free surface colored by the velocity on the right hand side.

Additionally our major task is to evaluate this large eddy turbulence model with experimental data of physical experiments like the backward facing step test for two-phase flow problems. The pictures below, taken from the BAW laboratory, show this experimental setup which serves for measurements in the future and comparisons to numerical simulations.

The main idea of large eddy turbulence models is based on the assumption that the anisotropic and inhomogeneous large-eddies have to be computed by direct numerical simulation (DNS), i.e. the grid resolution should be fine enough to resolve these large-eddies, while the effect of the isotropic and homogeneous small-eddies, which are generally smaller then the grid-resolution, are modelled by a subgrid stress tensor. This requested grid resolution down to the scale of isotropic and homogeneous eddies can still impose an high computational effort which can only be conquered by massive parallel computers. Hence, for reliable computations we parallelised this turbulence model as well, which enables us to examine and evaluate this model as accurate as possible in our ongoing research.

**Example 3:**

Another point of interest in the scope of federal waterways engineering consists in finding the optimal position for groins. A groin is a rigid structure built out from a shore to protect the shore from erosion, to trap sand, or to direct a current for scouring a channel. The left picture below shows groins located in the river Elbe (taken from [5]) and the right picture below shows the simulation of the velocity-field inbetween two groins. The velocity-field is visualised through a color map, which is projected onto the free surface, and a couple of additional velocity stream lines.

The simulation clearly shows at the red/blue boundary layer how the groins prevent the current velocity to diffuse and to become larger as the groins define and thus preventing it to loose more energy as wanted which would lead to a decrease in flow velocity.

[1] | J. Strybny, C. Thorenz, R. Croce, and M. Engel. A parallel 3d free surface navier-stokes solver for high performance computing at the german waterways administration. In The 7th Int. Conf. on Hydroscience and Engineering (ICHE-2006), Philadelphia, USA, September 2006. |

[2] | R. Croce, Ein paralleler, dreidimensionaler Navier-Stokes-Loeser für inkompressible Zweiphasenströmungen mit Oberflächenspannung, Hindernissen und dynamischen Kontaktflächen. Diplomarbeit, Institut für Angewandte Mathematik, Universität Bonn, 2002. |

[3] | J. Strybny, H. Nelles, Numerische 3D-Mehrphasenmodellierung zur Begutachtung von Hochwasserabflüssen im Nahfeld von Schleusen und Wehren. Wasserbauliche Mitteilungen, Heft 27, pp 411 - 422, Institut für Wasserbau und Technische Hydromechanik, TU Dresden, 2004. |

[4] | www.baw.de/vip/publikationen/Taetigkeitsberichte/Taetigkeitsbericht_2003/tb03_kap3_wasserbau_binnen.pdf |

[5] | http://www.elbetreff.de/ELBE/flussbauwerke/lassroenne1.jpg |