• Manev Nikola Military Academy “General Mihailo Apostolski” – Skopje, University "Goce Delčev" in Štip, Vasko Karangeleski bb, Skopje, Republic of North Macedonia
  • Dimitrovski Dame Faculty of Mechanical Engineering, “Ss. Cyril and Methodius” University in Skopje, P.O. Box 464, MK-1001, Skopje, Republic of North Macedonia
  • Mirakovski Zoran Faculty of Mechanical Engineering, “Ss. Cyril and Methodius” University in Skopje, P.O. Box 464, MK-1001, Skopje, Republic of North Macedonia
  • Jovcevski Igor Faculty of Mechanical Engineering, “Ss. Cyril and Methodius” University in Skopje, P.O. Box 464, MK-1001, Skopje, Republic of North Macedonia




free surface flow, computational fluid dynamics, Pelton turbine, Lattice Boltzmann Method


Computational fluid dynamics (CFD) has become an indispensable tool in the development and optimization of various machines and devices in the last decade. In most cases, researchers deal with single-phase flows and internal flows where all externally wetted walls are defined. In some cases, it is also necessary to analyze multiphase flow and free-surface flow. Using classical numerical methods such as the finite element method (FEM) or the finite volume method (FVM), the results are highly dependent on the size and quality of the computational grids. Particular attention should be paid to the conditions at the boundary between the individual phases of the fluid. In most cases, it is necessary to consider non-stationary conditions and the necessity of using non-stationary numerical methods. All the above properties of multiphase flows and their consequences in performing numerical analyses lead us to very long computational times and consequently the use of very powerful computers. Industry often needs results in a relatively fast time therefore many simplifications need to be considered. Recently a new approach for numerical simulations of multiphase and free-surface flows based on the Lattice Boltzmann method (LBM) started to be used. The method is very useful especially for development of small-scale hydraulic turbines, where the expense for development process is usually very limited. In this paper, some examples of the use of LBM in the calculation of free-surface flows and compare the results using classical CFD methods have been presented.


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