1. Modelling of turbulent flows with a disperse phase.

Within this area of study, models are developed and new proposal for turbulent flows with the dispersed phase (droplets, solid particles).

Closures for ensemble-averaged or spatially-filtered transport equations for turbulent flows, including two-phase flows, are analysed, new proposals are put forward and validated. The interest is focused on statistical approach with the use of probability density function (PDF) methods, modelling turbulent dispersion of particles in the Reynolds-averaged (RANS) description, as well as the residual (sub-grid scale) dispersion while the larger-scale structures of turbulent flow are resolved (LES, POD).

Practical importance of these studies relates to problems of chemical and process engineering, as well as conventional and distributed power production (eg. liquid fuel and coal powder industrial burners).


Particle-laden turbulent flow: coaxial confined jet,
snapshot, LES results (Łuniewski, 2011).

2. Methods for design and analysis of flow systems for small water turbines.

Research focuses on numerical modelling and analysis of three-dimensional flows in hydraulic machines. New computational models of flows around bodies of any shape are proposed, followed by the development of computer programs based on them.

This enables one to compute the velocity field and to calculate the surface pressure distribution on bodies generating lift forces. Previously developed vortex models for the design of marine propellers are adapted to free turbines and verified by tests in the cavitation tunnel. Currently, inverse methods for viscous/turbulent flows are in development. The methods are based on the transformation of Navier-Stokes equations to stream-function coordinates (SFC, von Mises). The transformation makes it possible to eliminate one geometrical variable (unknown in design problem). Instead, the stream function appears as a new coordinate dependent on flow velocity.

Additionally, work is carried on regarding the use of optimisation methods in conjunction with inverse methods for design of blading systems in water turbines.

Inverse problem: stream surfaces in blading system (Butterweck, 2012).

3. Computational methods for flows with interfaces.

An alternative approach to flow modelling is the use of a fully Lagrangian formalism, for example the Smoothed Particle Hydrodynamics (SPH).
The SPH method is increasingly often used for analysis of multiphase flows, flows with free surface, or systems with complex or variable geometry. The main advantage of SPH is no need of numerical grid. Continuous distributions of physical quantities are replaced by the corresponding integral approximations. The liquid is treated as a finite set of particles (representing fluid elements), for which calculations are made.

At the beginning, the big challenge was to perform the analysis which would allow us to compare various methods for the implementation of incompressibility constraint in SPH. Therefore, we performed a series of numerical tests, including a dual correction (for velocity and density), which is a qualitatively new solution and proves to be the only one of the proposals based on the projection method which gives accurate predictions of density fields in SPH. To achieve fully physical simulations of multiphase gas-liquid flows, where the processes occurring at the interface play a key role, several approaches have been implemented to allow modelling of surface tension. The simulation results of gas bubble rising in the liquid for different values of surface tension are in a very good agreement with the solutions obtained by other numerical methods and, also, experiments.

Presently, the work focuses on the development of the SPH approach for the case of nucleate boiling. The correct numerical modeling of phase-change issues involves the implementation of a number of physical phenomena, including nucleation, growth and detachment of vapor bubbles, transition to different boiling regimes with increasing heat flux through the wall. In addition, due to the Eulerian nature of the most commonly used methods, a major difficulty is the numerics, in particular the interface location tracking whose knowledge is crucial for the proper modelling of phase transitions. It is also required to take account of heat transfer in heterogeneous systems (in terms of thermodynamic properties).  SPH method, because of its Lagrangian nature, is ideally suited for this purpose. We have implemented the heat transport mechanisms, including free convection phenomena in the Boussinesq approximation. However, for systems where temperature differences cause large density differences, the Boussinesq approximation fails. Such situations often occur in industrial processes (e.g., die casting) and in astrophysics. Therefore, we proposed a qualitatively new technique of modeling convection in the SPH formalism.


Coalescence of two bubbles rising in liquid: SPH simulation (Szewc, 2012).

4. Numerical modelling of flow thermomechanics in granular media.

Research focuses on modelling of  flow and heat transfer in porous media. The practical motivation is to improve the coking process of coal.

For the purpose, the Lattice Boltzmann Method (LBM) is used to simulate the phenomena of fluid flow, heat transfer, plastic deformation and chemical reactions on a mesoscale level of a few grains. The LBM is promising for the simulations of viscous fluid flow and heat transfer in media with complex geometry.

Recently published work shows that LBM can also be used in a various and interesting engineering applications (internal combustion, flow of blood red cells, etc.). At present, the fluid flow and heat transfer are analysed in a granular medium with grains of temperature-affected geometry. Research is underway to add stresses at the contact surface of grains (structure-structure interactions) and to model chemical reactions with additional source terms.



Flow through simple model of porous media, LBM computation (Grucelski, 2012).