Innovative numerical methods to investigate internal flow in screw compressors

The purpose of this work is study the behavior of the internal flow in screw compressors. These machines are widely use in refrigeration, air conditioning, automotive field and industrial applications since they are very reliable and can reach good efficiency. Screw compressor performances are affected mostly by the tooth profile. In particular, parameters as sealing line and blow hole area must be minimized. Unfortunately profile curves and geometrical parameters, such as undercutting limits, are usually not available in the literature due to the need of manufacturing companies to protect their know-how and so it is difficult to find validation test cases. Since screw compressor are very complex machines which involves either moving and fixed parts, the CFD study of their behavior is difficult because it is necessary to generate a suitable time-dependent grid which fully describes the change in shape of the control volume. This problem is overcome with the innovative strategy presented on this work. It is based on a penalization method integrated in a Discontinuous Galerkin spatial discretization. The main idea behind penalization techniques is to add a source term in the momentum and energy conservation. This term is active only inside the solid part of domain which is uniquely determined by a proper level set function. If the time evolution of the level set function is known then the fluid-structure interaction can be described with a fixed mesh. It is possible to see the penalization approach as a method to describe the flow in a porous media: where the porosity tends to zero the behavior of the solid body is reproduced. Unfortunately the penalization factor is linked to the mesh: if the mesh is highly refined, the penalization factor can be set smaller than it can be done with a coarse mesh. So a trade-off has to be achieved between acceptability of results, which depends on the case under study, and computational cost. The proposed approach is applied on various standard test cases in order to evaluate its reliability and accuracy. The first tests are performed on the unsteady flow around a circular cylinder: the classical body fitted approach and the chosen penalization technique are compared in terms of predicted drag coefficient and Strouhal number. Comparison are performed on the periodic flow at Re=100 and on the unsteady flow generated by an impulsively started cylinder. Good agreement is obtained between the two methods and the differences reduce when the mesh and the time step are refined. After that the flow in a 2D screw compressor is investigated. The goal is to compare results obtained from simulation, such as flow rate and power, with the data available in the literature. After some problems regarding the setting of a proper boundary condition and the presence of backflow, some preliminary results are obtained. In particular, the mass flow is compared with results available in literature showing good qualitative agreement. However, the difficulty to find both geometrical and experimental data in the literature for 2D configurations makes impossible to perform a direct validation. The present work represents a first step to pave the way towards a complete simulation of a screw compressor. Future work should be devoted to the extension to 3D problems and adaptive mesh approaches which will make it possible to simulate full scale configurations at high Reynolds number.