An explicit, non-iterative, single equation formulation for an accurate one dimensional estimation of vaneless radial diffusers in turbomachines

The present paper proposes a very simple one dimensional (1-D) model that accounts for the energy loss caused by the fluid dynamic losses occurring in the vaneless diffusers of centrifugal compressors and pumps. Usually, the present techniques to design turbomachines (pumps, compressors and turbines) emphasize numerical methods and their use is relatively complex because several parameters need to be chosen and a lot of time is required to perform the calculation. For this reason, it is relevant to perform an accurate preliminary design to simplify the numerical computation phase and to choose a very good initial geometry to be used for accelerating and improving the search for the definitive geometry. However, today 1-D modeling is based on the classical theory that assumes that the angular momentum is conserved inside a vaneless diffuser, although the flow evolution is considered as non-isentropic. This means that fluid-dynamic losses are taken into account only for what concerns pressure recovery, whereas the evaluation of the outlet tangential velocity incoherently follows an ideal behavior. Starting from such considerations, a new conservation law for the angular momentum is analytically derived, which incorporates the same fluid-dynamic losses modeled by the thermodynamic transformation law that is employed for correlating pressure recovery with enthalpy increase. Similar arguments hold for incompressible flows. Detailed and very accurate three-dimensional flow simulations are employed to analyze if the new model is capable of predicting the outlet tangential velocity more accurately than the classical theory. Results provided for both compressible (centrifugal compressors) and incompressible (centrifugal pumps) flows and for different inlet velocity profiles show a significant accuracy improvement of the new conservation law in the prediction of the outlet flow conditions when compared with the classical theory, thus demonstrating that the proposed model can be employed in the preliminary design of vaneless diffusers (i.e., in the estimation of the outlet diameter) more effectively than the classical ideal theory. Furthermore, the model is validated against industrial experimental campaigns. Even further experimental data, reported in a previous paper by the same authors, confirm the reliability of the employed approach.