Reassessment of the Conventional: Numerical Validation of a One-Dimensional Model for the Prediction of Volute Losses

Abstract

The flow inside the volute of a centrifugal compressor is complex and three-dimensional. The fluid follows a swirling flow pattern, and under many operating conditions, the flow quantities are highly inhomogeneous in radial and circumferential directions. Despite the complex flow physics, the common one-dimensional approach to predict losses inside a volute is simple: The kinetic energy of each velocity component at volute inlet is charged with a loss coefficient. In case of the radial velocity, it is assumed to be constant, while the loss coefficient of the tangential velocity depends on whether the flow inside the scroll is de- or accelerated. In the former case, the loss of a sudden expansion is assumed, while in the latter case, it is presumed to be zero. The loss coefficient of the conical diffuser is also assumed to be equal to that of a sudden expansion. However, considering the complex flow physics inside the volute, it is questionable how valid these assumptions are. In this work, the authors present a comprehensive assessment of these conventional 1D predictions by investigating an extensive database of computational fluid dynamics (CFD) calculations of one volute as a standalone component. The volute has been supplied with different diffuser widths, and the inlet boundary conditions have been selected to allow for separate investigation of the effects of flow angle and flow rate. The aim is to validate the 1D model against the CFD results across the volute's entire operating range. Therefore, the CFD-predicted total pressure losses within the two subcomponents of the volute (the scroll and the conical diffuser) are assigned to the respective velocity components at volute inlet, in analogy to the 1D predictions. The results show that the loss coefficient of the radial velocity varies notably across the volute's loss map, opposing the 1D assumption of a constant loss coefficient. Conversely, the loss coefficient of the tangential velocity inside the scroll agrees well with the CFD results: High matching coefficients (i.e., lower than design flowrates) lead to high loss coefficients, which decrease almost continuously toward low matching coefficients (i.e., higher than design flowrates). The losses inside the conical diffuser depend not only on the matching coefficient but also on the flow angle at volute inlet, contrary to what the 1D model assumes. The fundamental characteristics of the global loss coefficient are predicted satisfactorily by the 1D model, while it generally overpredicts losses. Additionally, the CFD results reveal that the matching coefficient that gives minimum loss coefficients varies with the flow angle, which is not accounted for by the 1D model. Therefore, it is not adequate for assessing volute matching.