New Theoretical Shock Loss Model for Axial Fans Based on the Integral Momentum Equation

To analyze the pressure characteristic behavior of axial fans during the design process, an analytical estimation of the pressure characteristic is of interest for industry and academia. The loss models for turbomachines are traditionally based on the energy equation, i.e. the Bernoulli equation, in combination with loss coefficient. Different than the energy conservation equation, the integral momentum equation can deliver the pressure loss term without any empirical loss coefficient. In the present contribution, this issue has been addressed and the authors developed a new combined loss model especially for axial fans consisting of a slip factor model and a shock loss model. With the integral momentum approach, no empirical constants are needed for the shock loss model, in contrast to the energy equation-based models. In this work it is shown on the example of axial fan losses, that the integral momentum equation is a powerful method to estimate losses. This approach can also be extended to other applications and can be included on a broader basis in the classes of fluid mechanics and turbomachinery in the engineering education. For validation, several axial fans have been computed with CFD using the commercial solver ANSYS CFX 2023 and compared with the theoretical characteristics computed with the Euler turbomachinery equation in combination with the new combined loss model of the authors. The comparison of the theoretical predictions based on the integral momentum equation and the numerical computations are in very good agreement, showing that the theoretical loss model produces very reliable results and full axial fan characteristics.