Mathematics of Turbomachinery: Centrifugal Impeller

The mathematics required to design and analyze turbomachinery were gathered from many sources and presented in its entirety as a single source, step-by-step procedure. An impeller was then designed and analyzed. A one-dimensional (1D) model explains the mathematics for performance in detail. The 1D model lacked the ability to predict flow-related phenomena such as flow surge but highlighted the direct connection between blade angle and rotation direction with pressure rise and efficiency. For the present study, positive blade angles pointing in the direction of rotation (clockwise in the present study) provided higher pressure rise and higher losses. Negative blade angles pointing in the opposite direction of rotation (counterclockwise in the present study) resulted in lower pressure rise and lower losses. Flow surge was studied with a three-dimensional (3D) model. The 3D model confirmed counterclockwise rotation as the most efficient rotation direction and identified areas of flow surge. Both models found pressure rise across the turbomachine under study was higher for the clockwise rotation.