Extended Mean Line Theory for Axial Fans: Analytic Calculation of the Flow Characteristics for Off-Design Points

The use of axial fans is very common for industrial applications. The most common design case is the free vortex design. It ensures constant meridional velocity and hence an axi-symmetric and two-dimensional flow. Those designs have proved to be robust and to deliver good results. However, the free vortex model holds only at the design point. At off-design points the flow characteristics differ substantially from the free vortex model, whereby the extent of validity of a forced vortex model is obtained. Solving the equation of radial equilibrium for off-design points enables a more precise design prediction considering the impact of the variable meridional velocity and the angular momentum. This approach can be applied to free vortex models as well as forced vortex models. In the present work theoretical formulas for the flow characteristics at off-design points were developed and implemented. Three angular momentum profiles, one free vortex and two forced vortex models, were analyzed relative to the change in the meridional velocity and angular momentum profiles. The impact of these modifications on the performance characteristics of axial fans, such as pressure, efficiency, torque and hydraulic power was investigated. Comparing design prediction with numerical CFD validation leads to a precise and extensive analysis. The validity of the used approach is demonstrated. Thus a qualitative prediction of flow characteristics for any axial-impeller at off-design is obtained. This allows for a in depth understanding of the fundamental working principles and consequences of the radial equilibrium equation at the design and also at off design points.