Correction of the definition of mass flow parameter in dynamic inflow modelling

Abstract

The dynamic inflow model, which has been extensively developed by Peters and his co-workers for the last two decades, is a powerful tool for predicting the induced velocity distribution over a rotor disc. Scant attention has, however, been paid so far in using the model to analyse an autorotative rotor. The authors identified a necessary change to the mass flow parameter of the original model of Peters for autorotating rotors. In response, questions were raised by readers about how the modified and original inflow parameters should consistently be explained, why the original model of Peters is insufficient for autorotation, and how the validity of the modified mass flow parameter can mathematically be enunciated. Indeed, the discussion in the article by Murakami and Houston (2008) was held in a manner that readers might have received an impression that the modified model was derived independently of the original model, and the connection to the original model was not clearly presented. This technical note is written with an aim to elucidate the mathematically consistent relationship between the original and modified mass flow parameters, and it is confirmed that the original definition of the mass flow parameter contains an error in its definition. It is concluded that the unified mass flow parameter, which is presented in this article, should always be used in the dynamic inflow model.