A semi-empirical theory for the growth and bursting of laminar separation bubbles

Abstract

A simple pressure gradient criterion for the determination of the conditions under which re-attachment of a turbulent clear layer can occur is proposed. Application of this criterion to the laminar separation bubble problem, together with a simple bubble model and an approximate method of calculation of the momentum thickness growth over the bubble, leads to a method of prediction of the bubble growth. It is found that for a given imposed pressure distribution there exists a Reynolds number at separation below which re-attachment is impossible; this is associated with the so-called 'bursting' phenomenon. The predicted bursting parmeters are in good agreement with experimental observations; in particular, the value of Crabtree's pressure rise parameter is found to be weakly dependent upon the boundary-layer Reynolds number at separation, varying between the limits 0.27 to 0.36 over the range of practical significance. It is concluded that bursting occurs as a failure of the re-attachment process, as suggested by Woodward.