Parametric differentiation method to structural optimization problems

Abstract

The measured relationship between the total temperature and velocity profiles in an accelerating turbulent boundarylayer flow through a nozzle was found to differ from the Crocco relation, with the amount of departure being dependent upon an acceleration parameter ft which is related to nozzle shape. For accelerating flow the temperature-velocity relationship in the region beyond the viscous sublayer was similar to that for a laminar boundary layer and because of this correspondence, the eddy diffusivities for heat and momentum transfer em and €h at each probe location are believed not to have differed much from each other. Based on the agreement between the laminar and measured turbulent boundary-layer profiles beyond the viscous sublayer, a rather large departure from the Crocco relation is expected because of flow acceleration and the thermal boundary condition, i.e., cooling or heating. From these observations it does appear that previous investigations of the structure of turbulent boundary layers made near the exit of nozzles could have been influenced to some extent by the pressure gradient that still existed at the location of interest and/or by the upstream history of the flow through the nozzle.