Derivation of phenomenological turbulence theory in liquid with small additives of drag reducing agents

Paper considers the issue of deriving the phenomenological turbulence theory in liquids treated with small additives of drag reducing agent. It also proposes the concept that for practical purposes, it is the phenomenological theory, which is relevant, since it determines the parameters of the phenomenon in question in the absence of detailed knowledge of the mechanisms of additives action, which, despite many years of intensive studies, remain either unknown or not fully understood. Different additives have different effects on shear turbulence in pipes and channels and, accordingly, change the integral characteristics of the turbulent flow in different ways. Some additives affect only the narrow wall-bounded areas of the flow without changing the turbulent viscosity in the flow core, while others act throughout the entire flow volume and significantly change the turbulent viscosity. Additives of the first type affect a turbulent flow by changing the boundary conditions in known models without changing the model coefficients. Additives of the second type change both the boundary conditions and the coefficients of the model itself. It is shown that the von Karman modified theory (model) of shear turbulence is equally suitable for describing the turbulent flow of a liquid with additives of the both first and second types. The universal drag equation with experimentally determined transfer coefficients that follows from this model enables calculating the hydraulic drag coefficient depending on the properties of the drag reducing agent used.