Non-stationary flow of viscoelastic fluid in a cylindrical pipe

The problems of non-stationary flow of a viscoelastic fluid in a cylindrical pipe under the influence of a constant pressure gradient are solved based on the generalized Maxwell model. By solving the problem, formulas for velocity distribution, fluid flow, and other hydrodynamic characteristics were derived. Based on the formulas derived, transient processes under non-stationary flow of a viscoelastic fluid in a cylindrical pipe are analysed. Based on the results of the analysis, it was determined that the processes of transition of the characteristics of a viscoelastic fluid from a non-stationary state to a steady one at small values of the Deborah number practically do not differ from the transition processes of a Newtonian fluid. It is established that, when the Deborah number exceeds unity, the process of transition of a viscoelastic fluid from a non-stationary state to a steady one is of a wave nature, in contrast to the transition process of a Newtonian fluid, and the transition time is several times longer than the transition time of a Newtonian fluid. It was also discovered that during the transient process, perturbed flows could arise, leading to an instantaneous increase in fluid flow and other hydrodynamic characteristics. These perturbations occurring in non-stationary flows of a viscoelastic fluid can be stabilized by mixing with the Newtonian fluid. The implementation of this property is important in technical and technological processes preventing technical failures or malfunctions.