Establishment of a Reynolds average simulation method and study of a drag reduction mechanism for viscoelastic fluid turbulence

Abstract

Reynolds average simulation governing equations are derived for viscoelastic fluid turbulence using the Reynolds time-averaged method combined with the Navier–Stokes equations, the viscoelastic fluid finitely extensible nonlinear elastic-Peterlin constitutive equation, the viscoelastic fluid molecular conformation tensor transport equation, and the k−ε−v′2¯−f turbulence model. To identify the relevant viscoelastic terms, user-defined functions and the programing language C are used to write a simulation subroutine for the Reynolds average of viscoelastic fluid turbulence; this subroutine is embedded into computational fluid dynamics software to establish a simulation method for Reynolds average of viscoelastic fluid turbulence. Then, the flow field structure of viscoelastic fluid turbulence is analyzed. Using energy transport theory, expressions for the contribution of viscous, elastic, and Reynolds shear stress to the turbulent friction factor of viscoelastic fluid in a horizontal tube are established, and the turbulent drag reduction mechanism of the viscoelastic fluid is revealed. The simulated values for pressure drop, Fanning friction factor, and the drag reduction rate of viscoelastic fluid in tests are in good agreement with experimental values, and the average relative error is less than 12.37%. In addition, elastic shear stress is produced after the dissolution of drag reduction agents in water, which increases the turbulent friction factor; however, Reynolds shear stress is greatly reduced, and viscous shear stress is weakened by inhibiting the turbulence fluctuation, so the turbulent friction factor decreases; more importantly, the increase in the friction factor of the former is much smaller than that of the latter.