The effect of polymer additives on the components of the energy balance of a turbulent flow

Abstract

On the basis of the experimental data obtained, an analysis is made of the effect of polymer additives directly on the generation of turbulent energy, on the dissipation of the energy of the averaged motion, and on the density of the flux of the kinetic energy of the turbulence. The presence of polymer additives in the turbulent flow significantly changes the relationship between the generation of the turbulent energy and the dissipation of the energy of the averaged motion. Under the action of polymer additives, the density of the flux of kinetic energy decreases over the depth of the channel, which, in turn, brings about a decrease in the influx of energy from the averaged motion to the pulsed motion. The following definitions are adopted below: the x1 axis of a Cartesian system of coordinates coincides with the horizontal axis of symmetry of the channel and with the direction of the averaged motion of the liquid; the x2 axis is directed upward; the x3 axis is perpendicular to the lateral wall of the channel; the origin of coordinates, O, coincides with the lower plane (bottom) of the channel. Further, U0 is the mean velocity of the flow of liquid in the channel; Ui is the local component of the averaged velocity (i=1, 2, 3); H is the height of the channel; z=2x2/H; Re is the Reynolds number of the averaged flow;v is the coefficient of kinematic viscosity; ui is the pulsation component of the velocity (i=1, 2, 3); u* is rate of dynamic friction; A=(λ0−λpλ0 −1 is the coefficient of the lowering of the friction resistance with the flow of polymer solutions; λ0 and λp are the coefficients of the friction resistance with the motion of water and polymer solutions in a channel, respectively; c is the weight concentration of the polymer solution (%);τ 0 is the friction stress at the wall; U+ is the velocity of the flow at the axis of the channel.