Effect of finite Weissenberg number on turbulent channel flows of an elastoviscoplastic fluid

Direct numerical simulations are carried out to study the effect of finite Weissenberg number up to $Wi=16$ on laminar and turbulent channel flows of an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds number of $2800$ . The incompressible flow equations are coupled with the evolution equation for the EVP stress tensor by a modified Saramito model that extends both the Bingham viscoplastic and the finite extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic models. In turbulent flow, we find that drag decreases with both the Bingham and Weissenberg numbers, until the flow laminarises at high enough elastic and yield stresses. Hence, a higher drag reduction is achieved than in the viscoelastic flow at the same Weissenberg number. The drag reduction persists at Bingham numbers up to 20, in contrast to viscoplastic flow, where the drag increases in the laminar regime compared with a Newtonian flow. Moreover, elasticity affects the laminarisation of an EVP flow in a non-monotonic fashion, delaying it at lower and promoting it at higher Weissenberg numbers. A hibernation phenomenon is observed in the EVP flow, leading to large changes in the unyielded regions. Finally, plasticity is observed to affect both low- and high-speed streaks equally, attenuating the turbulent dissipation and the fragmentation of turbulent structures.

Turbulence modulation in thermally expanding and contracting flows

We present direct numerical simulations of developing turbulent channel flows subjected to thermal expansion or contraction downstream of a heated or cooled wall. Using different constitutive relations for viscosity we analyse the response of variable property flows to streamwise acceleration/deceleration by separating the effect of streamwise acceleration/deceleration from the effect of wall-normal property variations. We demonstrate that, beyond a certain streamwise location, the flow can be considered in a state of ‘quasi-equilibrium’ regarding semilocally scaled variables. As such, we claim that the development of turbulent quantities due to streamwise acceleration/deceleration is localized to the region of impulsive heating/cooling, while changes in turbulence occurring farther downstream can be attributed solely to property variations. This finding allows us to study turbulence modulation in accelerating/decelerating flows using the semilocal scaling framework. By investigating the energy redistribution among the turbulent velocity fluctuations, we conclude that a change in bulk streamwise velocity has a non-local effect which originates from the change in mean shear and modifies the energy pathways through velocity-pressure-gradient correlations. On the other hand, the wall-normal property gradients have a local effect and act through the modification of the viscous dissipation. We show that it is possible to superimpose and compare the two different effects when using the semilocal scaling framework.