Turbulent Thermal Convection of Complex Fluids
While, except for some common liquids and gases, like water and air, which can be assumed as Newtonian for practical calculations under ordinary conditions, most of the real fluids in nature and industrial processes are non-Newtonian fluids. The viscosity of non-Newtonian fluids can vary significantly with factors such as shear rate, temperature, and pressure, hence, they often exhibit more complex rheological behaviors compared to Newtonian fluids, such as viscoelasticity, plasticity, shearthinning and shear-thickening.
Among them, the elastic and plastic behaviors of the non-Newtonian fluids play a crucial role in determining the rheological properties and flow dynamics. Specifically, the relative effect of the elastic forces to the viscous forces in the viscoelastic fluids is commonly quantified by the Weissenberg number Wi, which is proportional to the product of the elastic relaxation time λ and the shear rate of the flow γ˙ . Regarding the fluid plasticity, a dimensionless Bingham number Bi is frequently used, which denotes the yield stress ratio to the viscous stress in the Saramito elastoviscoplastic model. In this case, the Bingham plastic fluid behaves as a rigid body at low stresses and as a viscous fluid at high stresses.
To study turbulent thermal convection of viscoplastic and viscoelastic fluids, in J. Song, C. Xu, and O. Shishkina, J. Comput. Phys. 525, 113732 (2025) an efficient and robust finite-difference algorithm for DNS of turbulent thermal convection of complex fluids was deve-loped. Specifically, the simulated non-Newtonian fluids are modelled by either viscoelastic Oldroyd-B or FENE-P (finitely extensible nonlinear elastic-Peterlin), or Saramito elastoviscoplastic constitutive equations based on the conformation tensor. The non-Newtonian solver is built on top of the open-source AFiD (www.afid.eu) code, which uses a pencil distributed parallel strategy to handle the large-scale wall-bounded turbulence computations efficiently. The solver uses the Kurganov–Tadmor scheme for the convective term and the semi-implicit time advancement scheme for the conformation tensor equations.
Remarkably, in our recent study C. Xu, C. Zhang, L. Brandt, J. Song and O. Shishkina, J. Fluid Mech. 1014, A22 (2025),the results for the heat transport modification for highly turbulent thermal convection with polymer additives agreed not only qualitatively but also quantitatively with previous experiments in a similar parameter range. Compared to Newtonian fluid, all non-Newtonian fluids demonstrated a significant reduction in the heat and momentum transport in turbulent RBC. Specifically, the fluid viscoplasticity decreases the heat transport by about 6.2% by suppressing and destroying the well-organized large-scale rolls established in the Newtonian flow. For the viscoelastic fluid, the convective velocities and heat transport are further reduced to about 16.6% as the large-scale rolls in Newtonian flow are replaced by several localized thin plumes that randomly detach from the wall. The elastoviscoplastic fluid has the combined effects of both plasticity and elasticity, thus a heat transport reduction of 20.4% is obtained. Moreover, the trace field clearly supports that our method and code can faithfully resolve the sharp gradients of conformation tensor and elastic stress in turbulent flows of complex fluids.
