Fully turbulent flows of viscoplastic fluids in a rectangular duct

Abstract

Turbulent flows of viscoplastic fluids at high Reynolds numbers have been investigated recently with direct numerical simulations (DNS) but experimental results have been limited. For this reason, we carry out an experimental study of fully turbulent flows of a yield stress fluid in a rectangular aspect ratio channel with a high-resolution laser doppler velocimetry (LDA) setup. We employ aqueous Carbopol solutions, often considered to be a simple yield stress fluid. We formulate different concentrations to address the effect of the rheology of the fluid on the turbulence statistics at an approximately constant Reynolds number. Additionally, we also perform experiments with a single Carbopol formulation at different Reynolds numbers to study its effect. The flow analysis is performed via rheology measurements, turbulence statistics and power spectral densities of velocity fluctuations. The addition of Carbopol to the flow increases turbulence anisotropy, with an enhancement of streamwise velocity fluctuations and a decrease in wall normal velocity fluctuations in comparison to water at the same mean velocity. This change is reflected on the power spectral densities of streamwise velocity fluctuations, where we observe a large increase in energy of large scale turbulent structures. Conversely, the energy of smaller scales is decreased in comparison to water, where the energy drops with a steeper scale than the Newtonian power law of $k_x^{-5/3}$. As we increase the Reynolds number with a Carbopol solution, the streamwise Reynolds stresses approach Newtonian values in the core, which suggests diminishing effects of shear-thinning. The power spectral densities reveal that the energy content at larger scales decreases slightly with the Reynolds number. However, the shear thinning effects do not disappear even as the Reynolds number approaches 50000.