PIV-based estimation of viscosity and pressure fields for a steady pseudoplastic flow

Abstract

Targeting a pseudoplastic fluid, we propose a method to simultaneously estimate viscosity and pressure fields from the velocity field data of particle image velocimetry (PIV). As a two-dimensional case study, we chose a steady two-dimensional wake structure behind a circular cylinder where local viscosity and pressure are dynamically coupled. The method involves PIV, momentum conservation equation of non-Newtonian fluids and rheological constitutive equations. The CMC (Carboxy Methyl Cellulose) aqueous solution of weight concentration of 0.1% is used as a test case of pseudoplastic fluid. Viscosity distribution is obtained through power law model and Carreau-Yasuda model as the constitutive equation. Pressure distribution is then calculated by substituting the viscosity into the momentum conservation equation. Applied results show pressure-lowering at the vortex cores and viscosity-lowering at their perimeters, stabilizing vortex attachment to the cylinder in the pseudoplastic fluid. We also analyze error propagation characteristics to conclude the feasibility of the present method and highlight the difference in error propagation characteristics during pressure estimation between Newtonian and pseudoplastic fluid flows.