Abstract
A method for simultaneous estimation of viscosity and pressure fields in inelastic shear-thinning fluids is developed by means of ultrasound velocity profiling technique (UVP). In the method, equation of continuity, rheological model and pressure Poisson equation are incorporated as data processing sequences for measured velocity distributions. The proposed method is applied to study the vortex street structure formed behind a circular cylinder, which shows viscosity–pressure coupling due to shear-thinning property of fluid. For demonstration, aqueous solution of CMC (carboxy methyl cellulose) of weight concentration of 0.1% is chosen as the working fluid with shear-thinning property. An alternating staggered pattern of low-pressure spots is successfully reconstructed for zero-shear-based Reynolds number, Re = 50–300. We have found that increasing Re resulted in decrease in vortex shedding Strouhal number because of vortex sustainability supported by shear-thinning property.Graphical abstract
Highlights
Flow over cylinder is a widely studied topic for Newtonian fluid flows (Williamson 1996) due to its relevance in many engineering problems
We propose a novel algorithm for ultrasound velocity profiling technique (UVP) to simultaneously estimate viscosity and pressure fields in vortex streets formed behind cylinder for unsteady flow of inelastic shear-thinning fluids which may be opaque
Viscosity is more correlated with enstrophy than with pressure which means that the shear-thinning characteristic of fluid is more dependent on kinematics than the dynamics of fluid
Summary
Flow over cylinder is a widely studied topic for Newtonian fluid flows (Williamson 1996) due to its relevance in many engineering problems. Main concern in working with non-Newtonian fluids is that they do not follow Newton’s law of viscosity and exhibit various relations between stress and strain rate. These fluids are classified as shear thinning, shear thickening, viscoelastic, thixotropic and rheopectic. The details of unsteady wake flow field, viscosity and pressure fields have not been investigated experimentally for shear-thinning fluids which are the motivation for this work. In our last work (Tiwari et al 2021), we used a momentum equation with Eulerian method to reconstruct the pressure field albeit for a non-Newtonian fluid with variable viscosity. Pressure Poisson equation: For incompressible flows, Poisson equation for pressure is derived by taking divergence of Eq (1) and is written as
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