Estimation of Rate of Strain Magnitude and Average Viscosity in Turbulent Flow of Shear Thinning and Yield Stress Fluids
Abstract
This paper presents a series of numerical simulations of nonNewtonian fluids in high Reynolds number flows in circular pipes. The fluids studied in the computations have shearthinning and yield stress properties. Turbulence is described using the ReynoldsAveraged NavierStokes (RANS) equations with the Boussinesq eddy viscosity hypothesis.
The evaluation of standard, twoequation models led to some observations regarding the order of magnitude as well as probabilistic information about the rate of strain. We argue that an accurate estimate of the rate of strain tensor is essential in capturing important flow features. It is first recognised that an apparent viscosity comprises two flow dependant components: one originating from rheology and the other from the turbulence model. To establish the relative significance of the terms involved, an order of magnitude analysis has been performed.
The main observation supporting further discussion is that in high Reynolds number regimes the magnitudes of fluctuating rates of strain and fluctuating vorticity dominate the magnitudes of their respective averages. Since these quantities are included in the rheological law, the values of viscosity obtained from the fluctuating and mean velocity fields are different. Validation against Direct Numerical Simulation data shows at least an order of magnitude discrepancy in some regions of the flow. Moreover, the predictions of the probabilistic analysis show a favourable agreement with statistics computed from DNS data.
A variety of experimental, as well as computational data has been collected. Data come from the latest experiments by Escudier et al. [1], DNS from Rudman et al. [2] and zerothorder turbulence models of Pinho [3]. The fluid rheologies are described by standard powerlaw and HerschelBulkley models which make them suitable for steady state calculations of shear flows. Suitable regularisations are utilised to secure numerical stability.
Two new models have been proposed taking as a basis a κ∊ κω roaches. They both incorporate modification of of strain calculation according to the points outlined above. The preliminary runs show improvements in results includign accurate mass flow rate prediction.
 Publication:

Icnaam 2010: International Conference of Numerical Analysis and Applied Mathematics 2010
 Pub Date:
 September 2010
 DOI:
 10.1063/1.3498171
 Bibcode:
 2010AIPC.1281.1696S
 Keywords:

 turbulence in shear flow;
 Reynolds number;
 NavierStokes equations;
 viscosity;
 47.27.E;
 47.27.Jv;
 47.10.ad;
 47.20.Gv;
 Turbulence simulation and modeling;
 HighReynoldsnumber turbulence;
 NavierStokes equations;
 Viscous and viscoelastic instabilities