A FENE-P <i>k</i>-<i>ε</i> Viscoelastic Turbulence Model Valid up to High Drag Reduction without Friction Velocity Dependence

• Main Authors: Michael McDermott, Pedro Resende, Thibaut Charpentier, Mark Wilson, Alexandre Afonso, David Harbottle, Gregory de Boer
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Applied Sciences
• Subjects: drag reduction; FENE-P fluid; viscoelastic RANS model; OpenFoam CFD
• Online Access: https://www.mdpi.com/2076-3417/10/22/8140

A viscoelastic turbulence model in a fully-developed drag reducing channel flow is improved, with turbulent eddies modelled under a <inline-formula><math display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ε</mi></mrow></semantics></math></inline-formula> representation, along with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. The model performance is evaluated against a wide variety of direct numerical simulation data, described by different combinations of rheological parameters, which is able to predict all drag reduction (low, intermediate and high) regimes with good accuracy. Three main contributions are proposed: one with a simplified viscoelastic closure for the <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><mi>L</mi><msub><mi>T</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></semantics></math></inline-formula> term (which accounts for the interactions between the fluctuating components of the conformation tensor and the velocity gradient tensor), by removing additional damping functions and reducing complexity compared with previous models; second through a reformulation for the closure of the viscoelastic destruction term, <inline-formula><math display="inline"><semantics><msub><mi>E</mi><msub><mi>τ</mi><mi>p</mi></msub></msub></semantics></math></inline-formula>, which removes all friction velocity dependence; lastly by an improved modified damping function capable of predicting the reduction in the eddy viscosity and thus accurately capturing the turbulent kinetic energy throughout the channel. The main advantage is the capacity to predict all flow fields for low, intermediate and high friction Reynolds numbers, up to high drag reduction without friction velocity dependence.