| Summary: | In this paper, we numerically investigate the turbulence modulation produced by long flexible fibres in channel flow. The simulations are based on an Euler–Lagrangian approach, where fibres are modelled as chains of constrained, sub-Kolmogorov rods. A novel algorithm is deployed to make the resolution of dispersed systems of constraint equations, which represent the fibres, compatible with a state-of-the-art, Graphics Processing Units-accelerated flow-solver for direct numerical simulations in the two-way coupling regime on High Performance Computing architectures. Two-way coupling is accounted for using the Exact Regularized Point Particle method, which allows to calculate the disturbance generated by the fibers on the flow considering progressively refined grids, down to a quasi-viscous length-scale. The bending stiffness of the fibers is also modelled, while collisions are neglected. Results of fluid velocity statistics for friction Reynolds number of the flow <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo><mn>150</mn></mrow></semantics></math></inline-formula> and fibers with Stokes number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>t</mi></mrow></semantics></math></inline-formula> = 0.01 (nearly tracers) and 10 (inertial) are presented, with special regard to turbulence modulation and its dependence on fiber inertia and volume fraction (equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>=</mo><mn>2.12</mn></mrow></semantics></math></inline-formula>·<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.12</mn></mrow></semantics></math></inline-formula>·<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></semantics></math></inline-formula>). The non-Newtonian stresses determined by the carried phase are also displayed, determined by long and slender fibers with fixed aspect ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>λ</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi></mrow></msub><mo>=</mo><mn>200</mn></mrow></semantics></math></inline-formula>, which extend up to the inertial range of the turbulent flow.
|
|---|