High-fidelity robust and efficient finite difference algorithm for simulation of polymer-induced turbulence in cylindrical coordinates

Turbulent Taylor–Couette flow of dilute polymeric solutions: a 10-year retrospective

“…a 50% enhancement. A recent numerical simulation of viscoelastic TC flow at Re = 10 000 has produced consistent results with these experimental observations [56]. Specifically, DR of ≈ 10.9% at Wi = 5, β = 0.97 and L = 80 that arises due to suppression of small-scale near wall vortices has been observed.…”

“…As described above, most if not all three-dimensional DNS of viscoelastic flows including the studies reviewed here make use of the FENE-P model due to its tight physical connection with kinetic theory of polymer solutions, simplicity and broad applicability to linear high molecular weight polymers [27,31,32,37,38,54,56]. In the FENE-P model, the conformation tensor C represents the ensemble average of the second moment of the end-to-end vector of the polymer chain described as: normal∂Cnormal∂t+bold-italicu⋅normal∇C=C⋅normal∇bold-italicu+false(normal∇bold-italicufalse)normalT⋅C−bold-italicτ.The polymer stress bold-italicτ is related to the conformation tensor C through the equation: bold-italicτ=ffalse(Cfalse)C−IWiand ffalse(Cfalse)=L2−3L2−tracefalse(Cfalse),where ffalse(Cfalse) is the Peterlin function.…”

“…The vertical black dash-dot line represents the purely elastic regime of Re≤1; the horizontal black dashed line denotes the critical Wi∼10 for the onset of ET; the black dotted line separates elastically and inertially dominated turbulence with El=0.01. The thin lines denote DNS results [25–27,31,32,37,54,56,58], while thick lines represent experimental findings [12,20,28,30,34,35,59,60]. The Wi for the experimental studies are estimated from the reported Re and El, and fluid properties; hence minor discrepancies may exist with the original experimental data.…”

“…In addition, many organic solvent-based constant viscosity solutions, namely, 'Boger fluids' [9] that are typically composed of a high molecular weight polymer (e.g. As described above, most if not all three-dimensional DNS of viscoelastic flows including the studies reviewed here make use of the FENE-P model due to its tight physical connection with kinetic theory of polymer solutions, simplicity and broad applicability to linear high molecular weight polymers [27,31,32,37,38,54,56]. In the FENE-P model, the conformation tensor C represents the ensemble average of the second moment of the end-to-end vector of the polymer chain described as:…”

“…For example, with an increase of Re or decrease of El, the turbulent TC flow can be sequentially classified as ET, EDT and finally IDT. The coherent flow structures in these typical turbulent states Song et al [31,25] Zhu et al [56] Lin et al [54] Lee et al [33] Groisman & Steinberg [20] Dutcher & Muller [12] Song et al [26] Latrache et al [28,29] Rajappan & McKinley [34] Latrache & Mutabazi [30] Lacassagne et al [57] Lacassagne et al [58] Wi ~ 10 are displayed in figures 2 and 3. In order to provide a clear mechanistic picture of how variation in Re and Wi affects the flow transitions and identify the unique features of each flow regime, one must perform an in depth analysis of the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kinetic energy production, spectral features as well as the self-sustaining cycles of turbulence in each of these three distinct flow states.…”