The Origin of Elastic Turbulence in the Taylor-Couette Flow: A Direct Numerical Simulation Study

Almost two decades ago, Groisman & Steinberg experimentally discovered an essentially smooth and temporally random flow state with broad temporal frequency spectra in curvilinear flows of dilute polymeric fluids in the limit of vanishing Re and Wi>>1 , i.e., very large elasticity number, E=Wi/Re, dubbed “purely elastic turbulence” (ET). Since the discovery of ET, three-dimensional Direct Numerical Simulation (DNS) of purely elastic turbulence has remained a grand challenge problem for the research community engaged in developing first-principal models and simulations that can predict faithfully the complex spatio-temporal dynamics of polymeric flows. To this end,  lack of fundamental understanding of the flow–microstructure coupling that leads to production of turbulent kinetic energy in an essentially spatially smooth flow has hampered mechanistic understanding of how ET is realized.  In this presentation, results of the first three-dimensional DNS simulation of ET in the Taylor-Couette flow of dilute polymeric solutions will be discussed. Specifically, it will be demonstrated that purely elastic instabilities lead to a chaotic flow composed of two distinct flow structures, namely, large-scale diwhirls that span the entire gap and travelling wave like flow patterns near the rotating inner cylinder. In turn, the influence of the polymeric body force associated with these flow structures on the enhancement of angular momentum transport and mixing, as well as production of turbulent kinetic energy in this inertialess flow will be discussed.