Low Reynolds number turbulence in nonlinear Maxwell-model fluids

Abstract

A generalized nonlinear Maxwell model which had previously been analyzed for plane Couette geometry is here applied to a lid-driven cavity flow. The full three-dimensional hydrodynamical problem is treated numerically. Depending on the relevant model parameters, both smooth laminar and low Reynolds number turbulent flows are found, strikingly similar to the experimentally observed elastic turbulence phenomena in polymer solutions. Representative results of the calculated flow patterns, as well as measures for the turbulent nature of the flow are presented graphically.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

“…The standard theoretical model for elastic turbulence provided by Steinberg et al . is that the chaotic motion is spatially smooth, but random in time 36 , 47 , 58 – 60 . The high value of the velocity PSD decay exponent is the result of stretching and folding of the elastic stress field, which transfers energy from small to large length scales, the direct opposite of the explanation of intermittency in conventional turbulence 2 , 3 .…”

Shear-stress-controlled dynamics of nematic complex fluids

“…However, as mentioned before, our approach is in principle fully capable of treating inhomogeneities as demonstrated, e.g., in Refs. [27] and [51], the latter study dealing with a full three-dimensional spatially resolved flow problem. Interestingly, there is a recent study of Das et al [26] suggesting that the chaotic orientational behavior of our present system at constant Γ transforms into a spatiotemporal chaos, when spatial fluctuations are allowed in the theory (via gradient terms in the free energy).…”

Enhanced Mixing at Low Reynolds Numbers Through Elastic Turbulence

“…Recently the model has been applied to a flow geometry which required the analysis of the full three-dimensional hydrodynamic problem [5]. It was observed that a self-generating time-dependent turbulent-like flow regime develops from steady forcing when the nonlinearities in the model are dominant.…”

“…A lid-driven cavity flow is chosen with a simple cuboid geometry, and a plate speed such that simulations run with the Reynolds number, Re ≈ 1. The no-slip boundary condition is used for the velocity field, whilst local zero-gradient Neumann conditions are used for π π π. Simulations are performed on an NEC SX-6 vector supercomputer, more details on the simulation techniques, and preliminary investigations can be found in [5].…”

“…A generic description of such a complex rheological behaviour is provided by a generalized nonlinear Maxwell model [3,4]. Depending on the choice of the relevant model parameters, numerical studies of a three-dimensional lid-driven flow, at low Reynolds numbers, demonstrated the occurrence of both laminar and turbulent flow behaviour [5].…”