Abstract
The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.
Highlights
Polymer additives are known for producing upward of 80% drag reduction in turbulent wall-bounded flows through strong alteration and reduction of turbulent activity [1]
The changes in flow dynamics induced by polymers do not lead to flow relaminarisation but, atmost, to a universal asymptotic state called maximum drag reduction (MDR) [2]
EIT has provided answers to previously unexplained phenomena such as early turbulence [6,22], it is a unique window into the creation of turbulence by means other than those known in Newtonian turbulence
Summary
Polymer additives are known for producing upward of 80% drag reduction in turbulent wall-bounded flows through strong alteration and reduction of turbulent activity [1]. Polymer additives have been shown to promote transition to turbulence [3], or even lead to a chaotic flow at very low Reynolds number as in elastic turbulence [4,5]. EIT could provide answers to phenomena that current understanding of MDR cannot, such as the absence of a log-law in finite-Reynolds numbers MDR flows [8,9], and the phenomenon of early turbulence It supports De Gennes’ picture [10] that drag reduction derives from two-way energy transfers between. Visualisations of numerical simulations indicate that thin sheets of locally high polymer stretch, tilted away from the wall and elongated in the flow direction, create trains of spanwise cylindrical structures of alternating sign (see Figure 2).
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