Energy conservation in turbulent flows of complex and simple fluids: mechanisms and new approaches

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When flow in a pipe or channel transitions from the laminar state to turbulence, its friction drag increases abruptly: i.e., energy dissipation is much higher in the latter. Turbulence, meanwhile, is ubiquitous in engineering applications; common examples include pipeline oil transferring, district heating/cooling systems, and the propulsion of ships, airplanes and vehicles. Techniques for turbulent drag reduction (DR) can therefore bring about massive benefit both economically (lower cost) and environmentally (less consumption of natural resources and less greenhouse gas emissions). Substantial DR - up to 80% - can be achieved by simply dissolving polymer additives into the fluid. Although polymers are not always permissible in practical applications, understanding of their DR effect will inspire new designs of flow-control techniques for reaching comparable levels of energy saving in simple fluids (without polymers). The most prominent problem in this area is the so-called maximum drag reduction (MDR): a universal asymptotic limit that bounds the level of DR reached by all different polymer solutions. Despite decades of research, MDR has remained the most important unsolved problem in the area of viscoelastic turbulence. Revealing its mechanism is not only of great fundamental interest, a clear picture of the dynamics in polymer solutions near the MDR regime is also pivotal for future developments in DR techniques in general. The proposed program focuses on the numerical computation of DR in turbulence, with a short-term goal set at the mechanism of MDR. The approaches we will take are inspired by a new conceptual framework proposed in our recent studies of simplified model flows. In addition to introducing a distinct perspective to MDR research, the framework also offers consistent explanations for all qualitative observations about MDR, showing great promise of guiding future research. Building on this progress, our plan divides into two directions: one aims at constructing a mechanistic depiction of MDR dynamics; the other focuses on validating our physical understanding in turbulence at realistic scales. Progress along this path will prepare us for our long-term goal: developing next-generation techniques for high levels of DR in simple Newtonian fluids. Polymers are insoluble, prohibited or undesirable in many situations; techniques for DR in simple fluids can thus reach a much broader range of applications. The level of energy saving achieved by existing techniques of such kind is however much lower than that of polymers. With better understanding of polymeric turbulence near MDR, new approaches can be envisioned in which the role of polymers is imitated so that turbulent dynamics can be tethered to MDR in the absence of these additives. Finally, the program is also designed with the training of highly qualified personnel (HQP) in mind. The proposed research breaks down into several projects for multiple students at both the graduate and undergraduate levels. Students working on these projects will build a solid background in fluid dynamics, polymer physics, rheology and applied mathematics. Meanwhile they will also receive systematic training in numerical computation and algorithm development. In addition to the academia, these skills are highly valued in a broad range of industrial sectors, especially the petroleum, chemical and manufacturing industries.