In dilute polymer solution, polymers are able to change the flow structures and suppress the intensity of turbulence, resulting in a considerable friction drag reduction (DR). Despite the extraordinary progress made in the past few decades, some critical questions remain unanswered. This dissertation will try to address two fundamental questions in dilute polymeric turbulence: (I) interactions between polymers and turbulent motions during the qualitative low-extent to high-extent drag reduction (LDR and HDR) transition in inertia-driven turbulence, (II) roles of the inertia- and elasticity-driven turbulent motions in the dynamics of high elasticity polymeric flows.
Many studies in the area of DR turbulence have been focused on the onset of DR and the maximum drag rection (MDR) asymptote. Between these two distinct stages, polymeric turbulent flows can also be classified into the qualitative LDR and HDR stages. Understanding the polymer-turbulence interactions during the drastic LDR-HDR transition is of vital importance for the development of efficient flow control technology. However, knowledge regarding this qualitative transition is still limited. In our DNS (direct numerical simulation) study, differences between the LDR and HDR stages are presented by a number of sharp changes in flow structures and statistics. Drag reduction in the flows is thus governed by two different mechanisms. The first is introduced at the onset of DR, which has been well explained by the indiscriminate suppression of turbulent fluctuations during the coil-stretch transition of polymers. The second mechanism starts at the LDR-HDR transition but its physical origin is not clear. Based on instantaneous observations and indirect statistical evidence, we proposed that polymers, after the LDR-HDR transition, could suppress the lift-up process of the near-wall vortices and modify the turbulent regeneration cycles. However, direct evidence to support this hypothesis is not available without a statistical analysis of the vortex configurations. Therefore, a new vortex tracking algorithm -- VATIP (vortex axis tracking by iterative propagation) -- is developed to analyze statistically the configurations and distribution of vortices. Implementing this method in the polymeric turbulence demonstrates that the lift-up process of streamwise vortices in the buffer layer is restrained at HDR, while the generation of hairpins and other three-dimensional vortices is suppressed. In addition, the characteristic lifting angle of conditional eddies extracted by a conditional sampling method is found to be larger in HDR than in the Newtonian turbulence. These observations all support our hypothesis about the mechanism of LDR-HDR transition.
Research on the low elasticity turbulence usually considered the flow motions to be Newtonian-like. Turbulence here is driven by the inertial force (and hence called ``inertia-driven'' turbulence (IDT)) while polymers are responsible for dissipating turbulent kinetic energy. In the high elasticity turbulence, recent studies found a completely different turbulent flow type in which turbulence is driven by the elastic force and polymers could also feed energy to the flow. The behaviors of this ``elasticity-driven'' turbulence (EDT) are of significant interest in this area because of its potential connection to the MDR asymptote. However, EDT is difficult to capture by the traditional pseudo-spectral DNS scheme (SM) as a global artificial diffusion (GAD) term is involved in the polymer constitutive equation to stabilize the simulation. In our study, a new hybrid pseudo-spectral/finite-difference scheme is developed to simulate the polymeric turbulence without requiring a GAD. All of the spatial derivative terms are still discretized by the Fourier-Chebyshev-Fourier pseudo-spectral projection except for the convection term in the constitutive equation which is discretized using a conservative second-order upwind TVD (total variation diminishing) finite difference scheme. The numerical study using the hybrid scheme suggests that turbulent flows can be either driven by the inertial or the elastic forces and respectively result in the IDT and EDT flows. A dynamical flow state is also found in the high elasticity flow regime in which IDT and EDT can be sustained alternatively. / Thesis / Doctor of Philosophy (PhD) / Turbulence is known to consume kinetic energy in a fluid system. To enhance the efficiency of fluid transportation, various techniques are developed. Especially, it was found that a small amount of polymers in turbulent flows can significantly suppress turbulent activity and cause considerable friction drag reduction (DR). Extraordinary progress has been made to study this phenomenon, however, some questions still remain elusive. This dissertation tries to address some fundamental questions that relate to the two typical polymeric turbulent motions: the inertia- (IDT) and elasticity-driven turbulence (EDT). In IDT, mechanisms of transitions between the intermediate stages are investigated from the perspective of vortex dynamics. The different effects of polymers at each stage of the flow lead to different flow behaviors. Particularly, starting from the low- to high-extent DR transition, the lift-up process of vortices is suppressed by polymers. The regeneration cycles of turbulence are thus modified, which results in qualitative changes of flow statistics. Numerical study on EDT is enabled by a newly developed hybrid pseudo-spectral/finite-difference scheme. A systematic investigation of the parameter space indicates that EDT is one self-contain turbulence driven purely by the elastic force. It can also interact with IDT and lead to a dynamical flow state in which EDT and IDT can alternatively occur.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/24887 |
| Date | January 2019 |
| Creators | ZHU, LU |
| Contributors | Xi, Li, Chemical Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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