#### Date of Award

12-15-2014

#### Document Type

Open Access Dissertation

#### Department

Mechanical Engineering

#### First Advisor

Guiren Wang

#### Abstract

Turbulence, as one of "the most important unsolved classical problem in physics" (R. Feynman, 1932), has been investigated for more than 130 years. Conventionally, turbulence is believed to be a phenomenon of high Reynolds numbers (Re). However, we find that turbulence can also be achieved at low Re by proper external forcing, either in macroflows or in microflows. In macroflows, the characteristics of high Re turbulence can be achieved in confined flows, when the bulk flow Re is around 400, by external forcing at its optimal frequency (Wang 2003; Wang 2006). Interestingly, the optimal narrow band of frequency is fixed (5- 6 Hz) independent of the bulk flow Re in either mixing layers or plane wakes. At the optimal frequency, an extremely fast mixing between initial two streams can be achieved. However, the mixing enhancement mechanism is still unknown. Therefore, we focus on both the dynamical process of the flow and the corresponding mechanism of the optimal frequency which significantly affects the dynamics of the fast mixing mechanism. The detailed dynamical process of the flows, especially the velocity and vorticity fields are investigated first. Then, the kinetic energy and the effect of each term in turbulent energy equation are studied in details. We found that, the strongly three-dimensional (3-D) nonlinear flow caused by streamwise vortex structures is the main reason of the fast mixing. It has two major roles: (1) enhances significantly the mean flow in vertical direction and increases the spreading rate of the mixing layer; (2) accelerate the evolution of flow from two-dimensional (2-D) to 3-D that again enhance the transport of turbulent energy, and thus the scalar and mixing as well. The existence of corner vortex is validated and its relation with streamwise vortex is also analyzed. Meanwhile, in order to explain the cause of the optimal frequency, both parametric study and numerical simulation are carried out. Several important phenomena are discovered to help understand this mysterious optimal frequency: (1) the frequency is not due to any known flow instability mechanism; (2) the frequency is insensitive to the changing of dimensions of all the downstream parts of the settling chamber, indicating the optimal frequency is not simply attributed to one-dimensional (1-D) acoustic resonance; (3) by numerical simulations, we find there do exist a low-frequency acoustic eigenmode around 6 Hz. The eigenfrequency qualitatively increases with the decreasing of lengths of all the parts, except the settling chamber; (4) the mixing enhancement is tightly related to the local geometry of splitter plate at the trailing edge and acoustically induced shedding vortices. A large curvature diameter of trailing edge inhibits the generation of the acoustically induced shedding vortex and significantly decrease the mixing enhancement. Hence, acoustic resonance could be related to the mechanism related to the optimal frequency. In microflows, turbulence in a low Re flow field in microchannel is recently realized for the first time when an electrokinetic (EK) force is applied to a pressure driven flow with two initial streams of different conductivities. The so-called micro EK turbulence is systematically investigated and many features of high Re turbulence, such as Kolmogorov -5/3 slope, Obukhov-Corrsin -5/3 spectrum, scaling law and exponential tail of probability density function (PDF) etc., have been amazingly found in microfluidics at the low Re microflow. The corresponding theory of the EK turbulence is proposed to help understand why there can be micro EK turbulence and the correspondingly observed phenomena. A new scaling law of the EK turbulence is theoretically suggested by direct derivation from Navier-Stokes equation and dimensional analysis, which is also verified experimentally. To successfully measure micro EK turbulence, a novel velocity measurement method — Laser Induced Fluorescence Photobleaching Anemometer (LIFPA) which has simultaneously ultrahigh spatial and temporal resolution, is developed, since so far no available velocimeters can measure the micro EK turbulence. The temporal resolution of LIFPA is theoretically investigated and experimentally compared to the standard micro Particle Imaging Velocimetry (μPIV) method. The results demonstrate the unbeatable temporal resolution and accuracy of LIFPA. Then, the error in LIFPA measurement is analyzed. Proper correction methods on the statistics of velocity measurement by LIFPA are introduced. We believe, the present work should have important impact on turbulence research, not only on phenomena, but also on the physical mechanisms, and as well as the relevant measuring technique. The present investigations have important practical applications in the fields where fast mixing is highly desired, such as the design of heat exchanger and chemical reactor in process industry, and Lab-on-a-chip.

#### Recommended Citation

Zhao, W.(2014). *Low Reynolds Number Turbulence: Mechanisms and Applications.* (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/2999