Doctor of Philosophy
Mechanical and Materials Engineering
The presence of spatially modulated flows is universal in nature. Distributed heating and surface roughness are the most common elements to cause non-uniformity in the flows. Spatially distributed heating leads to fundamentally distinct convection, different from the classical Rayleigh-Bénard instability. Interestingly, the onset of convective motion due to horizontal temperature gradients requires no critical conditions – a forced response. At the same time, surface roughness is known to significantly influence flow behaviours and heat transfer characteristics. The current work aims to analyze modulated flows and assess their potential as a mixing technique for low Reynolds number flows. Spanwise modulations (perpendicular to the flow direction) have been considered in a three-dimensional channel. A spectrally accurate algorithm has been developed based on the Fourier expansions and Chebyshev polynomials. The immersed boundary condition method is used to overcome challenges associated with surface irregularities at the boundaries. The algorithm is gridless and provides means for analyzing numerous patterns with minimal human labor. Thermal modulations at the boundaries result in the formation of rolls/streaks in low Reynolds number flows. The strength of streaks is determined by evaluating the spanwise gradient of the streamwise (along the flow direction) velocity component and the change in kinetic energy. For all forms of nonuniform heating, an additional pressure gradient is required to maintain the same mass flowrate as the reference Poiseuille flow. Adding geometric modulation with distributed heating produces stronger streaks, and a range of wave numbers exists where pressure losses are lower than the reference flow. An optimum wave number is identified in order to generate streaks efficiently for the periodic heating of grooved surfaces. These streaks play an essential role in shear layer dynamics and are subject to instabilities, which are of interest for mixing intensification. A linear stability algorithm has been developed to study the stability characteristics of modulated flows. This algorithm avoids challenges related to the classical DNS-based approach. It is shown that a new instability mode appears due to the thermal modulations, which outstandingly reduces the critical Reynolds number.
Summary for Lay Audience
Mixing is essential in many industries and applications. It is a known fact that turbulent flows generally provide better mixing compared to laminar flows. The smooth, orderly movement of the fluid layers in laminar flows makes it challenging to achieve faster mixing rates. However, depending on the applications, it can be non-beneficial or impractical to always have turbulent flows in the system. Therefore, a technique that can lead to intense mixing in laminar flows will greatly interest many industries such as food & beverage, pharmaceutical, chemical processing etc. In the current work, we have assessed the potential of surface roughness and patterned heating as a mixing technique for the low Reynolds number flows. Roughness is defined by any form of irregularities at the surface, while patterned heating is identified as heating and cooling of the same surface. An efficient and highly accurate algorithm has been developed to solve systems with roughness and heating patterns. It is shown that patterned heating creates rolls which can be beneficial for mixing enhancement. Combining patterned heating with surface roughness increases the strength of these rolls. The first step towards chaotic stirring is to determine the stability condition of these rolls. In other words, it is crucial to determine when these rolls become unstable. A linear stability algorithm has been developed that can quickly determine the conditions required for the onset of instability. This algorithm introduces a small disturbance in the system and checks if the disturbance grows or decays over time. It is observed that patterned heating results in instability at a very low Reynolds number. This instability's characteristic matches with those in literature, which induced chaotic mixing in laminar flows.
Panday, Shoyon, "Control of Shear Layers Using Heating Patterns" (2023). Electronic Thesis and Dissertation Repository. 9214.
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