Control of Shear Layers Using Heating Patterns
Abstract
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.