A fundamental limit on energy savings in controlled channel flow, and how to beat it

We show that a heating pattern applied to a surface with a corrugation pattern generates a propulsive effect. The same heating pattern applied to a smooth surface creates propulsion through nonlinear thermal streaming associated with pitchfork bifurcation. The combination of groove and heating patterns generates thermal drift, representing a forced response whose magnitude changes with the relative position of both patterns. Thermal drift is always present, while thermal streaming requires sufficiently intense heating. When both effects are active, a change in the relative position of these patterns produces rapid changes in the magnitude of propulsion, resulting in the formation of limit points. The strength of propulsion increases with a decrease in the Prandtl number and with an addition of uniform heating.

Section: Nonlinear Thermal Streaming Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Use of heated corrugations for propulsion

Floryan,

Aman,

Panday

2024

“…Recent results show that combining different forms of modulation, e.g. adding in-plane wall oscillations, can save net energy (Floryan 2023). It is known that transpiration activates nonlinear drift, which can be used for propulsion augmentation (Jiao & Floryan 2021 a , b ).…”

Section: Introductionmentioning

confidence: 99%

Effects of wall vibrations on channel flows

Haq

Floryan

2023

The effect of surface vibrations on the pressure-gradient-driven flows in channels has been studied. The analysis considered monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the pressure gradient correction required to maintain the same flow rate as without vibrations. Waves propagating upstream always increase pressure losses. Flow response to waves propagating downstream is more complex and changes as a function of the flow Reynolds number. Such waves reduce losses if the Reynolds number $Re <\ \sim\!\!100$ , but these waves must be sufficiently fast to reduce pressure losses for larger Re values. In general, the supercritical waves, i.e. waves faster than the reference flow, reduce pressure losses with the magnitude of reduction increasing monotonically with the wave phase speed and wavenumber. The need for an external pressure gradient is eliminated if sufficiently short and fast waves are used. Generally, the subcritical waves, i.e. waves with velocities similar to the reference flow, increase pressure losses. This increase changes somewhat irregularly as a function of the wave phase speed and wavenumber forming local maxima and minima. These waves can reduce pressure losses only if the Reynolds number becomes large enough. It is shown that subcritical waves with very small amplitudes but matching the natural flow frequencies produce significant pressure losses.

The use of patterned heating in controlling pressure losses within sloping channels

Floryan,

Wang,

Bassom

2024

The effectiveness of utilizing heating patterns as a drag-reduction tool in sloping channels is analysed. The usefulness of heating is judged by determining the pressure gradient required to maintain the same flow rate as in the isothermal case. The key to reducing pressure loss is the formation of separation bubbles, although these bubbles are washed away at relatively large Reynolds numbers. The bubbles reduce the direct contact between the stream and the side walls, thereby reducing the friction experienced by the flow. Moreover, the fluid inside the bubbles tends to rotate, a motion provoked by longitudinal temperature gradients. This rotation also seems to reduce the resistance. On the other hand, the existence of the bubbles tends to obstruct the stream, increasing the flow resistance. In general, channels oriented close to horizontal experience a relatively small pressure loss, but this loss grows markedly as the channel inclines towards the vertical. When modest heating is applied, the pressure loss is approximately proportional to the square of the associated Rayleigh number. It is also shown that if the heating wavelength is too short or too long, the heating loses its effectiveness. In certain circumstances, it turns out that the theoretical pressure-gradient reduction achieved by judicious heating is so large that it exceeds the pressure gradient required to drive the flow in the isothermal problem. The conclusion is that in these instances, a pressure gradient of the opposite sign must be applied to prevent flow acceleration.