On the use of transpiration patterns for reduction of pressure losses

Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ( $Re$ ), Bingham ( $Bi$ ) and slip ( $b$ ) numbers, as well as the groove periodicity length ( $\ell$ ) and the slip area fraction ( $\varphi$ ). By increasing $Bi$ , the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.

Section: Thick Channel Resultssupporting

confidence: 87%

Section: Inertial Flowsupporting

confidence: 90%

“…2006; Teo & Khoo 2014; Ren et al. 2018; Jiao & Floryan 2021). For instance, based on a numerical simulation study, Ren et al.…”

Section: Resultsmentioning

confidence: 99%

Section: Thick Channel Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Poiseuille flow of a Bingham fluid in a channel with a superhydrophobic groovy wall

Rahmani

Taghavi

2022

“…2006; Mamori, Iwamoto & Murata 2014; Gómez et al. 2016; Han & Huang 2020; Jiao & Floryan 2021 a , b ) even attaining sustained sub-laminar levels of drag (Min et al. 2006; Jiao & Floryan 2021 a , b ).…”

Section: Introductionmentioning

confidence: 99%

Effects of wall vibrations on channel flows

Haq

Floryan

2023

Self Cite

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.

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

Floryan

2023

We derive a limit on energy savings in controlled channel flow. For flow in a channel driven by pressure, shear or any combination of the two, and controlled via wall transpiration or spanwise wall motion, the uncontrolled laminar state requires the least net energy (accounting for the energetic cost of control). Thus, the optimal control solution is to laminarize the flow. Additionally, we raise the possibility of beating this limit. By simultaneously applying wall transpiration and spanwise wall motion, we show that it may be possible to attain sustained sub-laminar energy expenditure in a controlled flow. We provide a necessary design criterion for net energy savings.