Drag reduction due to spatial thermal modulations

2016

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Flow in a horizontal channel exposed to external heating which results in sinusoidal temperature variations along the upper and lower walls with a phase shift between them has been studied using a combination of analytical and numerical methods. The most intense convection is observed when the upper and lower hot spots are located above each other. It has been demonstrated that the heating results in a significant reduction of the pressure gradient required to drive the flow when compared to a similar flow in an isothermal channel. The drag reduction is associated with the formation of separation bubbles which insulate the stream from direct contact with the bounding walls. The fluid inside of the bubbles rotates due to horizontal density gradients, which further reduces the required pressure gradient. The magnitude of the drag reduction depends on the phase shift between the heating patterns and can increase by up to threefold when compared to the drag reduction which can be achieved by heating only one wall. A detailed analysis of the associated heat fluxes has been presented.

Section: Long Wavelength Heatingsupporting

confidence: 56%

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Drag reduction in a thermally modulated channel

2016

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“…It has been shown recently that spatially periodic heating gives rise to the superthermohydrophobic effect Hossain, Floryan & Floryan 2012), which leads to a significant drag reduction for small Re flows and thus could lead to the design of a new class of microfluidic devices. These predictions remain valid as long as the flow does not undergo transition to secondary states.…”

Section: Introductionmentioning

confidence: 99%

Mixed convection in a periodically heated channel

2015

Mixed convection in a channel with flow driven by a pressure gradient and subject to spatially periodic heating along one of the walls has been studied. The pattern of the heating is characterized by the wavenumber ${\it\alpha}$ and its intensity is expressed in terms of the Rayleigh number $\mathit{Ra}_{p}$. The primary convection has the form of counter-rotating rolls with the wavevector parallel to the wavevector of the heating. The resulting net heat flow between the walls increases proportionally to $\mathit{Ra}_{p}$ but the growth saturates when $\mathit{Ra}_{p}=O(10^{3})$. The most effective heating pattern corresponds to ${\it\alpha}\approx 1$, as this leads to the most intense transverse motion. The primary convection is subject to transition to secondary states with the onset conditions depending on ${\it\alpha}$. The conditions leading to transition between different forms of secondary motion have been determined using the linear stability theory. Three patterns of secondary motion may occur at small Reynolds numbers $\mathit{Re}$, i.e. longitudinal rolls, transverse rolls and oblique rolls, with the critical conditions varying significantly as a function of ${\it\alpha}$. An increase of ${\it\alpha}$ leads to the elimination of the longitudinal rolls and, eventually, to the elimination of the oblique rolls, with the transverse rolls assuming the dominant role. For large ${\it\alpha}$, the transition is driven by the Rayleigh–Bénard mechanism; while for ${\it\alpha}=O(1)$, the spatial parametric resonance dominates. The global flow characteristics are identical regardless of whether the heating is applied at the lower or the upper wall.

“…The same heating applied to moving fluid results in the reduction of drag experienced by this fluid. This so-called super-thermohydrophobic effect has been described in detail by Hossain, Floryan & Floryan (2012), and relies on the formation of small separation bubbles that isolate the moving stream from direct contact with the solid wall and thus reduce the shear stress acting on the fluid. The fluid movement inside separation bubbles is partially driven by the buoyancy gradients associated with the heating, which further contributes to the reduction of the required pressure drop.…”

Section: Introductionmentioning

confidence: 99%

Instabilities of natural convection in a periodically heated layer

2013

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Natural convection in an infinite horizontal layer subject to periodic heating along the lower wall has been investigated using a combination of numerical and asymptotic techniques. The heating maintains the same mean temperatures at both walls while producing sinusoidal temperature variations along one horizontal direction, with its spatial distribution characterized by the wavenumber α and the amplitude expressed in terms of a Rayleigh number Ra p . The primary response of the system takes the form of stationary convection consisting of rolls with the axis orthogonal to the heating wave vector and structure determined by the particular values of Ra p and α. It is shown that for sufficiently large α convection is limited to a thin layer adjacent to the lower wall with a uniform conduction zone emerging above it; the temperature in this zone becomes independent of the heating pattern and varies in the vertical direction only. Linear stability of the above system has been considered and conditions leading to the emergence of secondary convection have been identified. Secondary convection gives rise to either longitudinal rolls, transverse rolls or oblique rolls at the onset, depending on α. The longitudinal rolls are parallel to the primary rolls and the transverse rolls are orthogonal to the primary rolls, and both result in striped patterns. The oblique rolls lead to the formation of convection cells with aspect ratio dictated by their inclination angle and formation of rhombic patterns. Two mechanisms of instability have been identified. In the case of α = O(1), parametric resonance dominates and leads to a pattern of instability that is locked in with the pattern of heating according to the relation δ cr = α/2, where δ cr denotes the component of the critical disturbance wave vector parallel to the heating wave vector. The second mechanism, the Rayleigh-Bénard (RB) mechanism, dominates for large α, where the instability is driven by the uniform mean vertical temperature gradient created by the primary convection, with the critical disturbance wave vector δ cr → 1.56 for α → ∞ and the fluid response becoming similar to that found in the case of a uniformly heated wall. Competition between these mechanisms gives rise to non-commensurable states in the case of longitudinal rolls and the appearance of soliton lattices, to the formation of distorted transverse rolls, and to the appearance of the wave vector component in the direction perpendicular to the forcing direction. A rapid stabilization is observed when the heating wavenumber is reduced below α ≈ 2.2 and no instability is found when α < 1.6 in the range of Ra p considered. It is shown that α plays the † Email address for correspondence: mfloryan@eng.uwo.ca ‡ Current address: role of an effective pattern control parameter and its judicious selection provides a means for the creation of a wide range of flow responses.