4 results
Drag reduction and instabilities of flows in longitudinally grooved annuli
- H. V. Moradi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 865 / 25 April 2019
- Published online by Cambridge University Press:
- 19 February 2019, pp. 328-362
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The primary and secondary laminar flows in annuli with longitudinal grooves and driven by pressure gradients have been analysed. There exist geometric configurations reducing pressure losses in primary flows in spite of an increase of the wall wetted area. The parameter ranges when such flows exist have been determined using linear stability theory. Two types of secondary flows have been identified. The first type has the form of the classical travelling waves driven by shear and modified by the grooves. The axisymmetric waves dominate for sufficiently large radii of the annuli while different spiral waves dominate for small radii. The secondary flow topology is unique in the former case and has the form of axisymmetric rings propagating in the axial direction. Topologies in the latter case are not unique, as spiral waves with left and right twists can emerge under the same conditions, resulting in flow structures varying from spatial rings to rhombic forms. The most intense motion of this type occurs near the walls. The second type of secondary flow has the form of travelling waves driven by inertial effects with characteristics very distinct from the shear waves. Its critical Reynolds number increases proportionally to
$S^{-2}$, where
$S$ denotes the groove amplitude, while the amplification rates increase proportionally to
$S^{2}$. These waves exist only if
$S$ is above a well-defined minimum and their axisymmetric forms dominate, with the most intense motion occurring near the annulus mid-section. Geometries that give preference to the latter waves have been identified. It is shown that the drag-reducing topographies stabilize the classical travelling waves; these waves are driven by viscous shear, so reduction of this shear decreases their amplification. The same topographies destabilize the new waves; these waves are driven by an inviscid mechanism associated with the formation of circumferential inflection points, and an increase of the groove amplitude increases their amplification. The flow conditions when the presence of grooves can be ignored, i.e. the annuli can be treated as being hydraulically smooth, have been determined.
New instability mode in a grooved channel
- A. Mohammadi, H. V. Moradi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 778 / 10 September 2015
- Published online by Cambridge University Press:
- 10 August 2015, pp. 691-720
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It is known that longitudinal grooves may stabilize or destabilize the travelling wave instability in a channel flow depending on the groove wavenumber. These waves reduce to the classical Tollmien–Schlichting waves in the absence of grooves. It is shown that another class of travelling wave instability exists if grooves with sufficiently high amplitude and proper wavelengths are used. It is demonstrated that the new instability mode is driven by the inviscid mechanism, with the disturbance motion having the form of a wave propagating in the streamwise direction with phase speed approximately four times larger than the Tollmien–Schlichting wave speed and with its streamwise wavelength being approximately twice the spanwise groove wavelength. The instability motion is concentrated mostly in the middle of the channel and has a planar character, i.e. the dominant velocity components are parallel to the walls. A significant reduction of the corresponding critical Reynolds number can be achieved by increasing the groove amplitude. Conditions that guarantee the flow stability in a grooved channel, i.e. the grooved surface behaves as a hydraulically smooth surface, have been identified.
Stability of flow in a channel with longitudinal grooves
- H. V. Moradi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 757 / 25 October 2014
- Published online by Cambridge University Press:
- 25 September 2014, pp. 613-648
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The travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wavenumber
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta $ is larger than
$\beta _{tran}\approx 4.22$, but stabilizes the flow for smaller
$\beta $. It has been found that
$\beta _{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wavenumber has been determined. Special attention has been paid to the drag-reducing long-wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e. such grooves do not cause an early breakdown into turbulence.
Flows in annuli with longitudinal grooves
- H. V. Moradi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 716 / 10 February 2013
- Published online by Cambridge University Press:
- 25 January 2013, pp. 280-315
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Analysis of pressure losses in laminar flows through annuli fitted with longitudinal grooves has been carried out. The additional pressure gradient required in order to maintain the same flow rate in the grooved annuli, as well as in the reference smooth annuli, is used as a measure of the loss. The groove-induced changes can be represented as a superposition of a pressure drop due to a change in the average position of the bounding cylinders and a pressure drop due to flow modulations induced by the shape of the grooves. The former effect can be evaluated analytically while the latter requires explicit computations. It has been demonstrated that a reduced-order model is an effective tool for extraction of the features of groove geometry that lead to flow modulations relevant to drag generation. One Fourier mode from the Fourier expansion representing the annulus geometry is sufficient to predict pressure losses with an accuracy sufficient for most applications in the case of equal-depth grooves. It is shown that the presence of the grooves may lead to a reduction of pressure loss in spite of an increase of the surface wetted area. The drag-decreasing grooves are characterized by the groove wavenumber
$M/ {R}_{1} $ being smaller than a certain critical value, where
$M$ denotes the number of grooves and
${R}_{1} $ stands for the radius of the annulus. This number marginally depends on the groove amplitude and does not depend on the flow Reynolds number. It is shown that the drag reduction mechanism relies on the re-arrangement of the bulk flow that leads to the largest mass flow taking place in the area of the largest annulus opening. The form of the optimal grooves from the point of view of the maximum drag reduction has been determined. This form depends on the type of constraints imposed. In general, the optimal shape can be described using the reduced-order model involving only a few Fourier modes. It is shown that in the case of equal-depth grooves, the optimal shape can be approximated using a special form of trapezoid. In the case of unequal-depth grooves, where the groove depth needs to be determined as part of the optimization procedure, the optimal geometry, consisting of the optimal depth and the corresponding optimal shape, can be approximated using a delta function. The maximum possible drag reduction, corresponding to the optimal geometry, has been determined.
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