27 results
Experiments on flows in channels with spatially distributed heating
- A. Inasawa, K. Taneda, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 872 / 10 August 2019
- Published online by Cambridge University Press:
- 07 June 2019, pp. 177-197
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Flows in channels exposed to spatially distributed heating were investigated. Such flows are of interest as theoretical analyses suggest that heating leads to the reduction of pressure losses. A special apparatus providing the means for the creation of well-controlled spatially periodic heating with the desired intensity as well as precise control of the flow rate in flows with small Reynolds numbers was constructed. The apparatus works with air and provides optical access to the flow interior. The relevant theory has been generalized to handle the temperature fields measured in the experiments. The experiments were carried out for Reynolds numbers $Re<20$ and at a single Rayleigh number based on the peak-to-peak temperature difference and channel half-height of $Ra_{p}=3500$. Flow visualization and particle image velocimetry measurements demonstrated the formation of two-dimensional steady rolls whose size was dictated by $Re$, with the largest rolls observed for the smallest $Re$ and the roll size being gradually reduced as $Re$ increased until their complete elimination at the largest $Re$ used in the experiment. An excellent agreement between the theoretically and experimentally determined complex flow fields was found. Wall shear stresses extracted from the velocity measurements agree with their theoretical counterparts within the expected accuracy. The agreement between the experimental and theoretical velocity fields and their unique relation with the corresponding pressure fields indirectly verify the heating-induced pressure-gradient-reducing effect.
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.
Reduction of pressure losses and increase of mixing in laminar flows through channels with long-wavelength vibrations
- J. M. Floryan, Sahab Zandi
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- Journal:
- Journal of Fluid Mechanics / Volume 864 / 10 April 2019
- Published online by Cambridge University Press:
- 11 February 2019, pp. 670-707
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Pressure losses and mixing in vibrating channels were analysed. The vibrations in the form of long-wavelength travelling waves were considered. Significant reduction of pressure losses can be achieved using sufficiently fast waves propagating downstream, while significant increase of such losses is generated by waves propagating upstream. The mechanisms responsible for pressure losses were identified and discussed. The interaction of the pressure field with the waves can create a force which assists the fluid movement. A similar force can be created by friction, but only under conditions leading to flow separation. An analysis of particle trajectories was carried out to determine the effect of vibrations on mixing. A significant transverse particle movement takes place, including particle trajectories with back loops. The downstream-propagating out-of-the phase waves provide a large reduction of pressure gradient and significant potential for mixing intensification. Analysis of energy requirements demonstrates that it is possible to identify waves which reduce power requirements, i.e. the cost of actuation is smaller than the energy savings associated with the reduction of pressure gradient. The fast forward moving waves provide an opportunity for the development of alternative propulsion methods which can be more efficient than methods based on the pressure difference.
Natural convection and thermal drift
- Arman Abtahi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 826 / 10 September 2017
- Published online by Cambridge University Press:
- 08 August 2017, pp. 553-582
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An analysis of natural convection in a horizontal, geometrically non-uniform slot exposed to spatially non-uniform heating has been carried out. The upper plate is smooth and isothermal, and the lower plate has sinusoidal corrugations with a sinusoidal temperature distribution. The distributions of the non-uniformities are characterized in terms of the wavenumber $\unicode[STIX]{x1D6FC}$ and their relative position is expressed in terms of the phase difference $\unicode[STIX]{x1D6FA}_{TL}$. The analysis is limited to heating conditions which do not give rise to secondary motions in the absence of the non-uniformities. The heating creates horizontal temperature gradients which lead to the formation of vertical and horizontal pressure gradients which drive the motion regardless of the intensity of the heating. When the hot spots (points of maximum temperature) overlap either with the corrugation tips or with the corrugation bottoms, convection assumes the form of pairs of counter-rotating rolls whose size is dictated by the heating/corrugation wavelengths. The formation of a net horizontal flow, referred to as thermal drift, is observed for all other relative positions of the hot spots and corrugation tips. Both periodic heating as well as periodic corrugations are required for the formation of this drift, which can be directed in the positive as well as in the negative horizontal directions depending on the phase difference between the heating and corrugation patterns. The most intense convection and the largest drift occur for wavelengths comparable to the slot height, and their intensities increase proportionally to the heating intensity as well as proportionally to the corrugation amplitude, with the drift being a very strong function of the phase difference. Convection creates forces at the plates which would cause horizontal displacement of the corrugated plate and deform the corrugations if such effects were allowed. Tangential forces generated by the uniform heating always contribute to the corrugation buildup while similar forces generated by the periodic heating contribute to the buildup only when the hot spots overlap with the upper part of the corrugation. The processes described above are qualitatively similar for all Prandtl numbers $Pr$, with the intensity of convection and the magnitude of the drift increasing with a reduction in $Pr$.
Natural convection in a corrugated slot
- Arman Abtahi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 815 / 25 March 2017
- Published online by Cambridge University Press:
- 23 February 2017, pp. 537-569
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Analysis of natural convection in a horizontal slot formed by two corrugated isothermal plates has been carried out. The analysis is limited to subcritical Rayleigh numbers $Ra$ where no secondary motion takes place in the absence of corrugations. The corrugations have a sinusoidal form characterized by the wavenumber, the upper and lower amplitudes and the phase difference. The most intense convection occurs for corrugation wavelengths comparable to the slot height; it increases proportionally to $Ra$ and proportionally to the corrugation height. Placement of corrugations on both plates may either significantly increase or decrease the convection depending on the phase difference between the upper and lower corrugations, with the strongest convection found for corrugations being in phase, i.e. a ‘wavy’ slot, and the weakest for corrugations being out of phase, i.e. a ‘converging–diverging’ slot. It is shown that the shear forces would always contribute to the corrugation build-up if erosion was allowed, while the role of pressure forces depends on the location of the corrugations as well as on the corrugation height and wavenumber, and the Rayleigh number. Placing corrugations on both plates results in the formation of a moment which attempts to change the relative position of the plates. There are two limiting positions, i.e. the ‘wavy’ slot and the ‘converging–diverging’ slot, with the latter being unstable. The system would end up in the ‘wavy’ slot configuration if relative movement of the two plates was allowed. The presence of corrugations affects the conductive heat flow and creates a convective heat flow. The conductive heat flow increases with the corrugation height as well as with the corrugation wavenumber; it is largest for short-wavelength corrugations. The convective heat flow is relevant only for wavenumbers of $O(1)$, it increases proportionally to $Ra^{3}$ and proportionally to the second power of the corrugation height. Convection is qualitatively similar for all Prandtl numbers $Pr$, with its intensity increasing for smaller $Pr$ and with the heat transfer augmentation increasing for larger $Pr$.
Flow dynamics and enhanced mixing in a converging–diverging channel
- S. W. Gepner, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 807 / 25 November 2016
- Published online by Cambridge University Press:
- 18 October 2016, pp. 167-204
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An analysis of flows in converging–diverging channels has been carried out with the primary goal of identifying geometries which result in increased mixing. The model geometry consists of a channel whose walls are fitted with spanwise grooves of moderate amplitudes (up to 10 % of the mean channel opening) and of sinusoidal shape. The groove systems on each wall are shifted by half of a wavelength with respect to each other, resulting in the formation of a converging–diverging conduit. The analysis is carried out up to Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is based on a two-dimensional model and demonstrates that increasing the corrugation wavelength results in the appearance of an unsteady separation whose onset correlates with the onset of the travelling wave instability. The second part of the analysis is based on a three-dimensional model and demonstrates that the flow dynamics is dominated by the centrifugal instability over a large range of geometric parameters, resulting in the formation of streamwise vortices. It is shown that the onset of the vortices may lead to the elimination of the unsteady separation. The critical Reynolds number for the vortex onset initially decreases as the corrugation amplitude increases but an excessive increase leads to the stream lift up, reduction of the centrifugal forces and flow stabilization. The flow dynamics under such conditions is again dominated by the travelling wave instability. Conditions leading to the formation of streamwise vortices without interference from the travelling wave instability have been identified. The structure and the mixing properties of the saturated states are discussed.
Groove-induced changes of discharge in channel flows
- Yu Chen, J. M. Floryan, Y. T. Chew, B. C. Khoo
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- Journal:
- Journal of Fluid Mechanics / Volume 799 / 25 July 2016
- Published online by Cambridge University Press:
- 23 June 2016, pp. 297-333
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The changes in discharge in pressure-driven flows through channels with longitudinal grooves have been investigated in the laminar flow regime and in the turbulent flow regime with moderate Reynolds numbers ($Re_{2H}\approx 6000$) using both analytical and numerical methodologies. The results demonstrate that the long-wavelength grooves can increase discharge by 20 %–150 %, depending on the groove amplitude and the type of flow, while the short-wavelength grooves reduce the discharge. It has been shown that the reduced geometry model applies to the analysis of turbulent flows and the performance of grooves of arbitrary form is well approximated by the performance of grooves whose shape is represented by the dominant Fourier mode. The flow patterns, the turbulent kinetic energy as well as the Reynolds stresses were examined to identify the mechanisms leading to an increase in discharge. It is shown that the increase in discharge results from the rearrangement of the bulk fluid movement and not from the suppression of turbulence intensity. The turbulent kinetic energy and the Reynolds stresses are rearranged while their volume-averaged intensities remain the same as in the smooth channel. Analysis of the interaction of the groove patterns on both walls demonstrates that the converging–diverging configuration results in the greatest increase in discharge while the wavy channel configuration results in a reduction in discharge.
Drag reduction in a thermally modulated channel
- M. Z. Hossain, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 791 / 25 March 2016
- Published online by Cambridge University Press:
- 15 February 2016, pp. 122-153
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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.
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.
Flow in a meandering channel
- J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 770 / 10 May 2015
- Published online by Cambridge University Press:
- 30 March 2015, pp. 52-84
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A comprehensive analysis of the pressure-gradient driven flow in a meandering channel has been presented. This geometry is of interest as it can be used for the creation of streamwise vortices which magnify the transverse transport of scalar quantities, e.g. heat transfer. The linear stability theory has been used to determine the meandering wavelengths required for the vortex formation. It has been demonstrated that reduction of the wavelength results in the onset of flow separation which, when combined with the wall geometry, results in an effective channel narrowing: the stream ‘lifts up’ above the wall and becomes nearly rectilinear, thus eliminating vortex-generating centrifugal forces. Increase of the wavelength also leads to a nearly rectilinear stream, as the slope of the wall modulations becomes negligible. As shear-driven instability may interfere with the formation of vortices, the conditions leading to the onset of such instability have also been investigated. The attributes of the geometry which lead to the most effective vortex generation without any interference from the shear instabilities and with the smallest drag penalty have been identified.
Mixed convection in a periodically heated channel
- M. Z. Hossain, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 768 / 10 April 2015
- Published online by Cambridge University Press:
- 03 March 2015, pp. 51-90
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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.
Drag reduction in heated channels
- Daniel Floryan, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 765 / 25 February 2015
- Published online by Cambridge University Press:
- 23 January 2015, pp. 353-395
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It is known that the drag for flows driven by a pressure gradient in heated channels can be reduced below the level found in isothermal channels. This reduction occurs for spatially modulated heating and is associated with the formation of separation bubbles which isolate the main stream from direct contact with the solid wall. It is demonstrated that the use of a proper combination of spatially distributed and spatially uniform heating components results in an increase in the horizontal and vertical temperature gradients which lead to an intensification of convection which, in turn, significantly increases the drag reduction. An excessive increase of the uniform heating leads to breakup of the bubbles and the formation of complex secondary states, resulting in a deterioration of the system performance. This performance may, under certain conditions, still be better than that achieved using only spatially distributed heating. Detailed calculations have been carried out for the Prandtl number $\mathit{Pr}=0.71$ and demonstrate that this technique is effective for flows with a Reynolds number $\mathit{Re}<10$; faster flows wash away separation bubbles. The question of net gain remains to be settled as it depends on the method used to achieve the desired wall temperature and on the cost of the required energy. The presented results provide a basis for the design of passive flow control techniques utilizing heating patterns as controlling agents.
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.
Instabilities of natural convection in a periodically heated layer
- M. Z. Hossain, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 733 / 25 October 2013
- Published online by Cambridge University Press:
- 19 September 2013, pp. 33-67
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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 $\alpha $ and the amplitude expressed in terms of a Rayleigh number $R{a}_{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 $R{a}_{p} $ and $\alpha $. It is shown that for sufficiently large $\alpha $ 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 $\alpha $. 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 $\alpha = O(1)$, parametric resonance dominates and leads to a pattern of instability that is locked in with the pattern of heating according to the relation ${\delta }_{cr} = \alpha / 2$, where ${\delta }_{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 $\alpha $, where the instability is driven by the uniform mean vertical temperature gradient created by the primary convection, with the critical disturbance wave vector ${\delta }_{cr} \rightarrow 1. 56$ for $\alpha \rightarrow \infty $ 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 $\alpha \approx 2. 2$ and no instability is found when $\alpha \lt 1. 6$ in the range of $R{a}_{p} $ considered. It is shown that $\alpha $ plays the role of an effective pattern control parameter and its judicious selection provides a means for the creation of a wide range of flow responses.
Pressure losses in grooved channels
- A. Mohammadi, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 725 / 25 June 2013
- Published online by Cambridge University Press:
- 14 May 2013, pp. 23-54
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The effects of small-amplitude, two-dimensional grooves on pressure losses in a laminar channel flow have been analysed. Grooves with an arbitrary shape and an arbitrary orientation with respect to the flow direction have been considered. It has been demonstrated that losses can be expressed as a superposition of two parts, one associated with change in the mean positions of the walls and one induced by flow modulations associated with the geometry of the grooves. The former effect can be determined analytically, while the latter has to be determined numerically and can be captured with an acceptable accuracy using reduced-order geometry models. Projection of the wall shape onto a Fourier space has been used to generate such a model. It has been found that in most cases replacement of the actual wall geometry with the leading mode of the relevant Fourier expansion permits determination of pressure losses with an error of less than 10 %. Detailed results are given for sinusoidal grooves for the range of parameters of practical interest. These results describe the performance of arbitrary grooves with the accuracy set by the properties of the reduced-order geometry model and are exact for sinusoidal grooves. The results show a strong dependence of the pressure losses on the groove orientation. Longitudinal grooves produce the smallest drag, and oblique grooves with an inclination angle of ${\sim }42\textdegree $ exhibit the largest flow turning potential. Detailed analyses of the extreme cases, i.e. transverse and longitudinal grooves, have been carried out. For transverse grooves with small wavenumbers, the dominant part of the drag is produced by shear, while the pressure form drag and the pressure interaction drag provide minor contributions. For the same grooves with large wavenumbers, the stream lifts up above the grooves due to their blocking effect, resulting in a change in the mechanics of drag formation: the contributions of shear decrease while the contributions of the pressure interaction drag increase, leading to an overall drag increase. In the case of longitudinal grooves, drag is produced by shear, and its rearrangement results in a drag decrease for long-wavelength grooves in spite of an increase of the wetted surface area. An increase of the wavenumber leads to the fluid being squeezed from the troughs and the stream being forced to lift up above the grooves. The shear is nearly eliminated from a large fraction of the wall but the overall drag increases due to reduction of the effective channel opening. It is shown that properly structured grooves are able to eliminate wall shear from the majority of the wetted surface area regardless of the groove orientation, thus exhibiting the potential for the creation of drag-reducing surfaces. Such surfaces can become practicable if a method for elimination of the undesired pressure and shear peaks through proper groove shaping can be found.
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.
Drag reduction due to spatial thermal modulations
- M. Z. Hossain, D. Floryan, J. M. Floryan
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- Journal:
- Journal of Fluid Mechanics / Volume 713 / 25 December 2012
- Published online by Cambridge University Press:
- 26 October 2012, pp. 398-419
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It is demonstrated that a significant drag reduction for pressure-driven flows can be realized by applying spatially distributed heating. The heating creates separation bubbles that separate the stream from the bounding walls and, at the same time, alter the distribution of the Reynolds stress, thereby providing a propulsive force. The strength of this effect is of practical interest for heating with wavenumbers $\ensuremath{\alpha} = O(1)$ and for flows with small Reynolds numbers and, thus, it is of potential interest for applications in micro-channels. Explicit results given for a very simple sinusoidal heating demonstrate that the drag-reducing effect increases proportionally to the second power of the heating intensity. This increase saturates if the heating becomes too intense. Drag reduction decreases as ${\ensuremath{\alpha} }^{4} $ when the heating wavenumber becomes too small, and as ${\ensuremath{\alpha} }^{\ensuremath{-} 7} $ when the heating wavenumber becomes too large; this decrease is due to the reduction in the magnitude of the Reynolds stress. The drag reduction can reach up to 87 % for the heating intensities of interest and heating patterns corresponding to the most effective heating wavenumber.
Effect of streamwise-periodic wall transpiration on turbulent friction drag
- M. QUADRIO, J. M. FLORYAN, P. LUCHINI
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- Journal:
- Journal of Fluid Mechanics / Volume 576 / 10 April 2007
- Published online by Cambridge University Press:
- 28 March 2007, pp. 425-444
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In this paper a turbulent plane channel flow modified by a distributed transpiration at the wall, with zero net mass flux, is studied through direct numerical simulation (DNS) using the incompressible Navier–Stokes equations. The transpiration is steady, uniform in the spanwise direction, and varies sinusoidally along the streamwise coordinate. The transpiration wavelength is found to dramatically affect the turbulent flow, and in particular the frictional drag. Long wavelengths produce large drag increases even with relatively small transpiration intensities, thus providing an efficient means for improved turbulent mixing. Shorter wavelengths, on the other hand, yield an unexpected decrease of turbulent friction. These opposite effects are separated by a threshold of transpiration wavelength, shown to scale in viscous units, related to a longitudinal length scale typical of the near-wall turbulence cycle. Transpiration is shown to affect the flow via two distinct mechanisms: steady streaming and direct interaction with turbulence. They modify the turbulent friction in two opposite ways, with streaming being equivalent to an additional pressure gradient needed to drive the same flow rate (drag increase) and direct interaction causing reduced turbulent activity owing to the injection of fluctuationless fluid. The latter effect overwhelms the former at small wavelengths, and results in a (small) net drag reduction. The possibility of observing large-scale streamwise-oriented vortical structures as a consequence of a centrifugal instability mechanism is also discussed. Our results do not demonstrate the presence of such vortices, and the same conclusion can be arrived at through a stability analysis of the mean velocity profile, even though it is possible that a higher value of the Reynolds number is needed to observe the vortices.
Transient disturbance growth in a corrugated channel
- J. SZUMBARSKI, J. M. FLORYAN
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- Journal:
- Journal of Fluid Mechanics / Volume 568 / 10 December 2006
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- 10 November 2006, pp. 243-272
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Transient growth of small disturbances may lead to the initiation of the laminar–turbulent transition process. Such growth in a two-dimensional laminar flow in a channel with a corrugated wall is analysed. The corrugation has a wavy form that is completely characterized by its wavenumber and amplitude. The maximum possible growth and the form of the initial disturbance that leads to such growth have been identified for each form of the corrugation. The form that leads to the largest growth for a given corrugation amplitude, i.e. the optimal corrugation, has been found. It is shown that the corrugation acts as an amplifier for disturbances that are approximately optimal in the smooth channel case but has little effect in the other cases. The interplay between the modal (asymptotic) instability and the transient growth, and the use of the variable corrugation for modulation of the growth are discussed.
Thermocapillary convection and existence of continuous liquid layers in the absence of gravity
- J. M. Floryan, C. Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 277 / 25 October 1994
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- 26 April 2006, pp. 303-329
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Thermocapillary convection in an infinite liquid layer driven by a temperature gradient parallel to the interface in the absence of gravity is considered. It is demonstrated that the temperature field has to satisfy restrictive conditions in order for a continuous layer to exist. It is further shown that the same conditions apply to long finite layers. Such layers, when subject to heating that does not satisfy the existence conditions, undergo large deformations and possible break up if the layer is sufficiently long.