Stationary transverse rolls and U-rolls in limiting low Reynolds number mixed convective air flow near the convective threshold in a horizontal flat duct

Combined experimental flow visualization and temperature measurement are carried out in the present study to explore the buoyancy driven vortex flow patterns in a limiting low Reynolds number mixed convective air flow through a bottom heated horizontal flat duct. In Particular, attention is paid to the flow approaching the natural convection limit (Re=0) for Re=1.0 and 2.0 with the Rayleigh number near the critical level for the onset of convection for 1200?Ra?4000. Results from the flow visualization have revealed two unfamiliar vortex flow patterns which were not seen in our earlier study [Int. J. Heat Mass Transfer 44 (4) (2001) 705]. One is characterized by the stable stationary transverse rolls in the duct entry and stable longitudinal rolls in the downstream. Another is in the form of U-rolls. The relations of these two patterns with those reported in the literature from analytical, numerical and experimental studies are discussed. Moreover, stable longitudinal rolls along with nonperiodic traversing waves, and mixed longitudinal and transverse rolls as well as irregular cells which appear in the higher Reynolds number for 3.0?Re?5.0 are also noted here. The temporal and spatial characteristics of the unfamiliar vortex flows are inspected in detail. In addition, the flow formation processes leading to the two unfamiliar vortex flow structures are also examined carefully. During the flow formation we noted merging of longitudinal and transverse rolls to form U-rolls, splitting of rolls into cells and the reverse process of cell integration into rolls, aside from the generation of the longitudinal and transverse rolls. Finally, a flow regime map is provided to delineate various vortex flow structures observed in this study and in the previous study (cf. the above-mentioned reference) driven by the slightly supercritical and subcritical buoyancies for 1.0?Re?5.0.     

Buoyancy driven vortex flow and its stability in mixed convection of air through a blocked horizontal flat duct heated from below

Experimental flow visualization combined with transient temperature measurement are carried out here to explore the possible stabilization of the buoyancy drive vortex flow in mixed convection of air in a bottom heated horizontal flat duct by placing a rectangular solid block on the duct bottom. Two acrylic blocks having dimensions 40 × 20 × 5 mm³ (block A) and 40 × 20 × 10 mm³ (block B) are tested. The blocks are placed on the longitudinal centerline of the duct bottom at selected locations. How the location and orientation of the rectangular block affect the stability of the regular vortex flow is investigated in detail. Experiments are conducted for the Reynolds number varying from 3 to 30 and Rayleigh number from 3000 to 6000, covering a wide range of the buoyancy-to-inertia ratio. For longitudinal vortex flow, the presence of either block near the duct entry causes the onset points of the longitudinal rolls to move significantly upstream especially for the roll pair directly behind the block. Besides, the longitudinal vortex flow in the exit portion of the duct is destabilized by the block. The transverse vortex flow is found to be only slightly affected by the block when it is placed in the exit half of the duct. Significant deformation of the transverse rolls is noted as they pass over the block. However, they restore to their regular shape in a short distance. Substantial decay in the transient flow oscillation results in the region right behind the block. Elsewhere the flow oscillates at nearly the same frequency and amplitude as that in the unblocked duct. When the block is placed near the duct entry, stabilization of the vortex flow behind the block is more pronounced. This flow stabilization is more prominent for block B with its height being twice of block A. Placing the block with its long sides normal to the forced flow direction can also enhance the flow stabilization. For the mixed longitudinal and transverse vortex flow, placing the block near the duct inlet causes the transverse rolls to change to regular or deformed longitudinal rolls in the duct depending on the buoyancy-to-inertia ratio and orientation of the block. The flow stabilization by the block is substantial. Again the stabilization of the mixed vortex flow can be enhanced by increasing the block height and length and by placing the block with its long sides normal to the forced flow direction.     

Numerical 3-D Study of Poiseuille Rayleigh Benard Soret Problem in a Finite Extent Paralellipipedic Duct

This article deals with mixed convection of a binary mixture within a rectangular duct heated from below and under Soret influence. Going forward, the problem is referred to as the Poiseuille Rayleigh Benard Soret (PRBS) problem. We study the pattern formation of a binary mixture heated from below in the presence of a horizontal flow. When the system exhibits a supercritical bifurcation, either 2-D or 3-D convective structures appear. In a layer of infinite extent the presence of through-flow breaks the rotational symmetry, and the system at the convective threshold has to decide between longitudinal and transverse rolls among several unstable modes; we focus attention on transverse rolls. These rolls are generally unsteady and form traveling waves along the duct, and the presence of through-flow reduces the size of the region of convective instability. We show that the spanwise A_y aspect ratio has a strong influence on the threshold of convection, and in binary mixtures with a negative separation ratio N, and in distinction to the case for positive values of N; traveling waves can move against the direction of the mean flow. In general, nonlinear front propagation dominates the dynamics. The phase velocities and wave numbers of these fronts are determined. For the case of very long cells, we install continuity conditions in order to simulate an infinite duct. Changes in the outlet boundary conditions, in order to save the physics, influence the stability and wavelengths in the upstream.     

Structure of mixed convective longitudinal vortex air flow driven by a heated circular plate embedded in the bottom of a horizontal flat duct

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven longitudinal vortex rolls in low Reynolds number mixed convective air flow through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 15.1 to 99.2 and Rayleigh number from 3506 to 29,493. How the circular geometry of the heated surface affects the longitudinal vortex flow characteristics is investigated in detail. The results indicate that the longitudinal vortex rolls (L-rolls) in the duct core are induced at more upstream locations than those near the duct sides, which is completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and are slightly asymmetric. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, suggesting the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of new L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, which obviously results from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse steady-unsteady transition in the vortex flow.Based on the present data, a flow regime map is given to delineate various L-roll patterns driven by the circular heated plate. In addition, the boundaries separating these patterns are empirically correlated. Empirical correlations for the onset points of the L-rolls are also provided.     

Flow patterns and heat transfer enhancement in low-Reynolds–Rayleigh-number channel flow

This paper presents an experimental study on buoyancy-induced flow patterns and heat transfer characteristics of airflow through a horizontal rectangular channel. The channel had an aspect ratio of six, and its bottom and sidewalls were heated, whereas the top of the channel was cooled. The experiments were conducted at the Reynolds numbers 40 and Rayleigh numbers ranging from 100 to 4200. The Nusselt number and the temperature distributions on the top surface of the channel were measured simultaneously at different thermal/flow conditions, and the heat transfer characteristics of the channel was evaluated, together with the flow patterns in the channel. The results showed that due to the heated sidewalls, which was an `imperfect' factor comparing with the classic Rayleigh–Bénard channel, the longitudinal vortex rolls can occur at the Rayleigh number Ra=100, starting with number of rolls N=2 and then N=4 as the Ra increases, rather than the N=6 mode for the same channel with `perfect' sidewalls. In the present study, the six-roll mode occurred at Ra=1730 and above, but an initial trigger was required. Otherwise the four-roll mode would continue to be the dominant flow pattern at high Rayleigh numbers. It was demonstrated that significant heat transfer enhancement could be achieved in low Reynolds and Rayleigh number flow if the longitudinal vortex rolls were excited in the channel.     

Thermoconvective instabilities in an inclined porous channel heated from below

The thermoconvective instability in an inclined rectangular channel filled with a fluid saturated porous medium and heated from below with a uniform flux is investigated. A stationary parallel buoyant flow with a linear temperature change in the transverse direction is considered. The linear stability to transverse and longitudinal roll disturbances of this basic state is examined. The thermoconvective instability onset of transverse rolls occurs when the Darcy–Rayleigh number exceeds a critical value, that increases with the inclination angle. The critical Darcy–Rayleigh number is discontinuous at the inclination angle 23.4749° above the horizontal. It is shown that, when the inclination angle exceeds 31.3618°, either the transverse rolls are stable or a second discontinuous transition to a higher branch of instability occurs. The longitudinal rolls may be unstable for every inclination except for the vertical. A stability diagram is sketched displaying the geometrical conditions (inclination angle, aspect ratio) such that either the transverse rolls or the longitudinal rolls is the preferred mode of instability.     

Numerical prediction on laminar heat transfer in square duct with 30° angled baffle on one wall

A numerical investigation on periodic laminar flow and heat transfer behaviors in a three-dimensional isothermal wall square duct fitted with 30° angled baffles on lower duct wall only is presented. The computations based on a finite volume method with the SIMPLE algorithm have been conducted for the fluid flow in terms of Reynolds numbers ranging from 100 to 2000. The angled baffles with attack angle of 30° are mounted periodically on the lower duct wall to generate a longitudinal vortex flow through the tested duct. Effects of different baffle height and three pitch length ratios on heat transfer and flow characteristics in the duct are investigated. The study shows that the longitudinal vortex flow created by the baffle helps to induce impinging flows over the baffle trailing end sidewall and the inter-baffle cavity wall resulting in drastic increase in heat transfer rate over the test duct. The computational results reveal that the Nusselt number ratio and the maximum thermal enhancement factor values for using the angled baffle are, respectively, found to be about 7.9 and 3.1 at Re = 2000, BR = 0.3 and PR=1.5.     

Characteristics of vortex flow in a low speed air jet impinging onto a heated disk in a vertical cylindrical chamber

An experiment combining flow visualization and transient temperature measurement is carried out to investigate the characteristics of the mixed convective vortex flow resulting from a low speed air jet impinging onto a heated horizontal circular disk confined in a vertical adiabatic cylindrical chamber. Attention is focused on the conditions leading to the onset of the inertia and buoyancy driven vortex rolls and the effects of governing nondimensional groups on the steady and time dependent vortex flow. More specifically, experiments are conducted for the jet Reynolds number varied from 0 to 1082 and Rayleigh number from 0 to 18,790 for two different injection pipes. The results show that typically the steady vortex flow in the processing chamber consists of two inertia-driven and one buoyancy-driven circular vortex rolls. The secondary inertia-driven roll only appears at high jet Reynolds numbers. At low buoyancy-to-inertia ratio Gr/Re_j² the vortex rolls are steady and axisymmetric. But at certain high Gr/Re_j² the vortex flow becomes unstable and the vortex rolls are somewhat deformed. Besides, new vortex rolls can be induced by the additional thermal rising from the heated disk and the splitting of the primary inertia-driven roll. The temporal characteristics of the time periodic vortex flows are examined in detail. In the region dominated by the new rolls the flow oscillates significantly. Finally, empirical equations are proposed to correlate the oscillation frequency of the time periodic flow, and the size and location of the vortex rolls. Furthermore, the conditions for the onset of the buoyancy driven rolls are given. A flow regime map is provided to delineate the temporal state of the vortex flow.     

EFFECTS OF THERMAL BOUNDARY CONDITION ON BUOYANCY DRIVEN TRANSITIONAL AIR FLOW IN A VERTICAL CYLINDER HEATED FROM BELOW

A three-dimensional unsteady numerical computation was carried out here to investigate the effects of the thermal boundary condition on the convection flow in a vertical, bottom heated cylinder containing air. The thermal condition at the sidewall of the cylinder is assumed to be thermally well insulated or perfectly conducting. Results were obtained for air in a cylinder of finite aspect ratio (Gamma = 2) for various thermal Rayleigh numbers. The predicted results indicate that the flow in the sidewall insulated cylinder is highly asymmetric even at steady state and contains multicellular vortices. The flow formation processes leading to the above structures are relatively complicated. In the early transient two axisymmetric circular vortex rolls, one on top of another, appear. Then the rolls merge asymmetrically. In the late stage the flow deflection by the cylinder top and bottom results in a very complex flow. In the cylinder with a perfectly conducting sidewall the transition from a steady to a time dependent flow is subcritical. However, in the cylinder with an insulated sidewall the flow transition is supercritical.     

NUMERICAL STUDY OF RAYLEIGH-BE´NARD CONVECTION IN A CYLINDER

Numerical solutions of the three-dimensional equations for Rayleigh-Bénard convection in a vertical cylinder are presented. The energy and vorticity transport equations are solved using the Samarskii-Andreyev alternating direction implicit (ADI) scheme. A fast Fourier transform algorithm is used to solve for the vector potential. Solutions are presented for aspect ratios of 2 and 4, a Prandtl number Pr = 7, and Rayleigh numbers 12 h Ra h 37500. A conductive (no motion) state exists when Ra h Ra c = 1860. For Ra > Ra c , there are four main types of flow structures. These are concentric, radial, parallel, and cross rolls. The Nusselt number depends on the type of flow structure.     

A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models

This paper reports the effect of changing the aspect ratio on the heat transfer and flow quantities over in-line tube banks. Two types of in-line arrangements were employed; square and non-square configurations. The models that were examined are a standard k-ε model, SST k-ω model, v2-f model, EB k-ε model and EB-RSM model. The closer results to the experimental data and LES were obtained by the EB k-ε and v2-f models. For the square pitch ratios, the solution has faced a gradual change from a strong asymmetric to asymmetric and then to a perfect symmetry. The strong asymmetric solution was found by the very narrow aspect ratio of 1.2. However, the behaviour of cases of 1.5 and 1.6 became less strong than that predicted in the case of 1.2. In the larger aspect ratio of 1.75, the flow behaviour is seen to be absolutely symmetric for all variables under consideration except Nusselt number. For the very large pitch ratio of 5, the flow has recorded maximum distributions for all parameters on the windward side of the central tube with a perfect symmetric solution around the angle of 180° while the vortex shedding frequency has recorded minimum value and the Strouhal number; therefore, has given the smallest value. However, for the non-square pitch ratio of constant transverse distance, the solution is still asymmetric for all parameters with merely one stagnation at the angle of 52° at the case of the 1.5 × 1.75 while by increasing the longitudinal distance to 2 and 5, the solution provided a comprehensive symmetry for all variables with two vortices are fully developed mirrored in shape on the leeward side of the central tube. On the contrary, for the non-square pitch ratio of constant longitudinal distance, the flow of the case of 1.75 × 1.5 provided two stagnation locations at around 52° and 308° with a very similar solution to the case square ratio of 1.75 for all variables whereas by increasing the transverse distance to 2 and 5, the solution recorded was not perfectly symmetric resulting in two different vortices and one stagnation position located at the leading edge of the cylinder provided by the case of 5 × 1.5. In terms of vortex shedding effect, the reduction in the Strouhal number at a constant transverse pitch is less steep than those at a constant longitudinal pitch.     

Numerical investigation and analysis of heat transfer enhancement in channel by longitudinal vortex based on field synergy principle

3-D numerical simulations were presented for laminar flow and heat transfer characteristics in a rectangular channel with vortex generators. The effects of Reynolds number (from 800 to 3 000), the attack angle of vortex generator (from 15° to 90°) and the shape of vortex generator were examined. The numerical results were analyzed based on the field synergy principle. It is found that the inherent mechanism of the heat transfer enhancement by longitudinal vortex can be explained by the field synergy principle, that is, the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient. The longitudinal vortex improves the field synergy of the large downstream region of longitudinal vortex generator (LVG) and the region near (LVG); however, transverse vortex only improves the synergy of the region near vortex generator. Thus, longitudinal vortex can enhance the integral heat transfer of the flow field, while transverse vortex can only enhance the local heat transfer. The synergy angle decreases with the increase of Reynolds number for the channel with LVG to differ from the result obtained from the plain channel, and the triangle winglet performs better than the rectanglar one under the same surface area condition.     

Isotherms in a horizontal differentially heated cavity at intermediate Rayleigh numbers

Rayleigh-Benard convection in a horizontal, differentially heated, high aspect ratio fluid layer is considered. Experiments with three Rayleigh numbers (13900, 34800 and 51800) corresponding to different flow regimes have been performed. The temperature field in the fluid has been recorded in the form of interferometric projections, the fringe patterns representing isotherms. For steady and quasi-steady flow, the three dimensional temperature field has been obtained using an iterative algebraic reconstruction technique. Results show the formation of longitudinal rolls in the cavity at a Rayleigh number of 13900. The flow is unsteady at a Rayleigh number of 34800, but a strong indication of the formation of cubic rolls is seen. At a Rayleigh number of 51800, the flow field is completely unsteady with no discernible pattern. The local ray-averaged Nusselt numbers at each of the heated and cooled walls have been determined at the two lower Rayleigh numbers. The systematic variation of Nusselt number over each of the solid surfaces confirms the flow models proposed at these Rayleigh numbers. The average Nusselt number qualitatively matches the published correlations.     

Instabilities of vortex rings generated by surface-tension gradients between co-axial disks

Instabilities of vortex rings generated by surface-tension gradients between co-axial disks with Prandtl numbers of 0.001 and 0.01 are investigated by using the linear stability analysis (LSA) method. The continuity-vortex-energy equations are used as the perturbation equations for stability analysis and discretized using a Chebyshev-collocation method. The critical Reynolds numbers and the angular wavenumbers of the unstable mode are obtained for vortex rings with a range of aspect ratios between 0.05 and 1.2. From stability analyses, it is found that the product of the critical model and the aspect ratio approaches a constant when the aspect ratio decreases. The critical mode is m = 16 when the aspect ratio is 0.05. Analyses also indicate that the vortex rings must be of certain energy for the perturbations of flow to grow in amplitude. The viscosity of fluid can dampen perturbations if the magnitude of the stream function of the basic flow is below the critical value. The vortex rings generated by surface-tension gradients become unstable when the magnitude of the stream function is above the critical value.     

FLOW DEVELOPMENT OF CO-FLOWING STREAMS IN RECTANGULAR MICRO-CHANNELS

The diffusion and flow development characteristics of two co-flowing, laminar streams in a high aspect ratio rectangular micro-channel have been examined. A long, thin splitter plate initially separates the two streams such that fully developed flow in each of the two channels is established prior to merging. The co-flowing micro-channel has an aspect ratio of 16 with a width of 1006 μm and a height of 63 μm. Micro-Particle Image Velocimetry (μPIV) was utilized to observe the interaction between the streams for a range of flow rate ratios ranging from one to nine, for Reynolds numbers of one and ten. For flow rate ratios greater than one, a cross-stream pressure gradient exists immediately downstream of the splitter plate, which results in a strong lateral flow of the faster moving fluid into the slower moving fluid. Despite this rapid expansion, the fluids in the two streams do not mix. The two streams eventually recover a fully developed velocity profile across the entire channel. A model is presented to predict this development length based on the pressure imbalance between the two streams. The model is expressed in terms of the flow rate ratio between the streams, which is shown to be a function of channel aspect ratio. An asymptotic condition for the development length is found for high flow rate ratios and high aspect ratio channels. It is shown that existing entrance length relationships greatly underpredict this development length.     

Numerical study of convective heat transfer in T‐bifurcating channel

A numerical study of a three‐dimensional turbulent flow in a rectangular T‐bifurcating duct was performed. It focused on the analysis of heat transfer in the branching duct at 90 to the main flow. Including separation and reattachment phenomena, the flow seemed to be anisotropic. The closure system of the full set of Navier–Stokes equations governing the flow was based on the on one point statistical modeling using a low Reynolds number second‐order full stress transport model. For several aspect ratios, results show that in addition to the recirculation zone in the branching duct close to the upstream side; pairs of streamwise vortices were generated downstream of the junction zone with their centers moving towards the symmetry plane. The effect of the aspect ratio of the branching section in enhancing this phenomenon and flow rate effect on the heat transfer were particularly analyzed in this paper.     

Mixing between a sharp-edged rectangular jet and a transverse cross flow

The scalar mixing field of a turbulent rectangular jet issuing from a sharp-edged orifice with an aspect ratio of 10 into a cross stream flow in a square duct is investigated using marker nephelometry. Jet-to-cross stream velocity ratios of 2.0 and 3.4 are examined in this work. Results include contour plots and transverse profiles of the mean and concentration fluctuation intensity and jet trajectory paths and half concentration lengths expressed as a function of downstream position along the jet trajectory.     

Subsonic compressible flow in two-sided lid-driven cavity. Part I: Equal walls temperatures

This paper presents a numerical study of the laminar, viscous, subsonic compressible flow in a two-dimensional, two-sided, lid-driven cavity using a multi-domain spectral element method. The flow is driven by steadily moving two opposite walls vertically in opposite directions. All the bounding walls have equal temperatures. The results of the simulations are used to investigate the effects of the cavity aspect ratio, the Reynolds number and the Mach number on the flow. At lower Reynolds numbers, the flow pattern consists of two separate co-rotating vortices contiguous to the moving walls. For higher Reynolds numbers, initially a two-vortex flow is formed, which eventually turns into a single elliptical vortex occupying most of the cavity. For a higher aspect ratio, the flow patterns are dissimilar in that the streamlines become more and more elliptic. For aspect ratios as high as 2.5, at high Reynolds numbers, a three-vortex stage is formed. It is found that the compressibility effects are not very significant for Mach numbers less than 0.4. Dissipation of kinetic energy into internal energy changes the temperature field especially near the boundaries. Boundary layer studies suggest that the velocity and temperature boundary layer thicknesses are lower for higher Reynolds numbers. For engineering purposes, these thicknesses can be approximated by the existing flat-plate solutions.     

Numerical investigation and analysis of heat transfer enhancement in channel by longitudinal vortex based on field synergy principle

3-D numerical simulations were presented for laminar flow and heat transfer characteristics in a rectangular channel with vortex generators. The effects of Reynolds number (from 800 to 3 000), the attack angle of vortex generator (from 15° to 90°) and the shape of vortex generator were examined. The numerical results were analyzed based on the field synergy principle. It is found that the inherent mechanism of the heat transfer enhancement by longitudinal vortex can be explained by the field synergy principle, that is, the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient. The longitudinal vortex improves the field synergy of the large downstream region of longitudinal vortex generator (LVG) and the region near (LVG); however, transverse vortex only improves the synergy of the region near vortex generator. Thus, longitudinal vortex can enhance the integral heat transfer of the flow field, while transverse vortex can only enhance the local heat transfer. The synergy angle decreases with the increase of Reynolds number for the channel with LVG to differ from the result obtained from the plain channel, and the triangle winglet performs better than the rectanglar one under the same surface area condition. __________ Translated from Journal of Xi’an Jiaotong University, 2006, 40(9): 996–1000 [译自: 西安交通大学学报]     

Natural convection heat transfer between concentric rectangular parallelepipeds

Natural convection heat transfer between concentric rectangular parallelpipeds was studied numerically for low Rayleigh numbers Ra(≦ 3500) with aspect ratios of the inner parallelepiped of 2.0, 4.0, 6.0, and 8.0. It has been found that the flow patterns for the higher Rayleigh numbers in the space over the inner parallelpiped are ring or rectangular rolls. The number of rolls increases with the aspect ratio. The flow pattern in the side space is an oblong circulation, which extends into the bottom space. The local Nusselt number distribution on the top surface of the inner parallelpiped has peaks at the stagnation points. The relation between the Nusselt and Rayleigh numbers on the top surface is similar to that of the Rayleigh–Bénard convection obtained by Silveston (Chandrasekhar S.Hydrodynamic and Hydromagnetic Stability, 1961, p 68, Oxford University Press), while on the side and bottom surfaces the Nusselt number increases proportionately with the power of the Rayleigh number. © 2001 Scripta Technica, Heat Trans Asian Res, 30(2): 152–163, 2001