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.     

EFFECTS OF ASPECT RATIO ON VORTEX FLOW PATTERNS IN MIXED CONVECTION OF AIR THROUGH A BOTTOM-HEATED HORIZONTAL RECTANGULAR DUCT

Abstract

Buoyancy-induced vortex flow structures and the associated heat transfer were numerically investigated in a mixed convective airflow in a bottom-heated horizontal rectangular duct of different aspect ratios. The unsteady three-dimensional Navier-Stokes and energy equations were directly solved by a higher order upwind finite difference scheme. Results were presented in particular for Reynolds numbers ranging from 5 to 15, Rayleigh numbers up to 9000, and aspect ratios from 4 to 12. The predicted results clearly show significant differences in vortex structures induced in ducts with small and large aspect ratios. For an aspect ratio less than 6 the transverse vortex rolls are periodically generated in the duct entry and gradually transform into longitudinal rolls when moving downstream. The resulting vortex flow eventually evolves to a time periodic state with the upstream and downstream portions of the duct dominated by the transverse rolls and longitudinal rolls, respectively. For a large aspect ratio (A > 9) the transverse rolls prevail in the duct core, with two to three longitudinal rolls existing near each sidewall. The flow oscillation in the region dominated by the transverse rolls is much higher than that dominated by the longitudinal rolls. At high Ra the flow becomes chaotic in time, and the duct is filled with unstable irregular vortex rolls.     

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.     

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.     

Mixed convection between horizontal plates—I. Entrance effects

Entrance effects in mixed convection between horizontal, differentially heated plates were studied in nitrogen by laser Doppler anemometry in a range 1368 < Ra < 8300 and 15 < Re < 170. Two entrance lengths were deduced from velocity profiles: one for the onset of buoyancy-driven convective instability, and one for the full development of the mixed flow. Explicit expressions for both entrance lengths are given. In addition, unsteady longitudinal convection rolls were observed. These are discussed in terms of an admixture of transverse convection rolls and/or contributions from upstream turbulence. The experimental results show that the critical Ra for the transverse convection roils increases as Re increases.     

Mixed convection between horizontal plates—II. Fully developed flow

Fully developed velocity profiles of longitudinal convection rolls in mixed convection between horizontal plates were measured in nitrogen by laser Doppler anemometry for a range 2472 < Ra < 8300 and 15 < Re < 150. It is shown analytically and experimentally that the transverse velocities of the longitudinal convection rolls are independent of the forced flow. The experimentally and numerically obtained w-profiles (Pr = 0.71) are in good agreement with theoretical predictions (Pr → ∞) and other experimental results (Pr = 11.1 and 930) for Rayleigh-Benard convection. A detailed study of the longitudinal velocity modulation Δu[w_max(Ra), Re] is presented. Also, asymmetric roll patterns were found in spite of the small temperature differences used between the horizontal plates.     

Unsteady mixed convection in horizontal ducts with applications to chemical vapor deposition processes

Mixed convection in a horizontal rectangular duct of aspect ratio 4 heated from below with cold side walls was studied numerically for a non-Boussinesq fluid. Results are presented for a reduced temperature of 2.33 and a Rayleigh number of 130,700. The resulting flow field at Re = 25 consisted of four steady longitudinal vortices, symmetric about the duct centerline, with a leading transverse roll cell. A reduction to Re = 10 resulted in the introduction of traveling transverse waves. A further reduction Re = 5 resulted in a loss of symmetry about the duct centerline plane. Further work is underway to verify the Re = 5 results.     

The onset of convective instability in the thermal entrance region of plane Poiseuille flow heated uniformly from below

The onset condition of regular longitudinal vortex rolls in the thermal entrance region of plane Poiseuille flow heated from below is analyzed. Under propagation theory the stability equations are produced self-similarly, based on scale analysis. The onset position of secondary flow, which represents the starting point of mixed convection, is predicted as a function of the Prandtl number, Reynolds number and Rayleigh number. As expected, the critical position moves upstream as the Rayleigh number increases and an increase in Reynolds number makes the system more stable. The present predictions compare favorably with existing experimental data of water and air.     

Finite amplitude convection with longitudinal vortices in plane poiseuille flow—the effect of uniform axial temperature gradient

Finite amplitude convection with longitudinal vortex rolls for a steady hydrodynamically and thermally fully developed laminar forced flow between two infinite horizontal flat plates subjected to axially uniform wall heat flux is approached by a finite-difference solution using a combination of a boundary vorticity method and a line iterative relaxation technique. The governing equations with Boussinesq approximations are solved up to four times the critical value for the parameter (PrReRa). The onset of secondary flow in the form of longitudinal vortex rolls is indicated by a critical value (PrReRa)∗ which can be obtained by linear stability analysis with infinitesimal disturbance. The wave number in the post-critical flow regime is assumed to be that predicted by the linear stability analysis. The heat transfer mechanism is clarified by a detailed study of the field characteristics for flow and temperature using air (Pr = 0.7) as an example. A series of photographs depicting the gradual development of the longitudinal vortex rolls for air is also presented. Flow and heat transfer results are presented for Pr = 0.1, 0.7, 2, 10 and 100. A study of the Prandtl number effect reveals that the effect of secondary flow on pressure-drop parameter fRe can be neglected for Pr ? 10 and an asymptotic behavior for heat transfer results exists for Pr ? 2 in the post-critical regime.     

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.     

Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium

The combined effects of the double-diffusion and of the viscous dissipation on the convective instability in a fluid-saturated porous medium with a basic horizontal throughflow are investigated. A horizontal porous layer with an impermeable adiabatic lower wall and an impermeable isothermal upper wall is considered. The parallel boundary walls are assumed to have uniform, but unequal, concentrations of the solute. A linear stability analysis is carried out both numerically and by a first-order perturbation method. General disturbances having the form of oblique rolls are considered, reducing either to longitudinal rolls or to transverse rolls in the special cases of roll axes parallel or orthogonal to the basic flow direction, respectively. It is shown that the combined effects of viscous dissipation and mass diffusion may lead to the instability of the basic horizontal flow. Either the longitudinal rolls or the transverse rolls may be the preferred modes of instability depending on the value of the viscous dissipation parameter Ξ. The longitudinal rolls are the most unstable when Ξ < 61.86657.     

Mixed convection heat transfer in horizontal,concentric annuli for transitional flow conditions

Experiments have been performed to determine mixed convection flow and heat transfer in a horizontal, concentric tube annulus for Reynolds numbers in the range 2200 < Re < 5000. Within this range, flow conditions are turbulent and laminar, respectively, in regions of the annulus above and below the heated inner tube. For Reynolds numbers less than a critical value Re₁ which depends on the Rayleigh number, diameter ratio and longitudinal position, flow along the sides of the annulus is laminar and helicoidal. For Re >Re₁, there is a breakdown in the helicoidal motion, with subsequent transition to turbulence in the top and side regions of the annular passage. The local Nusselt number at the top of the inner tube is less than, equal to, and greater than that at the bottom for Re < Re₁, Re = Re₁, and Re >Re₁, respectively. The circumferentially averaged Nusselt number is weakly dependent on longitudinal position and may be correlated in terms of the Rayleigh and Reynolds numbers and the tube diameter ratio.     

Unstable vortex flow and new inertia-driven vortex rolls resulting from an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out here to investigate the possible presence of new inertia-driven vortex rolls and some unique characteristics of the time-dependent mixed convective vortex flow in a high-speed round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. How the jet Reynolds and Rayleigh numbers and jet-to-disk separation distance affect the unique vortex flow characteristics is examined in detail. Specifically, the experiment is conducted for the jet Reynolds number varying from 0 to 1623 and Rayleigh number from 0 to 63,420 for the jet-to-disk separation distance fixed at 10.0, 20.0 and 30.0 mm. The results indicate that at sufficiently high Re_j the inertia-driven tertiary and quaternary rolls can be induced aside from the primary and secondary rolls. At an even higher Re_j the vortex flow becomes unstable due to the inertia-driven flow instability. Only for H = 20.0 mm the flow is also subjected to the buoyancy-driven instability for the ranges of the parameters covered here. Because of the simultaneous presence of the inertia- and buoyancy-driven flow instabilities, a reverse flow transition can take place in the chamber with H = 20.0 mm. At the large H of 30.0 mm the flow unsteadiness results from the mutual pushing and squeezing of the inertia- and buoyancy-driven rolls since they are relatively large and contact with each other. It is also noted that the critical Re_j for the onset of unsteady flow increases with ΔT for H = 10.0 and 20.0 mm. But for H = 30.0 mm the opposite is true and raising ΔT can destabilize the vortex flow. Based on the present data, flow regime maps delineating the temporal state of the flow are provided and correlating equations for the boundaries separating various flow regimes are proposed.     

Stability of natural convection in an inclined square duct with perfectly conducting side walls

We have performed three-dimensional linear stability analyses for natural convection in an inclined square duct. The duct is heated from the bottom, while the lateral walls are assumed to be perfectly thermal conducting. Three-dimensional transverse rolls whose axes are normal to the axis of the duct occur from the motionless state when the Rayleigh number exceeds a critical value and the duct is placed horizontally (θ = 0°). However, it is found that when the duct is placed inclined (θ = 0.01°), a two-dimensional longitudinal roll which is unchanged in the axis of the duct occurs and is stable if the Rayleigh number is small.     

Flow visualization of annular and delta winlet vortex generators in fin-and-tube heat exchanger application

This study presents flow visualization and frictional results of enlarged fin-and-tube heat exchangers with and without the presence of vortex generators. Two types of vortex generators and a plain fin geometry were examined in this study. For plain fin geometry at Re=500, the horseshoe vortex generated by the tube row is not so pronounced, and the horseshoe vortex separates into two streams as it flows across the second row and consequently loses its vortical strength. This phenomenon may supports the “maximum phenomenon” in low Reynolds number region reported by previous studies. With the presence of annular vortex generator, the presence of a pair of longitudinal vortices formed behind the tube is seen. The strength of the counter-rotating vortices increases with the annular height and the strength of the longitudinal vortices is so strong that may swirl with the horseshoe vortices and other flow stream. For the same winlet height, the delta winlet shows more intensely vortical motion and flow unsteadiness than those of annular winlet. This eventually leads to a better mixing phenomenon. However, it is interesting to know that the corresponding pressure drops of the delta winlet are lower than those of annular winlet. Compared to the plain fin geometry, the penalty of additional pressure drops of the proposed vortex generators is relatively insensitive to change of Reynolds number.     

A further investigation of effects of jet-disk separation distance on steady mixed convective vortex flow resulting from a confined impinging air jet

We extend our previous study [J.C. Hsieh, T.F. Lin, Effects of jet-to-disk separation distance on the characteristics of mixed convective vortex flow in an impinging air jet confined in a cylindrical chamber, Int. J. Heat Mass Transfer 48 (2005) 511–525] here to further investigate how the jet-disk separation distance H affects the mixed convective vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. The experiment is conducted for the jet-disk separation distance varying from 40.0 to 60.0 mm and the jet flow rate is varied from 0 to 12.0 slpm (standard liter per minute) for the jet Reynolds number Re_j ranging from 0 to 1623. The temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0 °C for the Rayleigh number Ra ranging from 0 to 507,348. The data from the present study for the ratio H/D_j = 4–6 are compared with our previous study for H/D_j = 1–3. The results indicate that the critical jet Reynolds numbers for the onsets of the secondary and tertiary inertia-driven rolls and for the onset of the buoyancy-driven roll vary nonmonotonically with the jet-disk separation distance due to the complicate changes of the vortex flow structure with H. In the steady vortex flow, both the primary inertia-driven roll and the buoyancy-driven roll get larger at increasing jet-disk separation distance before they contact with each other for H/D_j = 1 and 2. But for H/D_j ≧ 3 the primary roll and buoyancy roll do not always grow at increasing H. Finally, empirical correlations are proposed for the critical conditions leading to the onsets of the inertia- and buoyancy-driven vortex rolls.     

Laser schlieren measurement of vertical flow past a heated horizontal circular cylinder

Flow past a heated horizontal circular cylinder in the vertically upward direction has been experimentally studied using a monochrome schlieren technique. Both free convection ((Gr)^1/3Re)=0 and mixed convection ((Gr)^1/3Re)=1011, 1055, 1095 and 1133 cases have been studied. The Reynolds number based on the cylinder diameter is set at 102 for the mixed convection, and four heating levels have been utilized with Grashof numbers of Gr=975, 1105, 1240 and 1370. The temperature distribution of the plume, the Strouhal number and the schlieren images have been reported. The vortex shedding frequency decreases with increasing Grashof number and a complete suppression of vortex shedding takes place at Grashof number of 1370. The wake is seen to become visibly narrow during the suppression of vortex shedding. The nondimensional temperature profile inside the plume is a strong function of Grashof number for free convection in comparison to that of mixed convection.     

Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re=1000, Re=1500 and Gr?10⁸ using a low Reynolds number k-ε model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar-turbulent transition and relaminarization of the flow. They also distinguish the Re-Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000?Re?1500, Gr?5×10⁷.     

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.     

Heat transfer in square duct fitted diagonally with angle-finned tape—Part 2: Numerical study

A numerical work has been conducted to examine turbulent flow and heat transfer characteristics in a three-dimensional isothermal-fluxed square-duct fitted diagonally with 30°-angle finned tapes. The computations are based on the finite volume method with the SIMPLE algorithm implemented. The air flow and heat transfer characteristics in the duct are presented for Reynolds number (Re) in a range of 4000 to 20,000. In the current study, a straight tape with 30°-angled fins mounted repeatedly on both sides is inserted diagonally into the test duct to generate a pair of longitudinal counter-vortices in assisting chaotic flow mixing in the duct including vortex-induced impingement (VI) effect. Effects of fin blockage ratio (BR = b/H) and pitch ratio (PR = L/H) on heat transfer and pressure drop behaviors in the duct are investigated and the results of the finned tape insert are compared with available measurements. The computation reveals that predicted results from the finned tape insert are in good agreement with measured data. The study indicates that the vortex flow can help to induce impingement/reattachment flows (VI effect) on the duct walls leading to drastic increase in the heat transfer rate over the duct. The rise of the BR and the reduction of the PR results in the increase in Nusselt number and friction factor values. The maximum thermal performance is found to be 1.95 for using the finned tape at BR = 0.2 and PR = 1 whereas the Nusselt number ratio is about 4.5 at lower Re.