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

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Buoyancy driven vortex ﬂow and its stability in mixed convection

of air through a blocked horizontal ﬂat duct heated from below

S.W. Chen, D.S. Shu, J.T. Lir, T.F. Lin

*

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, ROC Received 11 July 2005; received in revised form 19 February 2006

Available online 18 April 2006

Abstract

Experimental flow visualization combined with transient temperature measurement are carried out here to explore the possible sta-bilization 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 mm}3_{(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 lon-gitudinal vortex flow, the presence of either block near the duct entry causes the onset points of the lonlon-gitudinal rolls to move signifi-cantly 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, sta-bilization of the vortex flow behind the block is more pronounced. This flow stasta-bilization 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.

1. Introduction

Vortex flow in the form of steady regular longitudinal and time periodic downstream moving transverse rolls, and a mixture of both induced at slightly supercritical buoyancy in a mixed convective gas flow through a bottom heated horizontal flat duct has been known for some time

and is well documented in the literature[1]. At buoyancy

well above certain critical level unstable vortex ﬂow

appears and the vortex rolls become deformed and time dependent. At an even higher buoyancy irregular rolls pre-vail in the duct. The highly eﬃcient heat transfer associated with the unstable vortex ﬂow is most welcome by the tech-nological applications such as cooling of microelectronic

equipments [2] in which the eﬃcient energy transport is

of major concern. It is of interest to note that the micro-electronic components on the printed circuit boards exist-ing in the coolexist-ing channel for the microelectronic equipments can destabilize the coolant ﬂow and hence can enhance the heat removing rate. Over the past, the use of various wall-mounted protrusions to promote the heat transfer has been extensively studied for both laminar

*

Corresponding author. Tel.: +886 35 712121x55118; fax: +886 35 726440.

E-mail address:tﬂ[email protected](T.F. Lin).

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and turbulent ﬂows. However, in the chemical vapor

depo-sition (CVD) processes [3] used frequently to grow thin

crystal films on silicon substrates, the presence of the vortex flow will result in a non-uniform chemical vapor deposition, producing a thin crystal film of non-uniform thickness. Moreover, the unstable vortex flow will provoke a time-dependent deposition rate. Both the stable and unstable vortex flows are not welcome and should be avoided in the CVD design. Simple means such as lowering the chamber pressure, which can effectively reduce the

buoyancy eﬀects [3], and accelerating the main gas ﬂow

through the substrate inclination have been adopted in real CVD processes to stabilize the vortex flow. But it is rather costly in reducing the chamber pressure. Besides, the sub-strate inclination is only good for stabilizing the temporal oscillations of the vortex flow[4]. It is not effective in wip-ing out the spatial structures of the vortex flow. Other methods need to be sought to stabilize the temporal flow oscillations and to suppress the spatial vortex structure in the mixed convective duct flow. In this experimental study we explore how the buoyancy driven vortex flow and its stability are affected by a rectangular solid block mounted on the bottom of a horizontal flat duct heated from below. In what follows the relevant literature on the mixed convec-tive flow in horizontal blocked and unblocked flat ducts is briefly reviewed.

Previous studies on various aspects of the buoyancy induced vortex flow in an unblocked horizontal flat duct are reviewed first. In a long horizontal plane channel with the bottom plate at a higher uniform temperature than the top one by DT, the critical Rayleigh number for the onset of the vortex flow was found to be around 1708, as pre-dicted from experimental measurements and linear stability

theory[5,6]. Ostrach and Kamotani[7]and Kamotani and

Ostrach[8]experimentally noted that the longitudinal

vor-tex rolls appeared when the temperature difference became larger than a critical value corresponding to Ra = 1708. Above the critical point, the heat transfer rate is increased by the thermal instability and the temperature field is strongly influenced by the motion of the vortex flow. When

Ra > 8000, the vortex rolls become irregular. Hwang and

Liu[9]visualized the onset of secondary ﬂow and showed

that the wave number of vortex rolls remained constant along the ﬂow direction. Experiments conducted by

Incr-opera et al.[10]and Maughan and Incropera[11]disclosed

four flow regimes along the bottom plate-laminar forced convection, laminar mixed convection, transitional mixed convection, and turbulent free convection. The transition to turbulent flow was attributed to the breakdown of vor-tices due to the hydrodynamic instability. Besides, a corre-lation for the onset point was proposed. Criteria for the onset of vortex instability and the start of the transition from two-dimensional laminar flow to three-dimensional vortex flow in mixed convective air flow over an isother-mally heated horizontal flat plate were established by

Moharreri et al.[12]. The vortex ﬂow regime starts with a

stable laminar flow region where vortices develop and grow gradually and ends with an unstable flow region where the vortices mix together and collapse to form a two-dimen-sional turbulent flow regime.

In the mixed convection of nitrogen gas between two horizontal, diﬀerentially heated parallel plates,

Rosenber-ger and his colleagues [13,14] showed that the critical Ra

for the appearance of the transverse convection rolls increased with Re. They also found that at a high Ra, the longitudinal rolls were unsteady and snaking. Besides, they showed the regime of Ra and Re leading to a steady or

unsteady ﬂow. Nyce et al. [15] showed the variations of

velocity field in both axial and transverse directions which were consistent with the presence of both longitudinal roll and transverse wave instabilities. The transverse rolls were noted at a very low Reynolds number by Ouazzani et al. [16,17]. They also refined the regime map to include the transverse rolls. The recent flow visualization from Yu

et al.[1]showed that at a ﬁxed Ra but in reducing Re the

vortex ﬂow transformed from the structure prevailed by the longitudinal rolls to transverse rolls in sequence of stable longitudinal rolls, unstable longitudinal rolls, inter-mittent transitional vortex ﬂow, mixed longitudinal and transverse rolls, and transverse rolls. Photographic results Nomenclature

A aspect ratio, b/d

b, d, l test section width, height, length

g gravitational acceleration

Gr Grashof number, bgd3(Th Tc)/m2

Gr/Re2 buoyancy-to-inertia ratio

h length of the mounted block

k thermal conductivity

P1. . . P6 location of mounted block in the duct

Pr Prandtl number, m/a

Ra Rayleigh number, bgd3(Th Tc)/am

Re Reynolds number, Wmd/m

t time, s

tp period of ﬂow oscillation

T temperature

Tc temperature of the top plate

Th temperature of the bottom plate

Tm mean temperature, (Th+ Tc)/2

Wm mean velocity component in z direction

x, y, z dimensionless Cartesian coordinates all scaled with d

a thermal diﬀusivity

b thermal expansion coeﬃcient

h dimensionless temperature, (T Tm)/(Th Tc)

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from Cheng and Shi[18]revealed the convective instability and chaotic phenomena caused by the buoyancy forces.

Koizumi and Hosokawa [19] presented the sidewall

tem-perature proﬁle in a horizontal rectangular duct heated from below, which simulated a horizontal thermal CVD reactor. They found that although the ﬂow was unsteady but the time-averaged local mass transfer rate on the bot-tom wall can be almost uniform.

Fluid flow and heat transfer around a wall-mounted block in a channel have been extensively studied in recent years. Several different flow patterns are generated near the wall-mounted block such as horseshoe and corner vor-texes, and these vortexes significantly augment the heat and mass transfer from the surface of the block. Chyu and

Nat-arajan [20] experimentally showed that the mass transfer

rate was high at the side surface and lowest at the rear surface around a wall-mounted cube at high Reynolds

numbers. Igarashi[21] and Hsieh et al.[22] examined the

heat transfer around a mounted rib and proposed the rela-tions between the convection heat transfer coeﬃcient and the Reynolds number of the ﬂow and the aspect ratio of

the duct. Besides, Igarashi[23]classiﬁed the ﬂow patterns

around a prism into four types and suggested the average maximum and minimum heat transfer coeﬃcients for dif-ferent angles of attack to an air stream. Moreover, Chyu

and Natarajan [24] tested heat transfer for ﬁve diﬀerent

basic geometric blocks and suggested an inter-element spacing for array conﬁgurations based on the optimal heat transfer performance. In addition, the eﬀective use of mul-tiple wall-mounted ribs to enhance heat transfer in

turbu-lent channel ﬂow was demonstrated by Han et al.[25,26].

These studies focused mainly on the heated transfer aug-mentation by the mounted blocks. Very little is devoted to investigating the possible stabilization of the oscillating vortex ﬂow driven at high buoyancy-to-inertia ratio by mounting a block in a duct.

The above literature review clearly reveals that there has been a substantial amount of research carried out in the past on various aspects of vortex flow and heat transfer in mixed convection of gas in a horizontal unblocked flat duct. Moreover, the use of blocks to enhance the heat transfer and the associated flow characteristics have been extensively studied for both laminar and turbulent flows. In the present study an experimental investigation is carried out to unravel how a wall-mounted rectangular protrusion affects the buoyancy induced vortex flow struc-ture in the low Reynolds number mixed convection of air in a bottom heated horizontal flat duct. Attention will be focused on how the three regular vortex flow patterns, namely, the longitudinal, transverse and mixed vortex rolls, are influenced by the presence of the block in the channel. The effects of the block size and location in the channel on the vortex flow will be examined in detail. In the experi-ment the Reynolds number of the flow is varied from 3.0 to 30 and Rayleigh number from 3000 to 6000. Both the changes in the spatial and temporal structures of the vortex flows will be inspected carefully. It should be pointed out

here that the vortex ﬂow structures in mixed convection of air in a ﬂat duct are closely related to the Nusselt num-ber distribution on the duct bottom, according to our

numerical computation [27]. Thus the information on the

vortex flow characteristics is valuable in improving the design of CVD flow configurations.

2. Experimental apparatus and procedures

The experimental system established in the previous

study[1]is used here to investigate how the buoyancy

dri-ven vortex flow is affected by a rectangular block mounted on the duct bottom in mixed convective air flow through a horizontal flat duct heated from below.

2.1. Experimental apparatus

The experimental apparatus is schematically shown in Fig. 1. The open-loop mixed convection apparatus consists of three parts: wind tunnel, test section, and measuring bench for the velocity and temperature, which is connected with a data acquisition unit.

The test section is a rectangular duct of 240-mm wide and 300-mm long with the duct height of 20-mm between the top and bottom walls, providing an aspect ratio of A = 12. The bottom plate of the test section is made of a 15-mm thick, high purity copper plate and is electrically heated by DC power supplies. The top plate of the test sec-tion is made of a 3-mm thick glass plate and a 2-mm thick plexiglass plate with a gap width of 3-mm. This top plate is reinforced by copper alloy frames to keep it ﬂat. Distilled water is provided from a constant temperature circulation unit and ﬂows into this gap to control the upper plate temperature.

The working fluid is air which is driven into the system by a 7.5-hp air compressor and sent into a 300-l high pres-sure air tank. The air is first regulated by a prespres-sure regu-lator and then passes through a settling chamber, a contraction nozzle, a developing section, the test section, and finally discharges into the ambient surrounding. The developing section is 1690-mm in length, approximately 84 times of the duct height. This insures the flow being fully developed at the inlet of the test section for Re < 50. An outlet section of 190-mm long is added to the test section to reduce the effects of the disturbances from discharging the flow to the ambient surrounding of the open-loop wind tunnel.

The volume flow rate of air is controlled and measured by two Hasting HFC flow controllers designed especially for low volume flow rates, with accuracy better than 1%. A thermocouple probe, which is an OMEGA (model HYP-O) mini hypodermic extremely small T-type thermo-couple (33 gauge) implanted in a 1 in. long stainless steel hypodermic needle, supported by a three-way traversing stand is used to measure the instantaneous air temperature in the test section. In order to unravel the unsteady thermal characteristics of the vortex flow, the transient temperature

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oscillations are measured at selected detection points. The sampling rate of the data channel in the data acquisition unit is set at 0.08 s per scan which is much shorter than the period of the ﬂow oscillation in the low Reynolds num-ber mixed convective ﬂow considered here.

Visualization of the buoyancy driven vortex flow in the test section is realized by injecting smoke tracers at some distance ahead of the settling chamber. By using a 1.5– 2.5 mm plane light sheet from an overhead projector with an adjustable knife edge to illuminate the flow field con-taining these smoke particles, a sharp contrast could be achieved between the duct walls and smoke. Then the flow

photos from the top, side and end views of the test section can be taken.

2.2. Mounting the block and experimental procedures A rectangular block made of acrylic, which has low ther-mal conductivity and diﬀusivity (k = 0.16 W/m k and a= 1.7· 10 7m2/s), is inserted from the outlet of the test loop into the duct and is placed directly on the bottom of the test section at the designated location. The size and shape of the two blocks as well as the chosen locations to be tested here are schematically shown inFig. 2. Note that

Test Section Outlet Section Top View Window Screen Honeycomb Y Cooling Water Z Air Copper Mica Sheet Heater Bakelite Insulation Test Section Screen Honeycomb 20 mm Overhead Projector Camera Camera Overhead Projector 70 mm 1708 mm 1690 mm 300 mm 190 mm Settling Chamber &

Nozzle Developing_Channel _SectionTest Outlet_Section

Cooler Water Heater Pump Distilled Water Air Compressor Air Tank 300 l Dryer Air Tank 300 l Water Filter Oil Filter Pressure Regulator Flowmeter 0~3 slpm Flowmeter 0~15 slpm Smoke Generator 250 l SIDE VIEW TOP VIEW 0 X Z Camera Circular Pipe Settling Chamber & Nozzle

1708 mm Developing Channel 1690 mm 300 mm 190 mm 240 mm 440 mm

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the height of block B is twice of block A. Besides, at a given location the long or short sides of the blocks can be placed normal to the forced flow direction. These two different ori-entations of the blocks are expected to exert very different influences on the vortex flow patterns. The surfaces of the blocks are polished to become rather smooth in order to minimize the possible disturbances to the vortex flow from the surface roughness. Note that the forced air flow and the buoyancy driven natural convection flow considered here are both at relatively low speed in the flat duct and hence the block cannot be shaken or moved by the air flow in the test. In this study the blocks are placed at three different locations with their geometric centers all along the longitu-dinal centerline of the duct bottom, as indicated inFig. 2. According to the location and orientation of a given block, we have six different positions of the block in the test. They are designated as positions P1–P6indicated inFig. 2.

In each experiment the air compressor, dryer, DC power supplies, and the distilled water unit are turned on first and set at the predetermined levels. Meanwhile, the distilled water is circulated over the top plate and the top and bot-tom plates are controlled at the preset temperatures. Then all the experimental parameters are checked and recorded by the data acquisition unit. Usually, it takes about 3 h for the Rayleigh number and the distilled water tempera-ture to be raised to the test point, and another 2 h are needed to maintain the vortex flow at the stable or statisti-cal state. Finally we start the temperature measurement and flow visualization.

2.3. Analysis of data uncertainty

Uncertainties in the Rayleigh number, Reynolds num-ber and other independent parameters are calculated

(b) Positions

Unit: mm Block A

(a) Geometric size and shape Block B

Unit: mm

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according to the standard procedures established by Kline

and McClintock[28]. The uncertainties of the

thermophys-ical properties of air are included in the analysis. The funda-mental thermophysical properties of the working ﬂuid (air)

are a = 0.220 (cm2/s), b = 0.00335 (1/K), Pr = 0.737 and

m= 0.162 (cm2/s) at 30C and 0.997 bar. The ﬂuid

proper-ties are real time corrected based on the temperature and pressure detected at the inlet of the test section. In addition, the uncertainties of the control unsteadiness and tempera-ture non-uniformities on the top and bottom plates are accounted for in the evaluation of the data uncertainty. The analysis shows that the uncertainties of temperature,

Fig. 3. Top view ﬂow photos taken at mid-height of the duct for (a) without block, (b) block A located at P1, (c) block A located at P3, (d) block A located

at P5, (e) block A located at P2, (f) block A located at P4, and (g) block A located at P6, showing the eﬀects of the block location and orientation on

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volume ﬂow rate, dimensions, Reynolds number and Rayleigh number measurements are estimated to be

±0.15C, ±1%, ±0.005 mm, ±2% and ±5%, respectively.

3. Results and discussion

Selected results from the present flow visualization and temperature measurement are presented in the following to illustrate how the presence of a wall-mounted rectangu-lar block affects the vortex flow structures and their stabil-ity in the bottom heated horizontal flat duct over the range of the parameters covered here. Particular attention is paid to the effects of the block size, orientation and location on the longitudinal, transverse and mixed vortex flow patterns at long time when all the initial transients in the flow die out and the flow already reaches steady or statistical state.

3.1. Eﬀects of block on longitudinal vortex ﬂow

It is well known that at slightly supercritical buoyancy for the Reynolds number exceeding certain low value the resulting vortex flow in the unblocked duct at long time is in the form of steady longitudinal vortex rolls [1]. To illustrate the effects of the mounted block on this longi-tudinal vortex flow, the top view flow photos at steady or statistical state taken at the midheight of the duct (y = 1/2) with block A mounted at different locations and

orientations are shown in Fig. 3 for Re = 30.0 and Ra =

6003 along with that for the unblocked duct. Since the votex rolls induced in the mixed convection ﬂow considered here have the same diameter which is equal to the duct height, the top view ﬂow photos taken at the mid-height of the duct are representative for that taken at other

Fig. 4. Temporal structure of vortex ﬂow revealed from top and end view ﬂow photos at statistical state and time records of air temperature at selected locations at y = 1/2 and x = 0, 2 and 4 for block A mounted at (a) position P1and (b) position P2for Ra = 5008 at Re = 30.0 (Gr/Re

2

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horizontal planes. Hence only those photos taken at the mid-height are presented in this study. The short sides of the block are normal to the forced ﬂow direction in Fig. 3(b)–(d), while the long sides of the block are normal

to the forced ﬂow direction inFig. 3(e)–(g). A comparison

of the results inFig. 3(a) and (b) clearly indicates that the

onset points of the longitudinal rolls move substantially upstream especially for the pair of longitudinal vortex rolls directly behind the block when the block is placed near the duct entry. When the block is placed near the geometric center and exit end of the duct, the eﬀects of the block

on the longitudinal tolls are much milder (Fig. 3(c) and

Fig. 5. Top view ﬂow photos taken at mid-height of the duct for (a) without block, (b) block A located at P1, (c) block A located at P3, (d) block A located

at P5, (e) block A located at P2, (f) block A located at P4, and (g) block A located at P6, showing the eﬀects of the block location and orientation on

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(d)). We move further to investigate how the orientation of the block affects of the longitudinal vortex flow by placing the block with its long sides normal to the forced flow direction. The associated results given inFig. 3(e)–(g) again show that the longitudinal rolls appear at a much shorter distance from the duct inlet when the block is placed near the duct inlet. Besides, the vortex rolls directly behind the block are smaller in size and one more pair of vortex rolls are induced, compared to the unblocked duct. Note that the forced flow is blocked to a larger extent when the long sides of the block are normal to the forced flow direction. Hence this block orientation exhibits stronger effects on the vortex flow. Similar trend is noted for the effects of the block on the longitudinal vortex flow induced at differ-ent Rayleigh numbers.

To further manifest the effects of the block on the detailed characteristics of the longitudinal vortex flow, the top and end view flow photos along with the time records of the air temperature at selected locations for Re = 30.0

and Ra = 5008 are given inFig. 4 for the block A placed

near the duct inlet with its short and long sides respectively normal to the forced ﬂow direction. In these plots and

sim-ilar plots to be examined later the time t = 0 denotes an arbitrary time instant at steady or statistical state. The results inFig. 4(a) show that for the short sides of the block normal to the forced flow direction, the longitudinal vortex flow is still spanwisely symmetric. But in the region near the duct exit and behind the block the flow is in a low amplitude oscillation with time, as clear from the time records at the

locations z = 12 and x = 0 and 2. However, in the

unblocked duct our previous study[1]indicates that the cor-responding longitudinal vortex ﬂow is steady in the entire duct. Now as the long sides of the block are normal to the

forced ﬂow direction (Fig. 4(b)), the unstable region of

the longitudinal rolls is much larger by noting the temporal temperature oscillation at locations z = 9 and 12 and x = 0 and 2. Besides, the oscillation is stronger. Then, the effects of the block height on the longitudinal vortex flow are inspected by observing the top view flow photos at long time for blocks A and B placed at different locations and orientations. The results show that this change in the block height has very slight effects on the onset locations of the longitudinal rolls. Besides, for the block B the size of the lon-gitudinal rolls directly behind the block is nearly the same as

Fig. 6. Temporal structure of vortex ﬂow revealed from (a) top view ﬂow photos at statistical state and (b) time records of air temperature at selected locations at y = 1/2 and x = 0, 2, and 4 in the unblocked duct for Ra = 3003 at Re = 4.0 (Gr/Re2= 263.0, tp= 10.6 s).

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the other and we do not have an additional roll pair induced in the duct, unlike that for the block A. Finally, the desta-bilization of the longitudinal vortex ﬂow in the exit portion of the duct can be slightly stronger due to the presence of block B.

In summary, placing the block near the duct inlet can cause the earlier onset of the longitudinal rolls especially in the region directly behind the block and can destabilize the longitudinal vortex flow in the exit portion of the duct again behind the block. Both effects are expected to pro-mote the heat transfer in the flow. Moreover, with the long sides of block A normal to the forced flow direction an additional pair of longitudinal rolls can appear.

3.2. Eﬀect of block on transverse vortex ﬂow

The transverse vortex flow affected by block A mounted in two different orientations at various locations is

illus-trated inFig. 5by showing the top view photos at the

sta-tistical state for Re around 4.0 and Ra = 3007. When contrasted with the regular time periodic downstream mov-ing transverse rolls prevailed in the unblocked channel (Fig. 5(a)), the results in Fig. 5(d) and (g) indicate that the transverse vortex ﬂow is also little aﬀected by the block placed near the duct exit. But when the block is placed in the middle section of the duct, the transverse rolls

down-stream of the block are slightly deformed (Fig. 5(c) and

(f)). More speciﬁcally, the middle portion of the transverse rolls near the duct axis becomes somewhat distorted as they move over the block. The deformation of the transverse rolls as they move over the block can be more clearly seen from the corresponding side view ﬂow photos at the central vertical plane (x = 0). The results show that near the block the cross-sections of the transverse rolls are highly dis-torted. As the transverse rolls move further downstream the roll distortion decays gradually. At the duct exit the

Fig. 7. Temporal structure of vortex ﬂow revealed from top view ﬂow photos at statistical state and time records of air temperature at selected locations at y = 1/2 and x = 0, 2 and 4 for block A mounted at (a) position P4and (b) position P1for Ra = 3003 at Re = 4.0 (Gr/Re

2

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transverse rolls almost restore to their original regular shape. Now when the block is located near the duct inlet, significant distortion in the transverse vortex rolls is noted inFig. 5(b) for the short sides of the block normal to the forced flow direction. The transverse rolls become sinuous to some extent and knotted as they just pass over the block. In the downstream the transverse rolls restore noticeably and become nearly straight in the spanwise direction, but they still contain knots. It is of interest to note that when the long sides of the block are normal to the forced flow direction (Fig. 5(e)), two deformed longitudinal rolls are induced right behind the block and extend to the duct exit. These two longitudinal rolls break the transverse rolls into two portions in the duct and cause them to become highly distorted.

The results for the transverse vortex flow with blocks A and B placed at different orientations and locations indi-cate that the block height exhibits much greater effects on the transverse rolls especially when the blocks are placed near the duct inlet. In particular, for block B with its height

being twice of block A, a much larger region behind the block is dominated by the deformed longitudinal rolls when the long sides of the block are normal to the forced ﬂow direction.

To reveal the effects of the block on the temporal char-acteristics of the transverse vortex flow, the time records of the air temperature at selected locations in the unblocked duct are examined first for the case presented above with

Re = 4.0 and Ra 3000. The experimental results given

inFig. 6show that the entire ﬂow oscillates at the same

fre-quency (tp= 10.6 s) and amplitude in the duct core where

the fully developed transverse rolls prevail[1]. When block A is placed in the middle section of the duct, the results in Fig. 7(a) manifest that only in the small region right behind the block the flow oscillation is in a much smaller amplitude. Specifically, the reduction in the oscillation amplitude by the block presence is more than 50% by comparing the data in Figs. 6 and 7(a). Elsewhere the flow oscillates at nearly the same amplitude as that in the unblocked duct and the oscil-lation frequency of the flow is unaffected by the block. But

Fig. 8. Temporal structure of vortex ﬂow revealed from top view ﬂow photos at statistical state and time records of air temperature at selected locations at y = 1/2 and x = 0, 2 and 4 for (a) block B mounted at position P2for Ra = 3002 at Re = 4.0 (Gr/Re

2

= 263.0, tp= 10.6 s), and (b) a longer block

(h = 12 cm) mounted at position P2for Ra = 3005 at Re = 4.0 (Gr/Re 2

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when block A is mounted near the duct inlet, the flow oscil-lation is significantly suppressed in the entire downstream region behind the block (Fig. 7(b)). Note that the oscillation amplitude is also reduced by more than 50% in this region. Moreover, some irregularity in the temperature oscillation appears there. Outside this region the flow again oscillates at the same frequency as the unblocked duct.

Finally, the flow oscillation affected by block B is inspected. These results resemble qualitatively with those inFig. 7for block A. More specifically, the increase in the block height causes the flow in the small region right behind block B to become essentially steady, as evident from the time records of the air temperature at z = 3 and 6 and x = 0 given inFig. 8(a). But in the region near the duct exit large amplitude, irregular flow oscillation appears. Slightly less effective flow stabilization by mounting block B on the duct bottom with its short sides normal to the forced flow direction is also noted. Moreover, it is of interest to note

from the results in Fig. 8(b) that placing an even longer

block of 12-cm in length, 1-cm in height and 2-cm in width in the duct entry with its long sides normal to the ﬂow direc-tion can completely suppress the temporal ﬂow oscilladirec-tion in the duct. However, weak and somewhat deformed longitudi-nal rolls still appear in the duct.

3.3. Eﬀects of block on mixed vortex ﬂow

Finally, how the mixed longitudinal and transverse vor-tex flow is affected by the mounted block is examined. The results for block A with the long sides of the block normal to the forced flow direction for Re = 10.0 and Ra = 6002 suggest that the effects of the block on the mixed vortex flow get stronger when the block is mounted at the more upstream location, similar to its effects on the longitudinal and the transverse vortex flows already discussed above. Behind the block, the flow again deforms substantially. And when the block is placed near the duct inlet, the verse rolls in the duct core for the unblocked duct are

trans-Fig. 9. Top view flow photos showing the effects of block A mounted at positions P1and P2on the mixed vortex flow for (a), (b) and (c) Ra = 4003 and

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formed to the longitudinal rolls. But these longitudinal rolls are somewhat unstable and they become highly deformed in the exit half of the duct. It is of interest to illustrate the influences of the block orientation, when block A is placed near the duct inlet, on the mixed vortex flow prevailed at different buoyancy-to-inertia ratios for Re = 10.0 inFig. 9. The results inFig. 9(a) and (b) indicate that at a low buoyancy-to-inertia ratio the transverse rolls only exist in a small portion of the unblocked duct and they all change to steady regular longitudinal rolls due to the presence of the block with its short sides normal to the forced flow direction. At a slightly higher buoyancy the transverse rolls occupy a larger portion of the unblocked duct (Fig. 9(d)) and they are changed to slightly deformed longitudinal rolls (Fig. 9(e)) by the presence of the block. The corresponding time records of the air tem-perature indicate that the flow oscillation is significantly

suppressed by the block as the transverse rolls are changed to the longitudinal rolls behind the block. But near the duct exit large amplitude, irregular ﬂow oscillation begins to appear. At an even higher buoyancy-to-inertia ratio the block causes the vortex ﬂow downstream of it to become somewhat irregular (Fig. 9(h)). The associated time records

of the air temperature given in Fig. 10(a) again show the

suppression of the flow oscillation by the block presence, and in the exit half of the duct the flow oscillation is intense and irregular. Now when block A is placed near the duct inlet with its long sides normal to the flow direction, the mixed vortex flow is changed to regular longitudinal vortex flow (Fig. 9(c) and (f)) except at the relatively high

buoy-ancy-to-inertia ratio (Fig. 9(i)). At such high

buoyancy-to-inertia ratio the longitudinal vortex rolls are unstable and highly deformed in the exit portion of the blocked duct. The corresponding ﬂow oscillation shown in

Fig. 10. Temporal structure of vortex ﬂow revealed from top view ﬂow photos at statistical state and time records of air temperature at selected locations at y = 1/2 for block A mounted at (a) position P1and (b) position P2for Ra = 6002 at Re = 10.0 (Gr/Re

2

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Fig. 10(b) is nearly time periodic and in a large amplitude in this portion of the duct. Moreover, it is noted that by mounting a longer block of 8-cm in length, 1-cm in height and 2-cm in width the temporal ﬂow oscillation can be almost completely suppressed in the duct (Fig. 11).

To further illustrate the effects of the block height on the mixed vortex flow, the top view flow photos affected by blocks A and B placed near the duct inlet with two different orientations are compared for Re = 10.0 and Ra = 4002, 5004 and 6008. A close inspection of these results reveals that the regularization of the vortex flow by block B with a larger height is much more prominent. Specifically, steady longitudinal vortex flow prevails in the duct when block B is mounted near the duct inlet for all cases exam-ined here except for Re = 10.0 and Ra = 6008 in which some flow deformation is noted.

4. Concluding remarks

Experimental flow visualization and transient tempera-ture measurement have been carried out in the present study to explore how a wall-mounted rectangular block affects the vortex flow structure in mixed convection of

air through a bottom heated horizontal flat duct. Two acrylic blocks with different heights were mainly tested here. The effects of the block orientation and length are also examined. Each mounted block was placed along the longitudinal centerline of the duct bottom, and the Rey-nolds and Rayleigh numbers of the flow were respectively varied from 3 to 30 and 3000 to 6000 in the experiment. The major results obtained can be summarized in following:

(1) In the ranges of the Reynolds and Rayleigh numbers at which the longitudinal vortex flow prevails in the unblocked duct, placing block A or B near the duct entry causes earlier onset of the longitudinal rolls especially in the region directly behind the block and can destabilize the longitudinal vortex flow in the exit portion of the duct. When the block is mounted in the exit half of the duct, the longitudinal vortex flow is only slightly affected.

(2) The transverse vortex flow is also slightly affected by the block when it is placed near the duct exit or the geometric center of the duct bottom. However, the transverse rolls deform significantly as they pass over the block. Meanwhile the air temperature oscillation is in much smaller amplitude in the region behind the block. Elsewhere the flow is also time periodic and oscillates at nearly the same frequency and amplitude as that in the unblocked duct. When block A is placed near the duct inlet the transverse rolls downstream of the block become sinuous and knot-ted for the short sides of the block normal to the forced flow direction. But when the long sides of the block are normal to the forced flow direction, two deformed longitudinal rolls appear in the region behind the block and the transverse rolls are splitted into two portions and are somewhat distorted. Increasing the block height can regularize the longitu-dinal rolls. Suppression of the flow oscillation by the block is significant in the region behind the block. The flow behind block B can be completely stabilized. A further increase of the block length can completely stabilize the temporal flow oscillation in the duct. (3) For the mixed vortex flow in the unblocked duct, the

transverse rolls in the duct core can be significantly affected by the mounted block. The longitudinal rolls near the duct sides are less affected. Specifically, plac-ing block A near the duct inlet can change the trans-verse rolls to regular or deformed longitudinal rolls depending on the buoyancy-to-inertia ratio and ori-entation of the block. Flow stabilization by the block is prominent. More effective flow stabilization can be obtained by increasing the block height and placing the block with its long sides normal to the forced flow direction. Flow behind block B is essentially steady except in the exit portion of the duct. Moreover, a longer block can suppress nearly all the temporal flow oscillation in the duct.

Fig. 11. Temporal structure of vortex ﬂow revealed from top view ﬂow photo at statistical state and time records of air temperature at selected locations at y = 1/2 and x = 0, 2 and 4 for a longer block (h = 8 cm) mounted at position P2for Ra = 6008 at Re = 10.0 (Gr/Re2= 84.2).

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During the course of this investigation, it is realized that the transverse and mixed vortex flows can be partially sta-bilized by placing block A or B near the duct inlet. Specif-ically, in the region behind the block the vortex flow can be stabilized. Increasing the block height can produce more profound flow stabilization effects in a larger region. We need to systematically explore how the length, width, height and even the shape of the block affect the stability of the vortex flows. This needs to be investigated in the near future.

Acknowledgement

The ﬁnancial support of this study by the engineering division of National Science Council of Taiwan, ROC through the NSC83 0404 E009 054 is greatly appreciated. References

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