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

A further investigation of effects of jet-disk separation distance on steady

mixed convective vortex flow resulting from a confined impinging air jet

K.M. Chen, F.C. Hsieh, J.C. Hsieh, T.F. Lin

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 23 September 2008 Received in revised form 3 July 2009 Accepted 3 July 2009

Available online 25 August 2009

Keywords: Impinging jet Vortex flow

Jet-disk separation distance Buoyancy effects

a b s t r a c t

We extend our previous study [J.C. Hsieh, T.F. Lin, Effects of jet-to-disk separation distance on the charac-teristics 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 dis-tance 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 Rejranging 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/Dj= 4–6 are compared with our previous study for H/Dj= 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/Dj= 1 and 2. But for H/Dj=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.

Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Considerable amount of work has been carried out in the past to investigate the fluid flow and heat transfer in the round or slot jet impinging onto a large horizontal plate. Most of the studies focus on quantifying the highly efficient heat transfer associated with the high speed impinging jets. Thus the flow driven by the jet iner-tia is much stronger than the flow driven by the buoyancy. For in-stance, to explore the detailed vortex flow structure, Fitzgerald and Garimella[2]and Morris et al.[3,4]used numerical simulation and flow visualization to investigate the vortex flow characteristics for a liquid impinging jet, which were found to be influenced by the jet Reynolds number and jet-disk separation distance. For the appli-cations such as growth of semiconductor thin crystal films on heated silicon wafers through the chemical vapor deposition (CVD) processes, low speed impinging jets are often employed and the buoyancy-driven secondary flow can be relatively strong. Recently, the vortex flow structures resulting from a low speed gas jet impinging onto a heated horizontal disk confined in a verti-cal cylindriverti-cal chamber at low Rejwere visualized by Hsieh et al.[5],

which showed that the inertia and buoyancy-driven gas flow

recir-culation was typically in the form of three circular vortex rolls. In addition, the effects of the jet Reynolds number and jet-disk sepa-ration distance on the locations of the centers of the primary and secondary inertia-driven vortex rolls were investigated by Law and Masliyah[6]. Details on the size and locations of these vortex rolls affected by the jet Reynolds and Richardson numbers for a laminar confined slot jet were examined by Sahoo and Sharif[7]. For a confined laminar slot impinging jet the critical jet Reynolds number for the onset of unsteady flow was numerically shown to be between 585 and 610 by Chiriac and Ortega[8]. According to the turbulence intensity measurement at a nozzle exit, Lin et al.

[9] suggested that the jet at a Reynolds number smaller than

1226 may be regarded as in an initially laminar flow regime. Santen et al.[10,11]indicated that the onset of thermal instability became earlier at increasing buoyancy-to-inertia ratio. Moreover, a laminar impinging jet with small pulsation at the outlet of the jet was numerically simulated by Poh et al.[12]. Law and Masliyah[13]

found that the impinging jet flow structure was significantly influ-enced by the chamber geometry. More complete information on the flow associated with the impinging jets can be found from the critical reviews by Jambunathan et al.[14], and Viskanta[15].

As mentioned above, the gas jet impinging onto the substrate in the CVD chamber is at relatively low flow rate and the buoyancy in the flow is no longer small compared with the jet inertia with the 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2009.07.009

*Corresponding author. Tel.: +886 35 712121x55118; fax: +886 35 726440. E-mail address:tflin@mail.nctu.edu.tw(T.F. Lin).

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Reynolds and Rayleigh numbers, respectively, ranging from 0.01 to 100.0 and from 10,000 to 1,000,000. The importance of the buoy-ancy on the recirculating flow in a vertical CVD reactor was dem-onstrated by Wahl[16]. Similar investigations have been carried out for various types of the metal organic CVD reactor[17–19]. Re-cently, Vanka and his colleagues[20,21]conducted a series of com-putational studies to explore the effects of the flow rate, substrate rotation rate, and chamber geometry on the flow in impinging jet CVD reactors. Burwash et al.[22]reported that increasing the ratio of the jet-disk separation distance to the jet diameter could result in higher deposition efficiency and deposition density around the stagnation point on a wafer.

The above literature review clearly indicates that the chamber geometry plays an important role in the vortex flow induced in the chamber. More specifically, at increasing jet-disk separation distance the interactions between the inertia and buoyancy-driven vortex flows are expected to be more intense. Obviously, shorten-ing the jet-disk separation distance is beneficial in suppressshorten-ing the buoyancy-driven flow recirculations since Ra is proportion to H3_.

But a small jet-disk separation distance is more likely to cause un-wanted vapor deposition on the jet nozzle and top wall of the pro-cessing chamber. In the present study, we extend our earlier study

[1]to further investigate the effects of the jet-disk separation dis-tance on the characteristics of the vortex flow in a laminar jet impinging onto a horizontal heated disk confined in a vertical cylindrical chamber with a larger jet-disk separation distance (HDj= 4–6). The results will be compared with those in our

previ-ous study[1]for HDj= 1–3.

2. Experimental apparatus and procedures

In order to conduct the experiment at reasonably low cost, we use air as the working fluid in the present experiment to replace the inert gases normally employed in real CVD processes. In view of the similar thermodynamic and thermophysical properties for various gases, the results obtained here are still applicable to the CVD system. The experimental system established in our previous study[5]is employed here to investigate the effects of the jet-disk separation distance on the characteristics of inertia and buoyancy-driven vortex flow resulting from a round air jet impinging onto a

heated horizontal circular disk confined in a vertical cylindrical chamber. A schematic of the experimental system is shown in

Fig. 1. The present experimental system consists of five major parts: gas injection unit, processing chamber, heating unit, flow visualization unit, and temperature measurement unit.

The gas injection unit consists of a 2 HP air compressor, a flow meter, a smoke generator, filters, pressure regulator, and connec-tion and injecconnec-tion pipes. In the experiments, the air is drawn from the ambient by the compressor and sent into a 300-L and 100-psi high-pressure air tank and is filtered to remove moisture and tiny particles. Then, the air is mixed with smoke tracers in the smoke generator. It is later injected into the processing chamber through the injection pipe which is coaxial with the processing chamber. The injection pipe diameter is fixed at 10.0 mm and the pipe is thermally well insulated by a superlon insulation layer of 16.0-mm thick. The straight portion of the pipe is 600.0-16.0-mm long. This length of the constant cross-section portion of the injection pipe is selected to ensure that it is long enough to have a fully developed air flow at the outlet of the injection pipe. The air temperature at the cross section 600.0 mm upstream of the injection pipe exit is measured by a T-type thermocouple. The measured value is con-sidered as the temperature of the air injected into the processing chamber in view of the good thermal insulation over the pipe.

The processing chamber, which is made of 6.0-mm thick quartz glass to allow for the observation of the flow pattern in the cham-ber, is cylindrical and has a diameter of 291.0 mm. The distance be-tween the chamber top and bottom is 200.0 mm. To facilitate the flow visualization, the chamber top is made of an acrylic plate. Air is injected vertically downward from the injection pipe into the cylindrical chamber and impinges directly onto the heated disk. The outside surface of the chamber is thermally well insu-lated by a superlon insulator of 10.0-mm thick. The insulator can be opened during the flow visualization experiment.

The heating unit is designed to maintain the circular disk at the preset uniform temperature during the experiment. It is composed of a 10.0-mm thick copper plate of eight-inch in diameter, acting as the disk, placed above another 20.0-mm thick copper plate of the same diameter, which is heated by D.C. power supplies. The lower copper plate is then placed on a bakelite plate. A gap height of 1 mm is kept between the two copper plates allowing the thermal radiation and convection to transfer heat from the lower to upper Nomenclature

Dj diameter of jet at the injection pipe exit (mm)

Gr Grashof number, gbDTH3_/

_m

g gravitational acceleration (m/s2₎

H jet-to-disk separation distance (mm)

HDj ratio of the jet-disk separation distance to the jet

diam-eter, H/Dj

Qj jet flow rate (standard liter per minute, slpm)

r, h, z dimensional coordinates in cylindrical coordinate sys-tem

R,H, Z dimensionless coordinates r/Rc, h/360° z/H

Ra Rayleigh number, gbDTH3/

am

Rej jet Reynolds number, VjDj=

m

Rew local Reynolds number of the flow in the wall-jet region,

 uH=

m

Rewe local Reynolds number of the flow in the wall-jet region

at disk edge, uweH=

m

Rw radius of disk (mm)

Ta ambient temperature (°C)

Tf temperature of the heated disk (°C)

Tj temperature of jet at the injection pipe exit (°C)



u average radial velocity of the flow in the wall-jet region, Qj=ð2

p



uwe average radial velocity of the flow in the wall-jet region at disk edge, Qj/(2

p

Vj average velocity of the air jet at the injection pipe exit (m/s)

Greek symbols

a

b thermal expansion coefficient (1/K)

DT temperature difference between the heated disk and the

air injected into the chamber (°C)

m

U non-dimensional temperature, (T  Tj)/(Tf Tj)

q

l

plates. The heater attached onto the back side of the lower copper plate is divided into three concentric zones. Each zone is indepen-dently heated by a power supply. Additionally, to reduce the signif-icant energy loss from the sidewall of the copper plates and Teflon plate, the lateral surface of the entire heating unit is wrapped with a 16.0-mm thick thermal insulation layer of superlon. A proper control of the currents transferred from the power supplies to the heating coils leads to a nearly uniform disk temperature with a maximum deviation of 0.1 °C across the disk. The temperature of the upper copper plate at selected detection points is measured by three T-type thermocouples inserted into the plate by the small holes drilled on the backside of the plate.

A smoke-tracer flow visualization technique is employed to ob-serve the flow patterns induced by the air jet impinging onto the heated disk in the cylindrical chamber. The smoke is produced from burning incense prepared from sandalwood. The smoke is mixed uniformly in the smoke generator and is carried out by the inlet air and then sent into the cylindrical chamber. The gas flow pattern in the chamber is illuminated by the vertical and hor-izontal plane light sheets produced by passing parallel lights from

an overhead projector through adjustable knife edges. The time variations of the flow pattern from the side view are recorded by the Sony digital video camera DCR-PC330.

The air temperature in the processing chamber is measured by inserting a calibrated and corrected thermocouple probe into the chamber through 24 holes of 1.0 mm in diameter opened at the se-lected locations on the top of the chamber. The thermocouple probe is an OMEGA (model HYPO) hypodermic extremely small T-type thermocouple implanted in a 2.0-in. long stainless steel hypodermic needle.

Uncertainties in the Rayleigh number, jet Reynolds number and other independent parameters are calculated according to the standard procedures established by Kline and McClintock [23]. The uncertainties of the thermophysical properties of air are also included in the analysis. In addition, the uncertainties of the con-trol unsteadiness and temperature non-uniformity are accounted for in the evaluation of the data uncertainty. The analysis shows that the uncertainties of temperature, volume flow rate, Rej, Ra,

and HDjmeasurements are estimated to be less than ±0.2 °C, ±2%,

±2.3%, ±8.6%, and ±0.5%, respectively. To Vacuum

Chamber *20

Air Inlet

Control Unit (Heating Control Uunit & Data Acquisition Sysem)

291mm Test Section To Vacuum Chamber *20 12.7mm Air Compressor Dryer Water Filter Water Filter Air Tank Flowmeter 0~20 slpm 0~1 slpm Particle Filter Oil Filter By pass Pressure Regulator

Smoke Generator Developing Section (Adiabatic)

600mm Thermocouple T

Resistance heating coil

Holder Superlon (Insulator) Teflon (Insulator) Heater

z

r

To ambient *20To Vacuum To ambient *20

Chamber *20 To Vacuum Chamber *20 Water Filter T Copper

z

r

3. Results and discussion

In the present experiment the air flow in the chamber is at the atmospheric pressure. Three jet-disk separation distances are con-sidered with H = 40.0, 50.0 and 60.0 mm for the jet flow rate Qj

ranging from 0 to 12.0 slpm and the temperature difference be-tween the disk and the air injected into the chamberDT is varied from 0 to 25.0 °C. Some data from the previous study will be in-cluded here for comparison purpose. The dimensionless groups governing the flow are the ratio of the jet-disk separation distance to the injection pipe diameter, jet Reynolds number, and Rayleigh number (Grashof number). They are, respectively, defined as

HDj¼ H Dj ð1Þ Rej¼ VjDj

m

p

m

D

am

D

m

Thus in the present study HDj, Rej,and Ra , respectively, vary

from 4 to 6, 0 to 1623, and 0 to 507,348. Moreover, it is noted that the local buoyancy-to-inertia ratio for the wall-jet flow at the disk edge is an important parameter in dealing with the onset of the buoyancy-driven roll[1]. It can be expressed as

Gr Re2we ¼ Gr Re2j !  8Rw Dj  2 ð5Þ In what follows selected flow photos taken from the flow visu-alization and the measured temperature data are examined closely to delineate how the gas flow characteristics are affected by the jet-disk separation distance.

3.1. Effects of HDjon onset of inertia-driven vortex rolls

The effects of the jet-disk separation distance on the critical con-ditions for the appearance of the inertia-driven vortex rolls are illus-trated first. Here we investigate the onset of the inertia-driven rolls by visualizing the vortex flow in the chamber at various Rejfor an

unheated disk (Ra = 0) at increasing Rejuntil the vortex rolls start

to appear. Note that the lowest jet flow rate which can be accurately resolved in the present experimental apparatus is 0.1 slpm. Even at this small Qjthe primary inertia-driven roll is already seen in the

chamber for all jet-disk separation distances tested here (H = 10.0– 60.0 mm). Furthermore, for a continuing increase in Rej, the

second-ary and tertisecond-ary inertia-driven rolls appear in sequence resulting from the shearing effect of the strong primary roll, which is already discussed in the previous study[1].

Table 1summarizes the present data for the onset condition of the steady secondary and tertiary inertia-driven rolls at various

jet-Table 1

Critical condition for appearance of the inertia-driven vortex flow (DT = 0 °C).

Vortex roll Separation distance

(H, mm)

Flowrate (Qj, slpm)

Rej

Secondary inertia-driven roll 10.0 1.8 243

20.0 1.3 176

30.0 0.8 108

40.0 1.5 203

50.0 X X

60.0 X X

Tertiary inertia-driven roll 10.0 5.5 744

20.0 5.0 676

30.0 4.6 622

40.0 4.6 622

50.0 5.7 771

60.0 5.2 703

The roll does not appear in the range of the parameter tested in the present study, X.

HDj= 1 HDj= 2 HDj= 3 HDj=4 Jet θ=0° θ=180° Sidewall Heating plate Insulation

Primary inertia-driven roll Secondary inertia-driven roll Corner roll

HDj=5

HDj=6

disk separation distances. It is of interest to note from these results that at a small jet-disk separation distance for HDjincreased from 1

to 3 the onset of the secondary inertia-driven roll becomes earlier but the onset is delayed to a higher Rejat a larger jet-disk

separa-tion distance for HDjraised from 3 to 4. This nonmonotonic

varia-tion in the critical Rej for the onset of the secondary roll at

increasing HDjcan be attributed to the unusual change of the

sec-ondary roll with HDjshown inFig. 2. The results indicate that for

HDj63 the primary, secondary and corner rolls all grow in size

for an increase in HDj. But for HDjraised from 3 to 4 both the

pri-mary inertia-driven roll and corner roll also grow substantially in size while the secondary roll is squeezed to become smaller. So the critical jet Reynolds number for the onset of the secondary roll for HDj= 4 is higher. Note that the secondary roll is not seen in the

chamber for HDj= 5 and 6, which could be ascribed to the growth

of the primary roll at increasing HDjand it directly contacts with

the corner roll at this high HDj. No space is available for the

second-ary roll. In fact, for HDj= 5 and 6 the secondary roll is not induced

in the entire range of the Qjtested in the present study.

The typical pattern of the tertiary inertia-driven vortex roll for HDjvaried from 1 to 6 is shown inFig. 3. The flow is

axisymmet-ric even for the cases without steady state at long time for a high Rej(HDj= 4–6), and hence only the side view flow photos at the

vertical plane h = 0° are given here. The data inTable 1indicate that the onset of the tertiary roll takes place at lower Rejas HDj

increases from 1 to 3. This is simply because the primary iner-tia-driven roll is stronger at higher HDjfor a given Rej, which in

turn causes an earlier onset of the tertiary roll. However, the onset of the tertiary roll is delayed to a higher Rejfor HDjraised

from 4 to 5. This is conjectured to result from the fact that for HDj= 5 no secondary roll appears and the primary roll nearly

occupies the entire chamber at a high Rej. Thus it is more difficult

for the tertiary roll to be induced. But the critical Rejfor the onset

of the tertiary roll becomes smaller for a stronger primary roll as HDjis raised further from 5 to 6. It is noted fromFig. 3that the

vortex flow structures in the chamber for HDj= 5 and 6 are

signif-icantly different from that for HDj= 1–4 as the tertiary roll starts

to appear in the chamber, which in turn results in the nonmono-tonic variation in the critical Rejfor the onset of the tertiary roll

at increasing HDj.

Finally based on the present data given inTable 1, the onset conditions of the secondary and tertiary rolls can be expressed as

(a) for the secondary inertia-driven roll

Rej¼ 296:8  61:3  HD2j þ 13:8  HD

3

j ð6Þ

for 1 6 HDj64 and 108 6 Rej6243

(b) for the tertiary inertia-driven roll

Rej¼ 1489:3  719:5  HDjþ 191  HD2j  15:5  HD

3

j ð7Þ

for 2 6 HDj66 and 622 6 Rej6771.

When compared with our experimental data, the standard devi-ations of Eqs.(6) and (7)are, respectively, 7.2% and 5.5%.

3.2. Effects of HDjon onset of buoyancy-driven vortex roll

Next, the onset of the buoyancy-driven vortex roll is examined. When there is a temperature difference between the jet and disk the buoyancy-driven roll begins to appear in the region near the heated disk edge as Rejis decreased to a certain value for a given

Ra.Fig. 4shows some vortex flow patterns for the cases with the absence and presence of the buoyancy roll for various Rej and

HDjatDT = 5 °C. The measured critical values for the onset of

buoy-ancy roll for various H are summarized inTable 2. The buoyancy roll appears as the jet Reynolds number is below the critical value listed in the table. The data show that the critical Qjfor the onset of

buoyancy-driven roll is higher for a higherDT, indicating that the

buoyancy force is higher at a higherDT and the buoyancy roll

can appear in a wider range of Rej. It is also noted from the table

that for H = 20.0–40.0 mm the buoyancy-driven vortex roll always appears at certain higherDT even for Qjis raised to the highest

le-vel of 12.0 slpm tested here. Moreover, it is of interest to note from the experiment that the buoyancy roll always appears at the inter-mediate H of 30.0 mm forDT = 0.5 °C. The data given inTable 2

indicate the onset of the buoyancy roll for the small jet-disk sepa-ration distance with H = 10.0 and 20.0 mm occurs at a constant lo-cal buoyancy-to-inertia ratio at the disk edge Gr=Re2_we, as already observed in the previous study[1,5]. However, this is not the case for H = 40.0 mm. In fact, the critical buoyancy-to-inertia ratio in-creases significantly with H for a larger jet-disk separation distance with H = 40.0–60.0 mm. This can be attributed to the fact that only the primary inertia-driven roll and buoyancy-driven roll exist in the chamber and they are in close contact for H = 40.0–60.0 mm (Fig. 4), unlike that for H = 10.0 and 20.0 mm in which the inertia and buoyancy-driven rolls separate from each other. So the critical Gr=Re2

wefor the onset of buoyancy roll needs to be higher to

over-come the stronger mutual pushing of the two rolls at a higher H. Moreover, at the sameDT the critical Qjfor the onset of

buoy-ancy roll increases for HDjraised from 1 to 2 but decreases for HDj=5 Rej=947 Unsteady HDj=4 Rej=676 Unsteady HDj=3 Rej=676 Steady HDj=6 Rej=811 Unsteady

θ=0° Insulation Heating plate

Jet HDj=1 Rej=947 Steady HDj=2 Rej=730 Steady

Tertiary inertia-driven roll

Tertiary inertia-driven roll

Tertiary inertia-driven roll

Tertiary inertia-driven roll

Tertiary inertia-driven roll

Tertiary inertia-driven roll Sidewall

Fig. 3. Side view flow photos taken at the cross plane for various HDjand Rejwith

HDjraised from 4 to 6. For instance atDT = 5 °C, the critical Qj

in-creases from 2.8 to 8.0 slpm for HDjraised from 1 to 2 but

de-creases from 9.2 to 5.1 slpm for HDjraised from 4 to 6 (Table 2).

This variation of the critical Rejfor the onset of the buoyancy roll

again can be attributed to the changes of the vortex flow structure for HDjvaried from 4 to 6 (Fig. 5). Furthermore, empirical

equa-tions are proposed to correlate the data given inTable 2for the onset of the buoyancy-driven roll as

Gr=Re2

we¼ 34:0 ð8Þ

for 1 6 HDj62, 470 6 Ra 6 7516, and 379 6 Rej61542 and

ðGr=Re5weÞ 0:25

=HD3:5

j ¼ 0:00125 ð9Þ

for 4 6 HDj66, 30,065 6 Ra 6 507,348, and 811 6 Rej61542.

When compared with our experimental data, the standard devi-ations of Eqs.(8) and (9)are, respectively, 2.2% and 5.7%.

3.3. Effects of HDjon vortex flow characteristics

How the jet-disk separation distance affects the gas flow pat-tern at long time in the chamber with the disk unheated (DT = 0 °C) is demonstrated inFig. 6by presenting the steady state side view flow photos for the cross plane h = 0° and 180° for selected Qjat various H. First, the results for the disk unheated

manifest that at the lower Qjof 1.0 slpm (Fig. 6(a)) the primary

inertia-driven roll and the corner roll get bigger for an increase in HDjas a result of stronger entrainment of the jet. Moreover, the

primary and corner rolls contact with each other for HDj=4 even

at this low Qj. In addition to the primary and corner rolls, the

sec-ondary roll is induced in the chamber for the higher Qjof 3.0 slpm

for HDj54 (Fig. 6(b)). According to the side view photos the

pri-mary roll is significantly bigger and the corner roll is only mildly bigger for HDjincreased from 1 to 4. But this is not the case for

the secondary inertia-driven roll, as already discussed above. Note that as HDjis raised from 4 to 5 the primary inertia-driven roll

becomes relatively large for Qj= 3.0 slpm, causing not only the

(a) HDj = 1(Ra=470) Steady

(b) HDj = 2(Ra=3,758) Unsteady

(c) HDj = 4(Ra=30,065) Unsteady

(d) HDj = 5(Ra=58,721) Unsteady

(e) HDj = 6(Ra=101,470) Unsteady

Qj=3.0slpm (Rej=406) Qj=7.0slpm (Rej=947) Qj=9.0slpm (Rej=1,217) Jet θ=0° θ=180° Sidewall Heating plate Insulation Buoyancy- driven roll Qj=6.0slpm (Rej=811) Buoyancy- driven roll Qj=2.0slpm (Rej=270) Qj=8.0slpm (Rej=1,082) Qj=10.0slpm (Rej=1,352) Buoyancy- driven roll Qj=7.0slpm (Rej=947) Buoyancy- driven roll Qj=6.0slpm (Rej=811) Qj=5.0slpm (Rej=676) Buoyancy- driven roll

secondary inertia-driven roll but also the corner roll to disappear. Thus, the entire chamber is occupied by the primary roll. Further-more, at Qj= 3.0 slpm the center of the primary roll begins to

oscil-late and the time-dependent vortex flow occurs as HDjis raised

from 5 to 6.

Next, the effects of the jet-disk separation distance on the steady vortex flow with the desk heated are exemplified in

Fig. 5(a) by showing the steady state side view flow photos for

DT = 5 °C and Qj= 1.0 slpm at various H. The results clearly

indi-cate that the buoyancy-driven roll which dominates in the outer region of the chamber is much bigger for a larger H. This large increase in the size of the buoyancy roll with the jet-disk sepa-ration distance is due to the large increase in the Rayleigh num-ber associated with a small increase in H since Ra is proportional to H3_{, as mentioned above. It is of interest to note that at the}

larger H (30.0–60.0 mm) the radial extent of the buoyancy roll

is so large and it directly contacts with the primary inertia-dri-ven roll. However, the buoyancy force is much stronger than the inertia force as HDj is raised from 3 to 6 in a such lower

Qj(=1.0 slpm), which in turn results in the growth of the

buoy-ancy roll and the decay of the primary roll. For a higher Qj of

3.0 slpm the results in Fig. 5(b) show that the secondary iner-tia-driven roll exists in the chamber for the small H of 10.0 and 20.0 mm. At the larger H (=30.0 mm) the primary and buoy-ancy rolls contact with each other for larger HDjand the

second-ary roll does not appear. Besides, at this higher Qjthe growth of

the primary roll with H is much stronger than buoyancy roll. In fact, we note a slight decay of the buoyancy roll for HDjraised

from 3 to 4, which is opposite to that for the lower Qjof 1 slpm

shown inFig. 5(a). Furthermore, stronger mutual pushing of the primary and buoyancy rolls at a higher H causes the vortex flow

to become time-dependent for HDjraised to 5 and 6 in a such

higher Qj(=3.0 slpm).

3.4. Temperature distributions in vortex flow

In addition to the vortex flow characteristics presented above, selected results from the measured steady air temperature distri-butions in the vortex flow are shown inFig. 7along with the cor-responding side view flow photos for Qj= 1 slpm and DT = 5 °C

for H = 40.0 mm along a horizontal line at the middle horizontal plane between the disk and chamber top at h = 0°. The non-dimen-sional air temperatureUis defined as (T  Tj)/(Tf Tj). The air

tem-perature increases slightly with the radial distance measured from the jet axis and reaches a maximum in the region when the wall-jet separates from the disk surface. For a further increase in the radial distance the air temperature starts to decline due to the presence of the buoyancy-driven roll and drops sharply near the sidewall of the chamber. A close examination of the data fur-ther reveals that at increasing jet-disk separation distance the tem-perature peak moves toward to the jet axis, reflecting the fact that we have a smaller primary inertia-driven roll and a larger buoy-ancy-driven roll for a higher HDj. Thus the above nonmonotonic

ra-dial air temperature distributions result directly from the presence of the primary inertia-driven and buoyancy-driven vortex rolls in the chamber and the deflection of the impinging jet flow by these rolls. The above conclusion for the radial air temperature distribu-tions is further substantiated by the results given inFig. 8for a slightly higher Qjof 1.7 slpm.

Table 2

Critical condition for the onset of the buoyancy-driven vortex roll for various H. Separation distance (H, mm) DT (°C) Flowrate (Qj, slpm) Rej Ra Gr/ Rewe2 10.0 5.0 2.8 379 470 34.9 10.0 4 541 940 34.2 15.0 5 676 1409 32.9 20.0 5.0 8 1082 3758 34.2 10.0 11.4 1542 7516 33.7 15.0–25.0 30.0 0.5–25.0 40.0 5.0 9.2 1244 30,065 207 10.0 9.9 1339 60,130 358 15.0 10.4 1407 90,195 486 20.0 10.9 1474 120,260 590 25.0 50.0 5.0 6.7 906 58,721 763 10.0 7.2 974 117,442 1321 15.0 8.0 1082 176,162 1605 20.0 8.7 1177 234,883 1809 25.0 9.1 1231 293,604 2067 60.0 5.0 5.1 690 101,470 2274 10.0 6.0 811 202,939 3286 15.0 7.0 947 304,409 3622 20.0 7.5 1014 405,878 4207 25.0 7.9 1068 507,348 4739

The buoyancy-driven vortex roll always appears in the range of Qjtested in the

present study, .

(a)

(b)

Insulation Heating plate

HDj= 1 HDj= 2 HDj= 3 HDj=4 Jet θ=0° θ=180° Sidewall l l o r r e n r o C l l o r n e v i r d -a i t r e n i y r a m i r P

Insulation Heating plate

(a)

(b)

Insulation Heating plate

HDj= 1 HDj= 2 HDj= 3 HDj=4 Jet θ=0° θ=180° Sidewall l l o r r e n r o C l l o r n e v i r d -a i t r e n i y r a m i r P HDj=5

Insulation Heating plate

Fig. 6. Steady side view flow photos taken at the cross plane h = 0° and 180° for various HDjat DT = 0 °C (Ra = 0) for (a) Qj= 1.0 slpm (Rej= 135) and (b) Qj= 3.0 slpm

(Rej= 406).

4. Concluding remarks

An experiment combining flow visualization and temperature measurement is conducted in the present study to explore how the jet-disk separation distance affects the steady mixed convec-tive vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. The major results obtained in the present study can be briefly summarized in the following:

1. The secondary inertia-driven roll does not appear at a larger jet-disk separation distance for HDj= 5 and 6. Moreover, for HDj

raised from 1 to 3 the critical Rejfor the onset of the secondary

roll becomes earlier but the opposite is the case when HDjis

raised from 3 to 4.

2. The critical Rejfor the onset of tertiary inertia-driven roll varies

nonmonotonically with the jet-disk separation distance raised from 1 to 6 due to the complicate variations of the vortex flow structures with the jet-disk separation distance.

3. The buoyancy-driven roll always appears for HDj= 3 even at a

small temperature difference between the heated disk and injec-tion air. Moreover, for HDjincreased from 1 to 2 the critical Rejfor

the onset of the buoyancy-driven roll is delayed to a higher Rejbut

the onset becomes earlier as HDjis raised from 4 to 6.

4. For the cases with the disk unheated, the primary, secondary, and corner rolls all grow with HDjexcept that the secondary roll

decays as HDjis raised from 3 to 4.

5. For the cases with the disk heated, at low Rejboth the primary

inertia-driven roll and the buoyancy-driven roll get larger at increasing HDjfor a small jet-disk separation distance (HDj= 1

and 2). But for HDj=3 the primary roll and buoyancy roll

con-tact with each other, the primary roll decays and the buoyancy roll grows with the jet-disk separation distance at the lower Qj

of 1 slpm and the opposite is true at the higher Qjof 3 slpm.

6. The nonmonotonic radial air temperature distributions are found to result from the presence of primary inertia-driven and buoyancy-driven vortex rolls in the chamber and the deflection of the impinging jet flow by these rolls.

7. Empirical equations are proposed to correlate the conditions leading to the onsets of the primary, secondary, tertiary, and buoyancy rolls.

Acknowledgements

The financial support of this study by the engineering division of National Science Council of Taiwan, ROC through the contract NSC90-2212-E-009-059 is greatly appreciated.

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