Flow patterns and mixing characteristics of horizontal buoyant jets at low and moderate Reynolds numbers

International Journal of Heat and Mass Transfer 105 (2017) 831–846

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Flow patterns and mixing characteristics of horizontal buoyant jets at low and moderate Reynolds numbers Dongdong Shao a, Dingyong Huang b, Baoxin Jiang b,c, Adrian Wing-Keung Law b,c,⇑ a

State Key Laboratory of Water Environment Simulation & School of Environment, Beijing Normal University, Beijing, China School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore c Environmental Process Modelling Centre, NEWRI, Nanyang Technological University, Singapore, Singapore b

a r t i c l e

i n f o

Article history: Received 22 August 2016 Received in revised form 30 September 2016 Accepted 6 October 2016

Keywords: Horizontal buoyant jets Laminar and transitional regimes Instability Concentration decay Jet spread

a b s t r a c t Laminar horizontal buoyant jets have been found to exhibit peculiar behavior of unstable nature, e.g., bifurcation in the form of a vertical secondary plume deriving from the primary jet, due to the unstable stratification on one half of circumferential interface between the jet and the ambient fluid. However, whether and how this exceptional unstable jet behavior persists into the transitional regime with moderate Reynolds numbers (500 < Re < 2000) remains an open question. In this study, we explored the flow pattern and stability, i.e., the tendency to bifurcate, of horizontal buoyant jets with different densimetric Froude number (Fr) extending from low to moderate Reynolds numbers in the laboratory. The nonintrusive laser imaging technique of Planar Laser Induced Fluorescence (PLIF) was employed for the flow visualization and measurements. Three distinct flow patterns characterized with unstable small-scale structures, namely, ‘primary jet with vertical secondary plume’, ‘primary jet with pseudo secondary jet’ and ‘quasi-turbulent horizontal buoyant jet’, were identified in the Re–Fr parameter space determined from the visualization results. The substantive bifurcation reported earlier in the literature based on shadowgraph imaging was however not observed within the presumptive space in the present experiments. Quantitative concentration measurements using PLIF were further analyzed to study the jet mixing and spreading characteristics in the laminar and transitional regimes, including the decay of maximum concentration along the jet centerline, the cross-sectional concentration distribution at different downstream locations, as well as the concentration spread. Remarkably, the concentration decay/ spreading rates exhibited a first-decreasing-then-increasing/first-increasing-then-decreasing behavior respectively with Re within the test range, reconciling the contradictory trends reported in the literature and suggesting the existence of a Re threshold below which the viscous force will prevail and suppress the potentially enhanced mixing and entrainment of low Re jet due to its less uniformity and coherence. Beyond the threshold, strong correlation of the concentration decay and spreading coefficients with Fr also confirmed that the jet mixing and spreading are dependent on the buoyancy-generated turbulence. Overall, the experimental results provided new insight on the flow patterns and mixing characteristics of horizontal buoyant jets in the laminar and transitional regimes. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Horizontal round buoyant jets that are released at low and moderate Reynolds numbers, i.e., in the laminar and transitional regimes, can find their real-world applications in heat rejection in industrial systems [21], operation and maintenance of solar ponds [5], and accidental hydrogen leakage [20], to name just a few. In addition, physical modeling studies on marine outfall sys⇑ Corresponding author at: School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore. E-mail addresses: [email protected] (D. Shao), [email protected] (D. Huang), [email protected] (B. Jiang), [email protected] (A.W.-K. Law). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.022 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

tems that are in the form of turbulent buoyant jets are typically designed based on the densimetric Froude number (Fr) similitude. The resultant Reynolds number (Re) of the model flow may be orders of magnitude smaller than the prototype depending on the model-to-prototype scale ratio, and fall in the transitional regime [24]. While turbulent buoyant jets have received considerable attention in the past decades particularly vertical buoyant jets (see List [13] and Lee and Chu [12] for comprehensive reviews), studies on horizontal buoyant jets are fewer [2,8,22,27], and that associated with low and moderate Reynolds numbers are scarce. Horizontal buoyant jets at the low or moderate Reynolds number require special attention as peculiar flow behaviors have been

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reported in the literature. According to Arakeri et al. [5], bifurcation in the form of a plane plume deriving from the primary jet may occur when positively buoyant jets are discharged at low Reynolds numbers. Two distinct regions, namely, the core jet fluid and an annular layer of peripheral jet fluid were identified in their study. As the peripheral fluid had substantially lower velocity relative to the core fluid, the buoyancy force imposed was more likely to pull it apart from the core and form the plane plume, resulting in the bifurcation. Based on shadowgraph imaging, boundaries on the parameter space that defined the regime of jet bifurcation were established as Re > 100, Fr > 12.5 and Gr1/2 > 20, in which pffiffiffiffiffiffiffiffi Re = UD=m, Fr = U= g 0 D, and the Grashof number Gr = g 0 D3 =m2 (U denotes the mean jet velocity, D the nozzle diameter, g0 (=g  ðqa  qj Þ=qj ) denotes the reduced gravity, in which g is the gravitational acceleration, qj is the density of the jet fluid, and qa is the density of the ambient fluid, and m denotes the kinematic viscosity of the fluid). Querzoli and Cenedese [18] studied horizontal dense (negatively buoyant) jets at low Reynolds numbers. Direct bifurcation was not observed although the jets were within the bifurcation regime proposed in Arakeri et al. [5]. Instead, the bottom side of the jet was found to be characterized by the plume instability induced by the unstable stratification, which then accelerated the occurrence of the Kelvin–Helmholtz (K–H) instability at the upper shear layer and the transition to turbulence of the entire flow. They further reported that the Strouhal number that characterized the occurring frequency of the K–H vortex rings as well as the propagation speed of the perturbation wave increased with increasing buoyancy when Re was held constant at 1100. Reeder et al. [19] studied the near-field development of horizontal laminar gas jets (Schmidt number on the order of unity, Re ranges from 50 to 1200) using filtered Rayleigh scattering (FRS) technique. For 1.5 < Fr < 3, fluid was found to eject from the jet core to form a vertical central plume, whereas for Fr < 1, two separate peripheral plumes emanated from the side of the jet while ejection from the core was suppressed and ambient fluid was ingested into the core. Similar phenomena were also observed for jets with both positive and negative buoyancies. Deri et al. [6] confirmed the flow of peripheral fluid around the jet core and also identified a stagnation region, characterized by zero velocity, between the jet core and the plane plume due to the flow separation for horizontal laminar gas jets at Re = 340 and Fr = 3.4. It is worth pointing out that the majority of existing studies on horizontal non-turbulent buoyant jets, including those mentioned above were focused on the low Reynolds number regime (Re < 500). It is yet unknown whether the observed extremely unstable jet behavior, i.e., jet bifurcation, will persist into the transitional regime (500 < Re < 2000). Moreover, although the mixing behavior of laminar buoyant jets discharged at various inclinations (including the horizontal) had been reported earlier in Satyanarayana and Jaluria [21], their study was based on probe-based point measurements using intrusive thermal couples that might influence the transitional flow behavior. Quantitative scalar measurements with state-of-the-art non-intrusive laser diagnostic techniques on the mixing behavior under investigation is still lacking so far. In this study, we first examine the flow pattern and stability, i.e., the tendency to bifurcate, of horizontal buoyant jets at low and moderate Reynolds numbers, through flow visualization using Planar Laser Induced Fluorescence (PLIF). Quantitative concentration measurements were then further conducted using PLIF to study the jet mixing and spreading characteristics in the laminar and transitional regimes. The decay of the maximum concentration along the jet centerline, the cross-sectional concentration distribution at different downstream locations, as well as the concentration spread were examined using the processed PLIF data. The

effects of Reynolds and densimetric Froude number on the jet mixing and spreading characteristics, e.g., Re- and Fr-dependence of the concentration decay and spreading coefficients, were further examined in details to identify the mixing behavior within the parameter space. The paper is organized as follows. The experimental setup is briefly introduced in Section 2. The experimental results and relevant discussions are presented in Section 3. Specifically, the flow patterns as well as the associated unstable small-scale structures of the jet are elaborated in Section 3.1. We then analyze the decay of the maximum concentration along the jet axis in Section 3.2. The cross-sectional concentration profiles and the jet concentration spread are presented in Sections 3.3 and 3.4, respectively. The paper is concluded with the major findings obtained from the present study, as well as recommendation for future studies.

2. Experimental setup The experiments were conducted at the Hydraulic Modelling Laboratory, Nanyang Technological University, Singapore. Fig. 1 is a schematic diagram of the experimental setup. A glass tank of 2.85 m (length)  0.85 m (width)  1 m (height) was used to contain the ambient water, and a horizontal nozzle with an inner diameter of 5.8 mm was used to discharge a saline solution to emulate a dense jet (or brine) discharge. The nozzle was fixed onto a base to minimize its movement, and placed about half a meter above the bottom to avoid the effects of brine accumulation during the experiment. A storage container was used to prepare the saline solution, and two peristaltic pumps (Cole-Parmer Masterflex 77200-52) together transferred the saline solution into an elevated constant head tank. The overflow from the head tank was diverted back to the storage container. Several valves and a flowmeter (Krohne Altometer SC80AS) were used to control and measure the discharge flow rate. Planar Laser Induced Fluorescence (PLIF) was used in the present study for flow visualization as well as quantitative concentration measurements. For each jet generated, PLIF measurements were conducted at both the longitudinal section which cut through the vertical center plane of the jet, and a number of transverse vertical sections. For longitudinal PLIF measurements, two chargecoupled device (CCD) cameras with a resolution of 1600  1200 pixels (Dantec Dynamics FlowSense 2M) were positioned side by side to capture two contiguous horizontal image windows, in order to cover the entire flow trajectory in the current experimental settings. A self-constructed grid was lowered into the tank and aligned with the center plane of the nozzle, to assist in adjusting the focus of the cameras and to ensure that at least 10% overlap was accommodated between the two camera views to ensure continuity in the captured images. The horizontal offset of the individual window from the nozzle exit, which was the universal origin in the overall coordinates, can be inferred from the portion of the labeled grid covered in the calibration images. A 532 nm pulsed Nd:YAG laser (Dantec Dynamics New Wave MiniLase) was used as the light source. Preliminary trials showed that vortices and jet undulations generated in the flow being studied would attenuate the laser sheet, thus distort the portion of the image behind the flow structures. As such, the laser was deployed in two different ways as depicted in Fig. 1. For jets with Fr > 3.5, the laser sheet was emitted from the bottom of the tank, while a front laser emission arrangement was adopted for jets with Fr < 3.5 as the vortices, if any, were not strong enough to attenuate the laser sheet significantly. To measure the dye (Rhodamine B) concentration accurately, calibration was carefully carried out to relate the grayscale values in the recorded images to the corresponding dye concentrations. The calibration was performed in a pixel-by-pixel

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Fig. 1. Schematic diagram of experimental setup.

manner to account for the inherent non-uniformity of the light intensity across the laser sheet. Once the calibration was completed, the settings of the camera and the laser were kept the same throughout the entire experiment. Transverse PLIF was used to obtain the cross-sectional images of the jet at various downstream locations. The experimental setup was similar to Fig. 1 except that only one camera was used and the nozzle was rotated 90° clockwise to be in line with the camera axis. A front laser emission arrangement was adopted and the nozzle was shifted backward with discrete distances so that the laser light sheet illuminated different vertical sections away from the nozzle. The advantage of fixing the laser while shifting the nozzle was that the images would then be acquired at the same plane with fixed camera and laser settings. Hence, the need to carry out additional calibration was avoided. Before each experiment, the test tank was filled with tap water up to a depth of 750 mm and then left undisturbed to achieve a quiescent condition. Saline solution was prepared concurrently. A density meter (Anton Paar DMA 35N) was employed to ensure the desired density to be attained. The dye concentration in the saline solution was set at approximately 80 lg/L so that the grayscale values in the image window would show sufficient contrast and yet not exceed the calibration range. The temperature difference between the ambient water and saline solution was kept to within ±1 °C to avoid any thermal effect. Prior to image acquisition, the saline solution was discharged for five minutes to stabilize the flow. Thereafter, PLIF images were captured at 10 Hz. A total of 2000 images (1000 from each camera) were obtained and stored for subsequent processing. The field of view for the longitudinal (after two image windows pieced together) and transverse PLIF were 177 mm  73 mm and 64 mm  48 mm, respectively. The experimental conditions are listed in Table 1. Fig. 2 shows the distribution of the tests on the Fr–Re parameter space. Note that flow visualization was performed in tests A-, B- series and P1 shown in Fig. 2(a), and the results were used to identify the different flow structures and patterns. Test F-series shown in Fig. 2(b) featured instead experiments with constant-Fr-varying-Re and constant-Re-varying-Fr, which were mainly conducted to examine the unstable jet behavior in the laminar and transitional regimes as

well as the effect of buoyancy on the jet mixing and spreading characteristics.

3. Results and discussions 3.1. General flow patterns The jet bifurcation phenomenon reported in Arakeri et al. [5] was based on shadowgraph imaging, which could only provide a gross overall picture of the jet behavior under investigation. In this study, state-of-the-art PLIF technique was employed for more sophisticated flow visualization slicing through the different cross sections, to verify the occurrence of jet bifurcation in the presumptive range proposed in Arakeri et al. [5], particularly in the transitional regime (500 < Re < 2000), and explore the alternative flow patterns, if any, in the absence of jet bifurcation. The results from the flow visualization are shown in Figs. 3–5. Overall, the substantive bifurcation, i.e., the development of a separate flow that is completely independent of the primary jet, was not observed within the bifurcation regime suggested earlier by Arakeri et al. [5]. Rather, three distinct flow patterns, namely, ‘primary jet with vertical secondary plume’ (flow pattern I), ‘primary jet with pseudo secondary jet’ (flow pattern II) and ‘quasiturbulent horizontal buoyant jet’ (flow pattern III), were identified within the test range in the present study (see Fig. 2(a)). The following is a qualitative description of the three different jet patterns as well as the associated small-scale structures that are of unstable nature, including the peeling-off vortices, pseudo secondary jets, and downward plumes, resulted from the breakdown of the intermittently formed coherent large-scale K–H vortex rings in the transition to turbulence. An example of flow pattern I is shown in Fig. 3(a), which is an instantaneous longitudinal image of test A1 (Re = 221, Fr = 1.9). In this flow pattern, the underside of the jet has a thin sheet of fluid which is identical to the observed vertical plume in Querzoli and Cenedese [18]. The downward plume, which was also referred to in Querzoli and Cenedese [18], appears to be elongated close to the nozzle and vanishes downstream. Beneath the downward plume are hook-like streaks of fluid that have slightly up-curved

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Table 1 Experimental conditions. Exp. No.

Nozzle diameter D (mm)

Dq/qa (%)

Discharge velocity U0 (m/s)

Reynolds number Re = DU0/m

Jet densimetric Froude number Fr = U0/(Dg Dq/qa)1/2

Grashof number Gr1/2 = Re/Fr

A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 B7 B8 P1 F3 F4 F7 F8 F9 F11 F12 F13 F14 F15 F16 F18

5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8

0.50 0.52 0.52 0.52 0.52 0.52 1.61 1.61 1.61 1.58 1.58 1.58 1.58 1.58 -0.58 0.52 0.52 0.52 0.52 0.52 1.17 2.77 4.69 4.69 2.76 1.92 1.92

0.032 0.076 0.114 0.152 0.189 0.227 0.057 0.085 0.106 0.129 0.144 0.189 0.258 0.322 0.054 0.053 0.095 0.223 0.269 0.144 0.144 0.220 0.284 0.144 0.144 0.182 0.144

221 506 757 1005 1254 1504 376 563 700 862 964 1268 1717 2141 359 307 549 1295 1559 834 834 1273 1646 834 834 1054 834

1.9 4.4 6.6 8.8 11.0 13.2 1.9 2.8 3.5 4.3 4.8 6.3 8.6 10.7 3.0 3.1 5.5 13.0 15.6 8.3 5.6 5.5 5.5 2.8 3.6 5.5 4.4

116 115 115 114 114 114 201 200 200 201 201 201 200 200 121 99 100 100 100 100 149 231 299 298 232 192 190

(a)

20

Primary jet with vertical secondary plume Primary jet with pseudo secondary jet Quasi-turbulent horizontal buoyant jet Bifurcation regime proposed in Arakeri et al. (2000)

15

A6

Fr

A5 10

B8

A4 B7 A3 B6

A2

5

B5

P1 A1

0 0

B2

B1

B3

500

B4

1000

1500

2000

2500

Re

(b)

18 Constant-Fr-varying-Re group Constant-Re-varying-Fr group

16

F8

14 F7 12

Fr

10 F9

8 6

F4

F11

F16

F12

F13

F18

4 F3

F15 F14

2 0 0

500

1000

1500

2000

2500

Re Fig. 2. Distribution of experimental tests on the Fr versus Re parameter space: (a) flow visualizations; (b) quantitative concentration measurements.

tail ends due to an uneven speed of propagation along the streak. The formation of the horizontal streaks of fluid is of particular interest in this study and is termed as the ‘peeling off effect’. The phenomenon is elaborated via a series of instantaneous images from test A1 in Fig. 4. The peeling off effect begins with the development of small perturbations within the jet core (Fig. 4(a)). As the perturbations proceed, they grow into bigger bulges, and necks begin to develop (Fig. 4(b)). Afterwards, the necks narrow off and K–H instabilities emerge on the upper shear layer of the jet. As shown in Fig. 4(c), while the train of bulges begins to detach from the jet core, they remain linked to the downward plume forming hook-like streaks of fluid. Further along the trajectory, some of the fluid bulges that form the ‘hooked’ ends exhaust their circulation and split with the trailing fluid, resulting in disconnected puffs and streaks of horizontal fluid. Overall, the falling of the horizontal streaks of fluid resembles the ‘peeling-off’ from the jet. Comparing the results in different tests, the peeling off also appears to occur at a higher frequency when Re increases. An example of flow pattern II is shown in Fig. 3(b), which is an instantaneous longitudinal image of test B4 (Re = 862, Fr = 4.3). A weaker downward plume can be observed in the underside of the jet. As the tail ends of the formed horizontal streaks of fluid propagate at a slower speed, they coalesce into a slender streak of fluid with a higher concentration than the surrounding. However, through the scrutiny of hundreds of instantaneous images, the slender structure can be identified to be delinked to the primary jet at any instant, and it only suspends in the ambient fluid. A more prominent but contrasting example of the ‘pseudo secondary jet’ is shown in Fig. 3(c) for a positively buoyant jet test P1 (Re = 359, Fr = 3.0). In this case, the ‘secondary jet’ of P1 appears to be directly linked to the primary jet, unlike the above case where the suspension of the flow filament in the ambient fluid is discernible. Nevertheless, it is evident that a thin sheet of fluid exists between the ‘secondary jet’ and primary jet for both cases, and hence clear separation of the jet leading to a substantive bifurcation does not occur. Moreover, the secondary jet is of a lower concentration at the seeming ‘bifurcation’ point, and the concentration appears to increase further downstream. If it were to be

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described above for flow pattern I, are less evident in flow pattern II. Fig. 3(d) shows an instantaneous longitudinal image of test B8 (Re = 2141, Fr = 10.7) as an example of flow pattern III. Generally, this flow pattern resembles a typical turbulent horizontal buoyant jet, albeit with a Reynolds number still within the transitional range. The first few diameters from the nozzle represent the initial potential core region which is almost straight with no development of coherent structures at the edges. Subsequently, vortex roll-up begins and the generated K–H vortex rings grow in size along the flow path, resulting in vigorous entrainment of ambient fluid and jet spreading. Far downstream, the underside of the jet, which experiences unstable stratification with heavier jet fluid on top of lighter ambient fluid, i.e., the so-called buoyancyinduced instability, also develops plume-like structures that propagate vertically downwards and contribute to further jet spreading. Throughout the flow development, the coherent K–H vortex rings keep any potential secondary structure from emerging. The above flow pattern classification as well as the associated small-scale structures are further evidenced in the crosssectional images. From the instantaneous transverse images, the bifurcation mechanism proposed in Arakeri et al. [5] and Deri et al. [6] was not observed in any of the present tests. For instance, test B2 (Re = 563, Fr = 2.8) is associated with flow pattern I, and Fig. 5(a) and (b) present the instantaneous transverse images at x = 3D and 5D, respectively. They show that the downward plume does not develop solely from the peripheral fluid at either cross section, but are mainly fed by the jet core. Notably, the presence of two small streaks of fluid hanging on the side of jet at x = 3D (Fig. 5(a)) is consistent with the observation in Querzoli and Cenedese [18]. The two streaks of fluid coalesce into the downward plume as they extend vertically downward. However, the phenomenon is ephemeral, at x = 5D, the side plumes vanish as shown in Fig. 5(b). Fig. 5(c)–(e) present the instantaneous transverse images of test B4 (Re = 862, Fr = 4.3), which is characterized with the flow pattern II, at x = 3D, 5D and 7D, respectively. Clearly, the images provide further evidence of the flow pattern having weaker downward plumes as mentioned above. 3.2. Centerline concentration decay

Fig. 3. Representative instantaneous longitudinal images showing three distinct flow patterns appeared in horizontal buoyant jet at low and moderate Reynolds numbers: (a) flow pattern I – ‘primary jet with vertical secondary plume’ (Re = 221, Fr = 1.9); (b) flow pattern II – ‘primary jet with pseudo secondary jet’ (negative buoyancy, Re = 862, Fr = 4.3); (c) flow pattern II – ‘primary jet with pseudo secondary jet’ (positive buoyancy, Re = 359, Fr = 3.0); (d) flow pattern III – ‘quasiturbulent horizontal buoyant jet’ (Re = 2141, Fr = 10.7).

an actual bifurcated secondary jet, the concentration should be highest at where it bifurcates from the primary jet and decreases continuously downstream. As such, the secondary jet of P1, like B4, is also due to an accumulation of the streaks of fluid peeled off from the upward plume (note the difference between positively and negatively buoyant jets), and is therefore also a pseudo secondary jet. It is worth noting that a flow filament similar to the pseudo secondary jet discussed here is in fact discernible in Querzoli and Cenedese’s [18] Fig. 5, which shows the flow pattern of a comparable horizontal dense jet (Re = 1100, Fr = 7.4). Notably, the ‘puffs’ of fluid that detach away at the end of the jet core, as

The jet centerline trajectory was determined by an iterative process of locating the locus of the concentration maxima at a series of downstream cross sections [7]. Afterwards, the variation of the maximum concentration, or the minimum dilution, along the centerline can be obtained. Fig. 6(a) shows the evolution of the maximum concentration at the jet centerline normalized by the initial concentration of the jet discharge, Cm/C0, with distance along the jet centerline trajectory normalized by the nozzle diameter, s/D, for the constant-Fr-varying-Re series of tests. As shown in Fig. 2(b), for the constant-Fr-varying-Re series of tests (F4, F11-13, F16), Fr was held constant at 5.5, while Re varied in the range 549–1646. For the test with the smallest Re (F4), the centerline concentration starts declining from around 2D, initially at a mild rate until 6D after which a much steeper linear slope emerged on the log–log scale plot (Fig. 6(a)). As Re increased to 834 (F11) and 1054 (F16), the location where the decay of the centerline concentrated initiated was pushed steadily downstream. At the same time, the mild declining slope vanished, and the concentration appeared to decrease along a steep linear slope from the beginning. As Re increased further, the starting of the concentration decay moved back closer to the source again, and the initial pattern featuring the combination of a mild slope followed by a steep linear slope returned. We note that similar slope-change behavior was also reported in the velocity decay for pure water jets at Re = 1620–6750 in Todde et al. [23]. Thus, the behavior is directly

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a

b

Necking

Small perturbations Detachment of first bulge Downward plume

c

K-H instabilities

Further necking

d

Horizontal streak Fully detached first bulge Hook-like streak

Tearing of downward plume

Puff

e

f

Growth of K-H instabilities

Tearing of downward plume

Detachment of hook-like streak Tearing of downward plume

Puff

Puff

g

h

Detachment of hook-like streak Tearing of downward plume

Complete detachment of hook-like streak

Puff

Fig. 4. Demonstration of the development of the peeling-off effect.

linked to the fluid shears at the jet boundary. Fig. 6(b) presents the concentration decay profiles for the constant-Re-varying-Fr series of tests (F9, F11, F14-15, F18), with Re held constant at 834 while Fr varied in the range of 2.8–8.3 (see Fig. 2(b)). As shown in Fig. 6(b), beyond the potential core region (where the concentration remains constant) and a mildly declining portion, the subsequent steep decay in concentration was typically linear and its starting point moved steadily downstream with increasing Fr. The linear gradients for different Fr also appeared to be similar to each other. The centerline concentration decay profile for test F11 (the intersection of the constant Fr and Re series of tests) is presented in Fig. 6(c). The equation for the steep linear slope range of the concentration decay profile can be expressed as,

C m =C 0 ¼ a 

s  s 1 0

D

ð1Þ

in which a is defined as the centerline concentration decay constant and s0 the location of the virtual origin. Note that the distance from the jet exit to where the steep linear slope of the concentration decay profile begins is defined as the extent of the potential core or zone of flow establishment (ZFE), spc, in this study. The dependence of the concentration decay constant, a, the location of the virtual origin, s0, and the extent of the potential core, spc, on Re and Fr are further depicted in Figs. 7 and 8. As shown in Fig. 7(a), the extent of the potential core region for the constant-Fr-varying-Re series of tests in the present study (dark

circles) remained relative constant when Re increased from 549 to 1273 (average spc  6.6D). However, when Re increased further to 1646, spc dropped dramatically to 5.2D, approaching the asymptotic value for a turbulent buoyant jet. Similar trend of the reduction of potential core with increasing Re was also reported in the velocity and concentration decay results in Xia and Lam [26] and Todde et al. [23] for pure water jets (see inverted triangles and stars in Fig. 7(a)). Notably, Xia and Lam [26] also found that, generally, the mean concentration starts to decay earlier than velocity for pure water jets, resulting in the potential core determined from the concentration field to be shorter than that determined from the velocity field (empty inverted triangles versus filled inverted triangles). Fig. 7(b) shows the variation of the concentration decay constant, a, with Re. When Re increased from 549 to 834, a remained nearly unchanged. As Re increased further, a dropped steadily and considerably until Re reached 1273, after which a bounced back and attained 2.17 when Re = 1646. This combination of decreasing and increasing trends with Re reveals the complex interplay between the viscous and buoyancy effects, and they also reconcile the disparity reported in the literature. As illustrated in Fig. 7(b) and Table 2, while the majority of the previous studies [1,10,23,29], reported a steady increase of a with Re, O’Neill et al. [16] found the velocity decay constant for the lower one of the two discrete Reynolds numbers (680 and 1030) they tested for pure water jets to be larger instead. As shown in Fig. 7(b), the

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Fig. 5. Representative instantaneous transverse images: (a) x = 3D (Re = 563, Fr = 2.8); (b) x = 5D (Re = 563, Fr = 2.8); (c) x = 3D (Re = 862, Fr = 4.3); (d) x = 5D (Re = 862, Fr = 4.3); (e) x = 7D (Re = 862, Fr = 4.3).

two opposing trends indeed coexist in the data collected on the concentration decay of horizontal buoyant water jets in the present study (circles). Physically, this suggests that the enhanced mixing and entrainment of ambient fluid for low Re jets due to its less uniformity and coherence (manifested in the present study in the form of unstable small-scale structures elaborated above), i.e., the mechanism attributed to the reduced a for lower Re cases by previous studies (Refs. [1,15,23,29], only occurs above a Re threshold, below which the viscous force will prevail and suppress the mixing and entrainment altogether. It is also worth pointing

out that the trend of variation of the concentration decay constant indeed exhibits correlation with the underlying flow pattern. For instance, the local minimum in the concentration decay constant dataset (empty circles) shown in Fig. 7(b), i.e., test F12, is associated with flow pattern II (primary jet with pseudo secondary jet). The flow filament emanated from the primary jet appears to cause more scalar loss than the downward plume associated with flow pattern I (Fig. 3(a) versus Fig. 3(b) and (c)), which presumably results in the further enhanced concentration decay.

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(b) 1

Cm/C0

1

Cm/C0

(a)

F14 (Fr=2.8) F15 (Fr=3.6) F18 (Fr=4.4) F11 (Fr=5.6) F9 (Fr=8.3)

F4 (Re=549) F11 (Re=834) F16 (Re=1054) F12 (Re=1273) F13 (Re=1646) .1

.1 1

10

1

100

10

100

s/D

s/D

Cm/C0

(c) 1

Experimental data (present study) −1 Cm C0 = 2.3938 ⋅ ( s D − 3.5291) (R2=0.96) .1 1

10

100

s/D Fig. 6. Centerline concentration decay: (a) for the constant-Fr-varying-Re series of tests; (b) for the constant-Re-varying-Fr series of tests; (c) for test F11 (Re = 834, Fr = 5.6).

Based on the experimental data from the present study, the Re threshold, Recr, should be somewhere around 1273 for the present case (i.e., concentration decay of horizontal buoyant water jets). Notably, this Re threshold falls between the upper bound of the decreasing range Re = 680–1019 and lower bound of the increasing range Re = 1500–5163 of the aggregated velocity decay constant data for pure water jets from O’Neill et al. [16] (filled squares), Zarruk and Cowen [29] (filled diamonds) and Xia and Lam [26] (filled inverted triangles). Despite the fluctuation, the aggregated concentration decay constant data for pure water jets from Zarruk and Cowen [29] (empty diamonds) and Xia and Lam [26] (empty inverted triangles) also implied a local minimum at Re = 1500. As a further comparison, data from Abdel-Rahman et al. [1] and Todde et al. [23] suggested the Recr for the velocity decay of pure gas jet to be below 850 (see Table 2). Specifically, as shown in Fig. 7(b), data from Todde et al. [23] (stars) indicated that the velocity decay constant for pure gas jets is approximately constant for Re = 850–1620, and increase slightly at Re = 2175 and remains constant again afterwards. Besides horizontal buoyant jets, similar pattern of variation of the concentration decay constant with Re was also reported for vertical buoyant water jets in Ungate et al. [24] at different Fr. As shown in Fig. 7(c), their data also suggest that the critical Re increases with increasing Fr when Fr > 25, from Recr  712 at Fr  10 (neglect the obvious outlier at Re = 475) and Recr  662 at Fr  25 to Recr  1528 at Fr  100. The strong fluctuation is partly because the Fr was not strictly fixed in Ungate et al. [24] as in the present study. It is also interesting to note that the increase

in the concentration decay constant for pure water jets [26,29] relative to that for buoyant water jets (present study) in Fig. 7(b), as well as the variability illustrated in the data among different Fr groups in Ungate et al. [24] in Fig. 7(c), is consistent with the dependence of the concentration decay on Fr, which will be discussed later. Fig. 7(d) shows the variation of the location of the virtual origin, s0, with Re. Previous studies (Refs. [1,23,29] reported that, associated with the increase in a, the virtual origin moves upstream with Re, i.e., s0 decreases. Corresponding to the trend of variation of a shown in Fig. 7(b), the location of the virtual origin presented in Fig. 7(d) from the present study (circles) shows a clear firstincreasing-then-decreasing trend, while data from Zarruk and Cowen [29], Xia and Lam [26] and Todde et al. [23] all showed a steady decrease of s0 in their respective Re range tested. Theoretically, the extent of the potential core defined as the x-intercept of the concentration decay curve fitted using Eq. (1), is identical to the sum of the fitted concentration decay constant and virtual origin [26], i.e., spc ¼ s0 þ a  D. As shown in Fig. 7(a), the sum (gray circles) is found to fluctuate around the extent of the potential core spc determined above referencing the starting of the steep linear slope (dark circles), and exhibits a first-increasing-thendecreasing trend similar to the concentration decay constant and virtual origin. This observation is also consistent with the trend of variation of the start of concentration decay, i.e., the ‘apparent’ extent of potential core, shown in Fig. 6(a). Notably, as shown in Fig. 7(a) and (d), the extent of the potential core and the location of the virtual origin for the pure gas jet reported in Todde et al.

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(a)

(c) 30 Ungate et al. (1975): (Fr=~100) Ungate et al. (1975): (Fr=~50) Ungate et al. (1975): (Fr=~25) Ungate et al. (1975): (Fr=~10)

25

a

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0 100

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Re

(b)

(d) 8 Zarruk and Cowen (2008): Concentration Xia and Lam (2009): Velocity Xia and Lam (2009): Concentration Todde et al. (2009): Velocity Prensent study

6

s0/D

4

2

0

-2

-4 0

1000

2000

3000

4000

5000

6000

Re Fig. 7. Dependence of the concentration decay coefficients on Re (Fr was fixed at 5.5): (a) extent of the potential core, spc; (b) concentration decay constant, a; (c) concentration decay constant, a (cont’d); (d) location of the virtual origin, s0.

[23] are both steadily declining, which implies again that their tested Re range should be above the Recr and the laminarity of the flow was still playing a favorable role for the jet mixing and entrainment. The scatter of the data among the various studies in Fig. 7 is presumably attributed to the conditions at the jet exit (i.e., whether the jet is discharged from a smooth contraction nozzle with top-hat profile or from a long pipe with fully developed pipe flow profile), as well as the measurement region (i.e., whether the measurement is conducted close to the source (near field) or away from the source (far field)). The jet exit condition has been found to significantly affect the flow development downstream [28]. Generally, the mixing is enhanced even in the far field when the jet is discharged with the top-hat profile [14]. Deri et al. [6] also confirmed that a fully developed pipe flow profile leads to enhanced stability for the jet flow than the top-hat profile based on their experimental comparison of the two scenarios. Among the water jet studies compared herein, both the buoyant water jet in the present study and the pure water jet in Zarruk and Cowen [29] adopted fully developed pipe flow profile, while the buoyant water jet in Ungate et al. [24] as well as the pure water jet in O’Neill et al. [16], Kwon and Seo [10] and Xia and Lam [26] were produced from contraction nozzles. In addition, while O’Neill et al. [16] and Xia and Lam [26] conducted their measurements within the near field (2–14.4D and 20–40D, respectively), Zarruk and Cowen [29] focused their study on the far-field (60–80D), and Kwon and Seo [10] covered both near- and far-fields with measurements extending from the exit

up to 80D downstream. The present study is focused on the near field, with the maximum downstream coverage up to 25D for the test with the largest centerline trajectory (F8). The difference in the initial condition and measurement region must be considered when making the comparison. The increase in buoyancy, i.e., decrease in Fr when Re is fixed, increases the turbulent intensity and enhances the mixing and entrainment of ambient fluid into the jet flow due to the additional large-scale turbulence generated by the buoyancy [17,18,24,25]. In particular, Querzoli and Cenedese [18] found the range of transition to turbulent flow for a group of buoyant jets with constant Re (1100) and varying Fr (3.4–17.6) to be linearly proportional to Fr. As far as the decay coefficient is concerned, the enhanced mixing shortens the extent of the potential core region, spc, and accelerates the concentration decay, leading to a reduction in the concentration decay constant, a. Except for one outlier at Fr = 3.6 in the a versus Fr plot, clear positive correlations are shown in Fig. 8(a) and (b). The trend of variation of the present data revealed in Fig. 8(b) also appears to be extrapolative to data collected at higher Fr and closer Re range in Ungate et al. [24], which are in turn congruent with the velocity decay constants for pure water jets (as asymptotic values at Fr = 1) reported in O’Neill et al. [16] and Xia and Lam [26] at two bounding Re (680 and 1009), as well as the concentration decay constant for pure water jets reported in Xia and Lam [26] at Re = 1003. As mentioned above, additional check against asymptotic values can be made between the data for buoyant water jets and that for pure water jets from the various studies

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(a)

(b)

(c)

6 Present study 5

s0/D

4

3

2

1

0 0

2

4

6

8

10

Fr Fig. 8. Dependence of the concentration decay coefficients on Fr (Re is fixed at 834): (a) extent of the potential core, spc; (b) concentration decay constant, a; (c) location of the virtual origin, s0.

Table 2 Previous studies on the dependence of the velocity/concentration decay constant, a, on the Reynolds number, Re. Previous study

Flow type

Parameter

Re range

Major findings

Abdel-Rahman et al. [1] Todde et al. [23] Kwon and Seo [10] Zarruk and Cowen [29] O’Neill et al. [16]

Pure Pure Pure Pure Pure

Velocity Velocity Velocity Velocity, Concentration Velocity

1400–20000 850–6750 177–5142 1500, 4000 680,1030

a increases with Re; virtual origin moves upstream

gas jet gas jet water jet water jet water jet

shown in Fig. 7(a) and (b). Recently, Large Eddy Simulation (LES) results reported in Ghaisas et al. [8] also reported enhanced velocity decay for horizontal buoyant jets relative to non-buoyant counterparts at two Re (3200 and 24,000). Meanwhile, the variation of s0 presented in Fig. 8(c) appears random and does not seem to correlate with the trend of variation of a as the constant-Fr-varying-Re case shown in Fig. 7(d). Nevertheless, the sum of the concentration decay constant and virtual origin is found to closely agree with the extent of the potential core and correlates positively with Fr, which is also in line with the trend of variation of the extent of the ‘apparent’ potential core shown in Fig. 6(b). 3.3. Cross-sectional concentration profiles Cross-sectional concentration profiles at different downstream locations along the jet centerline trajectory for test F11 are

a for lower Re is larger

extracted from the mean concentration maps and presented as representative in Fig. 9(a). As shown in the figure, the thick solid line represents the centerline trajectory, and the thin solid curves represent the various cross-sectional concentration profiles from x = 1D onward with a uniform 1D interval. It is noted that the individual profiles have been scaled up to enhance the visualization. As illustrated in the figure, the profiles at the first two cross sections were top-hat and resembled that in the ZFE. From x = 3D onward, the buoyancy-induced instability sets in, resulting in the increasing spread of the lower half of the profile [9,11,18,27]. The asymmetry grew and persisted until the jet bent downward due to the negative buoyancy. Afterwards, the cross-sectional profiles restored the axisymmetry somewhat. Non-dimensional cross-sectional profiles of C/Cm are plotted against r/b+ (r is the radial distance from the jet centerline and b+ is the concentration spread width for the upper half of the jet using

D. Shao et al. / International Journal of Heat and Mass Transfer 105 (2017) 831–846

the e1 convention) in Fig. 9(d). Standard Gaussian profile is also plotted for comparison. As shown in the figure, within a short stretch of x = 7–9D, the upper half of the jet achieved selfsimilarity and the profiles collapsed onto the Gaussian profile The jet centreline made the largest deflection at x = 10D (note the marked further tilting of the cross section from x = 9D to 10D in Fig. 9(a)), upon which the upper half of the jet widened considerably, presumably due to the partial relaxing of the damping by the stable stratification on the mixing and spreading at the upper side of the jet. From x = 11D onward, the profiles of the upper half, while regaining self-similarity, bifurcated from the Gaussian curve with a wider tail end. On the contrary, the profiles of the lower half of the jet achieved reasonable self-similarity after x = 6D (except at x = 10D) and collapsed onto the same curve that was wider than the upper half counterpart as the spreading was enhanced on this side by the buoyancy-induced instability. From the test results, when Re and Fr of the discharge were both increased (e.g., F8 (Re = 1559, Fr = 15.6)), the jet remained horizontal for a longer distance and the centreline was only deflected abruptly at far downstream (Fig. 9(b)). The corresponding nondimensional cross sectional profiles exhibited consistent selfsimilarity, and collapsed well onto Gaussian at the upper half of the jet until the last few cross sections (Fig. 9(e)). The widening of the lower half was relatively less significant due to the weaker stratification with increased Fr. On the other hand, when Re and Fr of the discharge were both reduced (e.g., F3 (Re = 307, Fr = 3.1)), the jet centreline bent strongly with a large curvature (Fig. 9(c)). The non-dimensional cross sectional profiles were more scattered as the flow was much less coherent (Fig. 9(f)). At the same time, an obvious Gaussian profile can be observed on the upper half of the jet, whereas the low half widened considerably as the unstable stratification was stronger in this case. However, beyond x = 2D, the stratification effect was alleviated as the jet centreline trajectory curved downward and the cross section tilted further toward horizontal, and the lower half widened to decreasing degree relative to the upper half henceforth.

841

weaker stratification effect (larger Fr in the former case and more strongly curved jet centerline in the latter case) as mentioned above. The dependence of the spreading coefficients on Re and Fr was further analyzed as the concentration decay constant a above. Again, the constant-Fr-varying-Re and constant-Re-varying-Fr series of tests were used for the analysis. The variation of ssf with Re is shown in Fig. 11(a). Notably, ssf for the upper half of the jet was close to the extent of the potential core spc determined from the centerline concentration decay data, especially when Re was large. Besides, the lower half achieved self-similarity consistently later than the upper half counterpart, albeit with varying degree. Fig. 11(b) shows the variation of S with Re. While the spreading rate of the lower half of the jet was considerably larger and varied randomly, its upper half counterpart varies in a clear firstincreasing-then-decreasing trend with Re, with the peak at Re = 1273. This agrees closely with the trend of variation of the concentration decay constant a (Fig. 7(b)), reaffirming that it is

3.4. Jet concentration spread As mentioned above, the jet concentration spread b is quantified by fitting the cross-sectional profiles with the Gaussian curve as, 2

C=C m ¼ exp½ðr=bÞ 

ð2Þ

As the upper and lower halves of the jet spread at different rates, separate fittings are performed to derive jet concentration spread width for the upper (b+) and lower (b) half, respectively. The concentration spreading rate S is further determined by the following equation,

b ¼ S  ðs  s0 Þ

ð3Þ

Note that the virtual origin s0 in Eq. (3) is fitted using the jet concentration spread data, and is not necessarily identical to the virtual origin defined in Eq. (1) for the centerline concentration decay. Note also that only the portion of the jet with self-similar Gaussian profiles is analyzed here, and the distance from the jet exit to where the self-similar regime starts is noted as ssf. The variation of the jet concentration spread for test F11 is shown in Fig. 10 (a). The range valid for the spreading analysis is s = 7.1–9.4D and 8.7–13.7D for the upper- and lower half of the jet, respectively. The fitted spreading rate for the lower half is almost three times that of the upper half. As shown in Fig. 10(b) and (c), the contrast in the spreading rates between the upper and lower half of the jet for F8 and F3 was less significant compared to F11, due to the

Fig. 9. Cross-sectional concentration profiles at different downstream locations along the jet centerline trajectory: (a) for test F11 (Re = 834, Fr = 5.6); (b) for test F8 (Re = 1559, Fr = 15.6); (c) for test F3 (Re = 307, Fr = 3.1); (d) non-dimensional profiles for test F11; (e) non-dimensional profiles for test F8; (f) non-dimensional profiles for test F3.

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x=1D (s=0.90D) x=2D (s=1.90D) x=3D (s=2.90D) x=4D (s=3.90D) x=5D (s=4.93D) x=6D (s=5.97D) x=7D (s=7.0D)

C/Cm

1.2

x=1D (s=0.88D) x=2D (s=1.88D) x=3D (s=2.88D) x=4D (s=3.88D) x=5D (s=4.88D) x=6D (s=5.88D) x=7D (s=6.88D) x=8D (s=7.89D) x=9D (s=8.89D) x=10D (s=9.89D) x=11D (s=10.89D)

x=8D (s=8.05D) x=9D (s=9.10D) x=10D (s=10.21D) x=11D (s=11.43D) x=12D (s=12.62D) x=13D (s=14.15D) Gaussian curve

1.0

.8

.6

1.0

.8

.6

.4

.4

.2

.2

0.0

0.0 -3

-2

-1

x=12D (s=11.90D) x=13D (s=12.93D) x=14D (s=13.93D) x=15D (s=14.94D) x=16D (s=15.97D) x=17D (s=17.00D) x=18D (s=18.02D) x=19D (s=19.02D) x=20D (s=20.02D) x=21D (s=21.09D) x=22D (s=22.40D) Gaussian curve

C/Cm

1.2

0

1

2

-3

3

-2

-1

0

r/b+

r/b+

(d)

(e)

x=1D (s=0.91D) x=2D (s=2.04D) x=3D (s=3.46D) x=4D (s=5.19D) x=5D (s=7.39D) Gaussian curve

1

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-2

-1

0

1

2

3

r/b+

(f) Fig. 9 (continued)

the enhanced (reduced) mixing and spreading that leads to the enhanced (reduced) concentration decay and hence decreased (increased) concentration decay constant. Similar pattern was discernible in the reported variation of jet spreading cone angle with Re in Ungate et al. [24], corresponding to the pattern of variation of the concentration decay constant with Re in their study (Fig. 7(c)). Consistently, O’Neill et al. [16] also found the jet spreading rate to be greater for the larger Re case (the specific spreading rates were not given in O’Neill et al. [16], and only that for the larger Re could be retrieved). As shown in Fig. 11(b), the aggregated jet velocity spreading rate data [10,16,29] indicated that, in the laminar to transitional flow regime (Re = 680–1500), the velocity spreading rate (filled dark symbols) follows a first-increasing-then decreasing trend as in the concentration counterpart with the maximum falls between Re = 1030 and 1305 (the peak from the present study is sandwiched in between). S increases slightly from 0.106 at Re = 1500 to 0.114 at Re = 2163, and then levels off at the asymptotic value for turbulent jet afterwards. As the variation is small in this Re range, opposing trends had been reported from different studies, e.g., data from Kwon and Seo [10] indicated a slight steady

decrease in S with increasing Re for Re = 1305–5142, whereas Zarruk and Cowen [29] found that both velocity and concentration spreading rates increase slightly from Re = 1500 to Re = 4000, with the concentration spreading rates slightly larger than their velocity counterpart as expected. So are the aggregated concentration spreading rate data from Zarruk and Cowen [29], Xia and Lam [26] and the present study (empty circles) relative to the aggregated velocity spreading rate data (filled dark symbols), which is compounded by the enhanced spreading due to the buoyancy effect. The latter effect is directly revealed through the comparison of the spreading rates between buoyant water jets (present study) and pure water jets [26,29] in Fig. 11(b). Note that the spreading rates based on half-widths in O’Neill et al. [16] and Zarruk and Cowen [29] have been converted to spread width using the e1 convention. Again, the scatter of the data among the different studies is partly attributable to the differences in the jet exit condition and the measurement region. Besides, Ghaisas et al. [8] reported that the differential spreading between the upper and lower halves of the horizontal buoyant jet was reduced significantly when Re increased from 3200 to 24,000. However, the test results in the range of Re in the present study did not exhibit a clear trend as

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(a) 4

(b) 4 Present study: Upper half of the jet Present study: Lower half of the jet b+ D = 0.1186 ⋅ ( s D − 4.3314 ) (R2=1.00) 2 b− D = 0.3265 ⋅ ( s D − 6.2340 ) (R =0.99)

3

b /D

b /D

3

Present study: Upper half of the jet Present study: Lower half of the jet b+ D = 0.148 ⋅ ( s D − 1.8791) (R2=1.00) b− D = 0.1755 ⋅ ( s D − 2.008 ) (R2=0.99)

2

2

1

1

0

0 0

5

10

15

0

20

5

10

15

20

s/D

s/D

(c)

2.0 Present study: Upper half of the jet Present study: Lower half of the jet 2 b+ D = 0.054 ⋅ ( s D + 2.7704 ) (R =0.80) 2 b− D = 0.0995 ⋅ ( s D + 3.6342 ) (R =0.86)

b /D

1.5

1.0

.5

0.0 0

2

4

6

8

10

s/D Fig. 10. Jet concentration spread widths at different downstream locations along the jet centerline trajectory: (a) for test F11 (Re = 834, Fr = 5.6); (b) for test F8 (Re = 1559, Fr = 15.6); (c) for test F3 (Re = 307, Fr = 3.1).

the spread in the lower half varies rather randomly. Fig. 11(c) presents the variation of the virtual origin fitted using Eq. (3) for the jet spreading rate. Unlike the negative correlation between the Re-dependence of the concentration decay constant and that of its virtual origin, the s0 of the spreading rate curve for the upper half of the jet follows a similar trend of variation of the spreading rate and increases and then decreases with Re. The difference is presumably attributed to the type of the equation for Eqs. (1) and (3) (inverse first order versus linear). Finally, as stated in Section 3.2, the increase in buoyancy, i.e., decrease in Fr, is to enhance the mixing and spreading of the jet, and accelerate the development of the flow into self-similarity. The variation of ssf and S with Fr for the upper half of the jet shown in Fig. 12(a) and (b) clearly support this proposition. It is worth pointing out that, opposite to the positive correlation between the jet spreading rate and buoyancy observed for the laminar buoyant jet (Re = 834) in the present study, Papanicolaou and List [17] and Wang and Law [25] both reported a decrease in the jet spreading rate from turbulent jet to turbulent plume, suggesting completely different effects of buoyancy in the turbulent regime. Note also that, as a contrasting case to the present study on jets with buoyancy supplied at the source, buoyancy added off-source also tends to reduce the jet entrainment and thus spreading in the transitional regime [3,4]. The location of the virtual origin, s0, shows a rather randomly varying trend in Fig. 12(c), so are all data for the lower half of the jet in Fig. 12, which are affected by the

buoyancy-induced instability as well as the unstable small-scale structures discussed above. As such, further discussion on the spread at the lower half of the jet is not conducted. 4. Conclusions In this study, flow visualization experiments using PLIF were conducted to verify the occurrence of jet bifurcation in horizontal laminar buoyant jets, and to examine the alternative flow patterns, if any, in the absence of jet bifurcation. The test parameter space of Re–Fr included the presumptive bifurcation range suggested in Arakeri et al. [5], and also covered the development from the laminar to the transitional regime (500 < Re < 2000). The results showed that substantive bifurcation, i.e., the development of a separate flow that is completely independent of the primary jet, did not occur contrary to the previous suggestion. Instead, a number of small-scale structures that are of unstable nature, including peeling off vortices, pseudo secondary jets and downward plumes, which are resulted from the breakdown of the intermittently formed coherent large-scale K–H vortex rings in the transition to turbulence, were captured from the laser imaging results. Amongst the small-scale structures, the pseudo secondary jet resembles the bifurcation the most, however, the scrutiny of hundreds of instantaneous PLIF images reveals that it is only the coalescence of streaks of peeling-off fluid and not direct bifurcation from the primary jet. Based on the longitudinal and cross-sectional images,

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.5 O'Neil et al. (2004): Velocity Kwon and Seo (2005): Velocity Zarruk and Cowen (2008): Concentration Zarruk and Cowen (2008): Velocity Xia and Lam (2009): Concentration Present study: Upper half of the jet Present study: Lower half of the jet

.4

8

S

ssf/D

.3 6

.2 4

.1

Present study: Upper half of the jet Present study: Lower half of the jet

2

0

0.0 0

500

1000

1500

2000

0

1000

Re

2000

3000

4000

5000

6000

Re

(c)

10 Present study: Upper half of the jet Present study: Lower half of the jet

8

s0/D

6

4

2

0 0

500

1000

1500

2000

Re Fig. 11. Dependence of the jet spreading coefficients on Re (Fr is fixed at 5.5): (a) distance from the jet exit to the location where the jet achieves self-similarity, ssf; (b) jet spreading rate, S; (c) location of the virtual origin, s0.

three distinct flow patterns are identified with the parameter space tested in this study: flow pattern I (‘primary jet with vertical secondary plume’) features prominent downward plume (vertical secondary plume); flow pattern II (‘primary jet with pseudo secondary jet’) is characterized with pseudo secondary jet combined with weak downward plume; and flow pattern III (‘quasi-turbulent horizontal buoyant jet’) resembles a typical turbulent horizontal buoyant jet. The quantitative link of the flow pattern with the Re–Fr parameter space is established based on the visualization results. Quantitative PLIF measurements were further conducted to study the mixing and spreading characteristics of the horizontal buoyant jet in the laminar and transitional regimes. The decay of the maximum concentration along the jet centerline, the crosssectional concentration distribution at different downstream locations, as well as the concentration spread were analyzed using the processed PLIF data. Based on the test results from the constant-Frvarying-Re and constant-Re-varying-Fr series, the variation of concentration decay and spreading coefficients with Re and Fr were established. Specifically, when Fr was fixed at 5.5, the results showed that the concentration decay constant a first decreased and then increased as Re increased from 549 to 1646 with the minimum at Re = 1273, suggesting that the enhanced mixing and entrainment of ambient fluid for low Re jets due to their less uniformity and coherence, i.e., the mechanism attributed to the reduced a for lower Re cases by previous studies, only occurs above a Recr threshold, below which the viscous force prevails and sup-

presses the mixing and entrainment altogether. This finding provides a reconciliation to the opposing trends reported in the literature on the dependence of the velocity/concentration decay constant on Re in different Re ranges. Similar pattern of variation of the concentration decay constant with Re for vertical buoyant water jets reported in Ungate et al. [24] also suggested the Recr threshold to be Fr-dependent. The limited experimental data from the present study showed that the Re threshold for the present case (horizontal buoyant jets with Fr = 5.5) to be around 1273, which also tallied with the Re threshold for pure water jets based on data assembled from the literature. The extent of the potential core spc and the location of the virtual origin s0 varied with Re correspondingly. When Re was fixed at 834, the extent of the potential core and the concentration decay constant both correlated positively with Fr, which confirmed that the increase in buoyancy enhanced the mixing and entrainment of ambient fluid into the jet flow due to the additional large-scale turbulence generated by the buoyancy. The unstable stratification at the lower side of the jet increases the jet spread, leading to asymmetric cross sectional profiles of the concentration distribution for the horizontal buoyant jet. However, the asymmetry becomes less significant as the jet centerline continuously bends downward towards downstream. In terms of the Re-dependence, the concentration spreading rate at the upper half of the jet first increased and then decreased in the tested Re range which was consistent with the variation in the concentration decay

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10

Present study: Upper half of the jet Present study: Lower half of the jet

.5

.4

S

8

ssf/D

.6

6

.3

4

.2

2

.1

0.0

0 0

2

4

6

8

0

10

2

4

6

8

10

Fr

Fr

(c) 10 Present study: Upper half of the jet Present study: Lower half of the jet

8

s0/D

6

4

2

0 0

2

4

6

8

10

Fr Fig. 12. Dependence of the jet spreading coefficients on Fr (Re was fixed at 834): (a) distance from the jet exit to the location where the jet achieves self-similarity, ssf; (b) jet spreading rate, S; (c) location of the virtual origin, s0.

constant, and demonstrated that the enhanced concentration decay was due to the enhanced mixing and spreading of the jet. Both the variation of the distance from the jet exit to the location where the jet achieved self-similarity, ssf, and the jet spreading rate, S, for the upper half exhibited clear positive correlation with Fr. However, the spreading ratio between the upper and lower halves varied randomly with Re and Fr, which can be attributed to the disturbance due to the buoyancy-induced instability as well as unstable small-scale structures discussed above. Overall, the results from the present study reveal much more details of the horizontal buoyant jet from the laminar to transitional Re range, and also clarifies the inconsistencies in the mixing behavior reported in the literature. Currently, the PLIF data in the present study only allows the analysis of the concentration field. Further studies to examine the characteristics in both concentration and velocity fields and their correlation are recommended in the future. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51209005) and Doctoral Program of Higher Education of China (Grant No. 20110003120029). The authors appreciate the constructive comments and suggestions from the two anonymous reviewers on an earlier version of the manuscript.

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