THE MERGING OF TWO UNEQUAL AXISYMMETRIC PARALLEL TURBULENT JETS*

BARATIAN-GHORGHI Zahra, KAYE Nigel B., KHAN Abdul A., SMITH Jeffrey R.

Glenn Department of Civil Engineering, Clemson University, Clemson, SC, USA, E-mail: Gbarati@clemson.edu

THE MERGING OF TWO UNEQUAL AXISYMMETRIC PARALLEL TURBULENT JETS*

BARATIAN-GHORGHI Zahra, KAYE Nigel B., KHAN Abdul A., SMITH Jeffrey R.

Glenn Department of Civil Engineering, Clemson University, Clemson, SC, USA, E-mail: Gbarati@clemson.edu

Results of an experimental study of the merging of unequal parallel round turbulent jets are presented. Experiments were conducted for a jet axial separation to nozzle diameter ratio of 3.0 and the Reynolds numbers ranging from 8 000 to 15 000. The distance to the point where the jets are merged was measured for a range of jet source momentum flux ratios. Three different merger criteria were used based on the mean velocity profile, mean passive tracer concentration profile, and Reynolds stress profile. The results show that the concentration profile merges closest to the jet sources followed by the velocity profile with the Reynolds stress profile merging furthest from the nozzles. For all three profiles the merge distance is relatively insensitive to the momentum flux ratio, consistent with previous findings for slot jets and buoyant round jets. The measured merge distances are consistent with previously published results for equal round jets, though the poor spatial resolution of data in the literature means that limited comparison is possible. There are no studies of unequal jet merger currently in the literature that could be used for comparison.

turbulent jet, merging jets, unequal jets, experiment

Introduction

We consider the interaction and merging of two parallel round turbulent jets in a uniform quiescent environment. The interaction of round turbulent jets has many applications in environmental hydraulics as well as commercial and industrial fluid dynamics. For example, many waste water diffusers consist of a line of round jet outlets from which parallel interacting jets issue[1,2], while in industrial settings, gas fired boilers often have arrays of round gas inlets that lead to interacting jets[3]. Furthermore, the increased use of energy efficient under floor air distribution systems in commercial buildings has led to floor level arrays of jet outlets[4]

The interaction of rows of turbulent jets has been studied extensively with experimental measurements made of the velocity profiles[5-7]and tracer concentration profiles[8]. However, less work has been done on the merger of a pair of jets. Rathkrishnan[9]presented results for a series of experiments measuring the velocity profile of equal twin jets at a range of downstream distances. The jet separation (G) to nozzle diameter (D) ratio ranged from 2.3 to 3.0. The velocity profiles from each jet were observed to merge into that of a single jet (i.e., transitioned from a two peak to single peak profile) between 10-40 diameters downstream of the nozzles. However, the exact location at which they merged was not reported as the profiles were not taken close enough together in the streamwise direction. Yin et al.[10]also reported velocity profile measurements for equal twin jets and G/ D=1.5, 1.75 and 1.9. Again, the exact transition from dual jet to merged jet flow was not quantified. In both these studies only equal jets were examined.

Extensive work has been done on merging slot jets[11,12]. Although these papers presented much higher resolution data on the merging of the jets, the physics of slot jet merger is significantly different from that of round jets. Slot jet pairs have a pocket of trapped fluid between them that produces a low pressure re-circulation region which in turn draws the jets together very close to their source. Again, all of these studies focused on equal slot jet merger. Further studies have examined the case of buoyant round jet merger[13-15]though the results were not appropriate for the present study due to the different forces driving these flows (buoyancy as opposed to momentum).

The only work on unequal pairs of jets is that of Kaye and Linden[13]for buoyant jets and Karimpour et al.[16]for slot jets. In both cases they found that the merging distance was only a weak function of the ratio of the jet strengths. The jet strength was taken to be the buoyancy flux for the buoyant jets and the momentum flux per unit width for the slot jets. There are no published results for the merger of pairs of round unequal non-buoyant jets.

Fig.1 Schematic showing two axisymmetric turbulent jets with nozzle diameter D and axial separation G

This paper presents result for the near source flow and merging of two round turbulent jets with an axial separation to nozzle diameter ratio ofG/D= 3.0and for both equal and unequal jet source momentum fluxes. A schematic of the problem considered is shown in Fig.1. Results are presented for the distance from the sourcexm, at which the velocity, concentration and Reynolds stress profiles have merged to form a single jet. For fully turbulent jets this distance is a function of the jet axial separation G, the nozzle diameterD, and the momentum flux of each jet M1and M2. In non-dimensional form this is given by

where ψ=M1/M2is the ratio of the jet’s momentum fluxes, M and M2denote the momentum flux of jet 1 and jet 2 respectively. Without loss of generality we take jet 2 as the jet with the larger momentum flux ratio and therefore ψ≤1.

The remainder of the paper is structured as follows. Section 1 describes the merger criteria used for the velocity, concentration and Reynolds stress profiles. The experimental technique is described in Section 2 along with a description of the data analysis method and a discussion of the limitations of the measurements. Section 3 presents the results for the merger distance for profiles of velocity, Reynolds stress, and tracer concentration for both equal and unequal jets. The results are discussed and conclu-

1 sions drawn in Section 4.

Fig.2 Theoretical profiles for two equal jets created by the superposition of empirical expressions for the mean profile

1. Merger criteria

The point at which a pair of round jets can be considered merged will depend on whether the velocity, concentration or the Reynolds stress profile is used. A large volume of empirical evidence that shows that the mean velocity and concentration profiles are well described by a Gaussian function with width increasing linearly with distance from the source. In contrast the Reynolds stress profile can be represented by a double Gaussian function[17]. Simple superposition of the Gaussian and Reynolds stress profiles for two parallel round equal jets is shown in Fig.2. While it is not suggested that simple superposition accurately describes the mean profiles for the merging process, the figure does show that in the near field there are two distinct jets, whereas in the far field the profiles have coalesced to form a profile typical of a single jet.

For the Gaussian profiles (velocity and concentration) the merger point is taken to be the shortest distance from the nozzles that the velocity profile has a single as opposed to double peak. This is consistent with the definition of Fujisawa et al.[12].

For equal plumes this peak will be half way between the two jet centerlines though this will not be the case for unequal jets.

The Reynolds stress profile is slightly more complex and exhibits both local maxima and minima for asingle jet. The dual jet superposition shows two maxima and two minima in the near field but again coalesces into a single jet profile in the far field. The analogous definition for the Reynolds stress profile merger is the shortest distance from the nozzles at which there is only a single peak and single trough in the measured profile.

Fig.3 Schematic of the experimental setup

2. Experimental set-up

Two sets of experiments were run to measure the coalescence of a pair of parallel round jets. The first set measured the velocity field along the plane of symmetry formed by each jet axis (XY plane, see Fig.1) while the second measured the concentration of a passive tracer depth averaged normal to the plane of symmetry. All experiments were run with each jet issuing from 0.0127 m diameter nozzles with centerline separation G=0.038m for G/D =3.0. Both sets of experiments were run for a range of source momentum flux ratios.

2.1 Velocity and Reynolds stress measurements

The experiments were run in a 3 m×3 m tank with the depth of 1.2 m with the jet nozzles vertically aligned with the midpoint between the jets 0.6 m from the tank floor. The tank was large enough that there was no significant re-circulation flow influencing the jets near the nozzles. The jets were formed by draining water from a constant head tank that ensured steady flow conditions throughout each experiment. A sketch of the experimental setup is shown in Fig.3.

The stronger jet had a Reynolds number of approximately Re =15000 while the weaker jet had the Reynolds number ranged from Re=8000 up to 15 000. In all cases each jets Reynolds number was large enough to be in the fully turbulent regime.

The velocity and Reynolds stress measurements in the jets were made using a Sontek 10 MHz ADV, capable of measuring all three components of velocity at a frequency of 25 Hz and an accuracy of 1% of the measured velocity (±0.0025m/s ). Post-processing of the data was done using WinADV which reported average velocities in all three directions as well as the Reynolds stress and turbulence intensities. The ADV signal to noise ratio was kept above 15 for all tests through the use of various seeding materials including glass beads and rust particles. The probe records the velocity in a virtual cylinder 0.006 m in diameter and 0.009 m long. The probe used had a side facing configuration so the measurement cylinder axis was normal to the plane of symmetry. The 0.006 m diameter represents a significant fraction of the jet axis separation (0.038 m) meaning that the data are averaged over 1/6th of the separation distance. It also means that, particularly near the nozzles, regions of high shear will be poorly resolved. However, further from the nozzles where the jets merge the velocity gradients are smaller so averaging over a finite region is less significant.

The ADV was mounted on a traverse capable of moving the probe head in all three Cartesian coordinates. The traverse was driven by three computer controlled stepper motors. Each profile consisted of velocity measurements taken along a line normal to each jet axis.

The mean velocity and Reynolds stress measurements were based on 3 000 samples collected at 25 Hz over a two minute period. Measurements were taken every 0.0016 m in the transverse direction. The profile data were then smoothed using a low pass filter (three point rolling average). As the step size was smaller than the size of the measurement domain, the three point rolling average did not reduce the spatial resolu-tion of the data but rather increased the effective averaging time for the data. That is, the data for a 0.006 m cylinder were estimated by taking the average velocity and Reynolds stress at the center and 0.0016 m on either side of the centerline.

Before starting each series of experiments, the momentum flux ratio of the two jets was calculated based on the centerline velocities immediately downstream of the nozzles. For a given momentum flux ratio, an initial set of profiles were taken at 0.038 m increments in the streamwise direction. These profiles were plotted and the location at which the first merged profile was observed (based on criteria discussed in Section 1) was recorded. This was taken as the upper bound on the merging location. A second set of profiles were then recorded at either 0.0065 m-0.013 m increments in the streamwise direction. This second set was used to increase the spatial resolution of the merger point measurement. To account for the worst case error in this approach, the resulting velocity profile merge points are plotted with error bars that represent plus or minus twice the distance between adjacent profiles.

2.2 Tracer concentration measurements

A second set of experiments were run to measure the point at which the tracer concentration profiles merge. The measurements were made in a smaller visualization tank that had plexiglas walls on two sides. The same jet nozzles and constant head tank were used. The jet fluid was dyed using a red food coloring and measurements were made using a light attenuation technique. The technique uses the Lambert law of absorption which states that as light passes through an object, in this case the dyed jet fluid, it attenuates at a rate proportional to the local light intensity and the local dye concentration. This technique does not provide concentration data, but rather depth integrated concentrations. However, it was shown by Kaye and Linden[13]that the depth integrated concentration profile, as measured by this technique, gives profile sets that lead to the correct merge point as described in Section 1.

The technique involved shining a light through the jets and measuring the light intensity transmitted using a light sensitive CCD camera. This intensity was then compared to the intensity in the absence of the jets. From these two measurements, the depth integrated concentration in the jets can be calculated (see Kaye and Linden[13]and Dalziel et al.[18]for a full description of the experimental technique).

For each experiment the video camera recorded a short period of time before the jets were turned on in order to measure the background light intensity. Once the jets were turned on a video was recorded for 20 s to 60 s. After the experiment was complete the jet video and background image were used to calculate the light attenuation using the image analysis software DigiFlow[18]. This was done for each frame of the jet video and then the corrected video was averaged over approximately 10 s (240 frames) to give the mean concentration distribution. For each experiment the averaging time was the largest time possible before jet fluid started to re-circulate back into the field of view. This averaging time is considerably shorter than that used in the velocity and Reynolds stress measurements, and is also shorter than typical jet measurement averaging times reported in the literature. However, the averaging time resulted in smooth concentration profiles. A time series analysis of the light attenuation at particular points in the profile indicated that the 10 s averaging time resulted in a good estimate of the long-time average. The shorter averaging time needed is likely due to the experimental technique used. The depth integrated concentration measured using light attenuation is not a point measurement but rather is the sum of multiple point measurements at all depths through the jet. Therefore, unless the turbulent fluctuations in the tracer concentration are highly spatially correlated, the depth integrated light attenuation measurement will converge to a steady average much more rapidly than a series of point measurements.

Fig.4 Distance to velocity profile merge point for G/D=3.0 as a furction of momentum flux ratio for this study (squares)and Rathakrishnan et.al.[9]

Fig.5 Distance to Reynolds stress profile merge point as a function of momentum flux ratio

3. Experimental results

The experiments described in Section 2 were used to determine the distance from the nozzles to the merge point based on the various merger criteria dis-cussed in Section 1. Plots of the merge distance are shown in Figs.4-6 for the velocity, Reynolds stress and tracer concentration respectively.

Fig.6 Distance to tracer concentration profile merge point as a function of momentum flux ratio

The velocity profile merge point is relatively insensitive to the momentum flux ratio ψ. Over the range 0.3＜ψ＜1the merger distance measured varies over the relatively narrow range 5＜χm＜6.8. These results are smaller than the values measured by Rathakrishnan et al.[9]though the spatial resolution of their data is quite low. There are two possible explanations for this discrepancy. The first is the spatial resolution of their data. For example for G/D=2.3 Rathakrishnan et al.[9]plotted their last unmerged profile at a distance χm=4.4 and their first merged profile at χm=13.1. The data were plotted at the midpoint (χ=8.7) with error bars of ±4.4. Secondly, their data were collected for a number of different G/D values.

The merging distances reported indicate that for G/D =3.0the merging occurs 15 to 20 diameters downstream of the nozzles. Therefore, a substantial portion of the merging process occurs when the jet is not fully developed and the potential core has not been eroded. Taking the potential core length to be approximately L=6D[19]then between 30% and 40% of the flow occurs within the zone of flow establishment for the jets.

The Reynolds stress profile merge point varies over a slightly larger range for the range of ψ considered. For all cases the Reynolds stress profiles merged further downstream than the velocity profile. Whilemχ decreased slightly with decreasing ψ for the velocity profiles, the opposite was observed for the Reynolds stress profiles. No measurements of the Reynolds stress merge distance were possible for lower values of ψ as they were too far from the nozzle and the velocities in the jet were too low to be reliably measured by the ADV.

The 1.5 megapixel camera used enables the concentration to be measured with high spatial resolution. There was approximately 0.003 m between each measured profile in the streamwise direction. Error bars are not plotted for the concentration profile merge distance as the higher spatial resolution in the streamwise direction means that the error bars were essentially the same size as the symbols used to plot the data.

The tracer concentration profiles merge upstream of the velocity profiles and exhibit almost no dependence on the momentum flux ratio ψ. One would expect the concentration profile to merge upstream of the velocity profile as the concentration profile width increases more rapidly with distance from the source compared to the velocity profile. Papanicolaou and List[20]reported that the concentration profile half width was approximately 33% larger than the velocity half width. Assuming simple superposition of profiles the concentration profiles would merge at 0.75 times the velocity merge distance. To test this the ratio of the merging distances was calculated for the 10 cases where pairs of experiments existed in which the difference in the momentum flux ratios was less than 2% and found that on average χmconc./χmvel.=0.77.

4. Conclusions

Experimental measurements of the merger distance for the mean velocity, mean concentration, and Reynolds stress profiles have been presented for two parallel round turbulent jets. These measurements were made for both equal and unequal source strength jets and for a constant jet separation to nozzle diameter ratio G/D =3.0. This is the first such experimental study of pairs of round jets to consider unequal jets and to examine the merger of the concentration and Reynolds stress profiles.

The measurements of the distance from the source to the point where the jets merge was made for a range of values of the jet’s source momentum flux ratio ψ. Each profile, namely velocity, concentration and Reynolds stress has a different location for the merger point. Moving away from the jet sources the concentration profile merges first followed by the velocity profile and finally the Reynolds stress profile. The velocity profile experimental results were compared to the equal jet experiments of Rathakrishnan et al.[9]though little could be concluded due to the very low spatial resolution of their data.

For all three profiles considered the distance to the merge point is relatively insensitive to the ratio of the jet momentum fluxes. This is consistent with the experimental and theoretical findings of Kaye and Linden[13]for pairs of round buoyant jets, and the computational findings of Karimpour et al.[16]for slot jets. A systematic investigation of the role of the jet separation to diameter ratio is not conducted as the focus of the study is on the influence of the mome-ntum flux ratio on the merge distance. A detailed computational investigation of this ratio for slot jets was conducted by Karimpour et.al.[16]who found that once this ratio exceeded 20 the merge distance scaled on the separation was a constant though the physics of slot jet merger differs from that of round jet merger. Further experimental work is required to quantify the role of G/D on the merge distance and the related issue of the influence of the zone of flow establishment on the merging process.

Acknowlegments

The authors would like to thank Metz Danny and Elsea John for their assistance in building the experimental apparatus and setting up the instrumentation. Baratain Z. would also like to acknowledge the support of the Department of Civil Engineering, Clemson University for financial support through a research assistantship.

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September 22, 2011, Revised November 18, 2011)

* Biography: BARATIAN-GHORGHI Zahra (1981-), Female, Ph. D. Candidate