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Water tank measurements of buoyant plume rise and structure in neutral crossflows
Atmospheric Environment 35 (2001) 6105–6115
Water tank measurements of buoyant plume rise and structure in neutral crossflows Daniele Continia,*, Alan Robinsb a
Dipartimento di Energetica ‘‘Sergio Stecco’’, Universita" di Firenze, Via S. Marta 3, 50139 Firenze, Italy EnFlo, School of Mechanical and Material Engineering, University of Surrey, Guildford GU2 7XH, UK
b
Received 21 March 2001; received in revised form 19 July 2001; accepted 26 July 2001
Abstract In this paper, an experimental study of the rise and development of a single buoyant plume and a pair of in-line buoyant plumes is presented. The investigations were carried out at small scale in a water filled towing tank using both quantitative flow visualisation and local concentration measurements. The measured plume trajectories for a single plume were compared with the Briggs plume rise equation and predictions from a numerical integral model. Plume trajectories were studied for twin in-line plumes, with particular attention to changes in the plume trajectory, especially any additional rise that resulted from the interaction between the two plumes. Concentration field distributions in crosssections through both single and interacting twin plumes were obtained from the local concentration measurement system. These showed how the interaction affected the plume structure, notably the double vortex system that occurs in a fully developed plume. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Plume rise; Multiple plumes; Plume interaction; Towing tank; Modelling
1. Introduction Understanding the behaviour of multiple interacting plumes in terms of their average path and spread, as well as in terms of their shape, is a matter of considerable interest in environmental impact studies. Frequently, large power plants have two or more stacks placed only a few diameters apart; in some combined cycle gas turbine installations up to 8 or 10 stacks are present. Some waste incinerators have also been designed with two tall and slender stacks placed very near one another. Further examples abound in the petrol-chemical and process industries. In all these cases, strong interactions can arise between adjacent plumes, especially under favourable wind directions. Reliable analytical models exist for single plume rise evaluation (e.g. Briggs, 1974, 1975a, b), as well as integral models that relate the plume mass and momentum fluxes to the forces acting on a *Corresponding author. E-mail address: [email protected]fi.it (D. Contini).
plume and the entrainment rate of external fluid (e.g. Ooms and Mahieu, 1981; Robins and Aspley, 1994). Simple empirical corrections have been proposed for evaluating trajectories in multiple source cases (e.g. Briggs, 1974; Anfossi et al., 1978). These corrections apply to the part of the trajectories after the mixing process and they give the extra plume rise due to the interaction, with an enhancement factor, and do not usually take into account the manner in which the interaction depends on wind direction. Previous wind tunnel results, as well as field data analysis, (Overcamp and Ku, 1988; Briggs, 1984) show that the wind direction actually influences the multiple plumes mixing and consequently the extra plume rise. The strongest interaction for fixed distances between a pair of stacks is when the sources are aligned with the approaching flow. We carried out experiments not only for twin stack cases but also for single stack cases in order to obtain the trajectories without interaction and the trajectories for the maximum interaction. Single stack trajectories compare well with the results of both Briggs formula
1352-2310/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 1 ) 0 0 3 9 8 - 3
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and integral model numerical predictions. Our results regarding the trajectories of two-stack plumes show a decreasing interaction when the stack separation is increased. The interaction also becomes weaker if the momentum or buoyancy flux at the sources is decreased. However, even if the interaction in terms of additional plume rise becomes small the mixing of the two plumes generates relevant changes in the plume internal structure. Experimental studies with multiple plumes are a matter of great importance then in order to examine the performance of available models that describe plume rise, plume spread and dispersion and the reliability of the empirical parameters used to describe the rate of entrainment of ambient air into plumes and the consequent plume dilution and spreading. In this paper, a study of buoyant plume rise and plume structure for two interacting plumes is described; the work being undertaken not only to test models but also to provide a basis for the development of better models of plume interaction. The measurements were carried out in neutral flow conditions for both buoyant single and double plumes, the latter generated by two identical, in-line emissions. Attention is focussed on the two plume case, with only some example results given for single plumes. A more comprehensive description of the single plumes work can be found in Contini (1999). The experiments were performed at the University of Surrey in a water filled towing tank by means of quantitative flow visualisation to provide full-field information, and water sampling and dilution measurement using a colorimeter system to provide point concentration measurements. Water tanks prove to be a powerful and widely used tool for flow and plume dispersion studies because it is relatively simple to make visualisations by using coloured dyes and to generate stably stratified flows by means of salinity gradients in the water. For examples of such applications see Ohba et al. (1990), Snyder (1985), Hoult and Weil (1972) and Hunter (1992). The physics of plume interactions is very complicated and, as the measurements demonstrate, the consequences may affect almost the entire trajectory of the plumes involved. Our results show that interactions between two adjacent plumes may induce an increment in plume rise as large as 30% several tens of diameters downstream from the sources (which at full scale would be in the range from about 100 to 500 m). When plumes mix shortly after release, they form a larger single plume that is subject to the combined buoyancy flux of the two emissions. Consequently, the rise is increased (in theory, at maximum by as much as a factor of 21/3 or 26% for two plumes of equal strength) and the plume experiences greater rise induced spread than the single plumes in isolation. Consequently, ground level concentrations, usually the only indicator employed in environmental impact analysis, will be subject to a systematic error if the interaction is not correctly taken into account. The
situation becomes increasingly more complicated as the number of interacting plumes increases, thereby increasing the extra plume rise. The mixing process is more efficient when two (or more) plumes of equal or similar strength come into contact, as in the results reported here. However, if the plumes have very different strengths or the separation among the stacks is large enough, the plumes may interact without an effective mixing (Briggs, 1984). 1.1. Experimental set-up and equipment The experiments were performed in a water tank facility 12 m long, 1.2 m wide and with a maximum water depth of 1 m. The tank was used in a neutral stability state, being filled with fresh water. Buoyant emissions were simulated by releasing at the top of the tank a salt water solution from just below the surface, with the tip of the stacks immersed by about five diameters, i.e. the experiments were performed in an inverted set-up but results were reported in a standard co-ordinate system with the Z-axis increasing upward. Fig. 1(a) defines the co-ordinate system used in presenting the results and the notation used to describe the plumes. For twin in-line stack cases the origin of the reference system was the centre of the upwind stack. Interpretations of extra plume rise may depend on the reference system used. Fig. 1(b) shows a scheme of the interaction for two stacks plume cases. Fig. 1(c) shows the sampling system used for local concentration measurements and Fig. 1(d) shows the colorimeter measurement system. A small amount of a blue vegetable dye was added to the emissions and used as a tracer. The maximum value of the relative difference between the plume density, at the stack exit, rs and the environment density rw ; was 20% when brine was used as emission. The modified gravitational acceleration, g0 ¼
rs rw Dr g¼ g rw rw
was in the range 0pg0 p1:96 m s2. Results reported here refer to a relative density difference between the plume and the environment of 9.7% corresponding to a value of g0 equal to 0.95 m s2. The salt water and dye mixture was discharged from a 15 l reservoir by compressed air at 5 bar. A flow regulator and a set of flow-meters were used to regulate and measure the total flow rate to the sources. Each individual flow meter was also fitted with a needle valve that was used to balance the flow between the sources in use. A 2 1.65 m2 towing carriage runs along two stainless steel rails along the top edges of the tank. Models and emission sources that are to be towed are fixed to the carriage and accessed through a 1.35 1.35 m2 cut-out. Motion is provided by a flat track cable system driven by a
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Fig. 1. General definitions: (a) co-ordinate systems and notations used to describe the plumes, (b) scheme of the interaction for two stack plume cases, (c) sampling system used for local concentration measurements, and (d) colorimeter measurement system.
variable speed electric motor. The maximum speed of the carriage is 30 cm s1. Four different towing speeds (referred to as flow speeds), Ua ; were used in the experiments: 4.68, 8.86, 13.05 and 21.4 cm s1. The ratio between the emission vertical velocity and the flow speed was always high enough (generally between 1.8 and 17) in order to avoid stack-tip downwash phenomena. In the case referring to the single stack plume with the lowest flowrate and the maximum flow speed this ratio was about 1.1, though there was no evidence of stack downwash.
An image acquisition system using either a colour or black and white video camera with 8 bit resolution and an analogue and a digital video recorder was used to collect images from the water tank and to store them in a digital form on a computer. For such work, the plume was uniformly back-lit and recordings, typically between 12 and 50 s long, were taken showing the overall path and structure of the dye concentration field. Local concentration measurements were also obtained in order to analyse in detail single and double plume crosssections at different distances downstream from the
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source. The method involved collecting water samples during a run from a set of sampling tubes and subsequently analysing them in a colorimeter for dye colour intensity.
enabled the dilution ratio between the measurement and the emission to be evaluated.
3. Plume images and trajectories
2. Mean concentration measurement Sixteen water samples were collected simultaneously during the course of a tow over the length of the tank, or at least over a sufficiently long fetch to provide reliable mean concentrations. A sample of the source fluid and the water upstream of the release was also obtained. These two additional channels provided calibration data for each experiment, allowing the background dye concentration in the tank to be determined and dilutions to be expressed with respect to the source strength. A vacuum pump was used to create a low pressure inside the collection chamber so that the samples are sucked from the tubes and into storage bottles. A manually operated clamp was used to control the collection of samples. The overall suction flow-rate was controlled by adjusting the bleed flow of air into the collection chamber. Before commencing a run, all sample bottles were thoroughly rinsed with fresh water and dried to minimise cross-contamination. The external diameter of the sampling tube was 2.3 mm and the effective sampling diameter was typically 5 mm, based on the tow speed and suction rate. Once the samples had been collected, the next task was to analyse them in order to determine the dye dilution relative to the source strength. This task was performed by using the colorimeter, which responded to the light attenuation through the sample due to the dye concentration. A calibration was first carried out to relate colorimeter output to an arbitrary dye concentration scale. A range of calibration samples was produced by first mixing a very strong concentration of dye, which denoted 100%, and then repeatedly diluting this sample with 50% clear water in a volumetric flask. At each dilution level, a calibration bottle was filled to retain a sample of known strength relative to the starting mixture. The effects, on dye concentration measurements, of the presence of salt in the samples have been analysed and corrections, when necessary, have been made. In order to analyse a sample, the automatically controlled sampling needle (see Fig. 1(d)) was placed into the desired couvette on the carousel and the syringe pump set to operate twice. The acquisition program then sampled the voltage output from the colorimeter for 10 s from which an average was calculated. The calibration was then applied to determine the sample concentration relative to the calibration mixture, along with the background concentration and the source strength. This
Each plume video recording was accompanied by an equivalent duration background recording taken in the absence of emissions. A series of images was extracted from each and averaged. The ensemble average background image was subtracted to give a final image of the time-averaged plume. These final images were then scaled in order to fill all the grey-scale available with 8 bit resolution. Fig. 2 shows 12 cases of interacting plumes from two identical, in-line sources (i.e. the flow angle f between the line joining the two stacks and the wind direction was set to zero in all cases, the alignment for strong interaction). The images show three phases of plume developmentFthis is particularly clear in the cases where the separation between sources, d; is 22 source diameters (d ¼ 22D; D ¼ 7 mm). In the first phase the plumes are separate and behave as if isolated, except that the downwind plume experiences a modified flow field by being shielded by the upstream plume. Mixing between the plumes forms the second phase of the development. Here, the lower plume is entrained into the upper, an interaction that leads to an increased rate of plume rise relative to an equivalent single plume case. In the third phase, the plumes are well-mixed and behave again as an isolated plume from a single source. This will be discussed further in later sections where the structure of plume cross-sections is analysed. Video recordings of a 50 50 mm2 interval grid placed in the focal plane of the video-camera were used to calibrate the plume images and thus enable quantitative plume trajectory information to be obtained. A post-processing procedure of the grid image gave the scaling factor to convert distances measured in pixel terms to true physical units. The true distance between two adjacent pixels differed in the vertical and horizontal directions, but generally fell in the range from 1 to 1.6 mm. This also gives an indication of the spatial resolution of the imaging system. Image processing software was used to divide each image into vertical slices and to extract profiles of the pixel intensity Iðz; xÞ along each slice. The position of the stack centre was used as the origin of the reference frame. From the profiles, the mean plume height /ZS and vertical plume spread sz were obtained, referring to the centre of mass of the plume, as RN zIðz; xÞ dz /ZS ¼ R0N ; 0 Iðz; xÞ dz ð1Þ !1=2 RN /ZSÞ2 Iðz; xÞ dz 0 ðz R : sz ¼ N 0 Iðz; xÞ dz
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Fig. 2. Ensemble averaged images of interacting, in-line buoyant plumes with source diameter D ¼ 7 mm, density difference, DrXrw ¼ 0:097; emission rate, Q ¼ 1 l min1 (per source), source separation, d ¼ 4D; 10D and 22D (from top to bottom) and flow speed Ua ¼ 4:68; 8.86, 13.05 and 21.4 cm s1 (from left to right).
The approximation used is that the local intensity of the recorded pixels is proportional to the tracer concentration integrated along the direction normal to the camera field of view. Another approximation is that the distortion of the image at the border has negligible effect on the derived plume shape. This is true only for an ideal video-camera; in practice distortions are present and these are more important in double plume cases or where there are substantial sections of the plume away from the focal plane of the camera. Comparisons of the pixel intensity profiles, extracted from the final images of the plume, with point concentration measurements taken within the plume core show that the effect of distortion on plume trajectories evaluations are negligible in the experimental set-up used. Trajectories of single plumes are plotted in Fig. 3(a)– (c) for three different values of the discharge flow-rate: Q ¼ 0:56; 1 and 1.83 l min1 and four different values of
the flow speed, Ua ¼ 4:68; 8.86, 13.05 and 21.4 cm s1. The relative source density difference was Dr=rw ¼ 0:097 and the stack diameter was 7 mm in all cases. The results for the plume rise above the source are compared with predictions from the Briggs plume rise formula (A.5) (dashed lines) and with numerical results from an integral model (continuous lines). Both models are described in the appendix. The agreement between the two models and the experiments is very good for all the cases studied. The measured vertical spreads, sz ; from all the experiments are plotted in Fig. 3(d) as a function of average plume rise. The trend is almost linear, as is assumed in most plume rise models, and the linear leastsquare-fit gives a slope of 0.17. The trajectories of two interacting plumes were measured for four cross-flow velocities and for five source separations (so covering a range of strengths of interaction). Results are presented in Figs. 4(a)–(d) for sources 7 mm in diameter emitting 1 l min1 each at a
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Fig. 3. Examples of single plume trajectories derived from ensemble averaged video images, (a)–(c), compared with predictions from Briggs plume rise equation (dashed line) and an integral model (continuous line) and (d) vertical plume spread (sz ) as a function of the mean plume rise (/ZS) with a linear fit.
relative density difference of Dr=rw ¼ 0:097: Measured trajectories for isolated plumes are included in each figure; one case being a single discharge (as above), that represents the case of zero interaction, and the other being the combination of the two discharges released from a 9.9 mm diameter source (i.e. from a source of double the area of the 7 mm source), that represents the full interaction case. In the overall terms, the behaviour of the twin interacting plumes is similar for all the flow speeds analysed. Far from the source, all the trajectories for the range of source separations examined (d=D ¼ 0– 22) are contained between the two limiting cases of full and zero interaction. The additional rise resulting from the interaction decreases as the distance between the sources is increased, though some interaction, even if weak, is observable when the sources are separated by a distance equal to 22 diameters. In the region closer to the source, during the mixing process, the behaviour of the mean height is complex and values less than that in the equivalent single plume are observed. This arises due to two reasons. Firstly, the single plume trajectory has the upwind source as its origin and naturally lies above the plume from the downwind source. Secondly, the
calculation of the mean height, /ZS; from Eq. (1) biases the result towards the lower and more concentrated of the two interacting plumes. The results show extra-rise as large as 30% several tens of diameters downwind of the sources and this has significant consequences in terms of ground level concentrations. These results refer to in-line sources and this is the case in which the interaction is stronger, for each stack separation, because the two plumes mix very soon after discharge. Experiments indicate that the interaction provoking the extra plume rise weakens quite rapidly when f is increased because the plumes mix far away from the sources when they are already quite diluted. The extra plume rise can be evaluated with respect to the single stack trajectories referred to an origin of the reference system placed at the centre of the upwind stack. The Briggs formula (A.5) predicts that a plume with full interaction, having a buoyancy and a momentum twice larger than the case of zero interaction, will experience a plume rise 26% larger independent of the flow and plume characteristics and independent of the distance downwind of the stack. Our results mainly refer to near-source areas to put in evidence the mixing
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Fig. 4. Twin plume trajectories for a range of in-line source separations and flow speeds; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1 (per source): (a) Ua ¼ 4:68 cm s1, (b) Ua ¼ 8:86 cm s1, (c) Ua ¼ 13:05 cm s1 and (d) Ua ¼ 21:4 cm s1. Also shown are results for the full interaction (single source with D ¼ 9:9 mm, Q ¼ 2 l min 1) and for zero interaction (single source with D ¼ 7 mm, Q ¼ 1 l min1).
process and therefore they do not give exact information on the plume rise at large downwind distances. However, some indications can be extracted analysing the trajectories at the end of the measurement zones that are between 40 and 60 diameters downwind of the sources. Our results referring to full and zero interaction show relative differences in the plume rise between 21% and 31% being the larger values associated with the high values of the velocity ratio R ¼ Ws =Ua and slightly varying with X: For the different cases of two plume interactions reported in Fig. 4, the enhancement factor measured ranged from 24.8% (d ¼ 2D) to 21.9% (d ¼ 10D) for the cases of Fig. 4(a), which the prediction of Briggs model (Briggs, 1974) is between 24.7% and 16.6%. The results of Fig. 4(b) give extra plume rises, in relative terms, between 21% (d ¼ 2D) and 12.5% (d ¼ 10D), and the prediction of Briggs model are between 23.5% and 12.1%. In the cases of Fig. 4(c), the extra plume rise is between 19.2% (d ¼ 2D) and 6.2% (d ¼ 10D) and the predictions are between 22% and 8.7%. For the cases referring to the maximum crossflow speed analysed (Fig. 4(c)) the experimental extra plume rise is between 21.6% (d ¼ 2D) and 7.2% (d ¼ 10D) and the predictions are between 19.3% and 5.4%. The Anfossi et al. (1978) model gives somewhat higher
enhancement factors with respect to the Briggs model of about 1–7% (being larger for high values of d) of the plume rise referring to the single stack with zero interaction.
4. Plume cross-sections A detailed survey of the plume structure in different conditions was performed through local concentration measurements using the colorimeter system. Single plume and twin plume cross-sections were measured in planes normal to the wind direction at different distances, x, from the source. In Fig. 5(a), cross-section of a single plume is shown at x ¼ 380 mm from a 7 mm diameter source; concentrations are normalised to a maximum of unity. The flow-rate was 1 l min1, Ua was 8.86 cm s1 and the relative density difference at the source was 9.7%. The maximum concentration measured in this cross-section was equal to 2.3% of the source concentration. The mapping shows a basically symmetrical structure with two well-developed lateral lobes, marking the twin vortex structure within the plume. The maximum concentration occurs near the centre of these lobes, and not on the plume centreline,
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Fig. 5. Concentration field cross-section in a single, isolated plume measured 380 mm downwind of the source; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1, and Ua ¼ 8:86 cm s1. A small scale plume image showing the location of the measurement section is given in the inset.
y ¼ 0: The maximum concentration on y ¼ 0 is approximately 13 of the maximum concentration in the lobes. The total lateral width of the plume is about a factor of 1.5 greater than the vertical spread. This twin vortex structure develops as a consequence of the interaction between the plume and the cross-flow at the very early stages of the plume development (Smith and Mungal, 1998; Fric and Roshko, 1994). The vortex structure is a stable structure observable in long time average measurements. It has been frequently observed in the experimental work where ambient turbulence levels are low (e.g. Hewett et al., 1971; Tsang, 1971) and predicted by numerical simulations (Zhang and Ghoniem, 1993). The structure is also observed in the atmosphere, but only in low turbulence conditions or in short duration observations (Bennett et al., 1992). Often, turbulence and wind direction fluctuations bodily displace the mass-centre of the plume (Olivari and Palli, 1991) and the long time-average (e.g. the hourly average) of cross-section is observed to follow the traditional Gaussian shape. Three stages can generally be identified in the development of a single plume, though in these towing tank experiments only the first two are evident. In the
first near-source phase, the plume experiences large horizontal accelerations with rather small deformations and rises almost as if it were a solid body. In the second stage the twin, symmetrical vortex structure develops. During this stage significant entrainment of external fluid into the plume core takes place, chiefly through the base as a consequence of the secondary flow associated with the vortex system. In the final stage, the plume may break-up due to effects of ambient turbulence or split into two separate lobes (Zhang and Ghoniem, 1993). Cross-sections for a twin plume case (source diameter 7 mm, emission rate 1 l min1 per source, 1 Ua ¼ 8:86 cm s , DrXrw ¼ 9:7%) were measured at three downstream distances for a separation between the stacks equal to 22 stack-diameters. The results are shown in Fig. 6, where each cross-section has been normalised to one. The maximum concentration values were 22.3%, 7.9% and 3% of the source concentration at x ¼ 171; 213 and 375 mm, respectively. The first cross-section, at x ¼ 171 mm, was measured closer to the downstream source at a position where the plumes were beginning to mix. It shows an upper plume with a double vortex developed structure from the upstream source and a lower plume from the downstream source that has not yet developed this structure. This lower plume is about five times more concentrated than the upper one, has a larger vertical velocity and maximum density difference and rises into the centre of the upper plume, between the lateral lobes. The interaction is enhanced by the entrainment flow into the base of the upper plume. The second cross-section, at x ¼ 213 mm, shows the situation where mixing is more advanced. The smaller plume has been engulfed by the vortex structure of the upper plume. This at first leads to a rather symmetrical form, with no obvious vortex structure, which is similar to that observed in the early stages of an isolated plume. The maximum concentration is now found on the plume centreline. However, the vortices reform as the combined plume develops whilst travelling downwind, as the third cross-section, at x ¼ 375 mm, shows. The two lateral vortices are again present and maximum concentrations are again located near the centres of these vortices. The maximum plume concentration is only 1.4 times greater than the maximum concentration on the centreline, compared with about 3 in Fig. 5. The total width of the plume is almost equal to its total vertical spread, whereas in Fig. 5 this ratio is about 1.5. However, comparison of the two cases also shows that at this position the plume interaction leads to extra plume rise; in average terms by about 7%. The vortex pair is clearly not fully developed, in comparison with that shown in Fig. 5 for the single emission, because the development fetch from the region of interaction is considerably less than that of the single plume.
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Fig. 6. Concentration field cross-section in a twin plume at x ¼ 171; 213, 375 mm from the upstream source; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1 (per source), and Ua ¼ 8:86 cm s1. A small scale plume image is inset showing the location of the measurement section.
5. Accuracy Numerous general sources of random experimental error affected the experiments; e.g. fluctuations in the source flow rate, the flow speed, the source and environment density and in the video recordings and colorimeter concentration measurements. Some errors were peculiar to the method used; e.g. distortion in the lens systems and non-linear response affecting the video images, colorimeter calibration drift and probe positioning errors affecting the point measurement data. To determine ‘‘a priori’’ the accuracy of the results is difficult but a useful idea of the global effects of the various sources of error was obtained by repeating several times the experiments in nominally identical conditions. This analysis showed that calibration drift, with the colorimeter calibrated every day, generated average errors smaller than 3%, such that the stability of the flow speed was better than 0.2% and that the discharge flow rate could be measured within about 5%. Repeatability in the evaluation of trajectories shows a standard deviation in plume rise that is about 3% and the typical measurement repeatability, taken to be defined by two standard deviations, is therefore 6% of the mean plume rise. Experiments on point concentration measurements show a repeatability of about 15% in the dilution results.
6. Conclusions Towing tank experiments were carried out to investigate the interactions between two in-line, rising buoy-
ant plumes. Both quantitative flow visualisation and point concentration measurement techniques were used. Results for the rise of a single plume were in good agreement with both the Briggs formula and numerical results from an integral model. The double vortex structure in the developed plume was clearly shown by concentration measurements in a plume cross-section. The twin plume experiments gave quantitative evidence of significant extra-rise due to plume interaction that can be as large as 30% a few tens of stack diameters downwind of the sources. They also revealed how the interaction developed and showed that this first led to a destruction of the vortex structure in the plume from the upstream source and then to the subsequent reestablishment of the vortices in the combined plume. However, even at the farthest downwind position studied the combined plume had not fully attained the internal structure of a developed plume from a single source. The interaction between two rising plumes obviously depends on their relative positions and the present work only considered in-line arrangements, f=01. For small values of f the overall behaviour may be expected to be similar because the secondary flows associated with the plume vortices will ‘guide’ the lower and smaller plume into the central part of the base of the larger upper plume during the mixing phase. This will become less effective as the flow angle increases and eventually there will be direct interactions between the vortex systems in the two plumes. This will introduce considerable asymmetry during the mixing phase. The likely result is that the complete combination of the plumes will be a much more protracted affair and consequently any
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additional plume rise will be smaller. Eventually, the interaction will cease entirely at least in terms of extra plume rise. Preliminary results show that the effects of the interaction, on plume trajectories, rapidly decrease once f exceeds 301, in agreement with the results of Overcamp and Ku (1988) and are negligible once f approaches 901 (Mayland, 1997). Of course, the detail in this statement depends on the source separation but is generally true for the separations studied (Briggs, 1984). However the interaction, for non-aligned sources, will generate strong asymmetry of the resulting plume with respect to its centreline during the mixing phase. The relative extra-rise, for f ¼ 0; after the mixing process, due to the interaction between the two plumes has been found to be in good agreement with the prediction of available empirical formulae of Briggs (1974) and Anfossi et al. (1978). Of the two, the model of Briggs actually gives slightly better results for the experiments reported here. The interaction weakens when the separation between the stacks is increased and when the momentum or buoyancy flux of the sources is decreased. The enhancement factor usually employed in the empirical formulations can describe the plume interaction for downwind distances large enough such that the mixing process is ended; however, the mixing itself can generate complicated trajectories in the area near the stacks, as shown in our results. The shape of the plume is also greatly influenced and this has to be taken into account in integral models used to evaluate the plume rise. Therefore, a correct modelling of the interaction problems should address the complete trajectory and the shape of the plumes. Our results put in evidence the phases of the mixing for two in-line sources and further investigation is needed for sources not aligned with the windFpreliminary results show strong asymmetries in the cross-sections. Investigations for cases with a larger number of stacks are also needed. An analysis of the part of the twin plume trajectories in which the two plumes have combined into a single one shows that the slopes are similar to the slopes of single stack trajectories presenting full interaction (and not the the trajectory relative to zero interaction). This can be used to evaluate, with a best fit procedure, the shift DX that has to be made on the full interaction trajectory (towards the downwind stack) in order to correctly describe the twin plume trajectories for X greater than 2d (after the mixing process). Results show that a good approximation for all the data reported in Fig. 4 is to use DX ¼ ad with the coefficient a given by a ¼ 1:7 ðUa =Ws Þ þ 0:35: These relationships are valid for d between zero and 10D; the case relative to d ¼ 22D has not been included because the trajectories have not been measured for distances much larger than 2d and the results of the fit were not reliable. The coefficient a may actually depend on the density difference between the emissions and the crossflow, but the data reported here
refer to a fixed density difference and this aspect cannot be inferred.
Acknowledgements This research was been carried out with the financial support of the ‘‘Ministero della Universit"a e della Ricerca Scientifica e Tecnologica’’ in collaboration with the ‘‘Conferenza dei Rettori delle Universit"a Italiane’’ (CRUI) and of the British Council under the ‘‘BritishItalian collaboration in Research and Higher Education’’ 1998–99 programme. It was also been funded by the European Community through the Large Scale Facilities section of the Training and Mobility of Researcher (TMR) programme, contract ERBFMGECT980117.
Appendix. A The integral plume rise model used here evaluates the trajectory and spread of a single plume given the conditions at the source and in the external environment. The model is a top-hat integral model similar to the one described in Ooms and Mahieu (1981). The main assumptions are (I) the plume has no effect on the properties of the environment, (II) the plume is continuous, slender and with circular cross-section, (III) properties are uniform within the plume and (IV) entrainment takes place due to the plume’s motion relative to the environment. With these assumptions it is possible to write the equation of motion for the plume, that has to be integrated with the continuity equation ~Þ ¼ 0; referring to Fig. 1(a) for stationary flows: divðrU for notation: d ðrr2 Us Þ ¼ 2rrw Ve Ve ¼ ajDUt j þ bjDUn j ds þ turbulence effects;
ðA:1Þ
d dUa ; ðrr2 Us ðUs cos ðgÞ Ua ÞÞ ¼ rr2 Us sin ðgÞ dz ds
ðA:2Þ
d ðrr2 Us2 sin ðgÞÞ ¼ gr2 ðrw rÞ; ds
ðA:3Þ
d ðgr2 Us ðr rw ÞÞ ¼ rw Us sin ðgÞr2 N 2 : ds
ðA:4Þ
Eq. (A.1) represent the entrainment assumption through an entrainment velocity Ve proportional to the relative tangential velocity DUt and the relative vertical velocity DUn of the plume. In the present case environmental turbulence effects are not present. The constant a is taken to be 0.057 and the constant b is 0.6. Eqs. (A.2) and (A.3) represent the momentum equations in the x- and z-direction, respectively, and g is the
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gravitational acceleration. The symbol Ua indicates the flow speed and Us is the plume tangential speed. Eq. (A.4) is a buoyancy conservation equation and N is the Brunt–V.ais.al.a frequency that can be written as N2 ¼
g dya ya dz
Where ya is the ambient potential temperature. For incompressible fluids, g drw : N2 ¼ rw dz In the present case, both the flow speed as well as the flow potential temperature (neutral stratification) are constant so that the equation set is simplified. Procedures were implemented on a PC programme in order to solve these equations numerically and to evaluate the plume trajectories. The Briggs formula is obtained as an approximation to the equation set (Briggs, 1974; Weil, 1988) assuming that the plume is bent-over and neglecting the contribution of a to the total entrainment. The solution for the trajectory is then given by " #1=3 3Fm x 3Fb x2 ðr rs Þ z¼ 2 þ ; Fb ¼ gr2s Ws w ; rw b1 Ua2 2b22 Ua3 Fm ¼
rs 2 2 W r ; rw s s
ðA:5Þ
where Ws is the vertical plume speed at the source, rs the initial density and rs the initial radius (i.e. the source internal radius). The first term in the square bracket in Eq. (A.5) accounts for the plume momentum and the second one for its buoyancy. The entrainment coefficient should be b1 ¼ b2 ¼ b ¼ 0:6; however, comparisons with experimental results lead to some changes in the formula and the value of the entrainment coefficient was reformulated as two coefficients b1 and b2 ; having the values b1 ¼ 0:4 þ 1:2
Ua Ws
and
b2 ¼ b ¼ 0:6:
This is to describe better the jet part and this means the rise of neutrally buoyant plumes.
References Anfossi, D., Bonino, G., Bossa, F., Richiardone, R., 1978. Plume rise from multiple sources: a new model. Atmospheric Environment 12, 1821–1826. Bennett, M., Sutton, S., Gardiner, D.R.C., 1992. Measurements of wind speed and plume rise with a rapid scanning LIDAR. Atmospheric Environment 26A, 1675–1688. Briggs, G.A., 1974. Plume rise from multiple source. Proceedings of Cooling Towers Environment, Maryland.
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Coordinators: S.R. Hanna, J. Pell, CONF-740302, NTIS, pp. 161–179. Briggs, G.A., 1975a. Plume rise prediction. Lectures on Air Pollution and Environmental Impact Analyses, Workshop Proceedings. American Meteorological Society, Boston, 1975, pp. 59–111. Briggs, G.A., 1975b. Discussion of a comparisons of the trajectories of rising buoyant plumes with theoretical empirical models. Atmospheric Environment 9, 455–462. Briggs, G.A., 1984. Plume rise and buoyancy effects. In: Randerson, D. (Eds.), Atmospheric science and power production, DOE/TICF27601, USA Dept. of Energy, pp. 327–366. Contini, D., 1999. Studio di diffusione di inquinanti gassosi su modelli in scala ridotta in galleria del vento. Ph.D. Thesis, University of Florence, 1999 (in Italian). Fric, T.F., Roshko, A., 1994. Vortical structure in the wake of a transverse jet. Journal of Fluid Mechanics 279, 1–47. Hewett, T.A., Fay, J.A., Hoult, D.P., 1971. Laboratory experiments of smoke-stack plumes in a stable atmosphere. Atmospheric Environment 5, 767–789. Hoult, D.P., Weil, J.C., 1972. Turbulent plume in laminar cross-flow. Atmospheric Environment 6, 513–531. Hunter, G., 1992. The behaviour of plumes from point sources in stratified flows. Ph.D. Thesis, National Power Research and Technology Department, 1992. Mayland, J., 1997. Interaction of buoyant plumes in a cross flow. Final Year Project, Mechanical Engineering, University of Surrey. Ohba, R., Kakishima, S., Ito, S., 1990. Water tank study of plume rise and diffusion in a stably stratified layer under calm conditions. Il Nuovo Cimento C 13 (6), 1017–1028. Olivari, D., Palli, E., 1991. Investigation of fluctuating properties of a neutral plume using digital image analysis techniques. Atmospheric Environment 25A (8), 1635–1642. Ooms, G., Mahieu, A.P., 1981. A comparison between a plume path model and a virtual point source model for a stack plume. Applied Scientific Research 36, 339–356. Overcamp, T.J., Ku, T., 1988. Plume rise from two or more adjacent stacks. Atmospheric Environment 22 (4), 625–637. Robins, A.G., Aspley, D.D., 1994. Plume rise model specifications. In: ADMS 1.06 Technical Specifications. CERC Ltd, Cambridge. Smith, S.H., Mungal, M.G., 1998. Mixing, structure and scaling of the jet in a crossflow. Journal of Fluid Mechanics 357, 83–122. Snyder, W.H., 1985. Fluid modelling of pollutant transport and diffusion in stably stratified flows over complex terrain. Annals Review of Fluid Mechanics 17, 239–266. Tsang, G., 1971. Laboratory study of line thermals. Atmospheric Environment 5, 445–471. Weil, J.C., 1988. Plume rise. In: Venkatram, A., Wyngaard, J.C. (Eds.), Lectures on Air Pollution Modelling. American Meteorological Society, Boston, pp. 121–166. Zhang, X., Ghoniem, X.F., 1993. A computational model for the use and dispersion of wind-blown, buoyancy-driven plumesFI. Neutrally stratified atmosphere. Atmospheric Environment 27A (15), 2295–2311.
Water tank measurements of buoyant plume rise and structure in neutral crossflows Daniele Continia,*, Alan Robinsb a
Dipartimento di Energetica ‘‘Sergio Stecco’’, Universita" di Firenze, Via S. Marta 3, 50139 Firenze, Italy EnFlo, School of Mechanical and Material Engineering, University of Surrey, Guildford GU2 7XH, UK
b
Received 21 March 2001; received in revised form 19 July 2001; accepted 26 July 2001
Abstract In this paper, an experimental study of the rise and development of a single buoyant plume and a pair of in-line buoyant plumes is presented. The investigations were carried out at small scale in a water filled towing tank using both quantitative flow visualisation and local concentration measurements. The measured plume trajectories for a single plume were compared with the Briggs plume rise equation and predictions from a numerical integral model. Plume trajectories were studied for twin in-line plumes, with particular attention to changes in the plume trajectory, especially any additional rise that resulted from the interaction between the two plumes. Concentration field distributions in crosssections through both single and interacting twin plumes were obtained from the local concentration measurement system. These showed how the interaction affected the plume structure, notably the double vortex system that occurs in a fully developed plume. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Plume rise; Multiple plumes; Plume interaction; Towing tank; Modelling
1. Introduction Understanding the behaviour of multiple interacting plumes in terms of their average path and spread, as well as in terms of their shape, is a matter of considerable interest in environmental impact studies. Frequently, large power plants have two or more stacks placed only a few diameters apart; in some combined cycle gas turbine installations up to 8 or 10 stacks are present. Some waste incinerators have also been designed with two tall and slender stacks placed very near one another. Further examples abound in the petrol-chemical and process industries. In all these cases, strong interactions can arise between adjacent plumes, especially under favourable wind directions. Reliable analytical models exist for single plume rise evaluation (e.g. Briggs, 1974, 1975a, b), as well as integral models that relate the plume mass and momentum fluxes to the forces acting on a *Corresponding author. E-mail address: [email protected]fi.it (D. Contini).
plume and the entrainment rate of external fluid (e.g. Ooms and Mahieu, 1981; Robins and Aspley, 1994). Simple empirical corrections have been proposed for evaluating trajectories in multiple source cases (e.g. Briggs, 1974; Anfossi et al., 1978). These corrections apply to the part of the trajectories after the mixing process and they give the extra plume rise due to the interaction, with an enhancement factor, and do not usually take into account the manner in which the interaction depends on wind direction. Previous wind tunnel results, as well as field data analysis, (Overcamp and Ku, 1988; Briggs, 1984) show that the wind direction actually influences the multiple plumes mixing and consequently the extra plume rise. The strongest interaction for fixed distances between a pair of stacks is when the sources are aligned with the approaching flow. We carried out experiments not only for twin stack cases but also for single stack cases in order to obtain the trajectories without interaction and the trajectories for the maximum interaction. Single stack trajectories compare well with the results of both Briggs formula
1352-2310/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 0 1 ) 0 0 3 9 8 - 3
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and integral model numerical predictions. Our results regarding the trajectories of two-stack plumes show a decreasing interaction when the stack separation is increased. The interaction also becomes weaker if the momentum or buoyancy flux at the sources is decreased. However, even if the interaction in terms of additional plume rise becomes small the mixing of the two plumes generates relevant changes in the plume internal structure. Experimental studies with multiple plumes are a matter of great importance then in order to examine the performance of available models that describe plume rise, plume spread and dispersion and the reliability of the empirical parameters used to describe the rate of entrainment of ambient air into plumes and the consequent plume dilution and spreading. In this paper, a study of buoyant plume rise and plume structure for two interacting plumes is described; the work being undertaken not only to test models but also to provide a basis for the development of better models of plume interaction. The measurements were carried out in neutral flow conditions for both buoyant single and double plumes, the latter generated by two identical, in-line emissions. Attention is focussed on the two plume case, with only some example results given for single plumes. A more comprehensive description of the single plumes work can be found in Contini (1999). The experiments were performed at the University of Surrey in a water filled towing tank by means of quantitative flow visualisation to provide full-field information, and water sampling and dilution measurement using a colorimeter system to provide point concentration measurements. Water tanks prove to be a powerful and widely used tool for flow and plume dispersion studies because it is relatively simple to make visualisations by using coloured dyes and to generate stably stratified flows by means of salinity gradients in the water. For examples of such applications see Ohba et al. (1990), Snyder (1985), Hoult and Weil (1972) and Hunter (1992). The physics of plume interactions is very complicated and, as the measurements demonstrate, the consequences may affect almost the entire trajectory of the plumes involved. Our results show that interactions between two adjacent plumes may induce an increment in plume rise as large as 30% several tens of diameters downstream from the sources (which at full scale would be in the range from about 100 to 500 m). When plumes mix shortly after release, they form a larger single plume that is subject to the combined buoyancy flux of the two emissions. Consequently, the rise is increased (in theory, at maximum by as much as a factor of 21/3 or 26% for two plumes of equal strength) and the plume experiences greater rise induced spread than the single plumes in isolation. Consequently, ground level concentrations, usually the only indicator employed in environmental impact analysis, will be subject to a systematic error if the interaction is not correctly taken into account. The
situation becomes increasingly more complicated as the number of interacting plumes increases, thereby increasing the extra plume rise. The mixing process is more efficient when two (or more) plumes of equal or similar strength come into contact, as in the results reported here. However, if the plumes have very different strengths or the separation among the stacks is large enough, the plumes may interact without an effective mixing (Briggs, 1984). 1.1. Experimental set-up and equipment The experiments were performed in a water tank facility 12 m long, 1.2 m wide and with a maximum water depth of 1 m. The tank was used in a neutral stability state, being filled with fresh water. Buoyant emissions were simulated by releasing at the top of the tank a salt water solution from just below the surface, with the tip of the stacks immersed by about five diameters, i.e. the experiments were performed in an inverted set-up but results were reported in a standard co-ordinate system with the Z-axis increasing upward. Fig. 1(a) defines the co-ordinate system used in presenting the results and the notation used to describe the plumes. For twin in-line stack cases the origin of the reference system was the centre of the upwind stack. Interpretations of extra plume rise may depend on the reference system used. Fig. 1(b) shows a scheme of the interaction for two stacks plume cases. Fig. 1(c) shows the sampling system used for local concentration measurements and Fig. 1(d) shows the colorimeter measurement system. A small amount of a blue vegetable dye was added to the emissions and used as a tracer. The maximum value of the relative difference between the plume density, at the stack exit, rs and the environment density rw ; was 20% when brine was used as emission. The modified gravitational acceleration, g0 ¼
rs rw Dr g¼ g rw rw
was in the range 0pg0 p1:96 m s2. Results reported here refer to a relative density difference between the plume and the environment of 9.7% corresponding to a value of g0 equal to 0.95 m s2. The salt water and dye mixture was discharged from a 15 l reservoir by compressed air at 5 bar. A flow regulator and a set of flow-meters were used to regulate and measure the total flow rate to the sources. Each individual flow meter was also fitted with a needle valve that was used to balance the flow between the sources in use. A 2 1.65 m2 towing carriage runs along two stainless steel rails along the top edges of the tank. Models and emission sources that are to be towed are fixed to the carriage and accessed through a 1.35 1.35 m2 cut-out. Motion is provided by a flat track cable system driven by a
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Fig. 1. General definitions: (a) co-ordinate systems and notations used to describe the plumes, (b) scheme of the interaction for two stack plume cases, (c) sampling system used for local concentration measurements, and (d) colorimeter measurement system.
variable speed electric motor. The maximum speed of the carriage is 30 cm s1. Four different towing speeds (referred to as flow speeds), Ua ; were used in the experiments: 4.68, 8.86, 13.05 and 21.4 cm s1. The ratio between the emission vertical velocity and the flow speed was always high enough (generally between 1.8 and 17) in order to avoid stack-tip downwash phenomena. In the case referring to the single stack plume with the lowest flowrate and the maximum flow speed this ratio was about 1.1, though there was no evidence of stack downwash.
An image acquisition system using either a colour or black and white video camera with 8 bit resolution and an analogue and a digital video recorder was used to collect images from the water tank and to store them in a digital form on a computer. For such work, the plume was uniformly back-lit and recordings, typically between 12 and 50 s long, were taken showing the overall path and structure of the dye concentration field. Local concentration measurements were also obtained in order to analyse in detail single and double plume crosssections at different distances downstream from the
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source. The method involved collecting water samples during a run from a set of sampling tubes and subsequently analysing them in a colorimeter for dye colour intensity.
enabled the dilution ratio between the measurement and the emission to be evaluated.
3. Plume images and trajectories
2. Mean concentration measurement Sixteen water samples were collected simultaneously during the course of a tow over the length of the tank, or at least over a sufficiently long fetch to provide reliable mean concentrations. A sample of the source fluid and the water upstream of the release was also obtained. These two additional channels provided calibration data for each experiment, allowing the background dye concentration in the tank to be determined and dilutions to be expressed with respect to the source strength. A vacuum pump was used to create a low pressure inside the collection chamber so that the samples are sucked from the tubes and into storage bottles. A manually operated clamp was used to control the collection of samples. The overall suction flow-rate was controlled by adjusting the bleed flow of air into the collection chamber. Before commencing a run, all sample bottles were thoroughly rinsed with fresh water and dried to minimise cross-contamination. The external diameter of the sampling tube was 2.3 mm and the effective sampling diameter was typically 5 mm, based on the tow speed and suction rate. Once the samples had been collected, the next task was to analyse them in order to determine the dye dilution relative to the source strength. This task was performed by using the colorimeter, which responded to the light attenuation through the sample due to the dye concentration. A calibration was first carried out to relate colorimeter output to an arbitrary dye concentration scale. A range of calibration samples was produced by first mixing a very strong concentration of dye, which denoted 100%, and then repeatedly diluting this sample with 50% clear water in a volumetric flask. At each dilution level, a calibration bottle was filled to retain a sample of known strength relative to the starting mixture. The effects, on dye concentration measurements, of the presence of salt in the samples have been analysed and corrections, when necessary, have been made. In order to analyse a sample, the automatically controlled sampling needle (see Fig. 1(d)) was placed into the desired couvette on the carousel and the syringe pump set to operate twice. The acquisition program then sampled the voltage output from the colorimeter for 10 s from which an average was calculated. The calibration was then applied to determine the sample concentration relative to the calibration mixture, along with the background concentration and the source strength. This
Each plume video recording was accompanied by an equivalent duration background recording taken in the absence of emissions. A series of images was extracted from each and averaged. The ensemble average background image was subtracted to give a final image of the time-averaged plume. These final images were then scaled in order to fill all the grey-scale available with 8 bit resolution. Fig. 2 shows 12 cases of interacting plumes from two identical, in-line sources (i.e. the flow angle f between the line joining the two stacks and the wind direction was set to zero in all cases, the alignment for strong interaction). The images show three phases of plume developmentFthis is particularly clear in the cases where the separation between sources, d; is 22 source diameters (d ¼ 22D; D ¼ 7 mm). In the first phase the plumes are separate and behave as if isolated, except that the downwind plume experiences a modified flow field by being shielded by the upstream plume. Mixing between the plumes forms the second phase of the development. Here, the lower plume is entrained into the upper, an interaction that leads to an increased rate of plume rise relative to an equivalent single plume case. In the third phase, the plumes are well-mixed and behave again as an isolated plume from a single source. This will be discussed further in later sections where the structure of plume cross-sections is analysed. Video recordings of a 50 50 mm2 interval grid placed in the focal plane of the video-camera were used to calibrate the plume images and thus enable quantitative plume trajectory information to be obtained. A post-processing procedure of the grid image gave the scaling factor to convert distances measured in pixel terms to true physical units. The true distance between two adjacent pixels differed in the vertical and horizontal directions, but generally fell in the range from 1 to 1.6 mm. This also gives an indication of the spatial resolution of the imaging system. Image processing software was used to divide each image into vertical slices and to extract profiles of the pixel intensity Iðz; xÞ along each slice. The position of the stack centre was used as the origin of the reference frame. From the profiles, the mean plume height /ZS and vertical plume spread sz were obtained, referring to the centre of mass of the plume, as RN zIðz; xÞ dz /ZS ¼ R0N ; 0 Iðz; xÞ dz ð1Þ !1=2 RN /ZSÞ2 Iðz; xÞ dz 0 ðz R : sz ¼ N 0 Iðz; xÞ dz
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Fig. 2. Ensemble averaged images of interacting, in-line buoyant plumes with source diameter D ¼ 7 mm, density difference, DrXrw ¼ 0:097; emission rate, Q ¼ 1 l min1 (per source), source separation, d ¼ 4D; 10D and 22D (from top to bottom) and flow speed Ua ¼ 4:68; 8.86, 13.05 and 21.4 cm s1 (from left to right).
The approximation used is that the local intensity of the recorded pixels is proportional to the tracer concentration integrated along the direction normal to the camera field of view. Another approximation is that the distortion of the image at the border has negligible effect on the derived plume shape. This is true only for an ideal video-camera; in practice distortions are present and these are more important in double plume cases or where there are substantial sections of the plume away from the focal plane of the camera. Comparisons of the pixel intensity profiles, extracted from the final images of the plume, with point concentration measurements taken within the plume core show that the effect of distortion on plume trajectories evaluations are negligible in the experimental set-up used. Trajectories of single plumes are plotted in Fig. 3(a)– (c) for three different values of the discharge flow-rate: Q ¼ 0:56; 1 and 1.83 l min1 and four different values of
the flow speed, Ua ¼ 4:68; 8.86, 13.05 and 21.4 cm s1. The relative source density difference was Dr=rw ¼ 0:097 and the stack diameter was 7 mm in all cases. The results for the plume rise above the source are compared with predictions from the Briggs plume rise formula (A.5) (dashed lines) and with numerical results from an integral model (continuous lines). Both models are described in the appendix. The agreement between the two models and the experiments is very good for all the cases studied. The measured vertical spreads, sz ; from all the experiments are plotted in Fig. 3(d) as a function of average plume rise. The trend is almost linear, as is assumed in most plume rise models, and the linear leastsquare-fit gives a slope of 0.17. The trajectories of two interacting plumes were measured for four cross-flow velocities and for five source separations (so covering a range of strengths of interaction). Results are presented in Figs. 4(a)–(d) for sources 7 mm in diameter emitting 1 l min1 each at a
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Fig. 3. Examples of single plume trajectories derived from ensemble averaged video images, (a)–(c), compared with predictions from Briggs plume rise equation (dashed line) and an integral model (continuous line) and (d) vertical plume spread (sz ) as a function of the mean plume rise (/ZS) with a linear fit.
relative density difference of Dr=rw ¼ 0:097: Measured trajectories for isolated plumes are included in each figure; one case being a single discharge (as above), that represents the case of zero interaction, and the other being the combination of the two discharges released from a 9.9 mm diameter source (i.e. from a source of double the area of the 7 mm source), that represents the full interaction case. In the overall terms, the behaviour of the twin interacting plumes is similar for all the flow speeds analysed. Far from the source, all the trajectories for the range of source separations examined (d=D ¼ 0– 22) are contained between the two limiting cases of full and zero interaction. The additional rise resulting from the interaction decreases as the distance between the sources is increased, though some interaction, even if weak, is observable when the sources are separated by a distance equal to 22 diameters. In the region closer to the source, during the mixing process, the behaviour of the mean height is complex and values less than that in the equivalent single plume are observed. This arises due to two reasons. Firstly, the single plume trajectory has the upwind source as its origin and naturally lies above the plume from the downwind source. Secondly, the
calculation of the mean height, /ZS; from Eq. (1) biases the result towards the lower and more concentrated of the two interacting plumes. The results show extra-rise as large as 30% several tens of diameters downwind of the sources and this has significant consequences in terms of ground level concentrations. These results refer to in-line sources and this is the case in which the interaction is stronger, for each stack separation, because the two plumes mix very soon after discharge. Experiments indicate that the interaction provoking the extra plume rise weakens quite rapidly when f is increased because the plumes mix far away from the sources when they are already quite diluted. The extra plume rise can be evaluated with respect to the single stack trajectories referred to an origin of the reference system placed at the centre of the upwind stack. The Briggs formula (A.5) predicts that a plume with full interaction, having a buoyancy and a momentum twice larger than the case of zero interaction, will experience a plume rise 26% larger independent of the flow and plume characteristics and independent of the distance downwind of the stack. Our results mainly refer to near-source areas to put in evidence the mixing
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Fig. 4. Twin plume trajectories for a range of in-line source separations and flow speeds; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1 (per source): (a) Ua ¼ 4:68 cm s1, (b) Ua ¼ 8:86 cm s1, (c) Ua ¼ 13:05 cm s1 and (d) Ua ¼ 21:4 cm s1. Also shown are results for the full interaction (single source with D ¼ 9:9 mm, Q ¼ 2 l min 1) and for zero interaction (single source with D ¼ 7 mm, Q ¼ 1 l min1).
process and therefore they do not give exact information on the plume rise at large downwind distances. However, some indications can be extracted analysing the trajectories at the end of the measurement zones that are between 40 and 60 diameters downwind of the sources. Our results referring to full and zero interaction show relative differences in the plume rise between 21% and 31% being the larger values associated with the high values of the velocity ratio R ¼ Ws =Ua and slightly varying with X: For the different cases of two plume interactions reported in Fig. 4, the enhancement factor measured ranged from 24.8% (d ¼ 2D) to 21.9% (d ¼ 10D) for the cases of Fig. 4(a), which the prediction of Briggs model (Briggs, 1974) is between 24.7% and 16.6%. The results of Fig. 4(b) give extra plume rises, in relative terms, between 21% (d ¼ 2D) and 12.5% (d ¼ 10D), and the prediction of Briggs model are between 23.5% and 12.1%. In the cases of Fig. 4(c), the extra plume rise is between 19.2% (d ¼ 2D) and 6.2% (d ¼ 10D) and the predictions are between 22% and 8.7%. For the cases referring to the maximum crossflow speed analysed (Fig. 4(c)) the experimental extra plume rise is between 21.6% (d ¼ 2D) and 7.2% (d ¼ 10D) and the predictions are between 19.3% and 5.4%. The Anfossi et al. (1978) model gives somewhat higher
enhancement factors with respect to the Briggs model of about 1–7% (being larger for high values of d) of the plume rise referring to the single stack with zero interaction.
4. Plume cross-sections A detailed survey of the plume structure in different conditions was performed through local concentration measurements using the colorimeter system. Single plume and twin plume cross-sections were measured in planes normal to the wind direction at different distances, x, from the source. In Fig. 5(a), cross-section of a single plume is shown at x ¼ 380 mm from a 7 mm diameter source; concentrations are normalised to a maximum of unity. The flow-rate was 1 l min1, Ua was 8.86 cm s1 and the relative density difference at the source was 9.7%. The maximum concentration measured in this cross-section was equal to 2.3% of the source concentration. The mapping shows a basically symmetrical structure with two well-developed lateral lobes, marking the twin vortex structure within the plume. The maximum concentration occurs near the centre of these lobes, and not on the plume centreline,
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Fig. 5. Concentration field cross-section in a single, isolated plume measured 380 mm downwind of the source; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1, and Ua ¼ 8:86 cm s1. A small scale plume image showing the location of the measurement section is given in the inset.
y ¼ 0: The maximum concentration on y ¼ 0 is approximately 13 of the maximum concentration in the lobes. The total lateral width of the plume is about a factor of 1.5 greater than the vertical spread. This twin vortex structure develops as a consequence of the interaction between the plume and the cross-flow at the very early stages of the plume development (Smith and Mungal, 1998; Fric and Roshko, 1994). The vortex structure is a stable structure observable in long time average measurements. It has been frequently observed in the experimental work where ambient turbulence levels are low (e.g. Hewett et al., 1971; Tsang, 1971) and predicted by numerical simulations (Zhang and Ghoniem, 1993). The structure is also observed in the atmosphere, but only in low turbulence conditions or in short duration observations (Bennett et al., 1992). Often, turbulence and wind direction fluctuations bodily displace the mass-centre of the plume (Olivari and Palli, 1991) and the long time-average (e.g. the hourly average) of cross-section is observed to follow the traditional Gaussian shape. Three stages can generally be identified in the development of a single plume, though in these towing tank experiments only the first two are evident. In the
first near-source phase, the plume experiences large horizontal accelerations with rather small deformations and rises almost as if it were a solid body. In the second stage the twin, symmetrical vortex structure develops. During this stage significant entrainment of external fluid into the plume core takes place, chiefly through the base as a consequence of the secondary flow associated with the vortex system. In the final stage, the plume may break-up due to effects of ambient turbulence or split into two separate lobes (Zhang and Ghoniem, 1993). Cross-sections for a twin plume case (source diameter 7 mm, emission rate 1 l min1 per source, 1 Ua ¼ 8:86 cm s , DrXrw ¼ 9:7%) were measured at three downstream distances for a separation between the stacks equal to 22 stack-diameters. The results are shown in Fig. 6, where each cross-section has been normalised to one. The maximum concentration values were 22.3%, 7.9% and 3% of the source concentration at x ¼ 171; 213 and 375 mm, respectively. The first cross-section, at x ¼ 171 mm, was measured closer to the downstream source at a position where the plumes were beginning to mix. It shows an upper plume with a double vortex developed structure from the upstream source and a lower plume from the downstream source that has not yet developed this structure. This lower plume is about five times more concentrated than the upper one, has a larger vertical velocity and maximum density difference and rises into the centre of the upper plume, between the lateral lobes. The interaction is enhanced by the entrainment flow into the base of the upper plume. The second cross-section, at x ¼ 213 mm, shows the situation where mixing is more advanced. The smaller plume has been engulfed by the vortex structure of the upper plume. This at first leads to a rather symmetrical form, with no obvious vortex structure, which is similar to that observed in the early stages of an isolated plume. The maximum concentration is now found on the plume centreline. However, the vortices reform as the combined plume develops whilst travelling downwind, as the third cross-section, at x ¼ 375 mm, shows. The two lateral vortices are again present and maximum concentrations are again located near the centres of these vortices. The maximum plume concentration is only 1.4 times greater than the maximum concentration on the centreline, compared with about 3 in Fig. 5. The total width of the plume is almost equal to its total vertical spread, whereas in Fig. 5 this ratio is about 1.5. However, comparison of the two cases also shows that at this position the plume interaction leads to extra plume rise; in average terms by about 7%. The vortex pair is clearly not fully developed, in comparison with that shown in Fig. 5 for the single emission, because the development fetch from the region of interaction is considerably less than that of the single plume.
D. Contini, A. Robins / Atmospheric Environment 35 (2001) 6105–6115
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Fig. 6. Concentration field cross-section in a twin plume at x ¼ 171; 213, 375 mm from the upstream source; D ¼ 7 mm, DrXrw ¼ 0:097; Q ¼ 1 l min1 (per source), and Ua ¼ 8:86 cm s1. A small scale plume image is inset showing the location of the measurement section.
5. Accuracy Numerous general sources of random experimental error affected the experiments; e.g. fluctuations in the source flow rate, the flow speed, the source and environment density and in the video recordings and colorimeter concentration measurements. Some errors were peculiar to the method used; e.g. distortion in the lens systems and non-linear response affecting the video images, colorimeter calibration drift and probe positioning errors affecting the point measurement data. To determine ‘‘a priori’’ the accuracy of the results is difficult but a useful idea of the global effects of the various sources of error was obtained by repeating several times the experiments in nominally identical conditions. This analysis showed that calibration drift, with the colorimeter calibrated every day, generated average errors smaller than 3%, such that the stability of the flow speed was better than 0.2% and that the discharge flow rate could be measured within about 5%. Repeatability in the evaluation of trajectories shows a standard deviation in plume rise that is about 3% and the typical measurement repeatability, taken to be defined by two standard deviations, is therefore 6% of the mean plume rise. Experiments on point concentration measurements show a repeatability of about 15% in the dilution results.
6. Conclusions Towing tank experiments were carried out to investigate the interactions between two in-line, rising buoy-
ant plumes. Both quantitative flow visualisation and point concentration measurement techniques were used. Results for the rise of a single plume were in good agreement with both the Briggs formula and numerical results from an integral model. The double vortex structure in the developed plume was clearly shown by concentration measurements in a plume cross-section. The twin plume experiments gave quantitative evidence of significant extra-rise due to plume interaction that can be as large as 30% a few tens of stack diameters downwind of the sources. They also revealed how the interaction developed and showed that this first led to a destruction of the vortex structure in the plume from the upstream source and then to the subsequent reestablishment of the vortices in the combined plume. However, even at the farthest downwind position studied the combined plume had not fully attained the internal structure of a developed plume from a single source. The interaction between two rising plumes obviously depends on their relative positions and the present work only considered in-line arrangements, f=01. For small values of f the overall behaviour may be expected to be similar because the secondary flows associated with the plume vortices will ‘guide’ the lower and smaller plume into the central part of the base of the larger upper plume during the mixing phase. This will become less effective as the flow angle increases and eventually there will be direct interactions between the vortex systems in the two plumes. This will introduce considerable asymmetry during the mixing phase. The likely result is that the complete combination of the plumes will be a much more protracted affair and consequently any
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additional plume rise will be smaller. Eventually, the interaction will cease entirely at least in terms of extra plume rise. Preliminary results show that the effects of the interaction, on plume trajectories, rapidly decrease once f exceeds 301, in agreement with the results of Overcamp and Ku (1988) and are negligible once f approaches 901 (Mayland, 1997). Of course, the detail in this statement depends on the source separation but is generally true for the separations studied (Briggs, 1984). However the interaction, for non-aligned sources, will generate strong asymmetry of the resulting plume with respect to its centreline during the mixing phase. The relative extra-rise, for f ¼ 0; after the mixing process, due to the interaction between the two plumes has been found to be in good agreement with the prediction of available empirical formulae of Briggs (1974) and Anfossi et al. (1978). Of the two, the model of Briggs actually gives slightly better results for the experiments reported here. The interaction weakens when the separation between the stacks is increased and when the momentum or buoyancy flux of the sources is decreased. The enhancement factor usually employed in the empirical formulations can describe the plume interaction for downwind distances large enough such that the mixing process is ended; however, the mixing itself can generate complicated trajectories in the area near the stacks, as shown in our results. The shape of the plume is also greatly influenced and this has to be taken into account in integral models used to evaluate the plume rise. Therefore, a correct modelling of the interaction problems should address the complete trajectory and the shape of the plumes. Our results put in evidence the phases of the mixing for two in-line sources and further investigation is needed for sources not aligned with the windFpreliminary results show strong asymmetries in the cross-sections. Investigations for cases with a larger number of stacks are also needed. An analysis of the part of the twin plume trajectories in which the two plumes have combined into a single one shows that the slopes are similar to the slopes of single stack trajectories presenting full interaction (and not the the trajectory relative to zero interaction). This can be used to evaluate, with a best fit procedure, the shift DX that has to be made on the full interaction trajectory (towards the downwind stack) in order to correctly describe the twin plume trajectories for X greater than 2d (after the mixing process). Results show that a good approximation for all the data reported in Fig. 4 is to use DX ¼ ad with the coefficient a given by a ¼ 1:7 ðUa =Ws Þ þ 0:35: These relationships are valid for d between zero and 10D; the case relative to d ¼ 22D has not been included because the trajectories have not been measured for distances much larger than 2d and the results of the fit were not reliable. The coefficient a may actually depend on the density difference between the emissions and the crossflow, but the data reported here
refer to a fixed density difference and this aspect cannot be inferred.
Acknowledgements This research was been carried out with the financial support of the ‘‘Ministero della Universit"a e della Ricerca Scientifica e Tecnologica’’ in collaboration with the ‘‘Conferenza dei Rettori delle Universit"a Italiane’’ (CRUI) and of the British Council under the ‘‘BritishItalian collaboration in Research and Higher Education’’ 1998–99 programme. It was also been funded by the European Community through the Large Scale Facilities section of the Training and Mobility of Researcher (TMR) programme, contract ERBFMGECT980117.
Appendix. A The integral plume rise model used here evaluates the trajectory and spread of a single plume given the conditions at the source and in the external environment. The model is a top-hat integral model similar to the one described in Ooms and Mahieu (1981). The main assumptions are (I) the plume has no effect on the properties of the environment, (II) the plume is continuous, slender and with circular cross-section, (III) properties are uniform within the plume and (IV) entrainment takes place due to the plume’s motion relative to the environment. With these assumptions it is possible to write the equation of motion for the plume, that has to be integrated with the continuity equation ~Þ ¼ 0; referring to Fig. 1(a) for stationary flows: divðrU for notation: d ðrr2 Us Þ ¼ 2rrw Ve Ve ¼ ajDUt j þ bjDUn j ds þ turbulence effects;
ðA:1Þ
d dUa ; ðrr2 Us ðUs cos ðgÞ Ua ÞÞ ¼ rr2 Us sin ðgÞ dz ds
ðA:2Þ
d ðrr2 Us2 sin ðgÞÞ ¼ gr2 ðrw rÞ; ds
ðA:3Þ
d ðgr2 Us ðr rw ÞÞ ¼ rw Us sin ðgÞr2 N 2 : ds
ðA:4Þ
Eq. (A.1) represent the entrainment assumption through an entrainment velocity Ve proportional to the relative tangential velocity DUt and the relative vertical velocity DUn of the plume. In the present case environmental turbulence effects are not present. The constant a is taken to be 0.057 and the constant b is 0.6. Eqs. (A.2) and (A.3) represent the momentum equations in the x- and z-direction, respectively, and g is the
D. Contini, A. Robins / Atmospheric Environment 35 (2001) 6105–6115
gravitational acceleration. The symbol Ua indicates the flow speed and Us is the plume tangential speed. Eq. (A.4) is a buoyancy conservation equation and N is the Brunt–V.ais.al.a frequency that can be written as N2 ¼
g dya ya dz
Where ya is the ambient potential temperature. For incompressible fluids, g drw : N2 ¼ rw dz In the present case, both the flow speed as well as the flow potential temperature (neutral stratification) are constant so that the equation set is simplified. Procedures were implemented on a PC programme in order to solve these equations numerically and to evaluate the plume trajectories. The Briggs formula is obtained as an approximation to the equation set (Briggs, 1974; Weil, 1988) assuming that the plume is bent-over and neglecting the contribution of a to the total entrainment. The solution for the trajectory is then given by " #1=3 3Fm x 3Fb x2 ðr rs Þ z¼ 2 þ ; Fb ¼ gr2s Ws w ; rw b1 Ua2 2b22 Ua3 Fm ¼
rs 2 2 W r ; rw s s
ðA:5Þ
where Ws is the vertical plume speed at the source, rs the initial density and rs the initial radius (i.e. the source internal radius). The first term in the square bracket in Eq. (A.5) accounts for the plume momentum and the second one for its buoyancy. The entrainment coefficient should be b1 ¼ b2 ¼ b ¼ 0:6; however, comparisons with experimental results lead to some changes in the formula and the value of the entrainment coefficient was reformulated as two coefficients b1 and b2 ; having the values b1 ¼ 0:4 þ 1:2
Ua Ws
and
b2 ¼ b ¼ 0:6:
This is to describe better the jet part and this means the rise of neutrally buoyant plumes.
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