Interaction of Burning Droplets in a Linear Stream

Transcription

1 Interaction of Burning Droplets in a Linear Stream Nitesh Kumar*, Srikrishna Sahu Department of Mechanical Engineering Indian Institute of Technology Madras Chennai, INDIA Abstract In the present paper, linear streams of periodically generated mono-dispersed fuel (ethanol) droplets are investigated under ambient conditions. The purpose is to study convective interaction of burning droplets, and the role of surrounding air turbulence on combustion of interacting droplets. Droplet measurements (size, and separation distance) are obtained by Shadowgraph technique. In addition, long exposure flame visualization images are also recorded. Experiments are performed for different initial droplet sizes and inter-separation distances. Each case is considered with and without droplet stream burning corresponding to pure evaporation and combustion of droplets, respectively. The results show that interaction of neighboring droplet vapor clouds significantly reduces the evaporation rate of burning droplets within the stream in comparison to that of a freely falling isolated droplet, which can be predicted by the d 2 -law. Thus, smaller distance parameter (normalized droplet separation) results in smaller evaporation coefficients of interacting droplets. The distance parameter also influences the flame length since smaller the droplet spacing higher is the vapor accumulation, and so, longer is the flame. Far downstream, combustion of droplets promotes droplet collision and coalescence. Droplet combustion experiments are also performed with in a box of turbulence, which can generate at the center of the box nearly zero-mean turbulent flow field at required turbulent intensity. Preliminary results are presented. Experiments based on a suspended droplet at the center of the box identified non-stationary flame around the droplet when surrounding air turbulent intensity is high, which may even lower the evaporation rate of the droplet. Interaction of the flame surrounding the droplet stream and the turbulent air flow field was found to lead to collision and coalescence of droplets such that the overall effect of burning on droplet size is not significant in comparison to pure evaporation of droplets. Keywords Mono-sized droplets, Droplet burning rate, distance parameter, Flame length, Isotropic Turbulence *Corresponding Author

2 Introduction The evaporation and combustion of isolated fuel droplet (either stagnant or subjected to forced convection) has been extensively studied in past, which provides a basis for modeling spray combustion processes for various applications [1]. However, droplet to droplet interaction is not yet well taken in to account in the current models for droplet evaporation and combustion. Such interactions are very important when local droplet number density with in a spray is high, for example, close to fuel injectors. However, far away from the injector droplets tend to form clusters due to interaction with surrounding air turbulence resulting in significant spatial and temporal variation of droplet concentration [2]. The fuel droplets seldom burn individually within a droplet cluster. Instead, burning of clouds of droplets become important, and droplet evaporation is severely restricted due to simultaneous evaporation of neighboring droplets. Due to small inter-separation distances, oxidizer penetration is restricted in to the droplet clouds, and this leads to the so called group combustion of droplets [3], which may have profound effect on flame location and distribution of temperature, fuel vapor and oxidizer [4]. Since the spray combustion process is complex, a fundamental configuration for the study of interaction of evaporating and burning droplets is often desirable. Hence, experiments on interacting suspended droplets [5, 6] or droplet arrays [7] have been attempted in past. However, in spite of the advantage of a simple configuration, the suspended droplet set-up suffers due to the residual heat transfer between the bead and the suspended droplet. Also, the droplet size is always of the order of one millimeter, much larger than the droplet size encountered in spray combustion applications. Hence, experiments were conducted in a stream of mono-sized droplets freely falling under gravity, which offers a viable alternate to study interdroplet interaction. Since the droplets are generated periodically, and the droplet size and spacing can be effectively controlled, the time evolution of droplet size can be obtained for different droplet separation distances. Previous research works on droplet stream evaporation and burning highlighted that the droplet evaporation rate reduces for smaller droplet spacing in the stream [8, 9, 10], and thus the Nusselt and Sherwood numbers of monodisperse droplets are modified in comparison to those for isolated droplets [11, 12]. However, yet there is no general consensus on a suitable model for droplet evaporation within a reacting spray accounting for the finite droplet spacing. One of the reason behind this may be attributed to the influence of nature of fuel on flame phenomenon, which in turn affects the evaporation rate of droplets. In addition, because the droplet evaporation rate generally increases with higher air turbulent intensity, while it decreases with smaller droplet spacing, the two effects are in opposite to each other. Hence, the effect of surrounding air turbulence on burning of droplet clouds requires further attention. In past experimental works to study air turbulence effects on the vaporization rate of a suspended droplet have been based on both classical wind-tunnel grid-generated turbulence set-up where both mean and fluctuations of air flow influence droplet evaporation [13], or a droplet suspended within a homogeneous and isotropic flow with zero mean velocity (typically fan-stirred vessel [14]), where the effect of air turbulence alone can be considered. The current work focuses on studying droplet evaporation and combustion in a stream of periodically generated mono-sized droplets freely falling under gravity. At first, experiments are conducted under quiescent atmospheric conditions for different droplet size/spacing with in the stream. Then, combustion of droplets subjected to a turbulent environment within a box of turbulence is considered. The box of turbulence contains three pairs of loud speakers mounted on a non-confined frame. The two loudspeakers in each pair are oriented right opposite to each other such that all speakers point to the center of the box. The loud speakers generate synthetic jets, which interfere and mix at the central region of the chamber resulting in nearly zero-mean turbulent flow under atmospheric condition. To the best of our knowledge, earlier no other works considered such configuration for studying the effect of turbulence on droplet stream combustion. Initially, experiments are conducted for a single suspended droplet with in the box. Experimental Setup Fig.1 shows the schematic of the experimental setup for the droplet stream evaporation and burning experiments under quiescent atmospheric condition. A custom-built droplet generator (DG), which uses a piezo-crystal ring driven by a function generator, periodically produced stream of mono-sized droplets of pure ethanol (99% C 2H 5OH). The ethanol was pressurized with in a pressure vessel by compressed nitrogen gas. The pressure was maintained in the range of 0.2 atm to 1.2 atm in order to vary liquid flow rate to the DG to obtain different drop sizes. The pressurized liquid column of ethanol within the DG was perturbed by the actuation of piezoelectric crystal with a square wave signal (frequency ranging 5 KHz to 12 KHz) supplied by the function generator AFG Pin holes of sizes 50µm, 100µm, 150µm, 200µm are used in the drop generator to generate different sizes of the droplets. For a given fuel flow rate, the mono-dispersion was achieved at particular frequency,

3 and corresponding droplet size (D) and spacing between successive droplets (S) are specific to that flow rate. The droplet flow was downward in the direction of gravity. Table 1 lists the initial droplet size and normalized inter-droplet distances or the distance parameter, C (= S/D) for different droplet streams considered in the present experiments. A metal plate with central hole of 5 mm diameter was used to avoid any contact between the flame and the tip of the drop generator. A droplet stream once ignited by a pilot flame resulted in a self-sustained flame enveloping droplets in some portion of the top of the droplet stream. Fig. 1 Schematic of experimental setup The droplet stream was illuminated with a backlight, and the corresponding shadowgraph images were captured by a CCD camera (PCO pixelfy: 14 bit, 1040 x1392 pixel 2 ) equipped with a collecting lens. The camera exposure time was kept as 5 µs, thus instantaneous images of droplets could be captured. The droplet images were captured from the axial location z = 4 cm downstream of the injector exit (to avoid imaging liquid ligaments) up to z = 24 cm. The camera viewing area for all measurement locations was about 10 mm 14 mm. Thus, the spatial resolution of the camera was about 10µm/pixel. The measurements at different axial locations were carried out by simultaneously moving the camera and the backlight, instead of shifting the droplet generator. In order to image the flame around the droplet stream, long exposure images were captured using a digital camera. Pin hole (µm) Flow rate (ml/s) Frequency (KHz) Drop size (D) (µm) Nondimensional distance parameter (S/D) Table.1 Experimental observations for mono-sized droplet generation Fig.2 shows the schematic of the box of turbulence set-up, which can generate homogeneous and isotropic turbulent flow at its center. The set-up consists of 6 loud speakers (three pairs). The loudspeakers in a pair

4 face each other, and all six speaker points to the center of the box. Each speaker is driven by a sine-wave signal of frequency 50 Hz and amplitude of 80 mv generated by 16 bit National Instruments analogue output card with 8 channels (PCI6733). The signal from each output channel of the PCI card is amplified using power amplifiers. The amplified output signal varies from the range of 5V to 20V depending on the desired turbulent intensity at the center of the box. Each loudspeaker is equipped with a perforated plate on its top made of equally spaced holes of 6 mm diameter. Thus, during operation, each loudspeakers generate array of synthetic jets as they are actuated by the amplified signals. After appropriate balancing of the loudspeakers, the corresponding jets meet at the center to produce nearly zero-mean isotropic turbulence. The air flow turbulence was characterized by a two-component MINI-LDV system (manufactured by MSE.inc). For this purpose the whole room containing the box is seeded with micronsized particles from a fog-generator. In order to identify the spatial extent to which flow isotropy is retained around the box center, the location of the LDV probe region was varied vertically ±6 cm and horizontally ±3cm about the center of the box. Table 2 summarizes the two different turbulent conditions considered in the present experiments. Flow condition U mean V mean u rms v rms Isotropy (u rms/ v rms) case case Table.2 Turbulent flow conditions at center of the box of turbulence. The droplet generator was aligned such that the droplet stream passes through the center of the box of turbulence. The focused shadow graph images were capture by the camera as described earlier. The Shadow graph images were analyzed using image processing based on MATLAB in order to measure droplet size and identify droplet center (to calculate inter droplet distance). The long exposure photographs taken by digital camera were also processed to obtain flame length for different inter-droplet distances. Fig. 2 Schematic of Experimental setup with box of Turbulence Results and Discussions Droplet stream evaporation and burning under quiescent atmospheric condition Fig.3 presents shadowgraph images of the droplet streams for the four different operating conditions of the droplet generator. The images are shown for both pure evaporation and burning conditions for each case for two different axial positions z = 4 cm and 24 cm, respectively. The flame around burning droplets is not visible as it was not possible to image simultaneously individual droplets and the surrounding flames. No significant difference between the evaporating and burning droplet images can be observed close to the DG exit, however, differences are noticeable far downstream. It is very clear that, downstream to the droplet generator the droplet size reduction for evaporation case is not significant, which is due to low

5 transfer number (B) of ethanol droplets (B 0.1). Also, the inter separation distance increases as a consequence of droplet drag and acceleration due to gravity. However, for the combustion case, in addition, droplet collision and coalescence are significant resulting in the increment of droplet size and inter droplet distance downstream. As mentioned earlier, the shadow graph images were processed to obtain droplet size at different axial locations 4 cm to 24 cm from the exit of the DG. Assuming the initial velocity of the droplets to be same as that of the liquid jet at the DG exit, and considering that the droplets are freely falling under gravity, the time of arrival at different axial measurement location was evaluated. The time of droplet arrival at z = 4 cm is considered as the reference time. Fig.4 shows the plots (D/D o) 2 vs normalized time (= time//d o 2 ) for pure evaporation and burning cases respectively. The corresponding theoretical evolution of droplet size for both cases are also included for an isolated droplet falling freely under the same initial conditions as that of the droplet stream. The theoretical evolution of droplet size is according to the D 2 -law accounting for convection around droplets, as well as the correction factor for the effect of Stefan flow on the evaporation [1, 12] (a) z = 4cm (b) z= 24cm Fig. 3 Shadowgraph images of the pair of droplet stream under evaporation (e) and burning (b) for different droplet sizes. (a) (b) (c) (d) Fig.4 Fig. 4 (D/D 0) 2 2 vs t/d 0 for (a) D 0=136µm, (b)189 µm (c)438 µm (d)383 µm.

6 It is observed that for the pure evaporation case, the experimental and the theoretical trends are closer, however, this is attributed to low evaporation rate of ethanol droplets since only a slight reduction in droplet size can be observed. On the other hand the burning rate of droplet stream is considerably smaller than the prediction by theory for isolated droplets. Also, the droplet size seems to reduce first and then increase. This can be explained considering the initial and final stages of the droplet travel. For the initial period of droplet travel up to about a distance of 15 cm, the droplet spacing remains nearly same as the initial value. Since for each droplet there are two neighboring droplets which evaporate simultaneously, vapor concentration and temperature around the central droplet is not homogeneous, and the flame is also not symmetric. Thus, in comparison to burning of isolated droplet, the burning rate is lower, and the measured droplet size at any time is above the predicted size at the same time. As the droplets move further downstream, the natural convection currents are stronger and in opposite to the motion of droplets as well as the entrained air due to droplets. At some axial location, the flame speed is equal to the upward free convection current, and the flame is unable to proceed further down. This is evident in the long exposure images shown in Fig 5. The competition between drag on droplets due to its motion and gravitational force, and free convection current disturbs the periodically free falling droplets resulting in droplet collision leading to coalescence and thus larger droplet size, which dominates over the reduction in droplet size due to burning and evaporation after the droplets emerges out of the flame. Hence, the measured droplet size is larger during latter half of the droplet travel. K v/k o, where K o is the evaporation constant for isolated droplet (which is calculated theoretically), is presented in Table.3. It is observed that the ratio is less than one, which is as per the explanation provided above. Also, the ratio is smaller for smaller distance parameter. Figure.5 shows the long exposure flame photographs for different operating conditions. In general, the flame length (defined as the length of the flame observed from the initial position z = 4 cm up to the downstream distance where the flame terminates) reduces as the distance parameter i.e. ratio of interdroplet distance to droplet size increases. For smaller distance parameter, vapor around the droplet stream accumulates due to smaller time interval of successive droplets, hence the flame can travel longer. However, when the droplets are too close to each other the evaporation rate reduces resulting in low vapor concentration, thus the flame length is shorter again. This is further confirmed in Fig 6, which shows variation of flame width with respect to distance parameter. Similar trend as for flame length is observed. For all cases it seems the flame surround the droplets indicating group burning of droplet clouds. D(µm) S/D K v/k Table. 3 The ratio of evaporation coefficient K v /K o for droplet burning Fig.5 Long Exposure photographs of the burning droplet stream under different initial conditions. Fig. 6 (a) Flame length vs S/D

7 Fig.6(b) Flame width vs S/D Next, we present droplet combustion with in the box of turbulence for two different air flow turbulence conditions as shown in Table 2. Since the mean air velocity is nearly zero, the effect of turbulence on droplet burning can be exclusively studied. Initially, the experiments were conducted for a suspended ethanol droplet. Droplet evaporation and burning within the box of turbulence In the present experiments, the box of turbulence is operated for two different turbulent conditions at the center of the box (1 st case: isotropy = 95% and 2 nd case: isotropy = 52%). It is noted that the mean velocity for both the cases is negligible such that the effect of only turbulence on the burning and evaporation can be studied. Fig.7 compares flame images around the suspended ethanol droplet burning under ambient conditions (Fig.7a), and within the box operating under higher and lower turbulence intensity conditions (Fig.7b and 7c). It is observed that unlike the droplet burning under normal ambience, the flame for case 1 does not remain vertically upward all time. The flame moves around the droplet and even can orient downwards, which means the droplet burning occurs under the combined action of buoyancy and air turbulence. However, for case 2, with lower turbulent intensity, the flame is comparable to burning under normal quiescent condition. Fig.8 presents variation of square of normalized droplet size versus normalized time. For pure evaporation case (Fig.8a), the evaporation rate under higher turbulence intensity is higher in comparison to droplet burning under normal ambience, which in turn is not much different from case 2 corresponding to low turbulence intensity. However, interestingly, for the burning case (Fig. 8b) the evaporation rate for case 1 is smaller than the other two cases of droplet burning. This is due to unsteady flame around the droplet due to flame-turbulence interaction resulting in asymmetric flame thickness. Sometime the flame is oriented downward opposite to the free convection currents. Thus, the evaporation rate is lower, while opposite trend is observed for the pure evaporation case due to absence of flame. (a) (b) (c) t=0s t=1.065s Fig. 7 Flame around a suspended droplet burning under (a) quiescent ambience and within the box of turbulence operating at (b) higher isotropy and turbulent intensity (c) lower isotropy and turbulent intensity.

8 (a) Fig.9 Shadow graph images of droplet stream evaporation (e) and burning (b) at 20 cm location downstream from the generator under different turbulent conditions. (b) Fig. 8 (a) Suspended droplet evaporation (b) Suspended droplet burning. For droplet stream studies with in the box, results are presented for only one droplet size of 483 µm. Fig.9 shows droplet stream 20 cm downstream of the exit of DG for both evaporation and burning conditions under quiescent ambience and within box turbulence. It is observed that when the droplet stream is subjected to air flow with higher turbulent intensity, the monodispersity is lost as a consequence of droplet collision and coalescence since the droplets tend to respond to the surrounding air flow velocity fluctuation. This situation is even more prominent for the burning case, where additional buoyancy forces are present. Thus, the flame-turbulence interaction results in flapping of the bulk flame tube around the drop stream. The time evolution of droplet size is presented in Fig.10 and Fig.11 for pure evaporation and burning, respectively. Unlike, Fig 8(a) the droplet size variation is not evident in fig.10 for the pure evaporation of droplets. This highlights the role of droplet-droplet interaction, which reduces the droplet evaporation rate. For case 1 (higher turbulence intensity), the droplet size increases as a result of coalescence. The results are similar for the droplet burning case. This is in contrast to the difference observed between pure evaporation and burning of droplet stream under quiescent conditions as reported earlier. Fig.10 Droplet size variation for pure evaporation Fig.11 Droplet size variation for droplet burning. Apart from the droplet size variation, the flame structure analysis was done based on the long exposure photographs of flame as shown in fig.12. It is found that the flame length decreases with increase in the turbulent flow intensity for the same initial droplet size. It also shows that flame width almost remains

9 constant but it increases very less for higher turbulent intensity which again signifies the presence of cluster burning of the droplets. (a) (b) Fig. 12 Long exposure images of flame for turbulent conditions a) u rms=0.11m/s, u rms=0.21m/s b) u rms=0.39m/s, v rms=0.41m/s. Conclusion The present study focuses on the influence of inter droplet interaction on droplet evaporation rate and flame structure in a combusting stream of droplets under quiescent atmospheric condition as well as within a box of turbulence. The droplet motion was in the direction of gravity and the flame was selfsustaining. Experiments under quiescent atmosphere are performed for different droplet sizes/spacing. Shadowgraph images are captured at different axial locations of the droplet generator. The ratio of droplet spacing to size (the spacing parameter) was varied in the range 2.5 5, and it was found to be an important parameter, which significantly influences the droplet burning rate and also the flame length. The droplet size reduction was found to occur at a rate much smaller than that for a freely falling isolated droplet, which can be described by the D 2 -law. However, far downstream the competition between droplet drag, gravitational force and upward free convection current results in droplet collision and coalescence, which leads to increase in droplet size. The droplet evaporation coefficient was smaller for smaller spacing parameter. The box of turbulence was operated under nearly zeromean velocity of air flow for two different turbulent intensities. Experiments with single suspended droplet signified that the flame around the droplet is nonstationary when the air turbulent intensity is higher, and this may lead to even lower evaporation rate of droplets. The interaction of air turbulence and flame around the droplet stream promotes droplet collision, hence, the droplet size downstream of the injector was nearly constant for low turbulent intensity, while it showed increasing trend when the turbulence intensity is higher. The flame length decreases with the increase in the turbulent intensity whereas, flame width almost remains constant but it increases very less for higher turbulent intensity The authors would like to acknowledge the National Center for Combustion Research and Development (NCCRD), IIT Madras for providing the LDV instrument for turbulence characterization. Nomenclature B transfer number. DG Droplet generator. D diameter of droplet K evaporation rate l length S inter droplet distance t time U velocity in x - axis V velocity in y- axis w width z downstream location from the tip of droplet generator Subscripts 0 initial rms root mean square i position of droplet in an image. f flame v for droplet stream References. 1. W.A. Sirignano, Fluid Dynamics and Transport of Droplets and Sprays, Cambridge University Press, Zimmer, L., Ikeda, Y.: Simultaneous laserinduced fluorescence and mie scattering for droplet cluster measurements. AIAA journal 41 (11), ,(2003). 3. Chiu, H., Liu, T., Group combustion of liquid droplets. Combustion Science and Technology 17 (3-4), F. Akamatsu, Y. Mizutani, M. Katsuki, S. Tsushima, and Y. D. Cho: Measurement of the local group combustion number of droplet clusters in apremixed spray stream, Proc. Combust. Inst. 26, 1723 (1996). 5. T.A. Brzustowski, E.M. Twardus, S. Wojcicki, A. Sobiesiak: Interaction of two burning fuel droplets of arbitrary size, AIAA J. 17 (1979) M. Labowsky: Calculation of the burning rates of interacting fuel droplets, Combust. Sci. Technol. 2 (1980) Segawa D, Yoshida M, Nakaya S, Kadota T Autoignition and early flame behaviour of a spherical cluster of 49 monodispersed droplets. Proc Combust Inst 31: , (2007) 8. Silvermann M, Dunn-Rankin D (1994) Experimental investigation of a rectilinear droplet stream flame. Combust Sci Technol 100: C.-K. Chen, T.-H. Lin / Combustion and Flame 159 (2012) J.F. Virepinte, Y. Biscos, G. Lavergne, P. Magre, G. Collin:A rectilinear droplet stream in

10 combustion: droplet and gas phase properties, Combust. Sci. Technol. 150 (2000) G. Castanet, M. Lebouche, F. Lemoine, Int. J. Heat Mass Transfer 48 (2005) V. Depredurand, G. Castanet, F. Lemoine, Int. J. Heat Mass Transfer 53 (2010) Gokalp I, Chauveau C, Simon O, Chesneau X. Mass transfer from liquid fuel droplets in turbulent flow. Combust Flame 1992;89: Birouk, M.: Hydrocarbon droplet evaporating in a turbulent environment at elevated ambient pressure and temperature. Combust. Sci. Technol.186(10 11), (2014)

11