Observed in Gas Injection

Transcription

1 Characteristics into Liquid* of Jetting Observed in Gas Injection By Yasuhisa OZAWA** and Kazum i MOR I * * Synopsis The present study is concerned with jetting behavior of gas jets injected into water bath. Nitrogen gas (200' cm3f s) was injected into the water bath through an orifice of 0.1 N 0.3 cm in diameter located at the bottom. The gas jet behavior was observed directly by using a high speed cinecamera. The frequency of the bubble knocking at the bottom was measured with a microphone. It is found that the bubbling jetting transition of gas jets injected into water begins to occur when the gas flow velocity at the exit of an orifice exceeds the sonic velocity. This phenomenon is similar to the behavior of gas jets in mercury bath. In the sonic region the frequency of bubble knocking decreases with increasing gas flow velocity. Perfect jetting is found to occur at the highest gas flow velocity explored in the present study. The injection pressure in this case is 30 kgf/cm2. The initial expansion angle of jet increases with increasing gas flow velocity and agrees well with theoretical calculation. It is presumed that the speed of a gas jet which is equal to the sonic velocity at the exit of the orifice exceeds the sonic velocity just beyond the exit. I. Introduction The authors previously investigated the behavior of injected gas jets at a submerged orifice in a threedimensional'~ and in a two-dimensional2~ mercury bath. From photographing gas jet behavior by a high speed cinecamera, two regimes of gas flow were distinguished: bubbling and jetting. The bubblingjetting transition was found to occur in the sonic flow region. In the present study, to know the effect of physical properties on jet behavior, experiments of gas injection into a water bath have been done in the gas flow region of both the subsonic and the sonic velocity. It is also aimed to investigate the structure of the gas jets in detail. II. Experimental 1. Apparatus Figure 1 shows a schematic drawing of the experimental apparatus. The water vessel constructed from iron frames was of inner dimension of 40 cm width x 50 cm length x 100 cm height. To allow visual observation of the jet by the aid of illumination, acrylate windows were installed. The vessel bottom was an acrylate plate at the center of which an orifice was installed. The orifice diameter was varied as 0.1, 0.2 and 0.3 cm. In order to make an accurate measurement of gas flow rate overcoming the difficulty due to high vapor pressure from the water bath, gas flow meters were installed in both upstream and downstream gas lines.*** 2. Procedure The depth of the water bath (distilled water) was 25 or 50 cm,**** Nitrogen gas was injected into the bath at various gas flow rates in the range of cm3/s (M'=0.2'-' 11) at orifice conditions. Here, M' represents the nominal Mach number defined as the ratio of nominal gas flow velocity to the sonic velocity at room temperature. Both high speed films and still photographs of the jet were taken. The film speed was frames/s. The highest gas pressure was 30 kg /cm2 in gauge. To get additional knowledge on the bubblingjetting transition, the frequency of knocking produced from bubbling at the orifice exit was measured with a microphone located at the outer surface of the vessel bottom. This frequency and that of bubble formation were in substantial agreement. However, the knocking sound produced from the formation of small bubbles formation was too weak to be measured. Therefore, the measured frequency of bubble formation and that of knocking produced from bubbling are not precisely the same. III. Results and Discussion 1. Bubbling and Jetting Photograph 1 presents still photographs of im- Fig. 1. Schematic drawing of experimental apparatus. * ** *** **** Originally published in Tetsu-to-Hagane, 68 (1982), 98, in Japanese; Formerly presented to the 99th ISIJ Meeting, April 1980, 5162, at The University of Tokyo in Tokyo. English version received January 7, ISIJ Department of Metallurgy, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464. The measured values by the two gas flow meters almost agreed, when the readings of the gas flow meter in the down stream gas line were corrected for vapor pressure. The bath depth was 50 cm except in the experiment of which the result is shown in Fig. 7. (764) Research Article

2 Transactions ISIJ, Vol. 23, 1983 (765) Fig. 2. Bubbling jetting transition in the mercury and water. two systems of Photo. 1. Photographs water bath. showing bubbling (d0=0.2 cm) and betting in the mersed gas jets for the orifice of 0.2 cm in diameter. The lowest end of the photographs corresponds to the level of location of the orifice exit. At the lower gas flow rate the jet is seen expanding at the orifice exit (Photo. 1(a)). At the higher gas flow rate no expansion of the jet is shown (Photo. 1(b)). The former phenomenon is defined as bubbling, the latter is jetting. It is to be noted that the jet of the bubbling flow regime does not form completely discrete bubbles. This behavior of gas jets in the water bath may correspond to stem coalescence observed by Wraith and Chalkley3~ and is somewhat different from that in mercury. No detailed examination on this point of jet behavior was made in the present study. Observation was made exclusively on gas jet behavior in the vicinity of the orifice. As in the case of mercury, high speed films present data for the two flow regimes. In Fig. 2 time fractions for both bubbling and jetting are plotted against nominal Mach number M'. Closed and open circles represent data for the mercury bath and for the water bath, respectively. The dotted line represents the boundary nominal Mach number for the subsonic-sonic transition. It is clearly shown in Fig. 2 that jetting occurs in the sonic region. Transition from bubbling to jetting takes place in a transitional gas flow range. These features of jet behavior are very similar to those found in the mercury model. In the water model, however, the initiation of jetting occurs at a nominal Mach number somewhat lower than in the mercury model. The transition from bubbling to jetting occurs more abruptly in the water case than in the mercury case. These differences between the two models may come from the different effect of bath movement on jet behavior. Dtailed study on this problem will be made later. Fig. 3. Jet base diameter plotted against nominal Mach number. In Fig. 3 the average jet base diameter which was obtained from photographs of the jet is plotted against nominal Mach number. The average jet base diameter increases with increasing gas flow velocity in the subsonic region, while it decreases with increasing gas flow velocity in the sonic region. The decrease of the diameter in the sonic region is caused by the occurrence of jetting. 2. Knocking from Bubbling In the bubbling flow regime, knocking sounds are produced from the expansion of gas bubbles or pulses at the vessel wall in the vicinity of the orifice exit. The production of knocking sounds is considered to be essentially the same phenomenon as the " backattack " observed by Ishibashi et al.4~ Figure 4 illustrates knocking pulses caught by a microphone and recorded by an oscillograph. Figure 5 is the frequency of knocking for various orifice diameters plotted against the gas flow rate. Figure 6 shows the relation between the frequency of knocking and nominal Mach number. It is seen that an abrupt decrease in knocking frequency occurs, irrespectively of the orifice diameter, at just the critical nominal Mach number for the subsonic-sonic boundary, where the bubblingjetting transition begins to occur. In the upper right-hand corner of Fig. 6, knocking frequency expressed in an enlarged scale is plotted against M'. It is found that the frequency becomes zero at an injection pressure as high as 30 kgf/cm2 in gauge. Namely, perfect jetting with no bubbling is realized at that high pressure.

3 (766) Transactions ISIJ, Vol. 23, 1983 Fig. 4. Bubble knocking recorded by oscillograph. Fig. 7. Frequency of bubble knock plotted against gas flow depths. ing at the vessel bottom rate for the two bath Fig. 5. Frequency of bubble knocking at the vessel bottom plotted against gas flow rate. Fig. 8. Photograph and sketch of gas jet injected into water at high gas flow velocity. Fig. 6. Frequency of bubble knocking at the vessel bottom plotted against nominal Mach number. Figure 7 shows the frequency of bubble knocking at the vessel bottom plotted against the gas flow rate for the two bath depths. As seen from the figure, the frequency of bubble knocking is not influenced by the bath depth. 3. Structure of Jets in the Jetting Flow Regime The sonic gas jet exhausting into still gas phase is known to become a supersonic gas flow exhibiting a periodic or chain-like structure. The stream surrounding the jet has little effect on the first cell of the jet, which constitutes a very stable gas phase.5,6) In the previous study,2~ it was found that the values obtained for the length of residual gas jet had a trend against nominal Mach number very similar to that of the calculated values of the first cell length. However, the cell region of the supersonic jet could not be observed directly. The periodic patterns formed by the expansion and compression waves in a supersonic jet are generally observed by Schlieren photographs. However, in the present study it was possible to observe the shock pattern by still photographs with illumination of microflash (flash duration time : 2 ps.) Tiny droplets such as observed in the previous study2~ to be produced in the proximity of the orifice exit are presumed to have served to realize the observation of the shock pattern. Figure 8(a) is an example of the photograph of gas jets and (b) is the sketch showing the cell region surrounded by the shock waves. When a jet exhausts from a nozzle or an orifice, the jet undergoes rapid expansion. According to the study by Love et al.6~ for the expansion of free gas jets, the degree of expansion of a sonic jet expressed in terms of initial expansion angle B; is a function of the ratio of the jet pressure at the orifice exit and the hydrostatic pressure. The initial expansion angle 8; can be defined in the present case of gas injection into liquid (Fig. 8). In Fig. 9, B; obtained in the present study is plotted against nominal Mach number M'. When a supersonic jet exhausts from a nozzle into still air, it will undergo a two-dimensional expansion at the nozzle tip. Love et al.,6~ by using Prantle- Meyer equation for the two-dimensional expansion flow, calculated the initial inclination of the jet boundary 40 as a function of the ratio of the jet pressure at the orifice exit to the static pressure,* and

4 Transactions ISIJ, Vol. 23, 1983 (767) Fig. 9. Initial jet angle plotted against nominal Mach number. applied the calculated value of d B to the case of a supersonic jet exhausting into still air. In Fig. 9 the calculated initial expansion angle B; which is obtained by doubling 40 is plotted against the nominal Mach number and compared with the present result. Very interestingly, the experimental and calculated results are in close agreement. A close examination of the jet structure shown in Fig. 8 reveals the formation of a Mach disc which is originally observed in the free gas jet.5'6) In Fig. 10, Mach disc distance, that is, the distance from the orifice exit to the center of Mach disc, is plotted against M'. The experimental result is compared with observation for the first cell length and Mach disc distance both values of which are obtained for free gas jets in still air. There is reasonable agreement between the present experiments and the observation for the free gas jets. Thus, it has been found that gas jets in the liquid phase exhibit behavior similar to that of gas jets in the gas phase. As the case with mercury,2~ the sonic jet penetrates into water as a supersonic gas jet. It may be highly possible that the above feature of jet behavior is possessed by gas jets injected into other liquids irrespectively of their physical properties. 4. Profile of Gas Jets The profile of gas jets was obtained from photographing gas jets by a still camera. Examples of the profile of gas jets obtained are shown in Fig. 11. In the figure the profiles of imaginary conical gas jets the cone angles of which are 15, 20 and 30 deg are shown by broken lines and compared with the experimental gas jet profiles. As seen from the figure, except in the proximity of the orifice the diameter of gas jet increases with increasing gas flow rate. The cone angle of the submerged gas jet changes with gas flow rate. Thus, the assumption by Themelis et al.7) that the submerged gas jet expands with a constant cone angle does not agree with the present experimental results. No definite relationship was obtained between the gas jet profile and the orifice diameter for gas injection in the subsonic region. However, in the case of gas injection in the sonic region, the diameter of gas jet is found to increase with decreasing the orifice diameter. This could be ascribed to the fact that with decreasing the orifice diameter the gas Fig. 10. Mach d isc distance against nominal Mach number. Fig. 11. Gas jet boundary for variation of gas flow rate. (d0= 0.2 cm) pressure at the orifice exit increases, leading to the increase in the initial expansion angle. Iv. Comparison with Previous Studies Several of previous investigators have directed their attention to the marked difference in the jet behavior depending on gas injection condition.3'4'8> However, in the previous studies no pertinent definition of flow regimes of jet has been given. Moreover, criteria for the difference in the flow regimes have not yet been established. Ishibashi et al.4> in the investigation of air jet behavior in water, have observed two kinds of flow patterns very similar to those of bubbling and jetting observed in the present work. They used " bubble dispersion index " for the criterion of the two jet patterns. This is contrasted to the authors' observation that the bubbling jetting transition occurs in the " sonic flow region ". Ishibashi et al.4~ observed the abrupt decrease in the gas jet diameter and in the frequency of " back-attack " at an injection pressure as high as 2'-'3 kgf/cm2g (in gauge). Taking into account that this injection pressure corresponds to that of the gas injection in the sonic region, Ishibashi et al.4~ is considered to have observed the jetting behavior similar to that observed in the present study. Wraith and Chalkley,3~ in investigating the behavior of submerged gas jet in water in the subsonic region, found that at high injection velocities almost continuous coalescence between successive bubbles Research Article

5 (768) Transactions ISI1, Vol. 23, 1983 and the nozzle exit occurred, leading to forming a jet-like bubble-stem array. They observed that the transition to the jet-like bubble formation occurred at M'=0.16 when d0=0.325 cm. Hoefele and Brimacombe8> found that the transition from " bubbling " to " steady jetting " in the gas injection into water occurred at M'=0.2 (do= cm). This critical value of M' is close to that obtained by Wraith and Chalkley3~ for forming stem array. The base diameter of the gas jet whose flow behavior Hoefele and Brimacombe8~ classified as steady jetting is larger than the inner diameter of the nozzle. Therefore, the steady jetting observed in the study of Hoefele and Brimacombe8~ is considered to correspond to bubbling according to the authors' definition. Hoefele and Brimacombe8~ presumably defined the two regimes in accordance with continuity in the jet flow. In contrast to this, the authors have classified jet behavior by noting jet expansion at the orifice exit. V. Summary A study has been made of the observation of gas jets injected into a water bath. The results are summarized as follows. (1) The bubbling jetting transition of gas jets injected into water takes place in the sonic region. With increasing gas flow velocity, the time fraction for jetting increases more abruptly in the water case than in the mercury case. (2) In the sonic region the frequency of bubble knocking decreases with increasing gas flow velocity. Perfect jetting is found to occur at the highest gas flow velocity explored in the present study. The injection pressure in this case is 30 kgf/cm2g. (3) On the basis of the observation of the initial explansion angle and the shock waves of gas jets, it is presumed that the gas jet of flow velocity which is equal to the sonic velocity at the exit of the orifice becomes a supersonic jet just beyond the exit. (4) The cone angle of the submerged gas jet increases with increasing gas flow rate. Acknowledgements The authors wish to thank Associate Professor M. Sano in our laboratory for his helpful guidance and encouragement. Thanks are also due to Professor M. Yasuhara at Department of Aeronautical Engineering, Nagoya University, for his helpful discussion on fluid dynamic problems. A part of this study was supported by the Ishihara-Asada Research Grant of the Iron and Steel Institute of Japan. REFERENCES 1) K. Mori, Y. Ozawa and M. Sano: Trans. ISIJ, 22 (1982), ) Y. Ozawa and K. Mori : 7 etsu-to-hagane, 68 (1982), 90. 3) A. E. Wraith and M. E. Chalkley: Advances in Extractive Metallurgy, ed. by M. J. Jones, Institution of Mining and Metallurgy, (1977), 27. 4) M. Ishibashi, K. Shiraishi, S. Yamamoto and M. Shimada: Tetsu-to-Hagane, 61 (1975), ) M. Yasuhara: J. Japan Soc. Aeronaut. Space Sci., 23 (1975), ) E. S. Love, C. E. Grigsby, L. P. Lee and M. J. Woodling: NASA, TR R-6, (1959). 7) N. J. Themelis, P. Tarassoff and J. Szekely: Trans. AIMS, 245 (1969), ) E. 0. Hoefele and J. K. Brimacombe : Met. Trans., lob (1979), ) A. H. Shapiro: The Dynamics and Thermodynamics of Compressible Fluid Flow, The Ronald Press Co., New York, (1953), ) A. H. Shapiro : The Dynamics and Thermodynamics of Compressible Fluid Flow, The Ronald Press Co., New York, (1953), 83 & 84. Appendix If a supersonic gas flow with a Mach number M1 turns through an angle of 40 changing to the flow with a Mach number M2, 40 is given by Prantle- Meyer equation as follows. 48 = ~+ 1 tan-1 (I/)M2_ " 1 ~-1 ~+1 - tan-1 ~/M2-1...(A-1) M1 Put M1= 1, then 4a = ~+ ~-1 1 tan-1 ~1 +l \/M tan-1 ~/M2-1...(A-2) where, 40: half of the initial expansion angle of gas jets at the orifice exit. Let Po the gas pressure at the nozzle exit and P, the hydrostatic pressure at the position of the nozzle exit, then1 P 2,;-1 M2 K/(fv-1) P: - [(--'-)(' + -} (A-3 M2 = /{(po )(~-1»~,~ (A-4 From the previous study1) PS 2 ~-1 Po M, 2 PS + Substituting Eq. (A-5) into Eq. (A-4), one has For nitrogen gas flow M2 = 5.845M'2'7-5 K+ 1 (~+1)/2~ 2 2 ~-1...(A-6)...(A-7) Substituting Eq. (A-7) into Eq. (A-2) gives the relation between the initial expansion angle B; = 240 and the gas flow velocity. Research Article