ASME Cavitation and Multiphase Flow Forum, FED-Vol. 153, Washington, D.C., June 1993.

Transcription

1 ASME Cavitation and Multiphase Flow Forum, FED-Vol. 153, Washington, D.C., June THE INFLUENCE OF CAVITATION JET VELOCITY ON SUBMERGED WATER AND SPREADING Kenneth M. Kalumuck, Georges L. Chahine, and Gary S. Frederick DYNAFLOW, Inc Pindell School Road Fulton Maryland tel: fax: ABSTRACT Submerged jet flow data are typically based on non cavitating conditions. However, it is expected that cavitation would extract energy from the flow and alter jet mixing and spreading. In order to investigate the effect of the presence and the amount of cavitation on jet behavior, a series of experiments were run in which the cavitation number was varied by changing the ambient pressure for a fixed value of the jet discharge velocity. A range of conditions from no cavitation to developed cavitation was covered. Jet flow dispersion patterns were made visible by dye injection upstream of the nozzle and recorded with video strobe photography and high speed movies. Centerline jet velocities were measured as a function of distance from the nozzle with a pitot tube at distances up to 140 nozzle diameters. The presence of increasing amounts of cavitation in the jet flow was found to increase jet spreading and decrease jet velocity at a given distance downstream thus reducing the effective standoff distance of the jet. These results underline the importance of conducting tests at cavitation numbers comparable to those expected in practice. It also suggests that, for a fixed discharge velocity, jet performance would be expected to degrade at shallower depths and improve to some degree at greater depths (until cavitation is suppressed). Similarly, at a fixed ambient pressure, an increase in the nozzle discharge velocity may not improve results as much as expected due to an 1Ilcrease in the amount of cavitation. EXPERIMENTAL SETUP Experiments were conducted in DYNAFLOW's High Pressure Cell (HPC) capable of ambient pressures up to 3000 psi. A sketch of the HPC is presented in Figure 1. The HPC is a cylindrical pressure vessel with inside dimensions of approximately 9.5 inch diameter and 28 inch length with three quartz view ports circumferentially spaced and located near its mid length. Originally constructed for studies of deep hole drilling with cavitating jets, it includes a rotating fixture in which rocks are placed and rotated for cu tting beneath the jet. Ambient pressure is adjusted and maintained by a choke plate which acts as a back pressure valve i~ the outflow line. The jet flow is driven by a Weatherford five piston positive displacement pump capable of up to 20 gpm (U.S.) at 10,000 psi. More details of the experimental setup and the work conducted can be found in [1]. The jet nozzles utilized employed a smooth contoured contraction from the upstream diameter to the orifice to preclude separation. The nozzles were machined from 316 Stainless Steel pipe plugs with an orifice of in. Great care was taken in the fabrication to obtain smooth inner walls. The nozzles were mounted in-line to sections of stainless steel tubing that were inserted into the HPC feed tube. SCALING In many applications, it is desirable to maximize the "reach" or the downstream distance at which the jet can main tain a desired velocity or stagnation pressure. In many cases, controlled scale model experiments can be conducted to investigate the influence of different design and operating conditions on jet "reach". For proper scaling of the jet velocity versus distance relation and thus jet "reach", the nozzle shape should be identical to the full scale nozzle but reduced or increased in size by the scale factor. Other quantities must then be properly scaled. The basic scaling law to employ is the turbulent jet velocity 1

2 t decay relation [2]:.2: = Cdo u«x' where C = 6.3 in the absence of cavitation for a circular turbulent jet of initial diameter do and velocity U», and u is the centerline jet velocity at a distance x downstream of the nozzle. The other important factor is the Cavitation Number, a, given by: (j= P a -P tl D.P Here, IlP is the pressure drop across the nozzle, P a the ambient pressure, and P tl the vapor pressure of the liquid. The cavitation number must be approximately the same in the model and full scale systems for cavitation effects to be properly accounted for. Matching of the Reynolds Number is less important if the flow is highly turbulent in both model and full scale. The pressure drop across the nozzle, D.P, is taken to be the difference between the measured pressures in the line immediately upstream of the HPC and the ambient cell pressure. The discharge coefficient, Cd, is related to the volumetric flow rate, Q, the jet velocity at the nozzle exit, Uo, and the nozzle orifice diameter, do, by: Q Cd = 1rd2[],. "400 The jet velocity is related to D.P, and the liquid density p by Uo= [ -. Combining these, the discharge coefficient is found from the measured pressure drop and flow rate: C -~.fi!- d - v'75:p V 2. 7rdfi The jet velocity at a given downstream location, x, can be related to the jet pressure and flow rate by combining expressions (1,3,4) above to obtain Thus it can be seen that for the same pumping power (given by the product of pressure and flow rate), greater downstream velocities can be attained by increasing the flow rate (by increasing the jet diameter) (1) (2) (3) (4) (5) (6) than by increasing the nozzle pressure drop. An increase in the nozzle pressure drop is shown below to result, under certain conditions, in an increase in jet cavitation which decreases downstream velocities below those given by the idealized relations above. JET FLOW VISUALIZATION AND VELOCITY MEASUREMENTS Two types of tests were conducted: jet flow pattern visualization and jet velocity measurement downstream of the nozzle. The tests were conducted at two discharge velocities -36 and 200 m/s - at varying ambient pressures up to 1350 psi. These jet velocities correspond to pressure drops across the nozzle, IlP, of 95 and 2900 psi. The jet flow dispersion patterns were made visible by injection of a red dye into the feed pipe upstream of the nozzle. The dye injection system used in these tests consisted of a 0.5 liter stainless steel sample cylinder used as a dye reservoir, filled with red dye, and connected by pipe tee's in parallel with the main nozzle feed pipe just upstream of the entrance to the high pressure cell. Regulating valves were employed at the dye reservoir inlet and outlet and a ball valve in the main line between the reservoir inlet and outlet was used to adjust the main line pressure drop to enhance the flow through the dye reservoir. Using a Cannon Hi 8 Digital Video Camera and back lighting with a strobe light through a view port, video recordings were made of the jet flows made visible with dye injections. The strobe flash had a duration of 50 microseconds. Individual frames could then be taken from the video using a 35 mm camera and 21 inch color video monitor. The HPC quartz window view ports are 1.5 in. diameter. However, due to the jet being at a distance from the back lit view port, the area of illumination has a diameter of approximately 1.3 in. To observe different jet downstream locations, the nozzle was moved relative to the view port such that it was located at 0, 1, 2, and 3 inches above the top of the view port. At the highest location, the jet flow had spread to cover the entire field of view and thus useful pattern visualization could be obtained only at the first three locations. This corresponds to a distance of approximately 30 orifice diameters. High speed movies at frame rates from 3000 to 5000 frames per second were also taken with a HYCAM II 16 mm high speed camera with back and side lighting. Measurements of jet velocity were made using a pitot tube mounted to an arm that could be ro- 2

3 tated and translated from outside the cell The 1/8 in. O.D. pitot tube was fitted with 1/8 in. copper tubes which ran through the cell lid to a Pace P7D Transducer. Three interchangeable transducers were used having different maximum ranges (10 psi, 100 psi, and 250 psi). A CD-10 carrier demodulator signal conditioning unit and digital voltmeter were employed in conjunction with the transducers. The transducers were calibrated against a Heise Precision Pressure Gage. Readings of jet centerline velocity as a function of distance from the jet were obtained by adjusting both the height of the nozzle and the position of the pitot tube. Care was taken to align the pitot tube along the jet axis. In addition, the pitot tube was rotated across the jet to find the peak velocity at a given distance from the nozzle - which corresponds to the jet centerline velocity. Measurements were made at distances up to x = 15 in. (x/do ~ 140). CAVITATION NUMBER EFFECTS Classical submerged jet flow data (e.g. [2]) are typically based on non cavitatingjet flows. However, cavitation will be present in the jet flow for conditions at which the cavitation number, <T, defined above in equation (2), is below approximately 0.5. It is important to carry out scale model experiments at values of <T comparable to that expected at full scale, since cavitation extracts energy from the flow and could alter jet mixing and spreading. In order to investigate the effect that the presence and the amount of cavitation has on the behavior of the jet and on the downstream jet velocity, a series of experiments were run in which the cavitation number was varied by changing the ambient pressure in the cell for a fixed value of the jet discharge velocity (nozzle pressure drop). Ambient pressures, and thus <T, were selected such that the range of conditions from no cavitation to large amounts of cavitation was covered. This range of conditions at which to conduct the tests were selected by visually observing the amount of cavitation in the jet as the ambient pressure was varied. Figure 2 presents photographs of the effect of cavitation number variation on dye visualizations of the jet flows taken from videos over a range of <T for the case of D..P = 2900 psi (Uo = 200 m/s). Results at ambient pressures of 300, 700, and 1350 psi (corresponding to a = 0.1, 0.24, and 0.47, respectively) are shown. Shown for each case are views at two locations - the left edge of the view port is at the nozzle in the left frame and at 2 in. downstream in the right frame. The two frames for a given case were taken from a different experimen tal run at the same conditions. It should also be noted that these are views taken at a particular instant of time, and although the turbulent jet is steady in the mean, the instantaneous location of the turbulent structures - and thus the dye edge - varies in time (as is easily seen from the high speed movies and the videos). The case of P a = 1350 psi is approximately at cavitation inception, and negligible cavitation is observed. Moderate cavitation, within a few diameters of the nozzle, can be observed at a cavitation number of Significant amounts of cavitation persisting more than 12 diameters downstream can be observed in the jet flow for a = 0.1. The effect on jet velocity is shown in Figures 3 and 4 which compare the measured velocities for these three cases. (Figure 4 presents the data of Figure 3 normalized by the measured velocity for the case of P a = 700 psi). At P a = 300 psi, the increased cavitation is seen to decrease the downstream jet velocity by approximately 5-12 % relative to the case of P a = 700 psi. Similarly, suppression of cavitation by raising the ambient pressure to 1350 psi is seen to increase the downstream jet velocity by approximately 8-12 % over the P a = 700 psi case. (One measured point, at x = 9 in.; x/do = 85), does not follow this trend and is believed to be an experimental error. The measured discharge coefficients are also affected by the cavitation number. For P a = 700 psi, C«= At an ambient pressure of 300 psi, Cd drops to 0.94 while at P a = 1350 psi, Cd was measured to be This value larger than 1.0 could be due to the jet attaching slightly to the outside of the nozzle, thus effectively increasing the orifice size or to a combination of measurement uncertainties or both. The trend of decreasing discharge coefficients with increasing amounts of cavitation (decreasing <T), however, is clear, and is supported by the velocity measurements discussed above. An analysis of the spreading angle of the jets was conducted. Due to the unsteady movement of the dye edge by the turbulence, different instantaneous views of the jet will yield different angles. Thus an approximate average of the position of the dye edge was measured to estimate the spread angles. These estimates were made at a number of locations and for a number of different frames. The spread angle is defined to be that between one side of the jet and the other. Thus angles with respect to the center line are half these. The jet spreading angle was found to increase with 3

4 decreasing ambient pressure or cavitation number (11.3, 12.2, and 13 degrees for P; = 1350, 700, and 300 psi, respectively) which is consistent with the velocity and discharge coefficient behavior. For 6.P = 95 psi CUo = 36 m/s), (J" = 7.5 (well above inception) and there is no cavitation at P a = 700 psi. The ambient pressure was reduced to the lowest possible in our cell - 5 psi above atmospheric ((J" = 0.21). Only light cavitation was observed. Thus, for Uo = 36 mis, little influence of the ambient pressure was observed. This is consistent with the jet velocity measurements presented in Figure 5, where the effect of the reduced ambient pressure is seen to insignificantly change the measured jet velocities. There was also no measurable variation in discharge coefficient between the two cases. The results of jet velocities, spreading angles, and discharge coefficients all point to poorer jet performance with increased amounts of cavitation (decreasing (J") at 200 m/s discharge velocity. This underlines the importance of conducting tests at cavitation numbers comparable to those expected for the full scale application. It also suggests that, for a fixed discharge velocity,jet performance would be expected to degrade at shallower depths and improve to some degree at greater depths (until cavitation is suppressed). Similarly, at a fixed ambient pressure, an increase in the nozzle discharge velocity may not improve results as much as expected due to an increase in the amount of cavitation. This suggests that to increase the standoff distance at which a jet is effective, it is better to increase the flow rate through the use of larger nozzle diameters rather than by increasing the jet velocity with a higher pressure drop across the nozzle which will decrease the cavitation number. CONCLUSIONS The effect of variation of the cavitation number in submerged jet flows by varying the ambient pressure was seen to be significant when cavitation occurred. Relative to the case of (J" = 0.24, (700 psi ambient pressure), raising the ambient pressure to 1350 psi ((J" ;:::;; 0.5), prevented cavitation and resulted in an increase in measured downstream velocity of approximately 10 %. A reduction in ambient pressure to 300 psi ((J" ;:::;;0.1) resulted in a comparable decrease of approximately 10 % in jet velocity (below that of the case for (J" = 0.24). Discharge coefficients were seen to decrease and jet spread angles to increase with increasing cavitation (decreasing ambient pressure). Thus increased amounts of cavitation are seen to decrease downstream jet velocity which would likely decrease jet effectiveness, particularly at large standoffs, in any application where jet velocity or stagnation pressure are important. This is important to keep in mind when considering operating at significantly different depths and/or jet velocities. It also highlights the need to perform testing at cavitation numbers comparable to those expected in the actual full scale application. ACKNOWLEDGMENTS This work was supported by Imperial Oil Resources Limited. REFERENCES 1. Kalumuck, K. M. and Chahine, G. L., and Frederick, G. S. "Small Scale Experimental Evaluation of Submerged Water Jet Nozzles," DYNAFLOW, Inc., Technical Report , December Rajaratnam, N., "Developments in Water Science 5 - Turbulent Jets," Elsevier, Amsterdam, FIGURE L HIGH PRESSURE CELL (HPC) FOR rsr TESTING AND EXPERIMENTATION AT ELEVATED AMBIENT PRESSURES UP TO 3,000 PSI. o<j 4

5 .:t 1.2, ;: _ c. Po: (J 700 psig 0.14 >- t:: u o u3 >... M 1350psig ~... )( 300 psig 0.1 ~ >: t:: u ~ I ~ I [... )( -:... O.R~~~~-,--~-r~r-~~ ~~-- ---! 2.) I().<5-0 x.) It~ NONDIMENS!ON,\I. JfSTANC!: (.<!doj FIGURE.. THE INFLUENCE OF '/ARYING AMOUNTS OF ~AVIT" TION ON MEASURED DOWNSTREAM CENTERLINE JET IELOClTfES. 4P = 2,900 PSI. DATA OF FIGURE 4 NORMALIZED ON CASE FOR p, = 700 PSI. FIGURU Z. EFFECT OF CAVIT.-\TION NUMBER VARIATION ON JET FLOW VISUALIZeD WITH DYE. NOZZLE AT 1.EFT EDGE OF PHOTO..lP '" PSI. ;I) LARGE A/l.fOUNT OF CAVITATION AT 11 "'" 1>.1. ~) MODERATE CAVrTATTON :-.IEAR N07.7.U:. NEGUCiIOLE..:1 ("AVITATfON.vr lnc EI'TII1N \l g J lll > ~ SO -- PU: a )( 700 psig 0.24 M 0.47 M( -, 1350 psig -, :::::: psig Pa: (J 700 psig psig 0, NONDrMENSIONJ\L DISTANCE (x/do) ot-~-r~~~~~'-~~~~--~~~~ NONDIMENSIONAL DISTANCE C;<{do) FIGURE 3. TilE INfLUENCE OF VARYING AMOUNTS OF CAVITATION ON MEASl'RED DQWNSTIU!AM CENTERLINE JET VELOCITIES OBTAINl'D BY VARYING l'>. <lop= 2,900 PSI. p, FOR INCEPTION - I,350 PSI. FIGURE S. MEASURED DOWNSTREAM JET CENTERLINE VELOCITIES FOR <lop- 9S PSI SHOWING NEGLIGIBLE EFFECT OF AMBIENT PRESSURE CHANGE FOR THIS LOW SPEED JET. 5