Technical Note N-1331 THE COANDA-EFFECT OIL-WATER SEPARATOR: A FEASIBILITY STUDY BY D. Pal | DOCUMENT \ COLLECTION J February 1974 e ye 4 ; ange Sponsored by Director of Navy Laboratories Approved for public release; distribution unlimited. Civil Engineering Laboratory Naval Construction Battalion Center Port Hueneme, CA 93043 IN -183/ ie f Leh i : Aap a Yh) 1s i UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE 1. REPORT NUMBER 2. GOVT ACCESSION NO.} 3. RECIPIENT'S CATALOG NUMBER TN-1331 4. TITLE (and Subtitle) TYPE OF REPORT & PERIOD COVERED The Coanda-Effect Oil-Water Separator: A Feasibility Not final Study PERFORMING ORG. REPORT NUMBER 7. AUTHOR(s) CONTRACT OR GRANT NUMBER(s) D. Pal 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK CIVIL ENGINEERING LABORATORY Sas iu getimiai Naval Construction Battalion Center ZF61-512-001-058 » CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE February 1974 13. NUMBER OF PAGES 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) Director of Navy Laboratories UNCLASSIFIED Washington, D.C. 20376 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Oil-water separator Gravitation Coanda effect Coalescence Effluent Ultrafiltration Centrifugation Laminar flow 20. ABSTRACT (Continue on reverse side if necessary and identify by block number) An experimental investigation which establishes the feasibility of using the Coanda- effect in developing an oil-water separator is described. Tests conducted on an experimental model with an oil-water mixture containing 6% oil showed that the oil content in the effluent can be reduced to less than 3%. A three-stage separator has produced effluent in the range of 1%. Conceptual designs of a practical separator are discussed. The space DD , rents 1473 EDITION OF 1 Nov 65 1S OBSOLETE WOM IM 0 0301 0040224 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) 20. Continued. requirement for a Coanda-effect separator when compared with typical parallel-plate type separators of the same capacity is considerably smaller. Analytical expressions useful in designing a Coanda-effect separator of a given size are also given. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) INTRODUCTION The Navy is faced with very strict regulations covering the discharge of oily wastes from its ships and shore facilities. Such wastes primarily originate from ship’s bilges and ballast waters, oil spill recovery operations, fuel storage and transfer systems, and garage and maintenance activities. Technology and hardware are being developed to process such wastes so that effluent will meet EPA requirements. Current methods of separating oil from oil-water mixtures are centrifugation, gravitation, coalescence and ultrafiltration [1,2]. Centrifugation is an accepted method for separating water- oil dispersions or emulsions [2]. Commercial equipment is available for a wide range of applications. Despite their effectiveness, the power requirement, cost and maintenance of such systems is relatively high. The gravitation method of separating oil from oily wastes relies upon differences in densities of the fluids being separated. Commercially available API and Heil type parallel separators are based upon the gravitation principle. Because of the laminar flow requirements for separation such systems are normally bulky. Coalescence has been used quite extensively for removing finely dispersed water droplets from fuels. The basic mechanism behind this separation technique is the formation of larger oil drops on the coalescing material. The resulting larger drops are separated by gravity. The method, however suffers from fouling of the coalescing element and requires frequent maintenance. Finally, ultrafiltration uses a filtering process to separate water from oil. This method, although very effective, suffers from fouling of the filter element. The system requires frequent cleaning. A new method of separating free oil from oil-water mixtures [3] is under investigation at the Naval Civil Engineering Laboratory * (NCEL). This technique uses the fluid dynamic phenomenon, called “wall attachment, or Coanda effect’’, named after its discoverer, Henry Coanda. This effect is seen, for example, when one’s finger is held close to a thin stream of water issuing from a tap or when tea is poured from a badly designed teapot-spout. A preliminary investigation was conducted to establish the feasibility of using the Coanda effect for separating two immiscible liquids. This report describes in detail the feasibility program. *On 1 January 1974 redesignated the Civil Engineering Laboratory (CEL) of the Naval Construction Battalion Center, Port Hueneme, California. THEORY Consider a thin jet sheet, quasi-two-dimensional, flowing into an unbounded region. The jet gets deflected towards an adjacent wall. When such wall is relatively close to the jet axis, the jet gets attached to and flows along the wall enclosing a separation bubble as shown in Figure 1. As is evident, the jet undergoes considerable curving during its attachment thus generating a centrifugal force field on it. This results in a lower pressure within the separation bubble. The pressure pp in the separation bubble as derived in Appendix A is given by 38 Pepe = T/ib ——_-____ (1) B e o(1/t4 - 1) where P = free stream pressure, J jet momentum per unit span of the nozzle, b = nozzle width, 8 = angular location of the reattachment point, Oo = jet spread parameter, e =satamh! [oy /(s4 + So) | Ss 1 4 = axial distance between the reattachment point and the nozzle, y; = half width of the jet at the reattachment point, Ss = ob /3 = distance of the nozzle exit from a hypothetical origin of the jet. Using the theory discussed in Appendix A, dimensionless pressure (Po - Pp) bo/J was plotted against the plate offset D/b, for values of 7.7, 10 and 12 for the jet spread parameter o. Figure 2 shows the pressure difference between the separation bubble and the ambient as a function of D/b,. For a jet composed of a mixture of two fluids which do not mix such as oil and water, the lighter fluid flowing along the plate side of the jet seeks the separation bubble and gets trapped by it. If an outlet is provided at the center of the bubble, the accumulated oil can be tapped out while the water and rest of the oil flows out of the device. This is the principle of operation of the Coanda-effect oil-water separator. EXPERIMENTAL PROGRAM A test program was designed to determine the feasibility of using the wall-attachment effect in separating two liquids. Two experimental elements with different flow parameters were built and tested. The experiments were conducted in the Mechanical Systems Laboratory at NCEL using a mixture of regular tap water and hydraulic oil as the test fluid. The Wall Attachment Elements Based upon the theory developed in Appendix A, two experimental elements, namely, Elements No. 1 and No. 2 were designed. The 12-inch-long attachment wall of each element has an offset of 4 inches. The nozzles on Elements No. 1 and No. 2 are 1/4 and 3/8 inches wide respectively. The depth of flow passages on both elements is 1/4 inch. Element No. 1 was designed to carry 0.8 gpm of water flow whereas Element No. 2 has a flow carrying capacity of 1.5 gpm. The jet flow parameters such as reattaching distance xp, jet center line radius r and its half width yg at the reattachment point were determined from Figures A-2 through A-5 given in Appendix A. The jet spread parameter, o, for the above calculations was chosen to be 12. The dimensions of the elements are listed in Table l. Each element consisted of three major components: top and bottom cover plates, and the middle plate with the flow passages machined in it. For ease of fabrication and to facilitate flow visualization during tests, each component plate of the Elements was made of transparent plexi-glass sheet. Further, to extract the accumulated oil in the separation bubble, a 1/4 inch diameter outlet was provided in the top cover plate of each element. The general layout showing major dimensions of the elements is given in Figure 3. The elements were assembled by gluing the two cover plates to the middle plate. Feasibility Tests The experiments were performed using the test setup shown in Figure 4. The adjustment of supply water flow is possible by hand controlled valves provided on the flow line. A mixture of red hydraulic oil (Appendix B) and water was used as the test-fluid. The mixture was formed by injecting the oil into water stream before it entered the element. To form a homogenous mixture, the oil was released at the center of and parallel to the water flow in the pipe. The oil to the mixing junction was supplied by a variable flow pump (see details in Appendix B). The element was immersed in water throughout the test series. The supply water flow was measured by a rotameter. The static pressure in the water line was measured by conventional pressure gauges. The use of red oil in the test mixture allowed flow visualization through the elements. The photographs of flow patterns were taken by mounting a camera directly above the elements. The feasibility tests were conducted by running the oil Table 1. Parameters of the Test Elements Parameter alement Element al » 2 Nozzle width, bo? inches Wall offset, D, inches Attachment wall length, 2, inches Radius, D/b, Flow passage depth, h, inches Designed water flow, gpm Velocity at the nozzle at designed flow, feet/second Reynold’s number* at the nozzle, at 1335457 designed flow Jet Momentum at the nozzle, J lbs/ft Preducted pressure, Pp? within the separation bubble (from Figure 2) inches of H,0 Predicted Attachment distance, Xp (from Figure A-5) inches Predicted Jet center-line radius, r (from Figure A-4) inches Predicted half width of the jet, y (from Figure A-3) inches *Kinematic viscosity of water at 60 degrees F taken as 1.2 x 1079 £t2/second. water mixture containing 6 to 8% oil by volume through the elements. The optimum water flow rates were 0.8 gpm through Element No. 1 and 1.5 gpm through Element No. 2 respectively. The mixture jet reattachment distances from the corners were measured for both elements. They were found to be 7 inches for Element No. 1 and 7.5 inches for No. 2. These values are very close to the theoretically computed values listed in Table 1. The test results indicated that a portion of the oil in the mixture jet did accumulate in the separation bubble zone of the flow. A photograph of the flow pattern (Figure 5) through Element No. 2 at its optimum flow rate clearly shows the accumulation of oil in the separation bubble. This oil when extracted contained about 50% water. Consequently, improved designs for collecting oil transferred into the separation bubble were sought. One such design is that of providing a chamber at the top of the separation bubble. This chamber is connected to the separation bubble by means of holes in the top cover plate of the element, see Figure 6. Under optimum conditions, the oil captured by the separation bubble flows into the collecting chamber through the connecting holes. Next, the oil collected in the chamber is transferred by siphoning to an oil storage tank. Two different designs of the collecting chambers were tested. These are shown in Figures 7 and 8. Due to its shape and its greater depth, the collecting chamber design shown in Figure 8 is more efficient in collecting the oil. Tests conducted on the elements with modified design show that about 50% of the oil in the input flow can be extracted in this manner, whereas the remaining oil flows out with the attached water jet. Furthermore, the oil being extracted contained about 5Z water. Thus, a separating device based upon this concept appears to be capable of gross separation only. However, tests on elements with modified designs must be conducted before deriving final conclusions about the degree of separation obtainable. A photograph of the flow pattern through the Element No. 1 taken at its optimum flow rate is included as Figure 9. The accumulation of oil in the collecting chamber is clearly visible in this record. Tests On A Multi-Stage Element It was realized during the feasibility tests on the single- stage elements that to make the Coanda-effect separator suitable for practical applications, staging is necessary. The number of stages for the separator, however, depends upon the type of oily wastes being handled together with the quality of effluent desired. During the course of this study a three-stage test element was designed and built to evaluate the effect of staging. Figure 10 shows the sketch of the element’s middle plate with flow passages cut in it. Each stage of the element has a 1/4 inch wide nozzle. The depth of element’s flow passage was kept at 1/4 inch. The mixture jet in each stage is directed by a curved wall conforming to the curvature of a reattaching jet issuing parallel to a flat plate with an offset of 4 inches. This boundary was determined from flow governing equations given in Appendix A. The element was designed to handle 0.8 gpm of water flow through each stage. Each stage was provided with oil collecting chambers located directly on its separation bubble zone. The oil outlet line on each oil chamber was provided with a hand controlled valve for outgoing oil flow adjustment. The element was tested using the setup shown in Figure 4. The tests were conducted by varying the oil in the mixture from 6 to 8%. The test results indicate that each stage separated about 50% of the oil from its input flow. The effluent at the third stage outlet contained about 1% oil. The oil being extracted had about 3 to 5% water. Figure 11 shows the element undergoing tests. The flow pattern through the element is shown in Figure 12. The accumulation of oil in the collecting chambers and the separated oil flowing through the outflow lines are shown in the flow record. DISCUSSION Jet Velocity Distribution As mentioned earlier, the mixture jet during its attachment, develops a centrifugal acceleration. It was assumed prior to conducting the tests that the lateral acceleration so induced would force most of the oil in the jet into the separation bubble zone of the flow. The observed flow patterns through the experimental models on the other hand revealed that the oil particles were distributed uniformly over the entire cross- section of the jet. This important observation can be explained from theoretical considerations discussed in Appendix A. Consider the reattaching jet velocity profile described by Equation 2: Bisa ri 2 oy 4o(sts ) sts u(s,y) (2) O where the various symbols are defined in Appendix A. The width of a two-dimensional jet expanding into a similar fluid at any axial location can be derived easily from a linear relationship given in References 4 and 5. The half width, yy of the jet is given by b /2 (3) Oo It can be seen from Equation 2 that the jet velocity u(s,y) is maximum at its center-line and is 350 umax = ——S = (4) 40 (sts) Next, it can be deduced from Equations 2 and 3 that the jet velocity u(s,y) drops to 0.1814 umax at a distance equal to the half width of the jet from its center line. The centrifugal acceleration distribution in the jet can be derived from Equation 2 and is given by 3Jo 2, oy ik (Sh) a = re eee sech 49 (sts) (rty) sts (5) Again it is evident from Equation 4 that the centrifugal acceleration, u(s,y) is maximum at the jet center line and is 3Jo umax = do (sts )r (6) The acceleration drops sharply to approximately 0.0327 umax at the jet half-width points. The typical velocity and acceleration for the reattaching jets are shown in Figure 13. Because of the nature of lateral acceleration on the jet, the oil particles are distributed over the entire cross-section. Such a distribution of centrifugal acceleration affects the separating capability of a separator with this configuration. The mixture jet velocity and hence its centrifugal acceleration distribution can be improved by modified designs. One such design is shown in Figure 14. The device uses a splitter located at the nozzle center-line to divide the mixture jet into two sub-jets which flow along the curved walls as shown. The mixture jets flowing through the device will have velocity distribution as shown in the figure, i.e., from a maximum near the curved walls monotonically decreasing to zero at the separation bubble center. Such a velocity distribution will induce a monotonically decreasing centrifugal acceleration on the jet with a maximum near the wall. This configuration will force most of the oil into the separation bubble. The effluent flows out through the two outlets provided on the device. Such a design should improve the separating capabilities of the separator markedly. An experimental investigation is underway to evaluate this concept. Another possible improvement in the oil separation capability of the device can be accomplished by decreasing the static pressure within the separation bubble of the flow. This can be achieved by increasing the centrifugal force on the mixture jet which in turn can be increased by decreasing the radius of the jet center-line. The separation bubble pressure can also be decreased by increasing jet efflux momentum. An Automated Oil Extraction System It was observed during the feasibility tests that the rate of oil extraction from the oil collecting chambers of the elements affected the quality of oil being extracted appreciably. Too high an extraction rate disturbed the oil-water interface in the collecting chamber and the oil being extracted contained up to 50% water. A low oil extraction rate on the other hand reduced the rate of oil captured by the separation bubble of the flow. This resulted in more oil in the effluents thereby deteriorating the performance of the device. A system to control the oil extraction rate is, therefore, required for proper functioning of the separator. Such a system can be either a proportional or on-off type. Because of the simplicity of their design and their lower costs, systems of the on-off type are considered for this application. One such system, shown in Figure 15, uses the difference in electrical conductance of water and that of the oil. Practically all oils are electrical insulators. Water (excluding pure water) is capable of conducting electricity. The system of Figure 15 uses this property in sensing the oil-water interface in the collecting chamber by providing two electrodes at different heights in it. For sensing, the electrodes are connected to a 10 volt AC supply through a 1000 ohm resistor. The solenoid valve on the outgoing oil line is operated by the output of the amplifier which receives its input from a rectified voltage signal across the resistor in the sensing circuit. The use of AC supply in the sensing circuit minimizes the electrolysis in the collecting chamber. When the oil-water interface is below the bottom electrode, the resistance in the sensing circuit is very high and practically no current flows through it. This configuration leads to opening of the solenoid valve provided on the oil outlet line. As the oil is extracted the oil-water interface in the chamber eventually rises above the bottom electrode thereby decreasing the resistance in the sensing circuit. This results in a voltage across the resistor, which when amplified closes the solenoid valve and thus stops the oil extraction. The feasibility of the system will be determined by testing it on the experimental model of the separator. Alternative means of sensing the oil-water interface may be employed in the foregoing control system. Use of an ultrasonic transducer, although expensive, can sense the oil-water interface precisely. Another means of sensing which can be used is based upon the photo-electric principle. Irrespective of the type of sensing used, the basic design of the control system remains unchanged. COMPARISON WITH THE TYPICAL PARALLEL PLATE SEPARATORS It was learned from the feasibility tests that a separating device based upon the Coanda-effect principle is capable of gross separation only. Therefore, for an evaluation the separator should be compared with typical, laminar flow parallel plate separators. Because of its design configuration and the flow velocities through it, the Coanda-effect separator will have a considerably smaller physical size. For instance, a separator to treat 20 gpm of oil-water flow rate can be 1.5 feet long x 1 foot wide x 1.5 feet high; whereas typical parallel plate type separator [1] of the same flow capacity occupies 3 feet--3-1/2 inches x 3 feet--6 inches x 1 foot 7 inches of space. The physical size comparison of the Coanda-effect separators with typical parallel plate type separators for handling 20 and 100 fpm of mixture flow rates is given in Table 2. Because of its smaller size, for a given flow rate, the equipment cost of the Coanda- effect separator will be lower. Presently, the Coanda-effect separator is in its early stages of development and thus many design modifications are required, therefore, a comparison of its oil separating capabilities with that of the fully developed parallel plate separator is not possible. More work is required before such a comparison can be made. Finally, because of the simplicity of its design, the maintenance of the separator promises to be easier. Table 2. Physical Size Comparison of the Coanda Effect and Typical Parallel Plate Separators Maximum Designed Mixture Flow Coanda-Effect Parallel Through the Separator Plate Separator Separator 1 foot-6 inches 3 feet-3-1/2 inches Jlong nl foot long, 3 feet-6 inches wide, and 1 foot wide, and 1 foot-7 in 6 inches high inches high 3 feet long, 5 feet-9 inches long, 2 feet wide, 3 feet-6 inches wide, and 1 foot-6 and 3 feet-2 inches inches high high CONCLUSIONS AND RECOMMENDATIONS 1. The investigation conducted to date establishes the feasibility of using the Coanda effect principle in developing an oil-water separator. A separator based upon this concept will be considerably smaller than a laminar-flow separator of comparable capacity. 2. Feasibility tests conducted on an experimental model of the separator, with an oil-water mixture containing 6% oil (mixture flow rate of 1.5 gpm), show that the oil content can be reduced to less than 3%. The extracted oil contained only 5% water. To make the separator practical, staging is necessary. 3. Further, to improve the quality of extracted oil, an automated oil extraction rate controlling system is required. A concept of one such system given should be investigated by testing it on the experimental separator. 4. Improvements in the separating effectiveness of the separator can be accomplished by modifying the velocity distribution of the mixture jet to alter the centrifugal acceleration on it. A conceptual design of such a modification has been formulated. 10 aqeTd TeTTeied qessjo ue 07 BuTyoeIIY Jer [euoTsueUTGg-on], y Jer peyoezqy JusUyoeAeeYy FO 4UTOg “7 |8an3sty —<—gy———_ TL @TZZON TeuoTsuewtg-omy, Mal ) b/d ( £ 19). P, 1 10 100 1000 Db yee fo) Figure 2. Dimensionless pressure (p."Pp)b/J plotted against plate offset parameter D/b , for various values of CMO pee Omanidie lei 12 All Dimensions in Inches 1/4-d Hole Ter Drilled and Tapped 7 INa- -d Hole Drilled and Tapped B is 1/4 inch for Element No. B is 3/8 inch for Element No. 2 Figure 3. Sketch of the Test Element. 3 ‘dnjes sey aya JO DTJewWaYyoS “Hy VANSTY AoJep[Nssy eansserig -= Y o3e3 einssei = edtd p-*ut-| anor PATEA PEeTTOIqUOD puey see Je jeue Oo SUTTI3eS a J9]eM-TTO JueweTe 3se3 oye ee ae pesieuqns Sao ote sl ee a ee ee eee dn yotd-[To 8utqeoTy a7 dund aeysueij [To Tro V SS SSO uotjounl butxtwu Z27eEM-TTO [Tro pejerzedes dund uoTqo.efUT-TTO duns 94} 07 [Io > 14 ‘TEO %/ YATM zeqem udS G°*—T Fo a7e1 MOTI eIn}yxTW e 4e Z ‘ON QUoWSeTY YyYsnoiyq uszeqjed moTy ¢ 2an3sTty HES Oil Outlet Connecting Holes ee a Jet Attachment Point ae ay tN ee) A Soe Mixture inlet Cavity Separation bubble Chamber cover plate Mixture jet Oil-Water Inlet (ios OL Outlet: Separator Connecting Holes Figure 6. Single Stage Coanda Effect Oil-Water Separator Test Model. 16 “tequeyos SuUTJOeTTOO [TO |eyq Jo USTsep peTJtTpow *g oan3Ty ra gq-€ 3e uoTtTqIODeS | U 2TGqGnq uoTIesredas es uot jeredes WG (ANI TIN TNZA_ IMS —_—_ 7 A ea tel 5 OUETal HUN) koh | THO 3uzo33n9 pe AN aequey) 8uTIDeTTOD [to Jequey) 8urIDeTTOD TIO eoejang pesedel l SseToH But .eUU0) *tequeyo SUTJIeT[OD [TO ey} Jo seinjesyz u8tseq ‘/ ean8ty V-V 32 uotjoes auoZ eTGqng uoTIe1redas aUu0z eraang uot je1edes SITS IOS BW re ee li Ni a7eTd tea0p doy, eter V9IeTd A9A0D = zequey) B3UTIOETTOD TTO SoTOH | ZJequeyy ZULIOeTTOD TTo TFO egg 290 LY iL) i secgoeet ASAE 18 Flow pattern through the modified element no. 1 at 0.8 gpm water flow rate with 6% oil. Figure 9. 1/4 9/16 R NA All Dimensions in Inches Figure 10. The Sketch of Experimental 3-Stage Element ig) (°S9S893 snotaszd ayy wory TTO Tenptsez sy ST SZoequeyo butjoeTTOO |syjz ut sqzeTdozp TTo ouL) “wdb 6°OQ ST edTASp ybnozyA MoTZ eyL_ *ATUO MOTZ 7O7eM YZTM JUSWETS 4FSeq obeqs-se7YyR SUL “II eaznbta 20 al e ‘TIO %9 YIM MoTZ JEqemM wd3 6°¢C aotAep BSuTqutTedeaz e8eqs very} ey. Yysnozy} usreqqjed moTY “CT eansty 21 3Jo0 < 3Jo0 sik 40 (sts) mee 4o(sts\)r Centrifugal Acceleration Curve Velocity Distribution Curve 0.0327 “max ye w Distance perpendicular to the jet center line Figure 13. Reattaching Jet Axial Velocity and Centrifugal Acceleration Distributions 22 " ioe Effluents Foal soarconal Reattached jets Velocity Profile \\ Splitter Ly i> Separation Separation bubble zone bubble zone oil-water inlet Figure 14. Conceptual Design of a Modified Separator with Improved Jet Velocity Profiles. 23 wo sks wotqoerlAXY TLIO ue FO OTAeWeYUDS “CT eANsTy auoz eTqqng uotjeredes e7eTqd At9eA09 doz CRISS VATE zQ STeBULWI9} SuTSuUZS Joqueyg BSUTIOeTLTOD [tO \ Wa ATES LA SNL SW aoe JISqUT BATeA PTOUeTOS andano AOE LOT FTIOOY AeTITTduy AJeTJTTduy 07 Teusts 24 Appendix A EQUATIONS AND DATA DESCRIBING THE FLOW RESULTING FROM A TWO-DIMENSIONAL INCOMPRESSIBLE JET ISSUING PARALLEL TO AN OFFSET FLAT PLATE. This appendix lists the equations and data describing the flow resulting from a two dimensional incompressible jet issuing parallel to an offset flat plate. Wall Attachment Flow Analysis This problem has been treated in depth by Bourque and Newman [4], and by Sawyer [5] independently. The analysis conducted by Bourque and Newman is easier to understand and covers a wide range of flow parameters. In this study therefore only the results of Reference 4 were used. The analysis can be described by considering the flow of a two-dimensional jet issuing from a nozzle in a wall adjacent to a parallel plate with an offset D as shown in Figure A-l. The jet during its expansion entrains fluid from the surroundings by turbulent action. The entrainment of fluid from the plate side causes a pressure difference across the jet thus curving it toward the plate. If the plate is sufficiently long the jet strikes it and reattaches. The jet divides on striking the plate, sending part of the flow into the separation bubble. The flow equibilibrium is reached when the flow entrained by the plate side of the jet is equal to that into the separation bubble from the jet at the point of striking. This is the model used in the analysis of Reference 4. Further, the analysis is based upon the following assumptions: (1) The flow is incompressible and two dimensional, i.e., only thin jet sheets are considered. (2) The jet efflux velocity is uniform, i.e., the increase in its velocity with the reduced pressure in the separation bubble is neglected. The jet is submerged in a similar fluid and its velocity distribution is that of a free jet. (3) The jet entrains the same amount of fluid from each boundary. (4) Pressure within the separation bubble is constant and the jet center line is a circular arc up to the point of attachment. (5) The force on the plate due to skin friction forces are small and are neglected. The axial component of jet velocity used is 25 u(s,y) where So S ie 3Jo 2 Oy *t 4p (sts) Seen sts (2) axial distance from the nozzle, nozzle width, distance of the nozzle from a hypothetical origin of the jet where the flow originates, co-ordinate normal to the jet center line, jet spread parameter, to be determined experimentally, it has a value of 7.7 for a turbulent free jet, ob, /3 (see Reference 4). Before going any further some quantities must be defined as follows: free stream pressure Static pressure within the separation bubble radius of the center line of the reattached jet, density of the fluid, Angular location of the point of reattachment from the nozzle, distance of the plate from the nozzle axis, distance of the point of attachment from the corner, length of the plate jet momentum per unit span of the nozzle. The equation of the reattaching streamline is given by 3s 2 an = Git )-1 (A-1) oO = tanh =S (A-2) oO ty (A=3) 26 where t = tanh 1 s,ts Go) is the value of t at the point of reattachment, then the radius of the jet center line is derived from ot /te -1) (es) r/b 2 30 where t,and 8 are determined from the following equations: 2 D/b o(1/t,-1)(1-Cos 8) _— (hoG) e 30 and 3} Cosmen =e S/2. t,-1/2 ty (A-7) The half width of the jet at the reattachment point, i.e., y, can be easily derived from Equation A-4 and is y,/d, = se S tanh ae (A-8) Further, the distance of the reattachment point from the plane of the nozzle is o(1/t7-1) Sin 6 tanh’ 't, Se vest |) ee (A-9) Rio oe ae Sin 0 Finally, the mean pressure within the separation bubble is computed by 30 (A-10) Poy = Jip B o(1/t@-1) oO A wall attachment element can be designed using Equations (A-1) through (A-9). However, to use these equations conveniently, it is required that the flow parameters XR/bo> 1S//Doys ¥1/by and 8 be known as functions of the pre-determined parameter Dba These equations are complex and can not be expressed explicitly in terms of D/by alone. 27 A numerical scheme was devised to compute Xp/do> Es y1/b, for known values of D/do- The numerical method runs as follows. By inspection of Equation A-7, maximum and minimum values of ty which render 8 between 90 degrees and 30 degrees were determined. Since y; is positive, only positive values of rj must be considered. Further, it was determined from Equation A-7 that for 6 to lie between 90 degrees and 30 degrees, t, must range between O and 0.50. A known value of t, yields 6 from Equation A-7. For a selected value of o with known tj and 6, parameters D/Dats 1G/Deys ¥1/bo and xp/bo can be determined from Equations A-6, A-5, A-8 and A-10 respectively. Thus computing a set of values for Xp/Do r/bo and y1/b, for a known D/b,. A series of similar sets were computed by increasing ty by 0.05 each time up to a final value of 0.50. A total of three series of sets were computed for different 6 of 12, 10 and 7.7 respectively. For easy usage the parameters 6, y1/d5> E/De and xp/b, were plotted against D/do for values of D/b. ranging from 1 to 1000. These plots are shown in Figures A-2 through A-5. It should be added here that flow parameters become independent of the parameter D/bg for D/b, greater than 35. Also the analysis becomes inaccurate for D/by less than 3. Further, the value of o, , the spread parameter chosen can affect the flow parameters appreciably. One last remark of interest is regarding the value of o, the spread parameter to be used while using these curves. Because of the curvature effect ao of 7.7 does not apply. It is reported in Reference 1 that a value of 12 for o gives flow parameters values that are in fair agreement with the experimental data. 28 = Figure A-l. Reattaching streamline A two-dimensional jet reattached to an offset parallel plate. 29 OOOT 5 “ZT pue OT SZ°Z£ JO O JO SaNTeA snoTisea Zoy q/q itejewerzed jeszzo ajeTd ysutese pojjotd qutod juewyoej}eer Jol eyq Jo (g) UOTIeDOT APTNSUy Oo ‘ q/a OL OOT *Z-V o1n3TW OT OC OOT 30 OOOT "ZT pue oT *‘Z°Z JO O FO SonTea SNOTAPA OF “asa Jajoweied Jeszjo ojzeTd Jsutese pejjotd © yk fo) = q/a OOT OT "€-V e1n3Ty q/'é 31 1000 100 r/b Oo 10 10 100 1000 D/b |, ————w» Figure A-4. Jet center line radius Ps plotted against plate offset D/b, for various values of o of 7.7, 10 and We Bi. 1009 10 Figure A-5. 10 100 1000 D/b ,——— Reattachment distance x /b, plotted against plate offset for various values of o of 7.7, 10 and 12. 33 Appendix B SPECIFICATIONS OF OIL USED IN THE TEST MIXTURE AND THE OIL INSPECTION PUMP This appendix lists the specification of (a) the oil used in the test mixture (b) the oil inspection pump Hydraulic Fluid - Petroleum Base Mil. spec.: MIL-H-5606C Fed. Stock No.: FSN 9150-223-4134 Specific gravity: 0.88 to 0.90 Color: red Kinematic viscosity: 8.0 stokes at 40 degrees F to 0.10 stokes at 130 degrees F Oil Injection Pump Fluid Metering Corp FMI Model RRP-F with 3/8-inch piston, 0-100 cc/min at 50 psi. Variable flow with micrometer flow adjustment head. Electric motor drive. 115V, 4.5A at 60 cycles, 1725 rpm. ACKNOWLEDGMENTS John B. Curry assisted in the laboratory tests of the experimental elements REFERENCES Ibo Naval Civil Engineering Laboratory. Mechanical and electrical engineering department, letter report, YF38.554.001.01.001: Program plan for oily waste handling at navy shore establishment, by E.L. Ghormley, Ph.D., Port Hueneme, California, June 1972. Die S.M. Finger and R.B. Tabakin, Development of shipboard oil/water separation systems, ASME paper 73-ENAS-38, presented at the intersociety conference on Environmental Systems, San Diego, California, July 16-19, 1973. 36 U.S. Navy Case 56,734: Patent application on coanda effect oil=water separator, by A.J. Paszye, Ph.D: Ds Pall land JBe Cusays 15 June 1973. 34 4. C. Bourque and B.G. Newman, Reattachment of a two-dimensional imcompressible jet to an adjacent flat pole, the Aeronautical Quarterly. Voll xd Aug. 1960), ‘pp. 202328 Do R.A. Sawyer, The flow due to a two dimensional jet issuing parallel to a flat plate, J. Fluid Mech. Vol 9, 1960, pp. 543-60. 6. Naval Civil Engineering Laboratory. 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