JOURNAL OF THE OPTICAL SOCIETY OF AMERICA JUNE, 1953

An Optical Method for the Study of Impinging Jets in a Liquid StreamGEORGE G. KRETSCHMAR AND HENRY W. WEDAA

Michelson Laboratory, U. S. Naval Ordnance Test Station, Inyokern, China Lake, California(Received Februrary 10, 1953)

A method of analyzing the mixing characteristics of binary liquid jets in a liquid stream has been de-veloped. It consists of a modified schlieren system in which the aperture of the camera lens acts as a circularschlieren knife edge. The liquid stream which is to be studied is placed in the schlieren field. This liquidstream is in a glass tube which is contained in a rectangular glass-sided cell filled with liquid of about thesame index of refraction as the glass tube. This masks the refractive effect of the glass tube and much of thelens effect of the round cross section of the stream. It is shown that for a definite minimum energy of in-jection, the mixing becomes essentially complete at the end of the mixing region. The region of mixingappears on the photographs as a region of special turbulence above the jet openings in which the jet energyis being dissipated.

INTRODUCTION

IN connection with recent studies of rocket propellantliquids, it was desirable to know the rate and degree

of mixing of two liquids forced together from twoimpinging jets and maintained as a stream of mixedliquids by a surrounding glass tube.

Initial experiments using chemical indicators andphotographic recording were not very successful, butit was very evident that the volume ratio of the twoliquids must be maintained constant. Accurate injectionratios were achieved by the use of a positive displace-ment hydraulic injection equipment.

An optical method was devised for studying theliquid stream mixing. Two inert organic liquid mixtureswere brought together by means of two pairs of im-pinging jets, and the resulting liquid stream wasstudied by means of photographs of a spark dischargeprojected through the tube at right angles to the direc-tion of the stream flow.

The mixing studies here described were made witha single injector and tube system in which the angle ofimpingement of the jets was kept fixed. It might appearthat differences in angle of impingment and differencesin flow velocity would result in different mixing andflow characteristics. The work of Heidmann and

FIG. 1. Detail of injector design.

Humphrey' suggests this. The present work was,however, confined to a single injector configuration,but the second factor, the flow velocity, was carefullyinvestigated.

APPARATUS

The structure of the injector is shown in the detailedsketch of Fig. 1. The two liquids were forced throughthe 20-mil holes of the injector and impinged at theinjector surface at an angle of approximately 600.A -in. diameter glass tube, not shown in the drawing,was attached to the tapered projection of the injectorby means of a ground joint and sealing compound. Thecombined liquids traveled in a vertical directionthrough this glass tube.

In order to maintain an accurate ratio of injection ofthe two liquids, it was found necessary to use a hy-draulic injection system consisting of two accuratelybored stainless steel cylinders of equal diameters andstainless steel pistons fitted with 0-rings. The pistonswere connected to long screws, which were drivendownward by means of rotating nuts and connectingspur gears. The ratio of injection of the liquids was thesame as the gear ratio of the driving gears and was asaccurate as the machining of the gears, probablywithin one percent of the nominal ratio. Figure 2 is aphotograph which shows the injection apparatusconnected to the injector and flow tube.

The injector is connected to the cylinders by meansof copper tubing and pressure fittings. It will be ob-served that the flow tube is surrounded by a glass-sidedcell for the purpose of surrounding the flow tube witha liquid of nearly the same index of efraction as theglass of the flow tube. The glass of the tube then be-comes almost invisible by transmitted light, and mostof the cylindrical lens effect of the round cross sectionof the tube is neutralized. Glycerine, having an indexof refraction of 1.473, was found to be a good liquidwith which to surround the Pyrex flow tube.

I Marcus F. Heidmann, and Jack C. Humphrey, J. Am. RocketSoc. 22, 127 (1952).

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OPTICAL STUDY OF IMPINGING JETS

TiE OPTICAL SYSTEM

The method of observing the flow is an optical one.The optical set-up may be considered as a modifiedschlieren system.2' 3 By surrounding the flow tube withthe flat-sided cell containing a liquid of about the sameindex of refraction as the Pyrex glass of the flow tube,it is possible to project light through the flow tube witha minimum of distortion. Light is projected from a pointsource through a condensing lens and through themixing tube directly onto the lens of a camera. Thecondensing lens illuminates the mixing tube, whichthen becomes the illuminated object projected by the

CONDENSINGLENS

MIXINGTUBE PHOTOGRAPHIC

CAMERA PLATE

SPARK LENSLIGHT SOURCE

- m!---- - ~

-- n ---- -_A

MIXING TUBE

D 1 0 GM

33 GM I

B

IRIS DIAPHRAGMD. 30 CM

IMAGE OF TUBE0D 1-3GM

44 CM

FIG. 3. A. Optical arrangement of the schlieren system. B. Raydiagram of mixing tube, iris diaphragm of camera lens, and plateimage, drawn approximately to scale.

which the aperture of the camera lens obstructs themore widely refracted rays diverging from the flow tube'

Figure 3 is a diagram of the optical arrangement.The lower part of the figure shows the approximateimage and object sizes and the respective distances.It will be seen that the distances are fairly large withrespect to the sizes of object and image, so that thelight rays are approximately parallel.

The indices of refraction of the liquids used in thesestudies were carefully measured with an Abbe re-fractometer adjusted to sodium light. The average

FIG. 2. Positive displacement injection equipment.

camera lens onto the photographic film. Thus, theset-up is much like the ordinary optical projector inwhich an illuminated object is projected onto a screen.In the present set-up the focal point of the condensinglens is in the camera lens, the aperture of which actslike the knife edge of a circular schlieren system.4 Thisarrangement is thus a modified schlieren system in

2 V. F. Barnes, and S. L. Bellinger, J. Opt. Soc. Am. 35, 497(1945).

3 Keagy, Ellis, and Reid, Rand Report (R 164), The RandCorporation, Santa Monica, California, 1949.

4 Edmonson, Gayhart, and Olsen, J. Opt. Soc. Am. 42, 984(1952).

0 . M F

FIG. 4. Print of three tubes containing the quiescent liquids.

3

527June 1953

G. G. KRETSCHMAR AND H. W. WEDAA

A j GLAS

AIR / CALI X I

T0

FIG. 5. Woodworth's method of geometric ray tracing.

value for the index of refraction of the oxidizer simulantat room temperature was found to be 1.4971, that ofthe fuel simulant was 1.3480, and the mixed liquidshad an average index of 1.4541. The oxidizer simulant

The photographs were taken with single spark dis-charges from an apparatus designed and built by M. H.Hunt.5 The spark discharge time was approximately5 microseconds, thus effectively stopping the fluidmotion. The discharge was unfiltered. The main com-ponents of the light were from a single magnesiumelectrode. Single discharges could be convenientlyproduced by a triggering circuit which was built intothe equipment.

GEOMETRICAL THEORY

To understand the optics of the flow photographs itis enlightening to trace a few representative raysthrough diagrams of the enlarged cross sections oftubes containing the quiescent liquids.

Figure 4 is a reproduction of a spark photograph oftubes of quiescent liquids contained in the flat-sidedcell and immersed in glycerine. The tube marked 0contains the oxidizer simulant, that marked F containsthe fuel simulant, and M is the tube containing mixedliquids. The characteristics of these photographs are ac-

3 1 /

11

FIG. 6. Diagram of rays passing through a tubecontaining the oxidizer liquid.

has an index higher than that of the flow tube andsurrounding glycerine, the fuel simulant has a lowerindex, and the mixture has an index only slightly lower.

3~~~~~~~~~~~~~~~~

/ /LIQUID -135 Em

FIG. 7. Diagram of rays passing through a tubecontaining the fuel liquid.

LIQUID t1-1 45

45

I M-

4 .45

FIG. 8. Diagram of rays passing through a tube containingmixture of the two liquids.

counted for by means of the ray diagrams reproduced inFigs. 5-8. In the ray diagrams the half-circles representhorizontal sections across the tubes. They are drawnto scale, using the measured indices of the liquids. Theindices of the glass and surrounding glycerine havebeen taken as the same, namely, 1.47, and the enteringrays have been assumed to be horizontal and parallel.

The rays have been traced by a method of exact raytracing devised by Woodworth.6 The method is agraphical one in which lines are transferred from anindex diagram by means of a pair of draftman's tri-angles. Figure -5 is introduced in explanation of Wood-worth's method. The upper part of the figure shows aray AB which is bent at the interface to the directionBC. The lower part of the figure is the index diagram,in which the line segments 1 and 1.5 are drawn accordingto the index of refraction ratio of the air and the glassof the circular lens section.

5 M. H. Hunt, U. S. Naval Ordnance Test Station, TM No.7524-23, China Lake, California, June, 1950.

6 C. W. Woodworth, Microscope Theory (The Commercial Press,Ltd., Shanghai, 1924), pp. 45-52.

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OPTICAL STUDY OF IMPINGING JETS

FIG. 9. Series of films arranged in accordance with increasing flow rates.

The method of tracing the ray is as follows: Drawthe line PO to the center of the circle. Transfer the linePO to the index diagram going from air to glass,giving the line 'P'. Then P'O" is the direction of theray in the glass. This follows directly from Snell's law,as may be seen by drawing in the parallel line P"O"and the two projections from P' and O'. Then x/1 = sini,and x/1.5=sinr, from which it will be seen that sini/sinr= 1.5.

In Fig. 6 are shown four rays as they would appearif traced through the tube filled with oxidizer liquid-Oin the photograph of Fig. 4. It is seen that the rays 1,2, and 3 will converge as shown. An edge ray, however,represented by 4 in the diagram, will enter the liquidand then strike the glass at an angle greater than thecritical angle, so that total reflection will occur. Thisgives rise to the dark edge of 0 in Fig. 4, where the light

which has been reflected around the inner surface ofthe tube does not emerge to affect the photographicfilm.

The diagram of Fig. 7 is a representation of fourrays as they would appear if traced through the tubefilled with the fuel mixture. The diagram has beendrawn to scale from a comparator traverse of thenegative of tube F, Fig. 4. The actual traverse figures aregiven on the diagram, from which it will be seen thatthe glass tube walls are 0.138 cm thick, the line of totalreflection is 0.042 cm from the inner glass surface, andthe central bright region is 0.164 cm in width. Takingthe radius of this central region, which is 0.082, andmultiplying by 33/44, we get 0.062, the actual half-width of this central bright area at the object. For thisbright area to be produced by obstruction of lightrays at the lens aperture, ray 1 in the diagram wouldhave to be deviated

(1.5-0.062)/33 or about 0.043 radian.

It will be seen that this corresponds quite closely withthe actual geometrical condition in diagram Fig. 7,where ray 1 is found to diverge about 0.04 radian.

Ray 4 in Fig. 7 is also of particular interest. Bydrawing the line OT in the index scale, the position ofthe critical angle can be found. Ray 4 has been foundin this way. All rays above emergent ray 4 will betotally reflected, but a few near the point T' will enterand leave the liquid producing a small brightly illumi-nated line on the inner tube wall. It appears that asmall amount of diffused light from this locally il-luminated line is the cause of the light line just insideof the glass wall of the tube F in the photograph ofFig. 4. This line is very apparent on the negatives,although it is difficult to see in Fig. 4.

The third diagram, Fig. 8, represents the case of themixture, the middle tube M of the photograph of Fig. 4.On this diagram the central bright region is 0.55 cm in

width on the negative. The angle for obliteration bythe iris for the ray originating 0.27 cm up from the

0Z

0~~~~~~~~~~

I-e I- __ _

0

1-4 FLOW RA E IN CC PER SEC ND

FIG. 10. Height of region of mixing plotted against flow rates.

529June 1953

own

1 2 3 4 5

G. G. KRETSCHMAR AND H. W. WEDAA

2 3 4 6

FIG. 11. Average width of dark edges plotted against flow rates.

there is a definite, but not a large, lengthening of theregion of mixing with increasing flow rate. Such anincrease is to be expected because of the larger kineticenergy available in the higher jet velocities.

Comparing the photographs of Fig. 9, it will benoticed that those taken at the lower rates of injectionshow a much coarser flow structure than those taken atthe higher rates. The first two, in particular, have a verycoarse-grained striated appearance. Also it will benoted that the darkening at the edge of the flow ismuch sharper in the last four and that the apparentwidth of this darkening seems to be greater. Measure-ments were made of the widths of the dark edges at apoint 4.6 cm above the injector. The widths obtainedare tabulated as follows:

optical axis will then be approximately

(1.50-0.27)/33=0.037 radian.

In the ray diagram of Fig. 8, ray 2 has a deviation of0.02 radian, and ray 3 has a deviation of 0.07 radian.It will therefore be seen that somewhere between ray2 and 3 and closer to 2 there will be a ray which will becritical for obliteration, so that there should be a ratherwide opaque portion on each side next to the glasswalls of the tube. This does, in fact, correspond to theappearance of the tube M in Fig. 4. The unsymmetricalnature of the two sides is easily explained by the lackof centering of the light behind the tube when thephotograph was taken.

EXPERIMENTAL RESULTS

In Fig. 9 is presented a series of spark photographswhich shows the liquids in the process of injection andflow through the mixing tube. The photographs arearranged according to increasing injection rates. Themotion is essentially stopped as the exposure time isonly a few microseconds. It will be noted that there is adefinite area at the lower part of the tube in which theturbulence produced by the jet energy can be plainlyseen and that the upper edge of this area is quitedefinite. We have called this area the region of mixing.There is a slight increase in height of this region ofmixing, as the flow rate is increased. The increase inheight is not marked and is somewhat erratic. However,averaging the measurements on ten films taken ateach flow rate, the data presented in the graph of Fig.10 were obtained.

Since the top of the region of mixing is not sharp, itis necessary to use judgment as to the position of theterminal point. The top is considered to be the pointat which the fuzzy character of the cone disappears,giving way to the fine structure directly above the cone.Tenuous wisps above the main body of the mixingregion were neglected. In the graph it will be seen that

Left dark edgeRight dark edgeFinal averages

1.01 1.15 1.33 1.39 1.35 1.10 1.101.00 1.08 1.15 1.26 1.29 1.46 1.541.00 1.11 1.24 1.32 1.32 1.28 1.32

The values given in the table are in millimeters.They are arranged in order of increasing flow rates.Each number is the average of ten measurements onthe ten different films representing each flow rate. Thefinal averages of the left and right sides are plotted inthe graph of Fig. 11. From this graph it can be seenthat there is a rather uniform increase in the apparentedge darkening for the first three film groups up to themaximum value of 1.32 mm.

The observations lead to the conclusion that themixing is not complete for the slower speeds. There isapparently a minimum flow rate or minimum energy ofinjection necessary for the liquids to mix completely.At the slower speeds, the coarse structure of the flowstream suggests that unmixed portions have combinedagain into larger streamlets above the region of mixing.These streamlets or striations are due to the differentrefractive effects of the different liquid components.Careful examination of some of the photographs willshow an occasional streamer darting out of the mainstream into the edge-darkened region and close enoughto the glass to characterize it as a streamlet of theoxidizer component.

Likewise, the apparently sharper edge of the flowstream in the photographs taken at- the higher flowrates is characteristic of the completely mixed liquids.The smoother structure, together with the sharperflow stream, indicates that at these higher flow ratesthe mixing of the entire stream beyond the initialregion of mixing is essentially complete. From Fig. 11it will be seen that the point of complete mixingcorresponds to a rate of approximately 2 cc per sec.

We are grateful to Dr. C. Tait for suggesting thesestudies of liquid stream mixing. The use of a positivedisplacement equipment was suggested by H. P.Jenkins. E. D. Campbell developed the organic liquidmixtures which were used in the experiments.

530 Vol. 43