Manner of Liquid 0. L. KOWALKE University of Wimonsin, Madison, Wis.
REINMDS
glass duct in which a thin-metal circular orifice was mounted co-axially. If controlled beams of light slightly wider than the orifice were t1rrow.n from diametrically opposite directions across the orifice, tire observations and the photographs could he made at right angles to the beams. In a cylindrical glass tube tlio pattcrn of tire flow in any region will be symmetrieal on any diameter from the axis to the periphery of the tube. Therefore, the photogrsplrs taken are representative of the conditions throughout that zone. The apparatus shown in Figure 2 WRS found, after many trials, to be the rrrost convenient and productive: The Pyrex glms tubes, 50 mm. (2 inches) nominal diameter, were selected for clearness and shsence of striae, and the ends wore ground perpendicular to tho axis. Unless otherwise stated, the orificeswere of the circular square-edged variety, made from metal sheets ahout 1 mrn. (0.04 inch) thick. The assembly of glass tubes, orifice plate, and connections at the ends for liquid inlet and outlet was hcld together by four tie rods. Tho junctions of the glass tiibcs and the mctal orifice plate werc made liquidhight with deKhotinsky cement. In operation the assembly was laced in the vertical posit.ion to prevent air huhhlcs from the {quid from collecting on inside surfaces of the glass and obscuring the-vision. Ihe liquids uscd were either glycerol (77 per cent), distilled water, or mixtures of the two, depending on tho viscosity desired, and tho temperature rangc was 25" to 30" C. Various solids were suspcnded in the liquids, but none gave the intensity of rdocted light and prescrved the elearnoss in the liquid as did ordinary powdcred slurniniini.
NVMeIII
F I G ~ 1.E COEFFICIENTS OP DISCHARGE FOR CIRCDLAE SQUARE-EDQED ORIFICES
FIGURE 2. ARKANQEMBNTOF APPARATUS
T
HE thin-plate circular orifice, despite certain limitations, is used to measure liquids flowing in a pipe line. The coefficients of discharge of such orifices are dependent on the Reyiiolds number and on the ratio of the diameters of the pipe and orifice. The Reynolds number used in this paper is in consietent units and applies only to the orifice, not to the pipe. In the published data there are diirerences in the magnitudes of the coefficients of diseliarge for given Reynolds numbers, but in general the ooefficients vary as shown in Figure 1. The maximum magnitude of the coefficient of discharge is dependent on the ratio of pipe diameter to orifice diameter. The data of one investigator, for example, show a maximum of 0.9 for R ratio of 1.12, and for a ratio of 10 the maximum is 0.136. The usual metal apparatus used to obtain the data referred to shove does not permit visual inspection of the way the liquid flows, and in general the conclusions are based on pressure manifestations together with volunies delivered. On the other hand, apparatus made of glass would permit visual inspection and the making of photographs. Thus the manner of the floiv could he recorded. Orifice, mm.
Plans, Apparatus, and Procedures The plan comprised the circulation of a clear liquid, having fine solids in suspension, through a cylindrical
visaosity, p"ise
Reynolds No. Exposure, see.
n 8.35
Il.es6 146 1/20
h
d
6.35 0.12
6.35 0.12
780 1/20
1143 1/20
6.35 0 022 2,580 1/2U
FIGURE 3 &Iah-XEROF LIQUIDFLOW DOWNSTREAM WEEN UPWAED
216
FLOW
IS
Flow through a Pipe-Line Orifice
Orifice,, mm.
vin"""y Reynol
""""
B No EXPUBUIB, set.
a
b
3 1s 0 148 231 1/20
6.35 0.84 482 1/20
d 6.85 U.OU7 1280 1/20
G.35
0 .O%us
6050
1/ze
FIOURE4. Vrscons DRAGOF JETDOWNSTREAM FRUM ORIFICE WEENFLOW Is U P W ~ D
Photographic Data The following explanations are given to aid the reader in the interpretation of the photographic prints. The glass tube in all cases was completely filled with flowing liquid before pictures were taken. Thus, the liquid flowing from the upstream portion of the tube through the orifice in the shape of a jet had to push the liquid aside or forward in thedownstream portion. Since the liquid flowed upward the bottom of the print is the upstream region. The metal orifice sheet can be recognized as a white horizontal hand across the print. When the lei= is close to the tube and its diaphragm wide open, the depth of focus is small, hence the front edge of the orifice sheet is blurred; when the lens diaphragm is closed to f.18, the focus is sharper. The top of the print is the downstream region. For those prints whose negatives had '/m-seond exposure, the following interpretation should be made: The aluminum powder in suspension in the liquid reflects the light from the lamps into the camera in such a way that, if the aluminum particle is not moving forward, the image is a hlack dot. If the particle is moving, the image is a streak, the length of the streak being proportional to the rapidity of motion of the particle. For those prints whose .negatives were made by time exposure, the images of all particles are streaks. The prints show the conditions or manner of fiow in three regions-the downstream, the orifice plane, and the upstream.
o n u ground g h s .
The photographic negatives were made on suporsensitive panehrornatio motion pictiirc film 35 mrn. wide; the usual iime of C X I ~ S U T Cwas I r/so second. The negatives on thc 36mm. films
the field on tho prin'ts shbuld be white and the irnagcs of the particles dark, an arrangement which aided tho eye. During this study nearly eight hundred negatives were made of the various conditions of flow, and from these about two hundred Were chosen for making prints. The prints shown here are ouly a small fraction of those which were equally suitable. About 200 feet (60 meters) of motion pictures were also taken on 16-mm. film, which has proved effective as a classroom aid.
Downstream Region Figure 3 shom the forms of the jets of liquid flowing out of the orifice for a range of Reynolds xmmbers from 145 to 2560. The jet in a hores a passage through t.he surrounding 217
I\I)IISTItIAL A\D EUGINEEKIUG CIIE'MISIBY
21s
VOL. 30, NO. 2
h
Orifioe. rnm. Orifioe shape viscaaitp, poiae Vol. dehvered. ml./see. Velocity in orifice. cm./re-ere 1290 and 6O;,D, the behavior in the jet and the surrounding liquid is shown. respectively, in c and d. The jet may bc conceiveil as a combinatiun of a rapidly flowing core enveloped hy sheat,hs of liquid, the outermost slieath moving more slowly than the core. The tenacity of the combination depends largely on the viscosity of the liquid; for large Reynolds numbers the viPcosity is usually Im~.The outermost sheath of the swiftly
shape is definitely shown in Figure 4c; i t is discernible in d by a lighter shade of gray in which, upon elope inspection, the streaks are all oriented parallel to the axis; outside of that region the streaks are oriented in all directions. Thus the combined st.ream of the jet and the liquid dragged in has a conical shape, base downstream, for all the magnitudes of flow used. It was found in another study that, if air laden with smoke %%-ere forced out of an orifice into the atmosphere, the jet had a cylindrical form upon leaving the orifice. The jet of smoke dragged along the surrounding sir and mixed with it so that the combined stream was conical in shape. The photographs of this experiment are most convincing. On the basis of the above evidence i t follows that the region of lowest gage pressure downstream is where the jet begins to drag along liquid from the surroundings; and that the highest, pressure would be found mhere the base of the comhinrd stream is eqrial to the diameter of the pipe.
Downstream Orifice Plane During the preceding tests the flow in the orifice was observed wit11 a imgnifying glas., and it appeared that the diameter of the jet was less than that of the orifice. To test the validity of that opinion the device shown i n Figure 2 for the “Vertical Section at Orifice” was installed. .‘I fine wire was bent to form a right angle. One of these angles was fastened with deKhotinsky cement on each endof a diameter
7
011 INSIDE
(‘E IP
UPWARD
8 . 18
Heynoldx
u
flowing jet drags some of the surrounding liquid along but in turbuIent motion. The sheath next inward is then affected in a similar manner. The turbulence so produced affecte the linear flow of the core so that it, in turn, is forced into turbulence. Thus the original jet and the liquid which was dragged along (all nom in turbulent motion and combined into it single stream) have a conical Bhape. That conical
219
of the orifice, 0,on the downstream face so that the wire, W , projected up about 5 mm. Wires W were then carefully aligned parallel to the axis and coincident with the circumference of the orifice Since the distance between wires was equal to the diameter of the orifice, they served as range wires. If the jet had the same diameter as the orifice, the photograph should show the image of wires Wand that of the jet RF heing
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VOI,. 30, NO. 2
b Oritloe, mm. viacnlty. Reynolds D Exposure, see.
R”’.””
Oriflee, mm. viscositdr.
Reynol s NO Exposure. sea.
14.3 0.0318 235 1/20
d 14.3
0.0083
EO10 1/29
14.3 0.0318 235
Bulb
14.3 0.0083
win
Bulb
in contact; if there were a difference in diameter, the photograph would show a gap between each wire and the jet. Figure 5 records the various manifestations. In all cases the line of vision is perpendicular to the diameter between range wires W. All the oriliccs in these tests had square edges a t both the u p and the downstream faces, but the shapes differed. Figure 5a shows the jet flowing from a circular orifice 6.35 mm. in diameter. It is clear that the diameter of the jet is less than the distance between range wires W-that is, the orifice diameter. Figure 5b is the record of the flow
14.3
0.0083 1716
1/20
E.35
o.onea i3.100 1/20
through an oval-shaped orifice. The oval had two sides parallel, 4.5 mm. apart, and the long axis was 7.0 mm. The range wires were fastened on the parallel sides a t the middle, 4.5 mm. apart. The line of vision was parallel to the long axis. Again the distance across the jet is less than the distance between the range wires. Figure 5c is a record of the size and shape of the jet flowing from a rrctangular orifice 3.18 X 25.4 mm. The range wires were placed on the long (25.4-mm.) axis at the middle, 3.18 mm. apart. The line of vision was parallel to the long axis. The image of the jPt does not fill the space between the range wires.
FEBRUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
A circular orifice was constructed from a metal plate 3.18 mm. thick where the upstream edge of the hole was rounded on a 3.18-mm. radius. Range wires W were installed as on other circular orifices. The photographs of the jets flowing are shown in Figure 6 : a and b are for identical conditions of flow, but b'was a time exposure whereas a was exposed l/20 second. It is noteworthy that the time exposure reveals the jet to be the same size as the l/zo-second exposure. The flow in cis more rapid than in a and b. In every case, however, the distance across the jet is less than that between the wires. There is an interesting approximate equality between the ratio of the square of the distance across the jet to the square of the distance between the range wires and the coefficient of discharge of an orifice; for the square-edged variety it is 0.62, and for the rounded variety, around 0.80. Thus the ratio of the square of the distance across the jet to the square of the dktance between the wires is 0.56 in Figure 5a and 0.64 in Figure 8a, both square-edged orifices; it is 0.84 in Figure 6b, a rounded orifice. It may now be justifiable to direct attention again to the absence of images of moving particles between the range wires and the jets in Figures 5, 6, and 8. If moving particles were present, why was no light reflected from them? Is it probable that in the orifice adjacent to its periphery there is a sheath of liquid that is moving slowly, if a t all? The following experiments give a partial answer to that question: When a 74 to 77 per cent glycerol containing a little finely dispersed air was circulsted through a 3.18-mm. (l/B-inch) orifice a t the rate of 58 ml. (3.54 cubic inches) per second, a rather significant effect was observed. At first very small air bubbles gathered at the upstream edge of the orifice. These grew in size until they projected into the downstream region of the gIass tube, but all the while they clung to the periphery of the orifice. Periodically they would be brushed off and others would develop in their places. In the strong light the bubbles looked like candlelights set around the rim of the orifice. Arrow B points to these bubbles in the lefthand photograph of Figure 7. When the lens was placed as close as possible to the bubbles, the picture at the right was obtained. Since bubbles B are clearly inside the range wires W , they are clinging. to the inside of the orifice. A liquid moving slowly could have elongated the bubbles. But the pressure on the downstream side of the orifice is less than that on the upstream side, and that pressure difference would also elongate the bubbles. A rapidly moving liquid would have brushed the bubbles off e a d y and immediately. On the basis of the above experiments and those following, it is believed that the liquid adjacent to the periphery of the walls of the orifice is moving very slowly.
Upstream Region I n all cases the liquid, upon leaving the straightening tubes, T (Figure 2), flowed in straight lines to the orifice. The liquid in contact with the walls of the glass tube moved more slowly than that in the axis, as may be seen by the dots near the wall and the streaks in the axis in Figures 3b, 4b, and 6c. To get through the orifice, the liquid flowing up near the axis simply passes straight through; when the liquid flowing near the wall of the glass tube approached the orifice plane, it needs to turn inward towards the axis. When the volume of liquid pawing through the orifice and the Reynolds number were small, the liquids near the periphery of the glass tube upon approaching the orifice plane flowed across the angle made by the orifice plane and the glass tube, leaving the liquid in the angle nearly motionless (Figure 4b). On the ot.her hand, when the volume and the Reynolds number were large, the liquid, instead of flowing across the angle, approached closer to the orifice plane, turned more abruptly in-
221
ward towards the axis, and left but little motionless liquid in the angle. Figure 8 shows how the liquid approaches the sharp-edged orifice; a and b represent identical flow conditions, the volumes delivered',being 7.7 ml. per second They differ from each other only in time of exposure. The dot images in a indicate slow motion throughout the upstream region except in the axis close t o the orifice The core entering the orifice is definitely smaller than the jet leaving, which has a diameter nearly equal to the distance between the range wires. The viscous drag of the original core is plaiiily shown. The flow shown in c is 14.3 ml. per second, which corresponds to a Reynolds number of 1716. The core upstream is as large as the jet leaving the orifice. I n the upstream region, close to the orifice plane a t the left side, the streaks in the liquid flowing toward the core are about a9 long as the streaks in the core approaching the orifice. Thus the speeds of the liquids in those two regions are about the same. Figures 8d and e show the manner of flow when the volume delivered is 50 ml. per second. The plates differ from each other only in the time of exposure. I n the upstream region, a t the left side close to the orifice plane shown in d, the streaks in the liquid flowing diagonally toward the core are shorter than the streaks in the core close to the orifice, which means that the flow in the axis or core is faster than that in the diagonal stream. The manner of the flow for a n orifice 6.35 mm. diameter when the volume delivered is 54 ml. per second is shown in f. T h a t volume is nearly the same as the volume delivered in the flow for d. I n f, however, the orifice is only 6.35 mm. in diameter, and hence the linear velocity (ratio of volume delivered to area of orifice) in the orifice is 171 cm. per second, which is over five times as large as that in d. In the upstream region a t the left side near the orifice plane shown in f, the streaks in the liquid flowing diagonally toward the cone are much shorter than the streaks in the core near the orifice. The core is thus moving much faster than the adjoining liquid. The broad white band across the downstream face of the orifice is a shadow thrown by the orifice disk because the center of the lamp filament was below the orifice plane to obtain better illumination of the upstream side. The range wires are in the shadow and are not clearly disccrni ble. For Figures 8d, e, and f the line of vision was purposely shifted to the left of the axis to show as much as possible of the stream flowing from the left to the core. For the short focal distance used, only a limited field could be encompassed on the ground glass and the negative. Therefore the left side of the picture upstream is clearer than the right side. When the liquid flowing upward a t the periphery of the glass tube approaches the orifice plane and turns inward toward the axis, i t is playing an important part in determining the size of the jet that leaves the orifice. Its action is analogous to that of a sphincter muscle placed ahead of the orifice. If the flow corresponds to a Reynolds number less than 300, the core of liquid flowing into the orifice drags along enough adjacent liquid so that the combined volume is equal to the volume entering the glass tube. When the flow corresponds to a Reynolds number in the range 300 to 3000. the liquid a t the periphery of the glass tube, upon being turned inward along to the orifice plane, constricts the core of liquid flowing in the axis. The intensity of the constriction is modified by the ratio of the radii of the pipe to the orifice. If the radius of the pipe is ten times that of the orifice, the liquid from the periphery of the pipe must flow along the orifice plane for quite a distance, and its constricting effect is nearly constant for Reynolds numbers of 300 and over. If the radius of the pipe is only two and a half times that of the orifice, the constricting effect will not be constant until the Reynolds number exceeds 3000.
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When the liquid from the periphery of the glass tube is turned inward to constrict the core flowing in the axis, i t is sheared off and carried along through the orifice to form the jet which escapes into the downstream region. The shearing takes place at the upstream sharp edge of the orifice. The diameter of the sphincter-like ring of constricting liquid after shearing is less than that of the orifice. Thus i t seems certain that immediately adjacent to the periphery of the orifice there is a sheath of liquid moving very slowly and enveloping the rapidly flowing jet. That is the explanation proposed for the absence of images of illuminated particles between range wires W and the jet. When the upstream edge of the orifice is rounded, the constricting stream of liquid is bent into the orifice, and a thicker
VOL. 30. NO. 2
portion is sheared off by the rapidly flowing core. The combined masses of the core and the sheared liquid form a jet whose diameter is nearly that of the orifice. The enveloping sheath of slowly moving liquid adjacent to the peripheral surface of the orifice is thin. Thus the curvature of the upstream approach to the orifice dominates the size of the jet.
Acknowledgment The assistance of several students, particularly G. H. Cook, P. G. Ellis, and D. H. Gordon, in the construction and manipulation of the apparatus and in the making of photographic prints is gratefully acknowledged. RECEIVED August 2, 1937.
Gasoline-Alcohol Blends in \
c
Internal Combustion Engines
Y ONSIDERABLE interest in ethyl alcohol as a motor
fuel has existed in Europe for some time, especially in the countries which have no petroleum resources within their borders. Interest in this country and the Philippines (14) has been stimulated lately for various reasons, such as pessimistic forecasts (5) regarding the future of our petroleum supply and the problem of the recent surplus of farm products, which are a potential source for alcohol. There are also various technical reasons for the interest in alcohol. Ethyl alcohol with a n octane number of about 90 (2) is a desirable fuel from an antiknock standpoint. This octane number is appreciably higher than that of commercial premium motor fuels. S a s h and Howes (IO, Article 419) state that “were it not for this desirable property, alcohol fuels would not possess a single redeeming feature as compared with petrols, with the possible exception of their high latent heat, which, in certain circumstances, has a beneficial effect upon Volumetric efficiency and power output.” Higher apparent or “blending” octane number is observed when small amounts of alcohol are blended with gasoline; but, as the data given here will show, this varies greatly with the base fuel and the amount of alcohol added, approaching the actual octane number as the amount of alcohol is increased. Considerably less energy is liberated either on a weight or a volume basis (36 and 31 per cent, respectively) in the combustion of ethyl alcohol than with gasoline. This is a distinct disadvantage where weight or volume of fuel is important. However, considerably less air (40 per cent) is required for a given weight of alcohol which results in approximately the same energy liberation per standard unit volume of correct air-vapor mixture for each fuel (9). The volatility and vaporization characteristics indicate theoretically lower mixture temperatures with ethyl alcohol than with gaeoline (9) and therefore higher volumetric efficiency and greater power output, which is confirmed experimentally. This indicates the possibility of increases similar but smaller in amount for blends of the two fuels. Based on heating value alone, the value of ethyl alcohol per gallon as a fuel is about two-thirds that of gasoline. Owing to better antiknock characteristics, alcohol can be used in engines with higher compression ratios than can gasoline; this
L. C. LICHTY AND c . W.PHELPS Yale University, New Haven, Conn. tends to put the two fuels on a more nearly equal basis when each is used in a n engine with optimum compression ratio (10, paragraph 421). However, both theory (6’) and experiment (9, 12) show that present “standard” compression ratios would have to be more than doubled when using alcohol, before efficiencies would be reached to offset this difference in energy content per gallon. Also, it is generally believed that compression ratios for spark-ignition automotive engines will not reach a value much above 8 : l before some of the disadvantages of high compression will offset the gain in power and economy. Thus it appears that present compression ratios for spark-ignition automotive engines will not be doubled. Consequently, alcohol may always be a t a disadvantage compared to gasoline as a fuel for internal combustion engine use because of the low heating value of the alcohol, unless it is obtainable a t a lower cost than that of gasoline. Based on present costs, straight ethyl alcohol is a t a disadvantage as a motor fuel. Nevertheless, there has been considerable interest in and discussion of the possible use of small amounts blended with gasoline. The object of the tests reported here was to obtain data on the relative performance of gasoline and gasoline-ethyl alcohol blends as fuels under comparable conditions of internal combustion engine operation, extending the work previously done a t Yale (9)which compared ethyl alcohol and gasoline as separate fuels.
General Procedure Fuels and Apparatus The fuels used were a standard commercial gasoline, and blends of this gasoline with 5 , 10, and 20 per cent (by volume) anhydrous denatured ethyl alcohol. The gasoline, distributed in the New Haven district in June, 1936, was obtained from the stocks of the New Haven distributing plant. This gasoline is a nonleaded fuel with a specific gravity of 0.738 at 60” F. In some of the knock-rating and single-cylinder performance tests, the gasoline was leaded as indicated later.
