September 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
CSto at,least C ~ Othe ; n-paraffins of highest molecular weight are found in heavy lubricating stocks or in the crude wax obtained therefrom by conventional methods. Such waxes contain large percentages of high melting hydrocarbons other than normal and slightly branched paraffins, so that extractive crystallization pi ovides a means of selectively recovering the latter types. Production of low pour point distillate fuels is readily accomplished by extractive crystallization. This can be done in conjunction with the n-paraffin production described. Thus extraction of n-paraffins from light and heavy stove oils, which are also typical Diesel fuel components, reduced pour point from original values of - 5 " and +25" F. to -85Oand -80" F., respectively. A reaction temperature of 70" F. or below, in a light stove oil,(was found satisfactory for the production of a residue of pour point below -100' F. A substantial amount of n-paraffins may remain in the residue, especially a t higher reaction temperatures, but these consist predominantly of the lowest boiling n-paraffins present in the feed, which have the least effect on pour point. With heavy stove oil a reaction temperature of 65' F. was used in the listed run in order to obtain nearly complete removal of n-paraffins, since it was desired to achieve the ultimate pour point possible with this heavy stock. Octane number improvement of gasoline stocks can be obtained by extractive crystallization. Thus in the naphtha shown in Table I1 removal of 8% n-paraffins raised the octane number by 11 to 12 units. Extractive crystallization may be used as an alternative to solvent extraction for cetane number improvement of distillate fuels. Straight-chain hydrocarbons can be extracted from low quality straight run or cracked intermediates and used as an ingredient of the finished fuel. For this application an extract of high purity is not required. Recovery of straight-chain olefins from cracked stocks is a particularly interesting application, as there are many chemical uses for such olefins. For example, a 328' t o 672' F. A.S.T.M.
boiling range, thermally cracked distillate containing 15% straight-chain hydrocarbons gave a 15% yield of extract containing 96% straight-chain hydrocarbons and rich in straightchain olefins. CONCLUSION
Extractive crystallization Las unique advantages in several practical applications. The process has undergone extensive development on pilot plant scale so that its practical operability is ensured, and a commercial plant could be designed. Extractive crystallization constitutes a new and unique separation tool added to those available to the petroleum and chemical industries. In view of the widely varying potential applications, this process should find a place in future petroleum and chemical technology. ACKNOWLEDGMENT
The help and cooperation of A. L. Johnson, S. York, R. E. Melrose, J. L. Maloney, and R. W. Barnes are particularly acknowledged. LITERATURE CITED (1) Angla, B., Ann. Chim., 4, 639-98 (1949). (2) Bengen, F., U. S. Tech. Oil Mission, Reel 6, p. 263 [Ger. Patent Application 0.2.12438 (March 18, 1940)l. (3) Bengen, F., and Schlenk, W., Jr., Experientia, V/5,200 (1949). (4) Fetterly, L., U. S. Patent 2,499,820 (March 7, 1950). (5) Redlich, O., Gable, C. M., Beason, L. R. and Millar, R. W., J . Am. Chem. SOC..72.4161 (1950). (6) Redlich, O., Gable, 'C. 'M., Dunlop, A. K., and Millar, R. W., Ibid., 72, 4153 (1950). (7) Zimmerschiedl W. J., Dinerstein, R. A., Weitkamp, A. W., and Marschner, R. F., Ibid., 71, 2947 (1950): IND. ENC).CHEM..42, 1300 (1950). (8) Schlenk, W., Jr., Ann., 565, 2 0 4 4 0 (1949). (9) Smith, A. E., J. Chem. Phys., 18, 150 (1950). RECEIVED October 16, 19.50.
Blowoff of Flames from Short Burner Ports CHANNING W. WILSON
2129
AND
Enginnyring pOCeSS
development
NORVAL J. HAWKINS
CONSOLIDATED GAS, ELECTRIC LIGHT AND POWER CO. OF BALTIMORE, BALTIMORE 3, MD.
Among the factors having important influence on the performance of gas appliance burners, the form of the burner ports, and the character of fluid flow through them, have received least attention. Means for quantitative evaluation of their influence has not been available. An analytical expression ,is here developed, through application of the concept of a ('critical boundary velocity gradient" at the limits of the stable flame region, which may be used to correlate the occurrence of blowoff on burners having short cylindrical ports. The ports studied experimentally approximate closely in size and shape those found in many domestic gas appliance burners. The validity of the expression has been confirmed with two fuel gases, for several nort sizes, at flow rates in the viscous region.
Through this method of approach, especially by extension to include other port forms, a clearer understanding of this element of burner design and performance may be reached.
G
AS appliances provided for consumers in different parts of the country must be designed and adjusted so that they will give safe and satisfactory performance, when supplied with the type of fuel gas locally available. The fuel gases available in different localities may have widely different properties. The chemical composition, calorific value, density, and the distribution pressure of gas in a given community will depend on the relative availability of the necessary raw materials and other economic factors, and in one community the properties of the fuel may
2130
INDUSTRIAL AND ENGINEERING CHEMISTRY
be subject to variation because of seasonal fluctuations in the demand for the product. Burners of contemporary appliances differ as to their adaptability to a gas supply of varying composition, once adjusted to operate properly on a given gas. Thereafter, frequent readjustment of the burners cannot be contemplated, and variations in composition of the fuel gas supplied, from that with which the burner was initially adjusted, must be accommodated by those elements of design incorporated in the burner and appliance which contribute to “flexibility” of operation.
Vol. 43, No. 9
burner and fuel gas, stable flames occur within a range of variation of rate of fuel input and air-fuel mixture composition, limited on the one hand by the occurrence of “blowoff” and on the other by “flashback.” The range of operation permitted by them limits is different for fuel gases of different chemical composition, and for burners having different types and sizes of ports. The influence of burner port form on flame stability has not heretofore been well understood or extensively studied, and there has been possible for this reason, among others, no satisfactory general correlation between burner performance and fuel gas composition. As a result, it has been necessary to assemble a large amount of empirical information to describe the performance of many different types of fuel gases with a wide variety of burners (2,8). Lewis and Von Elbe (4) recognized the influence of fluid flow through the burner a t the limits of the stable flame region, and were able to describe this influence analytically for the case in which laminar flow occurs in long tubular burners, in which parabolic distribution of gas velocity across the tube exists. Blowoff occurs, for example, when the slope of the gas velocity distribution curve a t the burner tube wall exceeds a critical value. This “critical gradient” for blowoff is a function of the composition of the fuel gas-air mixture, for a given fuel gas, and does not depend on the burner tube dimensions. A different function is obtained when the chemical nature of the fuel gas itself is changed, so that curves of critical gradient against proportions of air and gas may be drawn which are characteristic of each fuel gas. In the usual appliance burners the flow of combustible mixture cannot be described by the parabolic distribution expression. It is a fact that, in practical applications, burner ratings recommended by the American Gas Association (I) correspond t o conditions in which the prevailing Reynolds number is less than the critical value for laminar flow. However, burner ports are not sufficiently long to permit the full development of parabolic velocity distribution. If the idea of the critical gradient a t blowoff can be applied to such burner ports, it will be necessary to describe the velocity distribution in the gas jet as it issues from the port. This investigation was undertaken for the purpose of extending the application of the hypothesis of Lewis and Von Elbe to forms of burner ports more nearly approximating the size and shape of those found in domestic gas appliance burners, in order to indicate a method of approach to a quantitative understanding of some elements of burner design on the performance charncteristics of the burner. DERIVATION OF VELOCITY GRADIENT A T THE TUBE WALL
The analytical expression derived by Lewis and Von Elbe for the velocity gradient a t the tube wall, when parabolic distribution of gas flow velocity exists is Figure 1. Velocity Distribution across Jet at Port Outlet ( A ) and Cross Section of Port ( B )
The fuel gas industry has for many years recognized that within a given community the range of variation of the fuel properties, which may be accommodated by the appliances to which the gas is supplied, is limited. The problem of determining these limits has been widely studied by individual utilities, the American Gas Association, and other agencies, and is commonly identified as that of “interchangeability of gases.”, The factors influencing burner performance and the development of improved burner design which will provide greater adaptability to variations in fuel gas composition, have been of special interest. The most important limitations of the flexibility of operation of burners used in contemporary gas appliances are imposed by the conditions necessary for the production of stable flames. Some of these conditions reflect elements of the burner design and adjustment, others the properties of the fuel gas supplied, and still others the environment in which the burner is used. For a given
Flow through short cylindrical ports is similar to the flow in the entrance section of a tube, in the region where the development of Poiseuille parabolic distribution of velocities is taking place. I t may be assumed that the fluid enters the port with a velocity that is uniform over the cross section of the port, except for a vanishingly thin layer next to the wall. A8 the fluid flows through the port, the layers of fluid nearest the wall are slowed down by friction, while the central core of the stream is simultaneously accelerated. At any cross-sectional plane downstream from the en‘trance,it may be assumed that a central circular region of uniform velocity exists, and from the boundary of this region outward toward the wall thevelocity decreases until it becomes zero,following a parabola whose vertex lies on the circumference of the constant velocity region. Figure 1illustrates diagrammatically a short cylindrical burner port. The axis of the port is in the plane of the diagram, and the direction of gas flow is indicated by the arrow. The entrance to
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
September 1951
the port is rounded 80 that no jet cont,raction will occur, and the linear gas velocity across the fluid stream will be uniform. The length of the port, u, is measured from the point of tangency of the rounded entrance to theport outlet. The average linear velocity a t any cross section is zc, and is equal to the velocity a t the entrance port. The maximum linear velocity, u, a t any cross s e c t i ~ n is that of the central core of the stream. The value of u is constant in the radial direction from the tube axis to the point r6. The velocity decreases between rg and the tube wall where T = R. This region between r6 and R is referred to as the boundary layer, and within it the gae velocity at any location, rZ,is denoted by u,. A t r , = r a , u c = u a n d a t r , = R,u,=O
(2)
The thickness of the boundary layer is 6 = (R-rs). In the boundary layer the velocity profile will be a parabola having the equation
The slope, or gradient, a t any point within the boundary layer may be found by differentiating Equation 3 with respect to T. dui -dr
u 6
= 2 3 (Ti
- 7-81
(4)
At the wall of the cylinder, ri = R, and the limiting value of Equation 4 at the wall is
The continuity condition requires that the volume of gas passing any crosa section of the fluid stream in unit time remain constant. Therefore, the volume of a cylinder having a cross-sectional area equal to that of the port and a length equal to the linear velocity a t the entrance must be equal to that of the solid of revolution formed by rotating the velocity profile a t any cross section downstream, about the port axis. Therefore, 4
R% = 3- Ru6
- 56- U P + u ( R - S)z
From this equation the thickness of the boundary layer, 6, is found t o be
(7)
Tlw :ivc~r;igc.linear gas velocity
2131 =
V / r R e ; hence
This repi,eaciits the limiting value of the gradient of the gas velocity profile at the tube wall, and may be compared with Equation 1 derived by Lewis and Von Elbe for the Poiseuille distribution \ V h c n 17 = 1-that is, when the value of the maximum velocity is t \rice the average velocity, characteristic of the Poiseuille dist,ribution--a(T) = 2. Thus, Equation 1 is the limiting form of Equation 11 when the port is sufficiently long for the full development of the parabolic distribution to take place. The method of quantitative evaluation of 7 at increasing distances from the port entrance is that developed by Schiller ( 7 ) for flow a t the ent,rance region of a tube. By considering three forces acting a t any cross section of the stream perpendicular to the direct,ion of flow Schiller derived an equation expressing the equilibrium between them. The bhree forces are an accelerative force due to the pressure drop, a fcrce due to the change in momentum (arising from the change in velocify profile with distance from the entrance), and the frictional force a t the wall. The accelerative force, P , in the direction of flow, may be evaluated by the Bernoulli equation because of the practically frictionless b e havior of the central core of the stream. The p r w u r e difference across the port, (PO- p ) , is related to the increaw in velocity of the central core, and
The second force, in the direction of flow, is that due to the change in momentum as the velocity distribution changes from a constant value across the cross section a t the port entrance to the form existing a t the plane of the port outlet. This force is
where the first integral represents the change in momentum of the central core, and the second integral that of the boundary layer. The value for ui in the boundary layer, given by Equation 3,must be substituted in Equation 13 before integration can be carried out, whereupon it is found that
F = zpua (R2
- 23 R
+ -16 2 ) - rpu2 ( R 2 - 15 14 R6 + 6
Substituting this value of 6 in Equation 5 there is obtained
15 (14)
The sum of the two forces is
If 7 is defined as the relative increase in velocity of the central core of fluid over the average velocity, it may be written = -u - ? i Q
Inserting I) into Equation 8 it becomes
Then, eliminating 8 by Equation 6
(F
2 + P ) = rR2p [: u2 + 12 ti* - !5 u?i + u ( 6 uti - 2uZ))'/a] 15 (16)
Letting
The third force in equilibrium, which acts in the direction o p posite to that of flow, is the frictional force a t the wall. This is obtained from Newton's law of friction stating that the #hear stress a t the wall is
Equation 9 becomes
The total force at the circumference of a cross section of tho fluid stream is therefore
INDUSTRIAL AND ENGINEERING CHEMISTRY
2132
The equation representing the equilibrium of the three forces states that
Vol. 43, No. 9
sponding values of y / R N as recalculated from Schiller's data ( 7 ) are tabulated below. Values of v / R N for Different Values of r)
0.1 0.2 0.3
or, upon substituting the value of us from Equation 3, remembering that the influence of friction applies only to the velocity in the boundary layer d
-(F dY
+ P ) = 4rRg-
U
47rpu
=
r)
U RN
0.4
0.5 0.6 0.7
0.8 0.85
(18)
0.9
0.95
By substituting for (F
1.0
+ P)from Equation 15
In order to apply the data in the preceding tabulation to experimental observations, the simplest procedure is t o calculate values of 9 ( q ) corresponding to the same selected values of q. Then for a selected value for relative port length, y/R, correspnding values of Reynolds number and 9 (7)can be determined and plotted as a curve. This has been done for a series of relative port lengths, from 2 to 10 radii, and the family of curves in Figure 2
By transforming and simplifying 6,000
4,OOC
4,000
Integrating bFtween the beginning of the tube, y = 0, and any point in the tube, a t which the maximum velocity is u-i.e., between the two boundaries Q and u-gives
'y .
.
-
ti
arc sin
5
166
- (6u2i
5u
2,000
P [L arc sin (T)] 4~ - 62i 3 d2 1,000
4 - 2u2)1/2+ (6u2i 15
- 2u2)1/2)11= y li
(21)
d
f
or
BOO 600
400
200
Transforming to the variable q
IO0
Figure 2. Coefficient at Different Reynolds Numbers for Short Cylindrical Burner Ports with Rounded Entrances
But 2R7i/v = N , the Reynolds number (based on the diameter). Using this number, and setting the terms within the brackets equal to f(~),the following equation is obtained
g = 81 ( N )
M7)l
(24)
This is a relation between the relative dimensions of a short cylindrical port and the relative gas velocity increase in the central core of the stream. For assumed values of q the corre-
were obtained. The appropriate value of q~ (7) to be used for calculating, by means of Equation 11, the critical velocity gradient a t blowoff in a given experiment can be determined easily with this graph. The Reynolds number is of course calculated from the observed total rate of flow, V , a t blowoff. APPARATUS AND EXPERIMENTAL PROCEDURE
For experimental determination of the blowoff limits of ethylene-air and propaneair flames, the general arran ement of apparatus was similar to that used by Lewis and Von E l k ( 4 )and others (6, 9). Individual fuel gases and air were admitted, through appropriate needle valves and calibrated capillary flowmeters, to a mlxing chamber. This was constructed of brass and had a volume of approximately 500 ml. Burner ports were attached to the outlet of the mixing chamber with suitable gas-
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1951
tight fittings. The mounting was such that the flames were vertical and upright. TUBULAR BURNERS. For purposes of comparison, it was first necessary to determine the curves of critical gradient a t blowoff, characteristic of each of the two fuel gases used, with tubular burners. These burner tubes covered a range of diameters approximately the same as that of the short burner ports. In this manner, comparable ranges of critical gradient and Reynolds number were covered by the two types of burners. The lengths of all tubular burners were a t least 100 times the diameter, in order that the full development of the parabolic velocity distribution would be assured. I n these determinations, as well as in those subsequently made with short ports, the Reynolds number was less than the critical value for laminar flow.
2133
PROCEDURE.The procedure followed in conducting the experiments was to adjust the fuel rate to a predetermined value by adjusting the deflection of the fuel flowmeter. Primary air was admitted to the burner, and its rate, as shown by the deflection on the air flowmeter, was adjusted by the needle valve. h small pilot flame was brought near the rim of the burner port, and it was observed that either a stable flame resulted or the blowoff limit was exceeded. I n the former case, the flame was extinguished, the rate of air flow increased, sufficient time allowed for mixing, arid another test made with the pilot flame. These steps were continued until an air flow rate was reached a t which the flame failed to remain stable on the burner. If the flow rate exceeded the blowoff limit, the air flow rate was reduced stepwise until a stable flame resulted. By careful adjustment of the air rate a condition was obtained when the flame would just fail to remain stable when the pilot light was brought near the burner rim. This is the blowoff limit. The fuel and air rates a t this point were recorded, and the room temperature and barometric pressure noted. The fuel rate was then changed and the operation repeated. iVith the determination of the port diameter, measured with calibrated microscope scale, sufficient data are available to calculate the limiting gas velocity gradient a t blowoff. EXPERIMENTAL D A T A
+DI-
BLOWOFF WITH TUBULAR BURNERS. The results of the determinations of critical gradient a t blowoff made with the tubular burners are shown in Figure 4 when plot,tcd against the corresponding fuel-air mixture composition. A curve characteristic of each fuel gas was obtained, similar in form to t’hose which have been published for other fuel gases ( 4 , 6 , 8 , 9 ) . Points representing individual blowoff determinations are omitted from these curves, but the reproducibility of the determinations was equally as good as that reported by other investigations.
Figure 3. Design of Experimental Burner Ports Diameter, -Relative Lengths, v / R , Radii2 4 6 10 Inches Height of Ports, Inches
CONSTRUCTION OF SHORTBURNERPORTS.The burner ports used were constructed of brass, in the general form illustrated in Figure 3. They consisted substantially of relatively short cylinders. The outlet ends of the ports where the flame occurred were circular and in a plane perpendicular to the axis of the port, The entrance ends had a rounded profile with a carefully made and gaged radius of curvature of 1/8 inch (0.32 cm.). The port length used later in calculations is that of the straight or cylindrical portion only. The ports fitted a recess in the top of the mixing chamber and were clamped between gaskets with a retaining ring. Four port diameters were studied: l/g, 3 / 1 ~ , I / d J and 6 / 1 ~ inch (0.318, 0.496, 0.635, and 0.794 cm.), respectively. Four sets of ports were constructed having the diameters listed above, and having relative lengths of 2, 4, 6, and 10 radii. FUELGASES. Ethylene of anesthetic grade was obtained in tanks. Propane, technical grade, was obtained from the Phillips Petroleum Co. in cylinders. The rate of flow of either of these fuel gases was controlled by a constant head overflow and a needle valve. The constancy of the fuel gases with regard to their blowoff behavior was checked from time to time. The propane was not pure, but contained small quantities of other hydrocarbons, and because of this, the composition of propane issuing from the tank tended t o change slightly as the contents of the tank were used. By the frequent checking of the blowoff with tubular burners, however, it was established that significant changes did not occur during the test reported here.
l,OOOh
I
4
1 8ERCEPIT
I
I FUEL
lo
I 12
I
Figure 4. Critical Gradient at Blowoff of Ethylene-Air and Propane-Air Flames on Tubular Burners
BLOWOFF WITH SHORT CYLINDRICAL PORTS.Representative data obtained in experiments with ethylene-air flames on the short cylindrical ports are plotted in Figure 5, where each point plotted corresponds to a blowoff determination. The distinguishing symbols each represent the data for a series of ports having different diameters but of equal relative length. The solid curve drawn is that obtained with the tubular burners, shown in Figure 4,not simply the “best” curve through the plotted points.
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
2134
Corresponding data for blowoff of propane-air flames, using the ports having relative lengths 4 and 10 radii, are illustrated in Figure 6. Again, the solid curve represents the data of Figure 4 obtained with tubular burners. DISCUSSION
It is apparent from examination of the data represented by Figures 5 and 6 that, with only a few exceptions, the individual points representing the critical gradient a t blowoff for the short cylindrical ports, calculated from observed rates of flow and the coefficient characterizing the Reynolds number and relative port
M
44000
Vol. 43, No. 9
tude of the contraction, as is well known from studies of orifice discharge coefficients. Considerable care was exercised in eliminating irregularities in the entrance surface and, although possible contributions from this source to the discrepancies cannot be ignored, it is believed that any resulting contraction or turbulence is of minor significance. If there is uncertainty about the location of the point of tangency with the cylindrical section, the value of the relative port length, required for estimation of the coefficient &), would be in doubt. The latter effect would result in the greatest uncertainty in data obtained with the shortest ports, as was in fact observed. However, reference to the curves in Figure 2 indicates that under the conditions prevailing in those experiments when the discrepancies were noted, an uncertainty of 0.03 cm. in the port length would result in an error of only about 5% in the value of p(v) selected. This will account for approximately half the magnitude of the discrepanices. The observed divergence may, however, indicate a limit to the applicability of the theoretically derived expression. If, for example, the assumed “vanishingly thin layer next to the wall” at the port entrance has a thickness comparable with that of the parabolic boundary layer developed in this very short port length, the use of the calculated value of the’coefficient ~ ( 7 would ) be expected to give incorrect values for the velocity gradient a t the port wall. It is estimated, for example, that with ports having a relative length of 2 radii, the parabolic boundary layer will have a thickness of about 0.03 cm. when the Reynolds number is of the order of 800. This is about 10% of the diameter of the ‘/B-inch 40.0 0 4.4
I
I
I
Figure 5. Critical Gradient at Blowoff of Ethylene-Air Flames on Short Cylindrical Ports length, are in good agreement with the critical gradient curvei determined with tubular burners. It may be concluded, therefore, that the suggested hypothesis is a satisfactory description of the velocity profile across the burner port and that the expressions derived for estimating the slope of the distribution curve near the wall are valid’over the range of variation of experimental conditions covered. Some of the data obtained with ethylene-air flames, especially with ports of the smaller diameters and relative port length of 2, diverged somewhat from the blowoff curves established with tubular burners. The reason for this divergence may be in the curvature of the port inlet. It is difficult to construct and gage with accuracy this rounded portion of the l/e and */Isinch diameter ports. The effect of such an inaccurately formed inlet might be twofold: (a) it could influence the velocity profile at the beginning of the cylmdricsl section, and (6) it could result in uncertainty as to the port length. Since one of the assumptions, on which the derivation of the expression for the velocity profile is based, is that the velocity a t the beginning of the cylindrical section is everywhere uniform, it is clear that any departure from smooth entrance curvature which would cause a contraction of the jet or otherwise introduce turbulence or nonuniform flow, would result in inaccurate data. The extreme case of a square-edged entrance would clearly result in jet contraction. However, even small radii of curvature a t the entrance greatly reduce the magni-
Figure 6. Critical Gradient at Blowoff of Propane-Air Flames on Short Cylindrical Burner Ports
port. Thus, if the vanishingly thin layer next to the wall had a thickness no greater than 1% of the port diameter it would already be significant in comparison with the parabolic boundary layer with which the theory is here concerned. It is believed that the contribution from this source to the divergence of the few observations noted is the most significant. However, the relative importance of the three possibilities is being investigated further. Although all experiments were carried out with single burner ports, it is not anticipated that the results obtained would be significantly different if multiport burners were used, provided
September 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
the porta were sufficiently separated so that the combustion producta from one do not approach and interfere with the flame at others. Lewis and Von Elbe (4) demonstrated that with natural gas flames on tubular burners the critical gradient at blowoff was influenced by the surrounding atmosphere and was lower at a given fuel-air composition when an atmosphere of carbon dioxide surrounded the flame. Similar results were observed in studies made at the American Gas Association Testing Laboratories on appliance burners (1). Results of that study indicated that the spacing between ports influenced the rate of flow at which blowoff occurred. When the ports were close together, blowoff occurred a t lower rates of flow. Adequate spacing of drilled ports to minimize this mutual influence of adjacent flames on the blowoff tendency is a recognized requirement in the design and manufacture of contemporary. burners, and has not been observed to be a severe restriction. However, the influence of thesurrounding atmosphere is important for application to a p pliance burners and may well bear independent investigation. Observations of h a s h back with the short’cylindrical ports have not yet been made. Preliminary considerations indicate that flash back will occur, with the ports used in this investigation] only at rates of flow 80 small that the applicability of Equation 11 is uncertain. For example, Nikuradse (6) has shown that Schiller’s calculation of the velocity profile does not agree with the experiment when y / R N exceeds a value of approximately 0.025. This would correspond, for a relative port length of 4, to a minimum Reynolds number of 160. Flash back will not occur with propane-air or with methane-air flames, in the ports which have been used, under these conditions. Fuel gases having greater burning velocities, such as hydrogen, acetylene, or possibly ethylene, may be suitable for testing the applicability of Equation 11.
all data obtained for the different ports with a given fuel fall on a single curve. This curve corresponds with that obtained with tubular burners, determined by the procedure of Lewis and Von Elbe. Some limitations to the application of the theoretically derived equation a r e examined and discussed. Those of importance refer to divergence of experimental data on blowoff from expected values when very short ports are used, and to the application a t very small rates of flow to hash back. NOMENCLATURE
F
= force due to change in momentum in the fluid stream as
g
=
N
=
P p
= =
r
=.
rs
=
u
=
ui
=
6
=
V y 6
SUMMARY
Blowoff of ethylene-air and propane-air flames from short cylindrical burner ports has been studied experimentally for Reynolds numbers less than the critical value for laminar flow. The port sizes varied from I/lg to 1/16 inch in diameter, and the relative port length from 2 to 10 radii. The port entrances were rounded with a radius of curvature of l / ~inch. The composition of the fuel-air mixture was varied, and the total rate of Bow a t which blowoff occwred was measured at the different proportions of fuel and air fer the different pcrts studied. An expression has been derived theoretically, by means of which the slope of the velocity distribution profile a t the port wall may be estimated. This expression is
where p ( q ) is a variable coefficient whose value depends on the Reynolds number. It is shown that ‘p (7)can be evaluated by a procedure developed by Schiller for expressing the velocity distribution in a fluid stream near the entrance of a tube. The experimental data obtained with the different ports can be correlated by eatimating the gradient of the velocity distribution at the port rim when blowoff occurred. When this critical velocity gradient is plotted against the composition of the fuel-air mixture
2135
11
= =
the velocity profile changes limiting value of the gradient, a t the port wall, of the
(- $)
velocity distribution profile, = Reynolds number, using the port diameter a8 the charac2Ra teristic length, = Y accelerative force, = s R * ( p - p o ) pressure a t port outlet pressure a t port entrance radius of cylindrical burner port distance along a. radius, from the port axis toward the port wall distance from the port axis of the interior surface of the boundary layer maximum linear velocity of flow within the fluid stream flowing through the port; the linear velocity a t the port axis linear velocity a t any point, i, in a cross section of the stream, a t a distance ri from the port axis average linear velocity of flow of the fluid stream flowing
v
through the port, = *RZ = volumetric rate of flow of fluid through the port = length of the port = thickness of the boundary layer, = ( R - T ~ ) =: relative increase in velocity of the central core of the u-?i
~(7= ) P
=
p p
= =
T
=
fluid stream over the average velocity, = __ 6 a function of 7,defined by Equation 10 kinematic viscosity of the air-fuel mixture, = e P fluid density coefficient of viscosity of the fluid flowing through the oort shearing stress a t the port wall, E
($3
LITERATURE CITED
(1) Am. Gas Assoc. Testing Laboratories, Bull. 10 (March 1940). (2) ZM.,36 (February 1946). (3) Am. Gas Assoc. Testing Laboratories, Research R e p t . 1106 (1949). (4) Lewis and Von Elbe, J. Chem. Phys., 11, 75 (1943).
(5) Prandtl-Tietjens, ”Applied Hydro- and Aeromechanics,” pp. 25-27, New York, hIcGraw-Hill Book Co.,1934. (6) Reiter and Wright, IND. ENG.CHEbf.. 42,691 (1950). (7) Schiller,Forschungsarb. V.D.I., 248, pp. 5-36 (1922). (8) “Third Symposium on Combustion, Flame, and Explosion Phenomena,” sect. on “Flame Stabilization and Quenching,”
Baltimore, Williams and Wilkins Co., 1949. (9) Von Elbe and Mentser, J. Chem. Phys., 13,89 (1945).
December 13, 1950. Presented before the Division of Gas and Fuel Chemistry at the 118th Meeting of the A h f E m c A l u CREMICAE SOCIETY Chicago, Ill. RECErVED
* * * * * Five papers will be presented at the Symposium on Flame Studies in Relation to Interchangeability of Fuel Gases before the Division of Gas and Fuel Chemistry at the 120th Meeting of the AMERICAN CHEMICAL SOCIETY, New York, N . Y . The Division of Gas and Fuel Chemistry and the Division of Physical and Inorganic Chemistry are cosponsoring the Symposium on Theoretical Aspects of Combustion and Gasification of Solid Fuels, in which fifteen papers will be presented.
