“I III; M I l )‘IIW f l 'le’l’fll Hit 1 'l 'l I wl ' W 102 592 THS COMPARISON OF Bflifi‘ECDS USED IN CALCULATING BURNING VELOCITEES OF FLAMES IN LAMINAR FLOW Thesis for degree 9?? M. S. MICHEGAN STATE UN F1” BEST??? C EAR E. BLUMAN THE‘élS This is to certify that the thesis entitled \ rj‘T“ -v *1 | r-\ LL 1 A A. 1' ~All'lu Lu;__) '. ['HJU, 1.1.-.37 .__. A .. _- \A 4H H d _ ' LIV ‘ .1 L41 _.. QF‘ 1‘. ..‘_l--' \ ".4 presented by ,,) "V k. 1,. b 'Ui. C11 L, has been accepted towards fulfillment of the requirements for __;_::_°__ degree in __ .1 . rw- [( ,n Date Wm 2 v 0-169 COMPARISON OF METHODS USED IN CALCULATING BURNING VELOCITIES OF FLAMES IN LAMINAR FLOW By Dean E. Bluman AN ABSTRACT Submitted to the College of Engineering of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1956 / /7 ‘- ‘ K . ‘ -\ /:-/// /3' K/// / Approved j f ':[,54/§?3jic Zzg’ - hi‘i\. / 7 <7 / ,' ‘ f THESlS Dean E. Bluman 1 One of the areas in the field of combustion theory and application which has been extensively investigated is the measurement of burning velocities of combustible mixtures. The burning velocity is the velocity with which a flame front moves normal to its surface through the adjacent unburned gas. It is a fundamental constant of the combustible mixture, and is important both practically, in the stabilization of flames, and theoretically, for theories of flame propogation. This discussion is limited to flames which appear above gases in non-turbulent flow, such as the familiar bunsen burner flame. Elementary considerations of continuum physics are applied in order to examine certain flame characteristics. It is shown that the overhang of the flame at its base and the rounding off of the flame tip effect the local burning velocities. Thus a distinction is drawn between apparent flame velocities and standard burning velocities. The more important of the many methods which have been used to measure flame speeds, such as the soap bubble, right cone, flame angle, total flame area, Dory's, and the particle track methods, are discussed. From a photograph of an actual flame, calculations were made by as many of these methods as was possible, in order to compare the results. It was found that a wide variance of the results occured, which is not always recognized in the literature. Dean E. Bluman 2 The methods which give apparent flame Speeds that most closely approximate the standard burning velocities are those which circumvent the effects of the flame base and tip. Also discussed were the various methods by which the flame front can be located. The direct photograph gives a reasonable approximation by considering the inside boundary of the visable flame, but for more accurate results the schlieren method is recommended. The schlieren method gives the location of the maximum rate of change of density of the mixture as it moves through the flame. This is con- sidered to be the true beginning of the combustion process. COMPARISON OF METHODS USED IN CALCULATING BURNING VELOCITIES OF FLAMES IN LAMINAR FLOW By Dean E. Bluman A THESIS submitted to the College of Engineering of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1956 Approved AC KN Oli’LlVIDGP-iENTS The author wishes to express his sincere appreciation to Professor Ralph M. Rotty for his guidance and encourage- rnent during the preparation of this thesis, and to those Inenmers of the faculty and staff of Michigan State University WEN) have given freely of their time and suggestions toward tflie completion of this work. II. III. V. VI. VII. VIII. IX. TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . THE SOAP BUBBLE TECHNIQUE . . . . . . . ELEMENTARY THEORY OF FLAME STRUCTURE . . GEOMETRIC ANALYSIS OF FLAME SHAPE . . . LOCATING THE FLAME FRONT . . . . . . . . THE CALCULATION OF APPARENT FLAME SPEEDS EXPERIMENTAL EQUIPMENT AND PROCEDURE . . DATA AND CALCULATIONS . . . . . . . . . CONCLUSION . . . . . . . . . . . . . . . LIST OF REFERENCES . . . . . . . . . . . 12 23 27 30 36 38 1+3 1+8 INTRODUCTION In our present highly mechanized society, our main source of power comes from the release of heat energy by the oxidation of hydrocarbon fuels. While it is true that water power is important in some parts of the country, and that the heat released by atomic fission and possibly even fusicni promises to provide more and more energy in the future, the mainstay of our power is the combustion of fossil fuels. Two basic types of heat engines, used to convert heat energy into mechanical power, are recognized by the engineer. The first is the familiar internal combustion engine in which the fuel is burned inside the power-producing machine and the products of combustion are expanded directly to pro- duce mechanical power. In the second type, the heat released by combustion is transferred by means of a heat exchanger in- to the working fluid of a cyclic heat engine, as in a steam power plant. Because of this difference, the problems of combustion chamber design are considerably different, but the broad principles of combustion are in many respects the Same. In this connection, it is obvious from a survey of ‘the literature that the average practicing engineer has little Or no conception of the true nature of combustion processes. From chemistry and physics it is learned that combustion is a process of rapid oxidation, that carbon dioxyde and water vapor are formed, and that heat quantities released can.be found in appropiate tables. Beyond this point, Amer- ican engineering practice dictates the trial and error method of design rather than the application of theoretical principles. In all fairness to the engineers, it should be noted that only a very small portion of flame characteristics ggn_be explained by theory, but in recent years the accent in industry has been toward research on a fundamental level. It is hoped that this trend will carry from the laboratory to the design and development engineering departments. Much information is available in the literature on both theoretical and experimental aspects of combustion, but in every case the reader will encounter repeated reference to major areas as yet unexplored or just barely touched upon. In recent years there have been several organized attempts to further our general fund of knowledge in this field. AGARD, The Advisory Group on Aeronautical Research and Devel- opment, North Atlantic Treaty Organization, annually publishes a book entitled "Combustion Researches and Reviews." The Combustion Institute has held (as of 195A) five international sympoSia on the subject, and the list of contributors and mem- laers composes an outstanding cross section of prominent names 1n.the field. Other private and governmental organizations, such as the U.S. Bureau of Mines, are also making outstanding contributions. As is the general practice in the field of combustion, this paper will use the definitions of terms and symbols as they are used by Lewis and von Elbel, except where they are different from common engineering practice. It is obvious that general problems in combustion are both physical and chemical in nature. Of necessity, the chemistry of combustion is omitted except for very general statements which are required for an understanding of the physical aspects. (The reader is referred to Lewis and von Elbe, Chapters I\through V, for a comprehensive discussion on the chemistry of combustion.) The general term "combustion" is defimd by the layman to refer to a chemical reaction between a "fuel" and oxygen which produces heat and light. Although this definition does not hold in-a few minor cases, it will suffice for our pur- poses here. Some compounds, such as ozone, acetylene, etc., are explosive by themselves, as they possesllarge negative heats of formation. However, there is no fundamental differ- ence between a combustion wave in a single-component explosive gas and a mixture of gases. This paper will be concerned primarily with combustion 'waves or flame fronts under non-turbulent conditions in hydro- carbon and air (or oxygen) mixtures. The difference between 'turbulent and laminar flow with respect to Reynolds number is Imell known, and only flames in laminar flow will be discussed. ‘ 1B. Lewis and G. von Elbe. Combustion, Flames, and Egplo- Sion of Gases. New York: Academic Press Inc., 1951. There seems to be some disagreement among scientists as to the actual mechanism of flame propagation, and many theories have been advanced on the subject. There seems to be general agreement, however, that the reaction proceeds via free radicals. For example, in the n-paraffin group, it is thought that a free radical is formed by the removal of an H atom from the molecule, which is then subject to attack by the addition of 02 to the free C valencez. Thus it is seen that "heat" is only a part of the story in flame propagation. An ignition source is generally a source of heat. How- ever, it is known that ignition sources, such as an electric spark, also create atoms and free radicals which can perpe- trate the reaction. Therefore, a combustion wave is propa- gated by the transfer of heat from the wave to the surround- ing gases, and also by molecular diffusion of free radicals. In this way, heat and diffusion are intenelated since the molecular activity is increased by a higher temperature level. The combustion process occurs as follows: A chemical reaction in the fuel and air mixture is initiated by the flow of heat and/or chain carriers from an ignition source. This reaction zone acts as an ignition source for the ad- joining layer of mixture. Thus, if the proper physical conditions are present, the reaction is a continuous one, and a combustion wave is formed. ‘ 2 Ibid, Page 172 It is necessary to distinguish between a combustion wave and a detonation wave. This can be done by noting that the speed of the combustion wave is small compared with the speed of sound in the explosive medium, while the speed of the detonation wave exceeds that of sound. This is the re- sult of a different type of process which causes the chemi- cal reaction in the highly compressed shock wave region. That is, the mixture is compressed to a high temperature by the shock wave so that the detonation wave can proceed faster than in the normal combustion wave where the increase in tem- perature of the unburned gases is due only to heat transfer and diffusion. Most combustible mixtures will support either type of wave, depending on the physical conditions of the situation, especially confinement and composition. For example, the familiar oxygen-acetylene welding torch main- tains a steady combustion wave when the constituents are in the right proportions, but if the flow is cut back, the flame reaches the "flash~back" point and a detonation wave is formed, as evidenced by the sharp sound produced. How- ever, if the percentage of one or the other of the conStit- uents is increased, or an inert gas is introduced, a dilution point is found where a detonation wave can no longer form. This is called limit pf detonability. Usually a combustion ‘wave can be maintained after this limit is past until further dilution causes the limit pf inflammability to be reached. Generally, a detonation wave is an undesirable phenomenon, and most humanly controlled combustion processes are of the combustion wave variety. Therefore, we will confine our definition of flame velocity to that of combustion waves. At this point it is advisable to make a distinction between true burning velocity and apparent flame velocity. Much confusion exists in the literature due to the varied usuage of terms pertaining to flame velocity. Obviously, flame speed depends primarily on the chemical composition and characteristics of the combustible mixture. However, the same mixture will burn with varying velocities in dif- ferent physical surroundings. This is due to several things, which will be discussed later. It is thus desirable to se- lect and define a "standard" burning velocity which is de- pendent only on the pressure, temperature and chemical composition of the combustible mixture. (Obviously, these should be defined for a numerical value of burning velocity to have any significance, and this has not been done in many-cases.) It is this phase of combustion, that is, the determina- tion of burning velocities of a wide variety of fuels, that a large percentage of the research in the field of combustion has been done.‘ The need for such basic information is readily apparent. It is the purpose of this paper to review the 'various methods by which flame velocities in laminar flow Ihave been measured and to discuss the advantages and disad- ‘vantages of each. As yet, no truly direct method of measuring standard 'burning velocity has been found. This is due partly to the fact that the combustion wave itself gives rise to complex physical manifestations, such as the motion of the unburned gas as it approaches the flame front,and the pressure drop, large or small, which always occurs across the wave front, and partly due to our inability to devise a method whereby the physical surroundings will not affect in any way the reaction process. Therefore, any physical measurement of this type should properly be called an apparent flame speed. Our criterion for judging a particular method of measuring flame velocity will be the degree to which we feel the result approaches the standard burning velocity. THE SOAP BUBBLE TECHNIQUE A large variety of experiments has been tried in an attempt to measure the burning velocities of combuStible mixtures. One of the most unique, and in many reSpects the most direct approach to the problem, is the soap bubble method. This method was devised by F. W. Stevens at the laboratories of the National Advisory Committee on Aeronau- tics. A ring of gold wire is suspended from above, as is a tiny electric Spark gap located in the center of the ring. A combustible mixture is then enclosed inside a soap bubble, the bubble being attached to the gold ring. When a spark is created at the gap, the mixture ignites and expands as a +0 ”GOLD RINO AND BUBBLE C- :3 am F’s—omemm \ 4 / Bangui {en-non 0F .SLlT FOR Tfnme ‘FHOTOGRAPH Fig. 1. Schematic of soap bubble experiment and expanding flame picture 8Pherical combustion wave. The soap bubble offers practically 9 no resistance to the enclosed gas, and so the combustion pro- cess is virtually one of constant pressure. The presence of the wire and the electrodes at the center of the flame causes some deformation at the top and bottom due to the heat sink effect. Also, in slow burning mixtures, there will be some convective rise. However, from high-speed pictures of the actual combustion process it was observed that a narrow horizontal midsection of the flame appeared to be unaffected. Therefore, all but this portion was blacked out and a piece of film was drawn with uniform velocity over the remaining slit and at a right angle to the horizontal. Thus a record of flame expansion with time was recorded. The perfect linearity of this variation is most impressive,as shown in Fig. 1. It gives convincing proof that the velocity of flame propagation is indeed perfectly steady and uniform. (As will be discussed later, this is of prime importance in other Inethods of determining burning velocity. While the most important result of this experiment is 'the positive proof of constant and uniform flame propagation, it has also been used by Stevens and others to measure flame velocities directly. The image left by the advancing flame Ifiront on the moving film starts as a point at the Spark gap arui expands linearly until the gas is consumed. Thus the Side of the picture makes an angle o< with the image of the Spark gap. The magnification factor (m) and the linear film V°14>city (Sf) are known, and the final radius (r2) of the flaune and the angle o< can be read from the photograph. 10 The subscripts u and b refer to the unburned and burned gases, reapectively. The burning velocity of the gas will be hereafter referred to as Su. From simple geometry, the speed of the flame in space (SS) is given by Ss=m5;tfln~“ We can define an expansion ratio (E) at constant pressure - in terms of the radii or the densities. afiflu E=(r. "“""' /9b where (r1) is the radius of the spherical bubble before ignition. The conservation of mass principle can be uti- lized to equate the mass of gas entering the wave with the mass leaving. Su/ou = 55/05 Combining and solving for the burning velocity, 5 1: S‘E‘ : S, -154M0‘_ A 7:" " 5 Thus the burning velocity may be calculated directly from the results of the bubble experiment. The soap bubble method would appear to give an accurate 'Value of the true burning velocity, but there are some compli- ¢3ations which can arise. As was mentioned previously, con- vection effects will cause some error in slow-burning mixtures, 81Hi the bubble-supporting ring and electrodes will absorb some heat. from the reaction. This technique obviously involves Some delicate and sensitive instruments to provide reasonable accuracy, but probably the most serious objection is the effect of the aqueous soap film on the combustible mixture. 11 It was found by subsequent investigators that the partial pressure of H20 vapor rapidly increased in the originally dry combustion gases until it equaled the partial vapor pressure of the atmosphere. This occurred with the use of a mixture of water, glycerine, and soap as the bubble substance. Another serious difficulty under the same con- ditions is the fact that the method is not suitable for use with hydrocarbon fuels, since they rapidly diffuse into and perhaps through the film causing a change in the measured chemical composition of the mixture. Some work is now being done using certain detergents in other solutes than water, but the results are not yet available. 12 ELEMENTARY THEORY OF FLAME STRUCTURE It has been tacitly assumed and then shown by the soap bubble technique that a combustible mixture does have a unique and constant burning velocity. It follows that if the proper amount of gas is flowing toward the flame front there will be a condition, or range of conditions, where the normal velocity of the unburned gas will be equal to the apparent flame velocity and a so-called "standing" combus- tion wave will result. This is a familiar phenomenon to the layman in such devices as gas stoves and furnaces, weld- ing torches, and the like, although in these cases the gas is ‘usually moving with turbulent flow. (The combustion.process in turbulent flow must be analyzed separately and will not lee included here.) Probably the standing combustion wave Inost familiar to the science student is the bunsen burner Iflame. This type flame has been used more than any other Inothod for determining flame speeds. It is most used above a. cylindrical tube where the velocity distribution of the gas is parabolic, but it is also used above nozzles, where time velocity distribution is uniform over the exit section. The other important measuring technique is the flat flame, t“1t 'this sometimes requires special burners, and will be dealt with separately. . . Ivu.k...$Vi1IsIII-.J . All 444% m V _ LP! 13 In any non-turbulent flame the general theory of the structure and stability of combustion waves in gas streams applies. This section of the paper is devoted to a descrip— tion of this theory as it applies to laminar flames. The combustion wave in laminar flow is examined by the use of continuum physics theory; thus the principles of con- servation of mass, momentum, and energy which govern the pro- cesses within the wave are expressed by the three hydrodynamic equations of change: the equation of continuity, the equation of motion, and the equation of conservation of energy. These equations, in conjunction with equations for diffusion and chemical reaction, determine the distribution of various molecules, as well as the changes in mass velocity, pressure and enthalpy throughout the wave. As was mentioned previously, a combustion wave differs from a detonation wave in that its velocity is very much less than the speed of sound in the mix- ‘ture. As shown in hydrodynamics, this implies that there is tassentially no pressure change across the wave front from the Inass acceleration. Thus it is usually assumed permissible to neglect the small effect of the pressure gradient across the “Have, and therefore the equation of motion, which determines ’tlle pressure change, may be ignored in low Mach number combus- tionprocesses. In a somewhat similar manner, other flame Phenomena or characteristics can be largely understood from . elementary considerations of heat conduction and diffusion, or conservation of mass and momentum principles. This will be apparent from the remainder of this section. it, Since the analysis of the inner wave structure is the most difficult part of combustion theory, this treatise will deal only with those problems which are essential to an under- standing of burning velocity measurement theory and which can be explained qualitatively by simple continuum theory. A combustion wave can be thought of as a series of elemen- tal layers of infinitesimal width. The surfaces of such layers may be chosen so that the temperature, or the concentration of some molecular species, or the rate of some process associated with chemical reaction is constant along the surface. If the t? wave does not change its curvature with time, and the gradients across the wave do not vary with time, the wave is said to be in steady state. A fixed reference axis can then be defined, so that the unburned gas flows across the layers. The waves may then be assumed plane-parallel to each other, so that the direction of the mass flow is known, say in the x-direc- tion, and a stream tube is considered through the layers. IMblecular flow in these stream tubes is due not only to a Ixressure gradient, but also by diffusion due to a concentra- tiion gradient of various molecular species. Referring to Ffiig. 2, the subscripts u and b again refer to the unburned 811d burned gases respectively, and the subscript (1) refers tCD the point of inflection in the temperature-versus-distance Cturve. This inflection point is generally considered to be tlles boundary between the preheat and reaction zones. If an element of unburned gas is followed through the tube, it is found that the temperature rises as shown in Fig. 2. In the 15 ‘ Paine" Re ACTION iorvi 2 ONE MA 55 "W 7'; 7'7 7'6 CONCENTRATnoN Tb TANT’ OF REM’ s TEMPEIATUEE 'fl Comewrnn'nou OF CHAIN Cflfllltls T... 3Fig. 2. Scheme of the Propagation and Structure of a combustion wave theory of heat conduction, it is shown that the rate of temper- t ature rise for one dimensional heat flow is given by 0C '37};- , where (X is the coefficient of thermal diffusivity. When this quantity is positive, as from (u) to (l), the element is re- ceiving more heat from the (b) direction than it can reject toward the (u) direction. After it has passed through point (1), the quantity is negative, that is, it is losing more heat than it is getting. The temperature does continue to :Ibid. Page 231. 16 rise, however, because the chemical reaction is still re- leasing heat. Similar arguments can be made for the other two quantities plotted above; in particular, the diffusion , of intermediate products such as atoms and free radicals which may serve as chain carriers in the reaction. However, while the temperature rises asymtotically to a maximum, the chain-carrier concentration may pass through a maximum and decrease toward a value corresponding to the thermal equili- brium between atoms, free radicals, and neutral molecules at the boundary b. This value at temperature b is determined partly by the dissociation of the products of combustion and partly by the diffusion which is taking place along the flow lines. I There are two physical aspects of a conical flame which effect the measurement of the burning velocity. One is the so-called "overhang," or deformation of the flame around the rim of the burner tube, and the other is the rounding off of the flame tip when theoretically, by simple geometrical con- siderations, the tip should be a sharp point. (This will be proven in the following section.) An analysis of these phen- omena are now given in the light of their effect on burning Velocity. Consider the diagram, Fig. 3, which shows a section of the flame and the burner rim (not to scale) and a series of flow lines and isotherms. Heat being transferred from the flame front to the unburned gas causes an eXpansion and therefore a divergence of the flow lines as they leave the 17 uFig. 3. Flow lines and isotherms of a combustion wave near a burner rim burner tube. The solid rim acts as“a heat sink for the flame and as a heat source for the entering gas, but these effects decrease rapidly toward the center of the tube so that for stream tubes toward the middle of the burner the heat evolu- tion of combustion is essentially adiabatic. Adiabatic com- bustion values are properties of those stream tubes which reach the flame front without a gain or loss of heat, and are differentiated by use of the superscript 0. It is seen that T10 and Tbo coincide with T1 and Tb, reSpectively, at some distance away from the burner rim, but as the effects of the rim come into play they separate and eventually T1 and Tb merge to form the edge of the flame. T1 and Tb are the same temperatures referred to in the one-dimensional flow analysis, except that now the conduction equation should be written as l1Time. Page 233. 18 VZT instead of '3';- since we are dealing with three- dimensional flow. . \ The surface defined by the T1 isotherm is considered to be the front of the combustion wave, and is used as the refer- ence surface whose movement relative to the gas stream deter- mines the direction and velocity of the combustion wave. Thus, the direction of the wave coincides with the normal to the sur- face, and the wave velocity is the normal component of the fluid velocity relative to the wave front. /0 and S are introduced to denote the density and the normal component of the mass velocity relative to the wave front. In Fig. L, a stream tube is shown across the wave front which encloses the elemental area dll. S“ \ \_ \ ‘\ i” at \\ -—\ ' \ ”'7'; SURFACE 5Fig. h. Relation between mass velocity and burning velocity glbid. Page 236. nah," ,i . 1-7.“..4 .19 The mass transferred across dy is //24 LKu aber- By the continuity equation, this is equal to /r, :3 d1". To define the wave velocity, we consider an imaginary tube of constant cross-section dll, and assume that the axial compo- nent of mass velocity along this tube is constant, so that /n 5,41, equals fl... 59.41, . The velocity.so defined, Su, is called the burning velocity. If the flow lines remained par- allel in the wave the subtended area would be M E. 462, , substituting and solving for Su, 35:1. 5K=“‘a. uufilm“ If we consider the tube to be extended to the b surface, the tube encloses a volume of the combustion zone equal to dll times zone thickness. Thus if q; is the average rate of heat evolutiog per unit volume, and if we assume dll to be unit area, the heat released in the volume is '7; times thickness. {This must equal the rate of supply of heat of combustion, or (9,0,5... , where Q is defined as the heat of combustion per 11nit mass of fresh gas. 1 times zone thickness 3‘ (9/... 5“ iIQIe quantity if and the zone thickness will both decrease near ‘tlle burner rim.as was shown previously. Since Q andI/g‘ are constant, it follows that the flame velocity must decrease, eunxi ultimately vanish at the point where the T1 and Tb iso- therms merge. This is proof of the statement made earlier in this paper that burning velocity is affected by the physical anI‘I‘oundings, and points up the distinction between "standard" buI'ning velocity, which is a constant, and apparent flame Speed. 20 The region between the flame fringe and the burner rim is usually called the "dead space." Evidently as two sinks, such as opposite sides of a burner, are brought together, the dead spaces will mergeand a "zone of quenching" is formed past which the flame cannot prop gate. The concept of a quenching distance is of practical importance in the design of such things as gas stoves, where the ports are smaller than the critical quenching distance so that the flame cannot flash back to the point of air entrainment. As would be expected, the critical quenching distance is a property of the combustible mixture. Consider now the tip of a conical flame. As shown in Fig. 5, when two plane waves intersect, there is a rounding off of the intersection. Converging heat from both waves causes T1 to be reached in the central stream before the extensions of the T1 lines of each flame meet. T» 7: 7:. “a"... 7: T: 7’» Lewis 6Fig. 5. Curvature of wave layers at the intersection of two combustion waves ‘67 It>1du, Page 237 21 Thus the T1 line and all the other isotherms curve to form a tip approximately as shown. Just as the flame velocity decreased at the burner rim, so it must increase at a point of sharp concave curvature such as the cone tip. In order to define "standard" burning velocity, a sec- tion of a plane wave at a distance from wave interSection or wave edge effects is now examined. The release of the heat of combustion in the wave causes a thermal expansion of the gas which exerts a force on the surrounding gases. However, since all surrounding stream tubes are exerting equal and opposite forces, the only direction the gas can expand is in the normal direction. Thus if the stream tube is inclined against the wave, the normal component of the velocity will increase while the tangential component remains a constant. {This is shown in Fig. 6 (a). 7Fig. 6a. Plane combustion wave inclined against the gas flow. Stream tube and wave layers lIbid. Page 239. III). . “INN“ 22 Plane combustion wave inclined against the Fig. 6b. . gas flow. Velocity vector diagram. Note that the enclosed segments of the wave layers have equal areas. Since the mass flow through any stream tube is a\con- stant, and d1 is a constant, it follows that O 0 #5 Sb 3 fl 5 .flu 5:: 'where the superscript 0 now applies specifically to a plane *wave remote from a heat sink. Suo is called the "standard" lourning velocity. If /5 is the angle between the exit velocity vector and the normal to the surface, alums: and 1/2‘41. caves=:/!5¢Wb Gv‘/3 Tflae tangential components remain constant across the wave and are denoted by Uu sin (X and Ub sinfl . Combining, H- ext» ‘WIlich relates the refraction of the stream to the expansion Of the gases . ~. 6. I...F.)-s~ ‘ 23 GEOMETRIC ANALYSIS OF FLAME SHAPES In general, there is only one shape a laminar flow flame can assume above a cylindrical burner. Consider the segment of a wave as shown in Fig. 7. It is assumed that the combus- -tion wave is represented by a single surface, that the burning velocity is constant over the surface, and that the flow lines retain their velocity and direction from the burner opening up to the flame surface. V'SR 5% “ AV __L‘_“_.. ,l a“ /r J, / / 97/ . / Consume» wave. / W M Fig. 7. Combustion wave above laminar flow The expression for the velocity distribution across a tube in laminar flow is the well-known Poiseuille equation, =.__£LE—- fififi.r‘ OQ* 19x¢vt ( ) .‘whel‘e R‘is the tube radius, r is the distance from the °°nter to the point in question, AP is the pressure drop in distance Ax , and/u. is the viscosity of the fluid.- 2h 4H? is a constant, 9% In fully developed laminar flow, 4' - and can be represented by the letter n. From geometrical a VI. considerations (“3: - 5;)/: _ LEI-(Rt_rx)l.- SJ] , “ii—15': tm O< = 5“ " .5“L When the expression for Uh of Poiseulle's equation is sub- stituted as shown, the equation assumes a form involving 'both the first and second orders of elliptic integrals. The solution to this equation is presented by H. Mache in "Die Physik der Verbrennungserscheinungen." Veit and Co., Leipzig, 1918. The solution, When plotted, gives an outline similar to that shown in Fig. 8. The solid line is the actual flame shape while the dotted line is the calculated shape. 8Fig. 8. Comparison of actual and ideal flame shapes above parabolic velocity distribution v. 8A. G. Gaydon and H. G. Wolfhard: Flames: Their Structure, ‘ggdiation and Temperature. London, England: Chapman and Hall Ltd., 1933, Page 32. 25 The flow through a properly designed nozzle gives essen- tially a constant velocity distribution across the exit area. Thus, in the differential equation above, Ufi, and therefore the entire right side of the equation is a constant. This integrates directly into a linear function, so that ideally the flame front is a right cone. The deviation of the actual from the ideal shape at the tip and base is very similar to that in Fig. 8, for the reasons discussed in the previous section. A Two special aspects of the above discussion are of inter- est. First, the mathematics of the situation produces a plus- or-minus solution to the differential equation. This shows up in the physical picture in that the flame may be anchored at the base in the normal way, or may be inverted by being anchored to a point sink in the center of the stream. The inverted flame has been used only rarely in the measurement of flame velocities, but its possibilities have not been fully explored. The other interesting aspect is the flat flame phen- omenon. Referring again to our differential equation, it is obvious that when the stream.velocity is equal at every point to the flame velocity, the equation reduces to % = o , . which.defines the flat flame. Note that this can appear only when.the gas velocity profile is a constant, since the flame 'velocity was assumed a constant over the entire surface. The flat flame method has the advantage that the flame velocity is equal to the gas velocity, which can be measured or calcu- lated directly. Powling built Special burners which use .3‘1 '3. i ,ll \‘Jlll. 26 grids in a regular burner tube and which result in a uniform velocity profile. This technique for measuring flame veloci- ties seems very well adapted for extremely slow-burning mix- tures, and unsatisfactory for fast burning mixtures. 27 LOCATING THE FLAME FRONT The development of the theory of burning velocity as discussed in Section III defines the burning velocity to be . normal to the T1 surface, which is called the flame front. The question immediately arises as to how this surface can be located or identified in an actual flame. There are three methods in.use at the present time: the direct photograph, the schlieren photograph, and the interferometer photograph. The direct photograph is obviously the easiest and cheapest to use, and gives fairly accurate results. It is, therefore, used most often. It is generally agreed that the flame front lies on the inner surface of luminescence, but this is somewhat hard to define with the human eye. The eye can recognize, however, the region of maximum rate of change in intensity, so this is assumed to be the flame front loca9 tion. "Schliere" is a German word meaning an inhomogeneous region.in.an.otherwise homogeneous matter. Generally, in a tranSparent body, schlieren are anything which cause an ir- regular deflection of light which.emmanates from a relative- 1y small area. They may be caused either by a change in the Irefractive index of the medium or a change in.thickness. A 81mPle example is a plate of poor quality glass. When.a light is Passed through it on to a screen, light and dark regions 28 are observed. It is important to realize that only the dark regions are in a straight line from the glass, since the light refracted away from them is scattered randomly. Toepler's schlieren arrangement is the most basic, al- though several variations are used. Suppose that a small source of light, such as a carbon arc, is half covered by a knife edge. The remaining light passes through a convex- convex lens and is focused on the lens of a recording camera. Another knife edge is placed across half of the camera lens so that when the light is undeformed by the absence of a test object, no light can enter the camera. The insertion of a test object, in this case a flame, between the lens and the camera lens causes certain light rays to deflect and enter the camera. If the two knife edges are rotated through 90°, a complete record of the schliere is obtained. The litera- ture is full of more complete discussions of schlieren tech- niques, so it will be omitted here. The important considera- tion is that the rate of change of density of the gases across a combustion wave is a maximum at the T1 surface so it is generally agreed upon by observers that the darkest schliere in the flame represents the true flame front as nearly as we can observe it. It has been shown that this schliere lies Just inside the surface as defined by the direct photograph. Thus only a small error is introduced by use of the direct Photograph, but for extremely accurate results, a schlieren a'pparatus should be used. 29 The one other important method is the interferometer, a device familiar to the science student. It is more expen- sive and more complicated than a schlieren set-up, but enables more quantitative results to be obtained. It enables the re- fractive index to be determined, whereas the schlieren method gives primarily the gradient of the refractive index. The . refractive index can be related by theory to the temperature of the flame, but has no more significance in the determina- tion of burning velocities than does the schlieren, so further discussion of it is omitted here. 30 'THE CALCULATION OF APPARENT FLAME SPEEDS A. Flames Above a Gas Stream with Parabolic Velocity Distribution Consider a flame front as shown in Fig. 9. Z.“ 5a H E Fig. 9. Flame shape and velocity vector diagram It is assumed that the flame speed is a constant over the sur- face, that the density is constant until it reaches the flame front, and that the flow lines are undeflected. The basic 'premise in the area (or Gouy's) method is the conservation of mass flow. Thus if A0 is the area of the burner mouth and U6 is the average gas velocity across the mouth, their 3product must be equal to the area of the flame front, Af: Imultiplied by the normal component of the velocity which we have previously defined as Sn. Ii 31 The A0 and U0 terms are readily measurable, and the area of the flame front can be calculated in several different manners, as discussed below. I 1. Right Cone Assume the flame is in the shape of a right cone, of base-radius equal to the radius, R, of the burner, and of height equal to the measured height, h, of the actual cone. Thus, from geometry, A; =‘W' R IR“? “" ‘ 2. Angle Method Referring again to Fig. 9, it can be shown that under the assumptions used in number 1, the following relation can be developed. .5“ Md: “0 5‘3u0d’V‘“ Thus the cone half-angle can be measured instead of the cone height. This should give the same results as the calculation ‘by method number 1 if the same cone is used. More accurate results will be obtained if the angle between the two relative- ly straight sides of the actual cone is used. 3. Actual Area Method The actual area of the flame may be closely approximated 'by a planimeter measurement. Consider Fig. 10. The flame is divided into sections of equal height as shown. The surface area of the section AF is 71'$(Y.+al where s is the distance AF, \ assumed to be a straight line. The area AFGC .- ., A 0*. gm). If 0‘ is the cone half-angle at this point, 5- l4/44““) 32 and therefore area AFGC =3": 5“““0’H’il Assume that the section is taken small enough-so that 0< is constant from r1 to r2. Then a new area, DHGC, can be defined where HG = 5?: and DC =Z.‘5:-‘ . The area DHGC equals 45k (K/ma + RA...) equals 1": 5(V.+V.,) . Thus multiplying the plane area DHGC by 2T? givesthe flame area around AF. If we determine the area DEBC with a planimeter, we obtain the sum 2": 5n("n*"’n+.). E? E3 CORREc‘TI’D Fume FRONT —-Ac'rum. Fum! FRONT G. H ” ,5 w 04‘ ,. 33‘ 9Fig. 10. Calculation of flame front area If this is multiplied by 21? we have the surface area of the flame front, Ar. This method is more accurate than number one because it takes into account the true shape of the flame. However, the velocity is still assumed constant over the area, which, as has been shown, will introduce some error. 9Ibid. Page 56. 31.1w. , .T 33 A. Dery's Method Dery's method neglects the base and the tip and assumes that there is a frustrum of a right cone between these two locations. The lateral surface area is given by 14;}: 7T5 (r, +Y.) where r1 and r2 represent the radii at the bottom and top surfaces of the frustrum, respectively, and s represents the lateral height. The volume rate of flow is now ’fl’(KF—K3)i:;~3. combining, 5... AK: 77" (V-h V3) 5(- . 7T(YJ+Y.,)(V:‘Vt-)a .— m 5“ 77's (v.+r.,) 5“ = (VI-V1.) (7/5 The radii and the lateral height can easily be measured from a photograph. Since the effects of the tip and the base are bypassed, this method would appear to give an apparent flame lvelocity closer to the standard burning velocity than the first three methods mentioned. It is also probable that the. effects of the curvature of the flow lines are cancelled out 'between.the two radii. 5.' Particle Track Method The particle track method was utilized by Lewis and von lithe to measure burning velocities and also the paths of flow liunes through the flame. They used a rectangular burner, and irrtroduced M80 particles into the combustible mixture. By ilgluminating the particles intermittently from the side, the Inausticle tracks could be followed, and the velocity could be measured at any point as a function of lengths of the path recorded while the light was on (or off) for a known length Bit of time. Figure ll shows a plot from their data of velocity versus distance r from the center of the burner. The impor- tant result here is the verification of the theory that the 0 56 '- vi 48 ‘ I <3 I 40‘ u I 5‘ 32. '- ‘: -3 ,4 2.4- u a > \S 3 16 1 3 3 8‘ Q 0 T r , f A j y Y' in CM. 0 o.” 0.16 0.1.4 0.3!. 0.04 Fig. 11. Relation between flame velocity and distance from center of burner .flame speed increases at the flame tip, decreases at the base to zero, and is virtually constant over the rest of the flame front. , Their burner had a width of only 0.755 cm, and this, In: doubt, eXplains the small ratio of constant burning velocity lures to the total area. A.possible weakness of the method is tune effect of the M80 particles on the velocity. Lewis and von Elbe report an su of 2133 by the particle track method and of Zaa‘lfi. 10 by the area method which is not a large dif- ference considering the inherent inaccuracies of both methods. lckiigh Speed Aerodynamics and Jet Propulsion Institute. r&1 sical Measurements in‘Gas Qynamics and Combustion. liriliceton, New firsey: Princeton University Press. lQSh. pages 1419,1420 ‘ 35 B. Flame Above a Gas Stream with Uniform Velocity Distribution The methods described in the previous section can all be applied to flames above a nozzle. It is expected that the results will be more accurate since a uniform velocity distri- bution was assumed but not realized. The one additional meth- od which can be used is to adjust the flow so that a flat flame is formed. In this case Uh equals Su directly. IL"... hex _ ._ 36 EXPERIMENTAL EQUIPMENT AND PROCEDURE An experiment was set up in the laboratory as is shown in Plate 1. Air from a 15 psig line and natural gas from a commercial line were metered separately in Precision Wet Test Meters after passing through pressure regulating tanks. The two flows were then mixed in a small cylindrical can and passed up a cylindrical brass burner tube of 9/16 inches inside diameter and 5/8 inches outside diameter. The tube length was about twenty inches which is more than sufficient to insure fully developed laminar flow at Reynolds numbers below the critical value of 2000. To completely eliminate diffusion burning, which is evidenced by the outer cone of faint luninescence, the burning should have taken.place in an evacuated container, but this was not feasible consider- ing the time available. An Exacta camera with bellows exten- sion attached was used to make a photograph of the stable flame. (See Plate 2). It was found that a slightly rich mixture was required in order to obtain a stable flame. (Stoichiometric mixture for natural gas is approximately 10% 'by volume.) This was probably due to the diffusion burning nwntioned above in which oxygen from the surrounding air dif- fuses toward the flame and reacts with the unburned gas. The .following data were taken: volume rates of flow of air and gas, the pressure and temperature of the air and gas, and a ;>icture of the stable flame (f2, 1/25 sec.). 37 Plate 1. Laboratory Equipment for Premixed Laminar Flow A. Gas mixing tank with.vertical burner tube. B. Precision Wet Test Meter for natural gas. C. Stop watch D. Precision Wet Test Meter for air. E. Gas and air flow-control valves. 38 DATA AND CALCULATIONS Rate of Flow of Air - 2.13 x 10-3 ftB/sec Pressure of Air - 1.2 in.H20 Temperature of Air - 82°F Rate of Flow of Gas - 0.33 x 10'3 ft3/sec Pressure of Gas - 0.1 in.H20 Temperature of Gas - 83°F The first step in the calculation is to find the average velocity, U o’ of the gas as it leaves the burner rim. The volume rate of flow divided by the area of the burner exit gives the average velocity. The volume of a gas is inversely proportional to its absolute pressure. Thus the volume of the air and gas will not change appreciably in flowing from.meter to the flame, and can be assumed constant. vtotal = vair‘t vgas = (2.13 + 0.33) x 10-3 ft3/sec :=2.k6 x 10-3 ft3/sec 3 3 - __ v 2.46461 A“.XIU - ‘t u“ A 1r(o.o«/7)'-/4 I '2’) /""“ As a check on the value of Reynolds number, assumed that the kinematic viscosity 7 is that of air at 80°F. R :- ‘ZD = [042-5 #/$A‘ $3.047 # q I -7 A7atur5 ftfiauc. == 3’ 3 which is much less than the critical value of 2000, and lami- nar flow is thus assured. 39 The picture of the flame shown on Plate 2 was printed with a magnification factor of five, so that all dimensions taken from the picture must be divided by that amount. Naturally, area measurements will be divided by 25. In order to calculate the flame speed by method number one outlined in the previous section, it is necessary to ob- tain the cone height and diameter from Plate 2. The height 7.4m of the cone is found to be h.S/S inches and the base dia- meter is 3/5 inches. Thus the lateral cone area is A+ = 7T RJR'—""'t+m = n- (.e)JI_.3)r.(,.,.-' 'fl’(.3)Juvs :8 = 0.5:: ha" And the apparent flame speed is SK .2 A. J. = Vw A! 3+ 1.46 nus“3 #3/A—ué‘ 0.58: A9» LIES,— ,_ ‘ I'M-{w = o. 605 147“. By method number two, the actual cone half-angle measures 1h.5° considering the long and relatively straight portion of the cone. .5... : a.“ a = Ina/25 (0,141,) = 0.345ft/414. IBy method number three the planimetered area was 3.h inches, so the actual flame area would be 11:3 a. o. 355' («3. .See Fig. 120 _ V -; I 5”,: #3 7"‘“””° KH- o.4/‘/-+f’/m,. 44+- o.'L:: - ' I». '5‘, a . 1‘1} , '9'. _.‘~ 'c' Plate 2. Enlarged Photograph of Bunsen Flame with Superimposed Calculation Lines *Acrvnl. F C LAM! ease: 11's “WT PLAN! Fnon‘r D /A/ c I S . , Actual area DEBC II 3.14. inches, by planimeter. Ln be By method number four, the sector of the cone was chosen as indicated in red on Plate 2, such that r1: 1/5 inch, r2 = .25/5 inches, and s=3.l/5 inches. Thus - _:____. s .. 5a: (L-VSHU- = 2%:“4‘”: 4.3451474“. Since the particle track method requires considerable special equipment which was unavailable, this method of measuring flame velocity could not be used experimentally to compare with the others. #3 CONCLUSION The experiment described in this paper was designed primarily to point out the differences in calculated flame velocity values using the different methods commonly en- countered in the literature, and not specifically to deter- mine an actual flame velocity for the mixture involved. The discrepencies obtained above are exactly what one encounters in a survey of the literature. For example, one investigator might measure flame velocity by the right-cone method and describe his answer as "burning velocity." Another investi- gator, using the same mixture, might calculate his answer by Dery's method and conscientiously label it an "apparent" flame velocity. The latter method probably gives an answer ' which is closer to the "standard" burning velocity, and yet the reader is led to believe that just the opposite is true. This is particularly true of the literature published in the pre-war years, when the present terminology had not been 'universally agreed upon. From the considerations discussed in the section on the 'bheory of flame structure, it is apparent that DerY's method should yield an apparent flame velocity almost equal to the - standard burning velocity, with the actual cone angle method Immuning a close second. From the calculations shown here, it3'would appear that both methods are equally accurate. In uh (v - . - fact, when the equation of Dery's method, 51.: ‘—L1;;)an , is examined, it is seen that illgrs) is nothing more than sin 0< of the angle method. However, it is more accurate to measure the three lengths of Dery's method than cx . For example, a one degree error in-measuring 0‘ produces a 7% error in Su. The right cone method should be used only for a comparison of relative burning velocities of different com- positions, and even then its use seems hard to justify con- sidering the ease of calculation of Dery's method. The actual flame area method is probably more reliable than the right cone method, but the plotting of the corrected flame front is certainly more laborious than Dery's method, and the results are not as meaningful. The inaccuracies of the right cone and total area methods result primarily from the inclusion of the tip and the base areas, in Which the flame velocity varies as indicated previously in Fig. 11. The assumption made for all of the above calculations that an average velocity could be assumed across the burner port will introduce some error in the results. This assump- ‘tion can be realized in practice by the use of a nozzle in- stead of a cylindrical tube as a burner. The only difficulty encountered is the increased danger of an explosion due to :flsshpback, but with a reasonable amount of care this danger can be minimized. The nozzle is therefore recommended over the straight burner tube‘for the most accurate results. A general consideration pertaining to conical flames is tflne burner diameter. The larger the diameter, the smaller 1+5 will be the percentage effect of the tip and the base. The size of the burner is limited by the change from laminar to turbulent flow. Here again the nozzle has the advantage in that larger flows can be obtained without turbulence. The particle track method could not be compared directly with flame speeds as calculated here. Experience of a variety of investigators indicates, however, that the method is an accurate one. The results are probably on the small side of. the standard burning velocity because the mass of the particles is large compared to the mass of the molecules of the react- ing gases. Thus an inertia lag of the particles is to be ex- pected across the flame front. This reemphasizes the need for care in selecting the particles to be used. They should be as small as possible and still be visible, but not small enough to have random motion. In stating the measured burning velocity of a mixture, special care should be taken to state the fuel-air or fuel- oxygen ratio, since the burning velocity is very much a ;function of this parameter. Thus for natural gas the maxi- inum burning velocity occurs in a mixture very close to the stoichiometric mixture which.is about 10% gas by volume, and falls to zero at the upper and lower limits of inflammabil- :ity, which are about 15% and 5% gas by volume,respectively. The maximum flame velocity for natural gas is about 1 ft/sec. 131 the experiment recorded in this paper, the fuel-air ratio was 13.5% by volume, so the order: of magnitude of the reported results seem reasonable. is It was stated early in the paper that the pressure and temperature of the unburned gas should be reported along with a value of burning velocity. The reason for this will now be discussed. Without exception, the burning velocity of a given mixture will increase with the temperature of the‘entering re- actants, but not nearly as rapidly as the well-known exponen- tial relation between chemical reaction rate and temperature. This points out that while the rate of chemical reaction has some effect on the burning velocity, it is not the only effect. Rather, the effect of the initial temperature in producing a moderate increase in Su indicates the importance of the trans- fer of matter and energy from the flame to the adjacent un- burned gas by virtue of molecular motion. The effect of the pressure on burning velocity is not nearly as well under- stood. In fact, a decrease in pressure will increase Su in some substances and decrease it in others. One important consideration is the effect of pressure on flame thickness. Low pressures tend to increase the thickness of the flame, ‘which has been assumed a surface in Space. Thus some exper- imental error is introduced. One final consideration is the flat flame technique. .An inverted flame can be stabilized above a nozzle by a annall wire located above and in the axis of the nozzle. A ciecrease in the flow rate will cause the cone angle to in- crease until the flame is flat. F‘urther decrease in the IfLow'rate can cause the flame to move downstream and stabil- ize itself somewhere‘between the nozzle and the wire. Such in a flame will often remain stable in this position even if the wire is removed. This points out the importance of extremely small forces which may be thought of in terms of pressure, thrust, or change in momentum which have been assumed negli- gible throughout this paper and throughout most of the liter- ature. (See Section III.) - In conclusion, most authorities agree that with the best of the methods described here (that is, the Dery's and cone methods) standard burning velocities can be measured within 10% of their true value. The need at present in this field of combustion is not for a new and more accurate measuring technique, but for a more complete understanding of the true nature of the combustion process, particularly in the quanti- tative sense. #8 LIST OF REFERENCES The Advisory Group for Aeronautical Research and Develop- ment, North Atlantic Treaty Organization. Combustion Researches and Reviews - 1955. London, England: Butterworths Scientific Publications, 1955, 187 pp. Combustion Handbogk. Cleveland, Ohio: The North American Mfg. Co., 1952, 321 pp. The Combustion Institute. Fifth Symposium (International) 0n Combustion. New York: RSInhold Publishing Corporation, 1955, 802 pp. Gaydon, A. G. and H. c. Wolfhard. Flames: Thgir Structure, Radiation and Temperature. London, England: Chapman and Hall Ltd., 1953, 3&0 pp. High Speed Aerodynamics and Jet Propulsion Institute. Physical Measurements in Gas Dynamics and Cogbustion. grinceton, New Jersey: Princeton University Press, 195k, 77 pp. Lewis, B. and G. von Elbe. Combustion, Flames, and Explosion of Gases. New York: Academic Press Inc., 1951. 795 pp. Zeldovich, Y. B. Theory of Flame Propogation. Translated from the Russian by Z. P. Khimi. National Advisory Committee for Aeronautics: Technical Memorandum #1282. Washington, D.C. June, 1951, 39 pp. MICHIGAN STATE UNIVERSI Y Imui llilifl'iilllil'es 12 O