STRUCTURE & CALCULATION OF A GAS FLAME

Y.V. Kryzhanovsky

V.N. Kryzhanovsky

STRUCTURE & CALCULATION OF A GAS FLAME

539.91.01

Translated by author from Russian

Kyiv 2012

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539.91.01 24.54 K 85

Kryzhanovsky Y.V. Structure and calculation of a gas flame: monography/ Y.V. Kryzhanovsky, V. N. Kryzhanovsky. – Kyiv, Ukraine, 2012. ISBN 978-966-188-200-2

The basic concepts and constants of gas burning have been defined. The mathematical apparatus for calculation of the characteristics of a gas flame to organize combustion process have been presented. The structure of a gas flame and the structure of a flame front were considered. Independence of structure of a flame front from turbulence was proved. The experimental results which were laid down in the base of phenomenological combustion theory of gases were presented. The book is intended for the researchers and the engineers working on combustion, and can be used as the education guidance.

Yuri Kryzhanovsky 01135, Kyiv, Peremogy ave., 16-34 +380 44 243 04 50 +380 67 465 27 92 [email protected]

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TABLE OF CONTENTS

1. 2. 3. 4. 5. 6. 6.1. 6.2. 7. 8. 9. 9.1. 9.2. 9.3. 9.4. 10. 10.1. 10.2. 11. 12. 12.1. 12.2.

Preface …………………………………………………………………….. Legend …………………………………………………………………….. Definition of a subject of inquiry and its phenomenological properties ….. Laminar flame …………………………………………………………… Turbulent flame ………………………………………………………….. Demonstration of the independence of chemical kinetics and combustion constants on turbulent characteristics at homogenous mixture burning…... Calculation of the thickness of a laminar flame front …………………… Calculation of λn and Un for different initial parameters ………………….. Comparison of the calculated thickness of a flame front with the space characteristics of a flame …………………………………………………. Physical interpretation of a Peclet number for a flame …………………… Calculation of the peak heat density of combustion ……………………… Calculation of length of a turbulent flame and combustion chamber ……. Structure of the laminar flame front ……………………………………… Temperature measurements on the flame front thickness ………………. Measurements of LPR concentrations on the flame front thickness ……… Chemical interpretation of the structure of a laminar front ……………… The general combustion mechanism of hydrocarbons ……………………. Formation of nitrogen oxides in a flame front …………………………… Formation of nitrogen oxides at a stage burning of gas ………………….. Definition of the minimum theoretical NОх concentration ……………….. Stabilization of a flame and the flame-out characteristic ………………… The microdiffusion mechanism of burning ……………………………….. Structure of a microdiffusion flame ………………………………………. Calculation of a microdiffusion flame ……………………………………. References …………………………………………………………………

3 4 5 7 8 9 18 21 23 28 28 30 32 33 39 43 47 49 51 57 59 60 60 65 67

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PREFACE The example of the combustion theory development described in this work is significant from the point of view of the methodological optimization of cognitive processes and the precise carrying over of these methods for the solutions of various applied problems. In this work on the instance of combustion theory the basic technology and algorithm of scientific researches is shown. The interconnection of all fundamental characteristics of combustion process presented by this theory and its practical efficiency is not only above than in existing directions, but also it gives physically adequate picture of the nature of phenomenon and establishes laws, constants and universal interconnections unknown earlier. The mathematical apparatus of the new combustion theory presented here can serve as the manual for making a database for advanced developments with the subsequent comparative analysis. Inconsistency of traditional directions of the theory of physical process and phenomenon is the sufficient reason for carrying out phenomenological controversial theory. Necessity of the development of such theory can be considered as the element of new scientific culture and ethics. In 1964 Kryzhanovsky Vladimir Nikolayevich has initiated the investigations related to the maximization of burning rate in the combustion chambers of gas-turbine engines. Misfit of design techniques and computational methods to test data pointed to the necessity of carrying out additional experiments and revising of basic positions of combustion theory of that time. I express huge gratitude to my father, Kryzhanovsky Vladimir Nikolayevich, for the possibility presented to me to work freely and to think freely about everything that interests me, being assured that my interests have social and spiritual worth.

Yuri Kryzhanovsky

5 LEGEND 1. Measured and non-dimensional quantities: Pe - the Peclet number; Re - the Reynolds criterion; П - the geometrical parameter of mouth of a burner; ε - turbulization level; n - polytrope constant; nCO2 - СО2 concentration; L – the Lewis number; L0 - stoichiometrical coefficient, m3/m3; S - - relative step; α - excess-air coefficient. 2. Process Parameters: U – flame front propagation rate, m/s; λ – a flame front thickness, m; ω - volume intensity of combustion (specific), s-1; V0 - a gas mixture volume flow, m3/with; v0 - Velocity of a gas mixture, km/s; v, - velocity of turbulent pulsations, m3/with; δ - gauge of crushing of moles, m; lт - turbulence gauge.

Physical properties of substances: Т - temperature (of gas mixture), 0C; Тг - combustion temperature (adiabatic), 0C; ρ – density, kg /m3; сp - heat capacity isobaric, kJ/kg K; a - thermal diffusivity, m2/s; D - diffusion coefficient, m2/s; Λ – average free length of molecules, m; v – average velocity of molecules, m/s; Qн - inferior heating value of gas, kJ/m3; Qv - volume heat density of burning kW/m3; J - diffusion current, kg/m2 s; W - volume flow, m3/s. Geometrical sizes: d0 - diameter of a burner, m; β - flame (or jet) expansion angle; DCC - diameter of combustion chamber; V – volume, m3; L – length, m; Subscripts: n - normal; 0 - standard conditions; L - the laminar torch; t - a turbulent torch; f – concerns to a torch; cc - «a cold cone» (flame zone); fr - flame front; cz - combustion zone; LP - limiting combustion product; oz - a outlet zone of combustion chamber; rz - a recirculation zone; c - at combustion; in - internal; ex – external; p - polytropic process.

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1. Definition of the subject of inquiry and its phenomenological properties The object of combustion theory of gases is a gas flame. The flame front is a flame part only. It follows from this that the stabile flame front takes place only in a case when the following conditions are met: the presence of certain concentration pattern of fuel and oxidizer, the presence of stabilization zone of a flame and the exhaust of combustion products. In the beginning we will consider a kinetic flame which diffusion processes of oxidizer and fuel do not influence. It will allow to eliminate the factors not significant from a point of view of chemical and physical kinetics of combustion. In the final chapter a comparison of the optimal diffusion flame from technological point of view termed a microdiffusion flame, with a kinetic flame will be made. So, a kinetic flame (further a flame) has physical fields of different structure located only in certain sequence and existing in unison. A flame consists of three characteristic zones: - flame front; - «a cold cone»; - a stabilization zone or a zone of reverse currents. The stabilization zone or the zone of reverse currents is a flame part in which formation of flame front in the concentration pattern of a gas mixture begins due to combustion products diffusion in this zone. The volume of a stabilization zone is a part of the first two ones simultaneously, therefore for simplification of the further reasoning we will consider flame volume equal to the sum of volumes of "a cold cone» and flame front. To the phenomenological characteristics of stabilization zone we will return after the examination of flame front structure. The flame can be laminar or turbulent. The models of a laminar and a turbulent flame are shown in Fig. 1.1.

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a)

b)

Fig. 1.1. The phenomenological models of laminar (a) and turbulent (b) flames. 1– «a cold cone», 2 – flame front, 3 – a stabilization zone.

The kinetic flame forms under the influence of the next factors. The shape of mouth of a burner determines the form of a stabilization zone in which flame front begins a steady forming. Flame front moves itself orthogonally to the vector of velocity of combustible mixture in direction from a stabilization zone with flame front propagation velocity, U. The flame front has thickness, λ. Flame front spreading in an immobile gas mixture is termed normal front. It can be characterized by normal propagation velocity, Un and by the thickness of normal flame front, λn. Value λn represents the size of a flat reaction wave (on a normal line to it) within which all the physical and chemical transformations of an initial gas mixture begin and finish. Specific volume intensity of combustion in the field of reaction wave can be presented as: ωn = Un / λn, [s-1].

(1.1)

Flame is characterized by the volume, Vf, and the volume intensity of combustion, ωf, i.e. by substance quantity (the volume of combustible mixture) which burns down in flame volume per unit time: ωf = W / Vf = S v0 / Vf , [s-1]

2. Laminar flame

(1.2)

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At laminar current the flow speed, vо, and the geometrical form of a burner does not influence flame front propagation rate, what explains the shape of laminar front quantitatively. The special researches show that flame front thickness in the basic part of length of laminar flame is constant. In the limits of accuracies of measuring, thickness of front does not depend on laminar flow velocity, sizes and the shape of elements of a burner. Thus the following takes place: Un = UL = const , λn = λL = const.

(2.1)

Let us consider phenomenological model of a laminar flame (Fig. 1.1а). Let velocity vо is constant on cross-section of a jet. Then for the flame volume of a circular burner that includes the volumes of “a cold cone” and flame front, it is possible to write down: VfL = VCCL + VfrL,

(2.2)

where for a circular burner with diameter, d0, VCCL = f LCC / 3. The length of “a cold cone” is defined by the converging of flame front that moves with speed Un to the centre of a burner, passing path d0/2. For the same time, flow with velocity v0 will translocate front on distance, LCC = d0 v0 / (2Un). The volume of front, VfrL = FfrL ∙ λn, where flame front square is defined by the standing what through all volume of a gas mixture per unit time the flame front goes with velocity Un, i.e. FfrL = W / Un. As a result for a circular burner it is received: VfL = (d0 + 6λn) W / (6Un).

(2.3)

Taking into account (1.1) for a laminar flame it is obtained: ωfL=6 Un / (d0 + 6λn).

(2.4)

Thus, for the given burner the volume characteristics of intensity of process are function only of chemical-physical properties of mixture.

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Analogously, assuming for a fantail (rectangular) burner VCCL = f LCC/2, it can be obtained: ωfL=4 Un / (d0 + 4λn). For the burner of any shape the relation (2.2) will be written as: ωfL=Π Un / (l + Πλn).

(2.5)

In this formula l and П are geometrical parameters of a burner (l – typical dimension of mouth of a burner; parameter П depends on the shape of a burner; so for a circular burner П = 6, and for a fantail burner П = 4). The view of the denominator demonstrates flame intensity never can exceed combustion rate in flame front what follows from a process phenomenology. For burners of different shapes and with different conditions of stabilization the specific volume combustion rate is defined by the following formulas (Tab. 1).

Tab. 1. The specific volume combustion rate for burners of different shapes and with different conditions of stabilization ωf = 6 Un / (d0 + 6λn) ωf = 6 Un / ((d0 –din)+ 6λn)

Circular burner with peripherical ignition Circular burner with central ignition

ωf = 4 Un / (b + 4λn)

Fantail burner with peripherical ignition

ωf = 2 Un / (b + λn)

Fantail burner with central ignition

ωf = 12 Un / ((d0 –dex)+12λn) ωf = 6 Un / (2r + 6λn)

Circular burner with double-sided ignition Centrally symmetric burner of any shape (peripherical flame holding), r – inradius.

3. Turbulent flame Distinction of a turbulent flame from a laminar flame consists that because of presence in aerodynamic flow pattern of turbulent vortexes and pulsations, flame front ceases to have clear boundaries, and multivector diffusion of front deprives of sense a concept «propagation rate of a turbulent flame front».

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For a turbulent flame it is univocal possible to define its specific volume intensity, using Eq. (1.2). Direct investigations of volume characteristics of a turbulent flame have shown that its volume intensity, ωtf does not depend on flow velocity and turbulence characteristics: ωft = ωfL = ωf = const.

(3.1)

Property (3.1) expels necessity for any speculative models of turbulent combustion at phenomenological level. On the basis of the above-stated it is possible to rewrite Eq. (2.4) for calculation of intensity of a turbulent flame in a view: ωft=Π Un / (l + Πλn).

(3.2)

4. Demonstration of the independence of chemical kinetics and combustion constants on turbulent characteristics at homogenous mixture burning The volumetrical combustion rate in laminar and turbulent flames ωf, being most a general characteristic of the kinetic combustion, does not depend on the flow rate, a flow regime and the turbulence characteristics. The quantity ωf for the given burner is defined by fundamental velocity Un and by characteristic of normal front with the dimensionality of length, λn, the same for burners of any shape and sizes. It will be shown this characteristic is the thickness of a normal flame front is the fundamental characteristic of flame front and the chemicalphysical constant of a combustible mixture, as well as velocity Un. Quantities Un and λn are related among themselves univalently through the phenomenological characteristics of combustion process: 1) the diffusion coefficient of a limiting product of reaction; 2) an adiabatic combustion temperature; 3) the initial parameters of a mixture. That fact that quantity ωft is completely spotted by chemicalphysical constants Un and λn and by the geometrical parameters of a burner l and Π

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and depends on them absolutely in the same way as ωfL, and has allowed to define chemical-physical constants on characteristics of a turbulent flame. From the equations (2.5) that have been written down for flames of two burners of various diameters, we receive relations directly linking Un and λn with ωf: Un = ωf1 ωf2 (d02 - d01)/ 6 (ωf1 – ωf2),

(4.1)

λn = (ωf2 d02 – ωf1 d01)/ 6 (ωf1 – ωf2).

(4.2)

Analogous relations can be received and by comparison of burners of the different shape. But the main sense of the equations (4.1) and (4.2) consists that independence ωf from flow regime means the same for - Un and λn. By definition, Un and λn are the integral expression of chemical-physical properties of a mixture displayed in chemical kinetics of combustion process, in certain sequence and transmutation intensity of substance in normal flame front; it is completely corresponds to their chemical-physical sense. In view of rather great number of interdependent chemical-physical processes in flame front and nonlinearity of their characteristics, it is absolutely impossible to admit that effect of turbulence on detailed chemical kinetics in all cases of a variation of parameters of turbulence is carried out in such a way that as a result we always have integral constants. The single conclusion here can be made: turbulent characteristics do not influence not only chemical-physical constants, but also details of chemical kinetics. It is naturally, that other integrated characteristics of the kinetic combustion should not depend on turbulence characteristics. In the light of this, that fact that flame radiation as the integral characteristic of combustion zone, does not depend on turbulence is absolutely natural. A flame radiates electromagnetic waves of various length and intensity, including visible ones, depending on composition and parameters of molecules and corpuscles in a reaction zone.

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In [1, p. 419] the data on comparison of the light intensity radiated by the laminar and turbulent propane-air flame at equal flow velocities and ratio of mixture is cited. For receiving various flow regimes the diameter of a burner has been changing. By means of a photoelectric cell the light intensity, transiting through a yellow light filter (mainly radiation of С atoms) and blue filter (mainly radiation of СН) was measured. It is revealed that at equal fuel flow rates the radiant intensities of the laminar and turbulent flame coincide. The relation of the light intensity, transiting through a blue or yellow light filter is identical for the laminar and turbulent flame. Thus, in the laminar and turbulent kinetic flames a equal concentrations of molecules and radicals are formed and have the same thermal and radiation characteristics. This fact rather convincingly says that both of flame types at a different macrostructure have equal microcomposition and that the chemical kinetics in both cases is identical. Independence of a Reynolds criterion from an ionic conductivity or strength of current transiting through the flame which has been put in an electric field [2 - 4] is so natural. Here the strength of current, irrespective of a flow regime, is proportional to the flow rate of a mixture of the given composition. In [3] stoichiometrical methane-oxygen mixtures with the different content of nitrogen, for example, were used. As a anode the burner was used, and the cathode represented a water-cooled spiral which had been put round a flame. The experimental results have strictly confirmed proportionality of the strength of current to the mixture flow rate. It means that in unit volume of a flame, irrespective of a flow regime, the same quantity of charged particles occur. Importance of this fact as the demonstration that a flow regime does not influence process kinetics increases because communication between velocities of chemical ionization and combustion is complex and does not represent linear relation from initial conditions, including from α [5].

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Therefore changing of kinetics under the influence of turbulence if it would occur, including the local changes α as it is supposed in [6], would detect at once change of a current of ionization. So, we again confirm that the demonstration of correctness of phenomenological equation (2.5) is at the same time and the most

general demonstration of

independence of chemical kinetics of combustion of homogeneous mixture from aerodynamic and turbulent characteristics of a flow. The effects viewed above are only special cases of the many possible acknowledgments of this standing. The some examples confirming relation ωft = ωfL = ωf = const. In [7] the photos of flames received on the burner with diameter dо = of 2,54 cm (Fig. 4.1) are given. An average flow rate is same - v0 = 2,14 m/s. A gas mixture: the Cambridge urban gas - air with Un = 41,8 cm/s. The calculated value of thickness of the laminar front λn = 1,9 mm (a substantiation of λn on an independent base will be given in the next chapter). Difference in the form of flames is caused by artificial turbulization of the flow the intensity of which has been changing by means of turbulators (the perforated plates) in limits, ε = 2,2-7,12 %. According to equation (2.5) volume intensity of the represented flames: ωft=68,15 s-1, whence it is possible to receive calculated volume of a flame: Vft = 15, 9 cm3 that is close to the average one measured on a photo Vtf (meas.) = 16,2 sm3; the discrepancy makes 1,85 %.

Fig.4.1. Photos of circular turbulent flames by [7]: dо =2,54 cm; Vо=2,14 m/s; turbulent scale l =1,63  1,87 mm; turbulence level: 1 – ε = 2,2%; 2 – 3,02; 3 – 3,8; 4 – 5,15; 5 – 6,05; 6 – 6,35; 7 – 7,12.

On fig. 4.2 the photos of the laminar and turbulent flames are presented at equal flow rates, ratios of mixture and the same diameters of the burners [1]. The measurings show that flame volumes are close one to another and equal in arbitrary units approximately 180.

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Fig. 4.2. A photo of the laminar (a) and turbulent (b) flames¸ taking place at equal flow rates, ratios of mixture and the same diameters of the burners. Let's consider now the data available in the literature about a so-called flat flame. Photos of a flat flame give the square of its cross-section which keeps a constant value on a normal line to a photo. Thus the flame volume is spotted by equation: Vft = Ff (meas) S, where Ff (meas) - the square of a longitudinal section of the flame, being measured on a photo. In Fig. 4.3 the photos of flat flames [8] are presented. Here the square of cross-section of a burner 40 х 40 mm was used. The two lateral walls of the burner had the continuation optical quartz bars with 150 mm altitude; on upper and low wall the auxiliary stabilizing burners have been placed. Apart 55 mm before a burner section were positioned turbulators of a different construction. Experiment was carried out on a gasoil-air mixture at velocity v0 = 33 m/s, Tmix = 440 - 470 K at changing only one parameter - turbulence level in limits ε = 1,7 - 15,0 %. Quantity Un for hydrocarbon-air mixtures with excess-air coefficient near 1,0 can be spotted by relation: Un = Un (0) (Tmix/T0) 1,95.

(4.3)

This relation extrapolate the data well. For Un(0) = 30 cm/s and Tmix = 455К is received Un = 71 cm/s. It corresponds, by the way, to average value of the data on Un in [8 and 9].

Fig. 4.3. Photos of turbulent flames in burner 40х40 mm for the same flow rates and various turbulence levels [8]. Calculated value λn =1,9 mm. Then, according to (2.5), assuming Π = 6; l = 4 cm, we receive ωf = 82 s-1, and flame volume: Vtf (meas) = F0V0 / ωf = 42 3300/82 = 643 cm3.

15 The average measured volume was, Vtf(calc.) = 636m3. The peak diversion Vtf (calc.) from the average value is 5 %, and Vtf (meas.) from Vtf (calc.) - hardly is more 1 %. As we see, coincidence is almost absolute. Let's view the data received on the fantail burner 50,8 х152,4 mm, with unclosed sides [10]. Both cases differ only by the turbulence level which is 7,0 % and 1,55 %. Quantity V0 =9,15 m/s; Un = 40 cm/s. Sectional areas of flames are 165 cm2 and 167 cm2 accordingly, and the same quantity in 1 sm3 the flame volume have on 1 sm of length of the slot. The mixture flow rate on 1 sm of length is equal 915 х 5,08 = 4648 cm3/s, then ωf = 27,8 s-1. The calculated value ωf in this case is defined by equation (2.5) when П = 4, practically coincides with the measured value: ωf = 4 40 / (5,08+4 0,19) = 27, 4 s-1. In the theory of the "superficial" combustion for small-scale turbulence the empirical formulas are received: Ut = β1 (l / λ)0,5 v’Un,

λt = β2 (lλv '/Un) 0,5.

(4.4)

Integrating, for example, on a surface of “a cold cone”, we receive: ωfrt = F-1 ∫∫ Ut / λt dF = (β1 / β 2) Un /λn.

(4.5)

Using (1.2) and assuming that intensity in flame front does not depend on the turbulence characteristics, it is possible to write down: ωf = 1/(1 / ωcc + 1 / ωn).

(4.6)

Using an average integral Ut and λt and on the base (3.1 and 3.2) we obtain: l / Π Un + 1 / ωn = l / Π Ut+1 / ωfrt .

(4.7)

Introducing ωtfr = β ωn we will receive: β = ΠUtUn / (Π UtUn + lωn (Ut - Un)).

(4.8)

Calculations show that for the hydrocarbon fuels with Un = 0,3 - 1,2 m/ s and dо = 0,04 - 0,4 m and vо = 30 m/s β = 0,3 - 0,04, i.e. the quantity ωtfr approximately 10 times less ωn, it is proved by numerous experimental data. In the Longvell reactor [11, 12, 13] at investigations of fuel-air mixtures at standard initial parameters at flow rate equals sound velocity, at completeness of combustion in the reactor η = 1,0 is received Qv = 330∙106 kcal/m3bar∙hour [14]. At increasing of the flow rate to a flame-out the quantity ηсг quickly falls (combustion products contains carbon, CO and even Н2) [15]. Thus, as it is considered, a limiting heat density of combustion for a stoichiometric mixture at atmospheric pressure and Tmix = 400 K is 2,67∙109 kcal/m3bar∙hour. In the viewed investigation as a fuel 2,2,4three-methyl-pentane and heptanes were used. Let's compare the result received above at η = 1 with calculation by our equations. For an explored gas mixture it is possible to take over Un = 0,32 m/s, λn = 0,002m, Н = 3300 kJ/m3. For do=0,00175 m; Π =6 and accordingly with (2.5) and (4.8) is received Qv (meas.) = 4,5∙105 kW/m3. If the factor of usage of reactor volume - 0,9 (as it quantity is appreciated in the literature), for example [16], we have Qv (meas.) = 4,0∙105 kW/m3 or 344∙106 kcal/m3bar∙hour that is close to received in [14]. At use of the jet conical and cylindrical front devices as a model of highly forced combustion chambers [17] with diameter of holes in lateral walls do=4mm at forcing of a cross-section of combustion chamber 120∙106 kcal/m2 the heat density of combustion zone is 3,72∙105 kW/m3 (320∙106 kcal/m3), and calculation for a single jet gives quantity of 3,77∙105 kW/m3 (324∙106 kcal/m3).

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Heat density of combustion in the conical and cylindrical perforated lattices which are used as a jet flame holder is not above, than in planar ones. That is, intersection of equal flames does not influence the sum intensity of process in combustion zone. Thus, intensity of process in Longvell reactor, as well as in other similar devices, is spotted by intensity of process in an individual circular flame with diameter do, as well as in any other case. Intensity of intermixing in reactor volume does not influence process. As it was shown on an example of experimental data [18, 19], the low-frequency pulsations essentially changing aerodynamics of a flame did not influence its volumetrical characteristics. Acoustic vibrations influence aerodynamics of a flow in the same way. With their help it is possible to intensify and to attenuate turbulence development in a flow [20]. Let’s compare macrostructures of the laminar and turbulent flames. Irrespective of flame type we will write down, Vf = Vcc + Vcz ,

(4.9)

where Vcc is flame volume occupied only a combustible mixture; Vcz – combustion process volume. For given burner at a constant flow rate of combustible mixture the value Vf remains constant, while at transition from laminar flow regime to turbulent one the volume ratio Vcc to Vcz is changing. Thus, as it was shown, microcomposition of a flame did not change, but the macrostructure was changing. For the laminar flame of the circular burner in uniform field of velocities a value of each of two parts of total amount of a torch is proportional to velocity v0, and the ratio between them is a constant, VccL/VczL= d0/6λn .

(4.10)

Write down relation for ωf in view, ωf =1/(Vcc/W+ Vcz/W) or:

ωf =1/(1/ωcc+ 1/ωcz).

(4.11) (4.12)

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For the laminar flame takes place: ωccL = W / Vcc = 6Un/d0, ωczL = W / Vcz = Un/λn = ωn.

(4.13) (4.14)

Thus, in a laminar flame the combustion zone volume is a flame front volume. Equation (4.12) we can rewrite in view ωf =1/ (d0/ 6Un + 1/ωn).

(4.15)

Accordingly (2.5) for a turbulent flame the common equation (4.12) and Eq. (4.15) are valid. Let’s rewrite Eq. (4.12) in view ωft =1/(1/ωcct+ 1/ωczt).

(4.16)

ωczt = β ωn.

(4.17)

Introducing that

by analogy with (4.15) we will write down ωft =1/ (d0/ 6Ut + 1/βωn)

(4.18)

Let's view a case of the strong turbulence; here according to [11] velocity of turbulent front is close to velocity of turbulent conduction, i.e. Uт ~ v’. Then on the basis of (2.5), (4.15) and (4.18) we receive d0/ 6Un + 1/ωn ≈ d0/ 6v’ + 1/βωn β = 6v’ Un / (6 v’ Un + d0 ωn (v’-Un)).

(4.19) (4.20)

Thus, a value β and consequently also an average intensity of combustion in volume of a turbulent flame Vcz, in process of increasing W, d0 and turbulence intensity is promptly decreasing. Experimental researches show that intensity of chemical transfomations in a turbulent flame front is much smaller, than in the laminar front. According to the data [21] where reaction rate was appreciated by strength of current of ionization, combustion rate in a turbulent flame was 10 times less, than in the laminar front.

18 In this work the investigations were fulfilled on the burner with diameter d0=0,3m; a gasoil-air mixture was applied; initial temperature Tmix = 240 0С. If Un = 1,0 m/s, λn = 0,0018m then ωn =555s-1. A flow rate was 30 m/s. For a case of natural tubal turbulence ε = 0,05, v ’ = 1,5 m/s. Introducing all data in (4.20), we receive the result matching [21]: β = 0,097.

A laminar flame front is completely occupied by reactant. The transition of a laminar flame into a turbulent one at the same conditions does not change reactant total in a flame otherwise the balance of the quantity of the mixture entering into a flame volume and of the quantity of the mixture burning down in it would be broken. It speaks about retention of the size of the "surface" of a laminar flame front in a turbulent one. As regards the macrostructure of a laminar front in a turbulent one, so in the most cases it is essentially deformed though it does not influence in any way the process of chemical transformations owing to the homogeneity of space and the extremely small effect of macroscopical detrusions of structure in conditions of chemical transformations. The way of reaction does not change even in that case when a normal (laminar) flame front has not time for forming completely. It is easy to show it on a Longvell reactor example. We will use the structure of fluxion received in [22]. For distance between internal and external spheres 0,03m, outlet velocity of an mixture close to 300 m/s and Un = 0,30 m/s on the active section of a jet the thickness of a fragment of a laminar flame front attains value that is almost 100 times less than λn: dλn = dr Un/v0=0,03 0,3/300 = 3 10-5m = 0,03 mm The further combustion process continues in the zone of intensive mixing that prevents making a full-size front. But it does not influence the general characteristic of burning. It proceeds by such a way, that the total intensity of process ωn, and the values Un and λn remain constant (though a structural laminar front is not present here). The introducing of these constants in Eq. (2.5) and for ωft, according to the property of kinetic combustion according to which ωft = ωfL, here again gives true result. Once again we will emphasize that a turbulent flame is such object in which the structural elements of its volume - «a cold cone» and combustion zone - are in

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indissoluble interconnection and the description of a turbulent flame front cannot be fulfilled beyond connection of these characteristics. From a physical point of view, turbulence in such degree can influence the process of kinetic combustion in which the energy of turbulent pulsations is comparable to the enthalpy of a combustible mixture; it practically cannot be revealed.

5. Calculation of the thickness of a laminar flame front So, we will consider flame front as the area that exists between two surfaces on which the chemical reactions and increasing of temperature from initial value Т0 to the peak adiabatic combustion temperature ТC begin (the forward boundary) and finish (the back boundary of front) accordingly. The thickness of normal flame front is more than free length of molecules and radicals, Λ, in combustion zone in some orders; the collision number of one corpuscle for residence time in a front can attain 106 - 107. Whatever a way of the chemical reactions (number of its links is only tens at burning of organic fuel) it is necessary to expect that distributing of reaction products in space, and, hence, the thickness and velocity of a flame front will be essentially spotted by the molecular diffusion laws. Such a method allows to avoid necessity of considering of chemical kinetics of a given mixture connected with intermediate reaction products, length and branching of chains. As Λ > 1 according to Tab. 10.2, NОх concentration is close to 40 mg/m3 also. The revealed ambiguity of dependence on Т0 of peak NOx concentration in a flame front is proved also by the fact described in [66]. At combustion temperature 1600K NOx concentration does not depend on Т0 and an excess-air coefficient. If combustion temperature is increasing above 1600K then NOx concentration is increasing, however, if TC is decreasing below 1600К then NOx concentration is decreasing also. Characteristicly that straight lines NOxmax = f (Т0) at TC = const are intercrossed in point T0 ≈ 0K (a Fig. 10.6). Graphs 4 and 5 on fig. 10.5 are received from [67] for combustion chambers of gas-turbine plants with air preheating in revivifiers and constant temperature in the turbine inlet 650 and 500 0С accordingly. These graphs are a special case of transiting of operating temperature in combustion chamber across 1600K.

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Various character of dependence NOx - Т0 at various combustion temperatures represents as theoretical interest for definition of kinetics of formation NOx at burning and has practical importance. The phenomenology of NO formation at combustion demonstrates that they are formed only within flame front and mechanisms of their formation should be considered together with LPR formation. The explanation of the results received here cannot be carried out on the basis of the thermal theory applied at present.

Fig. 10.6. Dependence of NOx - Tmix at Тc = const. 1 - Тc = 18750C; 2 - 1480; 3 - 1250. The data given in [66], temperature in combustion chamber outlet, t2 = const: 4 - t2 = 650 0С; 5 - 500.

11. Stabilization of a flame and the flame-out characteristic Flame stabilization in a gas mixture flow is a base of all processes of burning. The stabilizing zone of reverse currents (RCZ) represents the same reactor, as well as a flame front. Numerous observations of flames allow to guess that if the relation of an average temperature and size of RCZ less than certain value the flame is not stabilized in a flow and occurs flame-out. Velocity at which there is a flame-out is directly proportional to a size of RCZ. We already know that a flame front comprises of three typical zones. And the temperature in a point A of a front is close to self-ignition point of an intermixture. Thus, it is possible to guess that for flame stabilization a necessary size RCZ should be sufficient for formation of the OA segment of thickness of a flame front. Thus in RCZ the self-ignition temperature will be attained. In other words, RCZ should have such

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size that transiting time across it of a flow of an intermixture with velocity v0 would not less a formation time of a OA segment of a front, moving with velocity Un. I.e. a requirement of stabilization of a flame: LRCZ / v0 > λOA / Un

(11.1)

For calculation of critical values we will rewrite this expression in a view: LRCZmin / v0(fl-out) = λOA / Un

(11.2)

Example. For a stoichiometric methane-air mixture at standard conditions a ОА segment thickness of a normal front is about 0,25 mm, Un = 300 mm/s. For practical calculations RCZ length can be taken over six times more than stabilizer width, bst. Then at bst = 5 mm, LRCZ ≈ 30 mm, v0 (f-out) ≈ 36 m/s. For bst = 15 mm, v0 (f-out) ≈ 108 m/s, and etc. In actual practice at large sizes bst, the flame-out velocity is incremented in comparison with calculated one on 30 - 40 % at approaching of a size of the flow passage to bст at the expense of interacting RCZ of the stabilizer with turbulent flow structure. At normal parameters of stoichiometric mixture СН4 - air the stabilizer with width bst = 30 mm and with a size of the flow passage more than 30 mm provides a steady flame at flow rate close to a sound velocity (Fig. 11.1). Theoretically already this stabilizer (as the calculations with use of the data on ωf demonstrates) at parameters of a mixture of Tmix = 1000К and Pmix = 4 МPa can provide steady burning at flow rate close to M = 20.

Fig. 11.1. Association between flow rate at flame-out and a stabilizer typical dimension. (Methane-air; Рmix = 0,1 МPa; Тmix = 300 K; α = 1.)

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12. The microdiffusion mechanism of burning 12.1. Structure of a microdiffusion flame From calculations it is visible that at normal initial parameters for intermixture СН4-air the heat density of volume of combustion zone Qv makes more than 0,5 х 106 kW/m3. It is approximately at 10-15 times more, than in CC of GTP. With preheating of a gas mixture the value Qv attains 1,7 х 106 kW/m3, and at pressure 4 МПа and at preheating makes already almost 300 х 106 kW/m3. For usage of hydrogen fuel the peak heat density of burning of an intermixture increases almost in 20 times. The value of specific volume heat density, ωn increases approximately so. At solving a task of widening a gamut of a steady burning of diffusion flames, the investigations of dependence on excess-air coefficient of velocity at flame-out have been conducted at various sizes of round and flat stabilizers (Fig. 12.1). In the real airbreathing engine at the same parameters and the same stabilizer sizes the stability of burning essentially drops because of irregularity of concentration ratio of mixture in a stabilization zone and lack of homogeneous mixture.

Fig. 12.1. Flame-out characteristics of a circular (a) and a flat (b) stabilizer. 1 - Dн = 8мм; 2 - 14; 3 - 22; 4 - 32; 1 - аст = 7,5 mm; 2 - 12; 3 - 18.

For achievement of the peak stability of a flame it is necessary to use the flat stabilizers providing optimum concentration of an intermixture in RCZ i.e. optimized by an initial allocation of gas and arranging a microdiffusion flame (Fig. 12.2).

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The arranging of burning of gas in a diffusion flame when a fuel and an air are approaching to a flame front on the one hand and combustion products do not separate gas and air or their areas with various concentration is termed as the microdiffusion combustion mechanism. Formally such schema is analogous to the schema of turbulent burning of homogeneous mixture, but in this case the corpuscles of fuel shattered by a pulsation and air form a cellular structure where the gas or air mole is surrounded by the second component. Here gauge of crushing of moles of gas and air of the same order, as turbulence gauge, i.e. δ ~ lt.

Fig. 12.2. The schema of a microdiffusion flame in a combustion chamber. The turbulent flame front moves on a surface of meshes according to the go-ahead mechanism of transfer of a flame. Extending of process inside of moles occurs with the help of the microdiffusion mechanism. For the first time the analogous schema theoretically has been approximately viewed in [10]. The field of steady burning of a microdiffusion flame is shown in Fig. 12.3. From the received data it is visible that the microdiffusion flame on a small interval from the peak flame-out velocity has wide "platform" of steady burning over the gamut of α changes; this gamut almost 10 times more, than for the kinetic burning.

Fig. 12.3. Fields of stability of a microdiffusion flame on a right-angled collector-stabilizer. (1 bst = 7,5; 2 - 12; 3 - 18).

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The length of a microdiffusion flame for the values of a total excess-air coefficient exceeding a peak excess for a kinetic flame is the same, as at the kinetic flame for α = 1,2-1,5. It is caused by self-similarity of the mechanism of initial allocation of gas in an air flow when local values α around the stabilizer are conserved in the gamut of combustible concentrations and depend on general values α a little. Self-similarity of combustion process is attained by fuel allocation in a flow of an oxidizer by a great quantity of the small jets fed to it at an angle β near to a stabilizer edge. The value α in a recirculation zone behind the stabilizer is thus spotted only by the relative step of holes, S. In the base of calculation S, the depth of penetration of jets in an air flow, taking into account aerodynamic structure of their interacting lie down. For the flat stabilizer, Sflat = αRCZ L0 π / 8 Ks sinβ (ρgas / ρair)0,5 ,

(12.1)

where L0 - stoichiometrical coefficient; Ks - the coefficient which consider the change of a gas concentration on altitude of a jet . Thus, for the slot channels at the given initial parametres of gas and air and αг the uniform initial allocation of gas is provided at the same value Ssl irrespective of values of designed characteristics, including b. At αг = 1 and normal initial parametres of natural gas and air, at angle of feeding 90 о, Кs = 1,55 and L0 =9,45 m3/m3 occurs Ssl = 3,1. Generally coefficient Кs depends on a step between holes a little, but over the range of practical values of a step it is possible to consider it as a stationary value.

Fig. 12.4. Dependence of completeness of combustion on a relative step for a slot channel; fuel - natural gas (СН498 %) and air at normal initial parameters: b = 20mm, l = 14mm; water-cooled combustion chamber 100 х 100 mm, LCC = 600 mm, υair = 15 m/s: 1 - d =1,2 mm; 2 - 2,0; 3 - 3,0; -. boundary of a steady burning.

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Experimental data on completeness of combustion (Fig. 12.4) confirm the received result. The torch is not stabilized by a collecting channel at Ssl 6. If in (12.1) instead of αг we substitute limits of combustible concentrations: upper 0,6 and inferior - 1,9 we will receive: the minimal step Ssl = 1,86, and the maximum step - 5,9. It is agreed with experiment completely. At analogous analytical investigation it is possible to receive the reduced relative step for gas feeding systems with some rows of holes, Ssl(m)= 1/ Σm(1/Si)

(12.2)

Combustion rate at a double-row feeding of gas is always lower than at single-row because of lack of self-similarity of process. But taking into account various demands for combustion chambers besides high combustion rate, such as the supression of nitrogen oxides, the demand to a temperature profile etc., it is rather expedient can occur and usage of multi-row feeding systems. The special value it can have for the combustion chambers of GABP working with cryogenic fuels in field αb