SPECIFIC FEATURES OF IGNITION AND FLAMEHOLDING OF HYDROCARBON FUELS IN HIGH-SPEED FLOW

The paper describes the results of experimental investigations of a supersonic combustion chamber with solid and discrete cavities at the entrance Mach numbers of 3 and 3.5. Kerosene and propane were used as fuel. The conditions required for self-ignition and intense combustion of the fuels were determined. The possibility of e©cient combustion in a supersonic §ow was demonstrated. Analysis of applicability of existing criteria predicting the conditions of self-ignition and extinction of combustion has been performed based on the experimental results obtained.


INTRODUCTION
Scramjet engine is one of the candidates for hypersonic §ight propulsion system, which will be used in a wide range of §ight Mach numbers from 4 to 12 or higher.Therefore, it should be well operated in dual-mode and scramjet mode depending on the §ight Mach number [1].Originally, a lot of studies were performed for hydrogen-fuelled concepts of a supersonic combustion chamber, primarily for space transportation systems.In this case, the upper speed limit lies in the range of Mach numbers 1216 [2,3].There were also studies on hydrocarbon-fuelled scramjets with the upper speed limit on §ight Mach number established in the Mach range of 810 [4].In either case, the §ow velocity at the entrance of combustor can achieve a Mach number of 45.Liquid hydrocarbons are attractive solutions for the hypersonic §ight in view of their high volumetric energy content, lower cost, and relative simplicity of operational utilization.The di©culties of the use of hydrocarbon fuels as compared with gaseous systems are caused by the longer residence times required for vaporization, mixing, and completion of chemical reactions [57].In general, the key elements for successful operation

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of a liquid hydrocarbon-fuelled combustion chambers include deeper fuel spray penetration into air §ow for better mixing, generation of smaller liquid droplets for faster evaporation, and e¨ective §ame holding mechanisms with minimal drag.In practical scramjet engines, a liquid hydrocarbon fuel can also be used to cool the engine §ow path and absorb a part of heat imposed by the §ight environment.
It is widely recognized that the performance of a supersonic combustor is substantially in §uenced by fuel injection schemes [810] and §ame-holding systems [11,12].Several fuel-injection approaches, such as strut, wall, ramp (aeroramp), etc. have been proposed and extensively investigated [1315].Ef-¦cient mixing is the main objective in all these injection strategies since the total pressure loss and drag (resulting in overall thrust loss) are associated with these devices.The cavity-based §ameholder has been widely used and studied [11,12,1618] due to its advantages in stabilizing the §ame while minimizing the total pressure loss and eliminating the requirement for additional thermal protection to the §ameholder.Many studies were focused on understanding the §ame-holding mechanism of a single cavity in supersonic combustors and optimizing the cavity design [11,13,16,19].In some studies, multiple cavities were used in supersonic combustors [20,21].Numerous experiments have been carried out to study the e¨ect of cavity geometric parameters, namely, cavity length-to-depth ratio, o¨set ratio, aft-wall angle, and other parameters, such as injection pressure, injection location, passive and direct fuelling, and back pressure on the mixing and combustion characteristics of di¨erent fuels (hydrogen and hydrocarbons).In general, gaseous fuels, especially, hydrogen, are preferred over liquid hydrocarbon fuels because evaporation of the fuel is not necessary and, in addition, their di¨usivity is higher.Based on these considerations, the cavity-based §ameholding scheme was adopted in the present study in order to extend the region of con¦gurations which were not examined earlier.
The relatively slower reaction of hydrocarbon fuels can be accelerated by using gaseous pilot §ame or di¨erent combinations of struts or/and wall injection of both main hydrocarbon fuel and hydrogen pilot torch [2225].Fuel preheating can also accelerate mixing and ignition, particularly, if the level of heating and combustor conditions can ensure §ash vaporization [15,21].Evidently, such conditions can only be realized at high §ight speeds.In recent years, the investigation of hydrocarbon fuel combustion attained ever-increasing interest [19,21,26].Nevertheless, it should be noted that the most frequent experimental studies of combustion chambers were performed at the entrance Mach numbers of 1.52.5 for hydrogen-fuelled ramjets [46,13].
Many studies were focused on numerical simulation of reacting and nonreacting §ows in supersonic combustor for understanding the ignition process and §ameholding mechanism and for their optimization [2732].Calculations were carried out to simulate the physical processes occurring in the combustor §ow ¦eld and to determine the e¨ects of di¨erent fuel injection schemes on the overall scramjet combustion e©ciency [27,31].Di¨erent arrangements were compared in terms of species mixing e©ciency and overall combustion optimization.The numerical approach is based on solving the full three-dimensional (3D) Navier Stokes equations supplemented with combustion models of di¨erent complexity with di¨erent chemical reactions and chemical species [28].They could include a rate-controlling kinetic mechanism for combustion of di¨erent fuels in air.The chemical model is directly coupled with a turbulence model.In some cases, the location of fuel injectors and the angle of injector ori¦ces are varied to determine the optimum injection scheme.All combustor con¦gurations include a backwardfacing step, cavity, or struts [32] and their combinations [31] to provide §ameholding and stabilization in the combustor; for example, mixing e©ciencies are predicted for 10 di¨erent injection schemes.The comparative results indicate that the fuel injection con¦guration with opposing injector pairs located in the cavity, on the step, and the ramp are the most e©cient, resulting in 73 percent combustion e©ciency [30].Details of the §ow ¦eld inside the combustor as well as variation of mixing e©ciency, combustion e©ciency, and total pressure loss along the combustor length are presented and discussed in [28].
The obtained numerical results provide important information to aid in the understanding of physical processes that dominate the §ow.Review of combustion simulation in supersonic combustor (Scramjet) can be found in [33].
At present, there is no universal theory, which would explain the mechanism of fuel ignition and §ame stabilization by §ame holders of di¨erent shape, which form the §ows with recirculation zones.In spite of numerous studies of combustion chambers with supersonic §ow, up to now, there are no acceptable methods of calculation, which would allow predicting reliably the mechanism and conditions of ignition and combustion stabilization.As a rule, the calculation methods are based on empirical or semiempirical relations, which use the experimental results [7,31,34].Considering the complexity of the phenomenon and multiparametric character of the problem, these methods have limited applicability and do not always provide satisfactory results.
The present work is a continuation of investigations of combustion in supersonic §ows [35,36].The main purposes of the investigation were as follows: determine the conditions of hot kerosene ignition with di¨erent §ame holder shapes; study the e¨ect of di¨erent ways of fuel injection on ignition e©cacy; compare the e¨ectiveness of ignition and stabilization of liquid and gaseous fuels; and analyze self-ignition and §ame propagation in a supersonic combustor.

COMBUSTOR MODEL AND EXPERIMENTAL SETUP
The scheme of the model, the installation of injectors, and location of cavities are presented in Fig. 1.The channel dimensions at the injector exit are 100×100 mm, including the steps with a height of H = 25 mm on the top and bottom walls.
A rearward-facing step and an additional wall with a height of 16 mm form the cavity-based §ame holder.As a result, the open cavity with a length-to-depth ratio of L/h = 2.5 is obtained.The solid and discrete back walls are used that specify the name of a cavity type.The length of elements (posts) of a discrete wall is equal to the width of an injector, i. e., l = b = 12 mm.At tests, two types of fuel are used: kerosene and propane.The majority of experiments are carried out with kerosene, which is heated up to 560580 K.
The number of injectors is four.They are similar to those proposed in [37].Injector con¦guration and its dimensions are described in [35].Fuel is injected at the same angle as the injector ramp angle ω = 8 • .A speci¦c feature of this construction is the possibility of fast and convenient changes of injectors, variation of the Mach number and other experimental conditions.The injectors are developed as replaceable elements.Such a construction enhances considerably the experimental capabilities of the model.
Injectors of di¨erent geometry can be also installed.Each injector has two nozzles for fuel injection.One of the injectors is divided into two parts, and the Figure 1 Scheme of the model resultant ¤half-injectors¥ are located in the lower corners of the injector section.The nozzles for fuel injection are located as close as possible to the upper and side surfaces on the injector back §at face.The special holes in the insulator and injector section are made and a fuel supply system delivers fuel into the separation zone / shear layer behind injectors and into the boundary layer ahead of the injector ramps.
The combustion chamber has a 3D con¦guration.The modi¦cation of the combustion chamber geometry is basically intended to choose such geometry of the injectors and §ame holders, which might guarantee stable combustion within the wide range of §ight conditions.In previous experiments, it was found [36] that the solid cavity (across all injector section) was not e¨ective enough and did not provide the required e¨ectiveness of kerosene combustion.Then, the combustion chamber was tested also with a discrete (local) cavity.The local cavity was formed behind each injector ramp by means of a post.
Investigations were carried out in the connected pipe mode.First, a prechamber of a hot-shot wind tunnel IT-302M was used as a source of hot gas [38].Such approach allows one to get a high-enthalpy §ow with high pressure and temperature at the combustor entrance.The speci¦c feature of this wind tunnel is the decrease of §ow parameters during the operation time (100120 ms).Therefore, a large number of runs were carried out with the pressure multiplicator to maintain a constant value of equivalence ratio (ER).Models were tested at the following conditions at the duct entrance: Mach numbers M en = 2.97 and 3.49, total temperature T t from 2000 to 3000 K, static pressure P en = 0.080.25 MPa, and fuelair ER from 0.25 to 1.4.

MEASUREMENTS
During the tests, the following parameters were measured: the total §ow parameters in the ¦rst and second prechambers of wind tunnel IT-302M; air and fuel §ow rates; distributions of static pressure and heat §ux in the model channel; Pitot pressure and temperature at model exit; base pressure distribution on the back step of injector device and on the forward/backward wall of the cavity post; and §ow visualization at CH and OH-radicals wavelengths and in the visible range.Large amount of the measured stations (more than 120) allowed detailed distributions of static pressure and heat §ux including base pressure and pressure in transversal directions to be obtained.

RESULTS AND DISCUSSION
Comparison of pressure distribution along the combustion chamber with solid and discrete cavities with kerosene combustion con¦rmed that the modi¦cation of cavity caused changes in the distributions of the base pressure and pressure

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along the channel length.The maximum level of pressure growth in the combustion chamber appeared to depend on the cavity type.Moreover, the character of the pressure growth was di¨erent.The maximum pressure level in the combustion chamber with the discrete cavity was reached at a distance of about 150 mm from the fuel injectors (Fig. 2a).One can see that the pressure increases fast in this part of the combustion chamber and this growth occurs not only in the constant cross-section part but also in the base region, including the pressure on the injector insertion.Comparison of pressure level at di¨erent time instants demonstrates that the maximum pressure is already reached at 30 ms and remains constant up to approximately 70 ms, i. e., up to the end of setup operation time.
The maximum pressure level in the combustion chamber with the solid cavity was reached at approximately x = 235 mm (Fig. 2b), i. e., at the end of combus- tor with constant cross section (240 mm).Comparison of data for combustion chambers with discrete and solid cavities demonstrates that in the ¦rst case, the static pressure was 15% higher than in the chamber with solid cavity.Another feature of the process in the combustion chamber with solid cavity consists in the fact that at intense combustion, the pressure plateau was not obtained.A similar qualitative di¨erence for the two cavity types remained also on the top wall.The pressure in the channel with the solid cavity rose almost everywhere in the constant cross section.These data also show that the local cavity con¦guration may in §uence signi¦cantly the pressure distribution in the channel and the base pressure changes.This follows from the comparison of the results for the top and bottom walls.
The change of pressure in the base region behind the injector section and behind the one in the cavity has a complicated nature due to the 3D nature of the §ow caused by interaction of the jet-cavity posts, shock waves, and expansion waves.Therefore, three characteristic sections on the bottom (index ¤b¥) and top (index ¤t¥) walls can be considered.Measured in the experiments were: the pressure on the back-face injector section (Z = 0 mm); the pressure on the backward facing step between injectors (Z = 25 mm); and the pressure on the half-injector back-face near sidewall (Z = 45 mm).
The time dependence of the relative pressure testi¦es that the delay of ¤kin-dling¥ of combustor takes place (see Fig. 3b).Time ¤kindling¥ is time, during which pressure remains low and approximately constant [39], and intense combustion is not realized.Only beginning with the 25th millisecond, the pressure starts weakly to increase.One can see that in this case, the base pressure in the time history does not change up to 35 ms.At intense combustion (t > 35 ms), the pressure increases and has high nonuniformity in transversal direction.The base pressure in the combustor with the solid cavity increases twice only at the end of setup operation.Figure 3b demonstrates also that base pressure on the backward injector wall (curve 3, empty signs) of bottom injector section was, on the average, higher by 20%30% than on top injector section.
The application of the discrete cavity behind injectors entails signi¦cant growth of the base pressure.This is evident from the comparison of the data in Figs.3a and 3b.The base pressure in the combustion chamber with the discrete cavity is increasing during the whole mode of the combustion chamber operation.The base pressure in this case rises fast by a factor of 3.54 and has a clear plateau of pressure during 20 ms.The base pressure was di¨erent on the top and bottom walls of section and on backward facing steps between them.At intense combustion, high nonuniformity of pressure distribution in transversal direction remained approximately on the same level as in the combustion chamber with solid cavity.
As a result of kerosene combustion, pressure increase on the combustor walls occurs and certain pressure equalizing over the cavity width but the pressure on the bottom wall of the cavity ( §oor of cavity) has changed weakly.Furthermore, The data obtained showed that the §ow structure in the solid cavity was changed weakly during the combustion and had almost no e¨ect upon the ignition process.This can be seen from the comparison of visualization of a §ow in the channel with cavity without fuel supply and at combustion of kerosene (Figs.4a and 4b).Visualization of the §ow with combustion demonstrates that disintegration of kerosene jets occurs behind a cavity (see Fig. 4b) since there is no increase of temperature in the solid cavity.With a discrete cavity (Fig. 4c), there is almost full disintegration of kerosene jets, their screening e¨ect disappears and intense combustion is observed.In this case, the §ow becomes transonic or even subsonic (without shock waves).combustion stabilization occur behind the back solid wall (behind post).The pressure on the back wall of the cavity post has been increasing more than 3 times during combustion.The pressure growth on the back wall of the bottom cavity post was somewhat higher than that on the top wall that agrees with the results of pressure measurement on the backward wall of injector section.This distinction depends on di¨erent geometrical con¦gurations of the discrete cavity on the top and bottom walls of the combustion chamber.The results of the pressure measurement in the cavities con¦rmed this assumption.It was revealed that pressure on the back wall of solid cavity has changed slightly and achieved the maximum value only at the end of combustion.The character of pressure distribution on the back wall of a discrete cavity (front wall of cavity post) was di¨erent but its maximum level di¨ered weakly from the pressure on the back wall of the solid cavity.

One can assume that ignition and
For assessing the combustion e¨ectiveness, the growth of the static pressure in the combustor at combustion conditions is compared to the corresponding pressure in the ¤cold¥ experiment (without fuel supply).These data for the combustor with solid cavity are presented in Fig. 5b.Application of solid cavity is accompanied by moderate growth of relative static pressure approximately by a factor of 3 for the whole channel.Simultaneously, it can be seen that the increase in pressure continues only until the 40th millisecond, and then pressure decreases.Pressure distribution and corresponding §ow visualization have shown that intense combustion took place only in channels with constant cross section.In the divergent part of the combustor, the static pressure The solid cavity of the investigated geometry did not virtually a¨ect the ignition and combustion stabilization.This result may be conceivably explained by the absence of fuel in the cavity and by the screening e¨ects of air and fuel jets.This phenomenon has already been observed before in the study of single injectors of various con¦gurations [35].Actually, the application of cavites of such a shape leads only to the increasing of drag of the combustion chamber.Actually, the recirculation zone behind the cavity plays the role of a §ame holder like a backward-facing step.
Application of the discrete cavity results in the pressure growth at kerosene combustion not only in the base region, but also over the whole length of com- bustion chamber.The growth of the static pressure in the combustion chamber with discrete cavity compared to the corresponding pressure in the ¤cold¥ run (without fuel) is presented in Fig. 5a.One can see that in experiments with discrete cavity, the maximum pressure was approximately 60% higher than in the combustion chamber with solid cavity over the whole length of the combustion chamber, including its expanding section at x > 240 mm.Such a character of pressure distribution remained on the top wall of the model as well.Flow visualization con¦rmed that combustion was spread over the whole combustor and retained for more than 70 ms.
Use of the discrete cavity allowed speeding up the ¤kindling¥ of the combustion chamber and §ame propagation over the whole channel.Consequently, the static pressure in the base region increased more than by a factor of 2. This process is accompanied by a signi¦cant, more than 30%, growth of the average pressure over the whole combustor length.
It is evident that the total drag of the cavity post depends on the relation between pressures on front and back surfaces of the posts and their longitudinal and transversal nonuniformity.The results of determination of the average pressure on the post surfaces for solid wall (SC ¡ solid cavity) and for separate posts (DC ¡ discrete cavity) are presented in Fig. 6.
Comparison of the pressure distributions for two cavities demonstrates that pressure on the posts forming the discrete cavity was much lower (by a factor of 45) than the pressure on the back post of the solid cavity.One may expect that the drag of the cavity post has to be also signi¦cantly lower.One can see that the di¨erence in pressure values on the bottom (SC1 and DC1) and top (SC2 and DC2) walls was not large.However, the pressure on the top wall was always slightly higher (SC1 and DC1).
Investigation of the combustion chamber without cavity was carried out to compare the e¨ectiveness of ignition and §ame stabilization.In these tests, fuel was injected into the shear layer and into the base region (rim injection, see Fig. 1).The tests of the model were carried out with two fuel supply systems.The main part of the fuel was injected through injector ramps like in the tests with the cavity and, in addition, the smaller part of the fuel (up to 10%), was injected in parallel to the main stream in the isolator section.The total fuelair ER was close to 1.
The fundamental conclusion consists in the fact that kerosene ignition and combustion were not observed when the simultaneous kerosene injection into the §ow core and the base region of no-cavity combustion chamber was carried out.In these cases, the pressure distribution along the model channel di¨ers weakly from the pressure distribution in the test without fuel supply.Kerosene ignition and combustion did not also occur in the tests without fuel injection into the base region of the injectors.Installation of the discrete cavity resulted in the intense combustion over whole combustor length at P = 1.95 bar and T t = 2470 K. Similar results were obtained at Mach number 3 and 3.5.
At Mach number M = 3, the intense combustion in the combustor without discrete cavity was reached only at the maximum §ow parameters at the combustor entrance (P = 2.5 bar and T t = 3000 K).As in the tests with the cavity, the maximum pressure level was reached on the bottom wall but the combustion duration, which was determined from the pressure on the top and bottom walls, was approximately the same.The pressure in the base region on the top backward-facing step of the injector section was about 20% higher than in the test with solid cavity.This result can indicate fast pressure equalization in the combustion chamber under such conditions.
Analysis of time histories of pressure in the tests without and with fuel supply shows that kerosene combustion occurs in two stages.At the ¦rst stage, the static pressure started to rapidly increase at a distance exceeding X = 205 mm (Fig. 7).This region corresponds to the end of the channel with constant cross section.At the second stage, the position of the pressure maximum is shifted downstream.The typical pressure ¤gap¥ is situated behind the base backwardfacing step at time t = 55 ms (X = 15 mm), i. e., in the cross section behind the cavity.Duration of this ¤gap¥ was di¨erent for di¨erent cross sections of the combustor (time delay of ignition) as well as the maximum pressure level in these cross sections.The highest pressure was obtained at the end of the combustor with constant cross section (see Fig. 7).Apparently, combustion started in the local separation zone and then rapidly spread upstream and downstream along the boundary layer to the whole combustor length.
Qualitatively, the time histories of static pressure along the combustor remained the same in the tests with and without cavity.The maximum level of pressure, as well as heat §uxes on the top and bottom walls in the tests without cavity approximately corresponds to the experiments with the cavity.The distri-Figure 7 Process of ¤kindling¥ at kerosene combustion in the channel at M = 3: 1 ¡ X = 15 mm; 2 ¡ 55; 3 ¡ 115; 4 ¡ 205; 5 ¡ X = 368 mm; and 6 ¡ ER bution of heat §uxes fully corresponds to the pressure distribution in the model channel.The start of the pressure rise was shifted downstream by 3040 mm, i. e., approximately at the cavity width.Thus, the experiments performed have demonstrated that in the no-cavity tests, the kerosene supply in the base region of the injector wedges does not guarantee e¨ective ignition of even heated kerosene.
The data obtained allowed determining the fuel-rich §ame blowout: it occurs when the fuelair ER increases to the ER = 1.21.4.This limit is typical for investigated con¦gurations of combustors with and without cavity.In spite of the fact that fuel ignition starts in di¨erent points of the combustor and at the di¨erent instants of time, combustion breakdown occurs virtually simultaneously over the whole combustor.
Investigations of propane-fuelled combustion chamber were carried out at Mach numbers 3 and 3.5 in the run with the above-mentioned §ow parameters with kerosene combustion.As a result, intense combustion of propane at Mach number 3.5 was not observed under these conditions.The static pressure remained at the level of the test without fuel supply over the whole combustor length.Therefore, subsequent experiments at M = 3.5 were performed with §ow parameters at the combustor entry that increased up to the maximally achievable values in a hot-shot setup.At simultaneous increase of the total temperature up to 3000 K and static pressure up to 2.5 bar, the local ignition occurred only at the end of the combustion chamber with the constant cross section.However, even under these parameters, the intense combustion of propane in the combustor was not realized.In this context, the possibility of propane ignition at M = 3 was checked to determine the ignition and combustion conditions.Due to the absence of propane combustion at a Mach number of 3.5, the tests were performed under higher §ow parameters at the fuel entrance of the combustion chamber: total temperature T t = 3000 K and total pressure P t = 1.95 bar.The intense combustion of propane was obtained at these conditions during 60 ms (Fig. 8a).Here, the fast pressure growth up to the maximum value in the base region and along the whole channel should be noted.This level was kept right up to combustion breakdown.This result, perhaps, indicates high combustion e©ciency during propane combustion.The decrease of the total temperature to 2700 K at the same static pressure led to failure of even local propane ignition.
The distribution of heat §uxes in the experiments with propane combustion conforms to the changes of static pressure in the model channel (Fig. 8b).This level of heat §uxes was kept until combustion breakdown.Comparison of the maximum heat §uxes at combustion of kerosene and propane shows that their values are approximately identical.The same conclusion can be made from the Figure 9 CH-radicals luminescence of §ame, M = 3.5, discrete cavity comparison of pressure distributions at combustion of these fuels.This result indicates that the level of combustion e©ciency could be the same.At intense combustion of propane, the value of the combustion e©ciency and its character of changing were somewhat di¨erent from those in the experiment with kerosene combustion.Combustion e©ciency (CE) of propane increased along the channel and reached the maximum value CE = 0.65 near the exit of the combustor whereas combustion e©ciency of kerosene reached the value CE = 0.8 behind the exit of the combustion channel with constant cross section.This result conforms to the distributions of pressure and heat §ux in the channel.It should be noted that in the tests with the combustion chamber without cavity, the combustion e©ciency did not exceed the value CE = 0.55 in the mode of intense combustion.
The obtained results ascertain that in contrast to the previously well-known data, fuel ignition in the present tests occurred not in the recirculation zone behind the backward-facing step or in the cavity but in the vicinity of the shock wave / boundary layer interaction regions on combustion chamber walls or behind these regions, nearby the combustion chamber corner point.This conclusion was con¦rmed by visualization of OH/CH-radicals luminescence in the channel by means of a high-speed camera.The example of such visualization of CH-radical luminescence at combustion of kerosene at M = 3.5 is presented in Fig. 9.

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One can see that initially, fuel self-ignition occurred in the near-wall region of the §ow in the back part of combustor and then the §ame propagates upstream and downstream, including propagation into the recirculation zone through the boundary layer.If the Mach number decreases, combustion intensity substantially grows not only near the cavity but also in the cavity and in the §ow core that one can see in Fig. 4c.After fuel self-ignition in the recirculation zone behind the backward-facing step or behind the rear wall of the cavity, considerable rise of static pressure in the entire volume of the combustor occurs.
The study of the possible generalization and application of a criterion analysis in predicting conditions of self-ignition or combustion blowout, as well as in choosing the geometry of combustor and §ame holders, is of particular interest.Evidently, under complicated conditions of supersonic 3D §ow, the possibility of description of the stabilization conditions and combustion blowout is extremely important.Thus, to properly analyze the experimental results, a correlation should be chosen, which includes the largest number of the governing parameters determined from the experiments.The correlation suggested by Ozawa [40] is likely to be the most appropriate in this sense.The application of this correlation for supersonic chambers was approved and justi¦ed in [34].The advantage of this approach consists in the combination of the breakdown characteristics of the §ame with the geometric parameters of §ame holders and with the gasdynamic §ow structure.The disadvantage of this approach is the absence of such parameters, which explicitly account for fuel characteristics, i. e., its chemical kinetics.The type of fuel and its kinetic properties can be regarded with the aid of empirical coe©cients, which should be determined from the experimental data.
To estimate the §ow parameters in the recirculation zone and to consider the characteristics of the mixing layer, the stabilization parameter SP * was calculated, using the correlation of [40]: where P is the static pressure in the recirculation zone; ρ rz is the gas density in recirculation zone; T t is the total temperature; and τ rz is the time of fuel residence in the recirculation zone determined in [7].Complex (ρ rz ref k b ref /ρ 0 ref ) presents a correction required for the correlation of the data obtained with di¨erent §ow parameters and geometry of the combustor.Using the data of [34], it has been assumed that complex (ρ rz ref k b ref /ρ 0 ref ) is equal to 1.1 and c 1 = 0.025 is the empirical turbulent mass transfer coe©cient determining the turbulent mixing intensity.
For the conditions of intense combustion of kerosene, the values of criterion β rz (SP * ) are located in the region of stable combustion (Fig. 10).Here, β rz is the ER in the recirculation zone which is calculated using the approach of [7].In these experiments, the blowout of the intense combustion at Mach 3 is apparently related to the growth of local fuelair ER at the end of setup operation.The same results were obtained for intense combustion of propane: the values of β rz (SP * ) are also located inside the Ozawa£s loop or nearby its border.If combustion does not occur, the Ozawa£s parameter is located outside the stable combustion region.
Just like in the experiments with hydrogen [41,42], when only local fuel combustion occurs (blowo¨regime), at local combustion of hydrocarbon fuels, the values of criterion β rz (SP * ) are located in the region of stable intense combustion (see Fig. 10).Such a mode was realized at Mach 3.5 in the model without cavity under the following test conditions: static pressure below 1.5 bar and total temperature below 3000 K.In some cases, the value of SP * in the experiments in the blowo¨mode was close to the values in the experiments with the intense combustion.Such a di¨erence in combustion pattern, under approximately the same SP * values, can be explained by di¨erent fuel injection and mixing e©ciency.In some experiments with the intense combustion, blowout takes place at local fuelair ER much higher than that relevant to stable combustion loop for kerosene.It can be the result of inaccuracy of calculations of local fuelair ER, which is caused by assumptions concerning the calculation of fuel penetration into the recirculation zone and by inaccuracies in calculations of the total fuel mass §ow rate.
The results obtained demonstrate that the criterion by Ozawa can hardly be used to evaluate the limits of stable combustion.This conclusion is valid for the experiments with both kerosene and propane.This result may be caused by the failure to extend the two-dimensional §ow relations to the 3D §ows.More precise determination of combustion blowout limits (and, consequently, statistically based conclusions and recommendations) requires special experiments, which would include determining the local fuelair ER, recirculation zone geom-etry, and gas parameters in this zone.Nevertheless, one can claim (as applied to the results obtained) that the correspondence between Ozawa£s criterion and stable combustion region is a necessary but not su©cient condition for predicting intense combustion in combustors at supersonic speeds.

CONCLUDING REMARKS
The performed investigations showed the possibility to ensure e©cient combustion of hydrocarbon fuels (kerosene and propane) at supersonic §ow velocity at the combustor entrance without organizing special throttling or pseudoshocks.
The data obtained allow concluding that the application of discrete cavity speeds up the ¤kindling¥ of the combustor.It is accompanied by the signi¦cant, more than 50%, growth of the pressure over the whole combustor length, including the base pressure region.At the same time, the equalization of the base pressure and the pressure on the top and bottom cavity posts (on the cavity surfaces) occurs.
The solid cavity of the studied geometry has virtually no e¨ect on fuel ignition and combustion stabilization.This result may be explained by the absence of fuel in the cavity and by the screening e¨ects of air and fuel jets.
The drag of the posts forming the discrete cavity was much lower (by a factor of 45) than the drag of the rear wall of the solid cavity.
One can assert (as applied to the results obtained) that there is a correspondence between Ozawa£s criterion β rz (SP * ) and the region of stable combustion obtained in the experiments.However, this is shown to be a necessary but not su©cient condition for the intense combustion in the combustion chamber.This conclusion is valid for the experiments with both hydrogen and hydrocarbon fuels.

Figure 3
Figure 3 Relative base pressure in the channels with discrete (a) and solid (b) cavities at M = 3: 1 ¡ Z = 45 mm; 2 ¡ 25; and 3 ¡ Z = 0 mm.Empty signs refer to bottom walls (Z b ) and ¦lled signs refer to top walls (Zt)