Study on Combustion Performance of the Radial Staged Combustion Chamber with Lobed Nozzles

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College of Energy and Environment，Shenyang Aerospace University，Shenyang 110136，P.R.China

Abstract: In order to investigate the effect of the radial gradation of the lobed nozzles on the flow field organization，a cold water model experimental platform for a combustion chamber with radial?staged 13-point lobed nozzles is built.Compared with a series of combustion OH* luminescence experiments tested by the University of Cincinnati，the four corresponding working conditions of no load，partial load，cruise and take off are selected.The vortex structure，vorticity value，multi-combustion materiel field and combustion characteristics of the flow field in the radial staged combustion chamber of the lobed nozzles under the equivalence ratio，the fuel injection method，the fuel injection ratio and other factors are numerically studied.The results show that under different influencing factors，the varation trend of the hydroxyl flame field of the lobe combustion chamber is basically the same as that of the hydroxyl light emission experiment of the swirl combustion chamber，but the flame field shape is quite different.The local equivalent ratio has a greater influence on the relevant combustion performance of the combustion chamber.Under the conditions of lower equivalence ratio，three-stage air and fuel injection mode，and gradually transferring the fuel flow of the pilot circuit to the external circuit，the temperature field and flame field of the combustion chamber are more evenly distributed，the outlet temperature field quality is better，the combustion efficiency is higher，and the NOX emission is relatively low.These are basically consistent with the cold test results.The cold experimental results illustrate the importance of the influence of the flow field organization on the combustion organization and verify the reliability of the calculation results.

Key words：lobed nozzle；radial?staged combustion；aerodynamic characteristic；combustion characteristic

0 Introduction

Modern aero-engine combustion chambers are increasingly designed to have a lean local equiva?lence ratio with high levels of mixing to reduce tem?perature peaks［1］.The fuel injection method can af?fect the organization of oil and gas in the combustion chamber.It has a great influence on the local equiva?lence ratio in the combustion chamber，therefore，it has a decisive influence on the combustion organiza?tion of the combustion chamber.

In response to the needs of modern aeroen?gines，the lean direct injector（LDI）combustor has been proven to be a lean burn combustor in a promis?ing future［2］.The so-called“direct”injection of fuel into the combustion zone means that when the tem?perature and pressure at the inlet of the combustion chamber increase，and the fuel burns during the mix?ing process，the ignition delay time will be greatly shortened.When multiple small-sized fuel nozzles are used instead of the traditional large-sized noz?zles，the transportation distance will be reduced，the mixing speed will be accelerated，the uniformity of the fuel and air mixture will be improved，and the lo?cal hot spots will be reduced［3］.The overall average flame temperature in the combustion chamber can be kept at a low level.The LDI concept was originally designed to meet the emissions requirements of In?ternational Civil Aviation Organization（ICAO）that NOXemissions should be halved by 2026［4］.It main?ly relies on controlling the blending combustion of oil and gas in the lean combustion zone and reducing the flame temperature and NOXemissions.

The fuel staging concept is to control the load by dividing the fuel supply into different fuel cir?cuits.Only one fuel circuit is required in the no-load state，2—3 fuel circuits in the cruise state，and 3 fuel circuits in the take-off state［5］.In the past，few studies have been done on the multi-nozzle array LDI combustion chamber.In recent years，scholars have paid more attention to the multi-point fuel noz?zle flexible injection combustion chamber［6-7］.Based on the work of University of Cincinnati，National Aeronautics and Space Administration（NASA）has conducted an extensive research on the LDI staged combustion system.They carried out a systematic study on the 13-point nozzles grading arrangement，and its focus was on the grading combustor technol?ogy，with the goal of reducing NOXemissions dur?ing landing and takeoff cycles［8］.Compared with the traditional single large-size nozzle injection method，the NOXcontent of combustion in the staged injec?tion method is much lower［9］.At present，under the staged combustion mode，the focus is the NOXemission of the combustion chamber.However，there are few studies about the influence of the flow field organization of the staged combustion chamber on the combustion organization，as well as the per?formance parameters such as outlet temperature dis?tribution coefficient，combustion efficiency and total pressure loss.The research shows that under differ?ent inlet conditions，the fuel staged injection has a great influence on the droplet size，shape and flame structure of the fuel spray in the reaction zone［10］；and the temperature will increase with the increase of the equivalence ratio.

The number and arrangement of different noz?zles in the LDI staged combustion system have a large impact on the combustion field.Tacina et al.［11-12］conducted a series of early operable partial and overall emission tests on the multipoint lean direct injector（MLDI）sector and 9-point and 25-point uniform ar?ray arrangements.Studies have shown that under a high-load operation and a high oil-gas ratio，the ML?DI system outputs low NOXemissions and good flame stability as the number of nozzles increases.However，with the number of nozzles increasing for low load conditions，the fuel injection volume of a single nozzle becomes quite low，and effective fuel injection cannot be achieved［13］.A 9-nozzle array fu?el planner laser induced fluorescence（PLIF）image measured by Hicks et al.［14］showed that using multi?ple injection positions can quickly and efficiently at?omize fuel.Moreover，the use of segmented and al?ternating nozzles can significantly reduce the distri?bution factor of turbine inlet temperature.

Different fuel injection methods and distribu?tion ratios have a large impact on the flame position and spatial temperature distribution in the combus?tion chamber［15］.In view of the previous research re?sults，the lobed nozzle array in this paper adopts a 13 points 5×5 alternate arrangement of fork rows.Compared with the hydroxy light emission experi?ment of the multi-point spin-flow nozzle combustion chamber，we conduct an in-depth study on the flame position and distribution of the combustion chamber with radial stayed lobed nozzles under different oper?ating conditions.The lobed nozzles are originally used to study mixing process between primary and secondary flows.In recent years，Li et al.［16-17］have used lobe hydrocyclones instead of blade hydrocy?clones to improve fuel/air mixing process and flame stability.Based on the study of NOXemissions from different loads，the combustion efficiency，outlet temperature distribution coefficient，total pressure loss and other combustion characteristics of the tar?geted combustion chamber under different influenc?ing factors have been studied.

1 System Description

1.1 Calculation model

The radial staged combustor system studied in this paper was developed by the United Technolo?gies Aerospace System（UTAS），and the lobed nozzles are used to replace the spin flow nozzles.The entire system（Fig.1（a））consists of an inverted cone combustion chamber body and a multi-point lobed nozzle array.Multi-point means that the tradi?tional single large nozzle is replaced by multiple small nozzles.The combustion chamber system is composed of 13 small nozzle arrays that are arranged in an alternating arrangement of 5×5 fork rows（Fig.1（b））.The horizontal and vertical distances be?tween the edge of the lobe are 14 mm，and the dis?tance from the edge of the outer lobe to the edge of the combustion chamber is 15.9 mm.The lobed noz?zle（Fig.1（c））adopts a 6-petal structure［18］.The en?trance diameter is 15 mm.The entrance parallel end length is 15 mm.The lobe length is 10 mm.The lobe diameter is 24 mm.The inner ring diameter is 8 mm.And the peak and trough diameters are 3.5 mm.The total length of the combustion chamber is 255.8 mm.The side length of the front end is 207.8 mm.The side length of the trailing end is 83 mm.And the length of the parallel exit is 40 mm.

Fig.1 Geometric model of combustion chamber

1.2 Grid independence verification

Integrated computer engineering and manufac?turing code for computational fluid dynamics（ICEMCFD）meshing of ANSYS software is performed on the calculation model.Since the peaks and troughs of the lobed nozzle vary are great，this paper uses an unstructured grid for the entire calculation model.The lobed nozzle uses five layers of boundary layer encryption.Case-6（Take off ）grid independence test results（Table 1）show that the average exit speed and average temperature obtained by the three different numbers of grids are relatively close，and the difference between the number of the last two ad?jacent grids is small.The helicity in Fig.2 represents the vorticity values where theXaxis represents vari?ous positions in the flow direction of the combustion chamber.It can also be seen from Fig.2 that the dif?ference in the vorticity values of the latter two flow vortices at various positions in the flow direction of the combustion chamber is small.Taking into ac?count the calculation results，calculation accuracy and calculation time，the total number of meshes ul?timately used is about 2.96 million.

Table 1 Grid independence verification results

Fig.2 Grid independence verification results

1.3 Physical model and schem

The selection of turbulence model mainly con?siders the problems involved in the flow process and the amount of computer resources occupied.Xie et al.［19］used different turbulence models to explore the applicability of lobed nozzles.For the calculation process of the aero-engine combustion chamber，considering the above two factors and the test re?sults，we select the two equationk-emodels.Among them，the realizablek-emodel has a good ef?fect in the calculation of nozzle jet mixing and other problems，so the realizablek-eturbulence model is selected in the calculation process.The pressure gra?dient of the flowing inside the aeroengine combus?tion chamber is small，and the turbulent dissipation does not change much at the wall surface.The wall surface adopts the standard wall function method.The aero-engine combustion process is a two-phase flow，and the discrete phase model uses the Euler-Lagrange method.The fuel spray model uses the conical nozzle model.The combustion process in aero-engines is mainly turbulent diffusion flame，so the non-premixed combustion model is used for combustion model.The Euler-Lagrange random walk model is adopted for fuel particles，and the par?ticle sizes follow the Rosin-Rammler distribution.The beta probability density function is adopted to describe the kerosene particles distribution.The equilibrium chemical model is used for chemical re?action mechanisms.Eleven components are consid?ered in the combustion calculation，including C12H23，CH4，CO，CO2，H2，H2O，O2，H，OH，N2，and C（s）.The multi-step simplification reac?tion mechanism is used for combustion process，and the discrete ordinates（DO）radiation model is ad?opted to calculate the radiative heat transfer.

The boundary condition inlet is based on the mass inlet.We select the pressure outlet and the mixed wall surface for our study.We also use the SIMPLEC algorithm.We adopt the cell based green-Gauss for the variable gradient in the difference for?mat，the standard format for the pressure term，and the second-order upwind style for the kinetic energy term and the turbulence term.The equation conver?gence accuracy setting converges to 10-5.Since the combustion chamber studied in this paper contains multiple inlets，the hybrid initialization method is used.

The five rows of the radial lobed nozzles in the system are designed as three fuel circuits.They can be opened and closed as required，and the fuel flow of each fuel circuit can be controlled individually.The air distribution ratio of different types of fuel nozzles is as follows：The center pilot row nozzles provide 12.4% of the air to the combustion chamber；the mid?dle two rows of nozzles provide 38.8%；and the out?ermost two rows provide 48.8%.The three fuel cir?cuits can flexibly change the fuel distribution ratio.All the five rows of nozzles are for high power refuel?ing such as take-off and landing.The center pilot row and the middle row nozzles are for partial load refuel?ing.And the center pilot row nozzles are only for noload refueling.This method of fuel grading is to pro?vide full operability from idle to take-off，cruise and landing.For the convenience of the following discus?sion，only the center pilot row nozzle fuel injection is marked as“P”；the center pilot row and the interme?diate two rows of fuel are marked as“PI”，and all the five rows of fuel are marked as“PIO”.The parameter“FS”is used to describe the fuel distribution and rep?resents the ratio of fuel flow through a fuel circuit to the total flow.For example，“FSpilot”represents the center pilot exhaust circuit fuel flow rate/ total fuel flow rate.The specific calculation and simulation con?ditions are shown in Tables 2—6.

Table 2 Calculation conditions of unload (only pilot with varying ?)

Table 3 Calculation conditions of partial load (pilot and intermediate fuel circuits with varying ? and fu?el split)

Table 4 Calculation conditions of cruise (pilot and inter?mediate fuel circuits with varying fuel split)

Table 5 Calculation conditions of cruise

Table 6 Calculation conditions of take off

2 Experimental Facility

2.1 Experimental devices

According to the test experiment of the MLDI combustion chamber of the University of Cincinna?ti，a cold water model experimental device of a radi?al stage combustion chamber with lobed nozzles is built.Figs.3，4 are the schematic diagram and physi?cal diagram of the entire water model experimental system.The experimental devices include：A water supply system，a voltage stabilizing system，a lobed nozzle system，the experimental section and the con?trol system.The actual length of each characteristic of the experimental platform is three times of the cal?culation model.

Fig.3 Schematic diagram of the experimental system

The water supply system is mainly composed of four 0.8 m3water tanks，water pumps and pipes.The power of the water pumps is 2.2 kW controlled by the inverter.The maximum flow rate is 65 m3/h，and the rated flow rate is 24 m3/h.These meet the needs of the experimental maximum flow condition.The water tanks are connected by a connector.The voltage stabilizing system is composed of a pressure stabilizing water tank，a pressure relief valve and a pressure gauge.

Fig.4 Experimental facility of model chamber

Since the water supply system is a single pipe，in order to stably control the water flow of different nozzles，it is necessary to use a stabilized water tank for rectification and flow control according to the working conditions.The pressure gauge is used to observe the initial pressure of water flowing into the experimental section.The pressure relief valve is the protection system of the entire experimental de?vice.The lobed nozzle system consists of 13 ball valves，13 flow meters，13 lobed nozzles and the tracer lines.Flowmeter error is ±0.5%.The flow of each lobed nozzle line can be controlled by the ball valve and the flow meter.The experimental sec?tion consists of an inverted cone-shaped combustion chamber，a high-speed camera and a light box.The structure，size and changing shape of the vortex sys?tem in the combustion chamber can be traced and displayed by color ink and recorded with a highspeed camera.The light box provides sufficient light source for the experimental section，which is conve?nient for capturing the vortex structure in the com?bustion chamber.The control system controls the water pump and the electromagnetic flowmeter on the main pipeline，and can automatically adjust the frequency of the inverter through the program logi?cal controller component to adjust the flow to the fixed value required by the working conditions.

2.2 Experimental program

In this paper，two working conditions in the calculation scheme are selected for the cold state verification：Partial load and take-off.In the design and development of modern aero-engine combustion chambers，it is unrealistic to carry out precise exper?iments on prototypes of each new-type aero-en?gine［20］.Modeling experiments based on the model?ing theories and methods can achieve the expected results，and avoid huge expenditures，reduce the dif?ficulty of the experiment and the experimental peri?od，and are of great significance to the development of aviation technology［21-22］.Due to the relatively dif?ficult visual observation of air during the experi?ment，and the particle image velocity technology is relatively expensive，the water flow simulation ex?periment method based on the dimensionless criteri?on number can solve the problem of difficult obser?vation，and reduce a lot of costs and facilitate the construction of the experimental platform.

This paper uses ink as a tracer according to the Reynolds criterion in the dimensionless criterion number.In the model experiment，the water flow rate is adjusted by controling the water valve in front of the entrance of the lobe

where the subscript“a”represents air；and“w”water.The density and dynamic viscosity of water and air are constant，and the ratio of each charac?teristic length of the modelLw/Lais 3.Further?more，the ratio of the air velocity in the simulated working condition to the water velocity in the ex?perimental working condition can be calculated，and then converted into the water flow rate for the control of the modeling experiment.The experi?mental conditions of water flow modeling are shown in Tables 7—8，where FAR represents the mass ratio of fuel to air.

Table 7 Experimental conditions of partial load

Table 8 Experimental conditions of take off

3 Results and Discussion

3.1 Experimental results

3.1.1 Partial load（PI）experiment trace re?sults

Fig.5 shows the results of the water flow mod?eling experiment of the vortex structure in the com?bustion chamber when the fuel distribution ratio and the total equivalence ratio（only change the amount of combustion air）are changed under the partial load conditions.?displayed on the left is 0.35 and?displayed on the right is 0.41；the upper row of fuel allocation is FSpilot=0.35，and the lower row of fu?el allocation is FSpilot=0.26.The dotted line is per?pendicular to the plane of the front end of the com?bustion chamber and parallel to the central axis of the combustion chamber，which is the auxiliary line for observation.At higher equivalence ratios，the in?let water flow is smaller，the size and diffusion range of the vortex system are smaller，and the mu?tual interference between the vortex systems occurs relatively backward，mainly in the development sec?tion.When going from a higher FSpilotto a lower FSpilot，at?=0.35（Figs.5（a，c）），the vortex struc?ture downstream of each nozzle circuit is not much different，but the local tracer concentration has still more obvious variety.When FSpilot=0.26，the trac?er diffusion area and local concentration of the down?stream of the central pilot nozzle circuit are smaller than that when FSpilot=0.35，and the tracer diffu?sion area and local concentration of the downstream of the intermediate nozzle circuit are larger than that when FSpilot=0.35.In Figs.5（b，d），due to the re?duction in the amount of combustion air，the change of the tracer expansion area downstream of each noz?zle circuit is much smaller，and the overall tracer dif?fusion area is narrower，but the changes of the local concentration of the tracer can still be observed.

Fig.5 Trajectory tracer of the two-stage injection method experiment

3.1.2 Take off（PIO）experiment trace results

The PIO of the vortex system structure under different fuel distribution ratios is shown in Fig.6.The total equivalence ratio remains unchanged at 0.56.The air distribution ratio remains unchanged，and only the fuel distribution ratio is changed for comparison.As the fuel distribution ratio changes，the contribution of the central pilot nozzle circuit is reduced，and the fuel flow is increased to the exter?nal nozzle circuit.A significant change in the distri?bution of the tracer diffusion area throughout the combustion chamber can be observed in Fig.6（a）（FSP=0.34，FSI=0.37，FSO=0.29）.It shows that the tracer diffusion region downstream of each noz?zle circuit is relatively independent and compact，and the downstream diffusion structure of a single nozzle circuit is relatively complete in most regions.The tracer concentration downstream of the center pilot nozzle circuit is higher in the effective distribu?tion area.Figs.6（a—f），the fuel distribution chang?es by gradually shifting the fuel flow from the central pilot circuit to the external circuit，and the intermedi?ate circuit flow rate remains roughly unchanged.This fuel distribution method reduces the relative concentration of the local mass flow of the tracer，and the concentration distribution of the tracer in the en?tire flow field tends to be uniform.It can be seen from Fig.6（f）（FSP=0.12，FSI=0.39，FSO=0.49）that the tracer diffusion area downstream of the three fuel nozzle circuits is wider and the concentration distribu?tion is more uniform compared to those in Fig.6（a）（FSP=0.34，FSI=0.37，FSO=0.29）.

Fig.6 Trajectory tracer of the three-stage injection method experiment

3.2 Flow field structure simulation results

Due to the special geometry of the lobed noz?zle，there is a large-scale flow vortex in the down?stream jet mixing flow field，which is the main rea?son for enhancing the flow mixing［23］.In addition，sinceK-Hinstability can appear in any free shear layer，there will be flow vortices and orthogonal vor?tices.The high intensity turbulence generated by the vortex rupture significantly improves the overall mixing process［24-25］.

3.2.1 Vorticity value of flow vortex

In this paper，the orthogonal density criterion is used to define the flow vortex，and the dimension?less value of the velocity helicity is used to express the intensity of the flow vortex.Compared with oth?er vorticity detection and evaluation standards，its main advantage is to distinguish the flow vortex in positive and negative directions.This standard can track the formation and development of complex flow vortices.

Fig.7（a）shows the change of the vortex value along the flow direction with different equivalence ratios with the only changing of the total combustion air flow.In several working conditions under no load，due to the relatively low air flow rate，the overall change law of the vorticity values in several working conditions along the flow direction is basi?cally similar.The vorticity value is the largest at the exit，and then drops sharply.There is a certain in?crease at the beginning of the transition section，and then the drop remains at a low level.However，when the air flow increases significantly，it can be clearly seen that the vorticity value changes signifi?cantly in the transition section of the combustion chamber.There are obvious differences between the two working conditions under the partial load.At?=0.35，the total air flow is relatively large，and the vorticity value of the vortex flow direction is temporarily strengthened under the interference of adjacent vortex systems.Due to the strong interac?tion between the vortex systems，the subsequent large-scale coherent structure is severely broken，and the vorticity value is quickly weakened.When?=0.41，it is also strengthened in this section，but because the effect between adjacent vortex systems is relatively backward，there is still a certain vortici?ty value in the transition section.AfterX=0.12 m，the interaction between the vortex systems strength?ens，the vortex systems begin to break up and re?construct，and the vorticity value drops rapidly.

Fig.7 Vorticity varation along the flow direction under dif?ferent equivalent ratios

3.2.2 Vorticity value of orthogonal vortex

Fig.7（b）shows the change of the orthogonal vorticity values along the flow direction at different equivalence ratios with the only changing of the to?tal combustion air flow.In general，the variation law of the vorticity value of the orthogonal vortex is basically the same.The vorticity value is the largest at the outlet，and it rapidly weakens in the direction of the flow.Subsequently，due to dissipation and mutual interference between the vortex systems，the orthogonal vortex still has a certain enhance?ment，which is particularly evident atX=0.18 m.AfterX=0.18 m，it is already the end of the entire combustion chamber，and the vorticity value of the orthogonal vortex weakens rapidly due to the main?stream action.

3.2.3 Comparative analysis of experiment and simulation

Fig.8 shows the flow field vortex structure comparison and verification of the partial load（PI）and take-off and landing（PIO）with two-stage injec?tion method.Fig.8 displays the combustion chamber water flow tracing experiment and the water flow simulation calculation trajectory cloud images.It can be seen that the trace result of the experimental vor?tex system structure and the calculation of the drop?let trajectory are basically the same in its position，size and spatial extension along the experimental section.The experimental observations of stream?lines and the calculation results are in agreement，which proves that the numerical calculation is cor?rect and credible.This provides a reliable modeling basis for the future use of water simulation experi?ments to study the aerodynamic characteristics of the flow field in the aeroengine combustion chamber and the organization of combustion.

Fig.8 Comparison between the experimental and numerical simulation results

3.3 Comparison of combustion OH* distribu?tion

For the combustion mechanism of fuel oil，OH* is an oxidized radical produced by the fuel com?bustion reaction，so it is generally believed that the OH* concentration distribution can represent the combustion flame field.Therefore，OH* concentra?tion can be used as the basis for comparative analy?sis of actual measurement and calculation of combus?tion flames.The University of Cincinnati used the OH* chemiluminescence method in the actual mea?surement of the combustion flame of the swirl com?bustor.In this paper，the OH* concentration distri?bution of the lobe combustor calculated by combus?tion is compared with the experimental results of the swirl combustor［1］.The realizablek-eturbulence model is selected in the calculation process，and the standard wall function method is adopted to treat the wall surface.The Euler-Lagrange method is used as the discrete phase model.The fuel spray model is used for the conical nozzle model.Non-premixed combustion model is adopted and its radiation model is simulated with the DO method.Velocity inlet，pressure outlet and wall surface mixed wall surface are used for various boundary conditions.

3.3.1 No?load（P）

Fig.9 is a comparison chart of the measured re?sults of the hydroxyl group of the swirl combustion chamber and the calculation result of the OH* com?bustion of the lobe combustion chamber under differ?ent equivalent ratios when only the pilot exhaust nozzle is used.It can be seen that fuel is ignited and burned after being injected into the combustion chamber.As the equivalence ratio increases，the flame range becomes wider in the radial direction and longer in the axial direction.The local combus?tion temperature becomes lower and the flame core area gradually expands.Comparing the measured OH* of the flame experiment of the swirl combustor with the calculation result of the flame OH* of the combustion mechanism of the lobe combustor，we find that at low equivalence ratio（Fig.9（a）），the combustion flame of the swirl combustor experi?ment is fan-shaped.As the equivalence ratio increas?es，the fan-shaped surface becomes narrower（Fig.9（d））.The OH* concentration calculated by the combustion mechanism of the lobe combustor is mushroom-shaped when the equivalence ratio is low（Figs.9（a，b））.With the increase of the equivalence ratio，the mushroom shape gradually becomes ellip?soidal（Fig.9（c，d））.Due to the difference in the combustion organization of the lobe combustion chamber and the swirl combustion chamber，the shape of the combustion flame should be different under the same working conditions.

Fig.9 Pilot only v.s. ? with T3=496 K, p4=100 kPa,and ΔP=4.1%

3.3.2 Partial load（PI）

When the center pilot row nozzle and the interme?diate row nozzle use different fuel distribution ratios and different total equivalence ratios，the measured re?sults of the OH* flame chemiluminescence of the swirl combustion chamber，and the calculated OH*concentration results of the lobe combustion chamber are shown in Fig.10.At higher equivalence ratios，the heat release area becomes significantly larger.Under different fuel distribution ratios，when going from a higher FSpilotto a lower FSpilot，at?=0.35，Figs.10（a，c）show the reaction zone downstream of the central pilot nozzle loop and the intermediate nozzle circuit，and the heat release intensity changes significantly.The heat release intensity of the reaction zone down?stream of the center pilot nozzle circuit is reduced.The heat release region of the reaction zone down?stream of the intermediate nozzle circuit becomes lon?ger，and the flame distribution is more uniform.Com?paring the measured results of the swirling flame with the calculation results of the lobe flame，we find that the changes are basically the same，but the shape of the flame is somewhat different.

Fig.10 Pilot and intermediate fuel circuits with varying ? and T3=496 K, p4=360 kPa, ΔP=4.0%

3.3.3 Partial load（PIO）

Fig.11 shows the measured results of the OH*flame in the swirl combustion chamber and the cal?culated OH* concentration of the lobe combustion chamber under different fuel distribution ratios（PIO）.It can be seen that the measured trend of the swirling flame and the calculation result of the lobe flame are basically the same，but there are differenc?es in the organization，which leads to a significant difference in the flame shape.By changing the fuel distribution method，reducing the fuel contribution from the central pilot nozzle circuit and increasing the fuel flow to the external nozzle circuit，the distri?bution of OH* intensity levels has a large change.In Fig.11（a），due to the higher local equivalent，the local heat release intensity of OH* is higher，and the central pilot and intermediate fuel circuit domi?nate.The heat release area of the external nozzle cir?cuit is weak and limited in scope.In Figs.11（a—f），the fuel distribution is changed by transferring the fu?el flow of the central pilot circuit to the external noz?zle circuit，and the flow rate of the intermediate noz?zle circuit remains basically unchanged.This distri?bution method makes the fuel distribution more uni?form，and the local equivalent ratio is more even.The OH* luminous intensity of the swirling combus?tion chamber and the OH* concentration distribu?tion of the lobe combustion chamber are more uni?form.In Fig.11（f），the local equivalent ratios of the three fuel circuit reaction zones are very close to the total equivalent ratio of the combustion chamber.Even if there is a small but relatively bright heat re?lease zone in the downstream reaction zone of the central pilot circuit in Fig.11（e）.The intensity in Fig.11（f）is significantly reduced，which is similar to the intensity of other reaction zones in the com?bustion chamber.Such performance fully demon?strates the uniform fuel distribution fact.

Fig.11 All fuel circuits with varying fuel split with T3=580 K, p4=500 kPa,?=0.56, ΔP=3.8%

3.4 Combustion performance analysis

3.4.1 Outlet temperature distribution factor

The outlet temperature distribution factor（OTDF）is an important parameter for evaluating the quality of the temperature field at the outlet of the combustion chamber.The smaller the OTDF value is，the better the quality of the outlet tempera?ture field is，the longer the service life of the turbine blade is，and the higher the reliability of the work is.In general，the OTDF index should be controlled below 0.35，and is defined as

whereT4maxis the maximum temperature of the com?bustion chamber outlet；T4the average temperature of the combustion chamber outlet；andT3the aver?age temperature of the combustion chamber inlet.The OTDF values for each calculation condition are shown in Fig.12.Under no-load conditions，OTDF increases with the increase of the equivalence ratio.When the equivalence ratio increases at the partial load，OTDF also becomes larger（Case 1 and Case 3，Case 2 and Case 4），and when the fuel flow rate of the central pilot circuit is reduced，OTDF also be?comes smaller（Case 1 and Case 2，Case 3 and Case 4）.Under cruise conditions，when the PI in?jection method is used，the OTDF value is large，and the quality of the outlet temperature field is rela?tively poor.When the PIO injection method is used，the OTDF value is significantly reduced.The PIO injection method is used for take-off conditions.As the fuel flow from the central pilot circuit is transferred to the external nozzle circuit，the OTDF value gradually decreases.Overall，when the PIO fuel injection method is used，the vortex structure induced downstream of each nozzle circuit can be ful?ly utilized，and the oil-gas blending effect is better and the combustion is uniform.Therefore，OTDF is smaller and the quality of the exit temperature field is better.Diverting the fuel flow from the cen?tral pilot circuit to the external nozzle circuit can also improve the quality of the outlet temperature field.In addition，as the equivalence ratio increases，the OTDF value becomes larger and the quality of the outlet temperature field becomes worse.

Fig.12 Outlet temperature distribution factor

3.4.2 Emission analysis

The pollutant emission index is generally ex?pressed by EI，which can reflect the degree of con?version of chemical energy and thermal energy dur?ing the combustion process.The viation kerosene used in this article has a low N content，so fuelbased NOXis not considered.EI is defined as

Fig.13 shows the comparison between the cal?culated NOXemissions of the lobe combustion cham?ber and the experimental NOXemissions of the swirl combustion chamber for each operating condition.Under different operating conditions，the NOXemis?sions of the lobe combustion chamber and the swirl combustion chamber are basically the same.The overall NOXemissions of the lobe combustion cham?ber are slightly higher than the experimental values of the swirl combustion chamber.Under no-load con?ditions，the simulation calculation results are close to the experimental results.As the equivalence ratio increases，emissions also increase.Under this condi?tion，the local equivalent is relatively high，the fuel combustion is incomplete，the combustion tempera?ture is low，and the NOXemissions are also relative?ly low.When the equivalence ratio increases at the partial load，the NOXemissions become larger（Case 1 and Case 2，Case 3 and Case 4），and when the fuel flow of the central pilot circuit is reduced，the NOXemissions become smaller（Case 1 and Case 3，Case 2 and Case 4）.This is mainly because when the fuel flow of the central pilot circuit is trans?ferred to the external nozzle circuit，the local equiva?lence ratio becomes smaller，the local high tempera?ture decreases，and the generated thermal NOXnatu?rally becomes smaller.Under cruise conditions，dif?ferent fuel injection methods have a great influence on NOXemissions.The PIO injection method pro?duces significantly less NOXthan the PI injection method，and the NOXemissions increase when the fuel flow from the external circuit is transferred to the pilot nozzle.Since the take-off condition is a three-stage fuel injection method，the overall NOXemissions are low，and the NOXemissions also in?crease when the external circuit fuel flow is trans?ferred to the pilot circuit.The above analysis shows that the local equivalence ratio plays a vital role in NOXemissions.When the PIO fuel injection method is used，the local equivalent downstream of each nozzle circuit is relatively low，the vortex structure induced by the lobed nozzle can maximize participa?tion in the oil and gas blending process，and the NOXemissions are also low.When the external circuit fu?el flow is transferred to the central pilot circuit，the local equivalent ratio downstream of the central pilot circuit increases，and the magnitude of the local equivalent ratio downstream of each circuit is incon?sistent.This will cause local high temperature，un?even combustion，and increased NOXemissions.

Fig.13 NOX emission of different working conditions

3.4.3 Combustion efficiency

Combustion efficiency is an important parame?ter for evaluating the completeness of fuel combus?tion.There are many influencing factors，such as the geometry of the combustion chamber，the chem?ical reaction process，etc.The combustion efficien?cy is defined as

where EI is the pollutant emission index；and LHV the low heating value of the fuel.The results of com?bustion efficiency calculations for various operating conditions are shown in Fig.14.The combustion effi?ciency is overall above 98%.Among them，when the equivalence ratio increases under no-load condi?tions，the vorticity values of the flow vortex and or?thogonal vortex in the combustion chamber de?crease，the local equivalent is relatively high，and the combustion efficiency decreases gradually below 98%.When the equivalence ratio increases at the partial load，the combustion efficiency also becomes smaller（Case 1 and Case 2，Case 3 and Case 4）.When the fuel distribution ratio changes and the fuel flow of the center pilot nozzle circuit is transferred to the middle nozzle circuit，due to the reduction of the local equivalence ratio of the reaction zone down?stream of the center pilot nozzle circuit，the fuel combustion is relatively sufficient and the combus?tion efficiency becomes larger（Case 1 and Case 3，Case 2 and Case 4）.Under cruise conditions，the combustion efficiency is lower when PI fuel injection is used.When the PIO fuel injection method is ad?opted，the combustion efficiency is significantly in?creased.Both fuel injection methods increase the combustion efficiency as the fuel flow from the cen?tral pilot nozzle circuit is transferred to the external nozzle circuit.This is because the fuel distribution method changes，the distribution ratio of fuel to com?bustion air tends to be uniform，and the local equiva?lent is relatively low.The take-off conditions further confirm the changing characteristics of combustion efficiency during the cruise PIO injection mode.

Fig.14 Combustion efficiency of different conditions

3.4.4 Total pressure recovery coefficient

The total pressure recovery coefficient refers to the ratio of the total outlet pressure of the combus?tion chamber to the total inlet pressure.It is an index used to characterize the loss of pressure potential en?ergy when gas flows through the combustion cham?ber.The lower the total pressure recovery coefficient is，the greater the total pressure and power loss is，and the higher the fuel consumption rate is.Fig.15 is a comparison result of the total pressure recovery co?efficient of a multi-point lobed nozzle radial stage combustion chamber and a single large-lobed nozzle combustion chamber wheredp/pis the total pressure recovery coefficient.It can be seen that because the vortex system downstream of the multi-point lobe combustion chamber is more abundant than the sin?gle-point lobe combustion chamber，the interaction between the vortex systems is stronger，and the flow mixing brings additional total pressure loss.There?fore，the total pressure recovery coefficient of the multi-point lobe combustion chamber is generally smaller than that of the traditional single large-lobe combustion chamber，and the total pressure loss is greater.The total pressure recovery coefficient grad?ually increases as the equivalence ratio increases.This is related to the reduction of the dimensionless value of the vortex system structure at the high equiv?alence ratio as the total pressure recovery coefficient increases and the total pressure loss decreases.

Fig.15 Total pressure recovery coefficients of different in?jection modes

4 Conclusions

The water model experiments demonstrate that the vortex structure is induced by the radial cascade combustion chamber as the lobed nozzles form the initial section，transition section and development section.The vortex system downstream of each noz?zle circuit in the initial stage is relatively indepen?dent and complete.The vortex structure of the tran?sition section expands in scope while spiraling for?ward.The interaction between adjacent vortex sys?tems in the development section makes the reorga?nized large-scale coherent structure that fills most of the space of the combustion chamber.The threestage PIO injection method has a more uniform flow field distribution than the two-stage PI injection method.It can be seen from the numerical results of the cold state that the vorticity values of the flow vortex and the orthogonal vortex are similar along the flow direction.The vorticity value is the largest at the exit of the lobed nozzles，and then drops sharply.AsXranges between 0.06—0.08 m，the vorticity value starts to increase slightly due to mu?tual interference during the vortex systems.Subse?quently，due to the interference enhancement and dissipation effects，the single complete vortex sys?tem structure is broken.In addition，the vortex val?ue of the flow vortex is weakened and remains at a low level.The orthogonal vortex still has a certain amount of vorticity in the development stage due to the interaction between the vortex systems，and then is quickly weakened due to the mainstream ef?fect.When the total equivalence ratio increases with only the amount of combustion air increasing，the vortex values of the flow vortex and orthogonal vor?tex decrease at various positions along the flow di?rection.The agreement between the water flow modeling experiment and the numerical research re?sults verifies the feasibility of the modeling method and the credibility of the modeling results，although the similarity theory has certain limitations.

The comparison between the calculation re?sults of the OH* concentration distribution of the ra?dial cascade combustion chamber with the lobed noz?zles and the OH* luminescence experiment results of the swirl nozzle array combustion chamber dem?onstrates that the change law of the combustion field along the flow direction with each influencing factor is basically the same，but the different organization methods lead to differences in the shape of the com?bustion field.As the equivalence ratio increases，the distribution range of the combustion field increases.When the fuel flow of the central pilot nozzle circuit is gradually transferred to the external nozzle cir?cuit，the flame distribution of the entire combustion field is more uniform.

The following conclusions are drawn from the performance analysis of the radial cascade combus?tion chamber with lobed nozzles：When the total equivalence ratio increases，OTDF of the combus?tion chamber increases，the quality of the outlet tem?perature field deteriorates，the NOXemissions in?crease，and the combustion efficiency becomes low?er.For the three-stage fuel injection mode（PIO），the temperature field distribution of the combustion chamber is more uniform than that of the two-stage fuel injection mode（PI），the local equivalent ratio is smaller，the outlet temperature field quality is bet?ter，the NOXemissions are smaller，and the com?bustion efficiency is higher.When the fuel distribu?tion method is changed and the fuel flow of the cen?tral pilot nozzle circuit is gradually transferred to the external nozzle circuit，the quality of the tempera?ture field at the outlet of the combustion chamber be?comes better，the NOXemission decreases，and the combustion efficiency increases.Even if the total equivalence ratio is large，when the fuel distribution method is changed，the local equivalence ratio will be greatly reduced，and the various indices of the combustion chamber will also tend to be favorable.