Mixing and combustion characteristics in a scramjet combustor with different distances between cavity and backward-facing step

Mingjing LIU, Mingo SUN,*, Doning YANG, Guoyn ZHAO,To TANG, Bin AN, Hongo WANG

a Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China

b Department of Aerospace Science and Technology, Space Engineering University, Beijing 101416, China

KEYWORDS Backward-facing step;Cavity;Combustion;Scramjet combustor;Supersonic flow

Abstract The mixing and combustion characteristics in a cavity flameholding combustor under inlet Mach number 2.92 are numerically investigated with ethylene injection.Dimensionless distance is defined as the ratio of the actual distance to the height of the combustor entrance.The cavity shear-layer mode, the lifted cavity shear-layer mode, and jet wake mode with upstream separation are observed respectively with dimensionless distance equals to 1.5,4.5,and 7.5.In both non-reacting and reacting flow fields, the numerical results are essentially in agreement with the schlieren photography, flame chemiluminescence images, and wall pressure, which verify the reliability of the numerical method.The results of non-reacting flow fields show that the Backward-Facing Step(BFS)can promote the flow separation downstream at a fixed distance.The more forward the separation position is,the larger the separation zone is in the non-reacting flow field.Furthermore, the larger the separation zone is, the higher the intensity of combustion in the reacting flow field is.A reasonable distance can reduce the total pressure loss generated by the shock waves in the combustor.The flame presents remarkable three-dimensional characteristics in the reacting flow fields.When dimensionless distance equals to 4.5, there are flames near the side wall above the cavity and it is difficult for the flame stabilization in the center of the combustor,while the combustion intensity in the center of the combustor is higher than that near the side wall when dimensionless distance equals to 7.5.In the cavity flameholding combustors with a backward-facing step,the higher combustion intensity may bring much total pressure loss to the combustor.Thus, it is a good choice to achieve better thrust performance when dimensionless distance equals to 4.5 compared to the other two combustors.

1.Introduction

A stable and wide-range flight is the main focus of hypersonic vehicles,1and scramjet2is regarded as the most promising airbreathing propulsion device to achieve this goal.To broaden the working range of the scramjet, the Rocket-Based Combined Cycle (RBCC) engine becomes a viable option3.However, the residence time of the inflow is very short4, and thus the stability of the flame is very important for the flight.5–7The Backward-Facing Step (BFS) formed by the rocket has poor flame stabilization ability,8so it is usually combined with other types of flameholders.9Therefore,it is necessary to study the mixing and combustion characteristics in the cavity flameholding combustor with a BFS.

To achieve stable combustion in the supersonic flow, various flame stabilizers have emerged such as cavities,4,10BFSs,11,12and struts.13,14However, the recirculation zone in the BFS is small, which means that the flame is unstable.Therefore,it is common to use hydrogen as fuel in the combustors with the strut and BFS15,16because its ignition delay time is short.17,18Huang et al.19investigated the flameholding mechanisms of BFS and cavity in supersonic flows and found that installing a cavity can improve the performance of combustor.An20studied the flame stabilization of the cavity cooperating with the BFS when the inlet Mach number of the combustor varies from 2.10 to 2.92.It is found that the stable combustion of hydrocarbon fuel is difficult to achieve because the BFS with limited height cannot produce a large-scale recirculation zone in the combustor.

In this paper, both BFS and cavity are employed in the combustor.The cavity is used as a flameholder, while the BFS is used to simulate a shut rocket.Therefore,this combustor can be used as a reference for the RBCC engine.Meanwhile, an expansion fan is formed downstream of the BFS,resulting in serious flow distortion due to the sudden expansion of the combustor at the BFS.It is noticed that there have been numerous studies21–23about the shock-cavity interaction.Similarly,a reattachment shock wave is generated downstream of the BFS which also has a significant impact on the flow field structure in the cavity.However, the BFS is not an actively added device but a necessary configuration(the rocket that was shut down) in RBCC engine.In addition, the inflow gas deflects at the step position due to the sudden expansion of the combustor while the mainstreams have not changed significantly in Refs.21–23.

In the scramjet combustor with cavity flameholder, influenced by inflow condition,24,25combustor design,26,27and fuel scheme,28,29there are various flame stabilization modes in cavities.Micka and Driscoll24defined jet-wake stabilized combustion and cavity stabilized combustion mode.For cavity stabilized combustion,the flame exists in the low-speed region of the cavity shear layer,while the jet-wake stabilized combustion is in the wake of the fuel jet.

In previous studies,30–33the combustion characteristics of supersonic combustors with a single flameholder have been extensively studied, while in this cavity flameholding combustor with a BFS,the expansion fan formed by the BFS will have a significant impact on the mixing and combustion in the combustor.The cavity shear layer, the recirculation zone, and the jet wake will change under the influence of the expansion fan.Furthermore, the dimensionless distance is changed based on previous experimental results.34,35Three combustion modes are well restored and more detailed flow field structures are displayed and analyzed in this article.

2.Numerical methods

2.1.Governing equations

The Reynolds-Averaged Navier-Stokes(RANS)equation simulation has been widely used in engineering applications and academic research because it can capture the main characteristics of the flow field with small calculation efforts.For the combustion process, the density changes with the heat release process, so the Favre-averaged method is convenient in simulation.The governing equations of the compressible Navier-Stokes equations36can be written as

2.2.Numerical setup

Based on the previous experimental research,34,35the simulation research was carried out with the same combustor in this paper.Fig.1 shows the schematic diagram of the model combustor.The width of the combustor is 50 mm.Ethylene is vertically injected into the mainstream and the diameter of the orifices is 1 mm.The distance between the adjacent orifices is 12.5 mm.The equivalence ratio is 0.25.The more detailed parameters can be seen in Refs.34,35.The horizontal distances(d) between the BFS and the cavity are 60, 180, and 300 mm,and d/H are 1.5, 4.5, and 7.5, respectively.

The inflow conditions in simulations are shown in Table 1,which are consistent with those in the experiments.The corresponding flight altitude and Mach number are 30.0 km and 6.0, respectively.The nonslip boundary condition is applied to the walls of the combustors and the temperature condition of the wall is adiabatic.The inlet and ethylene injections are treated as pressure inlets.For the outlet, the parameters can be calculated by the internal cells because of the supersonic feature.

The in-house code employed with the finite volume method had shown excellent performance in solving the equations of Section 2.1.37The Shear Stress Transport(SST)k-ω turbulent model38was employed to calculate the turbulent viscosity for its good performance in the supersonic combustion process.For the time advancement method, 4-step 2nd-order Runge-Kutta method39was applied.To avoid the numerical divergence, the Courant-Friedrichs-Lewy (CFL) number was set to 0.1.The flow field was considered to reach the quasisteady state when the mass flow rate of the inflow and fuels jet approximately equal that of the outflow with an error below 1%.

The Flamelet-Progress Variable (FPV) combustion model was used to calculate the supersonic turbulent combustion which has been verified40–43previously.The GRI3.0 C2H4/air combustion model44was used to simulate the ethylene combustion process.

The FlameMaster V3.3.9 software package45was used to solve the steady flamelet equations.In Section 3.1, the reference pressures were set as 1.0, 1.5, and 2.5 atm (1 atm =105Pa) for three combustors, respectively.The temperatures of oxidant and fuel were set as 1000 K and 300 K,respectively.The laminar flamelet databases were generated with the assumption that the Lewis number is 1.The 52 laminar flamelet databases were generated,and turbulent flamelet databases46,47were obtained by averaging the ensemble employedwith the presumed-Probability Density Function (PDF)method48based on laminar flamelet databases.

2.3.Code verification

To increase the reliability of the results, the pressure ratio of the experiment (d/H = 4.5) is compared with the numerical result.Simulations based on coarse (9.51 million), medium(12.64 million), and refined (17.28 million) grids were conducted and compared with the pressure ratio of the experiment as shown in Fig.2.The wall pressures of the medium and refined grids are similar to each other while the result of the coarse grid is greatly deviating.The result shows that the medium grid is accurate enough and the simulation cost is moderate, and thus the medium grid is selected to perform the simulations.For combustors with different d/H, the grid density remains the same.All grids are refined near the wall and injection orifices.The height of the first grid near wall is set to 0.01 mm and the corresponding Y+equals approximately 12.

Fig.2 Comparison of lower wall pressure profiles between numerical and experimental results 34,35.

Fig.1 Schematic diagram of model combustors 34,35.

Fig.3 Time-averaged schlieren images of experiments34,35 and simulations in three combustors (reacting flow fields).

To further test the accuracy of simulation results, the Y-direction density gradient contours are compared with the time-averaged schlieren images in three combustors.Fig.3 (a) illustrates the reacting flow fields in three combustors.The white lines in Fig.3 (a) are the boundary lines of time-averaged flame images.In Fig.3 (b), the Y-direction density gradient is calculated based on the average integrated density along the spanwise direction.By comparing combustors with different d/H in Fig.3,it is easy to find that the flow fields of experiments and simulations are highly similar to each other.The simulations highly restore the flow field structure and flame stabilization modes, and thus the simulation results in this paper are of high credibility.

3.Results and discussion

The present section focuses on the combustion characteristics of cavity flameholding combustor with a Backward-Facing Step (BFS) based on adequate reliability verification in Section 2.3, and simulation results with different distances between BFS and cavity are analyzed in detail.The nonreacting flow fields and the reacting flow fields are analyzed in Sections 3.1 and 3.2, respectively.

3.1.Cold flow field

The normalized pressure profiles of simulations and experiments are all displayed in Fig.4 with high similarities.The pressure is normalized by the pressure at the isolator exist.It can be seen that the simulations have the same positions of low-pressure zones with experiments in three combustors,which shows that the results are creditable.The pressure contours in the center planes of combustors are shown in Fig.5.Fig.6 illustrates the time-averaged schlieren images and the numerical schlieren contours in combustors with different d/H.It can be found that the expansion waves, reattachment shock waves, compression waves, and bow shock waves in combustors cause the pressure variation along the lower wall by comparing Fig.5 and Fig.6.

Fig.4 Normalized pressure profiles on lower wall in three combustors (non-reacting flow fields).

There are two significant high-pressure peaks on the lower wall of the combustors in Fig.4.The first pressure peak is located near the fuel injection position because of the interaction between the mainstream and the ethylene jet,and the narrower channel means the higher pressure.The pressure also peaks after the compression wave at the trailing edge of the cavity.The static pressures decrease downstream of the BFS for three combustors, and the low-pressure points are all located at about 180 mm downstream of the leading edges.As seen in Fig.4,three lines are connected between the leading edges and the low-pressure points, and the included angles between the connecting lines and the horizontal line are about 12.5°.The diverging angles of the expansion fans are approximately 26°.

Fig.5 Pressure contours in center planes of three combustors (non-reacting flow fields).

Fig.6 Time-averaged schlieren images of experiments34,35 and simulations for three combustors (non-reacting flow fields).

When d/H = 1.5, the ethylene injection position is 25 mm upstream of the cavity.As seen in Fig.5, the expansion fan reduces the pressure in the downstream region at a fixed angle which means that the pressure near the jet is not affected by the BFS.Meanwhile, the pressure increases gradually in the equivalent isolation section and peaks when passing through the bow shock wave.Due to the channel contraction and gas impinging on the cavity ramp, a strong compression wave(see Fig.6) and a high-pressure point (see Fig.7) are formed above the cavity ramp.Besides this,the intersection and reflection of shock waves lead to the fluctuation of the lower wall pressure.

When d/H=4.5,there is sufficient space for gas expansion,and thus the pressure near the ethylene jet is lower than at the last combustor.Above the cavity, interaction occurs between the reattachment shock wave and the bow shock,which makes the reflected shock waves greatly weakened downstream of the combustor.Meanwhile, the high-velocity gas hits the cavity ramp, resulting in a weaker compression wave as shown in Fig.6.Therefore, the pressure fluctuation is smaller than that in the other two cases.

When d/H = 7.5, the BFS creates an area of low pressure upstream of the ethylene jet.The reattachment shock wave reflects and reaches the same position with the bow shock above the cavity.Different from d/H=1.5,the wider channel makes the average pressure lower,and the reattachment shock wave has reflected multiple times between the upper wall and the lower wall,which makes the pressure fluctuation amplitude smaller.

Fig.7 X-direction velocity (U) contours in three combustors and iso-surfaces (YC2H4 = 0.1) are contoured by U (non-reacting flow fields).

Fig.7 shows the velocity in the X-direction contours of non-reacting flow fields in three combustors.The jet penetration depths of the three simulations are compared in Fig.8.The flow field structures on the upper side of three combustors are similar to each other.There is a recirculation region at the bottom of BFS.Due to the sudden expansion of the combustor, the supersonic inflow deflects toward the step and an expansion fan is formed with higher velocity.The deflected supersonic gas changes the flow direction again after the BFS, which generates the reattachment shock waves downstream of the expansion fan.

When d/H = 1.5, the channel expands behind the orifices.On the one hand,the flow direction of the supersonic inflow in the lower side of the cavity does not change.On the other hand, the high pressure in the cavity is not conducive to fuel penetration in the mainstream.Thus,the jet penetration depth with d/H = 1.5 is low, as shown in Fig.8.Meanwhile, the recirculation region is limited inside the cavity.There is no large-scale separation and the boundary layer is affected by the strong compression shock wave and the reattachment shock wave.

When d/H = 4.5, the expansion fan provides a lowpressure zone which is beneficial to improving the penetration depth of fuel, as seen in Fig.9.Meanwhile, the mainstream deflection upstream of the reattachment shock wave produces a bulged cavity shear layer.This phenomenon appears in both experiments (see Fig.6) and simulations (see Fig.7).Furthermore,the lifted cavity shear layer produces a larger separation zone downstream of the cavity.

When d/H = 7.5, a small recirculation region forms upstream of the orifices under the influence of the reattachment shock wave.By observing the fuel distribution in Fig.8, it can be found that the ethylene is mixed with the inflow air upstream of the jets.Furthermore, the low velocity after the reattachment shock wave and wider combustor are conducive to the fuel mixing and cavity shear layer lifting.The separation zone is the largest among the three simulations.

Fig.8 Fuel distributions (lined by YC2H4= 0.1 in central section) in three combustors (length in X direction is 0.6 times original, nonreacting flow fields).

Fig.9 Mass exchange rates through lip of cavity in three combustors (non-reacting flow fields).

Fig.9 illustrates the mass exchange rate along the Xdirection ˙mZand the total mass exchange rate ˙m in combustors with different d/H.Mass exchange rate along X-direction ˙mZis defined as ˙mZ=ρVZ, where ρ and V are the density and the absolute value of velocity in the Y-direction respectively.Z means that it is an integral result along the Z-direction.Similarly, the total mass exchange rate ˙m is defined as ˙m=ρVA,where A is the cavity lip area.

The mass exchange rates rise rapidly at the cavity ramp.The lifting of the cavity shear layer is unfavorable for the mass exchange between the cavity and the mainstream, and therefore the mass exchange rate is much smaller than the others.For combustor with d/H = 1.5, the mass exchange rate reduces at the rear side of the cavity because the center of the recirculation region is located at the rear side of the cavity.

Fig.10 illustrates the mixing efficiency and total pressure recovery coefficient in three combustors.The mixing efficiencies are almost the same when X >0.2 m for combustors with different d/H.The mixing efficiency with d/H = 4.5 is small because the mainstream deflects downstream the injection,which is not conducive to the mixing.The mixing efficiency shows the same law as the mass exchange rate.The total pressure recovery coefficient keeps the same in the equivalent and drops suddenly at the BFS for each combustor.The BFS can

cause large total pressure loss in the combustor and the position of the BFS also has a great impact on the total pressure.As seen in Fig.10 (b), the total pressure recovery coefficient(ηPt) with d/H = 1.5 drops faster than the others.The intense shock wave is considered as the main cause of the total pressure loss.Previous analysis has shown that shock waves with d/H = 4.5 are weaker (see Fig.6) than the others, and thus the total pressure loss caused by shock wave will be smaller,as seen in Fig.10 (b).

3.2.Combustion flow field

Under the same equivalence ratio of 0.25, successful ignition and stable combustion are achieved in three combustors.The normalized pressure of experiments and simulations in three combustors are displayed in Fig.11.Similar to the nonreacting flow fields, low-pressure points are located downstream of the BFS in the reacting flow fields for combustors with different d/H.In the reacting flow fields, the lowpressure points move upstream.The low-pressure points are 0.1 m downstream of the BFS.As seen in Fig.11, three lines are connected between the leading edges and the lowpressure points, and the included angles between the connecting lines and the horizontal line are about 22°.In the nonreacting flow fields, the diverging angles of the expansion fans are approximately 26°.Therefore,the low-pressure point in the reacting flow fields is influenced by the expansion fan and the back pressure.

The combustion flow fields are influenced by the position of the BFS.As seen in Fig.11, the farther the distance between the BFS and the cavity is, the higher the pressure is.The high-pressure regions are all located downstream of the cavity.Therefore, the position of the BFS has a significant impact on the combustion of three combustors.

Fig.12 shows the velocity in the X-direction contours of the reacting flow fields in three combustors.The sonic lines drawn in black can represent the un-reacted zones.The flame chemiluminescence images of experiments and temperature contours of simulations are shown in Fig.13.The contours are the integral results along the Z-direction.

Fig.10 Mixing efficiency and total pressure recovery coefficient along streamwise direction in three combustors (non-reacting flow fields).

Fig.11 Normalized pressure profiles on lower wall in three combustors (reacting flow fields).

In the reacting flow fields, combustion changes the flow field structures greatly.By comparing Fig.7 and Fig.12, it can be found that the combustion promotes the further separation of the boundary layer.For both non-reacting and reacting flow fields, the farther the distance between the BFS and the cavity is, the larger the low-velocity zone is.For each combustor, the mainstream is highly compressed at the combustion zone.Compared to the non-reacting flow fields, the recirculation zones downstream of the BFS are changed by the back pressure, and the mainstream deflection angles at the BFS are small.

When d/H=1.5,the flame concentrates in the cavity shearlayer and the near-wall region downstream of the cavity,which is called the cavity shear-layer mode conventionally.49Two recirculation regions can be observed in the reaction zone of the combustor, one in the cavity and the other downstream of the cavity.In the reacting flow field, the jet wake lifts at the rear side of the cavity.Influenced by the backpressure,the recirculation region in the non-reacting flow field is elongated and a recirculation region is formed downstream of it.

When d/H = 4.5, the combustion is unsteady in experiments.The flame concentrates in the lower part of the combustor.In the simulation, the flame shows an obvious threedimensional effect.Affected by the expansion fan,it is difficult for flame stabilization because of the high velocity in the center of the combustor.The main flame is at the lifted cavity shear layer, while the flame exists in the boundary layer of the side wall, as seen in Fig.14.There are also two small hightemperature zones upstream of the injections in the corner boundary layer.On the one hand, the low-speed region of the boundary layer is conducive to flame stability.On the other hand, the 3-D streamlines in Fig.14 indicate that back-flow occurs under the combined influence of high-speed mainstream flow and combustion backpressure.The back-flow provides a small amount of fuel for combustion in the corner boundary layer which produces two high-temperature zones upstream of the injections.Fig.14 illustrates the iso-surfaces of the mass fraction of the ethylene (YC2H4= 0.1), the flame at the side wall consumes most of the fuel while there is still much fuel left in the center of the combustor above the cavity.In general,the combustion is stronger than that with d/H = 1.5.In this article,this combustion mode is called the lifted cavity shear-layer mode.Two larger recirculation regions can be observed downstream of the BFS affected by the higher backpressure compared to the last combustor.

Fig.12 X-direction velocity(U)contours of reacting flow fields in three combustors and iso-surfaces (YC2H4=0.1)contoured by U(X planes are lined by Ma = 1, reacting flow fields).

Fig.13 Flame chemiluminescence images of experiments34,35 and temperature contours lined by T = 1600 K of simulations in three combustors (reacting flow fields).

Fig.14 Temperature contours lined by Ma=1 and iso-surfaces(YC2H4=0.1)contoured by U in combustor with d/H=4.5(reacting flow fields).

When d/H=7.5,the flame front is upstream of the cavity.A larger recirculation region is formed upstream of the injection compared to the non-reacting flow fields.The recirculation region is conducive to the mixing and combustion upstream of the injection.Furthermore, large-scale flow separation occurs upstream of injection and the jet penetration depth is greatly improved.As seen in Fig.12 and Fig.13,ethylene is injected vertically into the center of the combustor,which means higher mixing efficiency.Different from the combustion with d/H = 4.5, it is oxygen-enriched near the side wall,and the combustion intensity in the center of the combustor is higher than that near the side wall.In this combustor,the BFS is far away from the main reaction zone and the backpressure has little effect on the downstream BFS.The mainstream deflects downstream of the BFS and an obvious reattachment shock wave exists downstream of the BFS.Meanwhile, the intense combustion in the combustor makes the mainstream compressed severely.The reattachment shock wave intersects with the oblique shock wave which forms a low-velocity zone at the intersection position.Shock trains are formed in the non-reacting zone above the cavity as shown in Fig.3 besides this.According to the characteristics of the flame, this combustion mode is named jet wake mode with upstream separation.

Fig.15(a) illustrates the combustion efficiency in the reacting flow fields of three combustors.In the previous analysis in Section 3.1,the mixing efficiency of the non-reacting flow field with d/H = 4.5 is slightly smaller than the others as seen in Fig.10, while the combustion efficiency of the reacting flow field with d/H = 4.5 is much higher than that with d/H = 1.5.When d/H = 7.5, the combustion efficiency at the injection is higher than 0 because the reaction occurred before the injection position.

For the combustors with the current configuration,the size of the separation region in the non-reacting flow field is regarded as the key factor to determine the combustion intensity in the reacting flow field.In the non-reacting flow field,the size of the separation region is larger in the combustor with a longer distance between the BFS and the cavity, as seen in Fig.7.When ignition occurs in the combustor, the separation region in the non-reacting flow field will provide a low-speed zone which facilitates the combustion process.Furthermore,the combustion intensifies the separation in reacting flow field.When a relative balance is formed between flow and combustion, the flame in the combustor will show a specific intensity as seen in Fig.12.In other words, the larger the separation region in the non-reacting flow field is, the more intense the combustion in the reacting flow field is.As seen in Fig.7 and Fig.12, the larger the separation region in the nonreacting flow field is, the more intense the combustion is.

Fig.15(b) illustrates total pressure recovery efficiency in three combustors.The previous study in Fig.10(b) has shown the total pressure loss in the non-reacting flow fields with different d/H.In the reacting flow fields, combustion will reduce the flow velocity in combustion which leads to a greater total pressure loss compared to the non-reacting flow fields.The more intense the combustion is, the greater the total pressure loss is.Generally speaking, the combustion efficiency with d/H=1.5 is much lower than the others while the total pressure recovery coefficient with d/H = 1.5 and d/H = 4.5 are much higher than that with d/H = 7.5.

Table 2 summarizes the combustion modes and key parameters in three combustors.ηcomis combustion efficiency and ηPtis total pressure recovery coefficient.F is the inner thrust of the combustor.

It is noticed that the combustion modes in the three combustors are different from each other with the same equivalence ratio.The distance between the BFS and the cavity determines the separation position of the boundary layer and therefore it may be more appropriate to name the combustion modes as suppressed combustion, partially separated combustion, and separated combustion.However, the BFS will cause much more total pressure loss compared with traditional combustors.Higher combustion efficiency does not mean higher thrust performance for the cavity flameholding combustor with a BFS.The separated combustion zone deflects the mainstream with d/H=7.5,as shown in Fig.12,which will cause a larger total pressure loss.

In summary, comprehensive consideration of combustion efficiency and flow loss is necessary to achieve better thrust performance.As seen in Table 2, the combustor inner thrust with d/H = 4.5 is higher than the others with ηcom=0.7220 and ηPt=0.4063.

4.Conclusions

The mixing and combustion characteristics of three supersonic combustors are investigated numerically based on previous experiments.The combustor uses a cavity as a flameholder,and a BFS is set on the opposite side of the cavity to simulate a shut rocket.The dimensionless distances between the cavity and the BFS of three combustors are 1.5, 4.5, and 7.5, respectively.Under the condition of Ma = 2.52, the simulation results in the non-reacting and reacting flow fields are studied,combined with the experimental phenomena.The main conclusions are drawn as follows:

Fig.15 Combustion efficiency and total pressure recovery coefficients along streamwise direction in three combustors (reacting flow fields).

Table 2 Combustion modes and key parameters of three combustors.

(1) In the non-reacting flow fields, the expansion fan generated by the BFS will create a low-pressure region downstream at a fixed angle.The longer the dimensionless distance is, the closer the low-pressure region is to the inlet of the combustor.This low-pressure region can promote the flow separation: the boundary layer separates downstream of the cavity when d/H=1.5;the cavity shear layer is lifted when d/H = 4.5; a recirculation zone is formed upstream of the injection when d/H = 4.5.

(2) The more forward the boundary layer separation position is, the larger the separation zone is.The size of the separation zone in the non-reacting flow field plays a leading role in the combustion of the reacting flow field.The large separation zone is beneficial to the ignition and mixing in the reacting flow field.Cavity shearlayer mode, the lifted cavity shear-layer mode, and jet wake mode with upstream separation are observed respectively in three combustors.It is considered more appropriate to name the combustion modes as suppressed combustion, partially separated combustion,and separated combustion.

(3) In the reacting flow fields,the flame presents remarkable three-dimensional characteristics in combustors with different d/H.Only the information of integration along spanwise direction can be observed in experiments.When d/H = 4.5, flame exists near the side wall above the cavity, while it is difficult for the flame stabilization in the center of the combustor because of the high velocity after the BFS.When d/H = 7.5, the fuel is fully mixed with the inlet air, it is oxygen-enriched near the side wall, and the combustion intensity in the center of the combustor is higher than that near the side wall.

(4) To achieve better thrust performance of the combustor,it is not a good choice to simply increase the combustion intensity because the high combustion intensity will bring much total pressure loss to the combustor.In addition, a reasonable distance (d/H = 4.5) between the cavity and BFS can decrease the total pressure loss generated by the shock waves in the combustor.Thus,a combustor with d/H = 4.5 has better thrust performance compared to the others.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos.11925207 and 12002381), the Scientific Research Plan of the National University of Defense Technology in 2019, China (No.ZK19-02), and the Science and Technology Foundation of State Key Laboratory, China(No.6142703200311).