Guangwei MA,Mingbo SUN,Guoyan ZHAO,Changhai LIANG,Hongbo WANG,Jiangfei YU
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China
KEYWORDS Asymmetric phenomenon;Cavity;Combustion;Injection scheme;Scramjet;Supersonic
Abstract The asymmetric separation has a crucial effect on the performance of the scramjet. In this study, the asymmetric separation and combustion in both rectangular and circular scramjets are investigated numerically, and the effect of injection scheme is analyzed. The characteristics of the flow field are analyzed based on sufficient code verification.In the rectangular scramjet,the separation tends to occur in the corner due to the corner boundary-layer effect.The separation is asymmetric and only two corners have serious separation. The fuel penetration depth in the separation zone increases and the combustion is intensified. When the injection scheme is uniform, both the combustion and separation become weak. In the circular scramjet, the separation and combustion are basically axisymmetric in the scramjet with one-row injection scheme.The asymmetric combustion becomes obvious in cases with multi-row injection scheme. When the injection orifices distribute intensively on the top and bottom sides, the strongest and weakest separations occur near these two sides respectively.When the distribution of orifices becomes uniform,the direction of separation cannot be predicted. For multi-row cases, the nonuniform injection scheme could result in violent combustion and asymmetric flow structures compared with the uniform injection scheme.©2022 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Scramjet1-2has been the most promising propulsion method for hypersonic vehicles due to its high specific impulse and simple structure.In general,the scramjet can be divided into rectangular and circular scramjets according to the configuration of the cross-section. Different scramjets have their special characteristics but the asymmetric separation occurs in all kinds of scramjets when the backpressure is high enough.The asymmetric separation has a significant effect on the combustion performance in scramjet and has gained widespread academic attention.3
To enhance fuel mixing and maintain robust combustion,an effective flameholder is necessary for the scramjet. Among various flameholders,4,5the cavity, which evolves from the backward-facing step,6becomes outstanding due to its low resistance and light weight. Wang et al.7carried out experiments of cavity-assisted hydrogen combustion and proposed three classic combustion modes.Li et al.8experimentally investigated the scale effect of the cavity-assisted scramjet combustor and the results showed that larger scramjet combustor had a broader rich blowout limit of combustion.Yao et al.9numerically studied the differences between the elliptic and circular scramjet combustors assisted with a cavity, and the authors found that the elliptic combustor itself played a role of a large open cavity, which enhanced the fuel mixing and combustion performance. Choubey et al.10numerically investigated the performance of a double cavity scramjet, and they found that the cavity length-to-depth ratio and inflow Mach number could be optimized.
The injection scheme11is of vital importance to the scramjet since it affects the mixing and combustion processes of the fuel.12Liu et al.13compared the combustion flow field of single and multiple jets upstream of the cavity. They found that the interaction between multiple jets promoted fuel mixing and enhanced combustion. Du et al.14performed Reynolds-Averaged Navier-Stokes (RANS) simulation of various injection schemes inside the cavity,and they found that the fuel distribution inside the cavity changed hugely under different jets arrangements. Sun et al.15studied the tandem and parallel multiple jets in supersonic crossflow, and they found that the distance between two jets could affect the mixing process and it should be optimized.
When the backpressure is high enough,the asymmetric phenomenon can change the flow structure and combustion mode of the scramjet. Qin et al.16numerically investigated the effect of fuel injection on the asymmetric shock trains, and they found that the asymmetric separation could be suppressed by proper fuel injection.Landsberg et al.17experimentally studied the combustion flow field of a circular scramjet.The OH PLIF images indicated that the asymmetric combustion appeared under the high equivalence ratio condition. Gao et al.18investigated the symmetric and asymmetric separation characteristics of a rectangular scramjet. It was observed that both the symmetric and asymmetric backpressure led to the asymmetric boundary layer separation.
Although there are numerous researches of rectangular and circular scramjets with various injection scheme, the effect of injection scheme on the asymmetric phenomenon has not been understood completely. In this article, the combustion flow fields of both rectangular and circular scramjets are numerically investigated by an in-house code, which adopts three-dimensional RANS simulation employed with the Flamelet/Progress Variable (FPV) combustion model.The widely used Shear Stress Transport (SST) k-ω turbulent model is implanted into the code. The simulation is compared with the experiment, and numerical results show sufficient accuracy. The main attention is paid to the asymmetric combustion and boundary layer separation in scramjets with different cross-sections. Ulteriorly, the effect of the injection scheme is investigated in rectangular and circular scramjets,respectively. The relationship between the asymmetric phenomenon and the distribution of the fuel orifices is revealed.Finally, the rectangular and circular scramjets are compared with each other qualitatively, and the similarities and differences are summarized.
2.1. Governing equations
The RANS simulation has been widely used in the engineering and academic research19because it can capture the main characteristics of the flow field with an acceptable computational cost. The FPV combustion model considers the nonsteady effect of the combustion20and is suitable for the complicated chemical reaction mechanism.21By applying the Favreaveraged method,the governing equations of the RANS simulation employing the FPV combustion model can be written as.
In the RANS simulation,a suitable turbulent model is necessary to calculate the turbulent viscosity μt.In this article,the SST k-ω turbulent model is employed due to its excellent performance in the supersonic combustion process. The SST k-ω model takes both the near-wall flow and the far-field flow into consideration,and our previous studies22,23have proved that it can solve the reacting flow in scramjet precisely. There are numerous researches24,25about the supersonic flow in scramjet, which employs the SST k-ω model. Therefore, the turbulent model in our code has enough accuracy for current study. The details of SST k-ω turbulence model can be found in previous research.26
2.2. Numerical setup
The in-house code22,23employed with the finite volume method is developed to solve the above governing equations of the flow field.The FPV combustion model is implanted into the code to calculate the process of supersonic turbulent combustion. To ensure accuracy and convergence, the structure grid is applied to the whole flow field. The Van Leer limiter is used to suppress numerical oscillation during the calculation. The Advective Upstream Splitting Method (AUSM)27and the central difference scheme are applied to the discretization of the convective term and viscous term respectively. The explicit 4-step 2nd-order Runge-Kutta method is employed in the time-stepping process. The Courant-Friedrichs-Lewy(CFL) number, which controls the speed of the calculation,is set to 0.1 firstly and improved to 0.2 in order to avoid the numerical divergence. The flow field is considered reaching the quasi-steady state when the residuals fall by 10-3and the mass flow rate of the inflow and fuels jet equals that of the outflow. For all cases, the combustion flow field is calculated based on the converged unfueled flow field, of which an area downstream of the fuel orifices is patched for ignition.
The fuel of the scramjet is ethylene,and the San Diego main hydrocarbon combustion mechanism,28-30which contains 39 species and 173 elementary reactions, is applied to stimulate the combustion process. The laminar flamelet databases exported from the FlameMaster31software,are used to generate turbulent flamelet databases by averaging ensemble employed with presumed-PDF method. The oxidizer and fuel side boundary conditions used to generate the databases are displayed in Table 1.However,the temperature of the oxidizer is increased to 1000 K due to the stagnation effect in the boundary layer. The reference pressure is set to 3 atm(1 atm = 101325 Pa),which approximately equals the highest pressure in the experiment.
Fig.1 displays the rectangular and circular scramjets in this article.The rectangular scramjet32is assisted with the dual par-allel cavity whose length-to-depth ratio is about 5. The dual parallel cavity is very common in rectangular scramjet.33,34The size of the inlet is 54.5 mm × 75 mm and the mass flow rate of the supersonic inflow is about 2 kg/s under Ma∞=6 flight condition. Six fuel orifices with diameter of 1.5 mm distribute on the upper and lower wall of the scramjet.The global equivalence ratio of the rectangular scramjet is 0.47.Two more injection schemes (Rectangular-2 and Rectangular-3) with twelve fuel orifices are numerically calculated to compare with the original injection scheme (Rectangular-1). It should be noted that because they have a larger injection area, the injection pressure of Rectangular-2 and Rectangular-3 is reduced to reach the same global equivalence ratio. The injection scheme of Rectangular-3 is more uniform than that of Rectangular-1 and Rectangular-2 in Z direction.
Table 1 Scramjet inflow and fuel jets conditions32.
The circular model scramjet35developed by University of Illinois is employed to investigate the effect of the injection scheme in the circular scramjet. The inlet of the scramjet is removed because the inflow conditions are post-shock conditions in the current study. The circular injection orifices are replaced by the square ones for simplicity. The length of the square orifices is 0.617 mm. The previous studies36-37have shown that the configuration of the orifice has a negligible effect on the flow field. Circular-1 in Fig. 1(b) is the original experimental configuration and the fuel orifices are uniformly distributed on the wall.Four more injection schemes are investigated. Circular-2 and Circular-3 are two-row and each row has eight orifices. In Circular-2, the orifices locate at the top(positive half of Y-axis) and bottom (negative half of Yaxis),while the right(positive half of Z-axis)and left(negative half of Z-axis) sides have no orifice. The orifices in Circular-3 are uniformly distributed on the wall.Circular-4 and Circular-5 are four-row. Similarly, the injection scheme of Circular-4 is nonuniform while the injection scheme of Circular-5 is uniform.
The boundary conditions32of inflow are set based on the post-shock conditions in Ma∞=6 flight condition.The parameters are shown in Table 1. The fuel is injected into the flow field at sonic speed. The inflow and fuel orifices are set as the pressure inlet boundary condition. The injection pressure of Rectangular-2 and Rectangular-3 is lower than that of Rectangular-1 to ensure the same global equivalence ratio.In addition,the global equivalence ratio of the circular scramjet is modestly set to 0.2 just in case the inlet unstart occurs if the equivalence ratio is high at the constant isolator.The nonslip and adiabatic conditions are applied to all the walls of the scramjet. The parameters of the flow field at the outlet are interpolated from the inner flow field due to the supersonic characteristic of the flow field. The whole flow field is initialized by the parameters of inflow for all cases. The pressure,mixture fraction, and progress variable are set to ideal values to ignite the fuel when patching the flow field.
2.3. Code verification
Fig. 1 Schematic of rectangular and circular scramjets (various injection schemes are also displayed).
To validate the accuracy of the in-house code, the experiment of Rectangular-1 is employed to compare with the numerical result. The results of three different girds are compared with each other to illustrate that the current result is independent of grid size. Fig. 2 depicts the wall pressure of the coarse(3.64 million), medium (7.29 million), and refined (11.50 million) grids, and the numerical results are compared with the experimental data.32The experimental pressure is measured only on the upper wall.Since the configuration of the scramjet is symmetric,the pressure of the upper and lower wall are both compared with the experimental data.The wall pressure of the medium and refined grids are almost similar to each other while the result of the coarse grid is greatly deviating. The coarse gird underestimates the highest pressure of the flow field near the cavity. The beginning of the boundary layer separation moves upstream in the flow field of the coarse gird. In the downstream of the cavity, the pressure of the coarse grid mismatches with the pressure of the medium and refined grid.The coarse grid cannot calculate the wall pressure and the position of the shock accurately. The above analysis shows that the medium grid is accurate enough and the simulation cost is moderate. The medium mesh is applied in Rectangular-1 in the following results. The grids of the other rectangular and circular cases have almost the same density as the medium grid. All grids are refined near the wall and injection orifices.
The pressure contour is also displayed in Fig. 2. The medium gird captures the basic structures in the combustion flow field. As shown in the wall pressure line and pressure contour in Fig.2,the pressure reaches the highest value near the cavity because of the violent combustion. The boundary layer separates from the wall due to the high backpressure. The asymmetric pressure contour shows that the separation of boundary layer is also asymmetric. The separation induces a shock in isolator and the speed of supersonic inflow decreases.In the downstream cavity, the pressure decreases because of the expansion of the scramjet wall.The internal energy is converted to kinetic energy. The shock is clearly captured in the expanding section, which implies that the simulation is accurate enough.
The wall pressure comparison quantitatively shows that simulation can predict the flow field precisely. In addition,the progress variable C contour is compared with the experimental High-Speed imaging Camera(HSC)image of the flame to verify the code. The progress variable is used to mark the region of the combustion. Because of the integral effect of experimental HSC image,the progress variable contour is a little different from the HSC image.However,the overall characteristics of the experimental and numerical results are similar to each other. As Fig. 3 displays, the asymmetric combustion in the experiment also occurs in the simulation, which couples with asymmetric separation of boundary layer. The combustion near the lower wall is the violent cavity assisted jet-wake stabilized combustion mode,7while the combustion near the upper wall is the cavity shear-layer stabilized combustion mode.7Both of the numerical and experimental results indicate that the combustion locates near the cavity, which shows the significant flameholding effect of the dual parallel cavity.
Due to the variation of the fuel distribution, the combustion flow field differs from each other under different injection schemes and cross-sections. The separation in the circular scramjet may have unique characteristics due to the absence of corner boundary-layer effect.35In this section, the effect of the injection scheme on the asymmetric separation and combustion is numerically analyzed in the rectangular and circular scramjets, respectively. Three injection schemes of the rectangular scramjet and five injection schemes of the circular scramjet are compared. The relationship between the separation direction and the injection scheme in circular scramjet is revealed based on the simulation results. Finally, the similarities and differences of the rectangular and circular scramjets are summarized.
3.1. Effect of injection scheme in rectangular scramjet
Fig. 2 Comparison of wall pressure between numerical and experimental results32 along center line on upper and lower wall of rectangular scramjet (pressure contour of medium grid is also displayed).
Fig.3 Comparison between numerical progress variable contour and experimental HSC image32.
The asymmetric separation in the rectangular scramjet occurs when the backpressure is high enough due to the combustion and heat release.38The configuration of the parallel dualcavity rectangular scramjet in this article is symmetric in Y and Z direction. As the streamwise slices contoured by mass fraction of OH (YOH) show in Fig. 4, when the combustion and heat release are violent, the asymmetric phenomenon becomes obvious because of the high backpressure.The center plane contoured by the Mach number indicates that the separation of boundary layer is asymmetric in Y direction. The stream volume ribbons recirculate upstream of cavity, and the separation zone near the lower wall is larger than the one near the upper wall. The iso-surfaces where mass fraction of C2H4equals 0.1 are also different in the lower and upper wall.The penetration depth of C2H4increases due to the large separation and low flow speed in the lower wall.
Fig.4 Flow field of Rectangular-1(center plane and streamwise slices are contoured by the Mach number and mass fraction of OH,respectively;pink solid line in center plane and blue solid line in streamwise slices are lines of sonic speed; stream ribbons are colored by local normal position).
Fig. 5 Streamwise slices contoured by Mach number for rectangular cases with different injection schemes (black solid line is line of sonic speed to show variation of flow path).
The slices contoured by Mach number and line of sonic speed for rectangular cases with different injection schemes are displayed in Fig. 5 to show the effect of the injection scheme. The boundary layer separation in the rectangular scramjet tends to occur in corners for all cases,which is consistent with the corner boundary-layer effect.35The separations in Rectangular-1 and Rectangular-2 are similar to each other although the injection pressure of Rectangular-2 is lower than that of Rectangular-1.In Rectangular-2,the penetration depth of the second row jets will increase due to the block effect of the first row. And a lot of researches39-40have proved that the double-row injection scheme of Rectangular-2 may benefit the penetration depth of the fuel jets. When the injection scheme becomes more uniform in Rectangular-3,the flow field becomes totally different. The boundary layer separation occurs in corners of the same side instead of diagonally opposite corners. The area of separation decreases and the beginning position of the separation moves downstream. The size of supersonic flow path becomes large and the speed of the main flow also increases in Rectangular-3.
In order to show the size of supersonic flow path quantitatively, the ratio of supersonic area in different X positions to the area of the scramjet inlet is calculated and displayed in Fig. 6. The range of X position covers the main range of boundary layer separation. The supersonic area ratios of Rectangular-1 and Rectangular-2 are the same to each other in the whole range. This implies that the effect of doublerow injection offsets the effect of the low injection pressure.The throat of flow path locates near the cavity because of the significant heat release and reaction. Compared to the other two rectangular cases, the supersonic area in Rectangular-3 increases a lot. Combining the results of Fig.5,one can see that the boundary layer separation becomes weak and the speed of main flow increases, when the injection scheme becomes uniform. The weak separation and combustion are coupled with the high main flow speed. High speed leads to weak combustion, and weak combustion further results in high-speed main flow. As a result of the mutual induction effect, the boundary layer separation becomes weak and the supersonic area ratio increases eventually.
Fig. 6 Supersonic area ratio (ηArea) in different X positions for rectangular cases with different injection schemes.
The violent combustion and heat release around the cavity would significantly change the configuration of the supersonic flow path.Fig.7 provides a detailed observation of the boundary of the supersonic area in various X positions for different rectangular cases to illustrate the asymmetric characteristics of the flow field.For all cases,the size of supersonic area is smaller around the cavity (X = 1.4 m) than the upstream(X = 1.2 m) and downstream (X = 1.5 m) area of the cavity,although the cross-section is the biggest for the X = 1.4 m slice. The high-pressure cavity compresses the main flow and the supersonic flow path contracts. Due to the corner boundary-layer effect, the boundary layer is separated from the wall and low-speed area around the corner is formed.The configurations of the supersonic flow path are similar to each other in Rectangular-1 and Rectangular-2, while it is totally different in Rectangular-3. This may be because the double-row injection scheme in Rectangular-2 has the same effect to the high-pressure injection scheme in Rectangular-1,but the one-row injection scheme with low injection pressure in Rectangular-3 is different. In addition, the supersonic area is smaller in Rectangular-1 and Rectangular-2 than in Rectangular-3, which implies that the combustion and heat release are more violent in the first two cases.
The asymmetric characteristics locally appear as the different separation states in the corners of rectangular cases.On the whole, the centroid deviation can also reflect the basic asymmetric characteristics of the flow field. As shown in Fig. 8,the centroid deviation Δr is defined as the deviation between the centroid of supersonic area (R2) and the centroid of cross-section (R1) in different streamwise position. The supersonic area is marked by red line while the cross-section is marked by black line in Fig. 8. Although Rectangular-3 has the biggest supersonic flow path,the centroid deviation of this case is higher than that of Rectangular-1 and Rectangular-2.The maximal centroid deviation of Rectangular-3 is about 15 mm. For Rectangular-1 and Rectangular-2, the centroid deviation can reach 5 mm and 10 mm, respectively. With the variation of the injection scheme, the difference of maximal centroid deviation can reach three times (Rectangular-3 to Recntangular-1). This indicates that the supersonic flow path deviates from the center line seriously, when the violent separation around corner occurs in the same side of the scramjet in Rectangular-3. Another interesting phenomenon is that when the number of injection orifices increases and the injection pressure decreases in Rectangular-2 and Rectangular-3,the centroid deviation increases.It is supposed that the number of injection orifices could be optimized to reach uniform combustion and thrust.
Fig. 7 Boundary of supersonic area (Ma = 1) in different X positions for different rectangular cases.
When the asymmetric boundary layer separation occurs,the jet penetration depth will also become different among jets in various Z positions due to the difference of the local pressure and flow speed. The change of jet penetration depth will affect the mixing and combustion of the fuel and further affect the performance of the scramjet. As Fig. 9 displays, the isosurfaces where the mass fraction of C2H4equals 0.1 are com-Fig.8 Deviation between centroid of supersonic area and crosssection in different X positions for rectangular cases with different injection schemes.pared among rectangular cases with different injection schemes. The front view images are contoured by the local pressure while the side view is contoured by various colors to indicate the position of jets in different Z positions. When the separation is violent, the speed and dynamic pressure of incoming flow are low.From the front view,it is observed that the jet penetration depth increases and the pressure of the jet windward side is low in the separation zone. On the contrary,the fuel penetration depth is small and the stagnant pressure is high when the separation is weak. From the side view, it is obvious that the larger the fuel penetration depth is, the shorter the iso-surface is in X direction. This is because the large penetration depth promotes the mixing of the fuel and the fuel consumes more quickly. The above phenomenon is coincident among different rectangular cases. The states of boundary layer separation are similar between Rectangular-1 and Rectangular-2 in Fig. 5. The configurations of fuel isosurface are the same to each other. However, with one-row injection scheme and low injection pressure, Rectangular-3 has a completely different fuel iso-surface. The penetration depths of Jet 1-Jet 4 are small and the pressure on the isosurface is high. Jet 5 and Jet 6 penetrate deeply because of the low speed in the separation zone. The small penetration depth leads to poor fuel mixing and combustion,and the speed of the main flow increases in Rectangular-3.
3.2. Effect of injection scheme in circular scramjet
Due to the simple structure and low resistance, the circular scramjet has drawn wide attention after Bulman and Siebenhaar41made a review of circular hypersonic propulsion. The characteristics of boundary layer separation are worthy to explore since the cross-section without corner is smooth in the circular scramjet. In this subsection, the combustion flow field of the circular scramjet is investigated and the effect of the injection scheme is studied. The main attention is paid to the asymmetric characteristics in the combustion flow field.In Fig. 10, the density gradient magnitude (|∇ ρ|) contour in center plane is displayed to show the shock structure. As the red solid line shows, the boundary layer separates from the wall due to the combustion near the cavity. The separation shock and reflected shock are clearly captured, and the bow shock is induced by the fuel jets. The recirculation inside the cavity and the separation zone can be observed in the Mach number contour. The streamwise slices are contoured by the progress variable, which reflects the progress of the chemical reaction. It is observed that the reaction becomes violent once the fuel enters the flow field. The combustion is axisymmetric in the circumferential direction as the streamwise slices show.The separation of boundary layer is also axisymmetric under the injection scheme of Circular-1.
Fig. 9 Iso-surface of mass fraction of C2H4 for rectangular cases with different injection schemes (front view image is contoured by pressure, and side view image is contoured by different colors to show position in Z direction).
Fig. 10 Flow field of Circular-1.
The combustion flow field of Circular-1 has axisymmetric characteristics. However, asymmetric combustion and separation occur under multi-row injection schemes.Fig.11 displays the Z = 0 plane (contoured by temperature) and two streamwise slices (contoured by progress variable). The black solid line is the line of sonic speed and the black dashed line is used to indicate the direction of minimal and maximal separation.Corresponding to Fig. 10, the one-row and uniformly distributed injection scheme leads to the axisymmetric combustion in Circular-1. The sonic lines in two streamwise slices are circles, which implies that the boundary layer separation is uniform. Circular-2 and Circular-3 are both two-row injection scheme, and asymmetric combustion occurs in these two cases. In Circular-2, the injection orifices mainly concentrate on the top and bottom sides of the circular wall. Due to the distribution of the injection orifices, the combustion becomes asymmetric. The combustion is violent on the bottom side,while it is weak on the top side.The boundary layer separation has similar characteristics, and the sonic lines in two streamwise slices are ellipses whose minor axis is in line with Yaxis. In Circular-3, the injection scheme is uniform but asymmetric combustion and separation still occur. And the direction of minimal and maximal separation is in line with Zaxis. Circular-4 and Circular-5 are both four-row injection schemes. When the injection orifices concentrate on the top and bottom sides in Circular-4,the combustion and separation are consistent with the injection scheme. This phenomenon is similar to Circular-2. However, when the injection scheme is uniform in Circular-5, the direction of minimal and maximal separation deviates from Y-axis. The asymmetric characteristics in Circular-5 are different from those in Circular-3.In conclusion,the combustion and separation are axisymmetric when the injection scheme is one-row and uniform. When the injection scheme is nonuniform in Circular-2 and Circular-4, the combustion and separation are consistent with the distribution of injection orifices. However, asymmetric combustion and separation still occur and cannot be predicted by the uniformly distributed injection scheme in Circular-3 and Circular-5.
The asymmetric combustion and separation will lead to the deformation of the flow path. Fig. 12 displays the pressure contour in the plane going through the black dashed line in Fig. 11, which marks the direction of minimal and maximal separation.The supersonic area ratio is also provided to show the effect of the injection scheme. It is observed that the pressure contour and sonic line (red solid line) are symmetric in Circular-1 whose combustion is uniform in circumferential direction.The pressure contour and sonic line are broadly similar to each other among Cricular-2 to Circular-5. And the boundary layer separation region at the bottom side covers a wider range than Circular-1.As the first dashed dot line shows,the high-pressure region moves a little upstream.As the second dashed dot line shows,the reattachment point of the boundary layer moves downstream in the last four cases. An interesting phenomenon is that the reattachment point of the nonuniform injection scheme (Circular-2 and Circular-4) locates at downstream area of the reattachment point of the uniform injection scheme(Circular-3 and Circular-5).Corresponding to the pressure contour, the supersonic area ratio of Circular-2 and Circular-4 is smaller than that of Circular-3 and Circular-5 in the isolator and the downstream area of the cavity. It is implied that the nonuniform injection scheme results in more violent combustion than the uniform injection scheme. The separation becomes more serious and the size of supersonic flow path decreases.
Fig.11 Z=0 plane(contoured by temperature)and streamwise slices(contoured by progress variable)for circular cases with different injection schemes (black dashed line in streamwise slices is used to show direction in which separation is asymmetric).
In order to explore the effect of injection scheme on the configuration of the supersonic flow path, Fig. 13 displays the boundary of the supersonic area in various X positions for circular cases.For Circular-1,the boundary keeps the circular configuration,which indicates that the combustion and separation in this case are axisymmetric. For other cases, the supersonic flow path deviates from the center line.Corresponding to the results of Fig.11,because the separation is weak in the top of the flow path and is strong in the bottom for Circular-2 and Circular-4,the boundaries of these two cases deviate to the top of the cross-section. For Circular-3, the flow path deviates to the right, which is in line with the direction of the minimal and maximal separation. The direction of the minimal and maximal separation deviates a little from Y-axis in Circular-5. Therefore, the boundary of Circular-5 has a subtle difference with that of Circular-2 and Circular-4.
Fig. 14 displays the centroid deviation of circular cases to investigate the asymmetric characteristics from the whole view.The definition of the centroid deviation is similar to that of rectangular cases.For Circular-1,which has one-row and uniformly distributed injection scheme, the centroid deviation is subtle and can be omitted. For two-row cases, the flow path deviates from the center line more obviously in Circular-2 with nonuniform injection scheme than in Circular-3 with uniform injection scheme.The four-row cases have the same characteristic, which implies that nonuniform injection scheme could lead to the violent asymmetric combustion and separation.Comparing the two-row cases with the four-row cases, it is obvious that the flow path deviates from the center line more seriously in the four-row cases. The cases with uniform and nonuniform injection schemes show similar characteristic.From the above analysis, it is suggested that uniform and one-row injection scheme should be applied to reach a homogeneous combustion when designing a circular scramjet.Compared with the rectangular scramjet, the line of centroid deviation of circular scramjet keeps the same trend of variation. When the asymmetric separation occurs, the maximal centroid deviation reaches the level of about 5 mm.
The cavity is the most important part of the scramjet due to its significant flameholding effect.42The mass exchange through the cavity lip surface can provide energy and free radicals to the residual fuel.43As shown in Fig. 15, the cavity lip surface is spread out from positive half of Y-axis. VRis the velocity perpendicular to the cavity lip surface, with positive direction pointing into the cavity. The cavity lip surfaces for different circular cases are displayed to investigate the characteristics of the mass exchange. For all cases, the flow enters cavity from the front and middle part of the cavity lip surface,and goes out from the back part.Although the above analysis shows that the combustion and boundary layer separation of Circular-1 are axisymmetric, the mass exchange rate of Circular-1 is a little asymmetric. However, the asymmetric characteristic is weak and the mass exchange keeps at the same level in different circumferential direction. For Circular-2 to Circular-5, the asymmetric characteristic becomes significant.For Circular-2 and Circular-4, the mass exchange rate is nonuniform and violent in the range of 90° to 270°. This is consistent with the results of Fig. 10. The most violent mass exchange occurs in the direction of maximal separation, and the mass exchange in the opposite direction is weak. When the injection scheme is uniform in Circular-3 and Circular-4,the distribution of the mass exchange rate changes hugely.For Circular-3, because the minimal and maximal separation locates at positive and negative half of the Z-axis,the distribution of mass exchange rate becomes complicated. The flow enters into the cavity in the range of 0° to 180° and goes out in the range of 180° to 360°. For Circular-5, the distribution of the mass exchange rate is similar to Circular-2 and Circular-4. However, the contour in the range of 0° to 180°is not completely symmetric to that in the range of 180° to 360°, since the direction of the minimal and maximal separation deviates a little from Y-axis.
Fig.12 Pressure contours in plane passing through black dashed line in Fig.11 and supersonic area ratio in different X positions for circular cases with different injection schemes.
Fig. 14 Deviation between centroid of supersonic area and cross-section in different X positions for circular cases with different injection schemes.
3.3. Comparison between rectangular and circular scramjets
Fig. 13 Boundary of supersonic area (Ma = 1) in different X positions for different circular cases.
Fig. 15 Mass exchange rate through cavity lip surface for circular cases with different injection schemes.
For cavity-assisted scramjet, the flameholding effect depends on the cavity where the flow speed is low, the temperature is high and the free radical is rich. Although the rectangular and circular scramjets in this article employ different cavity and injection schemes,there are some common characteristics.Therefore, Rectangular-1 and Circular-1 are compared in this subsection to show the similarities and differences between rectangular and circular scramjets. Fig. 16 displays the center plane contoured by Mach number and a streamwise slice contoured by mass fraction of OH for Rectangular-1 and Circular-1. In both rectangular and circular scramjets, the speed in the cavity is low and the cavity serves as an ignition source to the remaining mixture of fuel and air.The high backpressure caused by combustion leads to the boundary layer separation,the low-speed area in the separated boundary layer provides perfect environment for combustion. This forms a positive feedback, which finally enhances the combustion and separation. The white line in the center plane is sonic line which depicts the configuration of the supersonic flow path.Due to the combustion and heat release near the cavity, the supersonic flow path contracts near the cavity to form a shape similar to Laval nozzle.The throat of the supersonic flow path locates near the cavity in both rectangular and circular scramjets.
Due to the corner boundary-layer effect35in the rectangular scramjet,there exist some differences between rectangular and circular scramjets. From the streamwise slice contoured by mass fraction of OH in Fig.16,it is observed that the combustion in the separated boundary layer is different between the rectangular and circular scramjets. The flame concentrates near the corner in the rectangular scramjet because of the corner boundary-layer effect.35The combustion and separation are strong in the corner while they are weak in the center of the scramjet. In the circular scramjet, the OH concentrates near the wall due to the lack of corner. The configuration of the supersonic flow path is totally different between the rectangular and circular scramjets.
Fig.16 Center planes(contoured by Mach number)and streamwise slices(contoured by mass fraction of OH)in upstream side of cavity for rectangular and circular scramjets.
To present the similarities and differences between rectangular and circular scramjet in a clearer way, Fig. 17 provides a schematic diagram of the basic characteristics of asymmetric combustion and separation in rectangular and circular scramjets.After the fuel enters the flow field,its combustion and heat release lead to the high pressure near the cavity. When the backpressure is high enough at the isolator outlet, the boundary layer of the inflow would separate from the wall and the asymmetric phenomenon usually occurs.3In the separation zone, the flow speed is low and the fuel has enough residence time to mix with the air. Therefore, the combustion is enhanced by the separation.In turn,the combustion will cause high pressure and promote separation. The interaction between combustion and separation forms a positive feedback.Due to the positive feedback, the asymmetric combustion and separation will be solidified. The violent combustion and separation side will keep the violent state,while the weak side will keep the weak state. The above phenomenon exists in both rectangular and circular scramjets. The differences between the rectangular and circular scramjets are caused by the corner boundary-layer effect.35As Fig.17 shows,the combustion and separation are strong near the corner in the rectangular scramjet,while the condition of combustion and separation in circular scramjet mainly depends on the injection scheme. In circular scramjet, the direction of the minimal and maximal separation is consistent with the injection scheme if the injection scheme is nonuniform and multi-row. Under the uniform injection scheme condition, the direction of the minimal and maximal separation cannot be predicted.
Fig. 17 Schematic diagram of basic characteristics of asymmetric combustion and separation in rectangular and circular scramjets.
The effect of the injection scheme on combustion field in the rectangular and circular scramjet is investigated numerically.The relationship between the asymmetric phenomenon and the injection scheme is revealed. The rectangular and circular scramjets have their own special asymmetric characteristics,but there are also some similarities about the flow structure and combustion organization. The main conclusions are drawn as follows:
(1) In the rectangular scramjet, the separation tends to occur in the corner of the flow path due to corner boundary-layer effect. Both high injection pressure and two-row injection scheme can result in significant combustion and serious separation. With the exacerbation of the separation, the fuel penetration depth increases and the fuel consumes more quickly. The injection scheme affects the size and configuration of the supersonic flow path hugely. The maximal centroid deviation ranges from 5 mm to 15 mm with the variation of the injection scheme.
(2) In the circular scramjet, the one-row and uniformly distributed injection scheme leads to the uniform combustion and separation, while the asymmetric phenomenon occurs in other cases. The separation is in line with the injection scheme in cases with multirow nonuniform injection scheme. The separation state cannot be predicted if the injection orifices are uniform.The centroid deviation of the one-row case is less than 2 mm, while maximal centroid deviation can reach 6 mm in cases where the asymmetric separation occurs.
(3) The interaction between combustion and separation exists both in the rectangular and circular scramjets,which enhances the asymmetric separation and combustion.The throat of the supersonic flow path locates near the cavity regardless of the shape of the cross-section.The cavity-assisted rectangular and circular scramjets have some similarities of the asymmetric flow field,although they have their unique characteristics.
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 National University of Defense Technology in 2019, China (No. ZK19-02), the Postgraduate Scientific Research Innovation Project of Hunan Province,China (No. CX20200084), and the Equipment Pre-research Foundation of Key Laboratory, China (No. 6142703200311).
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