# A Preliminary Research on Combustion Characteristics of a Novel-Type Scramjet Combustor

Authors: Linqing Zhang; Juntao Chang; Wenxiang Cai; Hui Sun; Yingkun Li
Journal: International Journal of Aerospace Engineering
 (2022)

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## Abstract

In this work, a new configuration of strut-based scramjet is proposed, and a series of simulations are conducted to investigate its possibility of practical application. The simulation results are verified via the classical DLR ramjet and an experiment conducted on the connected pipe facility. The inlet area (Ain) and air intake height (H) of the combustor are varied independently to investigate their performance. The results indicate that the flow field and shock wave structure of such engine reveal similar characteristics as the classical DLR engine, and the variation in engine geometry can significantly affect its combustion characteristics. Moreover, the combustion efficiency could be enhanced by 2% as the Ain varied from 900π mm2 to 1100π mm2; increasing the air intake path (H) to 12 mm can increase the combustion efficiency by 25%. In general, the present work proposes a new geometry of the scramjet combustor; this combustor has possibility of practical application, but a further and detailed investigation is still needed.


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## Body

## 1. Introduction

The supersonic combustion ramjet draws attention throughout the world owing to its characteristics of simple structure, high speed, and low cost [1]. There are many researchers who have conducted a lot of efforts on the combustion characteristics of scramjet combustors; they found that the structure of the combustor plays a critical role in flame stabilization and its performance [2–5].So far, there are three types of the typical structures of scramjet combustor, i.e., the cavity- [2, 3, 6–15], strut- [5, 16], and backward-facing step-based combustor [4, 17–20]. The strut-based combustor was first proposed by Waidmann et al. [21]; they used hydrogen as the fuel to investigate the combustion characteristic of a typical strut-based scramjet combustor (DLR (German Aerospace Center) scramjet) via experimental approach; in this investigation, the flow features were clearly captured, and the chamber pressure was found to be enhanced with increasing of hydrogen mass flow rate. At the same time, the 2D cavity-based scramjet combustor fueled by kerosene and hydrogen was investigated by Vinogradov et al. [22]; the results indicated that the performance of the scramjet was highly dominated by the ignition and combustion process. After that, the backward-facing step-based scramjet was proposed by Witt [23] and Angus [24] from the Naval Postgraduate School; they used PMMA as fuel, and the engine was ignited using a pilot torch fueled by hydrogen; the research confirmed the feasibility of backward-facing step-based combustor in scramjet.With the deepening of researchers’ understanding of supersonic combustion, they noticed that enhancing combustion and mixing efficiency is the most effective method to improve the engine performance [25]. Thus, with the enrichment and development of various research methods, many researchers have conducted a lot of efforts to enhance the mixing and combustion efficiency by modifying the structure of the scramjet combustor, including changing the strut or cavity configuration [26], using multiple cavities [27–31] and so on. Sun et al. [31] conducted an investigation of the ignition process of hydrogen-fueled scramjet combustor; in such combustor, multicavities were involved. The results indicated that the multiple cavities were helpful to the diffusion of the fuel, and the location of the fuel injector played an important role in the fuel ignition performance. Huang [16] conducted an investigation on the effect of strut configurations of a typical strut-based DLR-type combustor. The effect of different radii of the strut tips on the combustion characteristics is studied, which varied from 0.211 mm to 2.853 mm. The results indicated that the shock wave system around the strut became more complicated as the radius was increased. And the combustion efficiency was highly related to the shock wave structure led by the strut configuration. Kummitha et al. [11, 32–34], Pandey et al., and Choubey et al. [35–38] conducted numerous investigations that attempted to obtain a higher combustion efficiency; they used different strut types of injectors and combustion chambers. The research reported that the combustion and mixing efficiency could be highly dominated by the engine geometry.With the development of experimental and analytical technology, recently, many researchers have made many detailed explorations of the effect of the structure of the scramjet combustor on its performance. Yang et al. [30] conducted an investigation of the multicavity solid-fueled scramjet; the influence of cavity shape on the characteristics of such combustors was studied. They investigated three types of cavities, i.e., flame-holding, narrow, and lobe cavities; the results indicated that the mixing and combustion efficiency could be significantly improved under the structure of narrow and lobe cavities. Meanwhile, Yang et al. [39] studied the injection structure of the same type of scramjet. In this research, the injector had three types of structure, i.e., circular at 60°, elliptical at 90°, and two-stage elliptical at 60°; they reported that the elliptical at 90°-type injector had the ability to improve the ignition and combustion performance, and the two-stage elliptical at 60°-type injector could enhance the combustion frequency compared to that of the circular at 60°-type injector. Recently, Kireeti et al. [40] numerically investigated the combustion characteristics of four strut injectors and doubly-dual cavity-based scramjet combustor. In this research, the four struts were cross-symmetrically distributed ahead of the doubly-dual cavity. The results indicated that a better mixing of the fuel and inlet air was obtained in such cases owing to the increased level of the shock layer. In addition to the influence of the flame holder structures, the structure of the engine isolator may also affect the engine performance. Motivated by this, Sharma et al. [41] conducted a numerical investigation on the influence of isolator section on the scramjet performance. The isolator length varied from 2.5D to 55D, where D represented the diameter of the injector. The results revealed that the variation of the isolator length could marginally enhance the mixing rate, and they found that the Prandtl-Meyer expansion fan generated at the flame holder could effectively isolate the combustor and isolator; thus, they concluded that the isolator could be designed based on the flow homogenization of the inlet air ahead of the combustor.The aforementioned combustor mainly focused on the two-dimensional shape (square cavity), which may increase the difficulty in practical applications of the scramjet and on the other hand increase the space occupancy of the engine. By this, the present research proposes a novel strut-based configuration of the engine, which is the annular strut-based combustor, and the combustion characteristics in different combustor geometry are discussed.In the present paper, the novel strut-based configuration of the scramjet was proposed, and preliminary research has been conducted. The governing equations and the models are introduced, and the simulation cases are validated against the benchmark cases, which are illustrated in Section2. The model is then applied to evaluate the combustion and mixing characteristics of such combustor under the effect of (1) air intake height (H) and (2) air intake area (Ain); this is described and discussed in Section 3. The key findings are summarized in Section 4.


## 2. Mathematical Method

### 2.1. Governing Equations of Fluid Domain

The governing equations of fluid domain could be written in the form below:(1)∂Q∂t+∂E∂x+∂F∂y+∂H∂z=∂Ev∂x+∂Fv∂y+∂Hv∂z+S,where Q, E, F, EV, FV, H, HV, and S are expressed in the following form:
(2)Q=ρρuρvρwρEρi,E=ρuρu2+pρuvρuwρE+puρiuci,F=ρvρuvρv2+pρvwρE+pvρivci,H=ρwρuwρvwρw2+pρE+pwρwci,Ev=0τxxτxyτxzuτxx+vτxy+wτxz+qx+∑i=1NρDimhi∂ci∂xρDim∂ci∂x,Fv=0τxyτyyτyzuτxy+vτyy+wτyz+qy+∑i=1NρDimhi∂ci∂yρDim∂ci∂y,Hv=0τxzτyzτzzuτxz+vτyz+wτzz+qz+∑i=1NρDimhi∂ci∂zρDim∂ci∂z,Sϕ=SρSρuSρvSρwSρEmi+Sρi.Theτ is shear stress, and qx, qy, and qz represent the heat fluxes in x, y, and z directions. Considering the multicomponent involved in the combustion field, ρDi is utilized to represent the diffusion of each component and could be calculated by
(3)ρDi=1−Xi1−ciμlSc+μtSct.Meanwhile, to calculate the viscosities of the gas mixture accurately, the Lennard-Jones equation is applied (as shown in Equation (4)). And the laminar and turbulent viscosities (μli/j and μti/j) of the mixture are calculated using the following formula:
(4)μl=∑i=17Xiμliϕi,ϕi=∑j=17Xj1+μli/μljMi/Mj1/4281+Mi/Mj,μl=a1ρkmaxa1ω,f2Ω,f2=tanhmax2k0.99ωy′,500μρy2ω2.The equation shown below is employed to calculate the thermal conductivityλ.
(5)λ=μlcpPrl+μtcpPrt.The pressure of gas mixture is given by Equation (6), and the Newton iteration method is used to calculate the temperature (T) of the flow field.
(6)p=∑i=17ρiMiRuT,(7)ρE−12ρu2+v2+w2=∑i=17ρi∫298TCpidT+hi298−RuT∑i=17ρiMi,where the Cpi used in Equation (7) is defined by Equation (8); the parameter αki (k=1,2,3,4,5) can be found in the chemical kinetics package:
(8)Cpi=a1i+a2iT+a3iT2+a4iT3+a5iT4.


### 2.2. Numerical Solution Method

In this research, the ANSYS Fluent 2019 is utilized to simulate the flow features in the present model. And to capture the shock wave lead by the supersonic flow in such systems more accurately, the monotone upstream-centered scheme for conservation laws (MUSCL) and advection upstream-splitting method by pressure-based weight function (AUSM) scheme are utilized to compute convective flux quantities. And, owing to the existence of the shear flow and flow separation phenomenon in the present scramjet combustor, thek‐ω SST (shear-stress transport) turbulence model proposed by Menter is used to simulate the turbulent flow in this research.


### 2.3. Chemical Reaction Model

The chemical reaction kinetic of CO and H2 mixture in the scramjet is described as Equations (9) and (10); we use a simplified one-step mechanism to simulate the reaction between the CO, H2, and O2. In this research, for the consideration of the effect of turbulence and high-speed flow in the scramjet, the finite rate/eddy dissertation model is applied to simulate the chemical reaction processes. The combustion mechanism is shown below. And the other parameters such as preexponential factors, activation energy, and temperature exponent could be obtained from the CHEMKIN kinetic package.
(9)2CO+O2⟶2CO2(10)2H2+O2⟶2H2O


### 2.4. Physical Model and Boundary Conditions

The physical model of the present research is an annular combustion chamber model, which is shown in Figure1. And, to reduce the computational cost, 1/4 of the model is selected, as shown in Figure 1(a). In Figure 1(b), the value of L1, L2, H, R, r, d, D, and w is 50 mm, 300 mm, 10 mm, 55 mm, 45 mm, 10 mm, 38 mm, and 10 mm, respectively (see Table 1(a)). There are four struts placed along the circumferential direction, and a fuel nozzle with a diameter of Dt=4mm is set at the middle of each strut bottom. The boundary conditions can be summarized as follows (see Figures 1(b) and 1(c)): (1) the inlet condition is set with the constant total pressure, temperature, and velocity of 1.5 MPa, 650 K, and 762 m/s, respectively; (2) pressure outlet condition at the engine outlet is set with the pressure of 101325 Pa and 300 K in temperature; (3) the symmetric boundary condition is utilized at two symmetric faces; (4) nonslip adiabatic boundary condition is employed at walls; and (5) the boundary condition of the fuel nozzle has the total pressure of 2 MPa, the velocity of 1362 m/s, and the total temperature of 1800 K (see Table 1(b)). And the fuel contains 50% of CO, 14% of H2, and 36% of N2.Figure 1
Physical model of the SFRJ used in this investigation.
(a)(b)(c)Table 1
(a) Geometry parameters of the present model; (b) detailed boundary condition.
(a)L1L2HRrdDwDt50 mm300 mm10 mm55 mm45 mm10 mm38 mm10 mm4 mm(b)InletPressure (MPa)Temperature (K)Velocity (m/s)1.5650762Fuel nuzzlePressure (MPa)Temperature (K)Velocity (m/s)218001362OutletPressure (Pa)Temperature (K)101325300Symmetric facesSymmetric boundary conditionWallsNonslip adiabatic boundary conditionThe grid separation of the surface is shown in Figure1(c), and the grids near the wall surface are refined to make sure the y+ is within the range of 1~5. And the total grid number is 2.7 million.


### 2.5. Case Description

Systematic simulations are conducted as shown in Table2. The simulations are performed to investigate the effect of the chamber geometry on the combustion characteristics. In cases 1-3, the parameter H is set as constant, and the parameters Ain are varied. In cases 2, 4, and 5, the parameters H are varied, and Ain is set as constant.Table 2
Simulation conditions.
Case numberR/mmr/mmH/mmAin/mm2Case 16050101100πCase 25545101000πCase 3504010900πCase 466.558.581000πCase 547.6535.65121000π


### 2.6. Grid Independency Study and Model Validation

To make sure the grid number is suitable for the current research, the grid independency study is conducted. We use three cases with different mesh numbers, i.e., the coarse mesh with 1.9 million cells, the moderate mesh with 2.7 million, and the refined mesh with 3.8 million cells. Theyplus is set to 1-5 for all the cases in the independency study. The results are shown in Figure 2; as seen in the figure, the pressure variations along the axial direction of the three cases exhibit significant differences between the coarse mesh and moderate and refined mesh. Thus, to save the computational resources and maintains accuracy of the simulation, the moderate mesh is utilized for the present study.Figure 2
Results of grid independency study.To ensure the accuracy of the present simulation, model validation is needed. In the present research, two experimental cases are utilized, i.e., the classical DLR model proposed by Deutsches Zentrum für Luft- und Raumfahrt [21] and a ground cold flow test conducted via the connected pipe facility.The classical DLR model is illustrated in Figure3(a); as shown in the figure, the strut is equipped at the position marked in Figure 3(a), and the hydrogen fuel is injected into the combustor with the speed of Mach 1. The grid separation is shown in Figure 3(b).Figure 3
Physical model of DLR engine.
(a)(b)The boundary condition of the air inlet and fuel inlet is described in Table3; the outlet is set as pressure outlet, and the no-slip wall condition is applied for all walls in the model.Table 3
Boundary conditions.
Air inletH2 inletInlet Mach number2.01.0Velocity (m/s)7301200Temperature (K)340250Pressure (Pa)100000100000Mass fraction of N20.7360Mass fraction of O20.2320Mass fraction of H2O0.0320Mass fraction of H201The schlieren interferogram obtained by experiment and numerical simulation is described in Figure4. It could be seen from the figure that the expansion wave and the reflected shock wave of the simulation conform well to the experimental result. And this indicates that the proposed method can accurately predict the flow field in the ramjet combustor.Figure 4
The schlieren interferogram obtained by experiment (up) and numerical simulation (down).The temperatures at different axial positions are described in Figure5; it could be seen from the figure that the trend of the temperature distribution obtained from the experiment and simulation is almost the same, which indicates that the proposed model can accurately predict the flow and combustion in such combustors.Figure 5
Distribution of the temperature obtained from experiment and simulation.To make sure the present model can predict the flow conditions accurately in the annular combustion chamber, a cold flow ground test is conducted via a connected pipe facility; the experimental model is almost the same as the model shown in Figure1(b), except the parameter L2 is 800 mm. The experimental engine is illustrated in Figure 6. Five pressure sensors are set on the engine along the axial direction, at the position of 350 mm, 450 mm, 550 mm, 650 mm, and 750 mm, with respect to the engine inlet. The experimental conditions are shown in Table 4.Figure 6
Scramjet engine.Table 4
Experimental conditions.
Pressure (MPa)Temperature (K)Velocity (m/s)1.5650762As for the simulation part, the boundary condition is the same as described in Section2.4 (Figure 2), and the physical model is the same as the experimental one. The result is shown in Figure 7. In this figure, the distribution of the pressure field is illustrated; unlike the flow patterns shown in Figure 3, in an annular flow field, the shock wave is mainly dominated by the strut placed along the circumferential direction, rather than the combustor wall. Thus, this may lead to the phenomena occurring in the middle of the two struts (marked with the square), and the cells with diamond shapes appear downstream of the flow field. In addition, it is worth noting that the low pressure region with the shape of a swallowtail could be observed at the bottom of the struts (as marked with the circle).Figure 7
Distribution of the pressure in the chamber.The results obtained from the experiment and simulation are shown in Figure8; it is worth noting that the results obtained from the simulation reveal a wave shape; this is believed to be caused by the abovementioned diamond-shaped pressure distribution. And it can also be seen that the pressure measured at the measuring points conforms well to the simulation result, which means that the proposed method can accurately predict the flow patterns in the combustor.Figure 8
Comparison between the experimental result and numerical result.


## 2.1. Governing Equations of Fluid Domain

The governing equations of fluid domain could be written in the form below:(1)∂Q∂t+∂E∂x+∂F∂y+∂H∂z=∂Ev∂x+∂Fv∂y+∂Hv∂z+S,where Q, E, F, EV, FV, H, HV, and S are expressed in the following form:
(2)Q=ρρuρvρwρEρi,E=ρuρu2+pρuvρuwρE+puρiuci,F=ρvρuvρv2+pρvwρE+pvρivci,H=ρwρuwρvwρw2+pρE+pwρwci,Ev=0τxxτxyτxzuτxx+vτxy+wτxz+qx+∑i=1NρDimhi∂ci∂xρDim∂ci∂x,Fv=0τxyτyyτyzuτxy+vτyy+wτyz+qy+∑i=1NρDimhi∂ci∂yρDim∂ci∂y,Hv=0τxzτyzτzzuτxz+vτyz+wτzz+qz+∑i=1NρDimhi∂ci∂zρDim∂ci∂z,Sϕ=SρSρuSρvSρwSρEmi+Sρi.Theτ is shear stress, and qx, qy, and qz represent the heat fluxes in x, y, and z directions. Considering the multicomponent involved in the combustion field, ρDi is utilized to represent the diffusion of each component and could be calculated by
(3)ρDi=1−Xi1−ciμlSc+μtSct.Meanwhile, to calculate the viscosities of the gas mixture accurately, the Lennard-Jones equation is applied (as shown in Equation (4)). And the laminar and turbulent viscosities (μli/j and μti/j) of the mixture are calculated using the following formula:
(4)μl=∑i=17Xiμliϕi,ϕi=∑j=17Xj1+μli/μljMi/Mj1/4281+Mi/Mj,μl=a1ρkmaxa1ω,f2Ω,f2=tanhmax2k0.99ωy′,500μρy2ω2.The equation shown below is employed to calculate the thermal conductivityλ.
(5)λ=μlcpPrl+μtcpPrt.The pressure of gas mixture is given by Equation (6), and the Newton iteration method is used to calculate the temperature (T) of the flow field.
(6)p=∑i=17ρiMiRuT,(7)ρE−12ρu2+v2+w2=∑i=17ρi∫298TCpidT+hi298−RuT∑i=17ρiMi,where the Cpi used in Equation (7) is defined by Equation (8); the parameter αki (k=1,2,3,4,5) can be found in the chemical kinetics package:
(8)Cpi=a1i+a2iT+a3iT2+a4iT3+a5iT4.


## 2.2. Numerical Solution Method

In this research, the ANSYS Fluent 2019 is utilized to simulate the flow features in the present model. And to capture the shock wave lead by the supersonic flow in such systems more accurately, the monotone upstream-centered scheme for conservation laws (MUSCL) and advection upstream-splitting method by pressure-based weight function (AUSM) scheme are utilized to compute convective flux quantities. And, owing to the existence of the shear flow and flow separation phenomenon in the present scramjet combustor, thek‐ω SST (shear-stress transport) turbulence model proposed by Menter is used to simulate the turbulent flow in this research.


## 2.3. Chemical Reaction Model

The chemical reaction kinetic of CO and H2 mixture in the scramjet is described as Equations (9) and (10); we use a simplified one-step mechanism to simulate the reaction between the CO, H2, and O2. In this research, for the consideration of the effect of turbulence and high-speed flow in the scramjet, the finite rate/eddy dissertation model is applied to simulate the chemical reaction processes. The combustion mechanism is shown below. And the other parameters such as preexponential factors, activation energy, and temperature exponent could be obtained from the CHEMKIN kinetic package.
(9)2CO+O2⟶2CO2(10)2H2+O2⟶2H2O


## 2.4. Physical Model and Boundary Conditions

The physical model of the present research is an annular combustion chamber model, which is shown in Figure1. And, to reduce the computational cost, 1/4 of the model is selected, as shown in Figure 1(a). In Figure 1(b), the value of L1, L2, H, R, r, d, D, and w is 50 mm, 300 mm, 10 mm, 55 mm, 45 mm, 10 mm, 38 mm, and 10 mm, respectively (see Table 1(a)). There are four struts placed along the circumferential direction, and a fuel nozzle with a diameter of Dt=4mm is set at the middle of each strut bottom. The boundary conditions can be summarized as follows (see Figures 1(b) and 1(c)): (1) the inlet condition is set with the constant total pressure, temperature, and velocity of 1.5 MPa, 650 K, and 762 m/s, respectively; (2) pressure outlet condition at the engine outlet is set with the pressure of 101325 Pa and 300 K in temperature; (3) the symmetric boundary condition is utilized at two symmetric faces; (4) nonslip adiabatic boundary condition is employed at walls; and (5) the boundary condition of the fuel nozzle has the total pressure of 2 MPa, the velocity of 1362 m/s, and the total temperature of 1800 K (see Table 1(b)). And the fuel contains 50% of CO, 14% of H2, and 36% of N2.Figure 1
Physical model of the SFRJ used in this investigation.
(a)(b)(c)Table 1
(a) Geometry parameters of the present model; (b) detailed boundary condition.
(a)L1L2HRrdDwDt50 mm300 mm10 mm55 mm45 mm10 mm38 mm10 mm4 mm(b)InletPressure (MPa)Temperature (K)Velocity (m/s)1.5650762Fuel nuzzlePressure (MPa)Temperature (K)Velocity (m/s)218001362OutletPressure (Pa)Temperature (K)101325300Symmetric facesSymmetric boundary conditionWallsNonslip adiabatic boundary conditionThe grid separation of the surface is shown in Figure1(c), and the grids near the wall surface are refined to make sure the y+ is within the range of 1~5. And the total grid number is 2.7 million.


## 2.5. Case Description

Systematic simulations are conducted as shown in Table2. The simulations are performed to investigate the effect of the chamber geometry on the combustion characteristics. In cases 1-3, the parameter H is set as constant, and the parameters Ain are varied. In cases 2, 4, and 5, the parameters H are varied, and Ain is set as constant.Table 2
Simulation conditions.
Case numberR/mmr/mmH/mmAin/mm2Case 16050101100πCase 25545101000πCase 3504010900πCase 466.558.581000πCase 547.6535.65121000π


## 2.6. Grid Independency Study and Model Validation

To make sure the grid number is suitable for the current research, the grid independency study is conducted. We use three cases with different mesh numbers, i.e., the coarse mesh with 1.9 million cells, the moderate mesh with 2.7 million, and the refined mesh with 3.8 million cells. Theyplus is set to 1-5 for all the cases in the independency study. The results are shown in Figure 2; as seen in the figure, the pressure variations along the axial direction of the three cases exhibit significant differences between the coarse mesh and moderate and refined mesh. Thus, to save the computational resources and maintains accuracy of the simulation, the moderate mesh is utilized for the present study.Figure 2
Results of grid independency study.To ensure the accuracy of the present simulation, model validation is needed. In the present research, two experimental cases are utilized, i.e., the classical DLR model proposed by Deutsches Zentrum für Luft- und Raumfahrt [21] and a ground cold flow test conducted via the connected pipe facility.The classical DLR model is illustrated in Figure3(a); as shown in the figure, the strut is equipped at the position marked in Figure 3(a), and the hydrogen fuel is injected into the combustor with the speed of Mach 1. The grid separation is shown in Figure 3(b).Figure 3
Physical model of DLR engine.
(a)(b)The boundary condition of the air inlet and fuel inlet is described in Table3; the outlet is set as pressure outlet, and the no-slip wall condition is applied for all walls in the model.Table 3
Boundary conditions.
Air inletH2 inletInlet Mach number2.01.0Velocity (m/s)7301200Temperature (K)340250Pressure (Pa)100000100000Mass fraction of N20.7360Mass fraction of O20.2320Mass fraction of H2O0.0320Mass fraction of H201The schlieren interferogram obtained by experiment and numerical simulation is described in Figure4. It could be seen from the figure that the expansion wave and the reflected shock wave of the simulation conform well to the experimental result. And this indicates that the proposed method can accurately predict the flow field in the ramjet combustor.Figure 4
The schlieren interferogram obtained by experiment (up) and numerical simulation (down).The temperatures at different axial positions are described in Figure5; it could be seen from the figure that the trend of the temperature distribution obtained from the experiment and simulation is almost the same, which indicates that the proposed model can accurately predict the flow and combustion in such combustors.Figure 5
Distribution of the temperature obtained from experiment and simulation.To make sure the present model can predict the flow conditions accurately in the annular combustion chamber, a cold flow ground test is conducted via a connected pipe facility; the experimental model is almost the same as the model shown in Figure1(b), except the parameter L2 is 800 mm. The experimental engine is illustrated in Figure 6. Five pressure sensors are set on the engine along the axial direction, at the position of 350 mm, 450 mm, 550 mm, 650 mm, and 750 mm, with respect to the engine inlet. The experimental conditions are shown in Table 4.Figure 6
Scramjet engine.Table 4
Experimental conditions.
Pressure (MPa)Temperature (K)Velocity (m/s)1.5650762As for the simulation part, the boundary condition is the same as described in Section2.4 (Figure 2), and the physical model is the same as the experimental one. The result is shown in Figure 7. In this figure, the distribution of the pressure field is illustrated; unlike the flow patterns shown in Figure 3, in an annular flow field, the shock wave is mainly dominated by the strut placed along the circumferential direction, rather than the combustor wall. Thus, this may lead to the phenomena occurring in the middle of the two struts (marked with the square), and the cells with diamond shapes appear downstream of the flow field. In addition, it is worth noting that the low pressure region with the shape of a swallowtail could be observed at the bottom of the struts (as marked with the circle).Figure 7
Distribution of the pressure in the chamber.The results obtained from the experiment and simulation are shown in Figure8; it is worth noting that the results obtained from the simulation reveal a wave shape; this is believed to be caused by the abovementioned diamond-shaped pressure distribution. And it can also be seen that the pressure measured at the measuring points conforms well to the simulation result, which means that the proposed method can accurately predict the flow patterns in the combustor.Figure 8
Comparison between the experimental result and numerical result.


## 3. Results and Discussion

### 3.1. Flow-Field Characteristics

In this section, case 2 is used to investigate the mixing characteristics of the combustor, without ignition. The distribution of the density is shown in Figure9; as described in this figure, an oblique shock wave is generated at the tip of the strut and gets crossed to another shock wave formed at the other strut, as marked with the square. The two-crossed shock waves are further extended to the shear layer generated by the fuel and incoming air and then reflected, which eventually leads to the cell with a diamond shape. It is worth noting that there are some weak shock waves generated at the end of the strut (marked with a circle), which is the same as the oblique shock wave; these weak shock waves are also crossed and reflected with each other and the shear layer.Figure 9
The distribution of the density at the surface ofr=50mm.The distributions of the density at the ISO surfaces parallel to theXOY plane between the two struts (as marked by the dashed line in Figure 9) are illustrated in Figure 10; as shown in the figure, the shock wave feature is mainly dominated by the strut. And at the position where the oblique shock wave is generated, the boundary layer becomes thicker (as marked by the square), and at the bottom of the strut, the density distribution shows a little discontinued behavior (as marked by the circle); this is believed to be caused by the weak shock wave mentioned above.Figure 10
The density distribution of different surface parallel to theXZ plane.The distribution of the Mach number and static pressure is illustrated in Figures11 and 12. It could be seen from Figure 11(a) that the velocity of the fuel increased rapidly near the fuel inlet and then decreases gradually downstream the flow field; and at the position marked by the circle (corresponding to the marked location at Figure 11(b)), the velocity goes even lower, which is mainly owing to the crossed shock wave. As described in Figure 12, a region with high speed and low pressure occurs around the bottom of the strut, owing to the expended jet flow at the fuel inlet; as the jet flow develops downstream, the pressure goes higher and becomes steady gradually.Figure 11
Distribution of the Mach number.
(a)
Distribution of the Mach number at the surface ofz=50mm(b)
Distribution of the Mach number at the surface ofy=0mmFigure 12
Distribution of pressure.The temperature distribution is shown in Figure13; the temperature decreases rapidly near the bottom of the strut and increases gradually downstream the flow field. It is noticed that the high-temperature zone mainly occurs around the center of the jet flow and could be significantly affected by the distribution of the shock wave (see Figure 13(a)). In addition, as shown in Figure 13(b), the temperature goes higher near the wall; this is believed to be caused by the crossing and reflecting effects of the shock wave, which reminds us that more attention should be paid to the thermal protection in this area.Figure 13
Distribution of temperature.
(a)
Temperature atz=50mm plane(b)
Temperature aty=0mm plane


### 3.2. Mixing Characteristics

Figures14 and 15 illustrate the distribution of the mass fraction of CO and H2. As shown in those figures, the mass fraction of gases goes higher near the fuel inlet and decreases gradually as the jet flow developed. And the gases are all concentrated in the shear layer owing to the characteristics of the jet flow (see Figures 14(a) and 15(a)) As shown in Figures 14(b) and 15(b), in the view of y=0mm plane, the jet flow goes up near the wall, and this is believed to be caused by the asymmetric expansion of the combustor.Figure 14
Distribution of mass fraction of CO.
(a)
Mass fraction of CO atz=50mm plane(b)
Mass fraction of CO aty=0mm planeFigure 15
Distribution of mass fraction of H2.
(a)
Mass fraction ofz=50mm plane(b)
Mass fraction ofy=0mm planeTo analyze the mixing characteristic more clearly, the mixing coefficient is calculated, which could be obtained via [26]
(11)ηmix=∫AαρuYfueldAṁfuel,where ρ is the density of the mixture, u is normal velocity, Yfuel represents the mass fraction of the fuel, A is the area of the ISO surface of the combustor, ṁfuel means the mass flux of the fuel, and α is the residual gas coefficient, regarded as the inverse of the equivalence ratio (Φ). And the equivalence ratio (Φ) could be calculated via
(12)ϕ=8YH2+4/7YCOYO2.The residual gas coefficientα is defined as
(13)α=1,ϕ<1,1/ϕ,ϕ≥1.The mixing efficiency at the plane ofz=50mm is illustrated in Figure 16; it could be seen from the figure that the mixing coefficient reaches the highest value at the location of the shear layer between the jet flow and incoming air. And as the jet flow moves downstream, the mixing coefficient goes higher. It could be also seen from the zoom in view of Figure 16, at the area of the recirculation zone, that the mixing coefficient is increased, which indicates that the mixing coefficient could be enhanced under the effect of the recirculated flow.Figure 16
The mixing efficiency at the plane ofz=50mm.Figure17 illustrates the mixing coefficient at y=0mm plane. It could be observed from the figure that the mixing coefficient is increased as the fuel jet flow develops downstream, and the mixing coefficient at the lower wall of the combustor is higher than that of the upper wall. It could be also observed from the zoom in view of the figure that the mixing coefficient near the bottom of the strut is lower than that of z=50mm plane. The reason behind is that the location is close to the combustor wall; this may not lead to a fully developed recirculation zone, which further leads to a decrease in the mixing coefficient.Figure 17
The mixing efficiency at the plane ofy=0.The distribution of the mixing coefficient is described in Figure18; the profile is obtained at the axis of y=0mm and z=50mm plane. It is noticed that at 75-150 mm, the mixing coefficient increases gradually, corresponding to the location of the core area of the jet flow; in this area, the diffusion effect is not quite significant, and the increase of the mixing coefficient is mainly owing to the weak shock waves at the bottom of the strut (see Figure 9 marked by the black circle). And at the range of 150 mm, the mixing coefficient increases rapidly; this is believed to be caused by the crossed shock wave shown in Figure 9 (marked by the red circle); the shock wave here can reduce the velocity of the jet flow and on the other hand enhance the mixing coefficient. It is worth noting that at the range of 125 mm-150 mm, the mixing coefficient decrease a little; this is mainly caused by the developed jet flow between the weak shock waves and the crossed shock wave (see the range between the black circle and red circle in Figure 9); in this range, the jet flow developed sufficiently without the disturbance of the shock wave, which leads to a decrease in the mixing coefficient on some level. After this, at the location of 275 mm, the mixing coefficient increased further; this is also corresponding to the location of the crossed shock wave, which indicates that the velocity is further reduced. It could be seen from the figure that the overall trend increased and reached its maximum at the outlet of the combustor, but an upward trend could still be observed at the outlet of the combustor; thus, an assumption could be made that if the length of the combustor is increased, the mixing coefficient could be further enhanced up to 100%.Figure 18
The mixing efficiency at the axis ofy=0mm and z=50mm plane.


### 3.3. Combustion Characteristics

In this section, the ignition is started to analyze the combustion characteristics of the present annular combustor. The distribution of the density is illustrated in Figure19; compared to the density of the noncombusted result shown in Figure 9, the overall trends are almost the same, except for the thickness of the jet flow.Figure 19
Density distribution of the surface atr=50mm.To analyze the density distribution in detail, the density along the axis (marked in Figure19) is obtained and compared with that of the noncombusted result. As shown in Figure 20, in the part of the isolator (0-100 mm) and the head of the extension region (100-125 mm), the densities are the same, owing to the combustion that is not involved in such region. However, for the regions where the combustion occurs (>125 mm), the density distribution shows few differences. It is worth to be noticed that the peaks described in Figure 20 conform to the location where the shock waves are crossed, and the locations of the shock wave crossing point of the two cases are the same, while at the second point around the location of 200 mm, a significant gap could be observed between the two cases. This indicates that the combustion may lead to some changes in the structures of the shock waves. And it could be seen from Figure 20 that the overall trend of the density for the combustion cases is higher than that of the noncombusted case; this is mainly caused by the combustion of the CO and H2; the products of those two working mediums may enhance the total density of the flow fields.Figure 20
The density distribution at the axis ofy=0mm and z=50mm plane.Figures21 and 22 illustrate the distribution of the reacting species (CO, CO2, and O2). The distribution of H2 is almost the same as that of CO; thus, the distribution of H2 is not provided. The mass fraction of CO is decreased as the fuel jet flow is developed, and this is mainly owing to the increase in the mass fraction of combustion products (see Figure 21). As shown in z=50mm plane of Figures 20 and 21, the combustion mainly occurs in the shear layer, strut bottom, and downstream the flow field; this corresponds to the results shown in Figure 16; the combustion occurs where the high mixing efficiency is obtained; thus, it could be concluded that the higher mixing rate can result in efficient combustion.Figure 21
Distribution of mass fraction of CO.
(a)
z=50mm(b)
y=0mmFigure 22
Distribution of mass fraction of CO2.
(a)
z=50mm(b)
y=0mmThe distribution of the temperature is shown in Figure23; the high temperature zone shows a cylindrical shape and expands as the jet flow developed. It could be seen that the higher temperature could be obtained at the shear layer and the recirculation zone near the bottom of the strut; the temperature at the shear layer can reach over 2400 K, and the temperature at bottom of the strut is higher than 2600 K. These regions are often regarded as the flame surface.Figure 23
Distribution of temperature.The heat of reaction is shown in Figure24; combined with the temperature distribution described above, the heat release at the flame surface is highest overall. And at the bottom of the strut, the heat release reaches the maximum and decreases gradually downstream of the flow field. It is worth noting that the heat release and temperature inside the jet flow are much lower than that of the flame surface. As described in Ref. [42], the flame surface is often regarded as the interface of the oxide rich region (outside the flame surface) and fuel reach region (inside the flame surface); the combustion inside the flame surface is mainly dominated by the chemical process; the combustion at the shear layer is controlled by diffusion process. In the diffusion process-controlled regions, i.e., the flame surface, the combustion occurs in stoichiometric ratio; thus, this may lead to a higher temperature and heat release rate in such region.Figure 24
Distribution of combustion heat release rate.The combustion efficiency is a key factor that can evaluate the combustion performance, which could be calculated via(14)ηi=1−∫ρYiudAṁi,in=1−ṁi,Aṁi,in,where ηi is the local combustion efficiency, Yi represents the local mass fraction, ṁi,in and ṁi,A are the initial mass flow rate and present mass flow rate at a certain surface, and the subscript i means the ith component.Based on the abovementioned equation, the combustion efficiency at the certain surfaceA could be defined as below:
(15)ηfuel=1−∑iṁi,A∑iṁi,in,The combustion efficiency is illustrated in Figure25; in this figure, the combustion efficiency is obtained at the axis defined by the surface of z=50mm (XOY) and y=0mm (XOZ). It could be seen from the figure that the overall trend of the combustion efficiency is increased downstream, and at the exit of the combustor, the combustion efficiency of H2 is 48.9% and CO is 61.4%, and the total combustion efficiency is 58.7%. It is worth noting that at the location around 80 mm, ηfuel is 0; this is corresponding to the phenomena described in Figures 14 and 15; in this area, the mass fraction of the fuel is almost 100%; thus, no combustion could be established under such condition.Figure 25
Combustion efficiency.


### 3.4. The Effect of Combustion Chrematistics in the Chamber Geometry

The mixing efficiency for different cases is illustrated in Figures26 and 27. As shown in Figure 26, the overall trend of the mixing efficiency is increased with the decrease of the Ain (see cases 1, 2, and 3), and they are all fully mixed at the outlet of the combustor. It is worth to be noticed that as Ain is decreased, the location where the mixing efficiency reaches 100% moves upstream of the flow field. As for the cases with different H (see cases 4, 2, and 5 in Figure 26), the mixing efficiency is increased with the increased value of H, and it is the same as the cases mentioned above; as the H is increased, the location of the 100% mixing efficiency moves towards the inlet of the combustor. It should be particularly noticed that as shown in case 4 of Figure 26, the fuel gas is not fully mixed even at the outlet of the combustor, which indicates that an overnarrow path of the annular combustor may negatively affect the mixing characteristics of the combustor.Figure 26
Mixing efficiency for different cases.Figure 27
Mixing efficiency for different cases aty=0mm plane.Figure27 illustrates the mixing efficiency of XOY plane at the position of y=0mm. As shown in the figure, the mixing efficiency has the same trend compared to the result shown in Figure 26. It is worth to be noticed that case 4 expresses a poor mixing efficiency, and this is believed to be caused by the nonfully expanded structure of the combustor.As mentioned above, the mixing efficiency is related to the structure of the shock wave; thus, the analysis based on the structure of the shock wave is presented. As described in Figure28, the shock waves are crossed at the center of the jet flow for all the cases. However, the location of the crossing point is not the same. As for cases 1, 2, and 3, the crossing point near the bottom of the nuzzle moves upstream as the inlet area is decreased; this is mainly owing to the decreasing of the angle between the shock wave and the strut as Ain is decreased. As described in Figure 28 cases 4, 2, and 5, the increase in H may lead to the increased angle between the shock wave and the strut, which further makes the crossed point move upstream. And those phenomena eventually lead to the difference in the mixing efficiency.Figure 28
Density distribution for different cases.The temperatures for each case are illustrated in Figure29; it could be seen from the figure, in cases 1-3, that the distribution of the temperature is almost the same, and the high-temperature zone is mainly concentrated on the surface of the lower wall. However, as shown in cases 4, 2, and 5, the temperature distributions are quite different; as for the case with the smallest H, the flame surface with the highest temperature expressed a trapezoid shape downstream of the flow field. And the flame surface temperature in the middle of the expansion region reaches 2400 K, which is lower than that of the cases with higher H. As for cases 2 and 5, the shape of the flame surface expressed an inverted triangle shape.Figure 29
The temperature distribution for cases 1-5.The distributions of heat release rate are shown in Figure30; the heat release rate is often used to describe the shape of the flame, and as shown in the figure, the flame shape expresses an inverted triangle shape in cases 1, 2, and 3. And the heat release is higher at the inlet of the fuel, which means that the combustion near the bottom of the strut is more sufficient; this further confirmed that the recirculation zone at the strut bottom has a positive effect on the combustion. It could be seen from cases 1, 2, and 3 that the heat release rate gets much lower compared to that of the fuel inlet; this is mainly owing to the reduction of the mass fraction of the fuel gas. And it is worth to be noticed that the heat release downstream in case 1 is a little lower than that of cases 2 and 3, which implies that the decreasing of the inlet area can enhance the heat release of the expansion region.Figure 30
The heat release distribution for cases 1-5.As shown in cases 4, 2, and 5 of Figure30, in case 4, the flame shape expresses a trapezoid shape; this is mainly dominated by the narrow path of the annular combustor; the distance between the upper and lower wall is too small, and the combusted jet flow is not fully developed. As the diameter of the path is increased (shown in cases 2 and 5), the inverted triangle shape appears downstream of the chamber; this means that the jet flow is fully developed with a larger path size. And as the size of the path is increased, the bottom tip of the inverted triangle flame moves away from the lower wall of the combustor.The combustion efficiency is shown in Figure31 and Table 5; it could be seen from the figure and table that the combustion efficiency increases as the inlet area is decreased, but the overall trend is almost the same, which implies that the variation of the inlet area has an insignificant effect of the combustion efficiency. However, for cases 4, 2, and 5, the combustion efficiency could be significantly enhanced as the height of the path is increased. This partially indicates that the combustion efficiency could be enhanced when the connected area between gas and air is increased.Figure 31
The distribution of the combustion efficiency for different cases.Table 5
Combustion efficiency at the exit of the combustor.
CaseCase 1Case 2Case 3Case 4Case 5Combustion efficiency (%)57.39358.68759.53142.96267.164As described in the paper [26, 43], the authors use three different configurations of the strut, i.e., single strut, double strut, and double struts with backward-facing steps. It could be observed that the combustion efficiency for single strut case is around 70% and for double strut case is almost 90%, and for the cases with backward-facing step struts, the combustion efficiency is larger than 90%. In our cases, the maximum combustion efficiency occurs in case 5 with the value of 67%, which is obviously lower than that of the double and backward-facing step struts and a little lower than that of single strut case. However, it is worth noting that the DLR engine utilized in the abovementioned references is fueled by hydrogen only, while in the present research, the CO and H2 mixture is applied as gaseous fuel, and the mass fraction of CO is much higher than H2, and the diffusion rate of H2 (1.29 cm2/s at 300 K and 101325 Pa) is much higher than that of CO (0.175 cm2/s at 300 K and 101325 Pa) in air; thus, this may lead to the lower combustion efficiency in the current engine structure. In addition, the abovementioned research is based on the DLR-type combustor, and the practical application is difficult to achieve; however, the annular strut-based combustor in this article offers the possibility of engineering application use. And it is worth to be noticed that the double and backward-facing step struts can significantly improve the combustion efficiency of the engine; this offers us an idea that the combustion efficiency could be improved via changing the strut configuration, and this will be the upcoming research of the project.


## 3.1. Flow-Field Characteristics

In this section, case 2 is used to investigate the mixing characteristics of the combustor, without ignition. The distribution of the density is shown in Figure9; as described in this figure, an oblique shock wave is generated at the tip of the strut and gets crossed to another shock wave formed at the other strut, as marked with the square. The two-crossed shock waves are further extended to the shear layer generated by the fuel and incoming air and then reflected, which eventually leads to the cell with a diamond shape. It is worth noting that there are some weak shock waves generated at the end of the strut (marked with a circle), which is the same as the oblique shock wave; these weak shock waves are also crossed and reflected with each other and the shear layer.Figure 9
The distribution of the density at the surface ofr=50mm.The distributions of the density at the ISO surfaces parallel to theXOY plane between the two struts (as marked by the dashed line in Figure 9) are illustrated in Figure 10; as shown in the figure, the shock wave feature is mainly dominated by the strut. And at the position where the oblique shock wave is generated, the boundary layer becomes thicker (as marked by the square), and at the bottom of the strut, the density distribution shows a little discontinued behavior (as marked by the circle); this is believed to be caused by the weak shock wave mentioned above.Figure 10
The density distribution of different surface parallel to theXZ plane.The distribution of the Mach number and static pressure is illustrated in Figures11 and 12. It could be seen from Figure 11(a) that the velocity of the fuel increased rapidly near the fuel inlet and then decreases gradually downstream the flow field; and at the position marked by the circle (corresponding to the marked location at Figure 11(b)), the velocity goes even lower, which is mainly owing to the crossed shock wave. As described in Figure 12, a region with high speed and low pressure occurs around the bottom of the strut, owing to the expended jet flow at the fuel inlet; as the jet flow develops downstream, the pressure goes higher and becomes steady gradually.Figure 11
Distribution of the Mach number.
(a)
Distribution of the Mach number at the surface ofz=50mm(b)
Distribution of the Mach number at the surface ofy=0mmFigure 12
Distribution of pressure.The temperature distribution is shown in Figure13; the temperature decreases rapidly near the bottom of the strut and increases gradually downstream the flow field. It is noticed that the high-temperature zone mainly occurs around the center of the jet flow and could be significantly affected by the distribution of the shock wave (see Figure 13(a)). In addition, as shown in Figure 13(b), the temperature goes higher near the wall; this is believed to be caused by the crossing and reflecting effects of the shock wave, which reminds us that more attention should be paid to the thermal protection in this area.Figure 13
Distribution of temperature.
(a)
Temperature atz=50mm plane(b)
Temperature aty=0mm plane


## 3.2. Mixing Characteristics

Figures14 and 15 illustrate the distribution of the mass fraction of CO and H2. As shown in those figures, the mass fraction of gases goes higher near the fuel inlet and decreases gradually as the jet flow developed. And the gases are all concentrated in the shear layer owing to the characteristics of the jet flow (see Figures 14(a) and 15(a)) As shown in Figures 14(b) and 15(b), in the view of y=0mm plane, the jet flow goes up near the wall, and this is believed to be caused by the asymmetric expansion of the combustor.Figure 14
Distribution of mass fraction of CO.
(a)
Mass fraction of CO atz=50mm plane(b)
Mass fraction of CO aty=0mm planeFigure 15
Distribution of mass fraction of H2.
(a)
Mass fraction ofz=50mm plane(b)
Mass fraction ofy=0mm planeTo analyze the mixing characteristic more clearly, the mixing coefficient is calculated, which could be obtained via [26]
(11)ηmix=∫AαρuYfueldAṁfuel,where ρ is the density of the mixture, u is normal velocity, Yfuel represents the mass fraction of the fuel, A is the area of the ISO surface of the combustor, ṁfuel means the mass flux of the fuel, and α is the residual gas coefficient, regarded as the inverse of the equivalence ratio (Φ). And the equivalence ratio (Φ) could be calculated via
(12)ϕ=8YH2+4/7YCOYO2.The residual gas coefficientα is defined as
(13)α=1,ϕ<1,1/ϕ,ϕ≥1.The mixing efficiency at the plane ofz=50mm is illustrated in Figure 16; it could be seen from the figure that the mixing coefficient reaches the highest value at the location of the shear layer between the jet flow and incoming air. And as the jet flow moves downstream, the mixing coefficient goes higher. It could be also seen from the zoom in view of Figure 16, at the area of the recirculation zone, that the mixing coefficient is increased, which indicates that the mixing coefficient could be enhanced under the effect of the recirculated flow.Figure 16
The mixing efficiency at the plane ofz=50mm.Figure17 illustrates the mixing coefficient at y=0mm plane. It could be observed from the figure that the mixing coefficient is increased as the fuel jet flow develops downstream, and the mixing coefficient at the lower wall of the combustor is higher than that of the upper wall. It could be also observed from the zoom in view of the figure that the mixing coefficient near the bottom of the strut is lower than that of z=50mm plane. The reason behind is that the location is close to the combustor wall; this may not lead to a fully developed recirculation zone, which further leads to a decrease in the mixing coefficient.Figure 17
The mixing efficiency at the plane ofy=0.The distribution of the mixing coefficient is described in Figure18; the profile is obtained at the axis of y=0mm and z=50mm plane. It is noticed that at 75-150 mm, the mixing coefficient increases gradually, corresponding to the location of the core area of the jet flow; in this area, the diffusion effect is not quite significant, and the increase of the mixing coefficient is mainly owing to the weak shock waves at the bottom of the strut (see Figure 9 marked by the black circle). And at the range of 150 mm, the mixing coefficient increases rapidly; this is believed to be caused by the crossed shock wave shown in Figure 9 (marked by the red circle); the shock wave here can reduce the velocity of the jet flow and on the other hand enhance the mixing coefficient. It is worth noting that at the range of 125 mm-150 mm, the mixing coefficient decrease a little; this is mainly caused by the developed jet flow between the weak shock waves and the crossed shock wave (see the range between the black circle and red circle in Figure 9); in this range, the jet flow developed sufficiently without the disturbance of the shock wave, which leads to a decrease in the mixing coefficient on some level. After this, at the location of 275 mm, the mixing coefficient increased further; this is also corresponding to the location of the crossed shock wave, which indicates that the velocity is further reduced. It could be seen from the figure that the overall trend increased and reached its maximum at the outlet of the combustor, but an upward trend could still be observed at the outlet of the combustor; thus, an assumption could be made that if the length of the combustor is increased, the mixing coefficient could be further enhanced up to 100%.Figure 18
The mixing efficiency at the axis ofy=0mm and z=50mm plane.


## 3.3. Combustion Characteristics

In this section, the ignition is started to analyze the combustion characteristics of the present annular combustor. The distribution of the density is illustrated in Figure19; compared to the density of the noncombusted result shown in Figure 9, the overall trends are almost the same, except for the thickness of the jet flow.Figure 19
Density distribution of the surface atr=50mm.To analyze the density distribution in detail, the density along the axis (marked in Figure19) is obtained and compared with that of the noncombusted result. As shown in Figure 20, in the part of the isolator (0-100 mm) and the head of the extension region (100-125 mm), the densities are the same, owing to the combustion that is not involved in such region. However, for the regions where the combustion occurs (>125 mm), the density distribution shows few differences. It is worth to be noticed that the peaks described in Figure 20 conform to the location where the shock waves are crossed, and the locations of the shock wave crossing point of the two cases are the same, while at the second point around the location of 200 mm, a significant gap could be observed between the two cases. This indicates that the combustion may lead to some changes in the structures of the shock waves. And it could be seen from Figure 20 that the overall trend of the density for the combustion cases is higher than that of the noncombusted case; this is mainly caused by the combustion of the CO and H2; the products of those two working mediums may enhance the total density of the flow fields.Figure 20
The density distribution at the axis ofy=0mm and z=50mm plane.Figures21 and 22 illustrate the distribution of the reacting species (CO, CO2, and O2). The distribution of H2 is almost the same as that of CO; thus, the distribution of H2 is not provided. The mass fraction of CO is decreased as the fuel jet flow is developed, and this is mainly owing to the increase in the mass fraction of combustion products (see Figure 21). As shown in z=50mm plane of Figures 20 and 21, the combustion mainly occurs in the shear layer, strut bottom, and downstream the flow field; this corresponds to the results shown in Figure 16; the combustion occurs where the high mixing efficiency is obtained; thus, it could be concluded that the higher mixing rate can result in efficient combustion.Figure 21
Distribution of mass fraction of CO.
(a)
z=50mm(b)
y=0mmFigure 22
Distribution of mass fraction of CO2.
(a)
z=50mm(b)
y=0mmThe distribution of the temperature is shown in Figure23; the high temperature zone shows a cylindrical shape and expands as the jet flow developed. It could be seen that the higher temperature could be obtained at the shear layer and the recirculation zone near the bottom of the strut; the temperature at the shear layer can reach over 2400 K, and the temperature at bottom of the strut is higher than 2600 K. These regions are often regarded as the flame surface.Figure 23
Distribution of temperature.The heat of reaction is shown in Figure24; combined with the temperature distribution described above, the heat release at the flame surface is highest overall. And at the bottom of the strut, the heat release reaches the maximum and decreases gradually downstream of the flow field. It is worth noting that the heat release and temperature inside the jet flow are much lower than that of the flame surface. As described in Ref. [42], the flame surface is often regarded as the interface of the oxide rich region (outside the flame surface) and fuel reach region (inside the flame surface); the combustion inside the flame surface is mainly dominated by the chemical process; the combustion at the shear layer is controlled by diffusion process. In the diffusion process-controlled regions, i.e., the flame surface, the combustion occurs in stoichiometric ratio; thus, this may lead to a higher temperature and heat release rate in such region.Figure 24
Distribution of combustion heat release rate.The combustion efficiency is a key factor that can evaluate the combustion performance, which could be calculated via(14)ηi=1−∫ρYiudAṁi,in=1−ṁi,Aṁi,in,where ηi is the local combustion efficiency, Yi represents the local mass fraction, ṁi,in and ṁi,A are the initial mass flow rate and present mass flow rate at a certain surface, and the subscript i means the ith component.Based on the abovementioned equation, the combustion efficiency at the certain surfaceA could be defined as below:
(15)ηfuel=1−∑iṁi,A∑iṁi,in,The combustion efficiency is illustrated in Figure25; in this figure, the combustion efficiency is obtained at the axis defined by the surface of z=50mm (XOY) and y=0mm (XOZ). It could be seen from the figure that the overall trend of the combustion efficiency is increased downstream, and at the exit of the combustor, the combustion efficiency of H2 is 48.9% and CO is 61.4%, and the total combustion efficiency is 58.7%. It is worth noting that at the location around 80 mm, ηfuel is 0; this is corresponding to the phenomena described in Figures 14 and 15; in this area, the mass fraction of the fuel is almost 100%; thus, no combustion could be established under such condition.Figure 25
Combustion efficiency.


## 3.4. The Effect of Combustion Chrematistics in the Chamber Geometry

The mixing efficiency for different cases is illustrated in Figures26 and 27. As shown in Figure 26, the overall trend of the mixing efficiency is increased with the decrease of the Ain (see cases 1, 2, and 3), and they are all fully mixed at the outlet of the combustor. It is worth to be noticed that as Ain is decreased, the location where the mixing efficiency reaches 100% moves upstream of the flow field. As for the cases with different H (see cases 4, 2, and 5 in Figure 26), the mixing efficiency is increased with the increased value of H, and it is the same as the cases mentioned above; as the H is increased, the location of the 100% mixing efficiency moves towards the inlet of the combustor. It should be particularly noticed that as shown in case 4 of Figure 26, the fuel gas is not fully mixed even at the outlet of the combustor, which indicates that an overnarrow path of the annular combustor may negatively affect the mixing characteristics of the combustor.Figure 26
Mixing efficiency for different cases.Figure 27
Mixing efficiency for different cases aty=0mm plane.Figure27 illustrates the mixing efficiency of XOY plane at the position of y=0mm. As shown in the figure, the mixing efficiency has the same trend compared to the result shown in Figure 26. It is worth to be noticed that case 4 expresses a poor mixing efficiency, and this is believed to be caused by the nonfully expanded structure of the combustor.As mentioned above, the mixing efficiency is related to the structure of the shock wave; thus, the analysis based on the structure of the shock wave is presented. As described in Figure28, the shock waves are crossed at the center of the jet flow for all the cases. However, the location of the crossing point is not the same. As for cases 1, 2, and 3, the crossing point near the bottom of the nuzzle moves upstream as the inlet area is decreased; this is mainly owing to the decreasing of the angle between the shock wave and the strut as Ain is decreased. As described in Figure 28 cases 4, 2, and 5, the increase in H may lead to the increased angle between the shock wave and the strut, which further makes the crossed point move upstream. And those phenomena eventually lead to the difference in the mixing efficiency.Figure 28
Density distribution for different cases.The temperatures for each case are illustrated in Figure29; it could be seen from the figure, in cases 1-3, that the distribution of the temperature is almost the same, and the high-temperature zone is mainly concentrated on the surface of the lower wall. However, as shown in cases 4, 2, and 5, the temperature distributions are quite different; as for the case with the smallest H, the flame surface with the highest temperature expressed a trapezoid shape downstream of the flow field. And the flame surface temperature in the middle of the expansion region reaches 2400 K, which is lower than that of the cases with higher H. As for cases 2 and 5, the shape of the flame surface expressed an inverted triangle shape.Figure 29
The temperature distribution for cases 1-5.The distributions of heat release rate are shown in Figure30; the heat release rate is often used to describe the shape of the flame, and as shown in the figure, the flame shape expresses an inverted triangle shape in cases 1, 2, and 3. And the heat release is higher at the inlet of the fuel, which means that the combustion near the bottom of the strut is more sufficient; this further confirmed that the recirculation zone at the strut bottom has a positive effect on the combustion. It could be seen from cases 1, 2, and 3 that the heat release rate gets much lower compared to that of the fuel inlet; this is mainly owing to the reduction of the mass fraction of the fuel gas. And it is worth to be noticed that the heat release downstream in case 1 is a little lower than that of cases 2 and 3, which implies that the decreasing of the inlet area can enhance the heat release of the expansion region.Figure 30
The heat release distribution for cases 1-5.As shown in cases 4, 2, and 5 of Figure30, in case 4, the flame shape expresses a trapezoid shape; this is mainly dominated by the narrow path of the annular combustor; the distance between the upper and lower wall is too small, and the combusted jet flow is not fully developed. As the diameter of the path is increased (shown in cases 2 and 5), the inverted triangle shape appears downstream of the chamber; this means that the jet flow is fully developed with a larger path size. And as the size of the path is increased, the bottom tip of the inverted triangle flame moves away from the lower wall of the combustor.The combustion efficiency is shown in Figure31 and Table 5; it could be seen from the figure and table that the combustion efficiency increases as the inlet area is decreased, but the overall trend is almost the same, which implies that the variation of the inlet area has an insignificant effect of the combustion efficiency. However, for cases 4, 2, and 5, the combustion efficiency could be significantly enhanced as the height of the path is increased. This partially indicates that the combustion efficiency could be enhanced when the connected area between gas and air is increased.Figure 31
The distribution of the combustion efficiency for different cases.Table 5
Combustion efficiency at the exit of the combustor.
CaseCase 1Case 2Case 3Case 4Case 5Combustion efficiency (%)57.39358.68759.53142.96267.164As described in the paper [26, 43], the authors use three different configurations of the strut, i.e., single strut, double strut, and double struts with backward-facing steps. It could be observed that the combustion efficiency for single strut case is around 70% and for double strut case is almost 90%, and for the cases with backward-facing step struts, the combustion efficiency is larger than 90%. In our cases, the maximum combustion efficiency occurs in case 5 with the value of 67%, which is obviously lower than that of the double and backward-facing step struts and a little lower than that of single strut case. However, it is worth noting that the DLR engine utilized in the abovementioned references is fueled by hydrogen only, while in the present research, the CO and H2 mixture is applied as gaseous fuel, and the mass fraction of CO is much higher than H2, and the diffusion rate of H2 (1.29 cm2/s at 300 K and 101325 Pa) is much higher than that of CO (0.175 cm2/s at 300 K and 101325 Pa) in air; thus, this may lead to the lower combustion efficiency in the current engine structure. In addition, the abovementioned research is based on the DLR-type combustor, and the practical application is difficult to achieve; however, the annular strut-based combustor in this article offers the possibility of engineering application use. And it is worth to be noticed that the double and backward-facing step struts can significantly improve the combustion efficiency of the engine; this offers us an idea that the combustion efficiency could be improved via changing the strut configuration, and this will be the upcoming research of the project.


## 4. Conclusion

In this work, a new configuration of the strut-based scramjet is proposed, and a series of simulations are conducted. The effects of the geometry of the combustor in such scramjets are investigated and analyzed. The key conclusions are summarized as(i)
The flow field of present engine shows the same characteristics as the classical DLR engine. The oblique shock wave is generated at the tip of the strut and gets crossed to another shock wave formed at the other strut. And the fuel jet flow goes up near the upper wall of the combustor, which is believed to be caused by the asymmetric expansion of the combustor(ii)
The investigation of the mixing characteristics indicates that the recirculation zone near the bottom tip of the strut can increase the mixing coefficient. And at the range 150 mm and 170 mm, the mixing coefficient increases rapidly; the reason behind that is the crossed shock wave; the shock wave here can reduce the velocity of the jet flow and on the other hand enhance the mixing coefficient(iii)
The research on the combustion field indicates that the temperature is higher near the shear layer and the strut bottom; the temperature at the shear layer can reach over 2400 K, and the temperature at bottom of the strut is higher than 2600 K. These regions are often regarded as the flame surface(iv)
IncreasingAin can lead to an increase in the overall trend of the mixing efficiency and reduce the combustion heat release rate and combustion efficiency. However, the case with the narrowest H expresses the poorest mixing characteristics and significantly affects the combustion efficiency. And the flame shape could be sensitive to the chamber geometryIn general, the present work proposes a new geometry of the scramjet combustor, and the feasibility of such combustors is investigated via numerical approach. The results indicate that the application for such combustors is possible, but further investigation is still needed.



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*Source: 3930440-2022-12-30.xml*