Abstract
The fuel in a scramjet combustor must be injected into a high-speed crossflow and mixed with supersonic air in a very short period of time in order for the scramjet jet to operate reliably. More generally, the supersonic air is produced by the lower cover, similar to a Laval type nozzle, of the scramjet combustor. However, significant variation in lower cover geometry is prone to produce unstable vortexes. The unstable vortexes are accompanied by nonuniform stress and strain and are detrimental to the lower cover, even to the combustor. Inspired by mechanical design, this study proposes to change lower cover geometry by decreasing its sizes and then evaluates effects of these changes on kerosene fuel–air interaction in the combustor. The evaluation is based on three-dimensional computational fluid dynamics with couple level set and volume of fluids, which characterizes the penetration height, span expansion area, shock wave angle, and Sauter mean diameter of kerosene jets for three different injection diameters (0.5, 1.0, and 1.5 mm). The simulated air–kerosene interactions reasonably agree with the past numerical findings at identical working conditions. This result demonstrates the effectiveness of the changed lower cover geometry for the scramjet combustor.
1. Introduction
Hypersonic air-breathing propulsion is crucial for scramjet engines because the technology can produce more efficient and flexible transportation than those used in a conventional rocket engine.1 For this purpose, the hypersonic vehicles are necessitated to operate at high Mach numbers, e.g., at Mach 8.2 Unfortunately, however, significantly high speed is prone to result in extremely short residence time of the free stream in the combustion chamber, which eventually leads to incomplete mixing and reduced combustion efficiencies.3 Hence, it is of great interest to explore the flow topology of the fuel injection into supersonic airflow.
Focusing on the aforementioned problem, a large number of analytical, experimental, and numerical studies have been reported.4 For example, Liu et al.5 studied effects of different injection pressures on kerosene fuel mixing in a cold supersonic combustor. Gugulothu and Nutakki.6 studied dynamic flow characteristics in a hydrogen fuel injection combustor with transversal fuel injection. Lakka Suneetha et al.7 studied impacts of a new diamond-shaped double-strut structure with backward steps on the combustion characteristics of a cavity-type scramjet jet. Prasanth P. Nair et al.8 proposed the use of strut-based flame stabilizers to improve the combustion efficiency of the disturbed scramjet jet. Yarasai et al.9 studied the performance and combustion characteristics of a cavity-type scramjet jet with a new strut injector. Li et al.10 studied the effective source location of axisymmetric mode screech tones under expanded supersonic cold jets. Bao et al.11 studied the intensity of the local flame generated by spark ignition in a scramjet combustor fueled with liquid kerosene at Mach 4. Pu et al.12 studied the mixing efficiency and total pressure loss of a scramjet combustor with a three-strut injector under different flow control schemes.
Although the flow topologies in the scramjet combustor have been the subjects of extensive experimental and numerical work,13,14 the adverse effects of the supersonic air on the scramjet combustor have not been considered in any detail. In the scramjet combustor, the supersonic air is generally produced by the lower cover, as schematically indicated by number 7 in Figure 1B. The lower cover has the same geometries as that of the Laval type nozzle and hence the same performances—the gas from the inlet of the combustor is accelerated to sonic velocity in the throat region and subsequently becomes supersonic as it expands in the diverging section. However, significant size differences between the throat region and diverging section make the lower cover geometry vary greatly in shape and configuration; see the red arrow in Figure 1B. Consequently, this variation produces an adverse stress gradient and a short radius of curvature at the lower cover. These results easily cause the velocity boundary to separate and form large-scale vortexes. More generally, the vortexes have serious consequences for the combustor under such harsh environments.
Figure 1.
Scramjet combustion chamber: (A) real prototype and (B) 3D geometric model: (1,6) flange, (2) rear cover, (3) pressure pad for the upper glazed window, (4) window of upper glass, (5) upper cover, (7) lower cover, (8) strut, and (9) cavity.
Inspired by mechanical design theory, this study proposes to change the lower cover geometry or reduce the size differences between the throat region and diverging section to alleviate the serious consequences caused by the supersonic air. To the authors’ knowledge, a detail for this aspect is previously unavailable in the open literature. Meanwhile, whether this reduction has an influence on the kerosene and air interaction in the combustor is the underlying question. For this reason, this paper focuses on the mixing characteristics of cold kerosene fuel supersonic flow in a scramjet combustor with the changed lower cover geometry. The simulations simulated in this paper are compared with the published simulations under the same working conditions (such as 0.5, 1.0, and 1.5 mm of the injection diameters) for verification.
2. Materials and Methods
2.1. Computation Fluid Dynamics Model
Based on the real prototype (Figure 1) and the previously simplified combustor (Figure 2A), the scramjet combustor with the changed lower cover geometry is schematically illustrated in Figure 2B. Detailed simplification of the real prototype is available in ref4 The primary specifications of the combustor in this study are listed in Table 1. Compared to the original combustor, the detailed alterations of the current model are (1) decreasing the angle from 15.9 to 6.0° and (2) reducing the length of the upper sloping edge from 24.6 to 12.4 mm at the throat region of the lower cover; see red arrows in Figure 2B. The relevant sizes were calculated through the relationship between inlet air speed and supersonic air speed.
Figure 2.
Scramjet combustor geometry.
Table 1. Scramjet Combustor Specifications.
| title | dimension |
|---|---|
| scramjet combustor | 600 × 50 × 80 mm (length × width × height) |
| cavity | 100 × 50 × 80 mm (length × width × height) |
| orifice | 1 mm (diameter), 20 mm height |
| inlet and outlet | 50 × 80 mm (width × height) |
Figure 3 schematically illustrates the computational model of the changed scramjet combustor, in which a total of 282,000 hexahedron cells were used. Different from the original model in ref (4) the densest mesh cells in the changed combustor model are merely located at the cavity. This discrepancy is primarily caused by the strong interaction appearing at the zone between the incident shock wave and the transverse cavity injection.
Figure 3.
Meshed scramjet combustor with the changed low cover geometry.
2.2. Methodology
In this study, the primary methodology includes the following two aspects. The first is used to investigate the kerosene fuel–air interaction. The second method is applied to evaluate the distribution of kerosene droplets.
2.2.1. Kerosene Fuel–Air Interaction
The approaches for the kerosene fuel–air interaction are briefly depicted below: the three-dimensional couple level set and volume of fluids (CLSVOF) model was used for the effects of the changed lower cover geometry on the air–kerosene interaction for better accuracy because the interface breaking and coinciding with another interface is prone to occur; due to the complexity of the mixing process between the incident shock wave and the transverse cavity jet, an additional remixing method was used; and equations such as the energy equations, the state of gaseous mixture equations, and the turbulent model equations were considered for all simulations based on the fuel–air interaction in the combustor. The above-mentioned equations are briefly presented, respectively, below.
For CLSVOF, the Navier–Stokes equation is
 |
1 |
and the continuity equation is
 |
2 |
where V⃗ is a velocity vector, D is the viscosity deformation tensor, and Fst is the body force due to the surface tension.
Energy equation for a droplet is
 |
3 |
where the heat flux q from the surrounding gas to a single droplet depends on
 |
4 |
where 
, T is the temperature
of gas, and Ts is the temperature of the
droplet.
The state equation of a gas mixture
 |
5 |
where Wk is the molar mass of the kth gas component, hok is the specific chemical energy, cvk is the specific heat capacity, Yk is the mass concentration of the kth gas component, and Rg is the universal gas constant.
The turbulent model, i.e., model of the two-equation shear stress transport, is
 |
6 |
 |
7 |
 |
8 |
where α* is the coefficient damping the turbulent viscosity, Fi (i = 1,2) is the bending function, and σi (I = k, ω) is the diffusion constant of the model.
We refer the readers to refs (4) and (15)–161718192021 for details of the equations.
2.2.2. Kerosene Droplet Distribution
For kerosene droplet distribution in the scramjet combustor, Sauter mean diameter (SMD) distribution is generally used. In this regard, a combination of the Blob model and the modified Kelvin–Helmholtz (K–H) and Rayleigh–Taylor (R–T) model was applied for the droplet atomization in the combustor with the changed lower cover geometry. The droplet atomization presented here is primarily involved in the primary atomization and droplets’ breakup. The relevant equations used for the SMD distribution are briefly described as follows. Note that the time should be calculated as the R–T model is incorporated into the K–H model for better accuracy.
(1) K–H model
 |
9 |
 |
10 |
where Λ is the surface wavelength of
the liquid jet at the maximum growth rate Ω, 
is the Ohnesorge number of the droplets, 
is the droplets Weber number, and r is
the droplet radius.
The average radius r*of the droplets after breakup is
 |
11 |
The velocity at which the droplet breaks up is
 |
12 |
where τb = 3.726B1r/ΛΩ.
(2) R–T model
 |
13 |
where ΩRT is the unsteady wave frequency at the maximum growth rate.
Breakup time τRT for the droplets is
 |
14 |
The average radius r* of the droplets after breakup is
 |
15 |
where KRT is a wavenumber and its size is determined by the following factors
 |
16 |
(3) Time standard for incorporating the R–T model into the K–H model
 |
17 |
where tb― droplets breakup time and t*―the characteristic time.
Detailed information on the K–H and R-T model II is available in refs (21 and 22).
Besides, the evaporation of kerosene droplets has also been included in all simulations to better evaluate the mixing quality. The nonequilibrium evaporation model is applied for the determination of the evaporation rate.21 The relevant formulas are
 |
18 |
 |
19 |
where ρg―the density of the gas, D―mass diffusion coefficient, and Nu―Nusselt number of the mass transfer. The thermal characteristics of gas and droplets for evaporation are presented below:
Ambient pressure p = 1.013 × 105 Pa, initial droplet temperature T = 300 K, static temperature of the gas (considering evaporation) T = 536 K, gaseous phase―air, liquid phase―kerosene, mass diffusivity (m2/s) = 2.88 × 10–5, thermal conductivity (W/m·k) = 0.0454, and the latent heat hL of evaporation = 226 kj/kg.
2.3. Boundary Conditions
The boundary conditions for the computational fluid dynamics (CFD) modeling in this study4 are depicted as follows. The stagnation temperature T0 is 300 K. The stagnation pressure P0 is 7.85 MPa. The inlet velocity is 210 m/s, the kerosene injection speed is 70 ms–1, the kerosene orifice diameters are 0.5, 1.0, and 1.5 mm, respectively, the injection angle is 90°, the injection pressure is 2 MPa, and the density, viscosity, and surface tension are designated to be ρ = 0.78 g/cm3, u = 2mPags, and σ = 23.6 × 10–3 N/m, respectively. The pressures at the inlet and outlet of the scramjet combustor are both set as 1.013 × 105 Pa. A no-slip boundary condition on the channel wall was not considered. The turbulence intensity is 8%, hydraulic diameter is 0.5, 1.0, and 1.5 mm, respectively, and for stability, the courant–Friedrichs–Levy number is required to be 0.5, with appropriate under-relaxation factors. Detailed information on the boundary conditions is available in ref (4).
All the simulations were performed in the commercial CFD software ANSYS Fluent 14.0 (ANSYS Inc., USA) by an implicit CFD code using the cell centered finite volume approach. A second-order upwind scheme was used to discretize the momentum and continuity equations with a coupled solver, i.e., a pressure-based (coupled) double precision solver. The convective fluxes were treated with the roe flux-difference splitting scheme, which is effective in improving the treatment and accuracy of the shock waves.23
3. Results
In this section, the feasibility and effectiveness of the scramjet combustor with the changed lower cover geometry are evaluated using the following four aspects, i.e., penetration heights, distribution of span expansion area, shock wave angle, and SMD of kerosene jets. These aspects are associated with combustor performances.
3.1. Numerical Accuracy
More generally, for reliable accuracy, there are two essential aspects to consider carefully.24 First, the effect of the mesh scale needs to be considered. The second section is focused on the convergence and discretization errors.
The current results have demonstrated that the grid scale has slight influences on the transversal injection flow field in the scramjet combustor.24 Thus, considering a balance of both accuracy and computational resources, we used a medium-sized grid, i.e., 282,000 hexahedron cells for all simulations in this study.
For the convergence and discretization error, it is believed that the calculation is considered to be convergent as all of the residuals of the flow field parameters are lower than a certain order of magnitude. To achieve this, we used 1.0 × 10–3 as the critical value to judge the solution convergence, in which the iteration number was set to be 1000, the average time step was designated as 10 μs, and a typical run actually took 2096 time-steps to a real time of about 19 ms. Figure 4 shows the residual evolutions of the flow field parameters with the iteration numbers for the different injection diameters. As observed, for the varying injection diameters of 0.5, 1.0, and 1.5 mm, all the calculations were stopped as the iteration numbers approximately reached 925.
Figure 4.
Residuals variation occurs with iteration steps at the three different injection diameters.
3.2. Penetration Height
The penetration heights of the kerosene jet in the scramjet combustor for three different injection diameters are listed in Figure 5. As seen from Figure 5, all the flow structures after mixing of air flow and kerosene herein are made of compression shock, compression shock perpendicular̀ to the wall, and bent central compression shock. These flowing structures agree well with those in ref (18).
Figure 5.
Penetration heights of the kerosene jet at the three different injection diameters.
For the different injection diameters of 0.5, 1.0, and 1.5 mm, the penetration heights of the kerosene droplets at the location of 600 mm are approximately 27, 30, and 33 mm related to the baseline of y = −40 mm (the black dashed line in Figure 5), respectively. It follows that the penetration height of the kerosene droplets is increased with the injection diameter in the combustor with the changed lower cover geometry.
3.3. Span Expansion Area
Figure 6 schematically illustrates the span expansion variations of the kerosene jet at three different injection diameters, respectively. Same as those in ref (4), these expansion areas were obtained within the XOZ plane, which is perpendicular to the orifice in the cavity 60 mm of the scramjet combustor (Figure 2). It can be seen from the calculation results that the span areas of kerosene injection, including expansion width and angle, increase with the increase of injection diameter. In detail, the expansion width and angles are approximately increased from (37 mm, 44°) to (42 mm, 55°) and then to (50 mm, 60°).
Figure 6.
Span expansion areas of the kerosene jet at three different injection diameters.
3.4. Shock Wave Angle
Figure 7 schematically illustrates the span expansion variations of the kerosene jet at three injection diameters. As observed, the shock wave angles all increased with the kerosene jet diameter. For the injection diameters of 0.5 to 1.5 mm, the angle of shock wave is increased from 60 to 68° and then to 71°; the jet height of the kerosene droplets, at the outlet of the combustor, is also increased from 28 to 30 mm and then to 32 mm.
Figure 7.
Shock wave angle of the kerosene jet at the three injection diameters.
3.5. Sauter Mean Diameter Distribution
Figure 8 schematically indicates the concentration distribution of the transversal kerosene jet at the three different injection diameters with/without evaporation considered. As seen from Figure 8, no matter whether the evaporation is considered, the concentration of kerosene droplets is varied along the flow direction as the injection diameter is varied; see Figure 2. It is inferred that the injection diameter influences the kerosene droplet distributions in the scramjet combustor with the changed lower cover geometry. In order to further evaluate the effects of the injection diameter, SMD distributions are used to investigate the exact variations of the kerosene droplets at the above-mentioned conditions.
Figure 8.
Concentration distribution of the transversal kerosene jet at three different injection diameters.
Figures 9 and 10 schematically illustrate the SMD distributions of the kerosene droplets along the x direction in the changed scramjet combustor without/with kerosene evaporation considered, respectively. In these pictures, the symbol Pd (%) represents the percentage of the SMD distribution on the cross-section vertical to the supersonic flow direction, and the “X” indicates the vertical length between the cross-section and the orifice in the cavity.
Figure 9.
SMD distribution of the kerosene droplets at the three different injection diameters (A) 0.5, (B) 1.0, and (C) 1.5 mm without the evaporation considered.
Figure 10.
SMD distribution of the kerosene droplets at the three different injection diameters (A) 0.5, (B) 1.0, and (C) 1.5 mm with the evaporation considered.
In Figure 9, without the evaporation considered, the concentration of the kerosene droplets varies along the x direction as the injection diameter is increased from 0.5 to 1.5 mm. Comparing (A) to (B) and (C) in Figure 9, one interesting finding is that the maximum number of the droplets with size of (0–50 μm) appears at different positions for the different orifice diameters. In detail, for the orifice diameter of 0.5 mm, the greatest number of (0–50 μm) droplets appears at the location about 50 mm away from the orifice, and the greatest number is 94.72%. However, for the orifice diameter of 1.5 mm, the greatest number of the (0–50 μm) droplets appears at the outlet of the combustor, and the relevant number is 90.41%. It should be noted that both 94.72 and 90.41% presented here are the smallest droplets of all the kerosene injection droplets in this study.
When the evaporation is considered, phenomena similar to those in Figure 9 are also observed in Figure 10. That is, for all the cases examined in this study, the greatest number of the (0–50 μm) droplets at the cavity is the maximum (such as 96.41, 94.34, and 93.05%) and the greatest number of the (0–50 μm) droplets at the outlet is the minimum (such as 70.90, 81.42, and 85.00%).
Comparison of Figures 9 and 10 indicates that at the outlet of the combustor, the number of the (0–50 μm) droplets reduces from 89.56% without evaporation to 70.90% with evaporation for the injection diameter of 0.5 mm and that for the injection diameter of 1.5 mm, the relevant number is decreased from 93.12 to 85.00%. Particularly, as the evaporation is considered, the reduction of the (0–50 μm) droplets is more obvious with the diameter decrease from 1.5 to 0.5 mm; see Figure 11B.
Figure 11.
Number of the (0–50 μm) droplets in the scramjet combustor with the changed low cover geometry. (A) Evaporation not considered. (B) Evaporation considered.
4. Discussion
From the given results in Section 3, it is seen that the orifice diameter has influences on the air–fuel interaction in the scramjet combustor with the changed low cover geometry. These results are basically attributed to the varying injection diameters, which result in the varying momentums of the kerosene jet from the orifice. To take an example, the increased injection diameter is accompanied by the increased momentum of liquid jet, thereby producing a larger inertia force and, as a result, a greater penetration height. However, the question of whether this combustor with the changed lower cover geometry can degrade the mixing efficiencies of the original combustor still remains to be answered. For this reason, in this section, the mixing characteristics between air and kerosene in this study have been evaluated by the quantitative comparisons with our published data.4 Note that these published predictions have been compared with the reported experimental measurements,25 and their qualitative results are in agreement with each other. The comparisons are focused on the following three aspects of penetration height, span expansion area, and shock wave angle under identified working conditions. Besides, due to the elevated temperature in the scramjet combustor, we have also verified the evaporation model in this study by comparing the Peclet number Pe with that by Tyurenkova.26
4.1. Penetration Height
Figure 12 schematically illustrates the comparison of the numerical results in this study with the simulations in ref Zhu et al.4 at the same injection diameters (such as 0.5, 1.0, and 1.5 mm). As observed, the predicted penetration heights in this study quantitatively agree well with the published data: (1) with the orifice diameter increase, the density variations in kerosene droplets are quite the same and (2) the penetration height is increased with the orifice diameter; particularly, their increase rates are almost equal to each other. For example, for the original scramjet combustor, the maximum penetration height at the outlet is increased from about 29 to 30 mm and then to 35 mm as the kerosene jet diameter increases from 0.5 to 1.5 mm (Figure 5 in ref (4)), while the maximum penetration height in the changed combustor is increased from about 28 to 30 mm and then to 35 mm. From the viewpoint of the penetration height, it is therefore inferred that the changed combustor can achieve the same performance as that of the original combustor.
Figure 12.
Comparison of the numerically calculated penetration heights with the published data by Zhu et al.4
4.2. Span Expansion Area
Figure 13 schematically illustrates a comparison of the span expansion areas in this study with Zhu’s.4 As observed, the calculated variation trends in span angle and expansion breadth in this study are good agreement with those in ref (4). For example, for the original scramjet combustor, as the kerosene jet diameter increases from 0.5 to 1.5 mm, either span angle or breadth is increased from (37°, 35 mm) to (50°, 40 mm) and then to (59°, 49 mm) (Figure 6 in ref (4)). However, for the changed combustor, the corresponding value is increased from (44°, 37 mm) to (55°, 42 mm) and then to (60°, 50 mm). The comparison indicates that the span angles and breadths in the original scramjet combustor are both smaller than those in the changed combustor. It follows, from the viewpoint of the span expansion area, that the scramjet combustor with the changed geometry can surely obtain the same performance as that of the original combustor.
Figure 13.
Comparison of the calculated span area with the published data by Zhu et al.4
4.3. Shock Wave Angle
Figure 14 schematically shows the numerical simulations results of this study in comparison with those from Zhu et al.4 at three injection diameters of 0.5, 1.0, and 1.5 mm. As observed, the angles of shock in either the original or changed combustor are both increased with the kerosene jet diameter increase. For the original combustor, the shock angle is increased from 57 to 65° and then to 69° (Figure 7 in ref (4)), while for the changed combustor, the corresponding value is increased from 60 to 68° and then to 71°. Further comparison indicates that the shock wave angles in the changed combustor are larger than those in the original combustor at the same injection diameter. Thus, from the viewpoint of the shock wave angle, it is concluded that the scramjet combustor with the changed geometry can surely obtain the same performance as that of the original combustor.
Figure 14.
Comparison of the calculated angles of the shock wave with the published date by Zhu et al.4
4.4. Evaporation Model
Figure 15 shows the comparison of the evaporation model in this study with the exact solutions provided with Tyurenkova.26 As depicted previously, this comparison is carried out by calculating the Peclet number of Pe. The formula Pe is
 |
20 |
where ṁ—mass flux, x = xw—the surface of the droplet, ρ—droplet density, and D—diffusion coefficient.
Figure 15.
Comparison of the evaporation model in this study with the published model by Tyurenkova.
And also, based on the SMD distribution and kerosene droplets mass flux in the scramjet combustor, eq 20 can further be simplified as follows
 |
21 |
where PdN—the percentage of the SMD distribution.
In addition, the symbol in Figure 15, IN, is a dimensionless parameter, which can be calculated by
 |
22 |
As seen from Figure 15, the Pe variation trends, relative to IN, at the different orifice diameters in this study are all the same as that in ref (26). In detail, the Peclet number Pe is gradually decreased with the increase in IN, and particularly, the values in Pe are all equal to zero as the IN value approaches 106. In this regard, the evaporation model used in this study is believed to be effective. However, it is worth noting that the Peclet number in ref (26) is larger than those in this study. This is basically due to the different boundary conditions and also the different geometries.
In addition, the total pressure losses in the changed scramjet combustor at the three different injection diameters were also calculated. The relevant results could be seen in Table 2. Compared with the pressure losses in the original combustor,4 as shown in Table 3, the pressure losses of the changed combustor are all greater than those of the original combustor. The maximum discrepancy in pressure loss appears at a diameter of 1.5 mm. The maximum discrepancy is 3.44 × 10–4. This indicates that the mixing characteristics of the changed and original scramjet combustors are comparable.
Table 2. Pressure Losses in the Changed Combustor at the Different Injection Diameters.
| injection diameter | inlet pressure (Pa) | outlet pressure (Pa) | pressure lose (Pa) |
|---|---|---|---|
| D = 0.5 mm | 785,000 | 637,480 | 147,520 |
| D = 1.0 mm | 785,000 | 617,000 | 168,000 |
| D = 1.5 mm | 785,000 | 581,602 | 203,398 |
Table 3. Pressure Losses in the Original Combustor at the Different Injection Diameters by Zhu et al.4.
| injection diameter | inlet pressure (Pa) | outlet pressure (Pa) | pressure lose (Pa) |
|---|---|---|---|
| D = 0.5 mm | 785,000 | 637,495 | 147,505 |
| D = 1.0 mm | 785,000 | 617,033 | 167,967 |
| D = 1.5 mm | 785,000 | 581,672 | 203,328 |
5. Conclusions
Inspired by mechanical design, in this study, we have proposed to change the lower cover geometry of the scramjet combustor in order to alleviate the adverse effects caused by the supersonic flow. For the evaluation of the effectiveness of the changed combustor, the mixing efficiencies of the air–kerosene interaction, including penetration height, span expansion area, shock wave angle, and SMD distribution with/without the evaporation considered, are investigated at the three different injection diameters. The simulations result in this study have been compared with those in the literature with good agreement. The main findings of this study are presented as follows.
For the scramjet combustor with the changed lower cover geometry, the increase trends of the penetration height, span expansion area, shock wave angle, and SMD distribution are quite the same as those in the original combustor. Particularly, it is worth noting that both the span area and shock wave angles in the changed scramjet combustor are larger than those in the original combustor at the same injection diameters. And also, the evaporation model in this study is consistent with that in the literature by comparing their Pe variation trends.
Changing the lower cover geometry or reducing the size differences between the throat region and diverging section of lower cover can surely alleviate the adverse effects from the supersonic air in the original scramjet combustor. This approach is helpful in improving the combustor performance.
However, slight disagreements in the mixing performance of these two different combustors are also observed. These disagreements may be caused by the different combustor geometries, which have effects on the flow rate of the air, the injection mass, and, consequently, the shear interaction between air and kerosene droplets. The simulations in this study may provide a possible research direction for improving the scramjet engine. Future work is now ongoing to update the existing experimental setup and quantitatively validate the obtained simulations.
Acknowledgments
The authors would like to thank the National Natural Science Foundation of China (grant no. 52175211), the Major Programs of Anhui Provincial Education Department (grant no. KJ2020ZD09), the Anhui Provincial Natural Science Foundation (grant no. 2108085ME164), the Anhui Provincial Collaborative Innovation program for colleges and Universities (grant no. GXXT-2023-030), the Anhui Provincial Collaborative Innovation program for colleges and Universities (grant no. GXXT-2023-032), and the Natural Science Research Program of Fu yang Normal University (grant no. 2021FSKJ1400) for the financial support for this study. The authors also thank the reviewers and editor for their valuable input on this manuscript.
Glossary
Abbreviations Full Abbreviations Name
- CLSVOF
couple level set and volume of fluids
- SMD
Sauter mean diameter
- CFD
computational fluid dynamics
- K–H
Kelvin–Helmholtz
- R–T
Rayleigh–Taylor
Author Contributions
∥ Peng and Zhou are co-first authors.
The authors declare no competing financial interest.
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