Application of multi-extruded fuel injectors for mixing enhancement of hydrogen gas at scramjet engine: computational study

Scramjet engines are considered a highly promising technology for improving high-speed flight. In this study, we investigate the effects of using multi-extruded nozzles on fuel mixing and distribution inside the combustion chamber at supersonic flow. Additionally, we explore the impact of an inner air jet on fuel mixing in annular nozzles. To model fuel penetration in the combustor, we employ a computational technique. Our study compares the roles of three different extruded injectors on fuel diffusion and distribution at supersonic cross-flow. Our findings reveal that the use of an inner air jet increases fuel mixing in the annular jet, while the use of extruded nozzles improves fuel distribution by enhancing the vortices between injectors. These results demonstrate the potential benefits of incorporating multi-extruded nozzles and inner air jets in the design of scramjet engines.


Governing equations and numerical methodology
The simulation of high-speed air stream with compressibility effects is mainly done via solving RANS equations for continuum domain [37][38][39][40] .The shock wave formation is inherently happened in our model and consequently, the energy equation must be considered in our modeling 41,42 .Meanwhile, the turbulence effects are also important in our model and SST model of turbulence is considered for the calculation of viscosity 31,42,43 .The secondary gas of hydrogen is also modeled as fuel jet and mass transport equation is also used with Fick.Law for estimation of the diffusion of hydrogen gas 44,45 .Reactions are not considered in this study.The air flow is considered as ideal gas in the present model [46][47][48][49][50][51] .
Figure 1 illustrates the shape of the injector and arrangement of the nozzle inside the model.The fuel jet is injected through annular nozzle while air jet is released from inner core of the nozzle.The size of outer and inner nozzle is equal and equivalent to circular nozzle with diameter of 0.5 mm.The jet distance of these injector in all configurations is 3.5 mm and the height of extruded nozzle of 2nd, 3rd and 4th nozzle is 0.5 mm, 1 mm and 1.5 mm.The length, width and height of computational domain are 80 mm, 5 mm and 6 mm, respectively.At inlet, air stream with Mach number of 4 and static temperature of 1000 K is applied.The fuel and air jets are released with Mach = 1 and 10% total pressure of supersonic air stream.Half of real model is simulated to reduce the computational cost 52 .The usage of theoretical method is conventional in engineering applications [53][54][55][56] .
The produced grid for the selected computational domain is displayed in Fig. 2. The structured grid is applied for the model because of the shock interactions.Besides, the resolution of generated grid must be high enough in the regions nearby the nozzle since these districts are potential for the high velocity and density gradient.The grid study is also done to obtain the proper size of grid for the present investigations.Table 1 presents the results of grid independency analysis and it is noticed that the fine grid is most efficient grid for the chosen model.

Results and discussion
The correctness of the achieved data from the computational study is evaluated to certify the precision of the applied approach.Figure 3 displayed the value of fuel penetration of single circular nozzle with diameter of 2 mm at supersonic flow.These outcomes advocate that the single-jet numerical solution is accurate in terms of the penetration downstream of jet 38 (Table 2).Figure 3a illustrates the primary feature of shock waves layer near these annular injectors at supersonic flow on the symmetry plane.The Mach contour of the proposed configuration reveals that the shear layer and jet bow shack significantly varies by the shape of injector on the jet plane.Indeed, the jet bow shock, which is produced by the velocity of fuel jet, deformed by the incoming air stream.When the simple injectors are used, the growth of shear layer is related to the total pressure of jet and free stream condition.However, in extruded jet configuration, the jet plume is related to the height of extruded nozzles.The difference of the shock layer for the model with inner air jet (Fig. 3b) with former annular cases (Fig. 3a) indicates that the high pressure of the coaxial fuel and air jet released from the extruded nozzle results separation shock upstream of the first nozzle.Hence, the formation of the barrel fuel jet is not changed under influence of the incoming supersonic flow.
Figure 4a illustrates the contour of mass on the symmetry plane for different annular lobe-nozzles.When the extruded injector is applied for the fuel mixing, the height of the fuel mixing zone is managed by the height of the extruded injectors.As confirmed by the mass contour, the concentration of the fuel jet and penetration height is directly varied by the nozzle height.Besides, the interactions of the fuel jet with main stream almost constant for all jets.In fact, the main advantageous of this concept is management of the fuel diffusion and the efficient fuel diffusion by the jet interactions even in last injectors.As depicted in Fig. 4b, the addition of inner air jet also has meaningful impacts on the concentration and diffusion of the fuel jet in proposed configurations.Comparison of coaxial nozzle with annular one shows that the usage of inner air flow substantially improves the circulation in the gap of injector which enhance the fuel mixing and diffusion of the fuel in the depth of the domain.Indeed, the fuel mixing is more efficient in this configuration.
The three-dimensional flow feature of annular jet configurations (Fig. 5a) disclosed the influence of the circulation in the gap of the injectors on the jet layer at supersonic flow.The comparison of different lobe-nozzle types shows that the fuel distribution inside the main stream is improved by the nozzle with 4-lobe shape.In facts, the fuel jet released from wider area in 4-lobe nozzles and this extend the fuel plume inside the combustion chamber.The injection of the air jet in the recommended jet arrangements (Fig. 5b) shows that the jet interactions are extremely amplified when inner air jet is coupled with annular fuel jets.Meanwhile, the effects of the upstream circulation on the distribution of the fuel jet is more pronounced in the coaxial air and fuel injection.
In Fig. 6, the jet stream along with fuel jet is investigated and displayed to reveal the importance of jet interactions on the mechanism of fuel diffusion in combustion chamber for the proposed models.As mentioned in the previous sections, the interactions of the air and fuel jet becomes extraordinary when extruded multi-nozzles is used in supersonic flow.As demonstrated in Fig. 6a, each jet has its own interactions with air stream in the   www.nature.com/scientificreports/extruded configurations and the formation of the vortex within the gap of extruded nozzle is extended by the height of the fuel nozzle.These two features are considerably important for the distribution of the fuel multi-jets.
As illustrated for the coaxial jet configurations (Fig. 6b), higher jet interactions are achieved by adding inner air jet and this extend the upstream circulations.Therefore, horseshoe vortex with stronger circulation extend to downstream.As the normal momentum of the fuel and air jets increases in this model, the pressure in the gap of nozzle is extended and this enables the formation of the vortex in this region.Therefore, the fuel distribution is more uniform in this configuration.
Comparison of the mixing zone and stream feature on two planes (x/D = 10 and 30) down stream of three suggested nozzle configurations are done in Fig. 7.In the vicinity of nozzle (Fig. 7a), the height of fuel penetration is less for annular injector while higher fuel penetration is noticed for the coaxial model.There are two main vortices behind the jet and strength and size of these vortices clearly disclose the role of injector type and existence of inner air jet in the planned configurations.The main circulations (Vortex A) is inherently produced by the normal velocity of fuel jet and second one (Vortex B) is related to the horseshoe vortex.In some nozzle the secondary vortex is not observed especially in the coaxial model.In the far distance (Fig. 7b), the position of these two vortices are changed and the concentration of the fuel gas becomes uniform by the usage of inner air jet.
Comparison of the circulation strength downstream of the proposed configurations is presented in Fig. 8.The variation of the circulation power indicates that replacing the annular jet with coaxial air and fuel jet decreases the circulation power in all models.Among these injector types, 3-lobe model has maximum circulation power and this is due to the formation of larger upstream circulation.The data of circulation shows that the impacts of injector types and nozzle is almost in range of 10 mm to 20 mm behind the first nozzle.
Figure 9 plots the changes of fuel mixing behind the fuel nozzles for the proposed extruded injectors.The mixing efficiency of coaxial air and fuel jet is almost 44% more than annular nozzle.The main performance of injector type is noticed near the injectors.In the coaxial nozzle configurations, the 3-lobe nozzle performs more efficient in fuel distribution than other injector configurations.

Conclusion
This study focuses on investigating the effects of multi extruded injectors on the fuel mixing mechanism in scramjet engines.Specifically, we examine the roles of three different types of nozzles located inside the engine's combustor, including annular and coaxial nozzles.To model the release of fuel jet from the extruded nozzles at supersonic cross flow, we develop a computational fluid dynamic approach.Through this approach, we compare the mixing efficiency and circulation power of each model.Our findings indicate that the use of coaxial jet nozzles decreases the circulation power, while achieving maximum fuel mixing efficiency.Additionally, we observe that the utilization of an inner air jet in the coaxial configuration further enhances fuel mixing in the nozzle gap.www.nature.com/scientificreports/

Figure 3 .
Figure 3.Comparison of Mach contour for (a) annular jet system (b) coaxial jet.

Figure 4 .Figure 5 .
Figure 4. Comparison of flow stream and fuel concentration on the symmetry plane for (a) annular jet system (b) coaxial jet.

Figure 6 .
Figure 6.Comparison of flow and jet interactions for (a) annular jets (b) coaxial jets system.

Figure 7 .
Figure 7.Comparison of mass concentration and stream of annular and coaxial jets at (a) X/D = 10, (b) X/D = 30 downstream of first jet.

Figure 8 .
Figure 8.Comparison of the circulation induced by jet type downstream of the injectors.

Figure 9 .
Figure 9.Comparison of the fuel mixing efficiency downstream of the injectors.