Parametric effect on the mixing of the combination of a hydrogen porthole with an air porthole in transverse gaseous injection flow fields

Acta Astronautica 139 (2017) 435–448

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Parametric effect on the mixing of the combination of a hydrogen porthole with an air porthole in transverse gaseous injection flow fields Lang-quan Li, Wei Huang *, Li Yan, Shi-bin Li Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China

A R T I C L E I N F O

A B S T R A C T

Keywords: Transverse injection Mixing efficiency Penetration depth Stagnation pressure loss Streamwise vorticity

The dual transverse injection system with a front hydrogen porthole and a rear air porthole arranged in tandem is proposed, and this is a realistic approach for mixing enhancement and penetration improvement of transverse injection in a scramjet combustor. The influence of this dual transverse injection system on mixing characteristics has been evaluated numerically based on grid independency analysis and code validation. The numerical approach employed in the current study has been validated against the available experimental data in the open literature, and the predicted wall static pressure distributions show reasonable agreement with the experimental data for the cases with different jet-to-crossflow pressure ratios. The obtained results predicted by the threedimensional Reynolds-average Navier – Stokes (RANS) equations coupled with the two equation k-ω shear stress transport (SST) turbulence model show that the air pothole has an great impact on penetration depth and mixing efficiency, and the effect of air jet on flow field varies with different values of the aspect ratio. The air porthole with larger aspect ratio can increase the fuel penetration depth. However, when the aspect ratio is relatively small, the fuel penetration depth decreases, and even smaller than that of the single injection system. At the same time, the air pothole has a highly remarkable improvement on mixing efficiency, especially in the near field. The smaller the aspect ratio of the air porthole is, the higher the mixing efficiency in the near field is. This is due to its larger circulation in the near field. The dual injection system owns more losses of stagnation pressure than the single injection system.

1. Introduction The scramjet (supersonic combustion ramjet) engine may be one of the most promising engine cycles for the hypersonic flight in the future [1]. An oxidizer tank is not required in these engine cycles, and they are simple in structure and low in cost. Moreover, the scramjet (supersonic combustion ramjet) engine is the most effective engine cycle when vehicles fly in or beyond the supersonic speed. Therefore, they are preferred to rocket and turbofan engines. The presence of these advantages has motivated researchers in recent years [2–5]. In the scramjet combustor, the mixing process is the initial phase for all the physical ones, and it is the primary factor to restrict the combustion process [6,7]. Hence, the realization of sufficient mixing is the key to the engineering implementation of the hypersonic propulsion system. Due to the short residence time of airflow within the scramjet combustor being on the order of milliseconds for typical flight conditions [8], an efficient injection strategy with high penetration and rapid mixing is required.

* Corresponding author. E-mail address: [email protected] (W. Huang). http://dx.doi.org/10.1016/j.actaastro.2017.07.048 Received 3 July 2017; Received in revised form 27 July 2017; Accepted 29 July 2017 Available online 31 July 2017 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.

Many injection schemes have been proposed to enhance the mixing process, and they have been studied theoretically [9], numerically [10] and experimentally [11]. One simplest and reliable approach of fuel injection for a scramjet engine is transverse injection from a wall orifice [12,13], because the transverse injection provides rapid fuel-air mixing and high jet penetration into the supersonic airflow [14]. At first, the majority of studies have concentrated on a single transverse jet at a variety of conditions such as jet-to-crossflow pressure ratio [15,16], jet-to-crossflow momentum flux ratio [17], molecular weight [18], injector geometry [19], injection angle [20], incoming air steam angle [21]. Huang and Yan [13] provide a detailed review on the transverse injection flow field from four aspects, namely the jet-to-crossflow pressure ratio, the geometric configuration of the injection port, the number of injection port and the injection angle. On the other hand, in order to increase the penetration and mixing, many devices such as strut [22–25], ramp [26], pylon [27], cavity [28–30], aerodynamic ramp [31], and any other combination have been offered and enhanced mixing and penetration substantially, but at the expense of a larger stagnation pressure

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pressure loss.

loss, increasing drag forces, and inciting considerable local heating loads [32]. In 2016, Huang [15] reviewed more than 130 documents and summarized systematically the research progress on the transverse jet in supersonic crossflow, especially on the interaction between jet and vortex generator and the interaction between jet and shock wave. A variation on the traditional single jet in crossflow is the multiple transverse injection system [33–38], and several variable conditions such as distributions of mass flow rate and momentum flux, combination of injection angles, arrangement of injector geometry and spacing variation in both the freestream and spanwise directions can be applied in this approach. Since the multiple transverse injection system does not have physical obstruction to the combustor flow in comparison with the mixing enhancement devices, the stagnation pressure loss, the drag forces, and the local heating loads are small. The transverse injection flow field with a multiple transverse injection system owns better mixing characteristics than that with a single transverse injection system due to the interactions among the injection flows. In 2006, Lee [33] studied the mixing characteristics of a dual transverse injection system and showed the schematic view of the dual transverse injection flow field. The horseshoe vortices, the separation bubble, and the recirculation wake flows are formed along the jet direction. The streamwise vortices roll up the injection flows, so the mixing process between the fuel and the freestream is accelerated, but the dual transverse injection scheme would induce a slightly larger total pressure loss. In 2015, the influence of the jet-to-crossflow pressure ratio arrangement of the multiple injection system with four square-shaped portholes arranged in tandem has been investigated by Huang [39], and the mixing performance is determined by the jet-to-crossflow pressure ratio of the primary injector. In 2016, Huang studied the mixing process induced by an array of three spanwise-aligned small-scale rectangular portholes, and the influences of the jet-to-jet spacing, the jet-to-crossflow pressure ratio and the aspect ratio of the injector on the flow field properties were evaludated [40]. Recently, a creative injection strategy has been proposed by Barzegar et al. [41–44]. The characteristics of the transverse hydrogen jet in presence of multi air jets have been comprehensively investigated by Barzegar and his coworkers from four aspects, namely the number of air jets and fuel jets, the pressure of the air jets, the fuel jet space and the number of the air jets downstream of each fuel jet. According to the obtained results, the influence of the air jets is significant, and the effect of air jets on mixing performances of transverse gaseous injection flow fields varies on various conditions. However, to the best of the authors' knowledge, the influence of the aspect ratio of the air porthole on the transverse injection flow field has rarely been investigated simultaneously in the open literature, and this issue is crucial for the design of the mixing device in supersonic crossflows. On the other hand, Computational Fluid Dynamics is an efficient approach to perform parametric studies and check whether design changes are worth testing experimentally. At the same time, it also provides important insight into complex flow phenomena like separations, shock wave, thus significantly improving the flowpath design process for relatively lower costs compared to costly experimental tests alone [45,46]. In the current study, the transverse injection flow field in a Mach 3.75 crossflow of air has been investigated numerically, and the numerical approaches are validated against the available experimental data in the open literature. The combustion process is out of the scope in this article, and it would be taken into consideration in the near future. However, the mixing process will go in a different way in the presence of combustion, especially taking into account diffusive character of combustion processes next to injection zones [47]. The dual injector system made up of a hydrogen porthole and an air porthole has been employed. The configuration is investigated in terms of variations in the aspect ratio of the air porthole in a parametric study. The influence of the aspect ratio of the air porthole on the supersonic mixing between the hydrogen and air has been evaluated. The main performance parameters concerned in the present study are mixing efficiency, penetration depth, and stagnation

1.1. Physical model The test section is a straight channel. The width of the flat plate is 30 mm, the height of the computational domain is 15 mm, and its total length is 200 mm. Fig. 1 shows the top view of the array of two rectangular portholes. The main configuration consists of a flat plate with a front hydrogen porthole and a rear air porthole arranged in tandem. The distance from the entrance of the channel to the trailing edge of the hydrogen porthole is 20 mm, and the origin of the coordinate system is set at the tailing edge of the fuel porthole. The width and length of hydrogen porthole are 0.5 mm and 2 mm respectively. The space between the hydrogen porthole and the air porthole is the same, and it remains constant, namely S ¼ 2 mm in Fig. 1. The aspect ratio of the air porthole is set to be 8:1, 2:1, 1:2 and 1:8 respectively corresponding to model B, model C model D and model E. In order to retain a constant air mass flow, the area of air porthole keeps constant, and its value is 2.0 mm2. The length and width of air porthole for each model can refer to Table 1. Model A is a traditional single jet flow field, and it is simulated for comparison. The air flows from left to right, and its air properties are set to be a Mach number M∞ of 3.75, a static pressure P∞ of 11090Pa and a static temperature T∞ of 78.43 K. The jet flow Mach number Mj is set to be 1.0 with a static temperature Tj ¼ 249 K, and these conditions are representative of a typical generic scramjet combustor. The hydrogen is set as the fuel for it is generally a more energetic fuel than hydrocarbon fuels for a Mach number in the range 4–10 [48]. The jet-to- crossflow pressure ratio is defined as the static pressure ratio of injectant and supersonic airflow. The jet-to-crossflow ratio of the hydrogen porthole is set to be 25.15, and the jet-to-crossflow ratio of air porthole is set to be 4.86 according to the previous studies carried out by the same authors [19]. 2. Numerical approaches In the current study, the three-dimensional Reynolds-average Navier – Stokes (RANS) equations coupled with the two equation k-ω shear stress transport (SST) turbulence model have been utilized to numerically simulate the transverse injection flow field. The steady state computational data have been obtained using a density based (coupled), implicit, second-order upwind, double precision solver of FLUENT version 6.3.26 [49]. A Dell workstation at the Science and Technology on Scramjet Laboratory, China, using up to 32 processors, provided a parallel computing environment for flow solutions. 2.1. The governing equations The RANS equations are considered for their ability to solve on coarse mesh and permit the simplification of steady flow with lower computational cost when compared with the other numerical methods, i.e. detached eddy simulation, large eddy simulation and direct numerical simulation. The governing equations are as follows [50]:

   ∂ðρYs Þ ∂
∂ ∂Ys þ ρDs ; s ¼ 1; 2; …; ns ρYs uj ¼ ∂t ∂xj ∂xj ∂xj

(1)

∂ρ ∂
 þ ρuj ¼ 0 ∂t ∂xj

(2)

 ∂τij ∂ðρui Þ ∂
þ : ρui uj þ δij p ¼ ∂t ∂xj ∂xj

(3)

 ∂ðρEÞ ∂
∂ þ ρHuj ¼ ∂t ∂xj ∂xj

436

ns ∂T X ∂Ys þ ρDs hs τij ui þ k ∂xj s¼1 ∂xj

! (4)

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Fig. 1. Schematic diagram of combination of a hydrogen porthole with an air porthole (unit: mm).

Table 1 Test cases (unit: mm). Model

Length

Width

The aspect ratio

A B C D E

0 4 2 1 0.5

0 0.5 1 2 4

– 8: 2: 1: 1:

1 1 2 8

Fig. 3. Convergence history for Model D.

2.2. The turbulence model The SST k-ω turbulence model is a combination of the Wilcox 1988 kω model in the near wall region and the standard k-ε model in the detached regions [51], and it is considered for its good prediction of mixing layers and jet flows [52], as well as insensitive to initial values [53]. At the same time, this model is less sensitive to specification of freestream turbulence level compared to the k-ω model, and it performs comparatively well in adverse pressure gradients and separated flows over either the k-ω or k-ε models [54]. The transport equations for k and ω can be refer to Ref. [55], see Eqs. (7) and (8). The sensitivity of the turbulence model on the predicted results of a transverse injection flow field with different jet-to-crossflow pressure ratios was investigated previously by the authors, see Ref. [52].

Fig. 2. Grid system of Model E.

Engineering analysis of hypersonic air-breathing propulsion assumes air is perfect gas, and its state equation is ns X Ys P ¼ ρRT Ms s¼1

(5)

where ρ is the gas density, ui and uj are the velocity components in the xi and xj directions, respectively, p is the pressure and T is the static temperature. τij is the molecular stress tensor, and it should be closed by the turbulence model. E is the total energy per unit volume.

E¼

ns X s¼1

Ys hs þ

 p 1
2 u þ v2 þ w2  2 ρ

  ∂ ∂ ∂ ∂k fk  Yk þ Sk ðρkÞ þ Гk þG ðρkui Þ ¼ ∂t ∂xi ∂xj ∂xj

(7)

  ∂ ∂ ∂ ∂ω ðρωÞ þ Гω þ Gω  Yω þ Dω þ Sω ðρωui Þ ¼ ∂t ∂xi ∂xj ∂xj

(8)

In these equations, Gω represents the generation of ω. Г k and Г ω represent the effective diffusivity of k and ω respectively. Dω represents the cross-diffusion term, Sk and Sω are user-defined source terms. The compressibility takes part in dissipation terms such as Yk and Yω and partially in the production of turbulence kinetic energy is defined as follows:

(6)

H is the total enthalpy per unit volume, ns is the total number of species, R is the universal constant of gas, Ms, Ys, Ds and hs are the molecular weight, mass fraction, mass diffusion coefficient and absolute enthalpy per unit mass of species s respectively.

437

Yk ¼ ρβ* kω

(9)

Yω ¼ ρβω2

(10)

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Fig. 4. Wall static pressure comparisons with different jet-to-crossflow pressure ratios.

Herein, β* and β are functions of F (Mt).

 β* ¼ βi 1 þ ζ * FðMt Þ  *

α¼ (11)

fk represents the production of turbulence kinetic energy, The term G

(12)


 fk ¼ min Gk ; 10ρβ* kω G

ζ* ¼ 1.5, and the compressibility function F(Mt) is defines as follows:

FðMt Þ ¼

0 Mt2  Mt02

Mt  Mt0 Mt > Mt0

2k α2

Mt0 ¼ 0:25

(17)

2.3. Grid system and the boundary conditions

(13)

The computational domain is structured by the commercial software Gambit. Fig. 2 represents the layout of the mesh employed in the numerical simulations for Model E. The mesh is multi-blocked, and the grids are distributed more densely near the wall and the porthole in order to resolve the boundary layer and ensure the accuracy of the numerical simulation. In the current study, only half of the grid system of all models is chosen for the following analysis due to its symmetrical configuration. The maximum of wall yþ needs to be less than 1.0 in order to obtain the

Where,

Mt2 ¼

(16)

fk is defined and it is affected by compressibility as well. The equation of G as follows:



β* β ¼ βi 1  i ζ* FðMt Þ βi

pffiffiffiffiffiffiffiffiffi γRT

(14) (15)

438

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Fig. 5. Wall pressure profile comparisons with different grid scales for all models with an air porthole.

are used to model the near-wall region flow, and the no-slip conditions (u ¼ 0, v ¼ 0, w ¼ 0) are assumed for the walls. The operational fluid is air, and it is assumed to be a thermally and calorically perfect gas with no reactions modeled, and the viscosity has been determined using massweighted-mixing-law. At the outflow, all the physical variables are extrapolated from the internal cells due to the flow being supersonic [57]. Cell fluxes have been computed using an AUSM scheme, and the Courant–Friedrichs–Levy (CFL) number is kept at 0.5 with proper under-relaxation factor to ensure stability. This is because that the large value causes the numerical results to diverge, while the smaller value slows down the numerical speeds [30]. The solutions can be considered as converged when most of the residuals reach their minimum values after falling for more than three orders of magnitude and the oscillation of the residuals are limited. At the same time, the computed inflow and the outflow mass flux is required to drop below 0.0001 kg/s. Fig. 3 shows the convergence history for Model D, and it represents the residuals of the variable parameters, including the velocities, energy, continuity, k and ω for the turbulence model, and the species considered in the current study, namely H2.

detailed vortex evolution process in the vicinity of the bottom wall, especially for the small-scale vortex. Because of the boundary layer requirement, the height of the first row of cells is set at a distance of 0.001 mm for the walls. The maximum magnitudes of yþ distribution along the bottom wall and the maximum of wall yþ are less than 1.0. This is proved to be suitable for the turbulent mixing simulation for supersonic flows, especially for the generation of the average flow field properties [56]. yþ is a non-dimensional parameter defined by equation (18).

yþ ¼

ρuτ yP μ

(18)

Herein, uτ is the friction velocity, yP is the distance from point P to the wall, ρ is the fluid density, and μ is the fluid viscosity at point P. The computational domain is a rectangle surrounded by adiabatic walls at the bottom, upper and left walls, supersonic inlet at the front boundary and sonic inlet at the injection port, an outlet at the back boundary and finally a symmetric condition on the right boundary. The adiabatic walls of the channel are defined to be isothermal at a temperature of Tw ¼ 300 K for all cases employed. The standard wall functions 439

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Fig. 6. Comparison of circulation for all models.

3. Code validation and grid independency analysis In order to verify the accuracy of the numerical method, a comparison has been made with the experimental data published by Aso et al. [58]. The experimental cases of Aso et al. [58] are of great value because they provide good spatial resolution of the wall pressure data, and cover a large range of injection pressure ratios. Fig. 4 depicts the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios with the experimental data obtained by Aso et al. [58], namely Pj =P∞ ¼ 4.86, 10.29, 17.72 and 25.15. In Fig. 5, the pressure is normalized with respect to the static pressure of the supersonic inflow, and the notations“SST k-ω” and “Experiment” denote the results obtained by the SST k-ω turbulence model and the ground experiment respectively. Although there are some discrepancies between the numerical results and the experimental data, the wall pressure trends are the same. These discrepancies may be induced by a variety of reasons, such as the numerical simulation cannot capture the turbulent intensity accurately, the insufficient grid resolution in the specific regions, the lower order spatially accurate upwind scheme and approximation error, the uniform assumption at the freestream inlet and the jet exit and the difference between the experimental setting and the boundary conditions employed in the numerical method. The predicted wall static pressure distribution of the case with the jet-to-crossflow pressure ratio being 10.29 matches better with the experimental data than those with the other ratios in the range considered in the current study, and this may imply that the incoming turbulence condition upstream of the injector is captured more accurately for this case, and this may imply that the incoming turbulence condition upstream of the injector is captured more accurately for this case. On the other hand, three grid scales are employed to perform the grid independence analysis in the physical model with an air porthole, namely the coarse, moderate and refined grids, and their numbers of cells are nearly 0.36 million, 0.68 million and 1.28 million for half of the models, respectively. Fig. 5 shows the wall pressure profile comparisons with different grid scales for all models with an air porthole investigated in this article. It is clearly shown that the grid scale makes only a slight difference to the numerical results. The number of time step increases with the increase of the number of grid cell in order to obtain a steady flow field, and this is relevant to the parallel computing environment and the numerical method employed as well [59]. At the same time, the stochastic error accumulation is proportional to the number of time steps and depends on accuracy of the scheme and approximation error [60]. It is observed that the predicted results obtained by the moderate grid show

Fig. 7. Static pressure counters on the symmetric plane of all models.

better agreement than those obtained by the refined grid. Therefore, the moderate grid is chosen to carry out the following simulation in order to save the computational cost and reduce the computation time. From the above discussion, it is found that the mathematical and computational models considered in current study can reasonably accurately simulate the interaction between the air stream and the injected fluid. A comparison between numerical results and published experimental data, as well as the grid independency analysis, has been provided by Huang et al. [52], and the numerical approach mentioned above has been utilized successfully in previous studies [61]. It is concluded that the mathematical and computational models can be used with confidence to investigate the parametric effects on the mixing of the combination of a hydrogen porthole with an air porthole in the transverse gaseous injection flow fields. 4. Results and discussion 4.1. Streamwise vorticity The transverse injection across the supersonic flow produces a strong vortex along the jet flow, and the vortex pair has an important role in the mixing process in high-speed flows. The pair of counter-rotating vortices is the major flow feature and is being the provider of streamwise vorticity ωx , which can generate the upwash motion of the boundary layer and the downwash motion of the high-speed mainstream. To understand the 440

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Fig. 8. The counters of streamwise vorticity in cross-section planes of all models.

that in front of the hydrogen porthole. It can be seen that the shocks reflected by up wall and reflects again from the down wall. The interaction of reflected shocks induced by transverse injection has a great impact on characteristics of the flow field and hydrogen/air mixing between fuel flow and crossflow. The variances of streamwise vorticity ωx contour at x ¼ 6.5 mm, x ¼ 18 mm and x ¼ 30 mm are demonstrated in Fig. 8, blue for a negative direction and red for a positive direction. When the vortex pair is near the wall, the low momentum boundary layer under the vortex pair will be disturbed. However, a new vortex pair with a contrary rotation is generated. At the same times, Fig. 8 demonstrates the gradual diffusion process of vertical structure along the streamwise evolution, and the magnitude of streamwise vorticity is reduced due to diffusion and shear action between vortices and high-speed freestream. In Fig. 8 (a), the magnitude of streamwise vorticity decrease with the decrease of aspect ratio, and the flow field without air jet has the largest magnitude of streamwise vorticity. Although the magnitude of streamwise vorticity in the flow field of Model E is the smallest, but it has the largest value of circulation in the near field. This may indicate that a larger amount of air engulfed into the jet plume in the flow field of Model E. What's more, the streamwise vorticity in the field of Model E is more close to wall, leading to better mixing between air and fuel layer. It can be found from Fig. 8 (c) that the streamwise vorticity is formed on the up wall of combustor. In combination with the static pressure counters in Fig. 7, we can find that

influence of streamwise vorticity on mixing characteristics, the circula tion in the y-z plane, which is defined as ∬ ωx ρudydz, is considered. The integral enstrophy in the cross-section y-z plane is evaluated in Fig. 6. As can be seen, the circulation of the flow field with air jet is higher than that of the flow field without air jet irrespective of the aspect ratio of the air porthole. This suggests that the flow fields with air jet would have better mixing characteristics. Obviously, the circulation of all flow fields considered in current study has a few jumps. The value of the circulation suddenly increased to around 850 at x ¼ 0 mm. In the section of x ¼ 0 mm to x ¼ 20 mm, there are two jumps of circulation in a dual injection system at the front and the rear injection holes, while there is a single jump of circulation in the single injection system. Moreover, in this section, Model E has the largest value of circulation, which may mean that the flow field of Model E has the highest mixing efficiency in the near field. Fig. 7 shows the static pressure counters in the symmetric plane of all models. A weak shock wave is generated at the inlet for both the top and bottom walls. Due to the strong interactions between high-speed crossflow and fuel injection, there is a high pressure jump ahead of hydrogen porthole. In a general sense, the strengths of the shock waves ahead of hydrogen porthole in the flow field without air jet are weaker than that in the flow fields with an air jet. On the other hand, it is possible that the distance between the fuel porthole and the air porthole is relatively small, so the pressure jump in front of the air porthole is not as obvious as 441

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the position of x ¼ 30 mm is located in the region where the bow shock induced by transverse injection interacts with the up wall, then reflects from the up wall. There are several such regions mentioned above downstream of the porthole. The bow shock and reflected shock interact with boundary layer, and the crossflow is strongly deflected by the shock waves in these regions. This gives rise to sharp velocity gradients and vortex formation, and it is responsible for several jumps of circulation at the downstream of the position x ¼ 20 mm.

processes of streamwise vorticity. The hydrogen flow is blocked by air jet and then extends in the spanwise direction in the transverse jet flow field with air jet, and the smaller aspect ratio of the air porthole is, the greater spanwise extension is. As the wake region behind the air porthole, the hydrogen flow expends toward this region, an then the vortex pair is formed along the jet flow and the jet mixing boundary is rolled up induced mainly by the vortex-pair vortices. It is well known that streamwise vorticity can generate the upwash motion of the boundary layer and the downwash motion of the high-speed mainstream. Observation of the combination of the hydrogen mole fraction and the streamlines at the cross-sectional plane x ¼ 12 mm in Fig. 9, hydrogen can be carried far away from the bottom wall in the flow field with higher core of the vortex structure, and therefore the higher core of the vortex structure means greater penetration depth. From the point of the hydrogen mass fraction contours on flat plate, the flow fields with an air porthole have less hydrogen distribution on flat plate downstream of the hydrogen porthole than the flow fields without an air porthole irrespective of the aspect ratio of the air porthole. As the aspect ratio of the air porthole increases, the distribution of hydrogen on flat plate increases slightly. Table 2 statistics the penetration depth of all flow fields investigated in this study. Some conclusions can be obtained by comparing the data in Table 2. Compared with the transverse injection flow field with a single jet, a large aspect ratio air porthole located downstream of the hydrogen porthole can improve the penetration depth. On the other hand, although small aspect ratio air porthole can not improve penetration depth, or even reduce penetration depth, but may be beneficial for mixing efficiency improvement. What's more, although the penetration depth of Model E is lower than that of Model A, the distribution of hydrogen on the flat plate of Model E is much less than that of Model A. This implies that the flow field with the smallest aspect ratio air porthole owns the highest mixing rate at the near field. When only the penetration depth is considered, the air porthole with a higher value of aspect ratio is more favorable. However, the tradeoff of mixing rate should be considered.

4.2. Penetration depth The fuel penetration depth is a parameter that determines the scramjet engine performance to a certain extent, because an ideal penetration can minimize wall heating and maximize combustion efficiency. In this paper, the fuel penetration depth is assessed by the height above the floor where the hydrogen mass fraction of the hydrogen plume reduces to 0.1. Fig. 9 shows the slices of the hydrogen mole fraction at the crosssectional plane x ¼ 12 mm for different models. It is observed clearly that the hydrogen distribution and vortex structure of the five models are distinctly different. The spread of the hydrogen is wider and more uniform in the flow field with an air porthole than in the flow field without air porthole. This implies that air porthole can promotes the mixing. For the flow fields with air jet, the smaller the aspect ratio of the air porthole is, the more uniform the hydrogen distribution is. This means that the flow field of Model E has the highest mixing efficiency in the near field. On the other hand, the vertical height of the core of the vortex structure decreases with the decrease of the aspect ratio of the air porthole. In the range considered in this study, when the aspect ratio of the air porthole is reduced to the minimum, the vertical height of the core of the vortex structure is lower in the flow field with an air porthole than that in the flow field without air porthole. Fig. 10 shows the 3D iso-surface colored by the injectant mass fraction being 0.1 and 0.5 and the hydrogen mass fraction contours on flat plate of five models considered in current study, and it offers a lot of information. By comparing the flow field structure of all models considered in current study, it is found that the air porthole and its aspect ratio have a clear effect on the geometry of the 3D iso-surface colored by the fuel mass fraction being 0.1 and 0.5. This implies that the air porthole and its aspect ratio have a significant influence on the formation and evolution

4.3. Mixing efficiency The mixing efficiency is one of the most important parameters. The combustion process strongly depends on the mixing process, and an enhancement of the mixing efficiency directly results in an enhancement

Fig. 9. The slices of the hydrogen mole fraction at the cross-sectional plane x ¼ 12 mm for different models. 442

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Fig. 10. The 3D iso-surface colored by the injectant mass fraction being 0.1 and 0.5 and the hydrogen mass fraction contours on flat plate of five models.

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and its value is 0.0291 for the hydrogen and air [63]. The streamwise progression of the mixing efficiency is calculated and plotted in Fig. 11 from the slice date of all flow fields considered in current study, and it is observed that the sufficient mixing is completed earlier in the flow field with an air porthole regardless of the value of the aspect ratio of air porthole. This implies that the air porthole is promising for reducing the size and weight of the scramjet engine. The aspect ratio of the air porthole has an obvious effect on the mixing efficiency in the near field, but in the far field, the mixing efficiency of all models with an air porthole reaches the maximum at the same distance downstream of the hydrogen porthole. In the case of lower values of the aspect ratio of the air porthole, higher mixing efficiency is shown in the near field. The hydrogen mass fraction contours in five cross-section planes and in flat plate of all cases are exhibited in Fig. 12. In the flow field of Model A, the counter –rotating vortex pair spreads the fuel producing a peachshaped plume cross section, and the shape of the counter-rotating vortex pair goes through a transition from the peach-shaped vortices to the kidney-shaped vortices. In the flow fields with air jet, the hydrogen flow is blocked by air jet, and different aspect ratios of the air porthole correspond to different hydrogen plume shapes. The spread of the fuel is wider in the flow field with lower aspect ratios of the air porthole, which is in favor of engulfing more cross-flow fluid. Comparison of the hydrogen mass fraction contours of five models in the cross-section at the same streamwise station, we observe that the hydrogen concentration of the case with lower aspect ratio of the air porthole is smaller. When only the mixing efficiency of the flow field is considered, the case with a lower aspect ratio of the air porthole is favorable.

Table 2 Penetration depth comparison of Models A, B, C, D and E (unit: mm). Model Penetration depth

A 5.88

B 6.62

C 6.25

D 6.09

E 5.18

Fig. 11. The streamwise progression of the mixing efficiency for all models.

4.4. Stagnation pressure losses of combustion in a scramjet combustor. The 3D iso-surface colored by the fuel mass fraction being 0.5 in Fig. 10 reveals the flow field structure near the porthole. The vortices generated by a jet interaction produce a large convection flow in the plane perpendicular to the streamwise direction, and they have a strong connection with the near field mixing performance due to the fact that the mixing process largely depended on flow convection at the near field but on mass diffusion at the far field. The concept of mixing length has been adopted to quantify the mixing capabilities of all models. The mixing length is evaluated by the downstream distance at which the maximum mass fraction has decayed to 0.5. An intuitive judgement of the extended length of the 3D iso-surface colored by the fuel mass fraction being 0.5 in the streamwise direction, Model E has the shortest mixing length and Model A has the longest length, which may mean that the flow field of Model E has the highest mixing efficiency in the near field. At the same times, the mixing length of the models with an air porthole increases with an increase in the value of the aspect ratio of the air porthole. 1 In order to evaluate the parametric effect on the mixing of the combination of a hydrogen porthole with an air porthole in the transverse gaseous injection flow fields, the mixing efficiency are chosen to analyze the mixing process and it is defined as follows [62].

m_ fuel; mixed ∫ αreact ρudA φ¼ ¼ m_ fuel; total ∫ αρudA

Fig. 13 shows the slices of the density contour and streamline on the cross-sectional plane x ¼ 12 mm for five models. It is obvious that there is a high density region with an arc shape that surrounds the vortex concentrated region. The shock wave caused by jet is the main reason for the high density region. Judging from the density of the high density region, there is a stronger shock wave in the flow field with air jet. This means that greater stagnation pressure loss occurs in the flow field with air jet. On the other hand, by comparing the low density regions, some conclusions can be obtained. The low density region of the flow fields with air jet is larger and more uniform, this suggests that amount of fuel is transported away from the fuel plume and a larger amount of air engulfed into the fuel plume, and it leads to better mixing between air and fuel. The same conclusion has been reached in the discussion mentioned above. The mixing process produces a loss of stagnation pressure. An excessive loss of stagnation pressure should be avoided because the loss of stagnation pressure results in a loss of thrust force. Therefore, it should be checked whether or not there are additional losses of stagnation pressure when the air porthole is placed in the transverse injection flow field. The definition of average stagnation pressure in the y–z plane is expressed in the following form:

P0 ðxÞ ¼ ∬ P0 ρudydz ∬ ρudydz

(19)

Herein P0 , ρ and u are the local stagnation pressure, density and velocity respectively. Fig. 14 shows the histories of average stagnation pressure along the streamwise direction normalized by the stagnation pressure at inflow. In general, the flow fields with air jet have more losses of stagnation pressure than the flow field without air jet. The case of a lower aspect ratio of the air porthole shows more loss of stagnation pressure, which is due to stronger shock waves in front of the porthole and larger circulation behind the air porthole. However, the increase of stagnation pressure loss in the flow fields with air jet is not so great considering the mixing enhancement or the penetration improvement with respect to that of the flow field without air jet.

Herein,

αreact ¼

α; α  αstoic αð1  αÞ=ð1  αstoic Þ; α > αstoic

(21)

(20)

α is the injectant mass fraction, αreact is the injectant fraction mixed in a proportion that react, m_ fuel; mixed is the mixed injectant mass flow and m_ fuel; total is the total injectant flow rate. ρ and u are the local density and velocity respectively, and A is the cross section of the axial station where mixing is evaluated. αstoic is the injectant stoichiometric mass fraction, 444

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Fig. 12. The hydrogen mass fraction contours on five cross-section planes and on flat plate of all cases.

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Fig. 13. The slices of the density contour and streamline on the cross-sectional plane x ¼ 12 mm for five models.

turbulence model were employed to simulate the mixing characteristics of the combination of a hydrogen porthole with an air porthole in the transverse gaseous injection flow fields, and the experimental model used by Aso et al. [58] was utilized to validate the numerical approaches. At the same time, the influences of the air porthole and its aspect ratio on the flow field properties were evaludated. The main focus is to analyze and compare the performance parameters of the transverse injection flow fields, such as the circulation, the fuel penetration depth the mixing efficiency and the stagnation pressure loss. Furthermore, the following conclusions are obtained: ● The dual transverse injection system with a front fuel porthole and a rear air porthole arranged in tandem can lead to more intense circulation irrespective of the aspect ratio of the air porthole, and resulting in higher mixing efficiency. The smaller the aspect ratio of the air porthole is, the higher the mixing efficiency in the near field is. ● The effect of air jet on the fuel penetration depth varies with different values of the aspect ratio of the air porthole. A large aspect ratio air porthole located downstream of the hydrogen porthole can improve the fuel penetration depth, and the fuel penetration depth decreases with the increase of the aspect ratio. The largest fuel penetration depth is 6.62 mm in the range considered in the current study. When the aspect ratio is relatively small, the fuel penetration depth is even smaller than that of the single injection system. ● In the case of higher values of the aspect ratio, higher fuel penetration depth, but lower mixing efficiency in near field are shown, and this suggests that the value of the aspect ratio should be carefully selected for a scramjet combustor because the mixing efficiency in the near

Fig. 14. The histories of average stagnation pressure along the streamwise direction normalized by the stagnation pressure at inflow.

5. Conclusion In this article, the three-dimensional Reynolds-averaged NavierStokes (RANS) equations coupled with the two equation SST k-ω

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field and the fuel penetration depth show opposite trends from each other with a variance in the value of the aspect ratio. ● Air jet not only enhances mixing, but also improves the fuel penetration depth when the aspect ratio is large enough. However, this dual transverse injection system investigated in current study suffered more loss of stagnation pressure with respect to the single injection system irrespective of the value of the aspect ratio.

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