The Effect of Ramp Location in a Strut Based Scramjet Combustor under non reacting flow field

The scramjet engine is considered to be the high-speed propulsive system for hypersonic air-breathing vehicles. Researchers focus on various geometries of strut injectors to enhance the mixing and combustion efficiencies of the scramjet combustor. This paper reveals the non-reacting flow characteristics of various ramp locations in a scramjet combustor with strut injection. The ramps are symmetrically placed at three different locations upstream of the strut within the combustor. Air enters into the combustor inlet with Mach number 2, and the fuel is injected at the sonic velocity from the strut. The 2D supersonic flow characteristics are numerically investigated using ANSYS 18.0 software. The steady-state flow simulations are performed in this study. The flow field is modelled using RANS equations, and the k-ω SST turbulence model and default constants are chosen to investigate the flow characteristics within the combustor. The flow characteristics of the ramp based DLR scramjet combustors are compared with the baseline DLR scramjet model. The computational results are validated with the experimental data. The shock wave interaction from the ramps enhances the distribution of hydrogen in the lateral direction of the flow than the baseline strut configuration. The ramps create recirculation regions that could enhance fuel-air mixing. The ramp induced strut based DLR scramjet engine provides increased total pressure loss of the baseline DLR scramjet.


Introduction
High-speed transportation depends on supersonic and hypersonic flights with a good understanding of fuel and air mixing performance inside the supersonic combustor is essential. Mixing of fuel with air and ignition and flame holding are the fundamental constrain in the design of the scramjet engine [1,2]. The main focus is on the fuel injection system because the fuel's residence time with air in the combustor is less than 1ms. Researchers have suggested different fuel injectors like flush wall injection [3][4][5][6][7][8], cavity-type injection [9][10][11][12][13][14][15], strut based injection [16][17][18][19][20][21], and their blends [22][23][24][25][26][27], etc., to augment mixing and flame holding techniques. The strut injectors of specific geometry enhance mixing and combustion efficiencies with optimum total pressure loss than other injection and flame holding configurations. The experiments on strut based DLR scramjet combustor were conducted with a hydrogen fuel injection system by Waidmann et al. [28]. The numerical investigation on a two-dimensional scramjet combustor with a flamelet model [29] is validated with the reported experimental results of the DLT strut scramjet combustor. Kummitha et al. [30] investigated the supersonic combustor with an innovative design of strut injector, which involves the modified double arrow strut and rocket models shows. The results show that the impinging of the first oblique shock is created from the strut leading edge that is very small when compared to the basic strut. Thus, multiple reflections of shock waves help the fuel to mix early with the supersonic airstream. Rocket strut fuel injector causes high-pressure rise due to impingement of shock wave occurs at the same location. Consequently, the pressure downstream of the strut is high in rocket and double strut-type fuel injector when compared to basic strut. Due to the inclined fuel injector, the combustion efficiency is significantly higher in the case of both double and rocket strut models. Therefore, the decrease in ignition delay is noted in double and rocket strut models than basic DLR scramjet models.
The study conducted by Kumaran and Babu [31] numerically simulated the hydrogen-fueled supersonic combustor employing a multistep chemistry model and compared it with the single-step reaction model to evaluate the performance of the combustor. The study findings disclosed that a multistep chemistry model could be an exercise to evaluate the insight properties of the combustion reaction like heat release rate, ignition delay, etc. Conversely, the single-step model can offer better results for the combustor's overall performance with a decrease in computational cost. Gerlinger and Bruggemann [32] have studied the mixing of hydrogen jets supplied from a strut injector under cold supersonic airflow conditions. It is indicated that the thickness of mixing layerand the total pressure loss increases by raising the strut lip thickness that is mainly owing to the increased diffusivity of the hydrogen at the outer strut wall and the more robust shock wave formation. Huang et al. [33] executed the numerical simulation studies on hydrogen-air reaction mechanism, the injection pressure and temperature variations of a strut-type scramjet combustor. Their study proved that shocks are formed from the strut is pushed out of the duct with the subsonic flow for increasing the temperatures and injection pressure.
Choubey and Pandey [34] executed the numerical simulation analysis on two strut configuration in a scramjet combustor model by changing the strut's angle of attack and asserted that zero angles of attack make a surge in mixing and combustion efficiencies. There is another work by the researchers [20], and it deals with the effect of altering the strut geometry and orientation in the combustor from the inlet. Furthermore, it is disclosed that the optimum lip height and position of the strut functions in an essential role in improving the combustion efficiency. Three strut positioning in a scramjet combustor was computationally examined by Kumar et al. [35]. It was identified that the maximum combustion efficiency and thrust had been attained by Pareto-optimal optimization studies accordingly position the struts in the combustor.
The numerical study of Athithan A A et al. [40] on the effect of double ramp configurations in a strut based scramjet combustor shows the distribution of hydrogen is enhanced in the double ramp combustor along spatial direction than normal DLR strut combustor. The study concluded that deceleration of flow at downstream of the strut due to the shocks and its interactions from the double ramps and strut, furthermore leads to more ignition delay.
The above literature reveals the performance of strut based DLR combustor with various active methods. The effect of ramps in a strut based scramjet combustor is not detailed in the open literature. The present study influences the performance of wall-mounted ramps in a DLR scramjet model under a non-reacting steady supersonic field. The ramps are located at the bottom and top walls of the duct towards the upstream of the strut injector. The numerical investigation is carried out using the two dimensional RANS equation with k-ω SST turbulence model. The flow shock patterns and overall performance of the 2D combustor provide acceptable results as that of 3D analysis [39]. The effect of the ramps is accessed based on shock generation and interactions with the shear layers, wall pressures of the combustor, and the stagnation pressure loss.

Numerical Modelling
The numerical studies of the scramjet model are accomplished by solving the two-dimensional momentum, mass, and energy conservative equations. In the current approach, the compressible Reynolds averaged Navier-Stokes equations (RANS) are solved with the SST k-ω turbulence model [36], which offers a good prediction of jet flows [37]. The flow governing equations [18] are discretized by the finite volume method framework of ANSYS18.0. The density-based solver with the implicit formulation and advection upstream splitting methods are adopted in this work [38]. The governing equations, i.e., mass, momentum, and energy equations written for the total enthalpy are expressed as: Continuity equation Energy equation The turbulence kinetic energy, k, and the specific dissipation rate, ω is obtained from the following transport equations: The terms, Gk represents the production of turbulent kinetic energy and Gω as the generation of ω, Гk and Гω represent the effective diffusivity of k and ω respectively, Yk and Yω represent the dissipation of k and ω due to turbulence, Dω represents the cross-diffusion terms and Sk and Sω as the userdefined source terms Figure 1 shows the configuration of the supersonic model combustors that have been numerically investigated under non-reacting field using commercial code ANSYS 18.0. The channel has an inlet height of 50mm an inlet Mach number of 2.0 and an inlet static temperature of 300k. The DLR scramjet model experimented with by Waidmann [28] is shown in Figure 1. In the DLR scramjet combustor, a wedge-shaped strut is located at 77mm downstream of the combustor entrance and 25 mm away from the bottom wall. The strut has a length of 32mm and a height of 6mm. The hydrogen jet is injected through 15 orifices of 1.0mm in diameter. The ramps are placed at the bottom and top walls of the combustor at three axial locations, 77mm, 50mm, and 33mm from the combustor inlet and are denoted as Case 2, Case3, and Case 4, respectively. The ramp dimensions are also detailed in Figure 1, and the performance of the ramp locations in the strut type scramjet model is compared with the baseline DLR model (Case 1). The incoming air at the combustor inlet is at Mach number 2, and the hydrogen fuel is injected parallel to the airstream at the sonic condition. The flow is considered compressible and two dimensional. The operating conditions of the scramjet combustor are identical for all the cases.  Table 1.

Grid independence study
The numerical solution accuracy to the problem mainly depends on grid size, hence for this investigation grid independence study has been performed. Three different grids, namely coarse (146146), medium (191607), and fine (290112) meshes, are employed to optimize the grid resolution for the convergence analysis. For the entire flow field, the y+ value is less than 1.0 (6.1e-7), which corresponds to the first-row cell height specified at 0.001 mm. Figure 4 shows the grid independence study, and it is found that the distribution of static pressure at the combustor's bottom wall for all the mesh size shows the variance of less than 1%. The medium and fine meshes show the same result, hence to reduce the computational time, the medium-sized mesh is considered for the analysis. The convergence criteria for the numerical simulation is considered based on the variation of the net mass flux of the flow across the combustor falls below 0.001kg/s, i.e., is less than 0.1% of the fuel mass flow.

Validation
The computational study is validated with the experimental results of Waidmann et al. [28] in terms of shadowgraph image and wall pressure plot and is shown in Figures 3 and 4, respectively. The inflow conditions for the experimental and numerical investigations are identical. The inlet flow to the combustor is Ma=2.0. The inflow parameters are presented in Table 1. The numerical result shows the shock generated from the strut, jet stream from the injector, and shock reflection pattern from the combustor wall is similar to that of the experimental result. The wall static pressure values at the  figure 4 for the validation at the steady-state condition. The simulation results of the wall static pressures along the axis are well-matched with the experiment result are shown in figure 4. The maximum wall static pressure is observed at X = 0.12m, for both experimental and numerical studies. It is noted that numerical results are in qualitative agreement with the experimental results of the reference [28].

Result and discussion
The numerical investigations on the flow characteristics of ramps positioned on the top and bottom walls of a DLR scramjet combustor under a non-reacting flow field are discussed and compared with the typical DLR model. Figure 5 shows the shadowgraph images of the different geometry profiles that provide the details about the shocks and shear layer patterns inside the duct. The leading edge oblique shock waves from the strut in the scramjet combustor undergo multiple shock reflections from the combustor walls that are observed from Case 1. These reflected shock waves interact with the trailing edge shock from the strut and impinge on the fuel stream shear layer. For case 2, additional shockwaves are observed at the leading edge of the ramps that interact with the oblique shock wave emanated from the strut that decelerates the flow downstream. The shock waves emanated from the trailing edges of the ramps and strut interact with the fuel stream downstream that may enhance mixing of the fuel-air stream downstream with the lesser supersonic stream than the case 1. The ramp related shocks interact with leading-edge shock from strut upstream of strut injector as the ramps are   Figure 6 shows the Mach number contour comparison of different scramjet combustor profile. It is seen that the oblique shock waves are created at the leading edge of the strut, which gets reflected into the strut from the bottom and top wall of the combustor. The flow separations are observed downstream of the ramps due to the shock boundary layer interactions. The flow separation increases as the ramps are moved toward the combustor inlet. The recirculation regions are formed at the trailing edge of ramps, and these recirculation regions will act as flame holders and enhance fuel-air mixing. Figure 7 shows the recirculation region formed inside the combustors. For case 1, small vortices are noticed near the trailing edge of the strut. However, for case 2, 3 and 4, the additional recirculation regions are formed near the top and bottom wall of ramps. The large vortices are observed downstream of the ramps for case 3 compared to other ramp cases. It is well known that recirculation will be formed at the downstream of a ramp or a backward facing step in a supersonic flow field. For case 3, the shock boundary layer interaction at the base of the ramps creates a flow separation downstream of the ramp. The flow separation regime is comparatively larger for case 3 compared to the other cases where the recirculation region is formed through the separation region.  Figure 8 (a, b). The wall pressure distribution is uniform for the typical DLR scramjet model till x=0.1m, subsequently, a wavy pressure profile is noted. The wavy nature of the pressure profile is due to the shock waves generated from the strut edges and its reflections from the combustor walls. An increase in static pressure profiles is observed for case 2 and case 3 from x = 0.05m due to the shock generated from the edges of the ramps. A peak pressure value is observed for case 4, at x = 0.1m due to the shock interactions and flow separation, which creates a compressive zone till the strut injection regime. It is notable that maximum static pressure from the bottom wall and midline of the duct at point x=0.1m to 0.15m, respectively. It is due to the intense shock wave reflections and flow separations inside the combustor.

Mass fraction of H2
The hydrogen mass fraction distribution at the three axial locations viz, X=0.15m, 0.2m, and 0.275m across the combustor are shown in Figure 9. At X = 0.15m, the distribution of hydrogen in the spatial direction is enhanced for case 2 than other configurations that may improve the combustion zone. Case 1 and case 4 show higher hydrogen mass fraction at X=0.2m, indicates that the shock waves' interaction with the fuel stream is less intense than case 2 and case 3. The hydrogen mass fraction is almost uniform for all the cases at X = 0.275 m, indicating that the fuel-air stream mixing is identical for all the configurations. The distribution of hydrogen near the walls of the combustor is negligible

Total pressure loss
The process of mixing with the shock waves is the irreversible process and causes the generation of entropy with total pressure losses. Generally, the more pressure losses occurs with an increase in mixing enhancement due to more oblique shock waves than other cases and their interaction with the shear mixing layer. The total pressure loss is calculated as, (4) Figure 12 shows the total pressure loss across the combustor at different locations. The higher pressure loss is noticed for the combustor with double ramps, due to the more shock wave interactions which decelerate the flow downstream and enhances total pressure loss compared to the DLR scramjet model (case1). It is observed that the maximum pressure loss of about 18% is observed for case 4 due to the shock waves interaction upstream of the strut, shock boundary layer interaction and flow separations create a compressive zone that decelerates the flow to the low supersonic condition compared to other ramp cases. For case 1, the total pressure loss of about 7%, which is comparatively lower than other cases with double ramps.

Conclusion
The numerical investigations of the normal DLR strut type scramjet combustor with upstream double ramps at the bottom and top walls of the combustor duct are carried out with non-reacting flow field conditions using the RANS equation. The effectiveness of the ramps locations along with the strut injection is analyzed based on the key parameters, such as wall static pressures, hydrogen mass fraction at various cross-sections, and total pressure loss across the combustor. The numerical results are validated with the reported experimental data, which shows higher correlations. The shadowgraph images show that more shock is formed for the double ramp DLR combustor than the typical DLR combustor model.  The shock boundary layer interactions and flow separation resulting in higher wall static pressure for case 4 are compared to other double ramp profiles.  The hydrogen distribution near the strut injector region enhances in the lateral direction as the ramps are positioned towards the combustor inlet.  The shockwaves from the ramps decelerate the supersonic airflow downstream of the strut compared with the DLR scramjet model. 12  In addition, more recirculation regions are formed for a double ramp combustor profile than the DLR scramjet model that acts as flame holders.  The total pressure loss of the flow increases compared to the baseline scramjet model due to the more shock waves interaction arises from the ramps. The reacting flow studies will reveal the effectiveness of ramps in the strut based combustor is considered for future investigations.

Nomenclature Ma
Mach number Po total pressure P Static pressure ρ density u velocity ṁ mass flow rate k turbulence kinetic energy ω specific dissipation rate Gk production of turbulent kinetic energy Gω generation of ω Гk and Гω effective diffusivity of k and ω Yk and Yω dissipation of k and ω Dω cross-diffusion terms