TY - JOUR
AU - Pandey, K, M
AB - Abstract The shear mixing and streamline vortices are the notable parameters to influence the air–fuel mixing in hypersonic flows. The shock wave development and Mach number significantly influence the shear mixing phenomenon. Hence, this research introduced an unconventional strut and tested its performance for the generation of shock waves at different flow conditions (M = 2,4,6). The Reynolds-averaged Navier–Stokes equations are solved to evaluate the performance of the new strut. Both the DLR scramjet strut injector and wavy wall strut injector are assessed for the shear mixing development. Turbulence for the association of shock waves, mixing layer, and the boundary layer has been modeled with the SST k-ω model. The variation in shock development and its interactions are investigated further with an increase in Mach number. The scramjet flow structure differentiation found the increased number of oblique shock waves with the wavy wall strut fuel injector. It increases the turbulence level with increased streamline vortices, turbulent intensity, and turbulent kinetic energy. The shock wave generation analysis at different Mach numbers (M = 2,4,6) found fewer interactions between the shock wave and shear layer with increased Mach number. From the examination of shock wave generation and its interaction with the shear layer and analysis of turbulent parameters, it is found that the wavy wall strut has an appreciable effect on shock-induced blend augmentation of fuel and air. Graphical Abstract Open in new tabDownload slide Graphical Abstract Open in new tabDownload slide computational fluid dynamics, shock waves, shear mixing layer, turbulence, vortices Highlights Numerical analyses of the scramjet internal flow field were studied. An innovative wavy wall strut fuel injector has been assessed for mixing enhancement. Turbulence parameters have been evaluated and compared for the basic and innovative strut. Wavy wall strut has a significant effect on increasing the turbulence level. Mixing of fuel and supersonic air has been improved with a wavy wall strut. Nomenclature P Pressure (Pa) T Temperature (K) ui Velocity in the x-direction (m/s) uj Velocity in the y-direction (m/s) τij Shear stress (N/m2) qi Heat flux in the x-direction (W/m2) ht Total enthalpy (J) et Total energy (J) YO2 Mass fraction of O2 YN2 Mass fraction of N2 YH2O Mass fraction of H2O YH2 Mass fraction of H2 k Turbulent kinetic energy (J/kg) ω Specific turbulent dissipation rate (1/s) ε Rate of dissipation of turbulent kinetic energy (J/kg.s) Γk Effective diffusivity of k (m2/s) Gk Generation of Turbulent kinetic energy, k Yk Dissipation of k Sk Source term, k Γω Effective diffusivity of ω Gω Generation of Turbulent kinetic energy, ω Yω Dissipation of ω Sω Source term, ω Dω Cross diffusion term DLR DLR strut (primary wedge strut) SZZ Strut zigzag (wavy wall strut) M Mach number NR Non-reacting flow 1. Introduction Scramjet technology is the most emerging and ongoing research due to its great applications like in aerospace, military, etc. From the design point of view, the scramjet engine consists of a straightforward structure with an inlet, combustor, and diffuser section. As the air moves with the combustion chamber's supersonic speed, the mixing of fuel and air is critical and challenging to improve scramjet performance. The presence of air (residence time) in the combustion chamber is in the order of 1/10th of milliseconds. At this period, the mixing of fuel and supersonic air should take place and complete the succeeding combustion. The scramjet combustors do not have sufficient mixing due to less interaction between the fuel and air stream. The interaction between the fuel and air streams can be increased by creating streamlined vortices, increased shear mixing, and turbulence. The design of shock waves strongly impels all these parameters in the supersonic flow field. Shock waves are acting as carriers or drivers for the penetration of one stream of fluid into another. It increases the mixing tendency with an increase in shear mixing layer thickness. The effect of shock impingement on the shear mixing layer depends on many parameters like the shock wave's strength, incident angle, fluid flow compressibility, etc. Andreopoulos, Agui, and Briassulis (2000) examined the interaction of shock waves and turbulence for various parameters. They found that the association of turbulence and a shock wave is a very complex and mutual phenomenon. After the interaction, both the turbulence and shock waves were affected by each other. They also found that interaction's effect depends on length scales, velocity, and compressibility of the flow field. Changes in fluctuation velocities and length scales are the most significant outcomes from the interaction of turbulence and shock waves. An increase in velocity fluctuations and length scales are the appreciable cases for enhancing the mixing phenomenon. Budzinski, Zukoski, and Marble (1992) studied shock waves' effect on mixing fuel and air with turbulence amplification. The amplification of turbulence presented in the impact of Rankine–Hugoniot relations. The authors also identified that with the interaction of shock waves, streamline vortices and pressure gradients that existed before and after the shock interaction were the causes for the amplification of turbulence. The straightforward visualization and understanding of the shock wave and shear layer interaction are essential for developing an efficient air-breathing vehicle. Experimental studies gave great insight into understanding the influence of shock wave and shear layer interaction in the supersonic flow field. Brummund and Nuding (1997) conducted an experimental study to investigate the effect of interchange between the shock wave and the shear layer for supersonic flows. In this research, the authors mainly investigated the possible mixing enhancement with the interaction of shock waves. The authors conducted experiments using the DLR experimental scramjet facility and analyzed the flow structure with the Rayleigh scattering method, Pitot tube method, and Schlieren flow visualization. This experimental study found a very appreciable spreading of the shear layer after the shock interaction. The concept of the compressible shear layer and its thickness variation for different flow conditions is the crucial parameter to be considered for high-speed compressible flows. Clemens, Mungal, Berger, and Vandsburger (1990) and Papamoschou and Roshko (1988) investigated the variation of large-scale structures concerning convective Mach number and its effect on mixing enhancement. For supersonic flows with parallel fuel injection with strut's help, oblique shock waves greatly enhance mixing with the air stream protrusion into the fuel stream. Buttsworth (1996) investigated the same concept by analyzing the association between the planar mixing regions and oblique shock waves. The author derived an expression for shock curvature, which governs the shock wave transmission in variable Mach number. The authors also derived a term for the shock-induced vortices with density and velocity gradients across the flow stream. The author estimated the possible mixing enhancement with a shock wave and mixing region interaction with this expression. Many researchers (Guirguis, 1988; Northam, Capriotti, Byingtonc, & Greenberi, 1991; Roy, 1991; Tillman, Patrick, & Paterson, 1991) investigated the streamlined vortices formation and its effect on influencing air–fuel blending in the supersonic flow field with different designs of strut fuel injectors. Marble, Zukoski, Jacobs, and Hendricks (1990) studied the augmentation of mixing with oblique shock waves for circular jet co-flowing streams. Menon (1989), Hyde, Smith, Schetzj, and Walkerd (1990), and Waitz, Marble, and Zukoski (1991) investigated the effect of oblique shock waves and its strike on the mixing region. In all these studies, the authors found a considerable variation in axial vortices in the downstream fuel injector. These vortices elevate the mixing enhancement with an increase in contact area among the flow streams. Drummond and Givi (1994) conducted a numerical study to evaluate the generation of strut induced streamline vortices. This research's primary aspiration is to understand the blending mechanism followed by the analysis of mixing enhancement techniques with different fuel injection struts. The shear mixing layer thickness has a strong capability to amplify the mixing of fuel and air. However, the interaction of shockwaves greatly influences the shear layer. Wepler, Huhn, and Koschel (2001) studied the shear mixing layer's growth with impingement of oblique shock waves. Numerical results were examined by predicting the flow structure with and without shock interaction for the non-reacting flow field. At different Mach numbers, both the internal flow structure and the shear mixing layer were examined. From this numerical investigation, the authors identified that the shear layer's thickness increases downstream of the interaction point. With an increase in convective Mach number, the growth rate of shear mixing layer thickness is decreasing. The authors also studied the shear mixing layer's behavior for the strength of shockwave impingement and its position with further investigation. Fang, Shen, Sun, and Hu (2018) conducted a numerical study to evaluate the effect of oblique shock wave association with turbulent structures and supersonic mixing layer. Numerical analyses were carried out by considering the large eddy simulation with the convective Mach number of 0.8. The authors differentiated the supersonic flow structure with and without shockwaves. It also identified a turning point and the existing three turn points for the shock-free shear layer. They also found hairpin vortices' development due to the baroclinic mechanism, diminishing vortices at the association point of shock waves, and shear layer. With the interaction of shock and mixing layer, it was observed that a decrease in vorticity thickness in the vicinity of interaction points increased more rapidly in the downstream. From this research investigation, the authors concluded that the shock wave enhances the shear mixing layer's thickness by acting as a carrier for the convection mechanism between the mainstream and shear layers. Choubey and Pandey (2016, 2017, 2018) conducted a numerical investigation on the scramjet internal flow field to analyze the mixing and combustion performance using passive techniques and optimized the flow parameters and flow path for the better mixing and combustion of fuel and supersonic air. A significant amount of research work was contributed for the scramjet technology by investigating the flame propagation and stabilization (Huang, Du, Yan, & Moradi, 2018), air–fuel mixing enhancement (Huang, Du, Yan, & Xia, 2019), and transverse fuel injection techniques (Huang, 2016). Liao, Yan, Huang, and Lang-quan (2018) investigated the mode transition of a scramjet combustor. Huang, Wu, Yang, Yanc, and Li (2020) and Huang (2015a and 2015b) studied the latest shock and boundary layer interaction and the effect of strut configuration, respectively. From the open literature, it is observed that the blending amplification of fuel and air for hypersonic flows is the emerging research area for the improvement of scramjet performance. This research's main target is to analyze the possible intermix magnification with the more oblique shock waves and their interactions with the shear mixing layer. Hence, in this research, an attempt has been made with an innovative strut fuel injector and its performance has been investigated at different Mach numbers. 2. Geometry Modeling The review of the shockwaves and its association with the shear layers found that the role of shock wave development and its interface with the turbulent and shear layer is imperative for enhancing the supersonic mixing layer. From the observation of DLR scramjet combustor (Waidmann et al., 1994, 1995; Waidmann, Brummund, & Nuding, 1996; Oevermann Michael, 2000) and its flow structure with the intersection of oblique shock waves shear layer, an inventive design of strut fuel injector is introduced. The DLR conventional wedge strut is redesigned with the wavy wall shape, as shown in Fig. 1. Except for the strut's length and base height, only the plane surfaces are changed with a wavy wall shape. Wavy wall strut consists of three bumps for both top and bottom surfaces with the amplitude and pitch of 0.4 and 4 mm, respectively. Figure 1: Open in new tabDownload slide Scramjet computational domains and wavy wall strut. Figure 1: Open in new tabDownload slide Scramjet computational domains and wavy wall strut. 2.1 Boundary conditions Dirichlet boundary conditions are defined for both the air and fuel inlet boundary of the computational domain by defining the known values of the incoming supersonic air stream and fuel stream (Table 1) (Waidmann et al., 1994, 1995). The flow parameters are extrapolated to the outlet. The walls of the combustion chamber are defined with no-slip and Neumann boundary conditions. Fuel is injected at the base of the strut. The composition of the mixture is described by specifying the mole fraction of the constituents. Table 1: Air and fuel inlet flow properties. Parameter/variable . Air . H2 . Mach 2.0 1.0 u (m/s) 730 1200 T (K) 340 250 P (KPa) 100 100 ρ (kg/m3) 1.002 0.096 YO2 0.232 0 YN2 0.736 0 YH2O 0.032 0 YH2 0 1 Parameter/variable . Air . H2 . Mach 2.0 1.0 u (m/s) 730 1200 T (K) 340 250 P (KPa) 100 100 ρ (kg/m3) 1.002 0.096 YO2 0.232 0 YN2 0.736 0 YH2O 0.032 0 YH2 0 1 Open in new tab Table 1: Air and fuel inlet flow properties. Parameter/variable . Air . H2 . Mach 2.0 1.0 u (m/s) 730 1200 T (K) 340 250 P (KPa) 100 100 ρ (kg/m3) 1.002 0.096 YO2 0.232 0 YN2 0.736 0 YH2O 0.032 0 YH2 0 1 Parameter/variable . Air . H2 . Mach 2.0 1.0 u (m/s) 730 1200 T (K) 340 250 P (KPa) 100 100 ρ (kg/m3) 1.002 0.096 YO2 0.232 0 YN2 0.736 0 YH2O 0.032 0 YH2 0 1 Open in new tab 3. Mathematical and Numerical Modeling The Reynolds-averaged Navier–Stokes (RANS) equations solve the scramjet internal flow field with two different strut fuel injectors' designs. This research is mainly concentrating on shock wave development with induced turbulence. Hence, the SST k-ω turbulence model has been considered to predict the streamline vortices and baroclinic mechanisms during the combination of shock and shear layer. All the flow governing equations are discretized with the finite volume method and form linear algebraic equations. A density-based solver with second-order upwind discretization and an implicit formulation has been chosen to solve flow variables. All the partial differential spatial terms are converted into linear difference terms using the second-order upwind discretization scheme to decrease the truncation error. The Courant–Friedrichs number has been limited (CFL = 1) to increase the stability of the solution. The convergence of flow variables is defined with 10e-5 to improve the approximation of results. The conservation equations are as follows (Shin, Moon, & Sung, 2015; Kummitha, Suneetha, & Pandey, 2017; Sailesh, Biraj, Ole, & Hari, 2017): Mass balance (the continuity equation): $$\begin{eqnarray} \it{ \frac{{\partial \rho }}{{\partial t}}} + \frac{\partial }{{\partial {x_\mathrm{ i}}}}{\rm{\,\,}}\left( {\rho {\it{ u}_\mathrm{ i}}} \right) = {\rm{\,\,}}0 \end{eqnarray}$$(1) Momentum balance: $$\begin{eqnarray} \frac{\partial }{{\partial t}}\left( {\rho {\it{ u}_i}} \right) + \frac{\partial }{{\partial {x_i}}}{\rm{\,\,}}\left( {\rho {\it{ u}_i}{\it{ u}_j}} \right) = {\rm{\,\,}} - \frac{{\partial \it{ P}}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_i}}}\left( {{\tau _{ij}}} \right) \end{eqnarray}$$(2) Energy equation: $$\begin{eqnarray} \frac{\partial }{{\partial t}}\left( {\rho {\it{ e}_\mathrm{ t}}} \right) + \frac{\partial }{{\partial {x_i}}}{\rm{\,\,}}\left( {\rho {\it{ h}_\mathrm{ t}}{u_j}} \right) = \frac{\partial }{{\partial {x_i}}}{\rm{\,\,}}\left( {{\tau _{\mathrm{ ij}}}{\it{ u}_i} - {\it{ q}_\mathrm{ i}}} \right) \end{eqnarray}$$(3) 3.1 Turbulence modeling Accurate and suitable turbulence modeling is a salient task to analyze the flow physics consisting of streamline vortices, shock waves, and the shear layers. To identify the right turbulence model, Kummitha (2017) studied different turbulence models for the DLR scramjet flow field compared with the experimental results. From this study, they found that the SST k-ω turbulence model results are closely matching with the practical. Earlier, many researchers (Wilcox, 1998; Erdem & Kontis, 2010; Huang, Liu, Li, Xia, Liu, & Wang, 2012; Ivanova, Berthold, & Aigner, 2013; Huang, 2014) explored the supersonic flows with different turbulence models and finally gave preference to the SST k-ω model due to its combined feature of k-ε and k-ω turbulence model. SST k-ω turbulence model consists of a blend function to combine the near-wall k-ω model with the free-stream k-ε model. This feature extends the suitability of the SST k-ω model for high-speed compressible flows. In this research, the two-equation SST k-ω model is modeled as follows: SST k-|$\omega $|model: $$\begin{eqnarray} \frac{\partial }{{\partial t}}\left( {\rho \it{ k}} \right) + \frac{\partial }{{\partial {x_i}}}\,\,\left( {\rho \it{ k}{\it{ u}_\mathrm{ i}}} \right) &=& \frac{\partial }{{\partial {\it{ x}_\mathrm{ j}}}}\,\,\left( {{\Gamma _\mathrm{ k}}\frac{{\partial \it{ k}}}{{\partial {\it{ x}_\it{ j}}}}} \right) \nonumber \\ && + {\it{ G}_\mathrm{ k}} - \,\,{\it{ Y}_\mathrm{ k}} + {\it{ S}_\mathrm{ k}}, \end{eqnarray}$$(4) $$\begin{eqnarray} \frac{\partial }{{\partial t}}\left( {\rho \omega } \right) + \frac{\partial }{{\partial {x_i}}}\,\,\left( {\rho \omega {\it{ u}_\mathrm{ i}}} \right) &=& \frac{\partial }{{\partial {\it{ x}_\mathrm{ j}}}}\,\,\left( {{\Gamma _\omega }\frac{{\partial \omega }}{{\partial {x_j}}}} \right) \nonumber \\ && + {\it{ G}_\omega } - \,\,{\it{ Y}_\omega } + {\it{ D}_\omega } + {\it{ S}_\omega }, \end{eqnarray}$$(5) where Gk and Gω represent the generation of kinetic energy (k) and production of specific dissipation (ω), respectively, and the dissipation term is designated with Yk and Yω for k and ω, respectively. Γk and Γω are significant diffusive terms. SST k-ω model combines the physics of the k-ε and k-ω models. This feature leads to the introduction of the cross-diffusion term Dω as described below: $$\begin{eqnarray} {\it{ D}_\omega } = \,\,2\left( {1 - {\it{ F}_\mathrm{ 1}}} \right)\rho {\sigma _{\omega ,2}}\frac{1}{\omega }\frac{{\partial \it{ k}}}{{\partial {\it{ x}_\mathrm{ j}}}}\frac{{\partial \omega }}{{\partial {\it{ x}_\mathrm{ j}}}}, \end{eqnarray}$$(6) where F1 represents the blending function as follows: $$\begin{eqnarray} {\it{ F}_\mathrm{ 1}} = {\rm{\,\,tanh}}\left( {\it{ arg}_\mathrm{ 1}^\mathrm{ 4}} \right), \end{eqnarray}$$(7) where $$\begin{eqnarray} \it{ arg}_\mathrm{ 1} = \,\,min\left[ {max\left( {\frac{{\sqrt \it{ k} }}{{{\it{ C}_\mu }\omega \it{ \it{ y}}}},\frac{{500\vartheta }}{{{\it{ y}^\mathrm{ 2}}\omega }}} \right),\frac{{4\rho {\sigma _{\omega \mathrm{ 2}}}\it{ k}}}{{CD_{\it{ k}\omega}{\it{ y}^2}}}} \right]. \end{eqnarray}$$(8) Here, y specifies the normal distance to the wall, and |$C{D_{k\omega }}$| is considered as a positive portion of the cross-diffusion term. 4. Grid Independence, Convergence, and Validation The generation of mesh for the computational domain is the most critical and challenging task because the numerical results are strongly affected by the grid size and mesh elements. Hence, it is required to conduct the grid independence study and evaluate numerical results for different grid sizes (coarse, medium, and fine), as shown in Fig. 3. Mesh refinement was considered at the walls of the domain, as shown in Fig. 2. With a decrease in grid size, the number of mesh elements will increase, and solution accuracy also increases, leading to increased computational time and cost. Hence, it is required to identify an optimum grid size by conducting the grid independence study by evaluating the variation of flow property (pressure) for different mesh elements (Fig. 3). The pressure profiles describe the accuracy for predicting pressure with an increase in the number of mesh elements for the combustor and diffuser section except in the isolator. There is no considerable deviation of the results for the moderate and fine grid. It indicates that the results are constant, with a further increase in mesh elements. Hence, in this research, numerical analysis has been performed with adequate grid size. Figure 2: Open in new tabDownload slide Grid generation with quadrilateral elements. Figure 2: Open in new tabDownload slide Grid generation with quadrilateral elements. Figure 3: Open in new tabDownload slide Grid independence study. (a) Wedge strut (combustor bottom wall, y = 0). (b) Wavy wall strut (bottom wall, y = 0). Figure 3: Open in new tabDownload slide Grid independence study. (a) Wedge strut (combustor bottom wall, y = 0). (b) Wavy wall strut (bottom wall, y = 0). 4.1 Convergence Convergence conditions for all variables in the related equations are specified as 10−5. Figure 4 shows the convergence of parameters with the residual left in the iteration process. The convergence history is shown up to 3000 iterations to understand the convergence of the solution with decreasing residual values. For the first 3000 iterations, it is observed that the convergence of k and ω has almost reached the defined convergence 10−5, but the remaining parameters have not yet achieved the convergence. However, the solution continued the iteration process until it satisfied the continuity equation |$( {\Delta \,\,\dot m = \,\,0} )$| and obtained the convergence. As the flow is non-reacting and steady, the iterations are converged at 47 351 iterations. Figure 4: Open in new tabDownload slide Convergence history. Figure 4: Open in new tabDownload slide Convergence history. 4.2 Validation The validation of numerical results is an important task to ensure the reliability of numerical results and the simulation tool's applicability. For the verification analysis, the DLR experimental scramjet combustor (Waidmann et al., 1994, 1995, 1996) simulated the same solver setup. Both the experimental (Waidmann et al., 1994, 1995, 1996) and numerical results are compared (Fig. 5). The comparison of pressure profile and flow structure (Fig. 5) found that the generation, impingement, and reflection of shock waves and pressure are comparable to the experimental results. There is a little discrepancy in numerical results in the wake region due to high turbulence and vortices. Figure 5: Open in new tabDownload slide Validation of numerical results with the experimental. Figure 5: Open in new tabDownload slide Validation of numerical results with the experimental. 5. Results and Discussion The scramjet internal flow field, the shock waves generation, and its association with the shear layer for both the DLR and innovative (wavy wall) strut have been evaluated by solving the Reynolds flow governing (RANS) equations. This research's key point is to enhance the mixing process with additional shockwaves compared with the primary wedge strut. The scramjet flow field was explored at different Mach numbers with cold flow simulations to identify shock development behavior and its interaction for the clear visualization of the interactivity between the shock and shear layer. The scramjet flow field with shock waves is visualized by predicting the density (Fig. 6) and pressure (Fig. 7) contours. From the inspection of pressure and density contour at Mach 2, it is found that the unconventional strut produced multiple oblique shockwaves from its wavy wall surface. For the primary wedge strut, only one oblique shock wave was generated. The expansion fan generated from the base of the primary strut is diminished after interacting with the boundary layer. In wavy wall strut, both the oblique and expansion fan undergo reflections separately and create multiple interactions with the shear layer. The number of intersections between the shock waves and the shear layer is three and five for the wedge and wavy wall strut, respectively. The first interaction point of a shock wave and shear layer is observed at x = 139 mm for wedge strut, whereas in the wavy wall strut, it is at x = 124 mm. It leads to early mixing with wavy wall strut. Figure 6: Open in new tabDownload slide Density contour flow structure for non-reacting flow field. Figure 6: Open in new tabDownload slide Density contour flow structure for non-reacting flow field. Figure 7: Open in new tabDownload slide Pressure contour flow structure for non-reacting flow field. Figure 7: Open in new tabDownload slide Pressure contour flow structure for non-reacting flow field. The shear mixing layer's thickness is an essential factor for assessing air–fuel mixing enhancement in supersonic flows. The shear mixing layer's thickness is more in the wavy wall strut from the scramjet flow field's interpretation for two different struts due to multiple shockwaves' interactions with the shear mixing layer. For the two struts, the shear mixing layer thickness increases in the downstream of the strut but comparatively, it is more in the case of wavy wall strut due to more interactions of the shear layer and shock waves (Fig. 6). The wavy wall strut's performance for the shock wave development and their interactions has been analyzed at different Mach numbers and compared with the primary wedge strut. From the inspection of pressure and density contours for various Mach numbers (Figs 6 and 7), the number of intersections between the shock and shear layer decreases with an increase in Mach number, the shock angle decreases, and comparatively, the early interaction of the shock wave and shear layer is the advantage of wavy wall strut. The analysis of flow parameters for both the wedge and wavy wall strut for different Mach numbers is an exciting task to get more insight into the scramjet internal flow field. The rise in temperature and pressure of the supersonic air before entering into the combustion chamber is a mild case to initiate early combustion and decrement of ignition delay. The pressure profile for the lower wall and middle of the combustor has been observed and plotted for both wedge and wavy wall strut concerning different Mach numbers (Fig. 8). The pressure profiles analysis found early pressure rise for the wavy wall strut at x = 0.1, 0.13, and 0.175 mm for Mach numbers 2, 4, and 6, respectively. Comparatively, the pressure rise for the wavy wall strut is more because of multiple impingements of shock waves at the same location on the combustor's lower wall. Figure 8: Open in new tabDownload slide Pressure profiles at (a) y = 0 (bottom wall of the combustor) and (b) y = 25 (middle of the combustor). Figure 8: Open in new tabDownload slide Pressure profiles at (a) y = 0 (bottom wall of the combustor) and (b) y = 25 (middle of the combustor). The region behind the strut (wake region) is the main area to sustain the combustion phenomenon with vortices. Figure 9 shows the cross-stream velocity profiles at different strut downstream locations to observe the wake-region flow field velocity. The wake region's flow stream has less velocity for the wavy wall strut than the primary strut. The flow stream velocity in the wake region is gradually increasing downstream due to the conservation of heat energy into kinetic energy. For Mach 2, the flow stream in the wake region for both wedge and wavy wall strut is approaching the same velocity along the length of the combustor. With an increase in Mach number, the difference in speed of the flow stream in the wake region for both wedge and wavy wall strut is also increasing. The flow stream's residence time for the wavy wall strut is more contrast to the wedge strut. The wavy wall strut significance is further analyzed with vortices formation, as shown in Fig. 10. The comparison of vortices contour found that the area of vortices formation is more in the wavy wall strut. These vortices increase the blending of air and fuel with an increase in shear mixing layer thickness. Figure 9: Open in new tabDownload slide Cross-stream velocity profiles at (a) X = 120, (b) X = 167, and (c) X = 275 mm. Figure 9: Open in new tabDownload slide Cross-stream velocity profiles at (a) X = 120, (b) X = 167, and (c) X = 275 mm. Figure 10: Open in new tabDownload slide Vortices formation for wavy wall and wedge strut. Figure 10: Open in new tabDownload slide Vortices formation for wavy wall and wedge strut. The distribution of hydrogen fuel is analyzed by evaluating the mass fraction profiles of H2 at different cross-stream locations, as shown in Fig. 11. The examination of hydrogen profiles found that hydrogen fuel's dissipation has been magnified in the radial direction for the wavy wall strut due to intensified streamline vortices. Hydrogen fuel's radial distribution at different Mach numbers is analyzed and it is found that with an increase in Mach number, the radial distribution growth has decreased due to high convective Mach number. With the increase in the combustion chamber's divergence angle, the radial distribution of H2 also increased. Figure 11: Open in new tabDownload slide Cross-stream hydrogen profiles at (a) x = 120, (b) x = 167, and (c) x = 275 mm. Figure 11: Open in new tabDownload slide Cross-stream hydrogen profiles at (a) x = 120, (b) x = 167, and (c) x = 275 mm. Turbulent intensity is an important parameter to assess the level of turbulence. With the association of shock wave and shear layer, the turbulent intensity varies with velocity fluctuations. Turbulent intensity (I) of the scramjet flow field for the conventional and unconventional strut is predicted at Mach 2, as shown in Fig. 12. The comparison of turbulent intensity found that the outspread of “I” in the cross-stream direction is more in the case of unconventional (wavy wall) strut. The strut wake region's turbulent intensity is better for wedge strut but not distributed in the radial direction. Turbulent kinetic energy (TKE) is another crucial parameter for evaluating the turbulence level and its effect. TKE is the function of fluctuation velocity. It is evaluated for both the wedge and wavy wall strut with different Mach numbers and shown in Fig. 13. With an increase in Mach number, the turbulent kinetic energy also increased. Comparatively, at a particular Mach number, the turbulent kinetic energy is more for wavy wall strut due to higher turbulent intensity and fluctuation velocity. Turbulent kinetic energy is more in the wake region's local area with a shock wave and shear layer interaction. It decreases in the downstream with the absence of vortices and shock wave interactions. Figure 12: Open in new tabDownload slide Turbulent intensity. Figure 12: Open in new tabDownload slide Turbulent intensity. Figure 13: Open in new tabDownload slide Turbulent kinetic energy. Figure 13: Open in new tabDownload slide Turbulent kinetic energy. 5.1 Performance parameters The unconventional strut performance has been evaluated further with mixing efficiency and total pressure losses. The mixing efficiency of the air–fuel mixture at any cross-stream location can be calculated with the average values. Mixing efficiency is the ratio of mass flux of H2 at a stoichiometric level to the total mass flux of H2, and the same is described as follows (Gerlinger, Stoll, Kindler, Schneider, & Aigner, 2008; Aravind & Kumar, 2019): $$\begin{eqnarray} {{\rm{\eta }}_{\rm{m}}} = \frac{{\int_{\rm{A}} {{\rm{\alpha }}{{\rm{\rho }}_{{\rm{gas}}}}{{\rm{\it{ Y}}}_{{{\rm{H}}_2}}}{\rm{\it{ udA}}}} }}{{{\rm{\it{ m}}}_{{{\rm{\mathrm{ H}}}_\mathrm{ 2}}}^ \cdot }},\,\,{\rm{with}}\,\,{\rm{\alpha }} = \left\{ {\begin{array}{@{}*{2}{c}@{}} {\mathrm{ 1},} & \quad {\emptyset \lt \mathrm{ 1}}\\ {1/\emptyset ,} & \quad {\emptyset \ge 1} \end{array}} \right\}, \end{eqnarray}$$(9) where α is the equivalence ratio (ϕ), YH2 hydrogen mass fraction, ρ, and “u” are the flow stream's density and velocity. The mixing phenomenon at supersonic speed is the cause for irreversibility, and it leads to amplify entropy and thereby losses in the total pressure of the flow stream. The total pressure losses intensify with a rise in the number of oblique shocks and their effect on an amalgamation of air and fuel. For a given location of the flow stream, the pressure losses are calculated with the following expression (Gerlinger et al., 2008; Aravind & Kumar, 2019). $$\begin{eqnarray} {\eta _t\mathrm{ }} = \it{ 1} - \frac{{\int_A {{\it{ P}_0}\rho \it{ udA}} }}{{\int_A {{\it{ P}_{\mathrm{ 0,inlet}}}\rho \it{ udA}}}} \end{eqnarray}$$(10) The mixing efficiency and pressure losses at Mach 2 for both the struts have been evaluated. From Fig. 14a, it is noticed that the complete mixing for wavy wall strut has been finished within a distance of 70 mm from the strut base (mixing initiation at x = 110 mm) to the point where 100% (x = 180 mm) mixing efficiency has achieved. With an increase in mixing efficiency, pressure losses also increase due to the entropy generation. Pressure losses (Fig. 14) gradually increase from the isolator section to the middle of the combustor with the development of shock train and decrease further downstream due to the vanishing of shock waves. The wavy wall strut has higher pressure losses due to more oblique shock waves and better mixing. Figure 14: Open in new tabDownload slide Performance parameters. (a) Mixing efficiency (Ma = 2). (b) Total pressure losses (Ma = 2). Figure 14: Open in new tabDownload slide Performance parameters. (a) Mixing efficiency (Ma = 2). (b) Total pressure losses (Ma = 2). 6. Conclusion The scramjet internal flow field has been studied numerically with conventional and unconventional struts for the possible mixing augmentation of the supersonic air and fuel. The internal flow field has been evaluated by visualizing the flow structure with density and pressure contour and velocity profiles. The scramjet flow structure differentiation found the increased number of oblique shock waves with the wavy wall strut fuel injector. The number of interactions between the shock wave and shear layer is three and five for the primary and wavy wall strut, respectively. After the interaction point, the shear layer thickness is more in the case of wavy wall strut. The wavy wall strut registered high pressure and temperature at the combustor entrance with the intensified shock strength. It leads to the chance of early combustion with decreasing ignition delay time compared with the wedge strut. The comparison of mass fraction profiles of H2 found the increased radial distribution of H2 for wavy wall strut. The wavy wall design enhances the turbulence level with increased streamline vortices, turbulent intensity, and turbulent kinetic energy. The increased turbulence level (disturbance) leads to the mixing enhancement. The shock wave generation analysis at different Mach numbers (M = 2,4,6) found fewer interactions between the shock wave and shear layer with increased Mach number. Finally, from the examination of shock wave generation and its interaction with the shear layer and analysis of turbulent parameters, it is found that the wavy wall strut has an appreciable effect on shock-induced blend augmentation of fuel and air. Conflict of Interest Statement None declared. References Andreopoulos Y. , Agui J. H., Briassulis G. ( 2000 ). Shock wave–turbulence interactions . Annual Review of Fluid Mechanics , 32 , 309 – 345 .. https://doi.org/10.1146/annurev.fluid.32.1.309 . Google Scholar Crossref Search ADS WorldCat Aravind S. , Kumar R. ( 2019 ). Supersonic combustion of hydrogen using an improved strut injection scheme . International Journal of Hydrogen Energy , 44 ( 12 ), 6257 – 6270 .. https://doi.org/10.1016/j.ijhydene.2019.01.064 . Google Scholar Crossref Search ADS WorldCat Brummund U. , Nuding J. R. ( 1997 ). Interaction of a compressible shear layer with shock waves: An experimental study . American Institute of Aeronautics and Astronautics , Meeting Papers on Disc, January, A9715456, AIAA Paper 97–0392 . https://doi.org/10.2514/6.1997-392 . Google Scholar OpenURL Placeholder Text WorldCat Budzinski J. M. , Zukoski E. E., Marble F. E. ( 1992 ). Rayleigh scattering measurements of shock enhanced mixing . American Institute of Aeronautics and Astronautics , AIAA/SAE/ASME/ASEE, Joint Propulsion Conference, 28th, Nashville, TN , 92 – 3546 . Google Scholar OpenURL Placeholder Text WorldCat Buttswortht D. R. ( 1996 ). Interaction of oblique shock waves and planar mixing regions . Journal of Fluid Mechanics , 306 , 43 – 57 . Google Scholar Crossref Search ADS WorldCat Choubey G. , Pandey K. M. ( 2016 ). Investigation on the effects of operating variables on the performance of two-strut scramjet combustor . International Journal of Hydrogen Energy , 41 ( 45 ), 20753 – 20770 .. https://doi.org/10.1016/j.ijhydene.2016.09.157 . Google Scholar Crossref Search ADS WorldCat Choubey G. , Pandey K. M. ( 2017 ). Effect of different strut + wall injection techniques on the performance of two-strut scramjet combustor . International Journal of Hydrogen Energy , 42 ( 18 ), 13259 – 13275 .. https://doi.org/10.1016/j.ijhydene.2017.04.024 . Google Scholar Crossref Search ADS WorldCat Choubey G. , Pandey K. M. ( 2018 ). Effect of different wall injection schemes on the flow-field of hydrogen-fuelled strut-based scramjet combustor , Acta Astronautica , 145 , 93 – 104 .. https://doi.org/10.1016/j.actaastro.2018.01.034 . Google Scholar Crossref Search ADS WorldCat Clemens N. T. , Mungal M. G., Berger T. E., Vandsburger U. ( 1990 ). Visualization of the structure of the turbulent mixing layer under compressible conditions . American Institute of Aeronautics and Astronautics , 28th Aerospace Sciences Meeting 08 January 1990–11 January 1990 Reno, NV, U.S.A. Paper No. 90-1978 . https://doi.org/10.2514/6.1990-500 . Google Scholar OpenURL Placeholder Text WorldCat Drummond J. P. , Givi P. ( 1994 ). Suppression and enhancement of mixing in high-speed reacting flow fields . In Buckmaster J., Jackson T. L., Kumar A. (Eds.), Combustion in high-speed flows. ICASE/LaRC interdisciplinary series in science and engineering , Vol. 1 (pp. 191 – 229 .), Springer , Dordrecht , https://doi.org/10.1007/978-94-011-1050-1_7 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Erdem E. , Kontis K. ( 2010 ). Numerical and experimental investigation of transverse injection flows . Shock Waves , 20 , 103 – 118 .. https://doi.org/10.1007/s00193-010-0247-1 . Google Scholar Crossref Search ADS WorldCat Fang X. , Shen C., Sun M., Hu Z. ( 2018 ). Effects of oblique shock waves on turbulent structures and statistics of supersonic mixing layers . Physics of Fluids , 30 , 116101 . https://doi.org/10.1063/1.5051015 . Google Scholar Crossref Search ADS WorldCat Gerlinger P. , Stoll P., Kindler M., Schneider F., Aigner M. ( 2008 ). Numerical investigation of mixing and combustion enhancement in supersonic combustors by strut induced streamwise vortices , Aerospace Science and Technology , 12 , 159 – 168 .. https://doi.org/10.1016/j.ast.2007.04.003 . Google Scholar Crossref Search ADS WorldCat Guirguis R. H. ( 1988 ). Mixing enhancement in supersonic shear layers: III - Effect of convective Mach number , American Institute of Aeronautics and Astronautics , 26th Aerospace Sciences Meeting 11 January 1988–14 January 1988 Reno, NV, U.S.A. Paper 88-0701 . https://doi.org/10.2514/6.1988-701 . Google Scholar OpenURL Placeholder Text WorldCat Huang W. ( 2014 ). Design exploration of a three-dimensional transverse jet in a supersonic crossflow based on data mining and multi-objective design optimization approaches . International Journal of Hydrogen Energy , 39 ( 8 ), 3914 – 3925 .. https://doi.org/10.1016/j.ijhydene.2013.12.129 . Google Scholar Crossref Search ADS WorldCat Huang W. ( 2015a ). Investigation on the effect of strut configurations and locations on the combustion performance of a typical scramjet combustor . Journal of Mechanical Science and Technology , 29 ( 12 ), 5485 – 5496 .. https://doi.org/10.1007/s12206-015-1150-6 . Google Scholar Crossref Search ADS WorldCat Huang W. ( 2015b ). Effect of jet-to-cross flow pressure ratio arrangement on turbulent mixing in a flow path with square staged injectors . Fuel , 144 , 164 – 170 .. https://doi.org/10.1016/j.fuel.2014.12.051 . Google Scholar Crossref Search ADS WorldCat Huang W. ( 2016 ). Transverse jet in supersonic cross flows , Aerospace Science and Technology , 50 , 183 – 195 .. https://doi.org/10.1016/j.ast.2016.01.001 . Google Scholar Crossref Search ADS WorldCat Huang W. , Du Z.-B., Yan L., Moradi R., ( 2018 ). Flame propagation and stabilization in dual-mode scramjet combustors: A survey , Progress in Aerospace Sciences , 101 , 13 – 30 .. https://doi.org/10.1016/j.paerosci.2018.06.003 . Google Scholar Crossref Search ADS WorldCat Huang W. , Du Z.-B., Yan L., Xia Z.-X. ( 2019 ). Supersonic mixing in air-breathing propulsion systems for hypersonic flights , Progress in Aerospace Sciences , 109 , 100545 . https://doi.org/10.1016/j.paerosci.2019.05.005 . Google Scholar Crossref Search ADS WorldCat Huang W. , Liu W.-D., Li S.-B., Xia Z.-X., Liu J., Wang Z.-G. ( 2012 ). Influences of the turbulence model and the slot width on the transverse slot injection flow field in supersonic flows . Acta Astronautica , 73 , 1 – 9 .. https://doi.org/10.1016/j.actaastro.2011.12.003 . Google Scholar Crossref Search ADS WorldCat Huang W. , Wu H., Yang Y.-G., Yanc L., Li S.-B., ( 2020 ). Recent advances in the shock wave/boundary layer interaction and its control in internal and external flows . Acta Astronautica , 174 , 103 – 122 .. https://doi.org/10.1016/j.actaastro.2020.05.001 . Google Scholar Crossref Search ADS WorldCat Hyde C. R. , Smith B. R., Schetzj A., Walkerd A. ( 1990 ). Turbulence measurements for heated gas slot injection in supersonic flow . American Institute of Aeronautics and Astronautics , 28 , 1605 – 1614 . Google Scholar Crossref Search ADS WorldCat Ivanova E. , Berthold N., Aigner M. ( 2013 ). A numerical study on the turbulent Schmidt numbers in a jet in crossflow . ASME Turbo Expo: Turbine Technical Conference and Exposition , GT2012-69294 , 949 – 960 .. https://doi.org/10.1115/GT2012-69294 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Kummitha O. R. ( 2017 ). Numerical analysis of hydrogen fuel scramjet combustor with turbulence development inserts and with different turbulence models . International Journal of hydrogen energy , 42 , 6360 – 6368 .. https://doi.org/10.1016/j.ijhydene.2016.10.137 . Google Scholar Crossref Search ADS WorldCat Kummitha O. R. , Suneetha L., Pandey K. M. ( 2017 ). Numerical analysis of scramjet combustor with innovative strut and fuel injection techniques . International Journal of Hydrogen Energy , 42 ( 15 ), 10524 – 10535 .. https://doi.org/10.1016/j.ijhydene.2017.01.213 . Google Scholar Crossref Search ADS WorldCat Liao L. , Yan L., Huang W., Lang-quan L. ( 2018 ). Mode transition process in a typical strut-based scramjet combustor based on a parametric study . Journal of Zhejiang University Science A (Appl Phys & Eng) , 19 ( 6 ): 431 – 451 .. https://doi.org/10.1631/jzus.A1700617 . Google Scholar Crossref Search ADS WorldCat Marble F. , Zukoski E., Jacobs J., Hendricks G. ( 1990 ). Shock enhancement and control of hypersonic mixing and combustion . In Proceedings of the 26th Joint Propulsion Conference , 16 July 1990–18 July 1990, Orlando, FL, U.S.A . https://doi.org/10.2514/6.1990-1981 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Menon S. ( 1989 ). Shock-wave-induced mixing enhancement in scramjet combustors . American Institute of Aeronautics and Astronautics , 27th Aerospace Sciences Meeting 09 January 1989–12 January 1989, Reno, NV, U.S.A. Paper, 89-0104 . https://doi.org/10.2514/6.1989-104 . Google Scholar OpenURL Placeholder Text WorldCat Northam G. B. , Capriotti D. P., Byingtonc S., Greenberi G. ( 1991 ). Mach 2 and Mach 3 mixing and combustion in scramjets . American Institute of Aeronautics and Astronautics , AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 27th, Sacramento, CA, Paper 91-2394 . Google Scholar OpenURL Placeholder Text WorldCat Oevermann Michael , ( 2000 ). Numerical investigation of turbulent hydrogen combustion in a scramjet using flamelet modeling . Aerospace Science and Technology , 4 ( 7 ), 463 – 480 .. https://doi.org/10.1016/S1270-9638(00)01070-1 . Crossref Search ADS WorldCat Papamoschou D. , Roshko A. ( 1988 ). The compressible turbulent shear layer: An experimental study . Journal of Fluid Mechanics , 197 , 453 – 477 .. https://doi.org/10.1017/S0022112088003325 . Google Scholar Crossref Search ADS WorldCat Roy G. D. ( 1991 ). Subsonic and supersonic mixing and combustion enhancement . ISABE Paper 91-7093 . OpenURL Placeholder Text WorldCat Sailesh C. , Biraj S. T., Ole G. D., Hari P. N. ( 2017 ). Numerical and experimental study of the leakage flow in guide vanes with different hydrofoils , Journal of Computational Design and Engineering , 4 ( 3 ), 218 – 230 .. https://doi.org/10.1016/j.jcde.2017.02.004 . Google Scholar Crossref Search ADS WorldCat Shin J. , Moon K. H., Sung H. G. ( 2015 ). Numerical simulation of hydrogen combustion in a model scramjet combustor using the IDDES framework . In Proceedings of the 20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference , AIAA , 3625 . https://doi.org/10.2514/6.2015-3625 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Tillman T. G. , Patrick W. P., Paterson R. W. ( 1991 ). Enhanced mixing of supersonic jets . Journal of Propulsion Power , 7 , 1006 – 1014 .. https://doi.org/10.2514/3.23420 . Google Scholar Crossref Search ADS WorldCat Waidmann W. , Alff F., Bohm M., Brummund U., Clauss W., Oschwald M. ( 1995 ). Supersonic combustion of hydrogen/air in a scramjet combustion chamber . Space Technology , 15 ( 6 ) 421 – 429 . Google Scholar Crossref Search ADS WorldCat Waidmann W. , Alft F., Brummund U., Bohm M., Clauss W., Oschwald M. ( 1994 ). Experimental investigation of the combustion process in a supersonic combustion ramjet (scramjet) . DLR Institute for Chemical Propulsion and Engineering , D-74239 , Hardthausen, Germany . Google Scholar OpenURL Placeholder Text WorldCat Waidmann W. , Brummund U., Nuding J. ( 1996 ). Experimental investigation of supersonic ramjet combustion (scramjet) . In Proceedings of the 8th International Symposium on Transport Phenomena in Combustion , San Francisco; CA . Taylor and Francis ; 1473 – 1484 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Waitz I. A. , Marble F. E., Zukoski E. E. ( 1991 ). An investigation of a contoured wall injector for hypervelocity mixing augmentation . American Institute of Aeronautics and Astronautics , 27th Joint Propulsion Conference 24 June 1991–26 June 1991, Sacramento, CA, U.S.A . https://doi.org/10.2514/6.1991-2265 . Google Scholar OpenURL Placeholder Text WorldCat Wepler U. , Huhn C., Koschel W. ( 2001 ). Numerical simulation of shock wave interaction effects on supersonic mixing layer growth . In Hirschel E. H. (Ed.), Numerical Flow Simulation II. Notes on Numerical Fluid Mechanics (NNFM) . Vol. 75 (pp. 217 – 228 .). Springer , Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-44567-8_13 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC Wilcox D. C. ( 1998 ). Reassessment of the scale-determining equation for advanced turbulence models . American Institute of Aeronautics and Astronautics , 26 , 1299 – 1310 .. https://doi.org/10.2514/3.10041 . Google Scholar Crossref Search ADS WorldCat © The Author(s) 2020. Published by Oxford University Press on behalf of the Society for Computational Design and Engineering. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
TI - Effect of wavy wall strut fuel injector on shock wave development and mixing enhancement of fuel and air for a scramjet combustor
JF - Journal of Computational Design and Engineering
DO - 10.1093/jcde/qwaa084
DA - 2021-01-25
UR - https://www.deepdyve.com/lp/oxford-university-press/effect-of-wavy-wall-strut-fuel-injector-on-shock-wave-development-and-fq1wM89NTh
SP - 362
EP - 375
VL - 8
IS - 1
DP - DeepDyve
ER -