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Molecular weight and injector configuration effects on the transverse injection flow field properties in supersonic flows
Aerospace Science and Technology 32 (2014) 94–102
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Molecular weight and injector configuration effects on the transverse injection flow field properties in supersonic flows Wei Huang a,∗ , Jun Liu b , Liang Jin a , Li Yan a a b
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 22 October 2013 Received in revised form 9 December 2013 Accepted 11 December 2013 Available online 16 December 2013 Keywords: Aerospace propulsion system Transverse injection Supersonic crossflow Molecular weight Jet-to-crossflow pressure ratio Jet plume
a b s t r a c t The transverse injection flow field in the high speed conditions is more complex than that in the low speed, and more information should be explored to improve the overall performance of the airbreathing hypersonic propulsion system. The three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations and the two equation SST k–ω has been employed to explore the influences of the molecular weight (hydrogen and nitrogen) and injector configuration (circular, square, diamond and equilateral triangular) on the mean flow field properties in the transverse injection strategy, and the wide range of the jet-tocrossflow pressure ratio (4.86, 10.29, 17.72 and 25.15) has been considered as well. The obtained results show that the low jet-to-crossflow pressure ratio can promote the mixing process between the injectant and the supersonic crossflow irrespective of the injectant species and the injector configuration, and the large molecular weight of the injectant can promote the mixing process as well when the jet-to-crossflow pressure ratio is fixed. The case with the equilateral triangular injector owns the highest mixing efficiency in the range considered in the current study, and it may be induced by the remarkable influence of the counter-rotating vortex pair. The injectant mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the low jet-to-crossflow pressure ratio, and the jet plume spreads in the spanwise direction more rapidly for the case with the diamond injector irrespective of the injectant species. © 2013 Elsevier Masson SAS. All rights reserved.
1. Introduction The mixing process between the injectant and the supersonic airstream is one of the crucial issues for the design of scramjet engine, and it has attacked an increasing attention worldwide [21, 4]. This is mainly induced by the very short residence time for the injectant in the supersonic flow [9]. Thus, lots of fuel injection strategies have been proposed in the past few years, i.e. transverse injection [8], strut [10], cavity [2], cantilevered ramp injector [13], et al. However, the transverse injection from a wall orifice has been proved to be one of the simplest and most promising configurations for the scramjet engine, and many experimental and numerical studies have been performed for this strategy. Mahesh [17] reviewed the fundamental understanding of transverse jets in both incompressible and compressible regimes, and he has deduced that more quantitative information should be available at high speeds. Recently, the parametric analysis on the supersonic flow has become a hotspot for the hypersonic airbreathing propulsion system [12], and this is the fundamental step for the optimization process
*
Corresponding author. Tel.: +86 731 84576452; fax: +86 731 84576449. E-mail address: [email protected] (W. Huang).
1270-9638/$ – see front matter © 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ast.2013.12.006
in the supersonic mixing and combustion flow field. As stated by Huang and Yan [8], the injector configuration is one of the most important aspects for the mixing improvement in the supersonic crossflow. Gruber et al. [7] compared the transverse injection flow field properties with a freestream Mach number being 2.0, and they stated that the injector configuration has only a slight impact on the transverse penetration in the near field. However, the lateral spreading of the elliptical injector is greater than that of the circular one. The flow field characteristic comparison for the circular- and elliptic-shaped injector was carried out numerically by Wang et al. [28], and they found that the jet maximum penetration in the elliptic injection is lower than that in the circular injection. This conclusion is somewhat different from that obtained by Gruber et al. [7]. Additionally, the penetration band in the elliptic injection is narrower than that in the circular injection, and the elliptic injector spreads rapidly in the spanwise direction. Srinivasan and Bowersox [24,16] gave a detailed characteristic comparison of the shock and vortex structures for diamond- and circular-shaped injectors, and they observed that a lateral counterrotating vortex pair is only generated in the flow field with the diamond injector, and it acts as a gas-dynamic flame holder. At the same time, the large scale structures in the plume/wake region
W. Huang et al. / Aerospace Science and Technology 32 (2014) 94–102
of the flow field are more organized in the case with the diamond injector. Further, Bowersox et al. [3] examined the near-field flows for the diamond- and circular-shaped injectors experimentally, and they found that the circular injector can induce larger total pressure loss. Tomioka et al. [27] investigated the supersonic combustion flow field with the diamond injector, and the obtained results show that the ability to attain ignition and mode-transition is weaker for the diamond injector. At the same time, the molecular weight of the injectant has a great impact on the mean flow field characteristics as well, and Schetz et al. [20] found that larger molecular weight can increase penetration. However, its effect is weak. Watanabe et al. [29] examined a wider range of injectant, namely hydrogen, helium, nitrogen and ethylene, and they observed that the hydrogen jet can obtain higher mixing efficiency than the ethylene jet for the studied injection conditions. However, to the best of the authors’ knowledge, the effects of the molecular weight and injector configuration have not been investigated synchronously, and they both have a great impact on the mean flow field properties for the transverse injection. At the same time, the influence of the injector configuration has rarely been studied in detail, especially the wider range of the injector geometric configuration, and the flow field properties for the different injector configurations are not clear. This deficiency is not of benefit to the improvement of the overall performance in scramjet engines. For more in-depth understanding the mean flow field properties in the transverse injection strategy, especially the molecular weight and injector configuration effect, the influences of the molecular weight and the injector configuration on the transverse injection flow field properties have been explored numerically in this article, and the effect of the jet-to-crossflow pressure ratio has been carried out as well. The jet-to-crossflow pressure ratio is set to be 4.86, 10.29, 17.72 and 25.15, and this is the same as that employed by Aso et al. [1].
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Fig. 1. The sketch for the transverse injection computational domain.
2. Physical model and numerical method In the current study, four injector configurations are chosen to inject the injectant into the supersonic crossflow, namely the circular port, the equilateral triangular port, the square port and the diamond port, and the area of the injector maintains the same, namely S = 0.3927 mm2 , and the other dimensions can be observed in Fig. 1(a). Fig. 1(a) depicts the top side of the transverse injection computational domain, and the origin is located at the intersectional point between the symmetrical plane and the entrance boundary for the computational domain. The wedgeshaped injector has been selected as one of the basic injector configurations because it can avoid the occurrence of the boundary layer separation ahead of the injection port [26,19]. Srinivasan and Bowersox [23] found that two new vortex features exist in the vicinity of the diamond injector, namely one located near the leading edge of the injector and the other located just downstream of the barrel shock wave. At the same time, the hydrogen and nitrogen are chosen as the injectant to explore the influence of the molecular weight on the transverse flow field properties. The supersonic airstream flows from left to right with a freestream Mach number of 3.75, a static pressure of 11 090 Pa and a static temperature of 78.43 K. The jet flow Mach number is set to be 1.0 with a static temperature being 249 K and a jetto-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15. The jet-to-crossflow pressure ratio is proved to be a crucial parameter for the transverse injection flow field properties [30,15,11]. The three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations and the two equation SST k–ω turbulence model has
been used to simulate the transverse injection flow field numerically, and the equations are solved along with density based (coupled) double precision solver of FLUENT [5]. The RANS approach is the efficient and rapid method to obtain the mean flow behaviors for the further mixing and combustion optimization in the supersonic flow [22,14], and the SST k–ω turbulence model is suitable to solve the flow fields with adverse pressure gradients [18], especially for the transverse injection flow field [6,25]. The local mass fraction of each species Y i is predicted through the solution of a convection–diffusion equation for the ith species, and the turbulent Schmidt number is set to be 0.7 [5]. The species are assumed to be ideal gases. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized to quicken the convergence speed, and the Courant– Friedrichs–Levy (CFL) number is kept at 0.5 with proper underrelaxation factors to ensure stability [13]. The no-slip conditions are assumed for the walls of the channel. At the outflow, all the physical variables are extrapolated from the internal cells because of the flow being supersonic. The air is assumed to be a thermally and calorically perfect gas, and the mass-weighted-mixing-law of viscosity is utilized. The solutions can be considered as converged when the residuals reach their minimum values after falling for more than three orders of magnitude, and the discrepancy between the computed inflow and the outflow mass flux is required to drop below 0.001 kg/s. At the same time, the computational domain is structured by the commercial software Gambit, and the grid is multi-blocked and highly concentrated close to the wall surfaces and the injectant
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Fig. 2. Wall static pressure distribution comparisons for different jet-to-crossflow pressure ratios.
port in order to ensure the accuracy of the numerical simulation. The height of the first row of cells is set at a distance of 0.01 mm for the walls, and the maximum of y + is less than 10. 3. Results and discussion In order to verify the accuracy of the employed numerical method, the experimental model studied by Aso et al. [1] has been employed to provide the wall pressure distributions for the cases with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15. The distance from the leading edge to the leading point of the injector is 330 mm, and the distance from the trailing point of the injector to the exit boundary of the computational domain is 220 mm, see Fig. 1(a). The height and width for the computational domain are 100 mm and 150 mm, respectively, see Fig. 1(b), and Fig. 1(b) depicts the computational mesh for the moderate grid scale employed in the current study. These geometric parameters are the same as those employed by Aso et al. [1], as shown in Fig. 1(a).
Fig. 2 depicts the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios with the coarse grid (16 8560 nodes), the moderate grid (36 5040 nodes) and the refined grid (51 5040 nodes), namely P j / P ∞ = 4.86, 10.29, 17.72 and 25.15, and the predicted results are compared with the experimental data obtained by Aso et al. [1]. It is clear that the numerical results show reasonable agreement with the experimental data, and the grid scale makes only a slight difference to the predicted results. This may imply that the numerical approach can be employed with confidence to simulate the transverse injection flow field, and the moderate grid scale is utilized to carry out the following simulations in order to reduce the computational cost. In Fig. 2, the upstream separation length is over-predicted for the cases with the jet-to-crossflow pressure ratio being 17.72 and 25.15, see Figs. 2(c) and 2(d), as well as the downstream recirculation length, see Figs. 2(a)–2(d). This discrepancy may be induced by the turbulent simulation, and the numerical simulation cannot capture the turbulent intensity accurately. However, the predicted wall static pressure distribution of the case with the jet-to-crossflow pressure ratio being 10.29 matches better
W. Huang et al. / Aerospace Science and Technology 32 (2014) 94–102
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Fig. 3. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 4.86, hydrogen (left) and nitrogen (right).
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. The SST k–ω turbulence model is more suitable to simulate the transverse injection flow field with a jet-to-crossflow pressure ratio being 10.29, and this conclusion is nearly the same as that obtained in Ref. [11]. The following results are obtained by the SST k–ω turbulence model. Figs. 3–6 show the injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15, respectively. In these figures, the left hand side is the hydrogen mole fraction contour, and the other side is the nitrogen mole fraction contour. It is clearly observed that the low jet-to-crossflow pressure ratio can enhance the mixing process between the injectant and the supersonic airstream, and this can be deduced from Table 1 and Figs. 7–10 as well. Table 1 depicts the mixing efficiency comparison for the cases with the hydrogen injection at x = 350 mm, and it is clearly observed that the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the injector configuration. At the same time, the mixing efficiency is the lowest for
Table 1 Mixing efficiency comparison for the cases with the hydrogen injection.
Square Diamond Circular Equilateral triangular
4.86
10.29
17.72
25.15
93.1% 94.8% 93.3% 94.6%
91.3% 91.0% 89.8% 91.5%
86.7% 86.4% 85.5% 86.6%
80.2% 83.9% 81.5% 85.4%
the case with the circular injector when the jet-to-crossflow pressure ratio is 10.29 and 17.72, and the mixing efficiency is the lowest for the case with the square injector when the jet-to-crossflow pressure ratio is 4.86 and 25.15. The equilateral triangular injector is the best injector configuration from the view of mixing improvement in the near field, and it is the best choice for the fuel injection strategy. Figs. 7–10 describe the hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15, respectively, and it is shown that the hydrogen mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the lower jet-to-crossflow pressure ratio. At the
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Fig. 4. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 10.29, hydrogen (left) and nitrogen (right).
same time, we can observe that the nitrogen can mix with the supersonic airstream more rapidly than the hydrogen for the case with the same jet-to-crossflow pressure ratio, and this may be induced by the difference of the molecular weight. In other words, this may imply that the injectant with a larger molecular weight can promote the mixing process in the supersonic flow. Additionally, it is noted that the jet plume leaves from the bottom wall for the cases with the nitrogen injection, and the mixing process may be accomplished in the core flow. The size of the jet plume for the cases with the nitrogen injection is much smaller than that for the cases with the hydrogen injection, see Figs. 3–6. At the same time, it is clearly observed that the jet plume for the case with the diamond injector spreads more rapidly in the spanwise direction irrespective of the injectant species, and this may be induced by the stronger effect of the counter-rotating vortex pair (CVP). The blockage effect of the case with the diamond injector is the largest as well, see Figs. 8–10, and this is induced by its special geometric configuration. Following is the case with the equilateral triangular injector, and the jet penetration for the equilateral triangular injector seems to be the highest in the range
considered in the current study. The effect of the counter-rotating vortex pair on the flow field properties of the diamond- and equilateral triangular-shaped injector is more remarkable, and this can further prove that the counter-rotating vortex pair makes a great difference to the mixing improvement in the transverse injection flow field. 4. Conclusions In the current study, the influences of the molecular weight and the injector configuration on the transverse injection flow field properties have been explored numerically by the threedimensional Reynolds-averaged Navier–Stokes (RANS) equations coupled with the SST k–ω turbulence model, and the effect of the jet-to-crossflow pressure ratio has been considered as well. The numerical method has been validated against the available experimental data in the open literature. We have come to the following conclusions.
• The SST k–ω turbulence model is suitable to simulate the transverse injection flow field in the supersonic flow, espe-
W. Huang et al. / Aerospace Science and Technology 32 (2014) 94–102
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Fig. 5. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 17.72, hydrogen (left) and nitrogen (right).
cially for the case with the jet-to-crossflow pressure ratio being 10.29, and this is consistent with the phenomenon observed by Huang et al. [11]. The discrepancy between the predicted results and the experimental data may be induced by the incoming turbulence simulation. • The mixing efficiency for the case with the equilateral triangular injector is the highest, and following is the case with the diamond injector. This may be induced by the special vortex structures generated in the transverse injection flow field. At the same time, this may imply that the effect of the counterrotating vortex pair is remarkable. The square injector is not suitable to be chosen as an injection strategy for the case with the low and high jet-to-crossflow pressure ratio, namely 4.86 and 25.15 in the range considered in this article. • The lower jet-to-crossflow pressure ratio is better for the mixing process between the injectant and the supersonic
airstream, and the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the injector configuration. The injectant mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the lower jet-to-crossflow pressure ratio. The jet plume for the case with the diamond injector spreads more rapidly in the spanwise direction irrespective of the injectant species. Acknowledgements
The authors would like to express their thanks for the support from the Hunan Provincial Natural Science Foundation of China (No. 12jj4047). The reviewers are thanked for their very constructive comments.
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Fig. 6. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 25.15, hydrogen (left) and nitrogen (right).
W. Huang et al. / Aerospace Science and Technology 32 (2014) 94–102
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Fig. 7. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 4.86.
Fig. 9. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 17.72.
Fig. 8. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 10.29.
References
[1] S. Aso, S. Okuyama, M. Kawai, Y. Ando, Experimental study on mixing phenomena in supersonic flows with slot injection, in: 29th Aerospace Sciences Meeting, Reno, Nevada, 1991, AIAA Paper 91-0016. [2] A. Ben-Yakar, R.K. Hanson, Cavity flame-holders for ignition and flame stabilization in scramjets: An overview, J. Propuls. Power 17 (4) (2001) 869–877. [3] R.D.W. Bowersox, H. Fan, D. Lee, Sonic injection into a Mach 5.0 freestream through diamond orifices, J. Propuls. Power 20 (2) (2004) 280–287. [4] D. Cecere, A. Ingenito, E. Giacomazzi, L. Romagnosi, C. Bruno, Hydrogen/air supersonic combustion for future hypersonic vehicles, Int. J. Hydrog. Energy 36 (2011) 11969–11984. [5] Fluent Inc., Fluent 6.3 User’s Guide, Fluent Inc., Lebanon, NH, 2006.
Fig. 10. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 25.15. [6] Z.X. Gao, C.H. Lee, Numerical research on mixing characteristics of different injection schemes for supersonic transverse jet, Sci. China, Technol. Sci. 54 (4) (2011) 883–893. [7] M.R. Gruber, A.S. Nejad, T.H. Chen, et al., Mixing and penetration studies of sonic jets in a Mach 2 freestream, J. Propuls. Power 11 (1995) 315–323.
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[8] W. Huang, L. Yan, Progress in research on mixing techniques for transverse injection flow fields in supersonic crossflows, J. Zhejiang Univ. Sci. A 14 (8) (2013) 554–564. [9] W. Huang, H. Qin, S.B. Luo, Z.G. Wang, Research status of key techniques for shock-induced combustion ramjet (scramjet) engine, Sci. China, Technol. Sci. 53 (1) (2010) 220–226. [10] W. Huang, Z.G. Wang, S.B. Luo, J. Liu, Parametric effects on the combustion flow field of a typical strut-based scramjet combustor, Chin. Sci. Bull. 56 (35) (2011) 3871–3877. [11] W. Huang, W.D. Liu, S.B. Li, Z.X. Xia, J. Liu, Z.G. Wang, Influences of the turbulence model and the slot width on the transverse slot injection flow field in supersonic flows, Acta Astronaut. 73 (2012) 1–9. [12] W. Huang, L. Ma, M. Pourkashanian, D.B. Ingham, S.B. Luo, Z.G. Wang, Parametric effects in a scramjet engine on the interaction between the air stream and the injection, Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 226 (3) (2012) 294–309. [13] W. Huang, S.B. Li, L. Yan, Z.G. Wang, Performance evaluation and parametric analysis on cantilevered ramp injector in supersonic flows, Acta Astronaut. 84 (2013) 141–152. [14] W. Huang, J. Yang, L. Yan, Multi-objective design optimization of the transverse gaseous jet in supersonic flows, Acta Astronaut. 93 (2014) 13–22. [15] A.R. Karagozian, Transverse jets and their control, Prog. Energy Combust. Sci. 36 (2010) 531–553. [16] K. Kobayashi, R.D.W. Bowersox, R. Srinivasan, N.R. Tichenor, C.D. Carter, M.D. Ryan, Experimental and numerical studies of diamond-shaped injector in a supersonic flow, J. Propuls. Power 26 (2) (2010) 373–376. [17] K. Mahesh, The interaction of jets with crossflow, Annu. Rev. Fluid Mech. 45 (2013) 379–407. [18] C.J. Roy, F.G. Blottner, Review and assessment of turbulence models for hypersonic flows, Prog. Aerosp. Sci. 42 (2006) 469–530.
[19] F. Sakima, T. Arai, J. Kasahara, M. Murakoshi, T. Ami, F. He, H. Sugiyama, Mixing of a hydrogen jet from a wedge shaped injector into a supersonic cross flow, Trans. Jpn. Soc. Aeronaut. Space Sci. 46 (154) (2004) 217–223. [20] J.A. Schetz, L. Maddalena, S.K. Burger, Molecular weight and shock-wave effects on transverse injection in supersonic flow, J. Propuls. Power 26 (5) (2010) 1102–1113. [21] J.M. Seiner, S.M. Dash, D.C. Kenzakowski, Historical survey on enhanced mixing in scramjet engines, J. Propuls. Power 17 (6) (2001) 1273–1286. [22] P.R. Spalart, Strategies for turbulence modeling and simulations, Int. J. Heat Fluid Flow 21 (2000) 252–263. [23] R. Srinivasan, R.D.W. Bowersox, Simulation of transverse gaseous injection through diamond ports into supersonic freestream, J. Propuls. Power 23 (4) (2007) 772–782. [24] R. Srinivasan, R.D.W. Bowersox, Transverse injection through diamond and circular ports into a Mach 5.0 freestream, AIAA J. 46 (8) (2008) 1944–1962. [25] A.T. Sriram, J. Mathew, Numerical simulation of transverse injection of circular jets into turbulent supersonic streams, J. Propuls. Power 24 (1) (2008) 45–54. [26] S. Tomioka, L.S. Jacobsen, J.A. Schetz, Sonic injection from diamond-shaped orifices into a supersonic crossflow, J. Propuls. Power 19 (1) (2003) 104–114. [27] S. Tomioka, T. Kohchi, R. Masumoto, M. Izumikawa, A. Matsuo, Supersonic combustion with supersonic injection through diamond-shaped orifices, J. Propuls. Power 27 (6) (2011) 1196–1203. [28] G.L. Wang, L.W. Chen, X.Y. Lu, Effects of the injector geometry on a sonic jet into a supersonic crossflow, Sci. China, Phys. Mech. Astron. 56 (2) (2013) 366–377. [29] J. Watanabe, T. Kouchi, K. Takita, G. Masuya, Large-eddy simulation of jet in supersonic crossflow with different injectant species, AIAA J. 50 (12) (2012) 2765–2778. [30] J. Watanabe, T. Kouchi, K. Takita, G. Masuya, Characteristics of hydrogen jets in supersonic crossflow: Large-eddy simulation study, J. Propuls. Power 29 (3) (2013) 661–674.
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Molecular weight and injector configuration effects on the transverse injection flow field properties in supersonic flows Wei Huang a,∗ , Jun Liu b , Liang Jin a , Li Yan a a b
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 22 October 2013 Received in revised form 9 December 2013 Accepted 11 December 2013 Available online 16 December 2013 Keywords: Aerospace propulsion system Transverse injection Supersonic crossflow Molecular weight Jet-to-crossflow pressure ratio Jet plume
a b s t r a c t The transverse injection flow field in the high speed conditions is more complex than that in the low speed, and more information should be explored to improve the overall performance of the airbreathing hypersonic propulsion system. The three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations and the two equation SST k–ω has been employed to explore the influences of the molecular weight (hydrogen and nitrogen) and injector configuration (circular, square, diamond and equilateral triangular) on the mean flow field properties in the transverse injection strategy, and the wide range of the jet-tocrossflow pressure ratio (4.86, 10.29, 17.72 and 25.15) has been considered as well. The obtained results show that the low jet-to-crossflow pressure ratio can promote the mixing process between the injectant and the supersonic crossflow irrespective of the injectant species and the injector configuration, and the large molecular weight of the injectant can promote the mixing process as well when the jet-to-crossflow pressure ratio is fixed. The case with the equilateral triangular injector owns the highest mixing efficiency in the range considered in the current study, and it may be induced by the remarkable influence of the counter-rotating vortex pair. The injectant mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the low jet-to-crossflow pressure ratio, and the jet plume spreads in the spanwise direction more rapidly for the case with the diamond injector irrespective of the injectant species. © 2013 Elsevier Masson SAS. All rights reserved.
1. Introduction The mixing process between the injectant and the supersonic airstream is one of the crucial issues for the design of scramjet engine, and it has attacked an increasing attention worldwide [21, 4]. This is mainly induced by the very short residence time for the injectant in the supersonic flow [9]. Thus, lots of fuel injection strategies have been proposed in the past few years, i.e. transverse injection [8], strut [10], cavity [2], cantilevered ramp injector [13], et al. However, the transverse injection from a wall orifice has been proved to be one of the simplest and most promising configurations for the scramjet engine, and many experimental and numerical studies have been performed for this strategy. Mahesh [17] reviewed the fundamental understanding of transverse jets in both incompressible and compressible regimes, and he has deduced that more quantitative information should be available at high speeds. Recently, the parametric analysis on the supersonic flow has become a hotspot for the hypersonic airbreathing propulsion system [12], and this is the fundamental step for the optimization process
*
Corresponding author. Tel.: +86 731 84576452; fax: +86 731 84576449. E-mail address: [email protected] (W. Huang).
1270-9638/$ – see front matter © 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ast.2013.12.006
in the supersonic mixing and combustion flow field. As stated by Huang and Yan [8], the injector configuration is one of the most important aspects for the mixing improvement in the supersonic crossflow. Gruber et al. [7] compared the transverse injection flow field properties with a freestream Mach number being 2.0, and they stated that the injector configuration has only a slight impact on the transverse penetration in the near field. However, the lateral spreading of the elliptical injector is greater than that of the circular one. The flow field characteristic comparison for the circular- and elliptic-shaped injector was carried out numerically by Wang et al. [28], and they found that the jet maximum penetration in the elliptic injection is lower than that in the circular injection. This conclusion is somewhat different from that obtained by Gruber et al. [7]. Additionally, the penetration band in the elliptic injection is narrower than that in the circular injection, and the elliptic injector spreads rapidly in the spanwise direction. Srinivasan and Bowersox [24,16] gave a detailed characteristic comparison of the shock and vortex structures for diamond- and circular-shaped injectors, and they observed that a lateral counterrotating vortex pair is only generated in the flow field with the diamond injector, and it acts as a gas-dynamic flame holder. At the same time, the large scale structures in the plume/wake region
W. Huang et al. / Aerospace Science and Technology 32 (2014) 94–102
of the flow field are more organized in the case with the diamond injector. Further, Bowersox et al. [3] examined the near-field flows for the diamond- and circular-shaped injectors experimentally, and they found that the circular injector can induce larger total pressure loss. Tomioka et al. [27] investigated the supersonic combustion flow field with the diamond injector, and the obtained results show that the ability to attain ignition and mode-transition is weaker for the diamond injector. At the same time, the molecular weight of the injectant has a great impact on the mean flow field characteristics as well, and Schetz et al. [20] found that larger molecular weight can increase penetration. However, its effect is weak. Watanabe et al. [29] examined a wider range of injectant, namely hydrogen, helium, nitrogen and ethylene, and they observed that the hydrogen jet can obtain higher mixing efficiency than the ethylene jet for the studied injection conditions. However, to the best of the authors’ knowledge, the effects of the molecular weight and injector configuration have not been investigated synchronously, and they both have a great impact on the mean flow field properties for the transverse injection. At the same time, the influence of the injector configuration has rarely been studied in detail, especially the wider range of the injector geometric configuration, and the flow field properties for the different injector configurations are not clear. This deficiency is not of benefit to the improvement of the overall performance in scramjet engines. For more in-depth understanding the mean flow field properties in the transverse injection strategy, especially the molecular weight and injector configuration effect, the influences of the molecular weight and the injector configuration on the transverse injection flow field properties have been explored numerically in this article, and the effect of the jet-to-crossflow pressure ratio has been carried out as well. The jet-to-crossflow pressure ratio is set to be 4.86, 10.29, 17.72 and 25.15, and this is the same as that employed by Aso et al. [1].
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Fig. 1. The sketch for the transverse injection computational domain.
2. Physical model and numerical method In the current study, four injector configurations are chosen to inject the injectant into the supersonic crossflow, namely the circular port, the equilateral triangular port, the square port and the diamond port, and the area of the injector maintains the same, namely S = 0.3927 mm2 , and the other dimensions can be observed in Fig. 1(a). Fig. 1(a) depicts the top side of the transverse injection computational domain, and the origin is located at the intersectional point between the symmetrical plane and the entrance boundary for the computational domain. The wedgeshaped injector has been selected as one of the basic injector configurations because it can avoid the occurrence of the boundary layer separation ahead of the injection port [26,19]. Srinivasan and Bowersox [23] found that two new vortex features exist in the vicinity of the diamond injector, namely one located near the leading edge of the injector and the other located just downstream of the barrel shock wave. At the same time, the hydrogen and nitrogen are chosen as the injectant to explore the influence of the molecular weight on the transverse flow field properties. The supersonic airstream flows from left to right with a freestream Mach number of 3.75, a static pressure of 11 090 Pa and a static temperature of 78.43 K. The jet flow Mach number is set to be 1.0 with a static temperature being 249 K and a jetto-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15. The jet-to-crossflow pressure ratio is proved to be a crucial parameter for the transverse injection flow field properties [30,15,11]. The three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations and the two equation SST k–ω turbulence model has
been used to simulate the transverse injection flow field numerically, and the equations are solved along with density based (coupled) double precision solver of FLUENT [5]. The RANS approach is the efficient and rapid method to obtain the mean flow behaviors for the further mixing and combustion optimization in the supersonic flow [22,14], and the SST k–ω turbulence model is suitable to solve the flow fields with adverse pressure gradients [18], especially for the transverse injection flow field [6,25]. The local mass fraction of each species Y i is predicted through the solution of a convection–diffusion equation for the ith species, and the turbulent Schmidt number is set to be 0.7 [5]. The species are assumed to be ideal gases. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized to quicken the convergence speed, and the Courant– Friedrichs–Levy (CFL) number is kept at 0.5 with proper underrelaxation factors to ensure stability [13]. The no-slip conditions are assumed for the walls of the channel. At the outflow, all the physical variables are extrapolated from the internal cells because of the flow being supersonic. The air is assumed to be a thermally and calorically perfect gas, and the mass-weighted-mixing-law of viscosity is utilized. The solutions can be considered as converged when the residuals reach their minimum values after falling for more than three orders of magnitude, and the discrepancy between the computed inflow and the outflow mass flux is required to drop below 0.001 kg/s. At the same time, the computational domain is structured by the commercial software Gambit, and the grid is multi-blocked and highly concentrated close to the wall surfaces and the injectant
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Fig. 2. Wall static pressure distribution comparisons for different jet-to-crossflow pressure ratios.
port in order to ensure the accuracy of the numerical simulation. The height of the first row of cells is set at a distance of 0.01 mm for the walls, and the maximum of y + is less than 10. 3. Results and discussion In order to verify the accuracy of the employed numerical method, the experimental model studied by Aso et al. [1] has been employed to provide the wall pressure distributions for the cases with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15. The distance from the leading edge to the leading point of the injector is 330 mm, and the distance from the trailing point of the injector to the exit boundary of the computational domain is 220 mm, see Fig. 1(a). The height and width for the computational domain are 100 mm and 150 mm, respectively, see Fig. 1(b), and Fig. 1(b) depicts the computational mesh for the moderate grid scale employed in the current study. These geometric parameters are the same as those employed by Aso et al. [1], as shown in Fig. 1(a).
Fig. 2 depicts the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios with the coarse grid (16 8560 nodes), the moderate grid (36 5040 nodes) and the refined grid (51 5040 nodes), namely P j / P ∞ = 4.86, 10.29, 17.72 and 25.15, and the predicted results are compared with the experimental data obtained by Aso et al. [1]. It is clear that the numerical results show reasonable agreement with the experimental data, and the grid scale makes only a slight difference to the predicted results. This may imply that the numerical approach can be employed with confidence to simulate the transverse injection flow field, and the moderate grid scale is utilized to carry out the following simulations in order to reduce the computational cost. In Fig. 2, the upstream separation length is over-predicted for the cases with the jet-to-crossflow pressure ratio being 17.72 and 25.15, see Figs. 2(c) and 2(d), as well as the downstream recirculation length, see Figs. 2(a)–2(d). This discrepancy may be induced by the turbulent simulation, and the numerical simulation cannot capture the turbulent intensity accurately. However, the predicted wall static pressure distribution of the case with the jet-to-crossflow pressure ratio being 10.29 matches better
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Fig. 3. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 4.86, hydrogen (left) and nitrogen (right).
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. The SST k–ω turbulence model is more suitable to simulate the transverse injection flow field with a jet-to-crossflow pressure ratio being 10.29, and this conclusion is nearly the same as that obtained in Ref. [11]. The following results are obtained by the SST k–ω turbulence model. Figs. 3–6 show the injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15, respectively. In these figures, the left hand side is the hydrogen mole fraction contour, and the other side is the nitrogen mole fraction contour. It is clearly observed that the low jet-to-crossflow pressure ratio can enhance the mixing process between the injectant and the supersonic airstream, and this can be deduced from Table 1 and Figs. 7–10 as well. Table 1 depicts the mixing efficiency comparison for the cases with the hydrogen injection at x = 350 mm, and it is clearly observed that the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the injector configuration. At the same time, the mixing efficiency is the lowest for
Table 1 Mixing efficiency comparison for the cases with the hydrogen injection.
Square Diamond Circular Equilateral triangular
4.86
10.29
17.72
25.15
93.1% 94.8% 93.3% 94.6%
91.3% 91.0% 89.8% 91.5%
86.7% 86.4% 85.5% 86.6%
80.2% 83.9% 81.5% 85.4%
the case with the circular injector when the jet-to-crossflow pressure ratio is 10.29 and 17.72, and the mixing efficiency is the lowest for the case with the square injector when the jet-to-crossflow pressure ratio is 4.86 and 25.15. The equilateral triangular injector is the best injector configuration from the view of mixing improvement in the near field, and it is the best choice for the fuel injection strategy. Figs. 7–10 describe the hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio being 4.86, 10.29, 17.72 and 25.15, respectively, and it is shown that the hydrogen mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the lower jet-to-crossflow pressure ratio. At the
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Fig. 4. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 10.29, hydrogen (left) and nitrogen (right).
same time, we can observe that the nitrogen can mix with the supersonic airstream more rapidly than the hydrogen for the case with the same jet-to-crossflow pressure ratio, and this may be induced by the difference of the molecular weight. In other words, this may imply that the injectant with a larger molecular weight can promote the mixing process in the supersonic flow. Additionally, it is noted that the jet plume leaves from the bottom wall for the cases with the nitrogen injection, and the mixing process may be accomplished in the core flow. The size of the jet plume for the cases with the nitrogen injection is much smaller than that for the cases with the hydrogen injection, see Figs. 3–6. At the same time, it is clearly observed that the jet plume for the case with the diamond injector spreads more rapidly in the spanwise direction irrespective of the injectant species, and this may be induced by the stronger effect of the counter-rotating vortex pair (CVP). The blockage effect of the case with the diamond injector is the largest as well, see Figs. 8–10, and this is induced by its special geometric configuration. Following is the case with the equilateral triangular injector, and the jet penetration for the equilateral triangular injector seems to be the highest in the range
considered in the current study. The effect of the counter-rotating vortex pair on the flow field properties of the diamond- and equilateral triangular-shaped injector is more remarkable, and this can further prove that the counter-rotating vortex pair makes a great difference to the mixing improvement in the transverse injection flow field. 4. Conclusions In the current study, the influences of the molecular weight and the injector configuration on the transverse injection flow field properties have been explored numerically by the threedimensional Reynolds-averaged Navier–Stokes (RANS) equations coupled with the SST k–ω turbulence model, and the effect of the jet-to-crossflow pressure ratio has been considered as well. The numerical method has been validated against the available experimental data in the open literature. We have come to the following conclusions.
• The SST k–ω turbulence model is suitable to simulate the transverse injection flow field in the supersonic flow, espe-
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Fig. 5. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 17.72, hydrogen (left) and nitrogen (right).
cially for the case with the jet-to-crossflow pressure ratio being 10.29, and this is consistent with the phenomenon observed by Huang et al. [11]. The discrepancy between the predicted results and the experimental data may be induced by the incoming turbulence simulation. • The mixing efficiency for the case with the equilateral triangular injector is the highest, and following is the case with the diamond injector. This may be induced by the special vortex structures generated in the transverse injection flow field. At the same time, this may imply that the effect of the counterrotating vortex pair is remarkable. The square injector is not suitable to be chosen as an injection strategy for the case with the low and high jet-to-crossflow pressure ratio, namely 4.86 and 25.15 in the range considered in this article. • The lower jet-to-crossflow pressure ratio is better for the mixing process between the injectant and the supersonic
airstream, and the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the injector configuration. The injectant mole fraction decreases more rapidly with the increase of the streamwise distance for the case with the lower jet-to-crossflow pressure ratio. The jet plume for the case with the diamond injector spreads more rapidly in the spanwise direction irrespective of the injectant species. Acknowledgements
The authors would like to express their thanks for the support from the Hunan Provincial Natural Science Foundation of China (No. 12jj4047). The reviewers are thanked for their very constructive comments.
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Fig. 6. Injectant mole fraction contour comparisons for different injector configurations at the cross-sectional plane x = 350 mm with the jet-to-crossflow pressure ratio P j / P ∞ = 25.15, hydrogen (left) and nitrogen (right).
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Fig. 7. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 4.86.
Fig. 9. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 17.72.
Fig. 8. Hydrogen mole fraction contours for different injector configurations at the symmetrical plane with the jet-to-crossflow pressure ratio P j / P ∞ = 10.29.
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