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Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species
Acta Astronautica 105 (2014) 17–23
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species Li Yan, Wei Huang n, Tian-tian Zhang, Hao Li, Xiao-ting Yan Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, People's Republic of China
a r t i c l e i n f o
abstract
Article history: Received 23 June 2014 Received in revised form 23 July 2014 Accepted 20 August 2014 Available online 28 August 2014
The mixing and combustion process has an important impact on the engineering realization of the scramjet engine. The nonreacting and reacting flow fields in a transverse injection channel have been investigated numerically, and the predicted results have been compared with the available experimental data in the open literature, the wall pressure distributions, the separation length, as well as the penetration height. Further, the influences of the molecular weight of the fuel and the jet-to-crossflow pressure ratio on the wall pressure distribution have been studied. The obtained results show that the predicted results show reasonable agreement with the experimental data, and the variable trends of the penetration height and the separation distance are almost the same as those obtained in the experiment. The vapor pressure model is suitable to fit the relationship between the penetration height, the separation distance and the jet-tocrossflow pressure ratio. The combustion process mainly occurs upstream of the injection port, and it makes a great difference to the wall pressure distribution upstream of the injection port, especially when the jet-to-crossflow pressure ratio is large enough, namely 17.72 and 25.15 in the range considered in the current study. For hydrogen, the combustion downstream of the injection port occurs more intensively, and this may be induced by its smaller molecular weight. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Aerospace propulsion system Transverse jet Supersonic crossflow Molecular weight Combustion
1. Introduction With the breakthrough of the sonic barrier, the hypersonic vehicle technique has attracted considerable attention worldwide [1–3]. The mixing and combustion process between a sonic jet and a supersonic crossflow has been the subject of interest in the aerospace engineering [4–9], and it makes a great difference to the engineering realization of the scramjet
n Corresponding author. Tel.: þ86 731 84576447; fax: þ86 731 84576449. E-mail address: [email protected] (W. Huang).
http://dx.doi.org/10.1016/j.actaastro.2014.08.018 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
engine [10]. This is due to the extremely low fuel residence times in the combustor [11]. In order to prolong the time for the mixing process, a special fuel injection strategy has been proposed by the researchers, namely the inlet injection scheme [12–14]. Huang and Yan [15] have provided a detailed review on mixing techniques for transverse injection flow fields from four aspects, namely the jet-to-crossflow pressure ratio, the injector configuration, the number of injectors and the injection angle. Lee [16,17] has investigated the nonreacting and reacting properties of a dual transverse injection system numerically, and the influences of the jet-to-crossflow momentum flux ratio and the distance between injection ports
18
L. Yan et al. / Acta Astronautica 105 (2014) 17–23
on the mixing and combustion characteristics have been discussed comprehensively. The obtained results have shown that the dual injection system would bring better mixing and combustion performance but more total pressure loss than the single injection system, and there exists an optimal distance between injection ports for the dual injection system. Gao and Lee [18] have compared the mixing characteristics of different injection schemes for supersonic transverse jet, namely the slot, circular-hole and two-stage injections, and the influences of the injection angle, the injector diameter and number on the mixing performance have been discussed numerically. It is found that the circular-hole injection can induce higher mixing efficiency, and the twostage injection is superior to the single-stage one. In addition, the influence of injectant species on the mixing properties in the transverse injection system has been carried out numerically by Watanabe et al. [19], and four different kinds of fuel have been taken into account, namely hydrogen, helium, nitrogen and ethylene. However, the combustion properties have not been considered. To the authors' best knowledge, the nonreacting and reacting flow properties in the transverse injection system is not clear for the design of the scramjet engine, and comprehensive investigations still need to be performed to determine the mixing and combustion properties with different types of fuel in a relatively accurate supersonic combustor environment. In the current study, the nonreacting and reacting flow fields in a transverse injection channel have been investigated numerically, and the numerical results have been compared with the available experimental data in the open literature. At the same time, the influences of the molecular weight of the fuel and the jet-to-crossflow pressure ratio on the wall pressure distribution have been discussed as well, and the jet-to-crossflow pressure ratio has been set to be 4.86, 10.29, 17.72 and 25.15. 2. Physical model and numerical method 2.1. Physical model The experimental model, as studied by Aso et al. [20] is employed as the physical model to provide data for validation of the numerical method, and this is due to its good two-dimensional flow field structure. The distance from the plate leading edge to the centerline of the injection port l¼330.5 mm, slot width w¼1 mm, are taken according to the experimental conditions employed, and the distance from the centerline of the injection port to the exit boundary of the computational domain is prescribed as 221.5 mm. We deal with the gas phase only, and the processes of atomization and spray formation are not taken into consideration in this study because all the materials are injected preheated to elevated temperatures [21]. The supersonic airstream flows from left to right. At the same time, the air properties are set to be a Mach number M1 of 3.75, a static pressure P1 of 11,090 Pa and a static temperature T1 of 78.43 K. The jet flow Mach number Mj is set to be 1.0, with a static temperature Tj ¼249 K and a jet-tocrossflow pressure ratio Pj/P1 ¼4.86, 10.29, 17.72 and 25.15.
2.2. Numerical method In the current study, the two-dimensional Reynoldsaveraged Navier–Stokes (RANS) equations are solved along with density based (coupled) double precision solver of FLUENT [22], and the SST k-ω turbulence model has been employed to simulate the transverse injection flow field for its good prediction of mixing layers and jet flows [23,24]. The SST k-ω turbulence model is a combination of the Wilcox 1988 k-ω model in the near wall region and the standard k-ε model in the detached regions [25]. At the same time, the one-step hydrogen-air mechanism and the Finite-rate/Eddy-dissipation reaction model have been used to simulate the reacting flow field, and the rate parameters for the one-step hydrogen-air mechanism can be referred to Ref. [26]. The hydrogen-air mechanism has only a slight impact on the mean flow properties in the reacting flow field [27], especially the wall pressure distribution [28], and the Finite-rate/Eddy-dissipation model has been proved to be more accurate for the simulation of the reaction flow field than the Eddy-dissipation model [29]. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized in the numerical process [30], and the Courant–Friedrichs–Levy (CFL) number is kept at 0.5 with proper under-relaxation factors to ensure stability. The standard wall functions are used to model the near-wall region flow, and 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 due to 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 used. The convergence criterion is the same as that stated clearly in Ref. [31]. Meanwhile, the computational domain is structured by the commercial software Gambit, and the computational domain is multi-blocked in order to cluster the grid around the injection port. The computational domain is a rectangle surrounded by adiabatic walls at the bottom, supersonic inlet at the left boundary and sonic inlet at the injection port, an outlet at the right boundary and finally a symmetric condition on the upper boundary. The turbulent intensities for the air and fuel are both set to be 10%. The number of cells is 114,111, and the height of the first row of cells is set at a distance to the wall of 0.001 mm, which results in a value of y þ o 2.0 for all the flow field. y þ is a non-dimensional parameter defined by: yþ ¼
ρuτ yP μ
ð1Þ
here in, uτ is the friction velocity, yP is the distance from point P to the wall, ρ is the fluid density, and μ is the fluid viscosity at point P. 3. Code validation 3.1. Case 1 Fig. 1 displays the wall pressure distribution comparisons for the single transverse injection system employed
L. Yan et al. / Acta Astronautica 105 (2014) 17–23
by Aso et al. [20], and the predicted results show suitable agreement with the experimental data. The turbulence model validation process can refer to Ref. [31], and another transverse injection case without chemical reaction has been studied comprehensively in this reference. In Fig. 1, the wall pressure has been nondimensionalized by the static pressure of the supersonic crossflow, the notations “CFD” and “EXP” denote the results obtained by the numerical simulation and the ground experiment respectively, as well as those stated in Figs. 2 and 3. It is obvious that the numerical results upstream of the injection port are all overestimated expect the case with the jet-tocrossflow pressure ratio being 10.29, see Fig. 1(b), and the predicted results downstream of the injection port are all underestimated, especially the peak pressure downstream the injection port. This discrepancy may be induced by the two-dimensional assumption and the difference between the experimental setting and the boundary conditions employed in the numerical method. Figs. 2 and 3 show the separation distance and the penetration height comparisons for different jet-to-crossflow
19
pressure ratios, respectively, and it is clearly observed that the separation distances and the penetration heights are all overestimated. At the same time, the vapor pressure model is utilized to fit the numerical and experimental data, and the vapor pressure model is expressed as follows: y ¼ ea þ x þ c ln x b
ð2Þ
here in, a, b and c are the fitting coefficients, x is the jet-tocrossflow pressure ratio, and y represents the separation distance and the penetration height in Figs. 2 and 3, respectively. 3.2. Case 2 In this subsection, a cavity-based dual-mode scramjet combustor model has been utilized to validate the numerical approach employed in the current study, and it has been tested comprehensively by Micka [32]. Its geometric dimensions as well as the boundary conditions can be referred to Ref. [29]. Fig. 4 shows the wall static pressure comparison for this scramjet combustor, and the notation
Fig. 1. Wall pressure distribution comparisons of the transverse injection flow field with different jet-to-crossflow pressure ratios, (a) Pj/P1 ¼4.86; (b) Pj/P1 ¼10.29; (c) Pj/P1 ¼ 17.72 and (d) Pj/P1 ¼25.15.
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Fig. 2. Separation distance comparison for different jet-to-crossflow pressure ratios, the fitted equations for the CFD and EXP data are y ¼ e2:1017286 þ 0:30340268=x þ 0:58892184 ln x and y ¼ e1:8352443 2:7787906=x þ 0:59750753 ln x , respectively.
9 EXP CFD
8
Fig. 4. Wall static pressure comparison for a cavity-based dual-mode scramjet combustor.
the strong three-dimensional effect and the chemistry– turbulence interactions, and this information should be explored further in the near future. From the above validation, we could obtain that the numerical approach with 114,111 cells is suitable to simulate the current physical model.
Penetration Penetratio height (mm)
7
4. Result and discussion 6
In this section, the nonreacting and reacting flow fields have been analyzed comprehensively, and the fuels, namely hydrogen and methane, have been utilized to analyze the influence of the molecular weight on the transverse injection flow field. At the same time, the effect of the jet-to-crossflow pressure ratio on the wall pressure distribution has been analyzed as well.
5 4 3 2 1 0
4.1. Nonreacting flow field 0
5
10 0
15 5
20
25
30
Pj/P Fig. 3. Penetration height comparison for different jet-to-crossflow pressure ratios, the fitted equations for the CFD and EXP data are y ¼ e 0:4549081 þ 0:95631958=x þ 0:80751499 ln x and y ¼ e0:8395556 6:3651005=x þ 0:38225472 ln x , respectively.
“Exp” denotes the data obtained by the ground test experiment. In Fig. 4, the wall pressure has been nondimensionalized by the static pressure of the supersonic airstream. Three grid scales have been employed to carry out the grid independency analysis, namely the coarse grid (21,016 cells), the moderate grid (37,976 cells) and the refined grid (53,076 cells). It is clearly observed that the results obtained by the moderate and refined grids are nearly the same, and they are more accurate than that obtained by the coarse grid. The numerical results are all overestimated, and they show reasonable agreement with the experimental data. This discrepancy may be induced by
Fig. 5 depicts the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios in the nonreacting flow field, (a) hydrogen and (b) methane, and it is observed that the pressure rise occurs more upstream with the increase of the jet-to-crossflow pressure ratio for different molecular weights of fuel. This phenomenon is the same as that observed in Ref. [31]. However, the separation distance for the methane is shorter when the jet-to-crossflow pressure ratio is 25.15, see Fig. 5(b), and it may imply that the small molecular weight of the fuel can promote the mixing process between the fuel and the supersonic crossflow. The separation distance is induced by the separation shock wave, see Fig. 6, and the longer separation distance is beneficial to the generation of the larger upstream recirculation zone. The upstream recirculation zone can promote the mixing process between the fuel and the supersonic airstream with lower velocity. At the same time, the peak pressures for hydrogen injection are larger than those for methane injection. In Fig. 6, the separation shock wave is induced by the obstacle of the
L. Yan et al. / Acta Astronautica 105 (2014) 17–23
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Fig. 5. Wall pressure distribution comparisons for different jet-to-freestream pressure ratios in the nonreacting flow field, (a) hydrogen and (b) methane.
Fig. 6. Schematic diagram of the supersonic jet-to-crossflow strategy.
fuel injection, and it will bring some drag force when the jet-to-crossflow pressure ratio is high enough.
4.2. Reacting flow field Fig. 7 shows the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios in the reaction flow field, (a) hydrogen and (b) methane, and it is obvious that the combustion process makes a great difference to the rise of the peak pressure upstream of the injection port, especially when the jet-to-crossflow pressure ratio is large enough, namely Pj/P1 ¼17.72 and 25.15 in the range considered in the current study. Meanwhile, the separation distance induced by the combustion is shorter than that cased by the mixing, especially when Pj/P1 ¼17.72 and 25.15, see Fig. 7, and this may imply that the mixing zone upstream of the injection port decreases with the occurrence of the intensive combustion. The increase of the combustion efficiency may induce the decrease of the mixing efficiency in the local cross-sectional area.
In order to explore the effect of combustion process on the transverse injection flow properties, the combustion product distribution has been provided; see Fig. 8. Fig. 8 represents the H2O mass fraction contours for different fuels when the jet-to-crossflow pressure ratio is 25.15, and it is clearly observed that the H2O mainly occurs upstream of the injection port. This is due to the organization of the recirculation zone where the fuel and air can be premixed partially at low velocities, and the recirculation zone is formed upstream of the jet exit because of the strong interaction between the shock wave and the boundary layer, see Fig. 6. This region is very important owing to its flameholding capability in combusting situations. At the same time, it is observed that the combustion process takes place more intensively downstream of the injection port when the fuel is hydrogen, see Fig. 8(a), and this induces a large wall pressure, see Fig. 7(a). This is induced by its smaller molecular weight, and it implies that the hydrogen is the most promising fuel for the hypersonic propulsion system [33,34]. The deflagrationto-detonation transition is out of the scope in the current
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Fig. 7. Wall pressure distribution comparisons for different jet-to-freestream pressure ratios in the reacting flow field, (a) hydrogen and (b) methane.
Fig. 8. H2O mass fraction contours for different fuels when the jet-to-freestream pressure ratio is 25.15, (a) hydrogen and (b) methane.
study; thus it has not been discussed, and for its deep information, refer to Ref. [35].
Due to the strong three-dimensional effect and the
5. Conclusions In the current study, the nonreacting and reacting flow fields in a transverse injection channel in supersonic crossflows have been investigated numerically, and the influences of the jet-to-crossflow pressure ratio and the molecular weight on the wall pressure distribution have been studied as well. In addition, the predicted results have been compared with the available experimental data in order to validate the numerical method employed in the current study, namely from the aspects of wall pressure distribution, separation distance and penetration height, as well as a typical dual-mode scramjet combustor. We have come to the following conclusions:
The predicted results show suitable agreement with the available experimental data in the nonreacting case, and the discrepancy may be induced mainly by the two-dimensional assumption. At the same time, the variable trends of the penetration height and the separation distance are nearly the same as those obtained in the experiment, and the vapor pressure model is suitable to fit the relationship between the penetration height, the separation distance and the jetto-crossflow pressure ratio.
chemical-turbulent interaction, the predicted results for the reacting case are overestimated, and they show reasonable agreement with the experimental data obtained by Micka [32]. The further information should be explored in the near future. The combustion process has a great impact on the wall pressure distribution upstream of the injection port, the increase of the combustion efficiency may induce the decrease of the mixing efficiency in the local crosssectional area. The combustion process mainly occurs upstream of the injection port for different kinds of fuel, and it occurs more intensively downstream of the injection port for the hydrogen due to its smaller molecular weight.
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No. 11272351) and the Hunan Provincial Natural Science Foundation of China (No. 12jj4047). References [1] W. Huang, S.B. Li, J. Liu, Z.G. Wang, Investigation on high angle of attack characteristics of hypersonic space vehicle, Sci. China Technol. Sci. 55 (5) (2012) 1437–1442. [2] G. Pezzella, Aerodynamic and aerothermodynamic trade-off analysis of a small hypersonic flying test bed, Acta Astronaut. 69 (2011) 209–222.
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[20] Aso S., Okuyama S., Kawai M., Ando Y., Experimental study on mixing phenomena in supersonic flows with slot injection, in: Proceedings of the 29th Aerospace Sciences Meeting, Reno, Nevada, AIAA, 1991, 91-0016. [21] N.N. Smirnov, V.B. Betelin, R.M. Shagaliev, V.F. Nikitin, I.M. Belyakov, Y.N. Deryuguin, S.V. Aksenov, D.A. Korchazhkin, Hydrogen fuel rocket engines simulation using LOGOS code, Int. J. Hydrog. Energy 39 (2014) 10748–10756. [22] Fluent Inc, Fluent 6.3 User's GuideFluent Inc., Lebanon, NH, 2006. [23] Bardina J.E., Huang P.G., Coakly T.J., Turbulence modeling validation, in: Proceedings of the 28th Fluid Dynamics Conference, Snowmass Village, CO, AIAA, 1997, 1997-2121. [24] W.Y.K. Chan, P.A. Jacobs, D.J. Mee, Suitability of the k-ω turbulence model for scramjet flowfield simulations, Int. J. Numer. Methods Fluids 70 (2012) 493–514. [25] E.M. Ivanova, B.E. Noll, M. Aigner, A numerical study on the turbulent Schmidt numbers in a jet in crossflow, J. Eng. Gas Turbines Power – Trans. ASME 135 (2013) 01150. [26] 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. [27] N.N. Smirnov, V.F. Nikitin, Modeling and simulation of hydrogen combustion in engines, Int. J. Hydrog. Energy 39 (2014) 1122–1136. [28] W. Huang, Z.G. Wang, S.B. Li, W.D. Liu, Influences of H2O mass fraction and chemical kinetics mechanism on the turbulent diffusion combustion of H2–O2 in supersonic flows, Acta Astronaut. 76 (2012) 51–59. [29] W. Huang, Z.G. Wang, L. Yan, S.B. Li, D.B. Ingham, Variation of inlet boundary conditions on the combustion characteristics of a typical cavity-based scramjet combustor, Proc. Inst. Mech. Eng., G:J. Aerosp. Eng. 228 (4) (2014) 627–638. [30] E. Erdem, K. Kontis, Numerical and experimental investigation of transverse injection flows, Shock Waves 20 (2010) 103–118. [31] 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. [32] D.J. Micka, Combustion stabilization, structure, and spreading in a laboratory dual-mode scramjet combustor, (Doctor dissertation) University of Michigan, USA, 2010. [33] S.M. Rainey, T.N. Veziroglu, Computer modeling and comparison of hydrogen-fueled and methane-fueled hypersonic vehicles, Int. J. Hydrog. Energy 17 (1) (1992) 53–61. [34] D. Cecere, E. Giacomazzi, A. Ingenito, A review on hydrogen industrial aerospace applications, Int. J. Hydrog. Energy 39 (2014) 10731–10747. [35] N.N. Smirnov, V.F. Nikitin, S.A. Shurekhdeli, Investigation of selfsustaining waves in metastable systems: deflagration-to-detonation transition, J. Propuls. Power 25 (3) (2009) 593–608.
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species Li Yan, Wei Huang n, Tian-tian Zhang, Hao Li, Xiao-ting Yan Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, People's Republic of China
a r t i c l e i n f o
abstract
Article history: Received 23 June 2014 Received in revised form 23 July 2014 Accepted 20 August 2014 Available online 28 August 2014
The mixing and combustion process has an important impact on the engineering realization of the scramjet engine. The nonreacting and reacting flow fields in a transverse injection channel have been investigated numerically, and the predicted results have been compared with the available experimental data in the open literature, the wall pressure distributions, the separation length, as well as the penetration height. Further, the influences of the molecular weight of the fuel and the jet-to-crossflow pressure ratio on the wall pressure distribution have been studied. The obtained results show that the predicted results show reasonable agreement with the experimental data, and the variable trends of the penetration height and the separation distance are almost the same as those obtained in the experiment. The vapor pressure model is suitable to fit the relationship between the penetration height, the separation distance and the jet-tocrossflow pressure ratio. The combustion process mainly occurs upstream of the injection port, and it makes a great difference to the wall pressure distribution upstream of the injection port, especially when the jet-to-crossflow pressure ratio is large enough, namely 17.72 and 25.15 in the range considered in the current study. For hydrogen, the combustion downstream of the injection port occurs more intensively, and this may be induced by its smaller molecular weight. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Aerospace propulsion system Transverse jet Supersonic crossflow Molecular weight Combustion
1. Introduction With the breakthrough of the sonic barrier, the hypersonic vehicle technique has attracted considerable attention worldwide [1–3]. The mixing and combustion process between a sonic jet and a supersonic crossflow has been the subject of interest in the aerospace engineering [4–9], and it makes a great difference to the engineering realization of the scramjet
n Corresponding author. Tel.: þ86 731 84576447; fax: þ86 731 84576449. E-mail address: [email protected] (W. Huang).
http://dx.doi.org/10.1016/j.actaastro.2014.08.018 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
engine [10]. This is due to the extremely low fuel residence times in the combustor [11]. In order to prolong the time for the mixing process, a special fuel injection strategy has been proposed by the researchers, namely the inlet injection scheme [12–14]. Huang and Yan [15] have provided a detailed review on mixing techniques for transverse injection flow fields from four aspects, namely the jet-to-crossflow pressure ratio, the injector configuration, the number of injectors and the injection angle. Lee [16,17] has investigated the nonreacting and reacting properties of a dual transverse injection system numerically, and the influences of the jet-to-crossflow momentum flux ratio and the distance between injection ports
18
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on the mixing and combustion characteristics have been discussed comprehensively. The obtained results have shown that the dual injection system would bring better mixing and combustion performance but more total pressure loss than the single injection system, and there exists an optimal distance between injection ports for the dual injection system. Gao and Lee [18] have compared the mixing characteristics of different injection schemes for supersonic transverse jet, namely the slot, circular-hole and two-stage injections, and the influences of the injection angle, the injector diameter and number on the mixing performance have been discussed numerically. It is found that the circular-hole injection can induce higher mixing efficiency, and the twostage injection is superior to the single-stage one. In addition, the influence of injectant species on the mixing properties in the transverse injection system has been carried out numerically by Watanabe et al. [19], and four different kinds of fuel have been taken into account, namely hydrogen, helium, nitrogen and ethylene. However, the combustion properties have not been considered. To the authors' best knowledge, the nonreacting and reacting flow properties in the transverse injection system is not clear for the design of the scramjet engine, and comprehensive investigations still need to be performed to determine the mixing and combustion properties with different types of fuel in a relatively accurate supersonic combustor environment. In the current study, the nonreacting and reacting flow fields in a transverse injection channel have been investigated numerically, and the numerical results have been compared with the available experimental data in the open literature. At the same time, the influences of the molecular weight of the fuel and the jet-to-crossflow pressure ratio on the wall pressure distribution have been discussed as well, and the jet-to-crossflow pressure ratio has been set to be 4.86, 10.29, 17.72 and 25.15. 2. Physical model and numerical method 2.1. Physical model The experimental model, as studied by Aso et al. [20] is employed as the physical model to provide data for validation of the numerical method, and this is due to its good two-dimensional flow field structure. The distance from the plate leading edge to the centerline of the injection port l¼330.5 mm, slot width w¼1 mm, are taken according to the experimental conditions employed, and the distance from the centerline of the injection port to the exit boundary of the computational domain is prescribed as 221.5 mm. We deal with the gas phase only, and the processes of atomization and spray formation are not taken into consideration in this study because all the materials are injected preheated to elevated temperatures [21]. The supersonic airstream flows from left to right. At the same time, the air properties are set to be a Mach number M1 of 3.75, a static pressure P1 of 11,090 Pa and a static temperature T1 of 78.43 K. The jet flow Mach number Mj is set to be 1.0, with a static temperature Tj ¼249 K and a jet-tocrossflow pressure ratio Pj/P1 ¼4.86, 10.29, 17.72 and 25.15.
2.2. Numerical method In the current study, the two-dimensional Reynoldsaveraged Navier–Stokes (RANS) equations are solved along with density based (coupled) double precision solver of FLUENT [22], and the SST k-ω turbulence model has been employed to simulate the transverse injection flow field for its good prediction of mixing layers and jet flows [23,24]. The SST k-ω turbulence model is a combination of the Wilcox 1988 k-ω model in the near wall region and the standard k-ε model in the detached regions [25]. At the same time, the one-step hydrogen-air mechanism and the Finite-rate/Eddy-dissipation reaction model have been used to simulate the reacting flow field, and the rate parameters for the one-step hydrogen-air mechanism can be referred to Ref. [26]. The hydrogen-air mechanism has only a slight impact on the mean flow properties in the reacting flow field [27], especially the wall pressure distribution [28], and the Finite-rate/Eddy-dissipation model has been proved to be more accurate for the simulation of the reaction flow field than the Eddy-dissipation model [29]. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized in the numerical process [30], and the Courant–Friedrichs–Levy (CFL) number is kept at 0.5 with proper under-relaxation factors to ensure stability. The standard wall functions are used to model the near-wall region flow, and 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 due to 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 used. The convergence criterion is the same as that stated clearly in Ref. [31]. Meanwhile, the computational domain is structured by the commercial software Gambit, and the computational domain is multi-blocked in order to cluster the grid around the injection port. The computational domain is a rectangle surrounded by adiabatic walls at the bottom, supersonic inlet at the left boundary and sonic inlet at the injection port, an outlet at the right boundary and finally a symmetric condition on the upper boundary. The turbulent intensities for the air and fuel are both set to be 10%. The number of cells is 114,111, and the height of the first row of cells is set at a distance to the wall of 0.001 mm, which results in a value of y þ o 2.0 for all the flow field. y þ is a non-dimensional parameter defined by: yþ ¼
ρuτ yP μ
ð1Þ
here in, uτ is the friction velocity, yP is the distance from point P to the wall, ρ is the fluid density, and μ is the fluid viscosity at point P. 3. Code validation 3.1. Case 1 Fig. 1 displays the wall pressure distribution comparisons for the single transverse injection system employed
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by Aso et al. [20], and the predicted results show suitable agreement with the experimental data. The turbulence model validation process can refer to Ref. [31], and another transverse injection case without chemical reaction has been studied comprehensively in this reference. In Fig. 1, the wall pressure has been nondimensionalized by the static pressure of the supersonic crossflow, the notations “CFD” and “EXP” denote the results obtained by the numerical simulation and the ground experiment respectively, as well as those stated in Figs. 2 and 3. It is obvious that the numerical results upstream of the injection port are all overestimated expect the case with the jet-tocrossflow pressure ratio being 10.29, see Fig. 1(b), and the predicted results downstream of the injection port are all underestimated, especially the peak pressure downstream the injection port. This discrepancy may be induced by the two-dimensional assumption and the difference between the experimental setting and the boundary conditions employed in the numerical method. Figs. 2 and 3 show the separation distance and the penetration height comparisons for different jet-to-crossflow
19
pressure ratios, respectively, and it is clearly observed that the separation distances and the penetration heights are all overestimated. At the same time, the vapor pressure model is utilized to fit the numerical and experimental data, and the vapor pressure model is expressed as follows: y ¼ ea þ x þ c ln x b
ð2Þ
here in, a, b and c are the fitting coefficients, x is the jet-tocrossflow pressure ratio, and y represents the separation distance and the penetration height in Figs. 2 and 3, respectively. 3.2. Case 2 In this subsection, a cavity-based dual-mode scramjet combustor model has been utilized to validate the numerical approach employed in the current study, and it has been tested comprehensively by Micka [32]. Its geometric dimensions as well as the boundary conditions can be referred to Ref. [29]. Fig. 4 shows the wall static pressure comparison for this scramjet combustor, and the notation
Fig. 1. Wall pressure distribution comparisons of the transverse injection flow field with different jet-to-crossflow pressure ratios, (a) Pj/P1 ¼4.86; (b) Pj/P1 ¼10.29; (c) Pj/P1 ¼ 17.72 and (d) Pj/P1 ¼25.15.
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Fig. 2. Separation distance comparison for different jet-to-crossflow pressure ratios, the fitted equations for the CFD and EXP data are y ¼ e2:1017286 þ 0:30340268=x þ 0:58892184 ln x and y ¼ e1:8352443 2:7787906=x þ 0:59750753 ln x , respectively.
9 EXP CFD
8
Fig. 4. Wall static pressure comparison for a cavity-based dual-mode scramjet combustor.
the strong three-dimensional effect and the chemistry– turbulence interactions, and this information should be explored further in the near future. From the above validation, we could obtain that the numerical approach with 114,111 cells is suitable to simulate the current physical model.
Penetration Penetratio height (mm)
7
4. Result and discussion 6
In this section, the nonreacting and reacting flow fields have been analyzed comprehensively, and the fuels, namely hydrogen and methane, have been utilized to analyze the influence of the molecular weight on the transverse injection flow field. At the same time, the effect of the jet-to-crossflow pressure ratio on the wall pressure distribution has been analyzed as well.
5 4 3 2 1 0
4.1. Nonreacting flow field 0
5
10 0
15 5
20
25
30
Pj/P Fig. 3. Penetration height comparison for different jet-to-crossflow pressure ratios, the fitted equations for the CFD and EXP data are y ¼ e 0:4549081 þ 0:95631958=x þ 0:80751499 ln x and y ¼ e0:8395556 6:3651005=x þ 0:38225472 ln x , respectively.
“Exp” denotes the data obtained by the ground test experiment. In Fig. 4, the wall pressure has been nondimensionalized by the static pressure of the supersonic airstream. Three grid scales have been employed to carry out the grid independency analysis, namely the coarse grid (21,016 cells), the moderate grid (37,976 cells) and the refined grid (53,076 cells). It is clearly observed that the results obtained by the moderate and refined grids are nearly the same, and they are more accurate than that obtained by the coarse grid. The numerical results are all overestimated, and they show reasonable agreement with the experimental data. This discrepancy may be induced by
Fig. 5 depicts the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios in the nonreacting flow field, (a) hydrogen and (b) methane, and it is observed that the pressure rise occurs more upstream with the increase of the jet-to-crossflow pressure ratio for different molecular weights of fuel. This phenomenon is the same as that observed in Ref. [31]. However, the separation distance for the methane is shorter when the jet-to-crossflow pressure ratio is 25.15, see Fig. 5(b), and it may imply that the small molecular weight of the fuel can promote the mixing process between the fuel and the supersonic crossflow. The separation distance is induced by the separation shock wave, see Fig. 6, and the longer separation distance is beneficial to the generation of the larger upstream recirculation zone. The upstream recirculation zone can promote the mixing process between the fuel and the supersonic airstream with lower velocity. At the same time, the peak pressures for hydrogen injection are larger than those for methane injection. In Fig. 6, the separation shock wave is induced by the obstacle of the
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Fig. 5. Wall pressure distribution comparisons for different jet-to-freestream pressure ratios in the nonreacting flow field, (a) hydrogen and (b) methane.
Fig. 6. Schematic diagram of the supersonic jet-to-crossflow strategy.
fuel injection, and it will bring some drag force when the jet-to-crossflow pressure ratio is high enough.
4.2. Reacting flow field Fig. 7 shows the wall pressure distribution comparisons for different jet-to-crossflow pressure ratios in the reaction flow field, (a) hydrogen and (b) methane, and it is obvious that the combustion process makes a great difference to the rise of the peak pressure upstream of the injection port, especially when the jet-to-crossflow pressure ratio is large enough, namely Pj/P1 ¼17.72 and 25.15 in the range considered in the current study. Meanwhile, the separation distance induced by the combustion is shorter than that cased by the mixing, especially when Pj/P1 ¼17.72 and 25.15, see Fig. 7, and this may imply that the mixing zone upstream of the injection port decreases with the occurrence of the intensive combustion. The increase of the combustion efficiency may induce the decrease of the mixing efficiency in the local cross-sectional area.
In order to explore the effect of combustion process on the transverse injection flow properties, the combustion product distribution has been provided; see Fig. 8. Fig. 8 represents the H2O mass fraction contours for different fuels when the jet-to-crossflow pressure ratio is 25.15, and it is clearly observed that the H2O mainly occurs upstream of the injection port. This is due to the organization of the recirculation zone where the fuel and air can be premixed partially at low velocities, and the recirculation zone is formed upstream of the jet exit because of the strong interaction between the shock wave and the boundary layer, see Fig. 6. This region is very important owing to its flameholding capability in combusting situations. At the same time, it is observed that the combustion process takes place more intensively downstream of the injection port when the fuel is hydrogen, see Fig. 8(a), and this induces a large wall pressure, see Fig. 7(a). This is induced by its smaller molecular weight, and it implies that the hydrogen is the most promising fuel for the hypersonic propulsion system [33,34]. The deflagrationto-detonation transition is out of the scope in the current
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Fig. 7. Wall pressure distribution comparisons for different jet-to-freestream pressure ratios in the reacting flow field, (a) hydrogen and (b) methane.
Fig. 8. H2O mass fraction contours for different fuels when the jet-to-freestream pressure ratio is 25.15, (a) hydrogen and (b) methane.
study; thus it has not been discussed, and for its deep information, refer to Ref. [35].
Due to the strong three-dimensional effect and the
5. Conclusions In the current study, the nonreacting and reacting flow fields in a transverse injection channel in supersonic crossflows have been investigated numerically, and the influences of the jet-to-crossflow pressure ratio and the molecular weight on the wall pressure distribution have been studied as well. In addition, the predicted results have been compared with the available experimental data in order to validate the numerical method employed in the current study, namely from the aspects of wall pressure distribution, separation distance and penetration height, as well as a typical dual-mode scramjet combustor. We have come to the following conclusions:
The predicted results show suitable agreement with the available experimental data in the nonreacting case, and the discrepancy may be induced mainly by the two-dimensional assumption. At the same time, the variable trends of the penetration height and the separation distance are nearly the same as those obtained in the experiment, and the vapor pressure model is suitable to fit the relationship between the penetration height, the separation distance and the jetto-crossflow pressure ratio.
chemical-turbulent interaction, the predicted results for the reacting case are overestimated, and they show reasonable agreement with the experimental data obtained by Micka [32]. The further information should be explored in the near future. The combustion process has a great impact on the wall pressure distribution upstream of the injection port, the increase of the combustion efficiency may induce the decrease of the mixing efficiency in the local crosssectional area. The combustion process mainly occurs upstream of the injection port for different kinds of fuel, and it occurs more intensively downstream of the injection port for the hydrogen due to its smaller molecular weight.
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No. 11272351) and the Hunan Provincial Natural Science Foundation of China (No. 12jj4047). References [1] W. Huang, S.B. Li, J. Liu, Z.G. Wang, Investigation on high angle of attack characteristics of hypersonic space vehicle, Sci. China Technol. Sci. 55 (5) (2012) 1437–1442. [2] G. Pezzella, Aerodynamic and aerothermodynamic trade-off analysis of a small hypersonic flying test bed, Acta Astronaut. 69 (2011) 209–222.
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