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Influence of jet-to-crossflow pressure ratio on nonreacting and reacting processes in a scramjet combustor with backward-facing steps
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Influence of jet-to-crossflow pressure ratio on nonreacting and reacting processes in a scramjet combustor with backward-facing steps Wei Huang*, Liang Jin, Li Yan, Jian-guo Tan Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
article info
abstract
Article history:
The jet-to-crossflow pressure ratio has a large impact on the combustion mode transition
Received 9 September 2014
in the scramjet engine, and this information needs to be explored comprehensively. The
Received in revised form
effect of the jet-to-crossflow pressure ratio on the mixing and combustion processes in a
6 October 2014
backward-facing step combustor has been investigated numerically, and two similar cases
Accepted 16 October 2014
have been utilized to validate the numerical approaches employed. The obtained results
Available online 7 November 2014
show that the wall pressure distribution for the nonreacting flow field has been predicted well, and the peak pressures are all a bit underestimated. However, the predicted wall
Keywords:
pressure distribution for the reacting flow field does not match well with the experimental
Aerospace propulsion system
data, and it is overestimated. When the hydrogen is injected only from the bottom wall of
Scramjet combustor
the combustor, the mixing efficiency decreases with the increase of the jet-to-crossflow
Backward-facing step
pressure ratio irrespective of the nonreacting or reacting flow field. When the hydrogen
Jet-to-crossflow pressure ratio
is injected simultaneously from the top and bottom walls, the separation shock wave is
Combustion
pushed forward to the entrance of the combustor, and it varies from an oblique one to a
Mode transition
normal one. This means that the jet-to-crossflow pressure ratio has a great impact on the combustion mode transition for the scramjet engine, and the stable ramjet/scramjet mode transition can be obtained by controlling the fuel injection scheme. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction From combustion point of view, hydrogen owns superior characteristics to any other hydrocarbon fuel in terms of ignitability, low ignition delay, and higher flame stability [1]. There inherent advantages turn it as the only potential fuel for scramjet engines. However, its low molecular weight can not promote the mixing and combustion process in
supersonic flows efficiently, and thus, some flameholding mechanisms have been proposed by the researchers, i.e. the wall-stalled cavity, the backward-facing step, the strut, the ramp. Due to its simple configuration, the backward-facing step has been widely employed in the flowpath of the scramjet engine [2e5], and the laminar flow field properties in the backward-facing step has been visualized by using the nanotracer planar laser scattering (NPLS) technique [6].
* Corresponding author. Tel.: þ86 731 84576447; fax: þ86 731 84576449. E-mail address: [email protected] (W. Huang). http://dx.doi.org/10.1016/j.ijhydene.2014.10.073 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 2 1 2 4 2 e2 1 2 5 0
The shadowgraphs, broadband flame emission photographs, and planar laser-induced OH fluorescence images have been combined by Abbitt III et al. [7] to investigate the influence of the chemical reaction on the supersonic reacting flow field with the hydrogen injected behind a rearwardfacing step, and this is the first complete flow visualization study for the hydrogen-air supersonic combustor. Karagozian et al. [8] have investigated the jet penetration and jet structure in a rearward-facing step combustor experimentally and theoretically, and the transverse gas jet has been injected behind the rearward-facing step as well. However, in their study, the jet-to-crossflow pressure ratio has not been varied, and its effect on the combustion process has not been studied as well. Altay et al. [9] have analyzed the influence of the equivalence ratio oscillation on combustion dynamics of propane-air flames in a backward-facing step combustor by varying the fuel injector location. They have found that the combustion dynamics are primarily induced by the flameevortex interactions, and the equivalence ratio oscillations own secondary effects on the dynamics. However, the effect of the equivalence ratio on the flow field properties has not been explored completely. From the above literature reviewed, the effect of the jet-tocrossflow pressure ratio on the flow field properties of the backward-facing step combustor has rarely been analyzed, and it has a large impact on the combustion mode transition in the scramjet engine. Therefore, this information needs to be explored further. In the current study, the effect of jet-to-crossflow pressure ratio on mixing and combustion processes in a twodimensional scramjet combustor has been investigated numerically, and the ram-to-scram mode transition process induced by the jet-to-crossflow pressure ratio has been analyzed as well. The jet-to-crossflow pressure ratio has been set to be 16.43, 25.15, 42.79 and 63.5.
Physical model and numerical method Physical model The combustor model with backward-facing steps studied in the present article is shown in Fig. 1, and it consists of an isolator, a constant area combustor and a diverging area combustor. The fuel is injected to the supersonic crossflow vertically 594.36 mm away from the entrance of the combustor. This means that the fuel injectors are located in
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the isolator [10], and the length of the isolator is 677.418 mm. The width of the injection port is 3.9624 mm, and the hydrogen is injected only from the bottom wall or from both top and bottom walls of the combustor. There is a backwardfacing step exist on the top and bottom walls respectively, and its height is 3.302 mm. The length of the combustor with the constant area is 551.18 mm, see Fig. 1, and that of the diverging area combustor is 1063.752 mm. The origin of the coordinate system is set at the entrance of the combustor, see Fig. 1. The air flows from left to right with the Mach number being 3.3, the static pressure being 48,166 Pa and the total temperature being 2333.333 K. The hydrogen is injected into the core flow with the sonic velocity and the total temperature being 277.7778 K. The jet-to-crossflow pressure ratio is set to be 16.43, 25.15, 42.79 and 63.5.
Numerical approach The two-dimensional Reynolds-averaged NaviereStokes (RANS) equations and the two equations SST k-u turbulence model has been utilized to simulate the combustor with backward-facing steps numerically, and the equations are solved along with density based (coupled) double precision solver of FLUENT [11]. The two-dimensional assumption may result in the inadequate result for the intensity of the shock wave, as well as the shock wave/boundary layer interaction [12]. However, it would quicken the decision process for the overall design of the scramjet combustor, and thus, it has been employed as the basis approach for the flowpath design of the scramjet engine. The Finite-Rate/Eddy-Dissipation model and the one step hydrogen-air mechanism have been used to model the combustion process in the scramjet engine, and they have been proved to be suitable for the combustion simulation [13,14]. The RANS method is the efficient and rapid approach to receive the mean flow properties for the further mixing and combustion optimization in the supersonic flow [15]. The SST k-u turbulence model is a combination of the Wilcox 1988 k-u model in the near wall region and the standard k-ε model in the detached regions [16], and it has been proved to be more suitable to capture the turbulent generating mechanisms induced by the shock wave and the boundary layer in the scramjet engine [17,18], as well as the flow field properties in jet flows [18,19]. Thus, it has been employed to couple with the two-dimensional Reynolds-averaged NaviereStokes (RANS) equations to simulate the flow field in the scramjet combustor with backward-facing steps, and the Reynolds-averaged NaviereStokes equations have been utilized due to its lower
Fig. 1 e Schematic diagram of the scramjet combustor with backward-facing steps employed in the current study.
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Fig. 2 e Schematic diagram of a nonreacting laboratory scale scramjet model (unit: mm).
residuals reach their minimum values after falling for more than three orders of magnitude. An additional convergence criterion enforced in this current study requires the difference between the computed inflow and outflow mass flux to drop below 1% of the total mass flow. The computational domain is structured by the commercial software Gambit, and the grid is multi-blocked and highly concentrated close to the wall surfaces, the injector and the backward-facing step in order to ensure the accuracy of the numerical simulation. The height of the first row of cells is set at a distance of 0.001 mm for the walls, and the total number of cells is 176,391. This is enough for the current study from the information obtained in the following section. The maximum of yþ is less than 20.
Code validation
Fig. 3 e Wall static pressure comparison for a nonreacting laboratory scale scramjet model.
computational cost compared with the other numerical methods, i.e. large eddy simulation and direct numerical simulation. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting approach (AUSM) flux vector splitting is employed to quicken the convergence speed, and the CouranteFriedrichseLevy (CFL) number is kept at 0.5 with proper under-relaxation factors to ensure stability [20]. The no-slip conditions are assumed for the walls of the combustor. 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 solutions can be considered as converged when the
In this section, two typical cases have been employed to validate the numerical approaches used in the current study, namely a laboratory scale scramjet model for the HyShot free flight scramjet program (Case 1) [21] and a typical cavity-based dual-mode scramjet combustor investigated experimentally by Micka (Case 2) [22], and the validate process for the single transverse injection flow field can be referred to Refs. [23,24]. The validate cases employed here own the similar configuration as that studied in this article.
Case 1 In Case 1, the inlet section of the scramjet model is 180 mm long. The upper and lower walls of its forward portion consist of ramps formed by two sharp nosed flat plates each at 9 incidence to the oncoming flow, see Fig. 2, and Fig. 2 depicts the schematic diagram of the laboratory scale scramjet model. 135 mm downstream from the leading edge, the angle of incidence of the plate surface varies abruptly to 12 creating a compression corner. The height of the 250 mm long combustor is 24 mm for the present paper. Downstream of the
Fig. 4 e Schematic diagram of a typical cavity-based dual-mode scramjet combustor [13].
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(64,337 cells), and it is clearly observed that the grid scale has only a slight impact on the wall static pressure distribution for the nonreacting scramjet model, see Fig. 3, and the peak pressure is a bit underestimated. This implies that the numerical method employed in the current study can be utilized with confidence to simulate the nonreacting flow field of the scramjet engine.
Case 2
Fig. 5 e Wall static pressure comparison for a typical cavity-based dual-mode scramjet combustor.
combustor, the upper and lower walls of the model diverge at angles of ±9 to the horizontal to form the nozzle, and the length of the nozzle is 295 mm. Due to its symmetry, only half of the flow field has been simulated. Three grid scales have been used to carry out the grid independency analysis, namely the coarse grid (31,997 cells), the moderate grid (48,167 cells) and the refined grid
In Case 2, the scramjet model includes a constant-area isolator and a combustor, see Fig. 4. The constant-area isolator owns a height of 25.4 mm, and it extends 358 mm from the entrance to the center of the fuel injector. The constant-area isolator is followed by a cavity flameholder, and its length and depth are 50.8 mm and 12.7 mm, respectively. The room-temperature hydrogen is injected sonically through a single port located 44.5 mm upstream of the leading edge of the cavity, and the width of the injector is 2.49 mm. There is a 349 mm long, 4 diverging section downstream of the trailing edge of the cavity. The air flows into the scramjet model from left to right with the Mach number being 2.2, the static pressure being 261 kPa and the static temperature being 1280 K. The hydrogen is injected at Mach 1, with its static pressure and static temperature being 438 kPa and 248 K, respectively. The mass fractions for O2, N2 and H2O in the air are 0.251, 0.611 and 0.138, respectively. Three grid scales have been utilized 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
Fig. 6 e Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/ P∞ ¼ 63.5.
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Result and discussion In order to evaluate the nonreacting and reacting processes in the scramjet combustor, the mixing efficiency, which is defined as follows, is taken into consideration in this paper, and it means the ratio of the mixed mass flow rate of hydrogen to that of the total one at the local plane [23]. Z areact rudA Z arudA
(1)
a; a astoic að1 aÞ=ð1 astoic Þ; a > astoic
(2)
4¼
mfuel;mixed
mfuel;total
¼
Herein areact ¼
Fig. 7 e Mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor.
cells), and it is observed that when the number of cells is large enough, namely the moderate grid employed in this article, the gird scale makes only a slight difference to the wall static pressure distribution, especially on the floor face of the cavity, see Fig. 5. The static pressures on the floor face and downstream of the trailing edge of the cavity are all overestimated, and this may be induced by the two-dimensional assumption.
where a is the injectant mass fraction, areact is the injectant fraction mixed in a proportion that can react, astoic is the injectant stoichiometric mass fraction, mfuel;mixed is the mixed injectant mass flow and mfuel;total is the total injectant flow rate. r and u are the local density and velocity respectively, and A is the cross section of the axial station where mixing is evaluated.
Nonreacting process Fig. 6 shows the Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor. It is clearly observed that the separation shock wave angle upstream of the injector increases with the
Fig. 8 e Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/ P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 2 1 2 4 2 e2 1 2 5 0
Fig. 9 e Mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor.
increase of the jet-to-crossflow pressure ratio, and the intensity of the upstream separation shock wave increases correspondingly. Due to the strong interaction between the upstream separation shock wave and the boundary layer on the top wall of the scramjet combustor, the phenomenon of the boundary layer separation occurs, and a recirculation zone
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with low velocity is formed on the top wall, see Fig. 6(c) and (d). At the same time, the recirculation zone enlarges and moves upstream with the increase of the jet-to-crossflow pressure ratio. However, the recirculation zone induced by the boundary layer separation is invisible in Fig. 6(a) and (b). Fig. 7 represents the mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor. It is obvious that the case with the smaller jet-to-crossflow pressure ratio owns the higher mixing efficiency, and this conclusion is consistent with that obtained in the three-dimensional transverse injection flow field [23]. This implies that the backward-facing steps exist can not vary the sequence of mixing efficiency in the current study, and this may be induced by the smaller dimensions of the backwardward steps compared with those of the scramjet model. In Fig. 7, it is obvious that the mixing efficiency increases monotonically with the increase of the horizontal distance irrespective of the value of the jet-to-crossflow pressure ratio. The maximum mixing efficiency is nearly 50%, and it occurs near the exit of the scramjet model for the case with the jet-tocrossflow pressure ratio being 16.43. In order to explore the effect of the transverse injection scheme on the flow field properties further, the hydrogen is injected from both the top and bottom walls of the scramjet model, and the recirculation zone appears on both the top and bottom walls even for the case with the smallest jet-tocrossflow pressure ratio, see Fig. 8(a). Fig. 8 depicts the Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected simultaneously from the top and bottom walls. Due to the diverging angle on the bottom wall, the size of the
Fig. 10 e Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
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enough, see Fig. 8(c). Its value is 42.79 in the range considered in the current study. When the jet-to-crossflow pressure ratio increases further, namely 63.5 in the present study, the separation shock waves generated upstream of the injector can not intersect any longer, and a normal shock wave is obtained in the core flow of the scramjet model, see Fig. 8(d). When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the mixing efficiency increases, and the largest mixing efficiency is over 60%, see Fig. 9.
Reacting process
Fig. 11 e Mixing efficiency comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor.
recirculation zone on the bottom wall is smaller than that on the top wall. With the increase of the jet-to-crossflow pressure ratio, the recirculation zones become larger and move upstream, and the recirculation zone induced by the reflected shock wave merges with that generated downstream of the injector when the jet-to-crossflow pressure ratio is large
Fig. 10 shows the Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor, and it is observed that the recirculation zone is visible for the case with the jet-to-crossflow pressure ratio being 25.15. This is different from that observed in the nonreacting flow field, see Fig. 6(b), and this is induced by the intensive combustion. Correspondingly, the intensity of the separation shock wave upstream of the injector becomes stronger. At the same time, the recirculation zone downstream of the second backward-facing step on the top wall moves upstream compared with that in the corresponding nonreacting case when the jet-to-crossflow pressure ratio is 42.79, see Fig. 10(c). When the jet-to-crossflow pressure ratio increases further, the separation shock wave is pushed forward to the entrance of the scramjet model, see Fig. 10(d), and the oblique shock wave varies to be nearly a normal one. Thus, its variable trend of the mixing efficiency is different, see Fig. 11, and its value is the largest. This implies that the
Fig. 12 e Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
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combustion efficiency for the case with the jet-to-crossflow pressure ratio being 63.50 is the lowest. Except this case, the mixing efficiency decreases with the increase of the jet-tocrossflow pressure ratio, and the values are all less than those obtained in the nonreacting cases. This is induced by the intensive combustion process. When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the boundary layer separates seriously, see Fig. 12, and the recirculation zone induced by the reflected shock wave nearly merges with that generated downstream of the injector when the jet-tocrossflow pressure ratio is 25.15, see Fig. 12(b). When the jetto-crossflow pressure ratio is 42.79, the separation shock waves can not intersect any longer, and a normal shock wave is generated in the core flow of the combustor. At the same time, the recirculation zone induced by the reflected shock wave merges with that obtained downstream of the injector completely, and this is beneficial to the improvement of the mixing efficiency, see Fig. 13. In Fig. 13, the mixing efficiency of the case with the jet-to-crossflow pressure ratio being 42.79 is the highest, and its value is nearly 50%. However, when the jet-to-crossflow pressure ratio increases further, the separation shock waves are pushed forward to the entrance of the combustor, see Fig. 12(d), and the intensity of the normal shock wave obtained in the core flow becomes stronger. Due to the divergence angle on the bottom wall of the combustor, the velocity downstream increases, and its Mach number is larger than 1.0 at the exit of the combustor. This may imply that the variation of the jet-to-crossflow pressure ratio has a large impact on the ramjet/scramjet mode transition, and we can obtain the mode transition process by controlling the fuel injection scheme, especially the fuel equivalence ratio adjustment [25]. The detailed information for the influencing factors on the mode transition can be referred to Ref. [26].
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Conclusions In this article, the nonreacting and reacting flow field properties in a scramjet combustor with backward-facing steps have been investigated numerically, and the effect of the jetto-crossflow pressure ratio has been considered as well. We have come to the following conclusions: The variation of the jet-to-crossflow pressure ratio has a large impact on the ramjet/scramjet mode transition, especially in the reaction flow fields, and a normal shock wave occurs in the core flow of the combustor with the increase of the jet-to-crossflow pressure ratio. When the hydrogen is injected only from the bottom wall of the combustor, the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the nonreacting or reacting flow field except the reacting case with the jet-to-crossflow pressure ratio being 63.50. When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the recirculation zone induced by the reflected shock wave moves becomes larger, moves upstream and merges with that obtained downstream of the injector with the increase of the jet-tocrossflow pressure ratio, and this is beneficial to the improvement of the mixing efficiency in the reacting flow field.
Acknowledgments The authors would like to express their thanks for the support from the Science Foundation of National University of Defense Technology (No. JC14-01-01) and the National Natural Science Foundation of China (No. 11272351). The reviewers are thanked for their comments.
references
Fig. 13 e Mixing efficiency comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor.
[1] Choudhuri AR, Gollahalli SR. Combustion characteristics of hydrogen-hydrocarbon hybrid fuels. Int J Hydrogen Energy 2000;25:451e62. [2] Huang W, Pourkashanian M, Ma L, Ingham DB, Luo SB, Wang ZG. Investigation on the flameholding mechanisms in supersonic flows: backward-facing step and cavity flameholder. J Vis 2011;14(1):63e74. [3] Cheng TS, Yang WJ. Numerical simulation of threedimensional turbulent separated and reattaching flows using a modified turbulence model. Comput Fluids 2008;37:194e206. [4] Cheng YT, Nie JH, Armaly BF, Hsieh HT. Turbulent separated convection flow adjacent to backward-facing step e effects of step height. Int J Heat Mass Transf 2006;49:3670e80. [5] Miki K, Schulz J, Menon S. Large-eddy simulation of equilibrium plasma-assisted combustion in supersonic flow. Proc Combust Inst 2009;32:2413e20. [6] Chen Z, Yi SH, Tian LF, He L, Zhu YZ. Flow visualization of supersonic laminar flow over a backward-facing step via NPLS. Shock Waves 2013;23:299e306.
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[7] Abbitt III JD, Segal C, McDaniel JC, Krauss RH, Whitehurst RB. Experimental supersonic hydrogen combustion employing staged injection behind a rearward-facing step. J Propuls Power 1993;9(3):472e8. [8] Karagozian AR, Wang KC, Le AT, Smith OI. Transverse gas jet injection behind a rearward-facing step. J Propuls Power 1996;12(6):1129e36. [9] Altay HM, Speth RL, Hudgins DE, Ghoniem AF. The impact of equivalence ratio oscillations on combustion dynamics in a backward-facing step combustor. Combust Flame 2009;156:2106e16. [10] Huang W, Wang ZG, Pourkashanian M, Ma L, Ingham DB, Luo SB, et al. Numerical investigation on the shock wave transition in a three-dimensional scramjet isolator. Acta Astronaut 2011;68:1669e75. [11] Inc Fluent. Fluent 6.3 user's guide. Lebanon, NH: Fluent Inc.; 2006. [12] Chenault CF, Beran PS. K-ε and reynolds stress turbulence model comparisons for two-dimensional injection flows. AIAA J 1998;36(8):1401e12. [13] Huang W, Wang ZG, Yan L, Li SB, Ingham DB. Variation of inlet boundary conditions on the combustion characteristics of a typical cavity-based scramjet combustor. Proc Institution Mech Eng Part G J Aerosp Eng 2014;228(4):627e38. [14] Huang W, Wang ZG, Luo SB, Liu J. Parametric effects on the combustion flow field of a typical strut-based scramjet combustor. Chin Sci Bull 2011;56(35):3871e7. [15] Spalart PR. Strategies for turbulence modeling and simulations. Int J Heat Fluid Flow 2000;21:252e63. [16] Ivanova EM, Noll BE, Aigner M. A numerical study on the turbulent Schmidt numbers in a jet in crossflow. J Eng Gas Turbines Power e Trans ASME 2013;135:011505. [17] Wang PY, Chen M, Xing F, Li Q. CFD numerical simulation of Hyshot scramjet (in Chinese). J Aerosp Power 2014;29(5):1020e8.
[18] Chan WYK, Jacobs PA, Mee DJ. Suitability of the k-u turbulence model for scramjet flowfield simulations. Int J Numer Methods Fluids 2012;70:493e514. [19] Bardina JE, Huang PG, Coakly TJ. Turbulence modeling validation. 28th fluid dynamics conference. Snowmass Village, CO: AIAA; 1997. Paper 1997-2121. [20] Huang W, Li SB, Yan L, Wang ZG. Performance evaluation and parametric analysis on cantilevered ramp injector in supersonic flows. Acta Astronaut 2013;84:141e52. [21] Mudford NR, Mulreany PJ, McGuire JR, Odam J, Boyce RR, Paull A. CFD calculations for intake-injection shockinduced-combustion scramjet flight experiments. 12th AIAA international space planes and hypersonic systems and technologies. Norfolk: Virginia; 2003. AIAA Paper 20037034. [22] Micka D. J. Combustion stabilization, structure, and spreading in a laboratory dual-mode scramjet combustor. Doctor dissertation. USA: University of Michigan; 2010. [23] Huang W. Design exploration of three-dimensional transverse jet in a supersonic crossflow based on data mining and multi-objective design optimization approaches. Int J Hydrogen Energy 2014;39:3914e25. [24] Huang W, Liu WD, Li SB, Xia ZX, Liu J, Wang ZG. Influences of the turbulence model and the slot width on the transverse slot injection flow field in supersonic flows. Acta Astronaut 2012;73:1e9. [25] Bao W, Hu JC, Zong YH, Yang QC, Wu M, Chang JT, et al. Combustion characteristic using O2-pilot strut in a liquidkerosene-fueled strut-based dual-mode scramjet. Proc Institution Mech Eng, Part G Journal Aerosp Eng 2012. http:// dx.doi.org/10.1177/0954410012464455. [26] Huang W, Yan L, Tan JG. Survey on the mode transition technique in combined cycle propulsion systems. Aerospace Sci Technol. 2014. http://dx.doi.org/10.1016/j.ast.2014.07.006.
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Influence of jet-to-crossflow pressure ratio on nonreacting and reacting processes in a scramjet combustor with backward-facing steps Wei Huang*, Liang Jin, Li Yan, Jian-guo Tan Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
article info
abstract
Article history:
The jet-to-crossflow pressure ratio has a large impact on the combustion mode transition
Received 9 September 2014
in the scramjet engine, and this information needs to be explored comprehensively. The
Received in revised form
effect of the jet-to-crossflow pressure ratio on the mixing and combustion processes in a
6 October 2014
backward-facing step combustor has been investigated numerically, and two similar cases
Accepted 16 October 2014
have been utilized to validate the numerical approaches employed. The obtained results
Available online 7 November 2014
show that the wall pressure distribution for the nonreacting flow field has been predicted well, and the peak pressures are all a bit underestimated. However, the predicted wall
Keywords:
pressure distribution for the reacting flow field does not match well with the experimental
Aerospace propulsion system
data, and it is overestimated. When the hydrogen is injected only from the bottom wall of
Scramjet combustor
the combustor, the mixing efficiency decreases with the increase of the jet-to-crossflow
Backward-facing step
pressure ratio irrespective of the nonreacting or reacting flow field. When the hydrogen
Jet-to-crossflow pressure ratio
is injected simultaneously from the top and bottom walls, the separation shock wave is
Combustion
pushed forward to the entrance of the combustor, and it varies from an oblique one to a
Mode transition
normal one. This means that the jet-to-crossflow pressure ratio has a great impact on the combustion mode transition for the scramjet engine, and the stable ramjet/scramjet mode transition can be obtained by controlling the fuel injection scheme. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction From combustion point of view, hydrogen owns superior characteristics to any other hydrocarbon fuel in terms of ignitability, low ignition delay, and higher flame stability [1]. There inherent advantages turn it as the only potential fuel for scramjet engines. However, its low molecular weight can not promote the mixing and combustion process in
supersonic flows efficiently, and thus, some flameholding mechanisms have been proposed by the researchers, i.e. the wall-stalled cavity, the backward-facing step, the strut, the ramp. Due to its simple configuration, the backward-facing step has been widely employed in the flowpath of the scramjet engine [2e5], and the laminar flow field properties in the backward-facing step has been visualized by using the nanotracer planar laser scattering (NPLS) technique [6].
* Corresponding author. Tel.: þ86 731 84576447; fax: þ86 731 84576449. E-mail address: [email protected] (W. Huang). http://dx.doi.org/10.1016/j.ijhydene.2014.10.073 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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The shadowgraphs, broadband flame emission photographs, and planar laser-induced OH fluorescence images have been combined by Abbitt III et al. [7] to investigate the influence of the chemical reaction on the supersonic reacting flow field with the hydrogen injected behind a rearwardfacing step, and this is the first complete flow visualization study for the hydrogen-air supersonic combustor. Karagozian et al. [8] have investigated the jet penetration and jet structure in a rearward-facing step combustor experimentally and theoretically, and the transverse gas jet has been injected behind the rearward-facing step as well. However, in their study, the jet-to-crossflow pressure ratio has not been varied, and its effect on the combustion process has not been studied as well. Altay et al. [9] have analyzed the influence of the equivalence ratio oscillation on combustion dynamics of propane-air flames in a backward-facing step combustor by varying the fuel injector location. They have found that the combustion dynamics are primarily induced by the flameevortex interactions, and the equivalence ratio oscillations own secondary effects on the dynamics. However, the effect of the equivalence ratio on the flow field properties has not been explored completely. From the above literature reviewed, the effect of the jet-tocrossflow pressure ratio on the flow field properties of the backward-facing step combustor has rarely been analyzed, and it has a large impact on the combustion mode transition in the scramjet engine. Therefore, this information needs to be explored further. In the current study, the effect of jet-to-crossflow pressure ratio on mixing and combustion processes in a twodimensional scramjet combustor has been investigated numerically, and the ram-to-scram mode transition process induced by the jet-to-crossflow pressure ratio has been analyzed as well. The jet-to-crossflow pressure ratio has been set to be 16.43, 25.15, 42.79 and 63.5.
Physical model and numerical method Physical model The combustor model with backward-facing steps studied in the present article is shown in Fig. 1, and it consists of an isolator, a constant area combustor and a diverging area combustor. The fuel is injected to the supersonic crossflow vertically 594.36 mm away from the entrance of the combustor. This means that the fuel injectors are located in
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the isolator [10], and the length of the isolator is 677.418 mm. The width of the injection port is 3.9624 mm, and the hydrogen is injected only from the bottom wall or from both top and bottom walls of the combustor. There is a backwardfacing step exist on the top and bottom walls respectively, and its height is 3.302 mm. The length of the combustor with the constant area is 551.18 mm, see Fig. 1, and that of the diverging area combustor is 1063.752 mm. The origin of the coordinate system is set at the entrance of the combustor, see Fig. 1. The air flows from left to right with the Mach number being 3.3, the static pressure being 48,166 Pa and the total temperature being 2333.333 K. The hydrogen is injected into the core flow with the sonic velocity and the total temperature being 277.7778 K. The jet-to-crossflow pressure ratio is set to be 16.43, 25.15, 42.79 and 63.5.
Numerical approach The two-dimensional Reynolds-averaged NaviereStokes (RANS) equations and the two equations SST k-u turbulence model has been utilized to simulate the combustor with backward-facing steps numerically, and the equations are solved along with density based (coupled) double precision solver of FLUENT [11]. The two-dimensional assumption may result in the inadequate result for the intensity of the shock wave, as well as the shock wave/boundary layer interaction [12]. However, it would quicken the decision process for the overall design of the scramjet combustor, and thus, it has been employed as the basis approach for the flowpath design of the scramjet engine. The Finite-Rate/Eddy-Dissipation model and the one step hydrogen-air mechanism have been used to model the combustion process in the scramjet engine, and they have been proved to be suitable for the combustion simulation [13,14]. The RANS method is the efficient and rapid approach to receive the mean flow properties for the further mixing and combustion optimization in the supersonic flow [15]. The SST k-u turbulence model is a combination of the Wilcox 1988 k-u model in the near wall region and the standard k-ε model in the detached regions [16], and it has been proved to be more suitable to capture the turbulent generating mechanisms induced by the shock wave and the boundary layer in the scramjet engine [17,18], as well as the flow field properties in jet flows [18,19]. Thus, it has been employed to couple with the two-dimensional Reynolds-averaged NaviereStokes (RANS) equations to simulate the flow field in the scramjet combustor with backward-facing steps, and the Reynolds-averaged NaviereStokes equations have been utilized due to its lower
Fig. 1 e Schematic diagram of the scramjet combustor with backward-facing steps employed in the current study.
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Fig. 2 e Schematic diagram of a nonreacting laboratory scale scramjet model (unit: mm).
residuals reach their minimum values after falling for more than three orders of magnitude. An additional convergence criterion enforced in this current study requires the difference between the computed inflow and outflow mass flux to drop below 1% of the total mass flow. The computational domain is structured by the commercial software Gambit, and the grid is multi-blocked and highly concentrated close to the wall surfaces, the injector and the backward-facing step in order to ensure the accuracy of the numerical simulation. The height of the first row of cells is set at a distance of 0.001 mm for the walls, and the total number of cells is 176,391. This is enough for the current study from the information obtained in the following section. The maximum of yþ is less than 20.
Code validation
Fig. 3 e Wall static pressure comparison for a nonreacting laboratory scale scramjet model.
computational cost compared with the other numerical methods, i.e. large eddy simulation and direct numerical simulation. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting approach (AUSM) flux vector splitting is employed to quicken the convergence speed, and the CouranteFriedrichseLevy (CFL) number is kept at 0.5 with proper under-relaxation factors to ensure stability [20]. The no-slip conditions are assumed for the walls of the combustor. 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 solutions can be considered as converged when the
In this section, two typical cases have been employed to validate the numerical approaches used in the current study, namely a laboratory scale scramjet model for the HyShot free flight scramjet program (Case 1) [21] and a typical cavity-based dual-mode scramjet combustor investigated experimentally by Micka (Case 2) [22], and the validate process for the single transverse injection flow field can be referred to Refs. [23,24]. The validate cases employed here own the similar configuration as that studied in this article.
Case 1 In Case 1, the inlet section of the scramjet model is 180 mm long. The upper and lower walls of its forward portion consist of ramps formed by two sharp nosed flat plates each at 9 incidence to the oncoming flow, see Fig. 2, and Fig. 2 depicts the schematic diagram of the laboratory scale scramjet model. 135 mm downstream from the leading edge, the angle of incidence of the plate surface varies abruptly to 12 creating a compression corner. The height of the 250 mm long combustor is 24 mm for the present paper. Downstream of the
Fig. 4 e Schematic diagram of a typical cavity-based dual-mode scramjet combustor [13].
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(64,337 cells), and it is clearly observed that the grid scale has only a slight impact on the wall static pressure distribution for the nonreacting scramjet model, see Fig. 3, and the peak pressure is a bit underestimated. This implies that the numerical method employed in the current study can be utilized with confidence to simulate the nonreacting flow field of the scramjet engine.
Case 2
Fig. 5 e Wall static pressure comparison for a typical cavity-based dual-mode scramjet combustor.
combustor, the upper and lower walls of the model diverge at angles of ±9 to the horizontal to form the nozzle, and the length of the nozzle is 295 mm. Due to its symmetry, only half of the flow field has been simulated. Three grid scales have been used to carry out the grid independency analysis, namely the coarse grid (31,997 cells), the moderate grid (48,167 cells) and the refined grid
In Case 2, the scramjet model includes a constant-area isolator and a combustor, see Fig. 4. The constant-area isolator owns a height of 25.4 mm, and it extends 358 mm from the entrance to the center of the fuel injector. The constant-area isolator is followed by a cavity flameholder, and its length and depth are 50.8 mm and 12.7 mm, respectively. The room-temperature hydrogen is injected sonically through a single port located 44.5 mm upstream of the leading edge of the cavity, and the width of the injector is 2.49 mm. There is a 349 mm long, 4 diverging section downstream of the trailing edge of the cavity. The air flows into the scramjet model from left to right with the Mach number being 2.2, the static pressure being 261 kPa and the static temperature being 1280 K. The hydrogen is injected at Mach 1, with its static pressure and static temperature being 438 kPa and 248 K, respectively. The mass fractions for O2, N2 and H2O in the air are 0.251, 0.611 and 0.138, respectively. Three grid scales have been utilized 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
Fig. 6 e Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/ P∞ ¼ 63.5.
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Result and discussion In order to evaluate the nonreacting and reacting processes in the scramjet combustor, the mixing efficiency, which is defined as follows, is taken into consideration in this paper, and it means the ratio of the mixed mass flow rate of hydrogen to that of the total one at the local plane [23]. Z areact rudA Z arudA
(1)
a; a astoic að1 aÞ=ð1 astoic Þ; a > astoic
(2)
4¼
mfuel;mixed
mfuel;total
¼
Herein areact ¼
Fig. 7 e Mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor.
cells), and it is observed that when the number of cells is large enough, namely the moderate grid employed in this article, the gird scale makes only a slight difference to the wall static pressure distribution, especially on the floor face of the cavity, see Fig. 5. The static pressures on the floor face and downstream of the trailing edge of the cavity are all overestimated, and this may be induced by the two-dimensional assumption.
where a is the injectant mass fraction, areact is the injectant fraction mixed in a proportion that can react, astoic is the injectant stoichiometric mass fraction, mfuel;mixed is the mixed injectant mass flow and mfuel;total is the total injectant flow rate. r and u are the local density and velocity respectively, and A is the cross section of the axial station where mixing is evaluated.
Nonreacting process Fig. 6 shows the Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor. It is clearly observed that the separation shock wave angle upstream of the injector increases with the
Fig. 8 e Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/ P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
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Fig. 9 e Mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor.
increase of the jet-to-crossflow pressure ratio, and the intensity of the upstream separation shock wave increases correspondingly. Due to the strong interaction between the upstream separation shock wave and the boundary layer on the top wall of the scramjet combustor, the phenomenon of the boundary layer separation occurs, and a recirculation zone
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with low velocity is formed on the top wall, see Fig. 6(c) and (d). At the same time, the recirculation zone enlarges and moves upstream with the increase of the jet-to-crossflow pressure ratio. However, the recirculation zone induced by the boundary layer separation is invisible in Fig. 6(a) and (b). Fig. 7 represents the mixing efficiency comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor. It is obvious that the case with the smaller jet-to-crossflow pressure ratio owns the higher mixing efficiency, and this conclusion is consistent with that obtained in the three-dimensional transverse injection flow field [23]. This implies that the backward-facing steps exist can not vary the sequence of mixing efficiency in the current study, and this may be induced by the smaller dimensions of the backwardward steps compared with those of the scramjet model. In Fig. 7, it is obvious that the mixing efficiency increases monotonically with the increase of the horizontal distance irrespective of the value of the jet-to-crossflow pressure ratio. The maximum mixing efficiency is nearly 50%, and it occurs near the exit of the scramjet model for the case with the jet-tocrossflow pressure ratio being 16.43. In order to explore the effect of the transverse injection scheme on the flow field properties further, the hydrogen is injected from both the top and bottom walls of the scramjet model, and the recirculation zone appears on both the top and bottom walls even for the case with the smallest jet-tocrossflow pressure ratio, see Fig. 8(a). Fig. 8 depicts the Mach number contour comparison for nonreacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected simultaneously from the top and bottom walls. Due to the diverging angle on the bottom wall, the size of the
Fig. 10 e Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
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enough, see Fig. 8(c). Its value is 42.79 in the range considered in the current study. When the jet-to-crossflow pressure ratio increases further, namely 63.5 in the present study, the separation shock waves generated upstream of the injector can not intersect any longer, and a normal shock wave is obtained in the core flow of the scramjet model, see Fig. 8(d). When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the mixing efficiency increases, and the largest mixing efficiency is over 60%, see Fig. 9.
Reacting process
Fig. 11 e Mixing efficiency comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection from the bottom wall of the combustor.
recirculation zone on the bottom wall is smaller than that on the top wall. With the increase of the jet-to-crossflow pressure ratio, the recirculation zones become larger and move upstream, and the recirculation zone induced by the reflected shock wave merges with that generated downstream of the injector when the jet-to-crossflow pressure ratio is large
Fig. 10 shows the Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios, and the hydrogen is injected only from the bottom wall of the combustor, and it is observed that the recirculation zone is visible for the case with the jet-to-crossflow pressure ratio being 25.15. This is different from that observed in the nonreacting flow field, see Fig. 6(b), and this is induced by the intensive combustion. Correspondingly, the intensity of the separation shock wave upstream of the injector becomes stronger. At the same time, the recirculation zone downstream of the second backward-facing step on the top wall moves upstream compared with that in the corresponding nonreacting case when the jet-to-crossflow pressure ratio is 42.79, see Fig. 10(c). When the jet-to-crossflow pressure ratio increases further, the separation shock wave is pushed forward to the entrance of the scramjet model, see Fig. 10(d), and the oblique shock wave varies to be nearly a normal one. Thus, its variable trend of the mixing efficiency is different, see Fig. 11, and its value is the largest. This implies that the
Fig. 12 e Mach number contour comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor. (a) Pj/P∞ ¼ 16.43, (b) Pj/P∞ ¼ 25.15, (c) Pj/P∞ ¼ 42.79 and (d) Pj/P∞ ¼ 63.5.
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combustion efficiency for the case with the jet-to-crossflow pressure ratio being 63.50 is the lowest. Except this case, the mixing efficiency decreases with the increase of the jet-tocrossflow pressure ratio, and the values are all less than those obtained in the nonreacting cases. This is induced by the intensive combustion process. When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the boundary layer separates seriously, see Fig. 12, and the recirculation zone induced by the reflected shock wave nearly merges with that generated downstream of the injector when the jet-tocrossflow pressure ratio is 25.15, see Fig. 12(b). When the jetto-crossflow pressure ratio is 42.79, the separation shock waves can not intersect any longer, and a normal shock wave is generated in the core flow of the combustor. At the same time, the recirculation zone induced by the reflected shock wave merges with that obtained downstream of the injector completely, and this is beneficial to the improvement of the mixing efficiency, see Fig. 13. In Fig. 13, the mixing efficiency of the case with the jet-to-crossflow pressure ratio being 42.79 is the highest, and its value is nearly 50%. However, when the jet-to-crossflow pressure ratio increases further, the separation shock waves are pushed forward to the entrance of the combustor, see Fig. 12(d), and the intensity of the normal shock wave obtained in the core flow becomes stronger. Due to the divergence angle on the bottom wall of the combustor, the velocity downstream increases, and its Mach number is larger than 1.0 at the exit of the combustor. This may imply that the variation of the jet-to-crossflow pressure ratio has a large impact on the ramjet/scramjet mode transition, and we can obtain the mode transition process by controlling the fuel injection scheme, especially the fuel equivalence ratio adjustment [25]. The detailed information for the influencing factors on the mode transition can be referred to Ref. [26].
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Conclusions In this article, the nonreacting and reacting flow field properties in a scramjet combustor with backward-facing steps have been investigated numerically, and the effect of the jetto-crossflow pressure ratio has been considered as well. We have come to the following conclusions: The variation of the jet-to-crossflow pressure ratio has a large impact on the ramjet/scramjet mode transition, especially in the reaction flow fields, and a normal shock wave occurs in the core flow of the combustor with the increase of the jet-to-crossflow pressure ratio. When the hydrogen is injected only from the bottom wall of the combustor, the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio irrespective of the nonreacting or reacting flow field except the reacting case with the jet-to-crossflow pressure ratio being 63.50. When the hydrogen is injected simultaneously from the top and bottom walls of the combustor, the recirculation zone induced by the reflected shock wave moves becomes larger, moves upstream and merges with that obtained downstream of the injector with the increase of the jet-tocrossflow pressure ratio, and this is beneficial to the improvement of the mixing efficiency in the reacting flow field.
Acknowledgments The authors would like to express their thanks for the support from the Science Foundation of National University of Defense Technology (No. JC14-01-01) and the National Natural Science Foundation of China (No. 11272351). The reviewers are thanked for their comments.
references
Fig. 13 e Mixing efficiency comparison for reacting cases with different jet-to-crossflow pressure ratios and hydrogen injection simultaneously from the top and bottom walls of the combustor.
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