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Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows
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 x x x ( 2 0 1 7 ) 1 e1 3
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Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows Lang-quan Li, Wei Huang*, Li Yan, Zhen-tao Zhao, Lei Liao Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
article info
abstract
Article history:
A good injection strategy with high penetration and mixing efficiency relates to the overall
Received 12 March 2017
performance of the airbreathing hypersonic propulsion system. In the current study, the
Received in revised form
transverse injection flow field with a vortex generator placed in front of jet has been
31 May 2017
investigated, and the jet mixing enhancement and penetration improvement induced by
Accepted 2 June 2017
the pulsed jet has been evaluated as well. The obtained results predicted by the three-
Available online xxx
dimensional Reynolds-average Navier e Stokes (RANS) equations coupled with the two equation k-u shear stress transport (SST) turbulence model show that the jet-to-crossflow
Keywords:
pressure ratio has an great impact on penetration depth and mixing efficiency in the steady
Pulsed jet
jet flow field. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency
Jet-to-crossflow pressure ratio
but lower penetration depth are shown. On the other hand, compared with the steady jet
Transverse injection
flow field, the pulsed jet flow field with the periodic variation of jet-to-crossflow pressure
Mixing efficiency
ratio of the fuel injection has better comprehensive performance, and the penetration
Penetration depth
depth and mixing efficiency are improved simultaneously. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The scramjet (supersonic combustion ramjet) engine may be one of the most promising propulsion systems for hypersonic vehicles in the near future, because an oxidizer tank is not required in these engines and high efficiency can be obtained when vehicles fly in or beyond the supersonic speed. The presence of these advantages has motivated the researchers in recent years [1e3]. The realization of sufficient mixing is the main challenge for the design of the scramjet engine on account of the short residence time of airflow within the scramjet combustor being on the order of milliseconds for typical flight conditions [4].
Therefore, a good injection strategy with large penetration depth and high mixing efficiency is required within the scramjet combustor. One simplest and reliable fuel injection strategy for a scramjet engine is transverse injection into the airflow, because transverse injection provides rapid fuel-air mixing and high jet penetration into the supersonic airflow [5,6]. At first, the majority of studies have concentrated on a single transverse jet at a variety of conditions such as jet-tocrossflow pressure ratio [7], jet-to-crossflow momentum flux ratio [8,9], molecular weight [10], injector geometry [11], injection angle [12], incoming air steam angle [13]. Threedimensional transverse jet in supersonic crossflow was optimized by Huang [14], and the multi-objective optimization
* Corresponding author. E-mail address: [email protected] (W. Huang). http://dx.doi.org/10.1016/j.ijhydene.2017.06.014 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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results were explored by the variance analysis method. Further, he and his co-workers investigated the influence of the pseudo shock wave induced by the back pressure on the mixing process between the fuel and air in the transverse injection flow field numerically [15]. Subsequently, a variation on the conventional single jet in crossflow is the multiple transverse injection system [16e18], and complication of an efficient injection system setup arise due to more parameters, including distributions of mass flow rate and momentum flux, injection angle and combination of injection angles, arrangement of injector geometry and spacing variation in both the freestream and spanwise directions [19]. In addition, many mixing enhancement devices such as strut [20e23], ramp [24], pylon [25], cavity [26e28], aerodynamic ramp [29], and any other combination have been offered and used to enhance mixing and penetration substantially, but at the expense of a larger pressure loss, increasing drag forces, and inciting considerable local heating loads [30]. In 2013, a novel injection strategy was proposed by Huang et al. [31], and it has been analyzed parametrically [31] and optimized by the multiobjective design optimization approach [32]. In 2015, the upstream and downstream regions of fuel injection slot were connected through a channel by Han et al. [33] to obtain efficient fuel/air mixing and combustion. Further, additional oblique shock wave was introduced in the transverse injection flow field in order to enhance the mixing process between the fuel and air [34e36], as well as the combustion efficiency of hydrogen injection into the supersonic cross-flow [37,38]. Multi air jets were introduced into the transverse injection flow field by Gerdroodbary et al. [39] to improve the mixing process between the fuel and air as well. In order to minimize the total pressure loss, as well as the drag force, and improve the jet penetration and mixing efficiency, the microramp is a viable mean [40e42]. The authors have investigated the influences of the microramp height and the jet-to-crossflow pressure ratio on the mixing process between the fuel and the supersonic crossflow, and the microramp has been proved to have a highly remarkable improvement in mixing characteristics such as mixing efficiency and fuel penetration depth, see Fig. 1 and Table 1, but at the expense of an excessive loss of stagnation pressure [43]. Fig. 1 depicts the mixing efficiency comparison for different models at the same jet-to-crossflow pressure ratio, (a) Pj/ P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, and (c) Pj/P∞ ¼ 25.15, and Models A, B, C and D are the case with the microramp height being 0 mm, 5.0 mm, 6.0 mm and 7.0 mm respectively. Table 1 summarizes and compares the penetration depths of Models A, B, C and D. Because of the tiny size, it can immerse into the boundary layer, thus the total pressure loss is obviously small. When the jet orifice is placed downstream the microramp, the counter vortices pairs (CVPS) produced by the microramp, the vortex shedding off the edge and a local separation at the base can enhance the mixing process. At the same time, the lowmomentum wake flow due to the blocking of the microramp provides an ideal condition to increase the jet penetration. On the other hand, the pulsed jet is a potential strategy for enhancing the mixing efficiency and improving the jet penetration [44], and it has been considered as a control approach for jets in crossflow [45,46]. The influences of the pulsation frequency, amplitude and waveform shape have been studied
theoretically and experimentally. The obtained results show that the pulsation frequency may greatly affect the jet penetration [47], and the pulsation amplitude is associated with the jet shear layer evolution [48]. The sinusoidal excitation at high jet-to-inflow velocity ratio can improve jet penetration [49]. Of course, the mixing efficiency can be further improved due to the pulsatile nature of the flow. Computational Fluid Dynamics is an efficient approach to perform parametric studies and check whether design changes are worth testing experimentally. At the same time, it also provides important insight into complex flow phenomena like separations and shock wave, thus it can significantly improve the flowpath design process for relatively lower costs compared with costly experimental tests alone [50,51]. According to the previous studies carried out by the authors [52], the jet-to-crossflow pressure ratio is one of the important factors for the supersonic jet-to-crossflow flow field. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency is shown. The higher jet-to-crossflow pressure ratio is, and the larger jet penetration depth is. Considering the respective advantages of the jet-to-crossflow flow fields induced by high and low jet-to-crossflow pressure ratios, User Defined Function can be used to realize the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-to-crossflow pressure ratios. Therefore, the flow field with better performance may be achieved, and the microramp has a highly remarkable improvement on mixing characteristics such as mixing rate and penetration. To the best of the authors' knowledge, the flow field induced by the pulsed jet and the microramp simultaneously has rarely been investigated in the open literature, and it is a promising mixing enhancement strategy in supersonic flows. Thus, the investigation of the flow field with a vortex generator placed in front of the pulsed jet is meaningful. Therefore, in this paper, the mixing enhancement induced by the pulsed jet and the vortex generator in a Mach 3.75 crossflow of air has been studied numerically, and this is the subsequent work of Ref. [43]. The main performance parameters concerned in the present study are mixing efficiency and penetration depth, and the influence of the pulsed jet on the flow field performance has been evaluated. The flow structure has been analyzed in combination with hydrogen mass/mole fraction contour and hydrogen mass fraction iso-surface in the near filed of the jet as well. In Sections, the Physical model, the Boundary condition setting and the Numerical approach are described in detail respectively. Section provides the Computing process, and the Code validation and grid independency analysis process is shown in Section. In Section Results and discussion, the mixing process induced by the vortex genesrator and the pulsed jet is analyzed from the flow structure and the performance parameters. At last, some conclusions are made according to the numerical simulation.
Physical model The test section is a straight channel, and Fig. 2 shows the plan and symmetric views of transverse gaseous injection
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 1 e Mixing efficiency comparison for different models at the same jet-to- crossflow pressure ratio, (a) Pj/P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, and (c) Pj/P∞ ¼ 25.15 [43].
model employed in this study. A vortex generator is mounted along the center of the flat plate with the leading edge of the vortex generator located 64 mm downstream from the leading edge of the flat plate, and the leading edges of the vortex generator and the flat plate are parallel, and the wall orifice with its diameter being 1 mm is located at 5 mm downstream the trailing point of the vortex generator. The origin of the
coordinate system is set at the leading edge of the flat plate, the width of the flat plate is 120 mm, the height of the computational domain is 80 mm, and its length is 680 mm. The width and the side length of the vortex generator are 24 mm and 20 mm respectively.
The setting of the boundary conditions and the realization of the pulsed jet Table 1 e Penetration depth comparison of Models A, B, C and D (unit: mm) [43]. Pj/P∞
Model A
Model B
Model C
Model D
10.29 17.72 25.15
3.70 4.74 5.59
6.27 6.68 7.13
7.53 7.72 8.43
9.37 9.64 9.65
The air flows from left to right, and its air properties are set to be a Mach number M∞ of 3.75, a static pressure P∞ of 11090Pa and a static temperature T∞ of 78.43 K. The supersonic freestream (air) is composed of 21% O2 and 79% N2, and this means that mass fractions for O2 and N2 are 0.21 and 0.79 respectively. The hydrogen is set as the injectant for it is
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 2 e Schematic of transverse gaseous injection with a vortex generator (unit: mm).
generally a more energetic fuel than hydrocarbon fuels for a Mach number in the range 4e10 [53], and its mass fraction is 1.0. The steady injection flow Mach number Mj is set to be 1.0 with a constant static temperature Tj ¼ 249 K. These conditions are representative of a typical generic scramjet combustor. The air is assumed to be a thermally and calorically perfect gas, and the mass-weighted-mixing- law of viscosity is employed. According to the previous studies carried out by the authors [11], the jet-to-crossflow pressure ratios of three steady jet flow fields are set to be 10.29, 17.72 and 25.15. At the outflow, all the physical variables are extrapolated from the internal cells due to the flow being supersonic [53], the no-slip conditions (u ¼ v ¼ w ¼ 0.0) are assumed for the walls of the channel, and the boundary inlet and the injector exit are both set to be pressure inlet. The thermal condition is that the heat flux along the walls is 0.0 by default. Based on the high-speed [47] and low-speed studies [49], the pulsation waveform shape is chosen as sine wave for the pulsed jet. The mean jet static temperature and flow Mach number are equal to the counterparts described above for the steady jet. The interval of the periodic variation of jet-to-crossflow pressure ratio of the pulsed jet flow field is 10.29e25.15. Further, in order to make the jet flow Mach number Mj to be 1.0, the stagnation and static pressures of the pulsed jet must satisfy the following relationship: P0 ¼ Pj
g g 1 2 g1 Mj 1þ 2
(1)
herein, P0 and Pj are the instantaneous stagnation and static pressures of the pulsed jet respectively, and g is the gas thermodynamic parameter. In order to realize the periodic variation of jet-to-crossflow pressure ratio of the fuel injection, the stagnation and static pressures of the pulsed jet can be described as
P25:15 2p P0 ¼ P10:29 1 þ 106 t 1 sin 9 P10:29 g g 1 2 g1 Mj 1þ 2
(2)
and P25:15 2p 106 t 1 sin Pj ¼ P10:29 1 þ 9 P10:29
(3)
herein, P10.29 and P25.15 represent the instantaneous static pressure of the pulsed jet when the instantaneous jet-to-crossflow pressure ratio of the pulsed jet is 10.29 and 25.15 respectively.
Numerical approaches The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations and the two equation SST k-u turbulence model has been utilized to numerically simulate the transverse injection flow field. The equations are solved along with density based (coupled) double precision solver of FLUENT. A Dell workstation at the Science and Technology on Scramjet Laboratory, China, using up to 32 processors, provided a parallel computing environment for flow solutions. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized to quicken the convergence speed. The governing equations are as follows [54]: vðrYs Þ v v vYs þ rDs ; s ¼ 1; 2; …; ns rYs uj ¼ vt vxj vxj vxj
(4)
vr v þ ruj ¼ 0 vt vxj
(5)
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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vtij vðrui Þ v þ rui uj þ dij p ¼ vt vxj vxj vðrEÞ v v þ rHuj ¼ vt vxj vxj
tij ui þ k
ns vT X vYs þ rDs hs vxj s¼1 vxj
(6)
v v v vu ðruÞ þ ðruui Þ ¼ Gu þ Gu Yu þ Du þ Su vt vxi vxj vxj
(7)
The compressibility takes part in dissipation terms such as Yk and Yu and partically in the production of turbulence kinetic energy is defined as follows:
!
The state equation of gas is ns X Ys P ¼ rRT M s s¼1
(8)
where r is the gas density, ui and uj are the velocity components in the xi and xj directions, respectively, p is the pressure and T is the static temperature. tij is the molecular stress tensor, and it should be closed by the turbulence model. E is the total energy per unit volume. E¼
ns X s¼1
Ys h s þ
p 1 2 u þ v2 þ w2 2 r
(9)
H is the total enthalpy per unit volume, ns is the total number of species, R is the universal constant of gas, Ms, Ys, Ds and hs are the molecular weight, mass fraction, mass diffusion coefficient and absolute enthalpy per unit mass of species s respectively. 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 [55], and it is considered for its good prediction of mixing layers and jet flows [52], as well as insensitive to initial values [56]. At the same time, this model is less sensitive to specification of freestream turbulence level compared to the k-u model, and it performs comparatively well in adverse pressure gradients and separated flows over either the k-u or k-ε models [57]. The transport equations for k and u can be refer to Ref. [58], see Eqs. (10) and (11). The sensitivity of the turbulence model on the predicted results of a transverse injection flow field with different jet-to-crossflow pressure ratios was investigated previously by the authors, see Ref. [52]. v v v vk fk Yk þ Sk ðrkui Þ ¼ Gk þG ðrkÞ þ vt vxi vxj vxj
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(10)
(11)
Yk ¼ rb* ku
(12)
Yu ¼ rbu2
(13)
*
herein, b and b are functions of F(Mt). b* ¼ b*i 1 þ z* FðMt Þ
(14)
b* b ¼ bi 1 i z* FðMt Þ bi
(15)
z* ¼ 1.5, and the compressibility function F(Mt) is defines as follows: FðMt Þ ¼
0 M2t M2t0
Mt Mt0 Mt > Mt0
(16)
where, M2t ¼
2k a2
(17)
Mt0 ¼ 0:25 a¼
(18)
pffiffiffiffiffiffiffiffiffi gRT
(19)
The term Gk represents the production of turbulence kinetic energy, and it is affected by compressibility as well. The equation of Gk is defined as follows: Gk ¼ min Gk ; 10rb* ku
(20)
The computational domain is structured by the commercial software Gambit. Due to its symmetrical configuration, only half of the grid system is chosen for the following simulation. Fig. 3 (a) represents the whole grid system for the employed model of this article. Fig. 3 (b) shows the structured grid in the vicinity of the injection and the vortex generator. The O-type
Fig. 3 e Grid system of the model, (a) the whole grid system (b) grids near injection and vortex generator. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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grid is used for the jet nozzle and the Y-type grid is used for the vortex generator, and the grid density is clustered towards the wall orifice and the vortex generator in order to ensure the accuracy of the numerical simulation. The grid density is relaxed towards outlet. A boundary layer grid is generated on the bottom wall with a first cell height of 0.01 mm, which results in a suitable value of yþ for all of the flow fields, and its maximum value is below 30.0 for all cases studied in the current study. This occurs in the vicinity of the vortex generator. yþ is a non-dimensional parameter defined by Eq. (21). yþ ¼
rut yP m
(21)
herein, ut is the friction velocity, yP is the distance from point P to the wall, r is the fluid density, and m is the fluid viscosity at point P.
Computing process The numerical simulation of the steady jet flow fields is carried out for the first step, and the Courant-Friedrichs-Lewy number defined as jujDt=Dl is ramped from 0.1 to 0.5 over almost the initial 10,000 steps with the progress of convergence to ensure stability, where u, Dt and Dl are the velocity, time and spatial steps respectively. The solutions can be considered as converged when most of the residuals reach their minimum values after falling for more than three orders of magnitude and the oscillation of the residuals are limited. At the same time, the computed inflow and the outflow mass flux is required to drop below 0.0001 kg/s. Further, the numerical simulation of the unsteady flow field is based on the steady flow field with the jet-to-crossflow pressure ratio being 10.29 in order to reduce computation time. In addition, the time step is set to be 10 ns for stability and detailed capture of the unsteady flow fields. The unsteady flow fields with the instantaneous jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15 in the eleventh cycle are used for the following investigation.
spatial resolution of the wall pressure data. A comparison between numerical results and the avaiable published experimental data, as well as the grid independency analysis, has been provided by Huang et al. [52]. Fig. 4 (a) shows the comparison of wall pressure profiles for different grid scales with the SST k-u turbulence model when the jet-to-crossflow pressure ratio is 17.12, and the grid scale makes only a slight difference to the numerical results. Although there are some differences between the numerical results and the experimental data, the wall pressure trends are the same. The maximum error percentage deviations upstream and downstream of the injection are about 46.90% and 23.81% respectively, and the separation length upstream of the injection is underestimated as well. This is related to the parallel computing environment and the numerical method employed [60]. The accumulation of stochastic error is proportional to the number of time steps and depends on the accuracy of the scheme and the approximation error. The numerical approach mentioned above has been utilized successfully in previous studies [61]. In order to investigate grid independency of the numerical simulations, three different grid scales of the model are employed, namely the coarse (348,331 cells), the moderate (492,474 cells), and the refined (707,199 cells) grids. Fig. 4 (b) depicts the wall pressure distribution comparison for the jet-to-crossflow pressure ratio being 10.29 with three different grid scales, and it is clear that the predicted results of three different grid scales match well. The discrepancy between the results predicted by the moderate and refined grids is much smaller than that between the results predicted by the coarse and moderate grids. Therefore, the moderate grid is chosen to carry out the following simulation in order to save the computational cost and reduce the computation time.
Results and discussion The analysis of flow structure
Code validation and grid independency analysis In the current study, the experimental cases of Spaid and Zukoski [59] are of great value because they provide good
The flow feature is associated with the mixing process, and the difference of the flow feature means the difference of the mixing performance. Therefore, the flow features of the
Fig. 4 e Comparison of wall pressure profiles for different grid scales, (a) validation of numerical methods, (b) grid independency analysis. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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steady and pulsed jets into supersonic crossflow are valuable to analyze. The 3D iso-surface colored by the injectant mass fraction being greater than 0.1, and the streamline distributions of the steady and pulsed jet flow fields with the jet-tocrossflow pressure ratio being 10.29, 17.72 and 25.15 are demonstrated in Fig. 5. At the same time, the hydrogen mole fraction contours on three cross-section planes and flat plate of the steady and pulsed jet flow fields with the jet-tocrossflow pressure ratio being 10.29, 17.72 and 25.15 are also depicted in Fig. 6. Judging from the streamlines in Fig. 5, a variety of vertical structures are generated downstream of the vortex generator, and the vortex structure downstream the injection is similar as the counter-rotating vortex pairs. These vortices roll up the jet surface, resulting in distorted 3D isosurface shown in Fig. 5 and the kidney-shaped plume appeared in Fig. 6. Comparing the three images of steady jet flow fields in Fig. 5 (a), (c), (e), with the increase of the jet-tocrossflow pressure ratio, the 3D iso-surface is thicker and the extension length is longer along the flow direction. This may indicate that the fuel and air can be mixed completely earlier in the case with lower jet-to-crossflow pressure ratios. According to the comparison of the hydrogen mole fraction contours on the same cross-sectional plane of the steady jet flow fields in Fig. 6 (a), (c), (e), the same inference can be obtained. Correspondingly, an interesting phenomenon appears in the pulsed jet flow fields shown in Fig. 5 (b), (d), (f). Although the instantaneous jet-to-crossflow pressure ratio is different, the flow field structures are almost the same. This may be the reason for the high frequency of jet oscillation. Referring to previous research conclusion, much lower or higher frequency may result in a quasi-steady flow field [26,27]. In the current study, this phenomenon is of great value. In Fig. 5, Judging from the size and the extension length of the 3D isosurface, when the jet-to-crossflow pressure ratio is relatively small, the fuel and air can be mixed completely earlier in the steady jet flow field. However, with the increase of the jet-to-
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crossflow pressure ratio, the advantage of the mixing performance of the pulsed jet flow field is gradually reflected. When the jet-to-crossflow pressure ratio is 25.15, this advantage is obvious. Moreover, there is a recirculation zone between the delta wing and the injection, and it is induced by the boundary layer separation caused by the subsequent adverse pressure gradient. In the case of higher jet-to-crossflow pressure ratio, more injectant would be brought into the recirculation zone in the steady jet flow fields according to Figs. 6 and 7. On the other hand, the hydrogen contents of the recirculation zone in the pulsed jet flow fields are almost the same, and more hydrogen content has been brought into the core flow. This phenomenon is beneficial for the mixing process between the fuel and air. Through the above analysis, the most prominent conclusion of this study is that the pulsed jet flow field with the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-to-crossflow pressure ratios can integrate the advantages of high and low jet-tocrossflow pressure ratios, and the flow field with better comprehensive performance is realized. In the following investigation, this conclusion will be validated by data obtained from the flow fields.
The analysis of performance parameters The mixing efficiency is one of the most important parameters because an enhancement of the mixing efficiency directly results in an enhancement of combustion in a scramjet combustor. The mixing efficiency is defined as follows [62]. Z m_ fuel; mixed ¼ 4¼ m_ fuel; total
areact rudA Z arudA
(22)
herein,
Fig. 5 e Comparison of the mass distribution and flow feature for the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 6 e Hydrogen mole fraction contours on three cross-section planes and flat plate of the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/ P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
areact ¼
a; a astoic að1 aÞ=ð1 astoic Þ; a > astoic
(23)
a is the injectant mass fraction, areact is the injectant fraction mixed in a proportion that react, astoic is the injectant stoichiometric mass fraction, m_ fuel; mixed is the mixed injectant mass flow and m_ fuel; 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. astoic is the injectant stoichiometric mass fraction, and its value is 0.0291 for the hydrogen and air [63]. The reactant fraction refers to the least-avaiable reactant, air, or fuel, depending on whether the mixture is lean or rich. In fuel-lean regions, the mixing efficiency parameter represents the fuel
fraction, and in fuel-rich regions the mixing efficiency refers to the air fraction [62]. In Eq. (22), 4 ¼ 1.0 indicates a perfectly mixed system, and the maximum value of fuel fraction must remain less than or equal to the stoichiometric ratio. When 4 ¼ 0.0, a must be 1.0, and this means that the injectant does not mix with the freestream. To probe into the underlying physics, the streamwise progression of the mixing efficiency is calculated and plotted in Figs. 8 and 9 from the slice data of the steady and pulsed jet flow fields evaluated at each streamwise station starting from the injection position with an increment of Dx ¼ 2 mm. For the steady jet flow fields, it is clear that the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio. This conclusion is consistent with that observed in the traditional transverse injection flow field, see
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 7 e Hydrogen mole fraction contours on the symmetry plane of the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
Ref. [64]. On the other hand, there are small discrepancies occur in the profiles of the mixing efficiency of the pulsed jet flow fields due to different instantaneous jet-to-crossflow pressure ratios of injection corresponding to different flow times. In order to evaluate the mixing performance of the pulsed jet flow fields, the comparison of the mixing efficiency for the steady and pulsed jet flow fields with the jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15 are exhibited in Fig. 9. It is clearly observed that along the streamwise direction, the mixing efficiency of the steady jet flow field is higher than that of the pulsed jet flow filed when the jet-to-crossflow pressure ratio is 10.29. When the jet-to-crossflow pressure ratio is 17.72, the mixing efficiencies of the steady and pulsed jet flow fields are nearly the same. However, when the jet-tocrossflow pressure ratio is 25.15, the mixing efficiency of the pulsed jet flow field has obvious advantages along the streamwise direction. These phenomena imply that the pulsating injection can make the mixing efficiency of the flow field to be at a stable and high level, even though the jet-tocrossflow pressure ratio of the fuel injection varies periodically.
The fuel penetration depth is also a parameter that determines the scramjet engine performance to a certain extent, because an ideal penetration can minimize wall heating and maximize combustion efficiency. In this paper, the fuel penetration depth is assessed by the height above the floor where the hydrogen mass fraction of the jet plume reduces to 0.1. Fig. 10 depicts the hydrogen mass fraction contours on the symmetric plane in the range of 0.1e1 for the steady and pulsed jet flow fields with the jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15, and Table 2 statistics the penetration depth of all flow fields investigated in this study. A lot of information are reflected in Fig. 10 and Table 2. The first one is that the jet-to-crossflow pressure ratio has an great impact on the jet penetration depth in the steady jet flow fields. The larger jet-to-crossflow pressure ratio is, the greater penetration depth is. Secondly, the hydrogen mass fraction contours of the pulsed jet flow fields with different instantaneous jet-to-crossflow pressure ratios are almost the same, and it is worth noting that the penetration depth of the pulsed jet flow fields is always higher than that of the steady jet flow fields irrespective of the value of the jet-to-crossflow pressure ratio. This implies that the pulsating injection can make the
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 8 e Effect of the jet-to-crossflow pressure ratio on mixing efficiency of the steady flow fields jet and the pulsed jet flow fields, (a) the steady jet flow fields, (b) the pulsed jet flow fields.
Fig. 9 e Mixing efficiency comparison for the steady jet and pulsed jet flow fields at the same jet-to- crossflow pressure ratio, (a) Pj/P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, (c) Pj/P∞ ¼ 25.15. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 10 e Comparison of the hydrogen mass fraction contour on the symmetry in the range of 0.1e1 for the steady jet flow fields and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
penetration of the flow field to be at a higher value, even though the jet-to-crossflow pressure ratio of the fuel injection varies periodically. For the steady jet flow field with a single jet-to-crossflow pressure ratio, the jet-to-crossflow pressure ratio has an great impact on the mixing efficiency and the jet penetration depth. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency but lower penetration depth are shown. This means that the realization of the steady jet flow field with faster sufficient mixing and higher penetration depth is contradictory when only the jet-to-crossflow pressure ratio is considered as the variable that affects the performance of the transverse injection flow fields. Compared with the steady jet flow field with a single jet-to-crossflow pressure ratio, the pulsed jet field has better comprehensive performance. In summary, the penetration depth and mixing efficiency are improved simultaneously.
Table 2 e Penetration depth of all flow fields considered in this study (unit: mm). Jet type
Steady jet Pulsating jet
Pj/P∞ 10.29
17.72
25.15
7.53 8.44
7.72 8.46
8.43 8.47
Conclusion In this article, the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations coupled with the two equation SST k-u turbulence model were employed to simulate the mixing characteristics of the transverse injection flow field with a delta wing vortex generator, and both pulsed and steady injections are simulated for comparison. The flow structures of the steady and pulsed jet flow fields with different jet-to-crossflow pressure ratios have been compared. The main focus is to analyze and compare the performance parameters of the transverse injection flow fields, such as the mixing efficiency and the fuel penetration depth. We have come to the following conclusions: The jet-to-crossflow pressure ratio has an great impact on the mixing efficiency and the jet penetration depth in the steady jet flow field. In the case of lower jet-tocrossflow pressure ratio, higher mixing efficiency but lower penetration depth are shown. The penetration depth for the steady jet increases from 7.53 mm to 8.43 mm, and that for the pulsed jet increases from 8.44 mm to 8.47 mm when the jet-to-crossflow pressure ratio increase from 10.29 to 25.15.
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Due to the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-tocrossflow pressure ratios, the penetration depth and mixing efficiency are improved simultaneously. The maximum penetration depth for the pulsed jet is 8.47 mm, and that for the steady jet is 8.43 mm. The pulsating jet is a promising injection strategy when compared with the steady jet at the same boundary conditions, and many parameters of the pulsating jet may be optimized to achieve better comprehensive performance of the trasverses injection flow field. This issue will be carried out by the multiobjective design optimization approach in the near future.
[10]
[11]
[12]
[13]
[14]
Conflict of interest statement [15]
The authors declare there is no conflict of interest regarding the publication of this paper. [16] [17]
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No.11502291) and a fund for owner of Outstanding Doctoral Dissertation from the Ministry of Education of China (No.201460). Also, the authors thank the anonymous reviewers for some very critical and constructive recommendations on this article.
[18]
references
[21]
[1] Huang W, Jin L, Yan L, Tan JG. Influence of jet-to-crossflow pressure ratio on nonreacting and reacting processes in a scramjet combustor with backward-facing step. Int J Hydrogen Energy 2014;39:21242e50. [2] Fureby C, Chapuis M, Fedina E, Karl S. CFD analysis of the HyShot II scramjet combustor. Proc Combust Inst 2011;33:2399e405. [3] Pecnik R, Terrapon VE, Ham F, Iaccarino G, Pitsch H. Reynolds-averaged Navier-Stokes simulations of the HyShot II scramjet. AIAA J 2012;50:1717e32. [4] 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;14:63e74. [5] Watanabe J, Kouchi T, Takita K, Masuya G. Characteristics of hydrogen jets in supersonic crossflow: large-eddy simulation study. J Propuls Power 2013;29:661e74. [6] Yan L, Huang W, Zhang TT, Li H, Yan XT. Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species. Acta Astronaut 2014;105:17e23. [7] Huang W. Transverse jet in supersonic crossflows. Aerosp Sci Technol 2016;50:183e95. [8] You Y, Lu¨deke H, Hannemann K. On the flow physics of a low momentum flux ratio jet in a supersonic turbulent crossflow. EPL 2012;97:24001e6 (24006). [9] Zhao M, Ye T, Cao C, Zhou T, Zhu M. Study of sonic injection from circular injector into a supersonic cross-flow using
[19]
[20]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
large eddy simulation. Int J Hydrogen Energy 2016;41:17657e69. Schetz JA, Maddalena L, Burger SK. Molecular weight and shock-wave effects on transverse injection in supersonic flow. J Propuls Power 2010;26:1102e13. Huang W, Liu J, Jin L, Yan L. Molecular weight and injector configuration effects on the transverse injection flow field properties in supersonic flows. Aerosp Sci Technol 2014;32:94e102. Aso S, Inoue K, Yamaguchi K, Tani Y. A study on supersonic mixing by circular nozzle with various injection angles for air breathing engine. Acta Astronaut 2009;65:687e95. Ali M, Islam AKMS. Study on main flow and fuel injector configurations for Scramjet applications. Int J Heat Mass Transf 2006;49:3634e44. 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. Huang W, Li MH, Yan L. Mixing augmentation mechanism induced by the pseudo shock wave in transverse gaseous injection flow fields. Int J Hydrogen Energy 2016;41:10961e8. Lee SH. Characteristics of dual transverse injection in scramjet combustor, Part 1: mixing. J Propuls Power 2006;22:1012e9. Huang W. Numerical investigation on staged sonic jet interaction mechanism in a supersonic cross flow. Proc Inst Mech Eng Part G J Aerosp Eng 2014;228(14):2641e51. Li ZW, Huai WX, Qian ZD. Study on the flow field and concentration characteristics of the multiple tandem jets in crossflow. Sci China Technol Sci 2012;55:2778e88. Huang W. Effect of jet-to-crossflow pressure ratio arrangement on turbulent mixing in a flowpath with square staged injectors. Fuel 2015;144:164e70. 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. Choubey G, Pandey KM. Effect of parametric variation of strut layout and position on the performance of a typical two-strut based scramjet combustor. Int J Hydrogen Energy 2017;42(15):10485e500. Huang W, Yan L. Numerical investigation on the ram-scram transition mechanism in a strut-based dual-mode scramjet combustor. Int J Hydrogen Energy 2016;41:4799e807. Huang W. Investigation on the effect of strut configurations and locations on the combustion performance of a typical scramjet combustor. J Mech Sci Technol 2015;29(12):5485e96. Seiner JM, Dash SM, Kenzakowski DC. Historical survey on enhanced mixing in scramjet engines. J Propuls Power 2001;17:1273e86. Vishwakarma M, Vaidyanathan A. Experimental study of mixing enhancement using pylon in supersonic flow. Acta Astronaut 2016;118:21e32. Huang W, Li MH, Ding F, Liu J. Supersonic mixing augmentation mechanism induced by a wall-mounted cavity configuration. J Zhejiang Univ Sci A 2016;17:45e53. Tian Y, Yang S, Le J, Su T, Yue M, Zhong F, et al. Investigation of combustion and flame stabilization modes in a hydrogen fueled scramjet combustor. Int J Hydrogen Energy 2016;41:19218e30. Huang W, Wang ZG, Yan L, Liu WD. Numerical validation and parametric investigation on the cold flow field of a typical cavity-based scramjet combustor. Acta Astronaut 2012;80:132e40. Yan Z, Bing C, Gang L, Wei B, Xu X. Influencing factors on the mode transition in a dual-mode scramjet. Acta Astronaut 2014;103:1e15. Portz R, Segal C. Penetration of gaseous jets in supersonic flows. AIAA J 2006;44:2426e9.
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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[31] 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. [32] Huang W, Li SB, Yan L, Tan JG. Multiobjective design optimization of a cantilevered ramp injector using the surrogate-assisted evolutionary algorithm. J Aerosp Eng 2015;28, 04014138. [33] Han X, Ye T, Chen Y. Effects of self-throttling on combustion enhancement in supersonic flow with transverse injection. Int J Hydrogen Energy 2015;40(25):8193e205. [34] Huang W, Wang ZG, Wu JP, Li SB. Numerical prediction on the interaction between the incident shock wave and the transverse slot injection in supersonic flows. Aerosp Sci Technol 2013;28:91e9. [35] Gerdroodbary MB, Jahanian O, Mokhtari M. Influence of the angle of incident shock wave on mixing of transverse hydrogen micro-jets in supersonic crossflow. Int J Hydrogen Energy 2015;40:9590e601. [36] Huang W, Tan JG, Liu J, Yan L. Mixing augmentation induced by the interaction between the oblique shock wave and a sonic hydrogen jet in supersonic flows. Acta Astronaut 2015;117:142e52. [37] Tahsini AM, Mousavi ST. Investigating the supersonic combustion efficiency for the jet-in-cross-flow. Int J Hydrogen Energy 2015;40:3091e7. [38] Hariharan V, Velamati RK, Prathap C. Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions. Int J Hydrogen Energy 2016;41:5833e41. [39] Gerdroodbary MB, Mokhtari M, Fallah K, Pourmirzaagha H. The influence of micro air jets on mixing augmentation of transverse hydrogen jet in supersonic flow. Int J Hydrogen Energy 2016;41:22497e508. [40] Bo W, Liu W, Zhao Y, Fan X, Chao W. Experimental investigation of the micro-ramp based shock wave and turbulent boundary layer interaction control. Phys Fluids 2012;24:1166e75. [41] Sun Z, Schrijer FFJ, Scarano F, Oudheusden BWV. Decay of the supersonic turbulent wakes from micro-ramps. Phys Fluids 2014;26, 025115. [42] Zhang Y, Liu W, Wang B, Sun M. Effects of micro-ramp on transverse jet in supersonic crossflow. Acta Astronaut 2016;127:160e70. [43] Li LQ, Huang W, Yan L. Mixing augmentation induced by a vortex generator located upstream of te transverse gaseous jet in supersonic flows. Aerosp Sci Technol 2017;68:77e89. [44] Randolph H, Chew L, Johari H. Pulsed jets in supersonic crossflow. J Propuls Power 2015;10:746e8. [45] Ombrello T, Carter C, Mccall J, Schauer F, Naples A, Hoke J, et al. Enhanced mixing in supersonic flow using a pulse detonator. J Propuls Power 2014;31. [46] Kouchi T, Sasaya K, Watanabe J, Shibayama H, Masuya G. Penetration characteristics of pulsed injection into supersonic crossflow. In: AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit; 2013. p. 1301e8.
13
[47] AIAA, High frequency supersonic pulsed injection. [48] Davitian J, Hendrickson C, Getsinger D, M'Closkey RT, Karagozian AR. Strategic control of transverse jet shear layer instabilities. AIAA J 2010;48:2145e56. [49] Narayanan S, Barooah P, Cohen JM. Dynamics and control of an isolated jet in crossflow. AIAA J 2003;41:2316e30. [50] Shang J. Computational fluid dynamics application to aerospace science. Aeronaut J New Ser 2009;113:619. [51] Vyas M, Engblom W, Georgiadis N, Trefny C, Bhagwandin V. Numerical simulation of vitiation effects on a hydrogenfueled dual-mode scramjet. 2010. NASA/TM-2010-216756, AIAA-2010-1127. [52] 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. [53] Xiao Y, Song W, Chen L, Wang D, Le J. Investigations on ethylene combustion in a scramjet combustor using resistance heaters. Proc Inst Mech Eng Part G J Aerosp Eng 2008;222:411e6. [54] Gao ZX, Lee CH. Numerical research on mixing characteristics of different injection schemes for supersonic transverse jet. Sci China Technol Sci 2011;54(4):883e93. [55] Ivanova EM, Noll BE, Aigner M. A numerical study on the turbulent schmidt numbers in a jet in crossflow. In: ASME turbo expo 2012: turbine technical conference and exposition; 2013. p. 949e60. [56] Bardina JE, Huang PG, Coakley TJ. Turbulence modeling validation, testing, and development. 1997. [57] Freeborn AB, King PI, Gruber MR. Swept-leading-edge pylon effects on a scramjet pylon-cavity flameholder flowfield. J Propuls Power 2012;25:571e82. [58] Erdem E, Kontis K. Numerical and experimental investigation of transverse injection flows. Shock Waves 2010;20:103e18. [59] Spaid FW, Zukoski EE. A study of the interaction of gaseous jets from transverse slots with supersonic external flows. AIAA J 2015;6:205e12. [60] Smirnov NN, Betelin VB, Shagaliev RM, Nikitin VF, Belyakov IM, Deryuguin YN, et al. Hydrogen fuel rocket engines simulation using LOGOS code. Int J Hydrogen Energy 2014;39:10748e56. [61] Huang W, Li LQ, Chen XQ, Yan L. Parametric effect on the flow and mixing properties of transverse gaseous injection flow fields with streamwise slot: a numerical study. Int J Hydrogen Energy 2017;42:1252e63. [62] Segal C. The scramjet engine: processes and characteristics. Cambridge University Press; 2009. [63] Huang W, Li LQ, Yan L, Liao L. Numerical exploration of mixing and combustion in a dual-mode combustor with backward-facing steps. Acta Astronaut 2016;127:572e8. [64] Huang W, Yan L. Progress in research on mixing techniques for transverse injection flow fields in supersonic crossflows. J Zhejiang Univ Sci A 2013;14:554e64.
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Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows Lang-quan Li, Wei Huang*, Li Yan, Zhen-tao Zhao, Lei Liao Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
article info
abstract
Article history:
A good injection strategy with high penetration and mixing efficiency relates to the overall
Received 12 March 2017
performance of the airbreathing hypersonic propulsion system. In the current study, the
Received in revised form
transverse injection flow field with a vortex generator placed in front of jet has been
31 May 2017
investigated, and the jet mixing enhancement and penetration improvement induced by
Accepted 2 June 2017
the pulsed jet has been evaluated as well. The obtained results predicted by the three-
Available online xxx
dimensional Reynolds-average Navier e Stokes (RANS) equations coupled with the two equation k-u shear stress transport (SST) turbulence model show that the jet-to-crossflow
Keywords:
pressure ratio has an great impact on penetration depth and mixing efficiency in the steady
Pulsed jet
jet flow field. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency
Jet-to-crossflow pressure ratio
but lower penetration depth are shown. On the other hand, compared with the steady jet
Transverse injection
flow field, the pulsed jet flow field with the periodic variation of jet-to-crossflow pressure
Mixing efficiency
ratio of the fuel injection has better comprehensive performance, and the penetration
Penetration depth
depth and mixing efficiency are improved simultaneously. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The scramjet (supersonic combustion ramjet) engine may be one of the most promising propulsion systems for hypersonic vehicles in the near future, because an oxidizer tank is not required in these engines and high efficiency can be obtained when vehicles fly in or beyond the supersonic speed. The presence of these advantages has motivated the researchers in recent years [1e3]. The realization of sufficient mixing is the main challenge for the design of the scramjet engine on account of the short residence time of airflow within the scramjet combustor being on the order of milliseconds for typical flight conditions [4].
Therefore, a good injection strategy with large penetration depth and high mixing efficiency is required within the scramjet combustor. One simplest and reliable fuel injection strategy for a scramjet engine is transverse injection into the airflow, because transverse injection provides rapid fuel-air mixing and high jet penetration into the supersonic airflow [5,6]. At first, the majority of studies have concentrated on a single transverse jet at a variety of conditions such as jet-tocrossflow pressure ratio [7], jet-to-crossflow momentum flux ratio [8,9], molecular weight [10], injector geometry [11], injection angle [12], incoming air steam angle [13]. Threedimensional transverse jet in supersonic crossflow was optimized by Huang [14], and the multi-objective optimization
* Corresponding author. E-mail address: [email protected] (W. Huang). http://dx.doi.org/10.1016/j.ijhydene.2017.06.014 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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results were explored by the variance analysis method. Further, he and his co-workers investigated the influence of the pseudo shock wave induced by the back pressure on the mixing process between the fuel and air in the transverse injection flow field numerically [15]. Subsequently, a variation on the conventional single jet in crossflow is the multiple transverse injection system [16e18], and complication of an efficient injection system setup arise due to more parameters, including distributions of mass flow rate and momentum flux, injection angle and combination of injection angles, arrangement of injector geometry and spacing variation in both the freestream and spanwise directions [19]. In addition, many mixing enhancement devices such as strut [20e23], ramp [24], pylon [25], cavity [26e28], aerodynamic ramp [29], and any other combination have been offered and used to enhance mixing and penetration substantially, but at the expense of a larger pressure loss, increasing drag forces, and inciting considerable local heating loads [30]. In 2013, a novel injection strategy was proposed by Huang et al. [31], and it has been analyzed parametrically [31] and optimized by the multiobjective design optimization approach [32]. In 2015, the upstream and downstream regions of fuel injection slot were connected through a channel by Han et al. [33] to obtain efficient fuel/air mixing and combustion. Further, additional oblique shock wave was introduced in the transverse injection flow field in order to enhance the mixing process between the fuel and air [34e36], as well as the combustion efficiency of hydrogen injection into the supersonic cross-flow [37,38]. Multi air jets were introduced into the transverse injection flow field by Gerdroodbary et al. [39] to improve the mixing process between the fuel and air as well. In order to minimize the total pressure loss, as well as the drag force, and improve the jet penetration and mixing efficiency, the microramp is a viable mean [40e42]. The authors have investigated the influences of the microramp height and the jet-to-crossflow pressure ratio on the mixing process between the fuel and the supersonic crossflow, and the microramp has been proved to have a highly remarkable improvement in mixing characteristics such as mixing efficiency and fuel penetration depth, see Fig. 1 and Table 1, but at the expense of an excessive loss of stagnation pressure [43]. Fig. 1 depicts the mixing efficiency comparison for different models at the same jet-to-crossflow pressure ratio, (a) Pj/ P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, and (c) Pj/P∞ ¼ 25.15, and Models A, B, C and D are the case with the microramp height being 0 mm, 5.0 mm, 6.0 mm and 7.0 mm respectively. Table 1 summarizes and compares the penetration depths of Models A, B, C and D. Because of the tiny size, it can immerse into the boundary layer, thus the total pressure loss is obviously small. When the jet orifice is placed downstream the microramp, the counter vortices pairs (CVPS) produced by the microramp, the vortex shedding off the edge and a local separation at the base can enhance the mixing process. At the same time, the lowmomentum wake flow due to the blocking of the microramp provides an ideal condition to increase the jet penetration. On the other hand, the pulsed jet is a potential strategy for enhancing the mixing efficiency and improving the jet penetration [44], and it has been considered as a control approach for jets in crossflow [45,46]. The influences of the pulsation frequency, amplitude and waveform shape have been studied
theoretically and experimentally. The obtained results show that the pulsation frequency may greatly affect the jet penetration [47], and the pulsation amplitude is associated with the jet shear layer evolution [48]. The sinusoidal excitation at high jet-to-inflow velocity ratio can improve jet penetration [49]. Of course, the mixing efficiency can be further improved due to the pulsatile nature of the flow. Computational Fluid Dynamics is an efficient approach to perform parametric studies and check whether design changes are worth testing experimentally. At the same time, it also provides important insight into complex flow phenomena like separations and shock wave, thus it can significantly improve the flowpath design process for relatively lower costs compared with costly experimental tests alone [50,51]. According to the previous studies carried out by the authors [52], the jet-to-crossflow pressure ratio is one of the important factors for the supersonic jet-to-crossflow flow field. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency is shown. The higher jet-to-crossflow pressure ratio is, and the larger jet penetration depth is. Considering the respective advantages of the jet-to-crossflow flow fields induced by high and low jet-to-crossflow pressure ratios, User Defined Function can be used to realize the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-to-crossflow pressure ratios. Therefore, the flow field with better performance may be achieved, and the microramp has a highly remarkable improvement on mixing characteristics such as mixing rate and penetration. To the best of the authors' knowledge, the flow field induced by the pulsed jet and the microramp simultaneously has rarely been investigated in the open literature, and it is a promising mixing enhancement strategy in supersonic flows. Thus, the investigation of the flow field with a vortex generator placed in front of the pulsed jet is meaningful. Therefore, in this paper, the mixing enhancement induced by the pulsed jet and the vortex generator in a Mach 3.75 crossflow of air has been studied numerically, and this is the subsequent work of Ref. [43]. The main performance parameters concerned in the present study are mixing efficiency and penetration depth, and the influence of the pulsed jet on the flow field performance has been evaluated. The flow structure has been analyzed in combination with hydrogen mass/mole fraction contour and hydrogen mass fraction iso-surface in the near filed of the jet as well. In Sections, the Physical model, the Boundary condition setting and the Numerical approach are described in detail respectively. Section provides the Computing process, and the Code validation and grid independency analysis process is shown in Section. In Section Results and discussion, the mixing process induced by the vortex genesrator and the pulsed jet is analyzed from the flow structure and the performance parameters. At last, some conclusions are made according to the numerical simulation.
Physical model The test section is a straight channel, and Fig. 2 shows the plan and symmetric views of transverse gaseous injection
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 1 e Mixing efficiency comparison for different models at the same jet-to- crossflow pressure ratio, (a) Pj/P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, and (c) Pj/P∞ ¼ 25.15 [43].
model employed in this study. A vortex generator is mounted along the center of the flat plate with the leading edge of the vortex generator located 64 mm downstream from the leading edge of the flat plate, and the leading edges of the vortex generator and the flat plate are parallel, and the wall orifice with its diameter being 1 mm is located at 5 mm downstream the trailing point of the vortex generator. The origin of the
coordinate system is set at the leading edge of the flat plate, the width of the flat plate is 120 mm, the height of the computational domain is 80 mm, and its length is 680 mm. The width and the side length of the vortex generator are 24 mm and 20 mm respectively.
The setting of the boundary conditions and the realization of the pulsed jet Table 1 e Penetration depth comparison of Models A, B, C and D (unit: mm) [43]. Pj/P∞
Model A
Model B
Model C
Model D
10.29 17.72 25.15
3.70 4.74 5.59
6.27 6.68 7.13
7.53 7.72 8.43
9.37 9.64 9.65
The air flows from left to right, and its air properties are set to be a Mach number M∞ of 3.75, a static pressure P∞ of 11090Pa and a static temperature T∞ of 78.43 K. The supersonic freestream (air) is composed of 21% O2 and 79% N2, and this means that mass fractions for O2 and N2 are 0.21 and 0.79 respectively. The hydrogen is set as the injectant for it is
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 2 e Schematic of transverse gaseous injection with a vortex generator (unit: mm).
generally a more energetic fuel than hydrocarbon fuels for a Mach number in the range 4e10 [53], and its mass fraction is 1.0. The steady injection flow Mach number Mj is set to be 1.0 with a constant static temperature Tj ¼ 249 K. These conditions are representative of a typical generic scramjet combustor. The air is assumed to be a thermally and calorically perfect gas, and the mass-weighted-mixing- law of viscosity is employed. According to the previous studies carried out by the authors [11], the jet-to-crossflow pressure ratios of three steady jet flow fields are set to be 10.29, 17.72 and 25.15. At the outflow, all the physical variables are extrapolated from the internal cells due to the flow being supersonic [53], the no-slip conditions (u ¼ v ¼ w ¼ 0.0) are assumed for the walls of the channel, and the boundary inlet and the injector exit are both set to be pressure inlet. The thermal condition is that the heat flux along the walls is 0.0 by default. Based on the high-speed [47] and low-speed studies [49], the pulsation waveform shape is chosen as sine wave for the pulsed jet. The mean jet static temperature and flow Mach number are equal to the counterparts described above for the steady jet. The interval of the periodic variation of jet-to-crossflow pressure ratio of the pulsed jet flow field is 10.29e25.15. Further, in order to make the jet flow Mach number Mj to be 1.0, the stagnation and static pressures of the pulsed jet must satisfy the following relationship: P0 ¼ Pj
g g 1 2 g1 Mj 1þ 2
(1)
herein, P0 and Pj are the instantaneous stagnation and static pressures of the pulsed jet respectively, and g is the gas thermodynamic parameter. In order to realize the periodic variation of jet-to-crossflow pressure ratio of the fuel injection, the stagnation and static pressures of the pulsed jet can be described as
P25:15 2p P0 ¼ P10:29 1 þ 106 t 1 sin 9 P10:29 g g 1 2 g1 Mj 1þ 2
(2)
and P25:15 2p 106 t 1 sin Pj ¼ P10:29 1 þ 9 P10:29
(3)
herein, P10.29 and P25.15 represent the instantaneous static pressure of the pulsed jet when the instantaneous jet-to-crossflow pressure ratio of the pulsed jet is 10.29 and 25.15 respectively.
Numerical approaches The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations and the two equation SST k-u turbulence model has been utilized to numerically simulate the transverse injection flow field. The equations are solved along with density based (coupled) double precision solver of FLUENT. A Dell workstation at the Science and Technology on Scramjet Laboratory, China, using up to 32 processors, provided a parallel computing environment for flow solutions. The second order spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is utilized to quicken the convergence speed. The governing equations are as follows [54]: vðrYs Þ v v vYs þ rDs ; s ¼ 1; 2; …; ns rYs uj ¼ vt vxj vxj vxj
(4)
vr v þ ruj ¼ 0 vt vxj
(5)
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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 x x x ( 2 0 1 7 ) 1 e1 3
vtij vðrui Þ v þ rui uj þ dij p ¼ vt vxj vxj vðrEÞ v v þ rHuj ¼ vt vxj vxj
tij ui þ k
ns vT X vYs þ rDs hs vxj s¼1 vxj
(6)
v v v vu ðruÞ þ ðruui Þ ¼ Gu þ Gu Yu þ Du þ Su vt vxi vxj vxj
(7)
The compressibility takes part in dissipation terms such as Yk and Yu and partically in the production of turbulence kinetic energy is defined as follows:
!
The state equation of gas is ns X Ys P ¼ rRT M s s¼1
(8)
where r is the gas density, ui and uj are the velocity components in the xi and xj directions, respectively, p is the pressure and T is the static temperature. tij is the molecular stress tensor, and it should be closed by the turbulence model. E is the total energy per unit volume. E¼
ns X s¼1
Ys h s þ
p 1 2 u þ v2 þ w2 2 r
(9)
H is the total enthalpy per unit volume, ns is the total number of species, R is the universal constant of gas, Ms, Ys, Ds and hs are the molecular weight, mass fraction, mass diffusion coefficient and absolute enthalpy per unit mass of species s respectively. 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 [55], and it is considered for its good prediction of mixing layers and jet flows [52], as well as insensitive to initial values [56]. At the same time, this model is less sensitive to specification of freestream turbulence level compared to the k-u model, and it performs comparatively well in adverse pressure gradients and separated flows over either the k-u or k-ε models [57]. The transport equations for k and u can be refer to Ref. [58], see Eqs. (10) and (11). The sensitivity of the turbulence model on the predicted results of a transverse injection flow field with different jet-to-crossflow pressure ratios was investigated previously by the authors, see Ref. [52]. v v v vk fk Yk þ Sk ðrkui Þ ¼ Gk þG ðrkÞ þ vt vxi vxj vxj
5
(10)
(11)
Yk ¼ rb* ku
(12)
Yu ¼ rbu2
(13)
*
herein, b and b are functions of F(Mt). b* ¼ b*i 1 þ z* FðMt Þ
(14)
b* b ¼ bi 1 i z* FðMt Þ bi
(15)
z* ¼ 1.5, and the compressibility function F(Mt) is defines as follows: FðMt Þ ¼
0 M2t M2t0
Mt Mt0 Mt > Mt0
(16)
where, M2t ¼
2k a2
(17)
Mt0 ¼ 0:25 a¼
(18)
pffiffiffiffiffiffiffiffiffi gRT
(19)
The term Gk represents the production of turbulence kinetic energy, and it is affected by compressibility as well. The equation of Gk is defined as follows: Gk ¼ min Gk ; 10rb* ku
(20)
The computational domain is structured by the commercial software Gambit. Due to its symmetrical configuration, only half of the grid system is chosen for the following simulation. Fig. 3 (a) represents the whole grid system for the employed model of this article. Fig. 3 (b) shows the structured grid in the vicinity of the injection and the vortex generator. The O-type
Fig. 3 e Grid system of the model, (a) the whole grid system (b) grids near injection and vortex generator. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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grid is used for the jet nozzle and the Y-type grid is used for the vortex generator, and the grid density is clustered towards the wall orifice and the vortex generator in order to ensure the accuracy of the numerical simulation. The grid density is relaxed towards outlet. A boundary layer grid is generated on the bottom wall with a first cell height of 0.01 mm, which results in a suitable value of yþ for all of the flow fields, and its maximum value is below 30.0 for all cases studied in the current study. This occurs in the vicinity of the vortex generator. yþ is a non-dimensional parameter defined by Eq. (21). yþ ¼
rut yP m
(21)
herein, ut is the friction velocity, yP is the distance from point P to the wall, r is the fluid density, and m is the fluid viscosity at point P.
Computing process The numerical simulation of the steady jet flow fields is carried out for the first step, and the Courant-Friedrichs-Lewy number defined as jujDt=Dl is ramped from 0.1 to 0.5 over almost the initial 10,000 steps with the progress of convergence to ensure stability, where u, Dt and Dl are the velocity, time and spatial steps respectively. The solutions can be considered as converged when most of the residuals reach their minimum values after falling for more than three orders of magnitude and the oscillation of the residuals are limited. At the same time, the computed inflow and the outflow mass flux is required to drop below 0.0001 kg/s. Further, the numerical simulation of the unsteady flow field is based on the steady flow field with the jet-to-crossflow pressure ratio being 10.29 in order to reduce computation time. In addition, the time step is set to be 10 ns for stability and detailed capture of the unsteady flow fields. The unsteady flow fields with the instantaneous jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15 in the eleventh cycle are used for the following investigation.
spatial resolution of the wall pressure data. A comparison between numerical results and the avaiable published experimental data, as well as the grid independency analysis, has been provided by Huang et al. [52]. Fig. 4 (a) shows the comparison of wall pressure profiles for different grid scales with the SST k-u turbulence model when the jet-to-crossflow pressure ratio is 17.12, and the grid scale makes only a slight difference to the numerical results. Although there are some differences between the numerical results and the experimental data, the wall pressure trends are the same. The maximum error percentage deviations upstream and downstream of the injection are about 46.90% and 23.81% respectively, and the separation length upstream of the injection is underestimated as well. This is related to the parallel computing environment and the numerical method employed [60]. The accumulation of stochastic error is proportional to the number of time steps and depends on the accuracy of the scheme and the approximation error. The numerical approach mentioned above has been utilized successfully in previous studies [61]. In order to investigate grid independency of the numerical simulations, three different grid scales of the model are employed, namely the coarse (348,331 cells), the moderate (492,474 cells), and the refined (707,199 cells) grids. Fig. 4 (b) depicts the wall pressure distribution comparison for the jet-to-crossflow pressure ratio being 10.29 with three different grid scales, and it is clear that the predicted results of three different grid scales match well. The discrepancy between the results predicted by the moderate and refined grids is much smaller than that between the results predicted by the coarse and moderate grids. Therefore, the moderate grid is chosen to carry out the following simulation in order to save the computational cost and reduce the computation time.
Results and discussion The analysis of flow structure
Code validation and grid independency analysis In the current study, the experimental cases of Spaid and Zukoski [59] are of great value because they provide good
The flow feature is associated with the mixing process, and the difference of the flow feature means the difference of the mixing performance. Therefore, the flow features of the
Fig. 4 e Comparison of wall pressure profiles for different grid scales, (a) validation of numerical methods, (b) grid independency analysis. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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steady and pulsed jets into supersonic crossflow are valuable to analyze. The 3D iso-surface colored by the injectant mass fraction being greater than 0.1, and the streamline distributions of the steady and pulsed jet flow fields with the jet-tocrossflow pressure ratio being 10.29, 17.72 and 25.15 are demonstrated in Fig. 5. At the same time, the hydrogen mole fraction contours on three cross-section planes and flat plate of the steady and pulsed jet flow fields with the jet-tocrossflow pressure ratio being 10.29, 17.72 and 25.15 are also depicted in Fig. 6. Judging from the streamlines in Fig. 5, a variety of vertical structures are generated downstream of the vortex generator, and the vortex structure downstream the injection is similar as the counter-rotating vortex pairs. These vortices roll up the jet surface, resulting in distorted 3D isosurface shown in Fig. 5 and the kidney-shaped plume appeared in Fig. 6. Comparing the three images of steady jet flow fields in Fig. 5 (a), (c), (e), with the increase of the jet-tocrossflow pressure ratio, the 3D iso-surface is thicker and the extension length is longer along the flow direction. This may indicate that the fuel and air can be mixed completely earlier in the case with lower jet-to-crossflow pressure ratios. According to the comparison of the hydrogen mole fraction contours on the same cross-sectional plane of the steady jet flow fields in Fig. 6 (a), (c), (e), the same inference can be obtained. Correspondingly, an interesting phenomenon appears in the pulsed jet flow fields shown in Fig. 5 (b), (d), (f). Although the instantaneous jet-to-crossflow pressure ratio is different, the flow field structures are almost the same. This may be the reason for the high frequency of jet oscillation. Referring to previous research conclusion, much lower or higher frequency may result in a quasi-steady flow field [26,27]. In the current study, this phenomenon is of great value. In Fig. 5, Judging from the size and the extension length of the 3D isosurface, when the jet-to-crossflow pressure ratio is relatively small, the fuel and air can be mixed completely earlier in the steady jet flow field. However, with the increase of the jet-to-
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crossflow pressure ratio, the advantage of the mixing performance of the pulsed jet flow field is gradually reflected. When the jet-to-crossflow pressure ratio is 25.15, this advantage is obvious. Moreover, there is a recirculation zone between the delta wing and the injection, and it is induced by the boundary layer separation caused by the subsequent adverse pressure gradient. In the case of higher jet-to-crossflow pressure ratio, more injectant would be brought into the recirculation zone in the steady jet flow fields according to Figs. 6 and 7. On the other hand, the hydrogen contents of the recirculation zone in the pulsed jet flow fields are almost the same, and more hydrogen content has been brought into the core flow. This phenomenon is beneficial for the mixing process between the fuel and air. Through the above analysis, the most prominent conclusion of this study is that the pulsed jet flow field with the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-to-crossflow pressure ratios can integrate the advantages of high and low jet-tocrossflow pressure ratios, and the flow field with better comprehensive performance is realized. In the following investigation, this conclusion will be validated by data obtained from the flow fields.
The analysis of performance parameters The mixing efficiency is one of the most important parameters because an enhancement of the mixing efficiency directly results in an enhancement of combustion in a scramjet combustor. The mixing efficiency is defined as follows [62]. Z m_ fuel; mixed ¼ 4¼ m_ fuel; total
areact rudA Z arudA
(22)
herein,
Fig. 5 e Comparison of the mass distribution and flow feature for the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 6 e Hydrogen mole fraction contours on three cross-section planes and flat plate of the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/ P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
areact ¼
a; a astoic að1 aÞ=ð1 astoic Þ; a > astoic
(23)
a is the injectant mass fraction, areact is the injectant fraction mixed in a proportion that react, astoic is the injectant stoichiometric mass fraction, m_ fuel; mixed is the mixed injectant mass flow and m_ fuel; 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. astoic is the injectant stoichiometric mass fraction, and its value is 0.0291 for the hydrogen and air [63]. The reactant fraction refers to the least-avaiable reactant, air, or fuel, depending on whether the mixture is lean or rich. In fuel-lean regions, the mixing efficiency parameter represents the fuel
fraction, and in fuel-rich regions the mixing efficiency refers to the air fraction [62]. In Eq. (22), 4 ¼ 1.0 indicates a perfectly mixed system, and the maximum value of fuel fraction must remain less than or equal to the stoichiometric ratio. When 4 ¼ 0.0, a must be 1.0, and this means that the injectant does not mix with the freestream. To probe into the underlying physics, the streamwise progression of the mixing efficiency is calculated and plotted in Figs. 8 and 9 from the slice data of the steady and pulsed jet flow fields evaluated at each streamwise station starting from the injection position with an increment of Dx ¼ 2 mm. For the steady jet flow fields, it is clear that the mixing efficiency decreases with the increase of the jet-to-crossflow pressure ratio. This conclusion is consistent with that observed in the traditional transverse injection flow field, see
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 7 e Hydrogen mole fraction contours on the symmetry plane of the steady jet and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
Ref. [64]. On the other hand, there are small discrepancies occur in the profiles of the mixing efficiency of the pulsed jet flow fields due to different instantaneous jet-to-crossflow pressure ratios of injection corresponding to different flow times. In order to evaluate the mixing performance of the pulsed jet flow fields, the comparison of the mixing efficiency for the steady and pulsed jet flow fields with the jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15 are exhibited in Fig. 9. It is clearly observed that along the streamwise direction, the mixing efficiency of the steady jet flow field is higher than that of the pulsed jet flow filed when the jet-to-crossflow pressure ratio is 10.29. When the jet-to-crossflow pressure ratio is 17.72, the mixing efficiencies of the steady and pulsed jet flow fields are nearly the same. However, when the jet-tocrossflow pressure ratio is 25.15, the mixing efficiency of the pulsed jet flow field has obvious advantages along the streamwise direction. These phenomena imply that the pulsating injection can make the mixing efficiency of the flow field to be at a stable and high level, even though the jet-tocrossflow pressure ratio of the fuel injection varies periodically.
The fuel penetration depth is also a parameter that determines the scramjet engine performance to a certain extent, because an ideal penetration can minimize wall heating and maximize combustion efficiency. In this paper, the fuel penetration depth is assessed by the height above the floor where the hydrogen mass fraction of the jet plume reduces to 0.1. Fig. 10 depicts the hydrogen mass fraction contours on the symmetric plane in the range of 0.1e1 for the steady and pulsed jet flow fields with the jet-to-crossflow pressure ratio being 10.29, 17.72 and 25.15, and Table 2 statistics the penetration depth of all flow fields investigated in this study. A lot of information are reflected in Fig. 10 and Table 2. The first one is that the jet-to-crossflow pressure ratio has an great impact on the jet penetration depth in the steady jet flow fields. The larger jet-to-crossflow pressure ratio is, the greater penetration depth is. Secondly, the hydrogen mass fraction contours of the pulsed jet flow fields with different instantaneous jet-to-crossflow pressure ratios are almost the same, and it is worth noting that the penetration depth of the pulsed jet flow fields is always higher than that of the steady jet flow fields irrespective of the value of the jet-to-crossflow pressure ratio. This implies that the pulsating injection can make the
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 8 e Effect of the jet-to-crossflow pressure ratio on mixing efficiency of the steady flow fields jet and the pulsed jet flow fields, (a) the steady jet flow fields, (b) the pulsed jet flow fields.
Fig. 9 e Mixing efficiency comparison for the steady jet and pulsed jet flow fields at the same jet-to- crossflow pressure ratio, (a) Pj/P∞ ¼ 10.29, (b) Pj/P∞ ¼ 17.72, (c) Pj/P∞ ¼ 25.15. Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Fig. 10 e Comparison of the hydrogen mass fraction contour on the symmetry in the range of 0.1e1 for the steady jet flow fields and pulsed jet flow fields, (a) the steady jet with Pj/P∞ ¼ 10.29, (b) the pulsed jet with instantaneous Pj/P∞ ¼ 10.29, (c) the steady jet with Pj/P∞ ¼ 17.72, (d) the pulsed jet with instantaneous Pj/P∞ ¼ 17.72, (e) the steady jet with Pj/P∞ ¼ 25.15, (f) the pulsed jet with instantaneous Pj/P∞ ¼ 25.15.
penetration of the flow field to be at a higher value, even though the jet-to-crossflow pressure ratio of the fuel injection varies periodically. For the steady jet flow field with a single jet-to-crossflow pressure ratio, the jet-to-crossflow pressure ratio has an great impact on the mixing efficiency and the jet penetration depth. In the case of lower jet-to-crossflow pressure ratio, higher mixing efficiency but lower penetration depth are shown. This means that the realization of the steady jet flow field with faster sufficient mixing and higher penetration depth is contradictory when only the jet-to-crossflow pressure ratio is considered as the variable that affects the performance of the transverse injection flow fields. Compared with the steady jet flow field with a single jet-to-crossflow pressure ratio, the pulsed jet field has better comprehensive performance. In summary, the penetration depth and mixing efficiency are improved simultaneously.
Table 2 e Penetration depth of all flow fields considered in this study (unit: mm). Jet type
Steady jet Pulsating jet
Pj/P∞ 10.29
17.72
25.15
7.53 8.44
7.72 8.46
8.43 8.47
Conclusion In this article, the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations coupled with the two equation SST k-u turbulence model were employed to simulate the mixing characteristics of the transverse injection flow field with a delta wing vortex generator, and both pulsed and steady injections are simulated for comparison. The flow structures of the steady and pulsed jet flow fields with different jet-to-crossflow pressure ratios have been compared. The main focus is to analyze and compare the performance parameters of the transverse injection flow fields, such as the mixing efficiency and the fuel penetration depth. We have come to the following conclusions: The jet-to-crossflow pressure ratio has an great impact on the mixing efficiency and the jet penetration depth in the steady jet flow field. In the case of lower jet-tocrossflow pressure ratio, higher mixing efficiency but lower penetration depth are shown. The penetration depth for the steady jet increases from 7.53 mm to 8.43 mm, and that for the pulsed jet increases from 8.44 mm to 8.47 mm when the jet-to-crossflow pressure ratio increase from 10.29 to 25.15.
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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Due to the periodic variation of jet-to-crossflow pressure ratio of the fuel injection between high and low jet-tocrossflow pressure ratios, the penetration depth and mixing efficiency are improved simultaneously. The maximum penetration depth for the pulsed jet is 8.47 mm, and that for the steady jet is 8.43 mm. The pulsating jet is a promising injection strategy when compared with the steady jet at the same boundary conditions, and many parameters of the pulsating jet may be optimized to achieve better comprehensive performance of the trasverses injection flow field. This issue will be carried out by the multiobjective design optimization approach in the near future.
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Conflict of interest statement [15]
The authors declare there is no conflict of interest regarding the publication of this paper. [16] [17]
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No.11502291) and a fund for owner of Outstanding Doctoral Dissertation from the Ministry of Education of China (No.201460). Also, the authors thank the anonymous reviewers for some very critical and constructive recommendations on this article.
[18]
references
[21]
[1] Huang W, Jin L, Yan L, Tan JG. Influence of jet-to-crossflow pressure ratio on nonreacting and reacting processes in a scramjet combustor with backward-facing step. Int J Hydrogen Energy 2014;39:21242e50. [2] Fureby C, Chapuis M, Fedina E, Karl S. CFD analysis of the HyShot II scramjet combustor. Proc Combust Inst 2011;33:2399e405. [3] Pecnik R, Terrapon VE, Ham F, Iaccarino G, Pitsch H. Reynolds-averaged Navier-Stokes simulations of the HyShot II scramjet. AIAA J 2012;50:1717e32. [4] 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;14:63e74. [5] Watanabe J, Kouchi T, Takita K, Masuya G. Characteristics of hydrogen jets in supersonic crossflow: large-eddy simulation study. J Propuls Power 2013;29:661e74. [6] Yan L, Huang W, Zhang TT, Li H, Yan XT. Numerical investigation of the nonreacting and reacting flow fields in a transverse gaseous injection channel with different species. Acta Astronaut 2014;105:17e23. [7] Huang W. Transverse jet in supersonic crossflows. Aerosp Sci Technol 2016;50:183e95. [8] You Y, Lu¨deke H, Hannemann K. On the flow physics of a low momentum flux ratio jet in a supersonic turbulent crossflow. EPL 2012;97:24001e6 (24006). [9] Zhao M, Ye T, Cao C, Zhou T, Zhu M. Study of sonic injection from circular injector into a supersonic cross-flow using
[19]
[20]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
large eddy simulation. Int J Hydrogen Energy 2016;41:17657e69. Schetz JA, Maddalena L, Burger SK. Molecular weight and shock-wave effects on transverse injection in supersonic flow. J Propuls Power 2010;26:1102e13. Huang W, Liu J, Jin L, Yan L. Molecular weight and injector configuration effects on the transverse injection flow field properties in supersonic flows. Aerosp Sci Technol 2014;32:94e102. Aso S, Inoue K, Yamaguchi K, Tani Y. A study on supersonic mixing by circular nozzle with various injection angles for air breathing engine. Acta Astronaut 2009;65:687e95. Ali M, Islam AKMS. Study on main flow and fuel injector configurations for Scramjet applications. Int J Heat Mass Transf 2006;49:3634e44. 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. Huang W, Li MH, Yan L. Mixing augmentation mechanism induced by the pseudo shock wave in transverse gaseous injection flow fields. Int J Hydrogen Energy 2016;41:10961e8. Lee SH. Characteristics of dual transverse injection in scramjet combustor, Part 1: mixing. J Propuls Power 2006;22:1012e9. Huang W. Numerical investigation on staged sonic jet interaction mechanism in a supersonic cross flow. Proc Inst Mech Eng Part G J Aerosp Eng 2014;228(14):2641e51. Li ZW, Huai WX, Qian ZD. Study on the flow field and concentration characteristics of the multiple tandem jets in crossflow. Sci China Technol Sci 2012;55:2778e88. Huang W. Effect of jet-to-crossflow pressure ratio arrangement on turbulent mixing in a flowpath with square staged injectors. Fuel 2015;144:164e70. 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. Choubey G, Pandey KM. Effect of parametric variation of strut layout and position on the performance of a typical two-strut based scramjet combustor. Int J Hydrogen Energy 2017;42(15):10485e500. Huang W, Yan L. Numerical investigation on the ram-scram transition mechanism in a strut-based dual-mode scramjet combustor. Int J Hydrogen Energy 2016;41:4799e807. Huang W. Investigation on the effect of strut configurations and locations on the combustion performance of a typical scramjet combustor. J Mech Sci Technol 2015;29(12):5485e96. Seiner JM, Dash SM, Kenzakowski DC. Historical survey on enhanced mixing in scramjet engines. J Propuls Power 2001;17:1273e86. Vishwakarma M, Vaidyanathan A. Experimental study of mixing enhancement using pylon in supersonic flow. Acta Astronaut 2016;118:21e32. Huang W, Li MH, Ding F, Liu J. Supersonic mixing augmentation mechanism induced by a wall-mounted cavity configuration. J Zhejiang Univ Sci A 2016;17:45e53. Tian Y, Yang S, Le J, Su T, Yue M, Zhong F, et al. Investigation of combustion and flame stabilization modes in a hydrogen fueled scramjet combustor. Int J Hydrogen Energy 2016;41:19218e30. Huang W, Wang ZG, Yan L, Liu WD. Numerical validation and parametric investigation on the cold flow field of a typical cavity-based scramjet combustor. Acta Astronaut 2012;80:132e40. Yan Z, Bing C, Gang L, Wei B, Xu X. Influencing factors on the mode transition in a dual-mode scramjet. Acta Astronaut 2014;103:1e15. Portz R, Segal C. Penetration of gaseous jets in supersonic flows. AIAA J 2006;44:2426e9.
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014
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[31] 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. [32] Huang W, Li SB, Yan L, Tan JG. Multiobjective design optimization of a cantilevered ramp injector using the surrogate-assisted evolutionary algorithm. J Aerosp Eng 2015;28, 04014138. [33] Han X, Ye T, Chen Y. Effects of self-throttling on combustion enhancement in supersonic flow with transverse injection. Int J Hydrogen Energy 2015;40(25):8193e205. [34] Huang W, Wang ZG, Wu JP, Li SB. Numerical prediction on the interaction between the incident shock wave and the transverse slot injection in supersonic flows. Aerosp Sci Technol 2013;28:91e9. [35] Gerdroodbary MB, Jahanian O, Mokhtari M. Influence of the angle of incident shock wave on mixing of transverse hydrogen micro-jets in supersonic crossflow. Int J Hydrogen Energy 2015;40:9590e601. [36] Huang W, Tan JG, Liu J, Yan L. Mixing augmentation induced by the interaction between the oblique shock wave and a sonic hydrogen jet in supersonic flows. Acta Astronaut 2015;117:142e52. [37] Tahsini AM, Mousavi ST. Investigating the supersonic combustion efficiency for the jet-in-cross-flow. Int J Hydrogen Energy 2015;40:3091e7. [38] Hariharan V, Velamati RK, Prathap C. Investigation on supersonic combustion of hydrogen with variation of combustor inlet conditions. Int J Hydrogen Energy 2016;41:5833e41. [39] Gerdroodbary MB, Mokhtari M, Fallah K, Pourmirzaagha H. The influence of micro air jets on mixing augmentation of transverse hydrogen jet in supersonic flow. Int J Hydrogen Energy 2016;41:22497e508. [40] Bo W, Liu W, Zhao Y, Fan X, Chao W. Experimental investigation of the micro-ramp based shock wave and turbulent boundary layer interaction control. Phys Fluids 2012;24:1166e75. [41] Sun Z, Schrijer FFJ, Scarano F, Oudheusden BWV. Decay of the supersonic turbulent wakes from micro-ramps. Phys Fluids 2014;26, 025115. [42] Zhang Y, Liu W, Wang B, Sun M. Effects of micro-ramp on transverse jet in supersonic crossflow. Acta Astronaut 2016;127:160e70. [43] Li LQ, Huang W, Yan L. Mixing augmentation induced by a vortex generator located upstream of te transverse gaseous jet in supersonic flows. Aerosp Sci Technol 2017;68:77e89. [44] Randolph H, Chew L, Johari H. Pulsed jets in supersonic crossflow. J Propuls Power 2015;10:746e8. [45] Ombrello T, Carter C, Mccall J, Schauer F, Naples A, Hoke J, et al. Enhanced mixing in supersonic flow using a pulse detonator. J Propuls Power 2014;31. [46] Kouchi T, Sasaya K, Watanabe J, Shibayama H, Masuya G. Penetration characteristics of pulsed injection into supersonic crossflow. In: AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit; 2013. p. 1301e8.
13
[47] AIAA, High frequency supersonic pulsed injection. [48] Davitian J, Hendrickson C, Getsinger D, M'Closkey RT, Karagozian AR. Strategic control of transverse jet shear layer instabilities. AIAA J 2010;48:2145e56. [49] Narayanan S, Barooah P, Cohen JM. Dynamics and control of an isolated jet in crossflow. AIAA J 2003;41:2316e30. [50] Shang J. Computational fluid dynamics application to aerospace science. Aeronaut J New Ser 2009;113:619. [51] Vyas M, Engblom W, Georgiadis N, Trefny C, Bhagwandin V. Numerical simulation of vitiation effects on a hydrogenfueled dual-mode scramjet. 2010. NASA/TM-2010-216756, AIAA-2010-1127. [52] 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. [53] Xiao Y, Song W, Chen L, Wang D, Le J. Investigations on ethylene combustion in a scramjet combustor using resistance heaters. Proc Inst Mech Eng Part G J Aerosp Eng 2008;222:411e6. [54] Gao ZX, Lee CH. Numerical research on mixing characteristics of different injection schemes for supersonic transverse jet. Sci China Technol Sci 2011;54(4):883e93. [55] Ivanova EM, Noll BE, Aigner M. A numerical study on the turbulent schmidt numbers in a jet in crossflow. In: ASME turbo expo 2012: turbine technical conference and exposition; 2013. p. 949e60. [56] Bardina JE, Huang PG, Coakley TJ. Turbulence modeling validation, testing, and development. 1997. [57] Freeborn AB, King PI, Gruber MR. Swept-leading-edge pylon effects on a scramjet pylon-cavity flameholder flowfield. J Propuls Power 2012;25:571e82. [58] Erdem E, Kontis K. Numerical and experimental investigation of transverse injection flows. Shock Waves 2010;20:103e18. [59] Spaid FW, Zukoski EE. A study of the interaction of gaseous jets from transverse slots with supersonic external flows. AIAA J 2015;6:205e12. [60] Smirnov NN, Betelin VB, Shagaliev RM, Nikitin VF, Belyakov IM, Deryuguin YN, et al. Hydrogen fuel rocket engines simulation using LOGOS code. Int J Hydrogen Energy 2014;39:10748e56. [61] Huang W, Li LQ, Chen XQ, Yan L. Parametric effect on the flow and mixing properties of transverse gaseous injection flow fields with streamwise slot: a numerical study. Int J Hydrogen Energy 2017;42:1252e63. [62] Segal C. The scramjet engine: processes and characteristics. Cambridge University Press; 2009. [63] Huang W, Li LQ, Yan L, Liao L. Numerical exploration of mixing and combustion in a dual-mode combustor with backward-facing steps. Acta Astronaut 2016;127:572e8. [64] Huang W, Yan L. Progress in research on mixing techniques for transverse injection flow fields in supersonic crossflows. J Zhejiang Univ Sci A 2013;14:554e64.
Please cite this article in press as: Li L-q, et al., Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.06.014