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Effects of micro-ramp on transverse jet in supersonic crossflow
Acta Astronautica 127 (2016) 160–170
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Effects of micro-ramp on transverse jet in supersonic crossflow Yujie Zhang a,b, Weidong Liu a,b,n, Bo Wang a,b, Mingbo Sun a,b a b
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 March 2016 Accepted 25 May 2016 Available online 28 May 2016
The effects of micro-ramp on the characteristics of transverse jet were investigated by the LES simulation at Mach 2.7, with recycling-rescaling method applied to reproduce the turbulent boundary layer. The transverse nitrogen jet in front of micro-ramp and behind micro-ramp were studied by comparison with plate jet. It is found that the micro-ramp can improve the penetration height obviously, while placing jet orifice behind micro-ramp, due to the low freestream momentum in ramp wake. On the other hand, when placing the jet orifice in front of micro-ramp, the improvement in penetration is quite slight, because most injection is above the boundary layer and micro-ramp has little influence on the main flow. It is also observed that unlike the periodic Kevin Helmholtz (K–H) vortices appeared in ramp wake, the periodic K–H vortices are not achieved in jet cases. & 2016 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Transverse jet Micro-ramp Supersonic flow
1. Introduction As one of the crucial issues influencing the mixing efficiency, ignition and flame holding in scramjet, the fuel injection has been investigated for many years. Due to its simplest and most conventional design, the transverse jet is the main method applied in scramjet. Considering requirements in engineering and restriction in study means, researchers mainly focus on time-averaged parameters of jet, such as penetration height, mass fraction distribution, total pressure loss in previous study. And the influence of jetto-freestream momentum flux ratio [1–5], configuration of injection orifice [4,6], molecular weight [6–8] on the averaged parameters are widely investigated for several years. Plenty of researches prove that the jet-to-freestream momentum flux ratio is the main factor influencing jet penetration height. With the advancement of experimental equipment, Rayleigh/ Mie scattering imaging technique [9], planar laser induced fluorescence (PLIF) [10,11] and ultrahigh-speed schlieren [12] are applied to study the turbulent behavior in transverse jet. Gruber et al. [9] indicated that the compressibility of the mixing layer was the main parameter affecting the behavior of turbulent structures. Ben-Yakar et al. [12] pointed out the velocity difference was the key point influencing the turbulent behavior in shear layer by the n Corresponding author at: College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China. E-mail address: [email protected] (W. Liu).
http://dx.doi.org/10.1016/j.actaastro.2016.05.032 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved.
stretching-tilting-tearing mechanism. Meanwhile, with the improvement of computational resources, large eddy simulation (LES) has provided further insight into the mixing progress and development of turbulent structures in jet plume [13–17]. According to the former study, two main disadvantages in transverse jet are outstanding. First, large supply pressures is needed to achieve high penetration in transverse jet. Second, some injection is seeded into the boundary layer, which often leads a phenomena know as flashback [18]. In addition, with demand of larger size scramjet emerging, to achieve a higher penetration and better mixing efficiency in main flow is very necessary. Aiming at improving the jet penetration and mixing efficiency, ramp injector is used as a viable mean, because of the vortex shedding off the edges and a local separation at the base [19,20]. In the traditional ramp jet, the direction of jet is general in streamwise and the configuration of ramp is unswept. Later, to produce a stronger pair of vortex, swept ramp was born [21,22]. Generally, to ensure strong pair of vortices and large separation region, the size of ramp is large. Thus, a thorny and inevitable problem emerges, that is how to minimize the added total pressure loss and drag when the traditional ramp injector is used in scramjet [21,23]. Lately, in the study of the shock-wave and boundary layer interaction (SWBLI), researchers used a micro-ramp immersing into the boundary layer to delay shock-induced turbulent boundarylayer separation [24,25]. The device can produce a counter vortices pairs (CVPs) in the near-wall region and upwash the low energy part of boundary layer into the main flow. Because of the tiny size, the micro-ramp always emerges into the boundary layer. Thus, the total pressure loss is obviously small. Also in the study of film-
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T0 Pj Tj ρj v 2j ρu2 J y1 Ap h c H η ϕ
Nomenclature density velocity exponent in j direction subgrid scale stress subgrid turbulent eddy viscosity coefficient subgrid length scale rate-of-strain tensor time energy Reynolds number Schmidt number boundary layer thickness stagnation pressure of inflow
ρ uj τijsgs vtsgs Δ¯ S T E Re Sc d P0
cooling jet [26,27], researchers placed the micro-ramp downstream the jet to produce CVPs that is in the contrary direction with the CVPs in jet plume. So the lift-off behave of CVPs in jet was much weaken. This application inspired us to using micro-ramp to produce CVPs that is in the same direction with CVPs in jet plume, then the jet penetration can be improved probably. Additionally, in the investigation of traditional ramp, Wilson et al. [28] placed the jet orifice in the front of ramp to enhance the penetration by the inclined ramp surface. Based on the idea mentioned above, the transverse jet placed in front of micro-ramp and behind micro-ramp are investigated by LES approach in this paper. First, the penetration and mixing efficiency in different jet cases are compared and the factors influencing the penetration are investigated. Then, the differences in injection plume distribution, streamwise vortex in different cases are studied. Last, statistical characteristics, such as time histories of the vortex structures, time correlation, mass fraction probability are analyzed.
stagnation temperature of inflow stagnation pressure of transverse jet stagnation temperature of transverse jet the momentum flux of transverse jet the momentum flux upstream jet orifice jet-to-freestream momentum flux ratio mass fraction of injection wedge half-angle of micro-ramp height of micro-ramp a chord length height of ramp wake mixing efficiency local equivalent ratio
(
∂ ρ¯ Y˜m ∂t
)+
μ ⎞ ∂Y˜ ⎤ 1 ⎛ μ ∂ ⎡ ˜ ⎢ ρ¯ Ym u˜ j − + t ⎟ m⎥ = 0 ⎜ Re ⎝ Sc Sct ⎠ ∂xj ⎦ ∂xj ⎣
where SGS stress
τijsgs
1
(5)
In these equations, the laminar and turbulent Prandtl numbers are given as Pr = 0.72 and Prt = 0.90. The subgrid kinetic energy k sgs is solved by the transport equation as expressed in Eq. (6).
∂ ( ρ¯ k sgs ) ∂t where
+
Pksgs
= −
∼ ∂ ( ρ¯ k sgsu j)
In the present study, the filtered dimensionless compressible Navier–Stokes equations for an ideal nonreactive gas are solved, with the one equation subgrid scale model (SGS) of Yoshizawa and Horiuti [29] used as below:
+
(1)
∂ ⎡ 1 1 sgs ⎤ τ¯ij + τ ⎥=0 ⎢ ρ¯ u˜ i u˜ j + p¯ δij − ∂xj ⎣ Re Re ij ⎦
(2)
( )
∂ ρ¯ E˜ ∂t
+
~ ∂T ∂ ⎡⎢ 1 κ 0 T0 + − u˜ i τji ρ¯ E˜ + p¯ u˜ j − κ κ ( ) t ∂xj ⎢⎣ ∂xj Re μ 0 u02 Re
−
μ ⎞ 1 ⎛ μ ∂Y˜ ⎤ + t ⎟ ∑ h˜ m m ⎥ = 0 ⎜ Re ⎝ Sc Sct ⎠ m ∂xj ⎥⎦
(
=
∂xj D sgs
and
τijsgs
ν sgs ⎞ ∂k sgs ⎤ ∂ ⎡ ⎛ ν ⎥ + Pksgs − D sgs ⎢ ρ¯ ⎜ + t ⎟ Prt ⎠ ∂xj ⎦ ∂xj ⎣ ⎝ Pr
(6)
is defined as below:
( ∂u∼i /∂xj ) /Δ
(7)
where the model constants are given as Cd = 1.0 and Cμ = 0.02075, following the work of Sun et al. [30].
2.1. LES equations
∂t
is modeled as below:
Δ¯ = ( ΔxΔyΔz ) 3
3/2
∂ ( ρ¯ u˜ i )
(4)
⎛∼ ⎞ 2 1∼ = − 2ρν ¯ tsgs ⎜ Sij − Skk δij ⎟ + ρ¯ k sgsδij ⎝ ⎠ 3 3
D sgs ≈ Cd ρ ( k sgs )
∂ ( ρ¯ u˜ j ) ∂ρ¯ + =0 ∂t ∂xj
τijsgs
vtsgs = Cμ Δ¯ k sgs
Pksgs 2. Numerical methods and the physical model
161
)
(3)
2.2. Physical model and simulation cases The micro-ramp in this paper is shown in Fig. 1(a), based on the physical model in Wang's paper [24]. Its height h is 3 mm, with a wedge half-angle Ap¼ 24° and a chord length c¼ 7.2 h. In this investigation, four different cases are simulated by LES. The simulation of transverse jet without ramp shown in Fig. 2 is denoted as ‘platejet’. Based on the different jet locations, there are two cases denoted as ‘front jet’, ‘back jet’. The jet locations are shown in Fig. 1(b). In each case, the origin of the Cartesian coordinate system is at the center of jet orifice. The fourth case is the micro-ramp placed in the flow field without jet, denoted as ‘ramp’. The mach number of inflow is 2.7 The stagnation pressure P0 and stagnation temperature T0 of inflow is 77.6 kPa and 300 K respectively. The corresponding unit Reynolds number Re is 6.95 × 106 The transverse sonic jet is from a circular orifice with diameter d ¼2 mm on the bottom wall. The stagnation pressure Pj of nitrogen jet is 136 kPa and the stagnation temperature Tj is 300 K with the jet-to-freestream momentum flux ratio J being 2.9. The origin of the Cartesian coordinate system is at the center of the orifice, and the X, Y, Z denote streamwise, transverse and spanwise directions, as shown in Fig. 2.
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Fig. 1. The configuration and locations of micro-ramp generator.
Fig. 2. Computational region sketch map of transverse jet without micro-ramp (the characteristic length d is 4 mm, which is the boundary layer thickness). Table 1. Grids distributions. Recycle region
Core region
X direction
Y direction
Z direction
X direction
Z direction
X þ ¼ 50
Y/d¼ 0∼2.5: Y þ ¼ 1–10
Zþ ¼14.5
Xþ ¼5
Zþ ¼5–12.5
2.3. Numerical schemes and grids Inviscid flux is solved with the fifth-order WENO scheme by Jiang and Shu [31], while viscous flux is discretized by the secondorder-accurate centered scheme. The time advancement is performed with the third-order Runge–Kutta scheme. To generate and sustain an unsteady incoming turbulent boundary layer, recyclingrescaling procedure of Xiao et al. [32,33] is adopted. The length of the recycling–rescaling region is 10d (the boundary layer thickness
Fig. 4. Penetration in different injection cases.
d is 4 mm, which is the characteristic length in the study). The recycle plane, computational region and boundary condition are shown in Fig. 2. The grid independence and the comparison between experiment and simulation have been done in early study as shown in
Fig. 3. Grid distribution in micro-ramp cases.
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163
Fig. 5. ρu2 contours in Z/d¼ 0 plane and mass fraction iso-surface y1 ¼0.8. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 6. Mass fraction contour of platejet and front jet in slice Z/d¼ 0. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
former studies [16,17]. The studies showed that the fine grid had the highest spatial resolution and could capture the small-scale structures in windward shear layer, which indicated that the distribution of the fine grid is reasonable. As this paper also focuses on the transverse jet in supersonic flow, the distribution scheme of fine grid mentioned in references [16,17] is adopted in this study, as shown in Table 1. And the girds distribution of recycle region and core region in all jet cases are the same. Considering complex
configuration of ramp, the immersed boundary method is adopted to enable a high-quality body-fitted grid around the micro-ramp generator, more details of this method are described in the work of Wang et al. [34]. The grid distribution around the micro-ramp is shown as in Fig. 3.
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penetration height of platejet, back jet and front jet are compared in Fig. 4. Obviously, the penetration height in back jet is the highest of all and the second highest case is the front jet. It can be observed that the penetration of platejet and front jet are nearly the same before X/d ¼1.8. But the penetration in front jet after X/ d¼ 1.8 has a slight increase. Considering the micro-ramp is located at the X/d ¼2.5, so this increase is mainly due to liftup of the inclined surface in micro-ramp. The former study [1–5] have shown that jet-to-freestream momentum flux ratio J is the key point to influence penetration height and the equation of J is shown in Eq. (8). In this study, the jet parameter is constant, so the freestream momentum flux ρu2 before jet orifice is the only variable in different cases. The freestream momentum flux ρu2 expressed in the denominator of Eq. (8) and the iso-surface of mass fraction y1 ¼ 0.8 are shown in Fig. 5. The black scale line is to measure the height of jet iso-surface and the ramp wake in different cases.
J=
Fig. 7. Mixing efficiency of different cases.
3. Results and discussions 3.1. Penetration height In this section, the method measuring the penetration height by averaged mass fraction [10] is adopted and the 10% iso-line of mass fraction is regarded as the penetration height. The
ρj v2j ρu2
(8)
In figure (a), it is observed that in the inflow boundary the freestream momentum flux is increasing with the arising of boundary layer in front of ramp. Markedly, after fluid flows across the micro-ramp generator, the freestream momentum flux decreases to about 0.01 sharply. With the ramp wake moving downstream, the freestream momentum flux and the thick of the wake both increase. Compared with other cases, due to the effect of micro-ramp, freestream momentum before jet orifice in back jet case is the smallest in the three jet cases. Thus, the jet-to-freestream
Fig. 8. Distribution of injection plume in different injection cases.
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165
Fig. 9. Steamwise vortices and mass fraction distribution at streamwise slice. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
momentum flux ratio is the largest in back jet case. And the penetration height is proportional to jet-to-freestream momentum flux ratio. So, the back jet case obtains the highest penetration. In this case, the penetration of mass fraction y1 ¼0.8 can reach Y/ d ¼1.8 as shown in figure (c), and the value in platejet case and front jet is 1.5 and 1.6, respectively, indicating that the liftup effect of micro-ramp in front jet case is slight, which is also shown in Fig. 4. The mass fraction contour of injection in slice Z/d¼ 0 is shown in Fig. 6. In the two figures, red dashed line is the height of inflow boundary layer. It can be seen that the core region of injection is mainly located in boundary layer. And for the sake of the small freestream momentum flux in boundary layer, most injection can penetrate into the main flow, as shown in Fig. 6. But, the microramp is mainly able to redistribute the fluid and energy in boundary layer [34]. So as shown in Figs. 4–6, micro-ramp has a slight impact to increase front jet penetration.
[35]:
η=
∫A
(
ρ ⋅u ⋅y1 ϕ
) dA
∫A ( ρ⋅u⋅y1 ) dA
⎧ 1, ϕ (y , z ) ≤ 1, y1 , ϕ (y , z ) = 14.79 × ϕ=⎨ ⎪ − 1 y1 ϕ ( ) ϕ ( ) > , , , 1 y z y z ⎩ ⎪
(9)
In the Eq. (9), A value of η = 1 indicates full uniformity and η = 0 indicates complete lack of injectant. A is area of the Y–Z plane, y1 is the mass fraction of the nitrogen and ϕ ( y, z ) is the local equivalent ratio at arbitrary location in Y–Z plane. The mixing efficiencies in different cases are shown in Fig. 7. In near flowfield, the difference in mixing is not obvious and the back jet case has a slight advantage. But in far flowfield, the curves of mixing efficiency have a rapid climb in back jet case, which shows a significant advantage in mixing. Thus, the back jet case obtains the best mixing not only in near flowfield but also in far flowfield.
3.2. Mixing efficiency 3.3. Distribution of the injection The mixing efficiency is calculated analogous to a simulated hydrocarbon gas with a molecular weight equal to nitrogen, such as ethylene. The expression of mixing efficiency η is as follows
3.3.1. Distribution of injection plume In this section, iso-surface of y1 ¼0.1 is regarded as the injection
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Fig. 10. Time histories of Q ¼ 0.1 iso-surface at X/d ¼16 in different cases.
plume boundary, as shown in Fig. 8. In the figures, the iso-surface mass fraction of y1 ¼0.1 is colored by normal height and the black line is the iso-line of normal height. In back jet case, the injection is the narrowest, but its penetration is the highest: the mass fraction of y1 ¼0.1 reaches Y/d ¼4 at X/d¼ 2.7 and Y/d ¼4.5 at X/ d ¼5.3. It also can be seen that the injection penetrate to Y/d¼ 3 at X/d ¼3 in front jet case and the penetration is Y/d ¼3 at X/d ¼11 in platejet. Compared with platejet case, the location that the jet reach Y/d¼ 3 is shorten about 8●d in front jet case.
case. In both of platejet and front jet at slice X/d¼ 4 and X/d¼8, the vortices is at the core region of injection. In the comparison of platejet and back jet case in figure (b) and (d), it is observed that the distribution of injection in back jet case is much higher than in platejet case and the streamwise vortex is at the bottom of injection all the time in back jet case. That means the streamwise vortex can make a little effect on the distribution of injection, which is not like the platejet and front jet case. In terms of the streamwise vortex area, the platejet has the largest area of all.
3.3.2. Distribution of streamwise vortex Fig. 9 shows the distribution of streamwise vortices contour in color with black solid line, black number and injection distribution in dashed red line with red number at X/d¼4 and 8. In figure (a), the location of streamwise vortices in front jet is almost the same with platejet case. The distribution of injection in front jet is a little higher than platejet case and the difference in height is nearly equal to the height of micro-ramp at X/d¼4. In figure (c), the slice is downstream the micro-ramp. In this slice, the streamwise vortices by micro-ramp is strong as shown in red color and the streamwise vortices by jet in front jet case is a little bit higher than in platejet
3.4. Statistics of jet plume 3.4.1. Instantaneous results at different slices To clarify the characteristic of vortex structures in the jet plume, the time histories of the vortex structures at intervals of ti = 50∙t¯ is shown in Fig. 10. t¯ is the non-dimensional time in simulation and it is equal to 1.7∙10−3 . The data is obtain at X/d ¼16. In all the four figures, it can be observed that K-H vortices surround the jet plume. In Fig. 10(a), the structures of K–H vortices seem to have periodicity in this case. Compared with ramp case in figure (a), the periodicity of other cases is not seen, which is
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167
Fig. 11. Time correlation of temperature and density at X/d ¼ 16 in different cases.
confirmed by time correlation analysis in next section. In other three cases, the penetration of K–H vortices are higher than that in ramp case. In back jet case, the vortices reach Y/d ¼4, which is clearly the highest. 3.4.2. Time correlation analysis In 3.4.1 Section, the K–H vortices look like have periodicity in ramp wake. To confirm the periodicity, time correlation is calculated in all the cases, as shown in Fig. 11. The coefficient of time correlation Rt is shown in Eq. (10). In the equation, the c′ represents the fluctuation of passive scalar, such as temperature and density in this study. It is observed that in ramp case the Rt of temperature and density have good periodicity and the Rt in other cases do not have obvious periodicity. That is coincides with the time histories iso-surface results in 3.4.1 Section. The time correlation results indicate that the jet before micro-ramp destroys the inflow condition in front jet case and the jet behind micro-ramp destroys the ramp wake in back jet case, so the inherent
periodicity induced by micro-ramp in ramp wake can not be reproduced.
Rt =
c′ ( x, y , z, t0 ) ∙c′ ( x, y , z, t0 + Δt ) 2
2
c′ ( x, y , z, t0 ) ∙ c′ ( x, y , z, t0 + Δt )
(10)
3.4.3. Probability distribution of mass fraction To compare the difference in mixing effect, this section focuses on the probability distribution of mass fraction at X/d¼ 16 and 25 as shown in Fig. 12 and Fig. 13. For facilitating the statistics, the mass fraction y1 is divided into ten uniform intervals from 0 to 1. At X/d¼ 16 and X/d¼ 25, the probability distribution of front jet and platejet is almost the same, the only difference is that the probability distribution in front jet is a bit higher than in the platejet case, because of the micro-ramp liftup effect. In the comparison of platejet and back jet case as shown in Fig. 12(b) and Fig. 13(b), the probability in the center region of platejet is lower
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Fig. 12. Probability distribution of mass fraction at X/d ¼16.
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Fig. 13. Probability distribution of mass fraction at X/d ¼25.
than in the back jet, indicating that the probability that main flow get into the center region of jet plume in back jet is higher than in platejet. So the mixing effect in back jet case is better than in platejet case. Also, the location of the mass fraction probability in back jet is the highest, as shown in former sections.
4. Conclusions In the present study, the effects of micro-ramp on the characteristics of transverse jet in supersonic crossflow were investigated by LES approach. The simulation results in front jet and back jet case were compared with platejet. The conclusions were summarized as follows: ● The micro-ramp can decreases the freestream momentum in boundary layer remarkably, so the jet placed behind micro-ramp can obtain a obvious increase in penetration. ● Because the most injection is above the boundary layer and micro-ramp mainly control the flow in boundary layer, the
penetration in front jet is increased slightly. And the micro-ramp has little effect on the injection distribution in front jet case. ● The back jet case has a significant advantage in mixing not only in near flowfield but also in far flowfield, however, the improvement in mixing efficiency is slight in the front jet case. ● Through the time correlation analysis, it is found that the K–H vortices in the ramp wake has good periodicity, but the periodicity of K–H vortices does not exist in platejet, front jet and back jet case. ● Compared with the probability distribution of mass fraction in platejet, it is found that the main flow can reach the center of jet plume easier in back jet case.
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (Nos. 91216120, 51406233).
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Gaseous Fuel Injection, AIAA 2009-1422. [19] J.M. Donohue, J.C. McDaniel Jr., Complete three-dimensional multiparameter mapping of a supersonic ramp fuel injector flowfield, AIAA J. 34 (3) (1996) 455–462. [20] C.P. Goyne, J.C. McDaniel, T.M. Quagliaroli, et al., Dual-mode combustion of hydrogen in a Mach 5, continuous-flow facility, J. Propuls. Power 17 (6) (2001) 1313–1318. [21] T.M. Abdel-Salam, S.N. Tiwari, T.O. Mohieldin, Effects of ramp side angle in supersonic mixing, AIAA J. 41 (6) (2003) 1199–1201. [22] S. Aso, Y. Yamane, Y. Ando, et al. A Study on Supersonic Mixing Flowfield with Swept Ramp Injector, AIAA 97-0397. [23] C. Rock J.A. Schetz Experimental and Numerical Studies of a Strut Injector for Round Scramjet Combustors, AIAA 2009-7313. [24] B. Wang, W.D. Liu, Y.X. Zhao, Experimental investigation of the micro-ramp based shock wave and turbulent boundary layer interaction control, Phys. Fluids 24 (2012) 055110. [25] Z. Sun, F.F.J. Schrijer, F. Scarano, et al., Decay of the supersonic turbulent wakes from micro-ramps, Phys. Fluids 26 (2014) 025115. [26] K.B.M.Q. Zaman, D.L. Rigby, J.D. Heidmann, Inclined jet in crossflow interacting with a vortex generator, J. Propuls. Power 26 (5) (2010). [27] A.F. Shinn, S.P. Vanka, Large eddy simulations of film-cooling flows with a micro-ramp vortex generator, ASME J. Turbomach., vol. 135, pp. 011004. [28] M.P. Wilson, R.D.W. Bowersox, D.D. Glawe, Experimental investigation of the role of downstream ramps on a supersonic injection plume, J. Propuls. Power 15 (3) (1999). [29] A. Yoshizawa, K. Horiuti, A statistically-derived subgrid-scale kinetic energy model for large-eddy simulation of turbulent flows, J. Phys. Soc. Jpn. 54 (8) (1985) 2834–2837. [30] M.B. Sun, J.H. Han, Z.G. Wang, Numerical study on self-sustained oscillation characteristics of cavity flameholders in a supersonic flow, J Aerosp. Eng. 222 (1) (2008) 95–102. [31] G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comp. Phys 126 (1) (1996) 202–228. [32] X. Xiao, J.R. Edwards, H.A. Hassan, Inflow boundary conditions for hybrid large eddy/reynolds averaged navier–stokes simulations, AIAA J. 41 (8) (2003) 1481–1489. [33] C.C. Fan, X. Xiao, J.R. Edwards, Hybrid large-eddy/reynolds-averaged navier– stokes simulations of shock-separated flows, J. Spacecraft Rockets 41 (6) (2004) 897–906. [34] B. Wang, W.D. Liu, M.B. Sun, et al., Fluid redistribution in the turbulent boundary layer under the microramp control, AIAA J. 53 (12) (2015) 3777–3787. [35] D.W. Riggins, C.R. Mcclinton. A Computational Investigation of Mixing and Reaction Flows in Supersonic Combustors, AIAA Paper 92-0626.
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Acta Astronautica journal homepage: www.elsevier.com/locate/aa
Effects of micro-ramp on transverse jet in supersonic crossflow Yujie Zhang a,b, Weidong Liu a,b,n, Bo Wang a,b, Mingbo Sun a,b a b
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 March 2016 Accepted 25 May 2016 Available online 28 May 2016
The effects of micro-ramp on the characteristics of transverse jet were investigated by the LES simulation at Mach 2.7, with recycling-rescaling method applied to reproduce the turbulent boundary layer. The transverse nitrogen jet in front of micro-ramp and behind micro-ramp were studied by comparison with plate jet. It is found that the micro-ramp can improve the penetration height obviously, while placing jet orifice behind micro-ramp, due to the low freestream momentum in ramp wake. On the other hand, when placing the jet orifice in front of micro-ramp, the improvement in penetration is quite slight, because most injection is above the boundary layer and micro-ramp has little influence on the main flow. It is also observed that unlike the periodic Kevin Helmholtz (K–H) vortices appeared in ramp wake, the periodic K–H vortices are not achieved in jet cases. & 2016 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Transverse jet Micro-ramp Supersonic flow
1. Introduction As one of the crucial issues influencing the mixing efficiency, ignition and flame holding in scramjet, the fuel injection has been investigated for many years. Due to its simplest and most conventional design, the transverse jet is the main method applied in scramjet. Considering requirements in engineering and restriction in study means, researchers mainly focus on time-averaged parameters of jet, such as penetration height, mass fraction distribution, total pressure loss in previous study. And the influence of jetto-freestream momentum flux ratio [1–5], configuration of injection orifice [4,6], molecular weight [6–8] on the averaged parameters are widely investigated for several years. Plenty of researches prove that the jet-to-freestream momentum flux ratio is the main factor influencing jet penetration height. With the advancement of experimental equipment, Rayleigh/ Mie scattering imaging technique [9], planar laser induced fluorescence (PLIF) [10,11] and ultrahigh-speed schlieren [12] are applied to study the turbulent behavior in transverse jet. Gruber et al. [9] indicated that the compressibility of the mixing layer was the main parameter affecting the behavior of turbulent structures. Ben-Yakar et al. [12] pointed out the velocity difference was the key point influencing the turbulent behavior in shear layer by the n Corresponding author at: College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China. E-mail address: [email protected] (W. Liu).
http://dx.doi.org/10.1016/j.actaastro.2016.05.032 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved.
stretching-tilting-tearing mechanism. Meanwhile, with the improvement of computational resources, large eddy simulation (LES) has provided further insight into the mixing progress and development of turbulent structures in jet plume [13–17]. According to the former study, two main disadvantages in transverse jet are outstanding. First, large supply pressures is needed to achieve high penetration in transverse jet. Second, some injection is seeded into the boundary layer, which often leads a phenomena know as flashback [18]. In addition, with demand of larger size scramjet emerging, to achieve a higher penetration and better mixing efficiency in main flow is very necessary. Aiming at improving the jet penetration and mixing efficiency, ramp injector is used as a viable mean, because of the vortex shedding off the edges and a local separation at the base [19,20]. In the traditional ramp jet, the direction of jet is general in streamwise and the configuration of ramp is unswept. Later, to produce a stronger pair of vortex, swept ramp was born [21,22]. Generally, to ensure strong pair of vortices and large separation region, the size of ramp is large. Thus, a thorny and inevitable problem emerges, that is how to minimize the added total pressure loss and drag when the traditional ramp injector is used in scramjet [21,23]. Lately, in the study of the shock-wave and boundary layer interaction (SWBLI), researchers used a micro-ramp immersing into the boundary layer to delay shock-induced turbulent boundarylayer separation [24,25]. The device can produce a counter vortices pairs (CVPs) in the near-wall region and upwash the low energy part of boundary layer into the main flow. Because of the tiny size, the micro-ramp always emerges into the boundary layer. Thus, the total pressure loss is obviously small. Also in the study of film-
Y. Zhang et al. / Acta Astronautica 127 (2016) 160–170
T0 Pj Tj ρj v 2j ρu2 J y1 Ap h c H η ϕ
Nomenclature density velocity exponent in j direction subgrid scale stress subgrid turbulent eddy viscosity coefficient subgrid length scale rate-of-strain tensor time energy Reynolds number Schmidt number boundary layer thickness stagnation pressure of inflow
ρ uj τijsgs vtsgs Δ¯ S T E Re Sc d P0
cooling jet [26,27], researchers placed the micro-ramp downstream the jet to produce CVPs that is in the contrary direction with the CVPs in jet plume. So the lift-off behave of CVPs in jet was much weaken. This application inspired us to using micro-ramp to produce CVPs that is in the same direction with CVPs in jet plume, then the jet penetration can be improved probably. Additionally, in the investigation of traditional ramp, Wilson et al. [28] placed the jet orifice in the front of ramp to enhance the penetration by the inclined ramp surface. Based on the idea mentioned above, the transverse jet placed in front of micro-ramp and behind micro-ramp are investigated by LES approach in this paper. First, the penetration and mixing efficiency in different jet cases are compared and the factors influencing the penetration are investigated. Then, the differences in injection plume distribution, streamwise vortex in different cases are studied. Last, statistical characteristics, such as time histories of the vortex structures, time correlation, mass fraction probability are analyzed.
stagnation temperature of inflow stagnation pressure of transverse jet stagnation temperature of transverse jet the momentum flux of transverse jet the momentum flux upstream jet orifice jet-to-freestream momentum flux ratio mass fraction of injection wedge half-angle of micro-ramp height of micro-ramp a chord length height of ramp wake mixing efficiency local equivalent ratio
(
∂ ρ¯ Y˜m ∂t
)+
μ ⎞ ∂Y˜ ⎤ 1 ⎛ μ ∂ ⎡ ˜ ⎢ ρ¯ Ym u˜ j − + t ⎟ m⎥ = 0 ⎜ Re ⎝ Sc Sct ⎠ ∂xj ⎦ ∂xj ⎣
where SGS stress
τijsgs
1
(5)
In these equations, the laminar and turbulent Prandtl numbers are given as Pr = 0.72 and Prt = 0.90. The subgrid kinetic energy k sgs is solved by the transport equation as expressed in Eq. (6).
∂ ( ρ¯ k sgs ) ∂t where
+
Pksgs
= −
∼ ∂ ( ρ¯ k sgsu j)
In the present study, the filtered dimensionless compressible Navier–Stokes equations for an ideal nonreactive gas are solved, with the one equation subgrid scale model (SGS) of Yoshizawa and Horiuti [29] used as below:
+
(1)
∂ ⎡ 1 1 sgs ⎤ τ¯ij + τ ⎥=0 ⎢ ρ¯ u˜ i u˜ j + p¯ δij − ∂xj ⎣ Re Re ij ⎦
(2)
( )
∂ ρ¯ E˜ ∂t
+
~ ∂T ∂ ⎡⎢ 1 κ 0 T0 + − u˜ i τji ρ¯ E˜ + p¯ u˜ j − κ κ ( ) t ∂xj ⎢⎣ ∂xj Re μ 0 u02 Re
−
μ ⎞ 1 ⎛ μ ∂Y˜ ⎤ + t ⎟ ∑ h˜ m m ⎥ = 0 ⎜ Re ⎝ Sc Sct ⎠ m ∂xj ⎥⎦
(
=
∂xj D sgs
and
τijsgs
ν sgs ⎞ ∂k sgs ⎤ ∂ ⎡ ⎛ ν ⎥ + Pksgs − D sgs ⎢ ρ¯ ⎜ + t ⎟ Prt ⎠ ∂xj ⎦ ∂xj ⎣ ⎝ Pr
(6)
is defined as below:
( ∂u∼i /∂xj ) /Δ
(7)
where the model constants are given as Cd = 1.0 and Cμ = 0.02075, following the work of Sun et al. [30].
2.1. LES equations
∂t
is modeled as below:
Δ¯ = ( ΔxΔyΔz ) 3
3/2
∂ ( ρ¯ u˜ i )
(4)
⎛∼ ⎞ 2 1∼ = − 2ρν ¯ tsgs ⎜ Sij − Skk δij ⎟ + ρ¯ k sgsδij ⎝ ⎠ 3 3
D sgs ≈ Cd ρ ( k sgs )
∂ ( ρ¯ u˜ j ) ∂ρ¯ + =0 ∂t ∂xj
τijsgs
vtsgs = Cμ Δ¯ k sgs
Pksgs 2. Numerical methods and the physical model
161
)
(3)
2.2. Physical model and simulation cases The micro-ramp in this paper is shown in Fig. 1(a), based on the physical model in Wang's paper [24]. Its height h is 3 mm, with a wedge half-angle Ap¼ 24° and a chord length c¼ 7.2 h. In this investigation, four different cases are simulated by LES. The simulation of transverse jet without ramp shown in Fig. 2 is denoted as ‘platejet’. Based on the different jet locations, there are two cases denoted as ‘front jet’, ‘back jet’. The jet locations are shown in Fig. 1(b). In each case, the origin of the Cartesian coordinate system is at the center of jet orifice. The fourth case is the micro-ramp placed in the flow field without jet, denoted as ‘ramp’. The mach number of inflow is 2.7 The stagnation pressure P0 and stagnation temperature T0 of inflow is 77.6 kPa and 300 K respectively. The corresponding unit Reynolds number Re is 6.95 × 106 The transverse sonic jet is from a circular orifice with diameter d ¼2 mm on the bottom wall. The stagnation pressure Pj of nitrogen jet is 136 kPa and the stagnation temperature Tj is 300 K with the jet-to-freestream momentum flux ratio J being 2.9. The origin of the Cartesian coordinate system is at the center of the orifice, and the X, Y, Z denote streamwise, transverse and spanwise directions, as shown in Fig. 2.
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Fig. 1. The configuration and locations of micro-ramp generator.
Fig. 2. Computational region sketch map of transverse jet without micro-ramp (the characteristic length d is 4 mm, which is the boundary layer thickness). Table 1. Grids distributions. Recycle region
Core region
X direction
Y direction
Z direction
X direction
Z direction
X þ ¼ 50
Y/d¼ 0∼2.5: Y þ ¼ 1–10
Zþ ¼14.5
Xþ ¼5
Zþ ¼5–12.5
2.3. Numerical schemes and grids Inviscid flux is solved with the fifth-order WENO scheme by Jiang and Shu [31], while viscous flux is discretized by the secondorder-accurate centered scheme. The time advancement is performed with the third-order Runge–Kutta scheme. To generate and sustain an unsteady incoming turbulent boundary layer, recyclingrescaling procedure of Xiao et al. [32,33] is adopted. The length of the recycling–rescaling region is 10d (the boundary layer thickness
Fig. 4. Penetration in different injection cases.
d is 4 mm, which is the characteristic length in the study). The recycle plane, computational region and boundary condition are shown in Fig. 2. The grid independence and the comparison between experiment and simulation have been done in early study as shown in
Fig. 3. Grid distribution in micro-ramp cases.
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163
Fig. 5. ρu2 contours in Z/d¼ 0 plane and mass fraction iso-surface y1 ¼0.8. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 6. Mass fraction contour of platejet and front jet in slice Z/d¼ 0. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
former studies [16,17]. The studies showed that the fine grid had the highest spatial resolution and could capture the small-scale structures in windward shear layer, which indicated that the distribution of the fine grid is reasonable. As this paper also focuses on the transverse jet in supersonic flow, the distribution scheme of fine grid mentioned in references [16,17] is adopted in this study, as shown in Table 1. And the girds distribution of recycle region and core region in all jet cases are the same. Considering complex
configuration of ramp, the immersed boundary method is adopted to enable a high-quality body-fitted grid around the micro-ramp generator, more details of this method are described in the work of Wang et al. [34]. The grid distribution around the micro-ramp is shown as in Fig. 3.
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penetration height of platejet, back jet and front jet are compared in Fig. 4. Obviously, the penetration height in back jet is the highest of all and the second highest case is the front jet. It can be observed that the penetration of platejet and front jet are nearly the same before X/d ¼1.8. But the penetration in front jet after X/ d¼ 1.8 has a slight increase. Considering the micro-ramp is located at the X/d ¼2.5, so this increase is mainly due to liftup of the inclined surface in micro-ramp. The former study [1–5] have shown that jet-to-freestream momentum flux ratio J is the key point to influence penetration height and the equation of J is shown in Eq. (8). In this study, the jet parameter is constant, so the freestream momentum flux ρu2 before jet orifice is the only variable in different cases. The freestream momentum flux ρu2 expressed in the denominator of Eq. (8) and the iso-surface of mass fraction y1 ¼ 0.8 are shown in Fig. 5. The black scale line is to measure the height of jet iso-surface and the ramp wake in different cases.
J=
Fig. 7. Mixing efficiency of different cases.
3. Results and discussions 3.1. Penetration height In this section, the method measuring the penetration height by averaged mass fraction [10] is adopted and the 10% iso-line of mass fraction is regarded as the penetration height. The
ρj v2j ρu2
(8)
In figure (a), it is observed that in the inflow boundary the freestream momentum flux is increasing with the arising of boundary layer in front of ramp. Markedly, after fluid flows across the micro-ramp generator, the freestream momentum flux decreases to about 0.01 sharply. With the ramp wake moving downstream, the freestream momentum flux and the thick of the wake both increase. Compared with other cases, due to the effect of micro-ramp, freestream momentum before jet orifice in back jet case is the smallest in the three jet cases. Thus, the jet-to-freestream
Fig. 8. Distribution of injection plume in different injection cases.
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165
Fig. 9. Steamwise vortices and mass fraction distribution at streamwise slice. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
momentum flux ratio is the largest in back jet case. And the penetration height is proportional to jet-to-freestream momentum flux ratio. So, the back jet case obtains the highest penetration. In this case, the penetration of mass fraction y1 ¼0.8 can reach Y/ d ¼1.8 as shown in figure (c), and the value in platejet case and front jet is 1.5 and 1.6, respectively, indicating that the liftup effect of micro-ramp in front jet case is slight, which is also shown in Fig. 4. The mass fraction contour of injection in slice Z/d¼ 0 is shown in Fig. 6. In the two figures, red dashed line is the height of inflow boundary layer. It can be seen that the core region of injection is mainly located in boundary layer. And for the sake of the small freestream momentum flux in boundary layer, most injection can penetrate into the main flow, as shown in Fig. 6. But, the microramp is mainly able to redistribute the fluid and energy in boundary layer [34]. So as shown in Figs. 4–6, micro-ramp has a slight impact to increase front jet penetration.
[35]:
η=
∫A
(
ρ ⋅u ⋅y1 ϕ
) dA
∫A ( ρ⋅u⋅y1 ) dA
⎧ 1, ϕ (y , z ) ≤ 1, y1 , ϕ (y , z ) = 14.79 × ϕ=⎨ ⎪ − 1 y1 ϕ ( ) ϕ ( ) > , , , 1 y z y z ⎩ ⎪
(9)
In the Eq. (9), A value of η = 1 indicates full uniformity and η = 0 indicates complete lack of injectant. A is area of the Y–Z plane, y1 is the mass fraction of the nitrogen and ϕ ( y, z ) is the local equivalent ratio at arbitrary location in Y–Z plane. The mixing efficiencies in different cases are shown in Fig. 7. In near flowfield, the difference in mixing is not obvious and the back jet case has a slight advantage. But in far flowfield, the curves of mixing efficiency have a rapid climb in back jet case, which shows a significant advantage in mixing. Thus, the back jet case obtains the best mixing not only in near flowfield but also in far flowfield.
3.2. Mixing efficiency 3.3. Distribution of the injection The mixing efficiency is calculated analogous to a simulated hydrocarbon gas with a molecular weight equal to nitrogen, such as ethylene. The expression of mixing efficiency η is as follows
3.3.1. Distribution of injection plume In this section, iso-surface of y1 ¼0.1 is regarded as the injection
166
Y. Zhang et al. / Acta Astronautica 127 (2016) 160–170
Fig. 10. Time histories of Q ¼ 0.1 iso-surface at X/d ¼16 in different cases.
plume boundary, as shown in Fig. 8. In the figures, the iso-surface mass fraction of y1 ¼0.1 is colored by normal height and the black line is the iso-line of normal height. In back jet case, the injection is the narrowest, but its penetration is the highest: the mass fraction of y1 ¼0.1 reaches Y/d ¼4 at X/d¼ 2.7 and Y/d ¼4.5 at X/ d ¼5.3. It also can be seen that the injection penetrate to Y/d¼ 3 at X/d ¼3 in front jet case and the penetration is Y/d ¼3 at X/d ¼11 in platejet. Compared with platejet case, the location that the jet reach Y/d¼ 3 is shorten about 8●d in front jet case.
case. In both of platejet and front jet at slice X/d¼ 4 and X/d¼8, the vortices is at the core region of injection. In the comparison of platejet and back jet case in figure (b) and (d), it is observed that the distribution of injection in back jet case is much higher than in platejet case and the streamwise vortex is at the bottom of injection all the time in back jet case. That means the streamwise vortex can make a little effect on the distribution of injection, which is not like the platejet and front jet case. In terms of the streamwise vortex area, the platejet has the largest area of all.
3.3.2. Distribution of streamwise vortex Fig. 9 shows the distribution of streamwise vortices contour in color with black solid line, black number and injection distribution in dashed red line with red number at X/d¼4 and 8. In figure (a), the location of streamwise vortices in front jet is almost the same with platejet case. The distribution of injection in front jet is a little higher than platejet case and the difference in height is nearly equal to the height of micro-ramp at X/d¼4. In figure (c), the slice is downstream the micro-ramp. In this slice, the streamwise vortices by micro-ramp is strong as shown in red color and the streamwise vortices by jet in front jet case is a little bit higher than in platejet
3.4. Statistics of jet plume 3.4.1. Instantaneous results at different slices To clarify the characteristic of vortex structures in the jet plume, the time histories of the vortex structures at intervals of ti = 50∙t¯ is shown in Fig. 10. t¯ is the non-dimensional time in simulation and it is equal to 1.7∙10−3 . The data is obtain at X/d ¼16. In all the four figures, it can be observed that K-H vortices surround the jet plume. In Fig. 10(a), the structures of K–H vortices seem to have periodicity in this case. Compared with ramp case in figure (a), the periodicity of other cases is not seen, which is
Y. Zhang et al. / Acta Astronautica 127 (2016) 160–170
167
Fig. 11. Time correlation of temperature and density at X/d ¼ 16 in different cases.
confirmed by time correlation analysis in next section. In other three cases, the penetration of K–H vortices are higher than that in ramp case. In back jet case, the vortices reach Y/d ¼4, which is clearly the highest. 3.4.2. Time correlation analysis In 3.4.1 Section, the K–H vortices look like have periodicity in ramp wake. To confirm the periodicity, time correlation is calculated in all the cases, as shown in Fig. 11. The coefficient of time correlation Rt is shown in Eq. (10). In the equation, the c′ represents the fluctuation of passive scalar, such as temperature and density in this study. It is observed that in ramp case the Rt of temperature and density have good periodicity and the Rt in other cases do not have obvious periodicity. That is coincides with the time histories iso-surface results in 3.4.1 Section. The time correlation results indicate that the jet before micro-ramp destroys the inflow condition in front jet case and the jet behind micro-ramp destroys the ramp wake in back jet case, so the inherent
periodicity induced by micro-ramp in ramp wake can not be reproduced.
Rt =
c′ ( x, y , z, t0 ) ∙c′ ( x, y , z, t0 + Δt ) 2
2
c′ ( x, y , z, t0 ) ∙ c′ ( x, y , z, t0 + Δt )
(10)
3.4.3. Probability distribution of mass fraction To compare the difference in mixing effect, this section focuses on the probability distribution of mass fraction at X/d¼ 16 and 25 as shown in Fig. 12 and Fig. 13. For facilitating the statistics, the mass fraction y1 is divided into ten uniform intervals from 0 to 1. At X/d¼ 16 and X/d¼ 25, the probability distribution of front jet and platejet is almost the same, the only difference is that the probability distribution in front jet is a bit higher than in the platejet case, because of the micro-ramp liftup effect. In the comparison of platejet and back jet case as shown in Fig. 12(b) and Fig. 13(b), the probability in the center region of platejet is lower
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Fig. 12. Probability distribution of mass fraction at X/d ¼16.
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169
Fig. 13. Probability distribution of mass fraction at X/d ¼25.
than in the back jet, indicating that the probability that main flow get into the center region of jet plume in back jet is higher than in platejet. So the mixing effect in back jet case is better than in platejet case. Also, the location of the mass fraction probability in back jet is the highest, as shown in former sections.
4. Conclusions In the present study, the effects of micro-ramp on the characteristics of transverse jet in supersonic crossflow were investigated by LES approach. The simulation results in front jet and back jet case were compared with platejet. The conclusions were summarized as follows: ● The micro-ramp can decreases the freestream momentum in boundary layer remarkably, so the jet placed behind micro-ramp can obtain a obvious increase in penetration. ● Because the most injection is above the boundary layer and micro-ramp mainly control the flow in boundary layer, the
penetration in front jet is increased slightly. And the micro-ramp has little effect on the injection distribution in front jet case. ● The back jet case has a significant advantage in mixing not only in near flowfield but also in far flowfield, however, the improvement in mixing efficiency is slight in the front jet case. ● Through the time correlation analysis, it is found that the K–H vortices in the ramp wake has good periodicity, but the periodicity of K–H vortices does not exist in platejet, front jet and back jet case. ● Compared with the probability distribution of mass fraction in platejet, it is found that the main flow can reach the center of jet plume easier in back jet case.
Acknowledgments The authors would like to express their thanks for the support from the National Natural Science Foundation of China (Nos. 91216120, 51406233).
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