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Numerical investigation on mixing and combustion of transverse hydrogen jet in a high-enthalpy supersonic crossflow
Acta Astronautica 116 (2015) 93–105
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Numerical investigation on mixing and combustion of transverse hydrogen jet in a high-enthalpy supersonic crossflow Chaoyang Liu n, Zhenguo Wang, Hongbo Wang, Mingbo Sun Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China
a r t i c l e i n f o
abstract
Article history: Received 20 April 2015 Received in revised form 22 June 2015 Accepted 24 June 2015 Available online 2 July 2015
Mixing and combustion characteristics of a three-dimensional unsteady reacting flowfield generated by transverse hydrogen jet into high-enthalpy supersonic crossflow are investigated numerically. A hybrid RANS/LES (Reynolds-Averaged /Large Eddy Simulation) method acting as wall-modeled LES is adopted, where the ninth-order WENO (Weighted Essentially Non-oscillatory) scheme is introduced to discretize the inviscid fluxes. The validations of numerical results are performed for the jet penetration height, timeaveraged and instantaneous structures of reacting flowfield. It is found that the Kelvin– Helmholtz instability of jet shear layer on the windward side of jet plume discontinuously induces large scale coherent structures, which promote the combustion by enhancing the fuel mixing and enlarging the reacting area. The chain reactions creating OH radical mainly occur in the lean-fuel region and the heat-releasing chain reactions consuming OH radical are in the rich-fuel region. In the boundary layer and windward shear layer where supersonic crossflow stagnates, a diffusion flame with autoignition first occurs and then propagates to the downstream of jet plume, which holds the flame stabilization of total flowfield. & 2015 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Transverse jet Supersonic crossflow Shear layer Autoignition Flameholding
1. Introduction The scramjet is an essential component of hypersonic air-breathing propulsion technology, which requires enhanced combustion efficiency of fuel and air [1]. Due to the extremely fast incoming airstream, mixing is slow compared to the limited residence time of fuel inside the combustor. Therefore, fast turbulent mixing and flameholding become the most critical technical issues associated with scramjet [2].
n
Corresponding author. Tel.: þ8615274952697; fax: þ86073184512301. E-mail address: [email protected] (C. Liu).
http://dx.doi.org/10.1016/j.actaastro.2015.06.023 0094-5765/& 2015 IAA. Published by Elsevier Ltd. All rights reserved.
Although different jet-injection configurations have been proposed to enhance the fuel mixing and maintain the stabilization of flame, the fuel injection from a wall orifice becomes one of the simplest but most efficient injection schemes [3]. The complicated structures and mixing enhancement mechanism resulting from the interaction of sonic transverse jet and supersonic crossflow have been investigated by many researchers in previous studies [4,5]. In order to stabilize the flame, wall injection coupled with a downstream cavity flameholder has been shown to be a promising candidate with moderate total temperature. Wang et al. [6] studied the interactions of jet and cavity in a supersonic condition using the large eddy simulation (LES) and pointed that moderate injection pressure may be beneficial to transport more fuel into the cavity to promote the ignition process
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under certain conditions. Micka et al. [7,8] experimentally investigated the combustion characteristics in a scramjet combustor with transverse jet upstream of cavity. The results indicated that there were two distinct flameholding modes for upstream fuel injection in the flowfield with high and low total temperature. Most of the previous studies were performed in the conditions with low and moderate enthalpy. However, a real supersonic combustor environment at flight speeds beyond Mach 8 is in high enthalpy. Ben-Yakar et al. [9] experimentally compared the time evolution of large scale vortices with hydrogen and ethylene transverse jet into highenthalpy supersonic crossflow, and found significant differences of the mixing properties in near-wall region. But the inherent mechanism of mixing and combustion enhancement resulting from large scale vortices was not clearly revealed. Won et al. [10,11] investigated the generation mechanism of large scale vortices and autoignition phenomenon using detached-eddy simulation (DES) in the conditions of BenYakar's experiment, whereas the interaction of turbulence and combustion as well as the physical and chemical mechanism that dominates the stabilization of flame was not answered. An accurate estimation and a deep physical understanding of the turbulent mixing and flameholding mechanism in the conditions of high total temperature play important roles in scramjet design [12]. The unsteady reacting flowfield is extremely complicated, and consists of multiplicate structures, such as the bow shock, barrel shock, Mach disk, separation shock and combustion wave. Purely experimental approach is not enough to acquire sufficient data to understand their inherent process. To obtain additional insights into the three-dimensional unsteady turbulent process and autoignition with sonic jet into the high-enthalpy supersonic crossflow, numerical simulation with high precision is an attractive choice. Despite the LES and DES have been used to investigate the large scale vortices in the transverse jet flowfield, their structures are somewhat obscure [13]. This primarily stems from the dissipative effect of conventional loworder upwind schemes, which may not be offset by singly increasing grid numbers. The too much dissipation induced by low-order schemes can suppress the actual physical structures. It is difficult for low-order schemes to capture fine structures in the reacting flowfield. Therefore, numerical approach with high-order schemes are urgently required to be applied. In present study, three-dimensional unsteady flowfield with a sonic jet injected into a high-enthalpy supersonic crossflow is numerically simulated by RANS/LES approach with ninth-order WENO scheme [14]. The ninth-order WENO scheme with high precision and low dissipation can capture the small scale vortices and shock very well in the flowfield [15,16]. The main objective of this paper is to develop further insights into the three-dimensional complex physics of jet mixing and flameholding mechanism. 2. Numerical approach 2.1. Governing equations The finite difference RANS/LES solver used in present simulation solves the Favre filtered compressible Navier–
Stokes equations of continuity, momentum, total energy and species transport for three-dimensional reacting flowfield [17]. For computational purpose, the governing equations are expressed in the conservative vector form as follows: ∂Q ∂ðE E v Þ ∂ðF F v Þ ∂ðG Gv Þ þ þ þ ¼W ∂t ∂x ∂y ∂z
ð1Þ
where Q represents a vector of conservative variables required to be solved for; E, F, G are vectors of inviscid fluxes, and Ev, Fv, Gv are vectors of viscous fluxes in x, y, and z directions, respectively; and W represents the chemical reaction source term. The specific expressions of above vectors are defined in previous reference [18]. 2.2. Turbulence models With the recent development of computational resources, LES has gradually become an efficient approach to solve turbulent flow and combustion problems, such as the separated flows, chemical non-equilibrium flows. While it is difficult to accurately simulate the flows in the near-wall region at high Reynolds numbers, due to high mesh resolution required. Then a hybrid method [13] blending Spalart–Allmaras RANS model and Yoshizawa sub-grid scale (SGS) model is adopted for capturing large scale turbulent structures in high Reynolds number flowfield. The blended equation can be given as below: 2 Dρν~ ∂ ∂ν~ ∂ν~ ¼ ρP v þ ρðν þ σ v1 ν~ Þ Dv þ ð1 F ÞρP Δ þ ρσ v2 ∂xj Dt ∂xj ∂xj ð2Þ where ν~ is molecular viscosity, ρ is the density. The specific expressions of P v , σ ν1 , σ ν2 , Dν , P Δ and blending function F in Eq. (2) has been given in our previous paper [19]. 2.3. Numerical methods The finite difference approach is used for the spatial discretization of the governing equations. The inviscid fluxes are discretized by the ninth-order WENO scheme and the viscous fluxes are discretized by fourth-order central difference scheme. In order to improve the computing efficiency, the time advancement is performed by means of a second-order dual time-step approach, the inner iteration of which is achieved by a lower-upper symmetric Gauss–Seidel (LU-SGS) method. An assumed sub-grid Probability Density Function (PDF) closure model is used for turbulence-chemistry interaction adopting a 9 species 19 step chemistry reaction mechanism for H2–air mixture [17]. 3. Code validation The present simulation is performed to investigate the mixing and flameholding mechanism with the transverse hydrogen jet into a high-enthalpy supersonic crossflow. In order to validate the simulation results, the flow conditions simulated is based on the experiment of Ben-Yakar, which maps the near-field flow characteristics and
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autoignition process of a sonic transverse hydrogen jet injected into the crossflow with flight-Mach number 10 total enthalpy flow conditions [20]. The experiment is carried out on a flat-plate with a circular port that allowed the jet of hydrogen to inject into the supersonic freestream at a constant mass flow rate. The jet port with a D¼ 0.002 m diameter is located at a distance of L1 ¼ 0.05 m downstream of the flat-plate leading edge. The static temperature and pressure of sonic hydrogen jet is 246 K and 4.9 105 Pa, respectively. The transverse jet injects into the crossflow of Mach number M1 ¼3.38, the static temperature and pressure of which is 1290 K and 3.24 104 Pa. The momentum flux ratio J of jet corresponding to the crossflow is 1.4 and the thickness of boundary layer ahead of the injection port is approximately δ1 ¼7.5 10 4 m. The detailed parameters of jetexit and crossflow are shown in Table 1. Considering actual computational costs, the threedimensional computational domain is confined to a finite local region near the injection port, which comprises of a solid surface that represents the flat-plate with a circular hole as the injection port. Fig. 1 shows the schematic diagram of the three-dimensional computational domain, which refers to the region ranging from 5D upstream to 10D downstream of the injection port in the streamwise direction. The scales of the domain in the normal and spanwise direction is 10D and 12D, respectively. Fig. 2 shows the overall grid system in the three-dimensional domain. In order to capture the coherent structures and instability of the reacting flowfield, the focused region of mesh is mainly concentrated in the vicinity of the jet-exit where coherent structures may initially generate. The number of grid points is 901 176 191 in the x, y and z directions, which leads to a grid resolution of Δx þ E5 15, Δy þ E1 15, and Δz þ E5 15 in the focused region basing on the thickness of entrance boundary layer. The grid resolution is high enough to capture the large-scale vortices in the flowfield. The inflow variables are obtained by a two-dimensional preliminary method using Reynolds-Averaged Simulation (RANS), the outputs of which at the distance of 20D from the flat-plate leading edge are used for the inlet profile parameters of threedimensional calculation to decrease the computational cost and time. A no-slip, no-penetration adiabatic condition is imposed at the lower wall; supersonic inflow condition is used at the inlet section; sonic jet-exit condition is set at the circular hole and other boundaries are treated as supersonic outflow. The physical time step is set as Δt¼0.05 δ1/u1, which satisfies the temporal resolution. Table 1 Supersonic crossflow and jet-exit flow conditions. Supersonic crossflow M1 T1, K p1 , Pa L1 , m δ1 , m Re1
3.38 1290 3.24 104 0.05 7.5 10 4 2.2 105
Sonic jet-exit flow Mj Tj, K pj , Pa D, m J ReD
1 246 4.9 105 0.002 1.4 1.5 105
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Fig. 1. Schematic diagram of computational domains and boundary conditions.
Fig. 2. Overall grid system in the three-dimensional computational domain.
Estimating precision and errors accumulation is necessary for numerical simulation of complex combustion gas dynamics in unsteady flowfield [21]. For uniform grid, the relative errors Serr of integration in three directions could be Serr ¼
3 X
1=N i
k þ 1
ð3Þ
i¼1
where Ni is the number of grid points in the direction of integration and k is the order of numerical scheme. Then the maximal number of time steps for solving present problem can be estimated by the following formula: 2 nmax ¼ Smax =Serr ð4Þ The allowable value of total error Smax ranges from 1% to 5%. The ratio of maximal allowable number of time steps and the actual number of time steps RS can be defined as: RS ¼ nmax =n
ð5Þ
where n is the actual number of time steps in simulation. The actual number of integration steps n performed before obtaining the results displayed in the figures is 6 105. As the value RS in present simulation is approximately
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1.5 103 which is high enough, therefore the accumulated error is very low. Combining the resolution analysis of grid scale with the precision and error estimation, we believe that precision of the numerical method and grid resolution can satisfy the necessary of the simulation. The jet penetration height is often used as a representative index to evaluate the flowfield characteristics of the transverse jet in crossflow, because it has important influence upon the mixing and combustion efficiency of jet and airstream in a scramjet combustor. It is also adequate for the validation and assessment of numerical results, which can be acquired easily in the experiment [10]. The comprehensive study about penetration height correlation was performed by Gruber et al. [22], who suggested a power law fit of the form 1=3 y x ¼ 1:23 DJ DJ
ð6Þ
Rothstein and Wantuck [23] used OH-PLIF to visualize the jet penetration trajectory and get another empirical correlation y 2:173 x 0:281 ¼ 0:443 ð7Þ DJ J DJ The penetration height and bandwidth of transverse jet in Ben-Yakar's experiment were obtained by manually
Fig. 3. Jet penetration and bandwidth of the transverse jet in crossflow.
tracking the visually observable outer edge of the jet from eight consecutive schlieren images [9]. The numerical penetration height and bandwidth of the transverse jet in crossflow are extracted by tracking the jet outer edges of H2 mass fraction 0.05 from eight consecutive images shown in Fig. 3, overlaid with the theoretical correlation and experimental data. It is found that Gruber's curve agrees well with present simulation results, but Rothstein and Wantick's is in good agreement with experimental data. Numerical jet penetration depth and bandwidth is a little lower than that acquired in the experiment, whereas their trend is in accordance. Fig. 4 shows the schlieren image acquired by Ben-Yakar and the density gradient contour of the time-averaged flowfield in present simulation. Compared with the experimental results, high-precision numerical approach captures the separation shock, bow shock and smeared shear layer observed in schlieren image very well. But the reattachment shock at the leeward side of jet plume is not visual. And the bow shock captured in the numerical results is slightly lower than that in the experiment, which is consistent with the trend of jet penetration height. The discrepancies between the experimental and numerical results may stem from the setting of the boundary conditions. We know that the turbulence intensity may have some influence upon the structures in the flowfield. In the actual experiment, the boundary layers of crossflow and jet contain turbulent effect and some unsteady disturbance with some characteristic scales. Furthermore, the wall in the experimental facility is not absolutely smooth, that may enhance the turbulent intensity in the near-wall flow. However, steady boundary conditions at jet-exit and inflow are used in present simulation, and the numerical solid wall conditions cannot match the real physical conditions very well. These deficiency causes a lack of turbulent intensity in flowfield, which may affect flow structures and result in the lower jet penetration and bow shock. Although there is a little difference between numerical simulation and experimental results, the trend of numerical results is consistent with the experimental data. So the numerical results can be considered relatively reliable.
Fig. 4. (a) Schlieren image with exposure time 3 μs; (b) the density gradient contour of the time-averaged flowfield.
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4. Results and discussion 4.1. Flow characteristics Statistical results discussed in the following are averaged over 5400 steps of unsteady reacting flowfield. In this time scale, the freestream passes through approximately a distance of 32D. Fig. 5(a) shows the time-averaged image of H2 mass fraction overlapped with divergence of velocity contour in center plane. The major flow structures such as the bow shock, barrel shock, Mach disk and separation shock are captured using RANS/LES approach. The H2 mass fraction gradually decreases along the streamwise, which indicates that mixing process occurs with traveling to the downstream. Fig. 5(b) shows the H2 mass fraction contour in the normal and spanwise plane. It is clearly found that a part of H2 appears in the upstream boundary layer due to the effect of separation zone ahead of the injection port. The stream lines at the spanwise plane x/D¼1 indicate that a pair of counter-rotating vortices (CRVs) formed in the near-wall region along the streamwise direction is induced by the transverse momentum of jet. This pair of CRVs then further grows in size along streamwise direction and the mixing process of the crossflow and transverse jet rapidly occurs. As it gradually grows in size and height, another pair of small scale trailing counter-rotating vortices (TCRVs) is induced at the leeward side of jet plume near the solid wall, which rotates in the opposite direction to the large one. A part of airstream at the leeward side of jet plume is entrained into large scale CRVs mixing with fuel, and the other part near the wall forms the TCRVs with the shear effect of large scale CRVs. Therefore, we believe that these two pairs of streamwise vortices still dominate the mixing process of the fuel and airstream in the supersonic reacting flowfield. Although the time-averaged results reveal that CRVs dominate the mixing process in the flowfield, the large scale coherent structures in the jet shear layer play very important roles in the mixing process near the periphery of the jet plume and near-wall region. The large scale vortices associated with their time-space evolution and
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convection are the most important phenomena observed in Ben-Yakar's experiment. However, the generation and development mechanism of large scale vortices is not understood very well. A comparison of consecutive schlieren images and the H2 mass fraction contours along with pressure isolines is shown in Fig. 6. The consecutive schlieren images with time correlation representing the first derivative of density are acquired using high-speed schlieren system, the interframing time of which is 1 μs. In order to vividly compare with experimental images, H2 mass fraction contours along with pressure isolines are used and the pressure isolines display the positions of bow shock in the instantaneous flowfield. The numerical simulation reproduces the generation, development and convection process of large scale vortices observed in the experiment and the time-correlated images are in good agreement with the schlieren images, which further validates the credibility of numerical results. A profound analysis of the coherence structures and their evolution process can give further insight into the enhancement of the near-wall mixing. From the consecutive images in both experiment and simulation, coherent structure as eddy 1 is initially generated at the windward side of jet plume near the injection port in frame 1. And then this coherent structure bends with the stretching of crossflow, resulting in large scale vortex formed as in frame 2. As it convects, this stretching process also enlarges the scale of vortex and causes the freestream to be engulfed by the jet shear layer as frame 3. But the frame 4 indicates that two vortices may appear almost at the same time, so we can conclude that vortices in the windward side of the jet are not generated periodically, but incontinuously. In frame 6, it is found that eddy 3 breaks into two small scale vortices with the interaction of low-speed jet and high-speed crossflow. But the small scale vortices merge into a large vortex again as frame 7 and 8. So the breakup and mergence of vortices may occur with the influence of crossflow. The pressure isolines show the bow shock in front of jet fluid, and the attached bow shock varies depending on the vortices. But the large scale vortices are affected by the bow shock at the same time.
Fig. 5. (a) Time-averaged image of H2 mass fraction overlapped with divergence of velocity contour in center plane; (b) image of H2 mass fraction in normal and spanwise planes.
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Fig. 6. Consecutive schlieren images and the H2 mass fraction contours along with pressure isolines with an interframing time of 1 μs.
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Fig. 7. Space-time trajectories of large-scale vortices.
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In order to make a quantitative comparison, the spacetime trajectories of large-scale vortices extracted from consecutive experimental and numerical images by identifying the center of large vortices are shown in Fig. 7. Due to the transient effect of flowfield, it is difficult to choose the starting frame of numerical results matching the first schlieren image. So the most homologous one is selected as the first frame. The comparison indicates that only the space-time trajectory of eddy 1 is in good agreement with experimental data, and marked discrepancy exists in other trajectories. But the trend of large-scale vortex trajectories is very similar. As the vortex velocity approaches that of freestream, the distance between adjacent vortices keep constant beyond three or four jet diameters downstream. Fig. 8 shows the consecutive instantaneous contours of H2 background obtained in center plane along with the negative divergence of velocity contours which describe the behavior of the shocks in the vicinity of jet exit, and the interframing time is 1 μs. The instantaneous contours represent the instability on the windward side of the jet plume and the starting process of the Kelvin–Helmholtz
Fig. 8. Instantaneous contours of H2 background obtained in center plane along with the negative divergence of velocity contours with an interframing time of 1 μs.
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Fig. 9. Instantaneous contours of H2 background obtained in center plane along with streamlines with an interframing time of 1 μs.
(KH) instability in this region, whereas the leeward side of the barrel shock does not show this instability. It is clearly found that the jet shear layer on the windward side of the jet plume in the near-wall region fluctuates, which is dominated by the KH instability existing in this region. KH instability is a convection instability and the oscillations are not self-excited but require a continuous source of disturbance to persist. The velocity near the shear layer is higher than that away from it, and this difference results in the KH type instability and the pressure fluctuation in the separation region ahead of the injection port provides the disturbance to maintain the KH instability [4]. It can magnify the instability of flowfield, and develops as a form of nonlinear. Then instability rapidly grows, magnifies and large scale vortex structures are induced. The attached bow shock and barrel shock in this region fluctuate due to the fluctuating coherent structures. Conversely, this fluctuating bow shock and barrel shock may further enhance the instability of the jet shear layer. The interaction of shock and vortices promotes the mixing process on the windward side of jet plume. Fig. 9 shows the instantaneous contours of H2 background obtained in center plane along with streamlines, the interframing time of which is 1 μs. The streamlines
distribution of transverse jet and crossflow represents that their mixing process firstly occurs in the shear layer on the windward side of jet plume. The very interesting phenomenon observed in the numerical results is that the fuel diffuses to upstream of jet-exit along the boundary layer. When a large scale coherent structure is generated, a counterclockwise spanwise vortex in the boundary layer is formed at the port leading side with the transverse momentum of jet, then a portion of fuel is entrained from the jet plume. At the same time, another clockwise separation vortex in front further transports it to the upstream. As the large vortices generate discontinuously, this process occurs accordingly. In the boundary layer, the residence time of flow is long and static temperature is very high. The fuel distributing in the upstream boundary layer is easily ignited, which may be beneficial to hold the flame in the downstream. 4.2. Flameholding mechanism Since the total enthalpy of the freestream in the experiment approaches 4 MJ/kg, namely the total temperature is about 4000 K, autoignition of the transverse H2 jet is achieved. The structures of jet flame are visualized
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Fig. 10. Numerical OH radical distribution superimposed with the stoichiometric isolines (top) and experimental OH-PLIF image (bottom) in center plane. Fig. 12. Instantaneous HRR contours superimposed with the stoichiometric isolines in center plane (top), axial and normal planes (bottom).
Fig. 11. Instantaneous contours of OH overlapped with the stoichiometric isolines in axial and normal planes.
using OH-PLIF, and combustion is maintained without a flameholder. The time-averaged and instantaneous flame structures are discussed in the following section basing on numerical results, and then autoignition effect and flameholding mechanism are further revealed. Fig. 10 shows the instantaneous OH distribution superimposed with the stoichiometric isolines and OH-PLIF image in center plane. Corresponding contours of OH in axial and normal planes are shown in Fig. 11. The OH radical as an intermediate production appears during H2 reacting with air and its sharp gradient is generally assumed to correspond to the flame front. In both experimental and numerical results, OH radical appears in the boundary layer and shear layer on the windward side of jet plume, but it is almost not visualized on the leeward side.
It is clearly found that numerical OH radical distributes at the upper side of stoichiometric isolines, while there is little at the opposite side. It indicates that chain branching reactions creating OH radical occur in the lean-fuel region above the stoichiometric isolines. As OH radical passes through the stoichiometric isolines, it is consumed by other chain reactions in a very short time. Therefore, the chain reactions consuming OH radical start at the richfuel side. Nondimensionalized instantaneous heat release rate (HRR) contours superimposed with the stoichiometric isolines are shown in Fig. 12. The HRR in a thick layer refering to the upstream boundary layer and windward shear layer facing toward the freestream is clearly higher than that in other regions. Heat is intensively released in regions that are confined into the regions within the stoichiometric isolines or along the lower side of the isolines, especially in the upstream region. It is further believed that heat-releasing chain reactions consuming OH radical mainly occurs in the rich-fuel regions below the stoichiometric isolines, whereas the chain branching reactions creating OH radical absorb heat. The other significant discovery is that the stoichiometric isolines coincide with the periphery of jet shear layer. The convection of large scale vortices analyzed in previous section facilitates the combustion by enhancing the mixing of the fuel and airstream and enlarging the reacting area. Therefore, it is very significant to understand the flow mechanism before flameholding is researched. The instantaneous flame structures are acquainted based on OH and HRR contours, and the results indicate that the flame mode in the upstream boundary and windward shear layer may be different from that in the downstream of jet plume. In order to reveal the
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Fig. 13. Profiles of mass fractions at x/D ¼ 2 and 1, corresponding to the upstream boundary layer and windward shear layer.
Fig. 14. Profiles of mass fraction at x/D¼ 5 and 8, corresponding to the downstream of jet plume.
Fig. 15. The static temperature and pressure profiles in normal direction at x/D¼ 2 (left) and 0 (right).
flameholding mechanism, it is very necessary to investigate the flame modes. The mass fraction profiles of H2, O2 and OH of averaged flowfield in different midline locations
which correspond to the upstream and downstream of jet respectively are extracted along the normal direction as Figs. 13 and 14. It is clearly seen from Fig. 13 that reacting
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region in the upstream boundary and windward shear layer is dominated by a diffusion flame mode, where the OH has peak values while O2 and H2 approach zero from opposite directions. The leakage of OH distribution at x/ D¼ 1 with more than one peaks is induced by the oscillations of the flame location, due to the instability of windward shear layer. Profiles of OH mass fraction in Fig. 14
Fig. 16. The static temperature and pressure profiles in normal direction at x/D ¼8.
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with two distinct peaks display that two main reacting regions exist in the downstream of jet plume. One is on the windward side of jet plume, where O2 and H2 decrease from opposite directions with a diffusion flame existing as the upstream of flowfield. And the other one is in the nearwall region, where O2 and H2 extensively coexist indicating that the flame basically occurs in the fuel-rich partially premixed mode. In summary, the upstream boundary layer and shear layer are dominated by diffusion flame and the near-wall region on the leeward side of jet plume exists fuel-rich partially premixed flame. In the flowfield of sonic transverse jet injecting into high-enthalpy supersonic crossflow, autoignition is confirmed to take place by OH-PLIF image, whereas it is difficult to clearly distinguish whether the jet flame is dominated by autoignition or flame propagation. Then the static temperature and static pressure profiles in three representative positions are extracted along normal direction as shown Figs. 15 and 16. Due to the low velocity in the boundary layer (x/D ¼ 2), the static temperature and static pressure at stoichiometric Ф ¼1 are 2382.13 K and 46.327 kPa, respectively. The ignition delay time in the boundary layer is approximately 3.98 μs estimated using CHEMKIN. In the time scale, the mixing gas convects to downstream with the distance of 3D at most. So it is believed that autoignition probably occurs in the downstream not away from present position. A similar approach
Fig. 17. Instantaneous temperature contours in center plane overlapped with stoichiometric isolines.
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Fig. 18. Instantaneous and averaged contours of H2O overlapped with stoichiometric isolines in center and axial planes.
is used to analyze the flame characteristic in the windward shear layer. As the airstream is stagnated through the bow shock, the static temperature and pressure at stoichiometric Ф ¼1 of x/D ¼0 approach 2552.02 K and 366.06 kPa. So the ignition delay time in the windward shear layer is only about 0.43 μs, so that we can believe that autoignition immediately occurs when fuel contacts high-temperature gas. The flow parameters in the downstream away from injection port are close to the freestream. The static temperature and pressure at stoichiometric Ф ¼ 1 of x/D ¼8 is about 1141.94 K and 23.314 kPa, and the ignition delay time is about 105.68 μs. The mixing gas travels to 130D in the downstream, so autoignition is very difficult to occur. Therefore, the fuel in the jet downstream is ignited by upstream flame. Basing on previous analysis, the flame in the boundary layer and windward shear layer near the injection port is a diffusion flame mode with autoignition, but a diffusion flame associated with flame propagation dominates the reacting region in the downstream. The consecutive instantaneous temperature contours in center plane overlapped with stoichiometric isolines are shown in Fig. 17, and the time interval is 1 μs. Thick bands
with high temperature exist in the periphery of boundary layer and windward shear layer above the stoichiometric isolines. The O2 and H2 immediately mix by diffusion in the boundary layer, where the temperature is high and residence time of flow is long. The conditions of autoignition is achieved, then combustion occurs. But the combustion process in the shear layer is more complex, which is powerfully coupled with turbulence. Two typical packets in the windward shear layer near the injection are tracked to analyze the autoignition process. The airstream behind the bow shock with high temperature and pressure is entrained into the boundary of jet by the large scale coherent structures and mixes with fuel rapidly. At the same time, high-enthalpy airstream impacts the transverse jet, the static temperature and pressure further increase with the ignition delay time decreased. Autoignition promptly occurs as soon as stoichiometric condition is satisfied. Pocket 1 with high temperature is formed in the shear layer near the injection, and it reacts with the transformation of jet shear vortices. The stoichiometric condition is easily achieved and the area of reaction are largely increased with the effect of large scale vortices, so combustion intensely occurs. But the temperature and
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pressure are relatively low, and the flame in the downstream can not be hold by autoignition mode. The diffusion flame in the shear layer and partially premixed flame in the near-wall region are maintained by upstream flame. We can conclude that the combustion in this reacting region is maintained by the autoignition process in the boundary layer and windward shear layer near the injection port. Fig. 18 shows the instantaneous and average contours of H2O mass fraction overlapped with stoichiometric isolines in center and axial planes. H2O is the final combustion production of H2 and O2. In both instantaneous and averaged contours, H2O that is mainly created by heat-releasing chain reaction in the rich-fuel region distributes within the stoichiometric isolines and in the regions covered by stoichiometric isolines. Then combustion production travels to the interior of jet plume with the effect of CRVs. 5. Conclusion We have numerically investigated the mixing physics and flameholding mechanisms for the unsteady reacting flowfield with transverse jet into high-enthalpy crossflow. Fine vortex structures and their convection characteristics have been captured with high precision WENO scheme. Significant conclusions that can be summarized as follows: 1. The generation and convection of large scale vortices in the windward shear layer are reproduced using highprecision numerical simulation, which promotes the combustion process by enhancing the fuel mixing and enlarging the reacting area. 2. The heat-absorbing chain reactions creating OH radical occur in the lean-fuel region above the stoichiometric isolines, whereas the heat-releasing chain reactions consuming OH radical and creating H2O are mainly in the rich-fuel region under the stoichiometric isolines. 3. A diffusion flame with autoignition dominates the reacting region of the boundary layer and windward shear layer where supersonic crossflow stagnates, then it propagates to the downstream of jet plume, which holds the flame stabilization of total flowfield.
References [1] J. Watanabe, T. Kouchi, K. Takita, G. Masuya, Characteristics of hydrogen jets in supersonic crossflow: large-eddy simulation study, J. Propul. Power 29 (3) (2013) 661–674. [2] Z.A. Rana, D. Drikakis, B.J. Thornber, Investigation of sonic jet mixing in a stream of supersonic crossflow using large eddy simulations, in: Proceedings of the 27th International Congress of the Aeronautical Sciences, 2010.
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[3] A. Ben-Yarkar, R.K. Hanson, Experimental investigation of flameholding capability of hydrgon transverse jet in supersonic crossflow, in: Proceedings of the 27th Symposium (International) on Combustion/The Combustion Institute, 1998. [4] Z.A. Rana, B. Thornber, D. Drikakis, Transverse jet injection into a supersonic turbulent cross-flow, Phys. Fluids 23 (2011) 1–21. [5] K. Mahesh, The interaction of jets with crossflow, Annu. Rev. Fluid Mech. 45 (2013) 379–407. [6] H.B. Wang, Z.G. Wang, M.B. Sun, N. Qin, Large eddy simulation based studies of jet-cavity interactions in a supersonic flow, Acta Astronaut. 93 (2014) 182–192. [7] D.J. Micka, J.F. Driscoll, Combustion characteristics of a dual-mode scramjet combustor with cavity flameholder, Proc. Combust. Inst. 32 (2009) 2397–2404. [8] D.J. Micka, J.F. Driscoll, Stratified jet flames in a heated (1390 K) air cross-flow with autoignition, Combust. Flame 159 (2012) 1205–1214. [9] A. Ben-Yakar, M.G. Munga, R.K. Hanson, Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows, Phys. Fluids 18 (2006) 1–16. [10] S.H. Won, I.S. Jeung, B. Parent, J.Y. Choi, Numerical investigation of transverse hydrogen jet into supersonic crossflow using detachededdy simulation, AIAA J. 48 (6) (2010) 1047–1058. [11] S.H. Won, I.S. Jeung, J.Y. Choi, DES investigation of the ignition of hydrogen transverse jet into high enthalpy supersonic crossflow, in: Proceedings of the AIAA Paper 2009-1557, 2009. [12] S. Kawai, S.K. Lele, Mechanisms of jet mixing in a supersonic crossflow: a study using large-eddy simulation, in: Proceedings of the AIAA Paper 2008-4575, 2008. [13] S.H. Kim, P. Donde, V. Raman, K.C. Lin, C. Carter, Large eddy simulation based studies of reacting and non-reacting transverse jets in supersonic crossflow, in: Proceedings of the AIAA Paper 20120482, 2012. [14] H.B. Wang, N. Qin, M.B. Sun, Z.G. Wang, A dynamic pressure-sink method for improving large eddy simulation and hybrid Reynoldsaveraged Navier–Stokes/large eddy simulation of wall-bounded flows, Proc. Inst. Mech. Eng. G: J. Aerosp. Eng. 226 (1107) (2011) 1107–1120. [15] C.W. Shu, High order weighted essentially nonoscillatory schemes for convection dominated problems, Soc. Ind. Appl. Math. 51 (2009) 82–126. [16] S. Balsara Dinshaw, C.W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405–452. [17] H.B. Wang, N. Qin, M.B. Sun, H.Y. Wu, Z.G. Wang, A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) model for supersonic turbulent combustion, Sci. China Technol. Sci. 54 (10) (2011) 2694–2707. [18] H.T. Toh, Large eddy simulation of supersonic twin-jet impingement using a fifth-order WENO scheme, Faculty of Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2003. [19] H.B. Wang, Z.G. Wang, M.B. Sun, N. Qin, Simulations of combustion with normal and angled hydrogen injection in a cavity-based supersonic combustor, Proc. Inst. Mech. Eng. G: J. Aerosp. Eng. 228 (4) (2014) 530–541. [20] A. Ben-Yakar, Experimmental Investigation of Mixing and Ighition of Transverse Jet in Supersonic Crossflows, Stanford University, California, 2000. [21] N.N. Smirnov, V.B. Betelin, R.M. Shagaliev, V.F. Nikitin, et al., Hydrogen fuel rocket engines simulation using LOGOS code, Int J. Hydrogen Energy 39 (2014) 10748–10756. [22] R.M. Gruber, A.S. Nejad, T.H. Chen, C.J. Dutton, Mixing and penetration studies of sonic jets in a Mach 2 freestream, J. Propuls. Power 11 (2) (1995) 315–323. [23] M.B. Sun, S.P. Zhang, Y.X. Zhao, Y.H. Zhao, J.H. Liang, Experimental investigation on transverse jet penetration into a supersonic turbulent crossflow, Sci. China Technol. Sci. 56 (8) (2013) 1989–1998.
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Numerical investigation on mixing and combustion of transverse hydrogen jet in a high-enthalpy supersonic crossflow Chaoyang Liu n, Zhenguo Wang, Hongbo Wang, Mingbo Sun Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China
a r t i c l e i n f o
abstract
Article history: Received 20 April 2015 Received in revised form 22 June 2015 Accepted 24 June 2015 Available online 2 July 2015
Mixing and combustion characteristics of a three-dimensional unsteady reacting flowfield generated by transverse hydrogen jet into high-enthalpy supersonic crossflow are investigated numerically. A hybrid RANS/LES (Reynolds-Averaged /Large Eddy Simulation) method acting as wall-modeled LES is adopted, where the ninth-order WENO (Weighted Essentially Non-oscillatory) scheme is introduced to discretize the inviscid fluxes. The validations of numerical results are performed for the jet penetration height, timeaveraged and instantaneous structures of reacting flowfield. It is found that the Kelvin– Helmholtz instability of jet shear layer on the windward side of jet plume discontinuously induces large scale coherent structures, which promote the combustion by enhancing the fuel mixing and enlarging the reacting area. The chain reactions creating OH radical mainly occur in the lean-fuel region and the heat-releasing chain reactions consuming OH radical are in the rich-fuel region. In the boundary layer and windward shear layer where supersonic crossflow stagnates, a diffusion flame with autoignition first occurs and then propagates to the downstream of jet plume, which holds the flame stabilization of total flowfield. & 2015 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: Transverse jet Supersonic crossflow Shear layer Autoignition Flameholding
1. Introduction The scramjet is an essential component of hypersonic air-breathing propulsion technology, which requires enhanced combustion efficiency of fuel and air [1]. Due to the extremely fast incoming airstream, mixing is slow compared to the limited residence time of fuel inside the combustor. Therefore, fast turbulent mixing and flameholding become the most critical technical issues associated with scramjet [2].
n
Corresponding author. Tel.: þ8615274952697; fax: þ86073184512301. E-mail address: [email protected] (C. Liu).
http://dx.doi.org/10.1016/j.actaastro.2015.06.023 0094-5765/& 2015 IAA. Published by Elsevier Ltd. All rights reserved.
Although different jet-injection configurations have been proposed to enhance the fuel mixing and maintain the stabilization of flame, the fuel injection from a wall orifice becomes one of the simplest but most efficient injection schemes [3]. The complicated structures and mixing enhancement mechanism resulting from the interaction of sonic transverse jet and supersonic crossflow have been investigated by many researchers in previous studies [4,5]. In order to stabilize the flame, wall injection coupled with a downstream cavity flameholder has been shown to be a promising candidate with moderate total temperature. Wang et al. [6] studied the interactions of jet and cavity in a supersonic condition using the large eddy simulation (LES) and pointed that moderate injection pressure may be beneficial to transport more fuel into the cavity to promote the ignition process
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under certain conditions. Micka et al. [7,8] experimentally investigated the combustion characteristics in a scramjet combustor with transverse jet upstream of cavity. The results indicated that there were two distinct flameholding modes for upstream fuel injection in the flowfield with high and low total temperature. Most of the previous studies were performed in the conditions with low and moderate enthalpy. However, a real supersonic combustor environment at flight speeds beyond Mach 8 is in high enthalpy. Ben-Yakar et al. [9] experimentally compared the time evolution of large scale vortices with hydrogen and ethylene transverse jet into highenthalpy supersonic crossflow, and found significant differences of the mixing properties in near-wall region. But the inherent mechanism of mixing and combustion enhancement resulting from large scale vortices was not clearly revealed. Won et al. [10,11] investigated the generation mechanism of large scale vortices and autoignition phenomenon using detached-eddy simulation (DES) in the conditions of BenYakar's experiment, whereas the interaction of turbulence and combustion as well as the physical and chemical mechanism that dominates the stabilization of flame was not answered. An accurate estimation and a deep physical understanding of the turbulent mixing and flameholding mechanism in the conditions of high total temperature play important roles in scramjet design [12]. The unsteady reacting flowfield is extremely complicated, and consists of multiplicate structures, such as the bow shock, barrel shock, Mach disk, separation shock and combustion wave. Purely experimental approach is not enough to acquire sufficient data to understand their inherent process. To obtain additional insights into the three-dimensional unsteady turbulent process and autoignition with sonic jet into the high-enthalpy supersonic crossflow, numerical simulation with high precision is an attractive choice. Despite the LES and DES have been used to investigate the large scale vortices in the transverse jet flowfield, their structures are somewhat obscure [13]. This primarily stems from the dissipative effect of conventional loworder upwind schemes, which may not be offset by singly increasing grid numbers. The too much dissipation induced by low-order schemes can suppress the actual physical structures. It is difficult for low-order schemes to capture fine structures in the reacting flowfield. Therefore, numerical approach with high-order schemes are urgently required to be applied. In present study, three-dimensional unsteady flowfield with a sonic jet injected into a high-enthalpy supersonic crossflow is numerically simulated by RANS/LES approach with ninth-order WENO scheme [14]. The ninth-order WENO scheme with high precision and low dissipation can capture the small scale vortices and shock very well in the flowfield [15,16]. The main objective of this paper is to develop further insights into the three-dimensional complex physics of jet mixing and flameholding mechanism. 2. Numerical approach 2.1. Governing equations The finite difference RANS/LES solver used in present simulation solves the Favre filtered compressible Navier–
Stokes equations of continuity, momentum, total energy and species transport for three-dimensional reacting flowfield [17]. For computational purpose, the governing equations are expressed in the conservative vector form as follows: ∂Q ∂ðE E v Þ ∂ðF F v Þ ∂ðG Gv Þ þ þ þ ¼W ∂t ∂x ∂y ∂z
ð1Þ
where Q represents a vector of conservative variables required to be solved for; E, F, G are vectors of inviscid fluxes, and Ev, Fv, Gv are vectors of viscous fluxes in x, y, and z directions, respectively; and W represents the chemical reaction source term. The specific expressions of above vectors are defined in previous reference [18]. 2.2. Turbulence models With the recent development of computational resources, LES has gradually become an efficient approach to solve turbulent flow and combustion problems, such as the separated flows, chemical non-equilibrium flows. While it is difficult to accurately simulate the flows in the near-wall region at high Reynolds numbers, due to high mesh resolution required. Then a hybrid method [13] blending Spalart–Allmaras RANS model and Yoshizawa sub-grid scale (SGS) model is adopted for capturing large scale turbulent structures in high Reynolds number flowfield. The blended equation can be given as below: 2 Dρν~ ∂ ∂ν~ ∂ν~ ¼ ρP v þ ρðν þ σ v1 ν~ Þ Dv þ ð1 F ÞρP Δ þ ρσ v2 ∂xj Dt ∂xj ∂xj ð2Þ where ν~ is molecular viscosity, ρ is the density. The specific expressions of P v , σ ν1 , σ ν2 , Dν , P Δ and blending function F in Eq. (2) has been given in our previous paper [19]. 2.3. Numerical methods The finite difference approach is used for the spatial discretization of the governing equations. The inviscid fluxes are discretized by the ninth-order WENO scheme and the viscous fluxes are discretized by fourth-order central difference scheme. In order to improve the computing efficiency, the time advancement is performed by means of a second-order dual time-step approach, the inner iteration of which is achieved by a lower-upper symmetric Gauss–Seidel (LU-SGS) method. An assumed sub-grid Probability Density Function (PDF) closure model is used for turbulence-chemistry interaction adopting a 9 species 19 step chemistry reaction mechanism for H2–air mixture [17]. 3. Code validation The present simulation is performed to investigate the mixing and flameholding mechanism with the transverse hydrogen jet into a high-enthalpy supersonic crossflow. In order to validate the simulation results, the flow conditions simulated is based on the experiment of Ben-Yakar, which maps the near-field flow characteristics and
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autoignition process of a sonic transverse hydrogen jet injected into the crossflow with flight-Mach number 10 total enthalpy flow conditions [20]. The experiment is carried out on a flat-plate with a circular port that allowed the jet of hydrogen to inject into the supersonic freestream at a constant mass flow rate. The jet port with a D¼ 0.002 m diameter is located at a distance of L1 ¼ 0.05 m downstream of the flat-plate leading edge. The static temperature and pressure of sonic hydrogen jet is 246 K and 4.9 105 Pa, respectively. The transverse jet injects into the crossflow of Mach number M1 ¼3.38, the static temperature and pressure of which is 1290 K and 3.24 104 Pa. The momentum flux ratio J of jet corresponding to the crossflow is 1.4 and the thickness of boundary layer ahead of the injection port is approximately δ1 ¼7.5 10 4 m. The detailed parameters of jetexit and crossflow are shown in Table 1. Considering actual computational costs, the threedimensional computational domain is confined to a finite local region near the injection port, which comprises of a solid surface that represents the flat-plate with a circular hole as the injection port. Fig. 1 shows the schematic diagram of the three-dimensional computational domain, which refers to the region ranging from 5D upstream to 10D downstream of the injection port in the streamwise direction. The scales of the domain in the normal and spanwise direction is 10D and 12D, respectively. Fig. 2 shows the overall grid system in the three-dimensional domain. In order to capture the coherent structures and instability of the reacting flowfield, the focused region of mesh is mainly concentrated in the vicinity of the jet-exit where coherent structures may initially generate. The number of grid points is 901 176 191 in the x, y and z directions, which leads to a grid resolution of Δx þ E5 15, Δy þ E1 15, and Δz þ E5 15 in the focused region basing on the thickness of entrance boundary layer. The grid resolution is high enough to capture the large-scale vortices in the flowfield. The inflow variables are obtained by a two-dimensional preliminary method using Reynolds-Averaged Simulation (RANS), the outputs of which at the distance of 20D from the flat-plate leading edge are used for the inlet profile parameters of threedimensional calculation to decrease the computational cost and time. A no-slip, no-penetration adiabatic condition is imposed at the lower wall; supersonic inflow condition is used at the inlet section; sonic jet-exit condition is set at the circular hole and other boundaries are treated as supersonic outflow. The physical time step is set as Δt¼0.05 δ1/u1, which satisfies the temporal resolution. Table 1 Supersonic crossflow and jet-exit flow conditions. Supersonic crossflow M1 T1, K p1 , Pa L1 , m δ1 , m Re1
3.38 1290 3.24 104 0.05 7.5 10 4 2.2 105
Sonic jet-exit flow Mj Tj, K pj , Pa D, m J ReD
1 246 4.9 105 0.002 1.4 1.5 105
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Fig. 1. Schematic diagram of computational domains and boundary conditions.
Fig. 2. Overall grid system in the three-dimensional computational domain.
Estimating precision and errors accumulation is necessary for numerical simulation of complex combustion gas dynamics in unsteady flowfield [21]. For uniform grid, the relative errors Serr of integration in three directions could be Serr ¼
3 X
1=N i
k þ 1
ð3Þ
i¼1
where Ni is the number of grid points in the direction of integration and k is the order of numerical scheme. Then the maximal number of time steps for solving present problem can be estimated by the following formula: 2 nmax ¼ Smax =Serr ð4Þ The allowable value of total error Smax ranges from 1% to 5%. The ratio of maximal allowable number of time steps and the actual number of time steps RS can be defined as: RS ¼ nmax =n
ð5Þ
where n is the actual number of time steps in simulation. The actual number of integration steps n performed before obtaining the results displayed in the figures is 6 105. As the value RS in present simulation is approximately
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1.5 103 which is high enough, therefore the accumulated error is very low. Combining the resolution analysis of grid scale with the precision and error estimation, we believe that precision of the numerical method and grid resolution can satisfy the necessary of the simulation. The jet penetration height is often used as a representative index to evaluate the flowfield characteristics of the transverse jet in crossflow, because it has important influence upon the mixing and combustion efficiency of jet and airstream in a scramjet combustor. It is also adequate for the validation and assessment of numerical results, which can be acquired easily in the experiment [10]. The comprehensive study about penetration height correlation was performed by Gruber et al. [22], who suggested a power law fit of the form 1=3 y x ¼ 1:23 DJ DJ
ð6Þ
Rothstein and Wantuck [23] used OH-PLIF to visualize the jet penetration trajectory and get another empirical correlation y 2:173 x 0:281 ¼ 0:443 ð7Þ DJ J DJ The penetration height and bandwidth of transverse jet in Ben-Yakar's experiment were obtained by manually
Fig. 3. Jet penetration and bandwidth of the transverse jet in crossflow.
tracking the visually observable outer edge of the jet from eight consecutive schlieren images [9]. The numerical penetration height and bandwidth of the transverse jet in crossflow are extracted by tracking the jet outer edges of H2 mass fraction 0.05 from eight consecutive images shown in Fig. 3, overlaid with the theoretical correlation and experimental data. It is found that Gruber's curve agrees well with present simulation results, but Rothstein and Wantick's is in good agreement with experimental data. Numerical jet penetration depth and bandwidth is a little lower than that acquired in the experiment, whereas their trend is in accordance. Fig. 4 shows the schlieren image acquired by Ben-Yakar and the density gradient contour of the time-averaged flowfield in present simulation. Compared with the experimental results, high-precision numerical approach captures the separation shock, bow shock and smeared shear layer observed in schlieren image very well. But the reattachment shock at the leeward side of jet plume is not visual. And the bow shock captured in the numerical results is slightly lower than that in the experiment, which is consistent with the trend of jet penetration height. The discrepancies between the experimental and numerical results may stem from the setting of the boundary conditions. We know that the turbulence intensity may have some influence upon the structures in the flowfield. In the actual experiment, the boundary layers of crossflow and jet contain turbulent effect and some unsteady disturbance with some characteristic scales. Furthermore, the wall in the experimental facility is not absolutely smooth, that may enhance the turbulent intensity in the near-wall flow. However, steady boundary conditions at jet-exit and inflow are used in present simulation, and the numerical solid wall conditions cannot match the real physical conditions very well. These deficiency causes a lack of turbulent intensity in flowfield, which may affect flow structures and result in the lower jet penetration and bow shock. Although there is a little difference between numerical simulation and experimental results, the trend of numerical results is consistent with the experimental data. So the numerical results can be considered relatively reliable.
Fig. 4. (a) Schlieren image with exposure time 3 μs; (b) the density gradient contour of the time-averaged flowfield.
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4. Results and discussion 4.1. Flow characteristics Statistical results discussed in the following are averaged over 5400 steps of unsteady reacting flowfield. In this time scale, the freestream passes through approximately a distance of 32D. Fig. 5(a) shows the time-averaged image of H2 mass fraction overlapped with divergence of velocity contour in center plane. The major flow structures such as the bow shock, barrel shock, Mach disk and separation shock are captured using RANS/LES approach. The H2 mass fraction gradually decreases along the streamwise, which indicates that mixing process occurs with traveling to the downstream. Fig. 5(b) shows the H2 mass fraction contour in the normal and spanwise plane. It is clearly found that a part of H2 appears in the upstream boundary layer due to the effect of separation zone ahead of the injection port. The stream lines at the spanwise plane x/D¼1 indicate that a pair of counter-rotating vortices (CRVs) formed in the near-wall region along the streamwise direction is induced by the transverse momentum of jet. This pair of CRVs then further grows in size along streamwise direction and the mixing process of the crossflow and transverse jet rapidly occurs. As it gradually grows in size and height, another pair of small scale trailing counter-rotating vortices (TCRVs) is induced at the leeward side of jet plume near the solid wall, which rotates in the opposite direction to the large one. A part of airstream at the leeward side of jet plume is entrained into large scale CRVs mixing with fuel, and the other part near the wall forms the TCRVs with the shear effect of large scale CRVs. Therefore, we believe that these two pairs of streamwise vortices still dominate the mixing process of the fuel and airstream in the supersonic reacting flowfield. Although the time-averaged results reveal that CRVs dominate the mixing process in the flowfield, the large scale coherent structures in the jet shear layer play very important roles in the mixing process near the periphery of the jet plume and near-wall region. The large scale vortices associated with their time-space evolution and
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convection are the most important phenomena observed in Ben-Yakar's experiment. However, the generation and development mechanism of large scale vortices is not understood very well. A comparison of consecutive schlieren images and the H2 mass fraction contours along with pressure isolines is shown in Fig. 6. The consecutive schlieren images with time correlation representing the first derivative of density are acquired using high-speed schlieren system, the interframing time of which is 1 μs. In order to vividly compare with experimental images, H2 mass fraction contours along with pressure isolines are used and the pressure isolines display the positions of bow shock in the instantaneous flowfield. The numerical simulation reproduces the generation, development and convection process of large scale vortices observed in the experiment and the time-correlated images are in good agreement with the schlieren images, which further validates the credibility of numerical results. A profound analysis of the coherence structures and their evolution process can give further insight into the enhancement of the near-wall mixing. From the consecutive images in both experiment and simulation, coherent structure as eddy 1 is initially generated at the windward side of jet plume near the injection port in frame 1. And then this coherent structure bends with the stretching of crossflow, resulting in large scale vortex formed as in frame 2. As it convects, this stretching process also enlarges the scale of vortex and causes the freestream to be engulfed by the jet shear layer as frame 3. But the frame 4 indicates that two vortices may appear almost at the same time, so we can conclude that vortices in the windward side of the jet are not generated periodically, but incontinuously. In frame 6, it is found that eddy 3 breaks into two small scale vortices with the interaction of low-speed jet and high-speed crossflow. But the small scale vortices merge into a large vortex again as frame 7 and 8. So the breakup and mergence of vortices may occur with the influence of crossflow. The pressure isolines show the bow shock in front of jet fluid, and the attached bow shock varies depending on the vortices. But the large scale vortices are affected by the bow shock at the same time.
Fig. 5. (a) Time-averaged image of H2 mass fraction overlapped with divergence of velocity contour in center plane; (b) image of H2 mass fraction in normal and spanwise planes.
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Fig. 6. Consecutive schlieren images and the H2 mass fraction contours along with pressure isolines with an interframing time of 1 μs.
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Fig. 7. Space-time trajectories of large-scale vortices.
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In order to make a quantitative comparison, the spacetime trajectories of large-scale vortices extracted from consecutive experimental and numerical images by identifying the center of large vortices are shown in Fig. 7. Due to the transient effect of flowfield, it is difficult to choose the starting frame of numerical results matching the first schlieren image. So the most homologous one is selected as the first frame. The comparison indicates that only the space-time trajectory of eddy 1 is in good agreement with experimental data, and marked discrepancy exists in other trajectories. But the trend of large-scale vortex trajectories is very similar. As the vortex velocity approaches that of freestream, the distance between adjacent vortices keep constant beyond three or four jet diameters downstream. Fig. 8 shows the consecutive instantaneous contours of H2 background obtained in center plane along with the negative divergence of velocity contours which describe the behavior of the shocks in the vicinity of jet exit, and the interframing time is 1 μs. The instantaneous contours represent the instability on the windward side of the jet plume and the starting process of the Kelvin–Helmholtz
Fig. 8. Instantaneous contours of H2 background obtained in center plane along with the negative divergence of velocity contours with an interframing time of 1 μs.
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Fig. 9. Instantaneous contours of H2 background obtained in center plane along with streamlines with an interframing time of 1 μs.
(KH) instability in this region, whereas the leeward side of the barrel shock does not show this instability. It is clearly found that the jet shear layer on the windward side of the jet plume in the near-wall region fluctuates, which is dominated by the KH instability existing in this region. KH instability is a convection instability and the oscillations are not self-excited but require a continuous source of disturbance to persist. The velocity near the shear layer is higher than that away from it, and this difference results in the KH type instability and the pressure fluctuation in the separation region ahead of the injection port provides the disturbance to maintain the KH instability [4]. It can magnify the instability of flowfield, and develops as a form of nonlinear. Then instability rapidly grows, magnifies and large scale vortex structures are induced. The attached bow shock and barrel shock in this region fluctuate due to the fluctuating coherent structures. Conversely, this fluctuating bow shock and barrel shock may further enhance the instability of the jet shear layer. The interaction of shock and vortices promotes the mixing process on the windward side of jet plume. Fig. 9 shows the instantaneous contours of H2 background obtained in center plane along with streamlines, the interframing time of which is 1 μs. The streamlines
distribution of transverse jet and crossflow represents that their mixing process firstly occurs in the shear layer on the windward side of jet plume. The very interesting phenomenon observed in the numerical results is that the fuel diffuses to upstream of jet-exit along the boundary layer. When a large scale coherent structure is generated, a counterclockwise spanwise vortex in the boundary layer is formed at the port leading side with the transverse momentum of jet, then a portion of fuel is entrained from the jet plume. At the same time, another clockwise separation vortex in front further transports it to the upstream. As the large vortices generate discontinuously, this process occurs accordingly. In the boundary layer, the residence time of flow is long and static temperature is very high. The fuel distributing in the upstream boundary layer is easily ignited, which may be beneficial to hold the flame in the downstream. 4.2. Flameholding mechanism Since the total enthalpy of the freestream in the experiment approaches 4 MJ/kg, namely the total temperature is about 4000 K, autoignition of the transverse H2 jet is achieved. The structures of jet flame are visualized
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Fig. 10. Numerical OH radical distribution superimposed with the stoichiometric isolines (top) and experimental OH-PLIF image (bottom) in center plane. Fig. 12. Instantaneous HRR contours superimposed with the stoichiometric isolines in center plane (top), axial and normal planes (bottom).
Fig. 11. Instantaneous contours of OH overlapped with the stoichiometric isolines in axial and normal planes.
using OH-PLIF, and combustion is maintained without a flameholder. The time-averaged and instantaneous flame structures are discussed in the following section basing on numerical results, and then autoignition effect and flameholding mechanism are further revealed. Fig. 10 shows the instantaneous OH distribution superimposed with the stoichiometric isolines and OH-PLIF image in center plane. Corresponding contours of OH in axial and normal planes are shown in Fig. 11. The OH radical as an intermediate production appears during H2 reacting with air and its sharp gradient is generally assumed to correspond to the flame front. In both experimental and numerical results, OH radical appears in the boundary layer and shear layer on the windward side of jet plume, but it is almost not visualized on the leeward side.
It is clearly found that numerical OH radical distributes at the upper side of stoichiometric isolines, while there is little at the opposite side. It indicates that chain branching reactions creating OH radical occur in the lean-fuel region above the stoichiometric isolines. As OH radical passes through the stoichiometric isolines, it is consumed by other chain reactions in a very short time. Therefore, the chain reactions consuming OH radical start at the richfuel side. Nondimensionalized instantaneous heat release rate (HRR) contours superimposed with the stoichiometric isolines are shown in Fig. 12. The HRR in a thick layer refering to the upstream boundary layer and windward shear layer facing toward the freestream is clearly higher than that in other regions. Heat is intensively released in regions that are confined into the regions within the stoichiometric isolines or along the lower side of the isolines, especially in the upstream region. It is further believed that heat-releasing chain reactions consuming OH radical mainly occurs in the rich-fuel regions below the stoichiometric isolines, whereas the chain branching reactions creating OH radical absorb heat. The other significant discovery is that the stoichiometric isolines coincide with the periphery of jet shear layer. The convection of large scale vortices analyzed in previous section facilitates the combustion by enhancing the mixing of the fuel and airstream and enlarging the reacting area. Therefore, it is very significant to understand the flow mechanism before flameholding is researched. The instantaneous flame structures are acquainted based on OH and HRR contours, and the results indicate that the flame mode in the upstream boundary and windward shear layer may be different from that in the downstream of jet plume. In order to reveal the
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Fig. 13. Profiles of mass fractions at x/D ¼ 2 and 1, corresponding to the upstream boundary layer and windward shear layer.
Fig. 14. Profiles of mass fraction at x/D¼ 5 and 8, corresponding to the downstream of jet plume.
Fig. 15. The static temperature and pressure profiles in normal direction at x/D¼ 2 (left) and 0 (right).
flameholding mechanism, it is very necessary to investigate the flame modes. The mass fraction profiles of H2, O2 and OH of averaged flowfield in different midline locations
which correspond to the upstream and downstream of jet respectively are extracted along the normal direction as Figs. 13 and 14. It is clearly seen from Fig. 13 that reacting
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region in the upstream boundary and windward shear layer is dominated by a diffusion flame mode, where the OH has peak values while O2 and H2 approach zero from opposite directions. The leakage of OH distribution at x/ D¼ 1 with more than one peaks is induced by the oscillations of the flame location, due to the instability of windward shear layer. Profiles of OH mass fraction in Fig. 14
Fig. 16. The static temperature and pressure profiles in normal direction at x/D ¼8.
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with two distinct peaks display that two main reacting regions exist in the downstream of jet plume. One is on the windward side of jet plume, where O2 and H2 decrease from opposite directions with a diffusion flame existing as the upstream of flowfield. And the other one is in the nearwall region, where O2 and H2 extensively coexist indicating that the flame basically occurs in the fuel-rich partially premixed mode. In summary, the upstream boundary layer and shear layer are dominated by diffusion flame and the near-wall region on the leeward side of jet plume exists fuel-rich partially premixed flame. In the flowfield of sonic transverse jet injecting into high-enthalpy supersonic crossflow, autoignition is confirmed to take place by OH-PLIF image, whereas it is difficult to clearly distinguish whether the jet flame is dominated by autoignition or flame propagation. Then the static temperature and static pressure profiles in three representative positions are extracted along normal direction as shown Figs. 15 and 16. Due to the low velocity in the boundary layer (x/D ¼ 2), the static temperature and static pressure at stoichiometric Ф ¼1 are 2382.13 K and 46.327 kPa, respectively. The ignition delay time in the boundary layer is approximately 3.98 μs estimated using CHEMKIN. In the time scale, the mixing gas convects to downstream with the distance of 3D at most. So it is believed that autoignition probably occurs in the downstream not away from present position. A similar approach
Fig. 17. Instantaneous temperature contours in center plane overlapped with stoichiometric isolines.
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Fig. 18. Instantaneous and averaged contours of H2O overlapped with stoichiometric isolines in center and axial planes.
is used to analyze the flame characteristic in the windward shear layer. As the airstream is stagnated through the bow shock, the static temperature and pressure at stoichiometric Ф ¼1 of x/D ¼0 approach 2552.02 K and 366.06 kPa. So the ignition delay time in the windward shear layer is only about 0.43 μs, so that we can believe that autoignition immediately occurs when fuel contacts high-temperature gas. The flow parameters in the downstream away from injection port are close to the freestream. The static temperature and pressure at stoichiometric Ф ¼ 1 of x/D ¼8 is about 1141.94 K and 23.314 kPa, and the ignition delay time is about 105.68 μs. The mixing gas travels to 130D in the downstream, so autoignition is very difficult to occur. Therefore, the fuel in the jet downstream is ignited by upstream flame. Basing on previous analysis, the flame in the boundary layer and windward shear layer near the injection port is a diffusion flame mode with autoignition, but a diffusion flame associated with flame propagation dominates the reacting region in the downstream. The consecutive instantaneous temperature contours in center plane overlapped with stoichiometric isolines are shown in Fig. 17, and the time interval is 1 μs. Thick bands
with high temperature exist in the periphery of boundary layer and windward shear layer above the stoichiometric isolines. The O2 and H2 immediately mix by diffusion in the boundary layer, where the temperature is high and residence time of flow is long. The conditions of autoignition is achieved, then combustion occurs. But the combustion process in the shear layer is more complex, which is powerfully coupled with turbulence. Two typical packets in the windward shear layer near the injection are tracked to analyze the autoignition process. The airstream behind the bow shock with high temperature and pressure is entrained into the boundary of jet by the large scale coherent structures and mixes with fuel rapidly. At the same time, high-enthalpy airstream impacts the transverse jet, the static temperature and pressure further increase with the ignition delay time decreased. Autoignition promptly occurs as soon as stoichiometric condition is satisfied. Pocket 1 with high temperature is formed in the shear layer near the injection, and it reacts with the transformation of jet shear vortices. The stoichiometric condition is easily achieved and the area of reaction are largely increased with the effect of large scale vortices, so combustion intensely occurs. But the temperature and
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pressure are relatively low, and the flame in the downstream can not be hold by autoignition mode. The diffusion flame in the shear layer and partially premixed flame in the near-wall region are maintained by upstream flame. We can conclude that the combustion in this reacting region is maintained by the autoignition process in the boundary layer and windward shear layer near the injection port. Fig. 18 shows the instantaneous and average contours of H2O mass fraction overlapped with stoichiometric isolines in center and axial planes. H2O is the final combustion production of H2 and O2. In both instantaneous and averaged contours, H2O that is mainly created by heat-releasing chain reaction in the rich-fuel region distributes within the stoichiometric isolines and in the regions covered by stoichiometric isolines. Then combustion production travels to the interior of jet plume with the effect of CRVs. 5. Conclusion We have numerically investigated the mixing physics and flameholding mechanisms for the unsteady reacting flowfield with transverse jet into high-enthalpy crossflow. Fine vortex structures and their convection characteristics have been captured with high precision WENO scheme. Significant conclusions that can be summarized as follows: 1. The generation and convection of large scale vortices in the windward shear layer are reproduced using highprecision numerical simulation, which promotes the combustion process by enhancing the fuel mixing and enlarging the reacting area. 2. The heat-absorbing chain reactions creating OH radical occur in the lean-fuel region above the stoichiometric isolines, whereas the heat-releasing chain reactions consuming OH radical and creating H2O are mainly in the rich-fuel region under the stoichiometric isolines. 3. A diffusion flame with autoignition dominates the reacting region of the boundary layer and windward shear layer where supersonic crossflow stagnates, then it propagates to the downstream of jet plume, which holds the flame stabilization of total flowfield.
References [1] J. Watanabe, T. Kouchi, K. Takita, G. Masuya, Characteristics of hydrogen jets in supersonic crossflow: large-eddy simulation study, J. Propul. Power 29 (3) (2013) 661–674. [2] Z.A. Rana, D. Drikakis, B.J. Thornber, Investigation of sonic jet mixing in a stream of supersonic crossflow using large eddy simulations, in: Proceedings of the 27th International Congress of the Aeronautical Sciences, 2010.
105
[3] A. Ben-Yarkar, R.K. Hanson, Experimental investigation of flameholding capability of hydrgon transverse jet in supersonic crossflow, in: Proceedings of the 27th Symposium (International) on Combustion/The Combustion Institute, 1998. [4] Z.A. Rana, B. Thornber, D. Drikakis, Transverse jet injection into a supersonic turbulent cross-flow, Phys. Fluids 23 (2011) 1–21. [5] K. Mahesh, The interaction of jets with crossflow, Annu. Rev. Fluid Mech. 45 (2013) 379–407. [6] H.B. Wang, Z.G. Wang, M.B. Sun, N. Qin, Large eddy simulation based studies of jet-cavity interactions in a supersonic flow, Acta Astronaut. 93 (2014) 182–192. [7] D.J. Micka, J.F. Driscoll, Combustion characteristics of a dual-mode scramjet combustor with cavity flameholder, Proc. Combust. Inst. 32 (2009) 2397–2404. [8] D.J. Micka, J.F. Driscoll, Stratified jet flames in a heated (1390 K) air cross-flow with autoignition, Combust. Flame 159 (2012) 1205–1214. [9] A. Ben-Yakar, M.G. Munga, R.K. Hanson, Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows, Phys. Fluids 18 (2006) 1–16. [10] S.H. Won, I.S. Jeung, B. Parent, J.Y. Choi, Numerical investigation of transverse hydrogen jet into supersonic crossflow using detachededdy simulation, AIAA J. 48 (6) (2010) 1047–1058. [11] S.H. Won, I.S. Jeung, J.Y. Choi, DES investigation of the ignition of hydrogen transverse jet into high enthalpy supersonic crossflow, in: Proceedings of the AIAA Paper 2009-1557, 2009. [12] S. Kawai, S.K. Lele, Mechanisms of jet mixing in a supersonic crossflow: a study using large-eddy simulation, in: Proceedings of the AIAA Paper 2008-4575, 2008. [13] S.H. Kim, P. Donde, V. Raman, K.C. Lin, C. Carter, Large eddy simulation based studies of reacting and non-reacting transverse jets in supersonic crossflow, in: Proceedings of the AIAA Paper 20120482, 2012. [14] H.B. Wang, N. Qin, M.B. Sun, Z.G. Wang, A dynamic pressure-sink method for improving large eddy simulation and hybrid Reynoldsaveraged Navier–Stokes/large eddy simulation of wall-bounded flows, Proc. Inst. Mech. Eng. G: J. Aerosp. Eng. 226 (1107) (2011) 1107–1120. [15] C.W. Shu, High order weighted essentially nonoscillatory schemes for convection dominated problems, Soc. Ind. Appl. Math. 51 (2009) 82–126. [16] S. Balsara Dinshaw, C.W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405–452. [17] H.B. Wang, N. Qin, M.B. Sun, H.Y. Wu, Z.G. Wang, A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) model for supersonic turbulent combustion, Sci. China Technol. Sci. 54 (10) (2011) 2694–2707. [18] H.T. Toh, Large eddy simulation of supersonic twin-jet impingement using a fifth-order WENO scheme, Faculty of Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2003. [19] H.B. Wang, Z.G. Wang, M.B. Sun, N. Qin, Simulations of combustion with normal and angled hydrogen injection in a cavity-based supersonic combustor, Proc. Inst. Mech. Eng. G: J. Aerosp. Eng. 228 (4) (2014) 530–541. [20] A. Ben-Yakar, Experimmental Investigation of Mixing and Ighition of Transverse Jet in Supersonic Crossflows, Stanford University, California, 2000. [21] N.N. Smirnov, V.B. Betelin, R.M. Shagaliev, V.F. Nikitin, et al., Hydrogen fuel rocket engines simulation using LOGOS code, Int J. Hydrogen Energy 39 (2014) 10748–10756. [22] R.M. Gruber, A.S. Nejad, T.H. Chen, C.J. Dutton, Mixing and penetration studies of sonic jets in a Mach 2 freestream, J. Propuls. Power 11 (2) (1995) 315–323. [23] M.B. Sun, S.P. Zhang, Y.X. Zhao, Y.H. Zhao, J.H. Liang, Experimental investigation on transverse jet penetration into a supersonic turbulent crossflow, Sci. China Technol. Sci. 56 (8) (2013) 1989–1998.