- Email: [email protected]
Investigation on combustion mode and heat release in a model scramjet engine affected by shocks
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation on combustion mode and heat release in a model scramjet engine affected by shocks Duo Zhang a, Donggang Cao b, Guoqiang He a, Bing Liu a, Fei Qin a,* a
Science and Technology on Combustion, Internal Flow and Thermal-structure Laboratory, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, PR China b Faculty of Aerospace Engineering, Technion Israel Institute of Technology, Haifa, 3200002, Israel
highlights A model scramjet engine is investigated using Large Eddy Simulation. The heat release rate of premixed/diffusion combustion mode is analyzed. A flame filter is conducted to evaluate the contributions to heat release. The influence of combustion modes on heat release rate is assessed.
article info
abstract
Article history:
A model scramjet engine in which the 1.0 Ma hydrogen jet mixes and reacts with the 2.0 Ma
Received 20 July 2019
surrounding airstream is investigated using large eddy simulation. The flame structure is
Received in revised form
analyzed with a focus on the relationship between premixed/diffusion combustion mode
5 September 2019
and heat release in the supersonic reacting flow. The flame filter is used to evaluate the
Accepted 9 September 2019
contributions to heat release rate by different combustion modes qualitatively and quan-
Available online 30 September 2019
titatively. Results show that the heat is released from a combination of premixed combustion mode and diffusion combustion mode even when the fuel and airstream are
Keywords:
injected into the combustor separately. Local mode-transition occurs as the supersonic jet
Large eddy simulation
flame propagates and interacts with shocks. The diffusion combustion mode dominates
Scramjet engine
during the ignition stage and the premixed combustion becomes dominant during the
Combustion mode
intensive combustion region. When the shock wave impinges on the flame, the combus-
Heat release
tion area decreases a little due to the compression effects of the shock. However, the heat release rate is significantly improved in the interaction region since the shock could increase the air entrainment rate by directing the airflow toward the fuel jet and enhance the mixing rate by inducing vorticity due to baroclinic effects, which is good for flame stabilization in the supersonic flow. For the present case, 33.3% of the heat is released by diffusion combustion and 66.7% of the heat is released by premixed combustion. Thus the premixed combustion mode is dominant in terms of its contributions to heat release in the model scramjet engine. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (F. Qin). https://doi.org/10.1016/j.ijhydene.2019.09.063 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Nomenclature A Cc, Ck Dm E fd fp Fd Findex Fp h HRR HRRd HRRp k Ma Mm p q Q T uj Vj,m Ym D m n r zd zp hd hp tij um U ~ sgs
area constants mixture diffusivity energy diffusion flame filter premixed flame filter diffusion flame index using the logarithmic function flame index using the logarithmic function premixed flame index using the logarithmic function enthalpy heat release rate heat release rate of diffusion combustion heat release rate of premixed combustion kinetic energy Mach number the molecular weight of the mth species pressure heat flux second invariant of the velocity gradient tensor temperature velocity in j-direction diffusion velocity in j-direction of the mth species mass fraction of the mth species local grid size dynamic viscosity kinematic viscosity density diffusion combustion contribution coefficient to combustion area premixed combustion contribution coefficient to combustion area diffusion combustion contribution coefficient to heat release rate premixed combustion contribution coefficient to heat release rate viscous stress tensor production mass rate of the mth species the antisymmetric part of the velocity gradient tensor filter Favre average sub-grid scale quantity
Introduction Supersonic combustion has obtained increasing attention due to its application to scramjet engines, which are promising candidates for the future air-breathing propulsion systems [1,2]. The successful development of performing engines for the scramjet-powered vehicles would depend, to a large extent, on the sound understanding of supersonic
28331
combustion. Up to now, remarkable achievements have been made in the field of supersonic combustion [3], which has strongly supported the success of several flight tests [4,5]. However, the present knowledge about the detailed mechanism of supersonic combustion process is not deep and wide enough to support further development of advanced scramjet and combined cycle engines in future. With the rapid progress in computing capabilities, large eddy simulation (LES) has become a more dominant method for numerical studies on turbulent combustion in recent years [6,7]. The LES approach applied for supersonic combustion studies reveal insight physics and improve overall prediction accuracy by capturing eddies that play fundamental roles in mixing and combustion [8]. With LES methodology, the instantaneous three dimensional vortices and flame structures are visualized and characterized in detail by many researchers [9e12]. For more in-depth understanding of the high-speed turbulent combustion, flame stabilization and combustion mode are analyzed. Explanations of the stabilization mechanisms are proposed based on premixed and nonpremixed flames [13e15], auto-ignition [16,17], and turbulence-flame interactions [18,19]. However, it is still a big challenge to analyze the mechanism of flame stabilization in the supersonic flows because the instantaneous stabilization position fluctuates rapidly [20e22]. Moreover, the nonpremixed combustion, partially-premixed combustion, premixed combustion and auto-ignition could contribute simultaneously to flame stabilization [14,23]. Analyzing combustion modes is an important issue, which motivates the development of analysis methods and tools. Temperature or an individual species concentration (OH, HO2) has been employed for the detection of critical features such as ignition, extinction, and flame fronts in traditional flame diagnostics [24]. Flame index is often employed to identify non-premixed and premixed combustion modes [25e27]. The scalar dissipation rate based on the mixture fraction is also extensively used to study the turbulent combustion [28,29]. More recently, chemical explosive mode analysis (CEMA) has been extended and employed to identify the flame structure and stabilization mechanism [30e32]. These methods are expected to offer a glance of the turbulent flow, fuel-air mixing and combustion. Identification of flame structure and combustion modes remains a hot subject for high-speed propulsion systems that are actively studied. It has become clear that the true stabilization picture of the jet flame involves a compromise between fully premixed and non-premixed combustion as been addressed by these methods. However, the links and interactions between different combustion modes haven't been fully understood as the flame propagates unsteadily. This is especially true for the supersonic combustion in scramjet engines [33]. When the fuel is injected into the chamber, the combustible mixture is formed leading to the consequent chemical reactions and heat release. Due to the high flow speed and the short residence time in the combustor of a scramjet, both combustion mode and heat release vary along the channel length as flame propagates downstream. It is necessary to find out the distributions of different combustion modes and their relationships with the heat release in the supersonic flow within a finite length combustor. Furthermore, quantitative study should be
28332
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
further conducted to investigate the contributions to heat release by different combustion modes, though the combustion regimes have been qualitatively distinguished. In the present study, the mixing and combustion processes between the hydrogen jet at 1.0 Ma and the co-flow airstream at 2.0 Ma in a scramjet engine model are investigated using large eddy simulation together with a partially stirred reactor (PaSR) combustion model and a 27-step H2-air reaction mechanism. Comparisons are made between experimental data and calculation profiles to validate the accuracy of the LES results which are further used to identify the flame structure and combustion modes. The premixed flame index and diffusion flame index are derived from the traditional flame index to separate premixed combustion region from the diffusion combustion zone. The flame filters are also defined to calculate the heat release rate by different combustion modes. Then the focus of the present study is placed on the qualitative and quantitative assessment on the contributions to heat release by premixed combustion and non-premixed combustion in the supersonic reacting flow by introducing the contribution coefficient.
Model scramjet engine The present study is based on a geometry configuration that is experimentally investigated at the German Aerospace Center (DLR). It is featured with a rectilinear combustion chamber with a slanted upper wall and a wedge-shaped flame-holder at the base of which hydrogen is injected into the supersonic surrounding airstream [34e36]. A schematic of the scramjet experimental facility is shown in Fig. 1. The combustor consists of a one-sided divergent channel with a 3 angle to compensate for the expansion of the boundary layer. The base cross section has a height of 50 mm and a width of 40 mm, which is connected to a Laval nozzle. The preheated air is expanded through the nozzle and flows into the combustion chamber at 2.0 Ma. The hydrogen jet enters the combustion section from the base of the wedge with an angle of 12 . The fuel is injected parallel to the air stream at the sonic speed using the fuel nozzle. After being expanded from the Laval nozzle, the supersonic air stream enters the combustor at p ¼ 0.1 MPa and T ¼ 340 K, whereas the hydrogen is injected at p ¼ 0.1 MPa and T ¼ 250 K. Combustion is initiated by a spark in a hydrogen tube with a small amount of oxygen. The periodicity in the span-wise direction is imposed since three fuel injection holes are used in the computational configuration. All coordinates of the present study are relative to a coordinate system where the tip of the wedge has the coordinates
x ¼ 35 mm and y ¼ 25 mm, and the lower wall of the flow channel has the coordinate y ¼ 0 mm.
Governing equations and numerical methods The governing equations for the reactive flow are the balance equations of mass, momentum, energy, and species. In LES, all variables are decomposed into resolved and unresolved (subgrid) components by a spatial filter so thatf ¼ f~ þ f ' , where f~ ¼ r f =r is the Favre-filtered variable, and the LES governing equations can be expressed as [37,38]: 8 vr v > ~j ¼ 0 þ ru > > vt vx > j > > > > > > v v > > ~j þ pdij tij þ tsgs ~i Þ þ ~i u ¼0 ru > ðru ij > < vt vxj i > > v ~ v h ~ sgs > > ~j þ q~j u ~i tij þ Hsgs ðrEÞ þ ðrE þ pÞu ¼0 þ sj > j > vt vxj > > > > > > > > : v ðrY ~ m Þ þ v rY ~mu ~mV ~ j;m þ Y sgs þ qsgs ¼ u_ m ~j rY j;m j;m vt vxj
(1)
Here, r is the density, (ui)i¼1,2,3 is the velocity vector in Cartesian coordinates, p is the pressure, Ym is the mass fraction for the mth species, and u_ m is the production mass rate of the mth species. The total energy of the system is the sum of the internal energy and the kinetic energy. As a result, the filtered total energy is given as the sum of the filtered internal energy, the resolved kinetic energy, and the subgrid kinetic energy. The filtered viscous stress tensor t ij is approximated as: 8 > ~ij 1S~kk dij > t ¼ 2m S > ij < 3 > ~j ~ i vu 1 vu > > : S~ij ¼ þ 2 vxj vxi
(2)
The one equation eddy model is used to calculate the subgrid stress tensor with the following expressions [39e41]: 8 2 sgs > tij ¼ 2nk S~ij þ ksgs dij > > > 3 > > > < pffiffiffiffiffiffiffiffi sgs nk ¼ Ck k D > > > sgs sgs 3=2 > > ~i k vk v sgs v nk vksgs > sgs vu > : ~j k u þ þ Cc ¼ tij vxj vxj sk vxj vt vxj D
(3)
For H2-air combustion, the 27-step reactions chemical mechanism is employed [42], and the PaSR combustion model is adopted to close the LES governing equations for reacting flows [43,44]. The LES equations are solved by the code from
Fig. 1 e Geometry of the model scramjet engine (mm).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
OpenFOAM, which is based on unstructured collocated finite volume method using Gauss theorem [45]. The density-based solver rhoReactingFoam is used with a second-order CrankNicholson time-integration scheme. The TVD (Total Variation Diminishing) compatible flux limiter is used, and the diffusive fluxes are reconstructed using central differencing of the inner derivatives [46]. The CFL number is less than 0.3, which corresponds to a physical time step at the order of 1 108 s. All variables are prescribed at inflow boundaries with Dirichlet conditions. Neumann conditions are used at outflow boundary where all variables are extrapolated from the interior ones. At fixed walls, the nonslip conditions are applied. Three grids with approximately 6 million (Grid_1), 12 million (Grid_2), and 19 million (Grid_3) cells are used for the simulations. Local refinement of the computational grids has been performed with a great attention. The grids are clustered towards the walls as well as in the wake region and the shear layer region to resolve the mixing and chemical reactions.
Results and discussion The rig has been experimentally investigated with a wide range of measurements, including CARS measurements of the temperature, LDV and PIV measurements of the velocity et al. [34,35,43]. Comparisons between the experimental data and the numerical results using three different grids are made to validate the simulation methods involved in the present study. Fig. 2(a) presents the time-averaged temperature profiles as well as CARS-measured data at different stream-wise locations. The hydrogen is injected into the surrounding airstream resulting in the combustible mixture. At the first location where x ¼ 78 mm, a local temperature minimum in the middle of the chamber together with two temperature maxima at the boarder of the jet could be observed in the figure. It indicates that chemical reactions start to occur at the interface between the hydrogen jet and the airstream, but only a small amount of heat is released due to limited mixing. At the location x ¼ 125 mm, vigorous combustion takes place releasing a large amount of heat in a narrow central region. It is featured with a sharp peak since there are large gradients around the mixing and reacting layer. With the increase of downstream distance, the shear layer grows and the flame spreads widely. Farther downstream where x ¼ 233 mm, the
28333
combustion intensity weakens due to the consumption of reactants, leading to a small peak value in the profiles. However, with the mass and heat transfer in the turbulent flow, the high temperature zone expands and the temperature profiles become wider compared to the profiles at x ¼ 125 mm. Fig. 2(b) shows the velocity profiles with the experimental data at different locations. Note that the fuel is injected at the base of the strut (x ¼ 67 mm) at sonic speed. Just a little downstream distance from the strut at x ¼ 78 mm, strong reverse velocity is observed on each side of the fuel jets because of the recirculation zones formed at the base of the strut, which is helpful to enhance mixing and to hold flame. The mass, momentum, and energy are exchanged between the fuel jet and the airstream along the channel length with the development of the shear layer. The profiles at x ¼ 125 mm have a relatively small minimum-peak in the middle as the recirculation region gradually shrinks. At the downstream location where x ¼ 207 mm, the core flow is accelerated in the divergent chamber with a similar magnitude of velocity to the outer flow. Thus the profiles become relatively flat at this location. In order to visualize the flow field, Fig. 3 shows the isosurface of the second invariant of the velocity gradient (Qcriterion) colored by heat release rate (HRR) with the contours of density gradient magnitude. And Fig. 4 presents the isosurface of the vorticity colored by temperature with the contours of Mach number. When the supersonic air flow encounters the wedge-shaped strut that leads to the convergence of the channel, an oblique shock is formed at the tip of the wedge due to the compression effect. The induced shocks reflect off the upper and lower chamber walls and interact with the shear layer where mixing and chemical reactions take place. Relatively weak expansion fans and the following recompression shocks could also be observed at the upper and lower corners of the wedge. A slight asymmetry is noticed due to the divergent combustor and the nature of turbulence. Furthermore, the recirculation regions are found just downstream of the strut base featured with low speed. This is good for mixing and flame-holding in the scramjet engine. A shear layer is formed between the fuel jet and the airstream. Initially the shear layer is relatively flat and then it becomes pronounced and distorted. With the development of the shear layer, the stream-wise vortex interacts with the span-wise vortex resulting in the complex patterns with three
Fig. 2 e Comparison between simulation results and the experimental data [35] at different locations: (a) temperature and (b) velocity.
28334
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 3 e Iso-surface of the Q-criterion colored by heat release rate with the contours of density gradient magnitude. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4 e Iso-surface of the vorticity colored by temperature with the contours of Mach number. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
dimensional features. The shear layer grows with increasing downstream distance due to vortex stretching, baroclinic torque, heat release, volumetric expansion, and diffusion. And the vortex structures eventually develop into longitudinal vortices that dominate in the far flow field. When the hydrogen mixes and reacts with the surrounding air stream, diffusion, convection, and chemical reactions take place simultaneously. Combustion occurs in multiple modes including premixed combustion and diffusion (non-premixed) combustion depending on the local mixing status. The flame index, which is defined as the degree of alignment of the fuel and the oxidizer gradients FI ¼ VYF ,VYO , has been a useful measure to distinguish the local premixed or diffusion flame [25]. In the premixed flame, the gradients of fuel and oxidizer are aligned so that the rapid consumption of the reactants across the flame results in a positive value of the flame index. On the contrary, the gradients of fuel and oxidizer oppose one another in the non-premixed or diffusion flame. Therefore, the positive FI represents the premixed combustion mode while the negative FI indicates the diffusion combustion mode in the jet flame. In order to avoid getting too small or too large values, the flame index is combined with a logarithm function as [47]:
Findex ¼
FI log ðjFIj þ 1Þ jFIj þ 1 10
(4)
The contours of flame index, temperature, and heat release rate are presented in Fig. 5. It suggests that the supersonic reacting flow could be thoroughly divided into three regions. The first region is just down the strut where the hydrogen jets discharge in the wake of the flame holder and mix with the surrounding air. Diffusion combustion with small heat release rates is observed in the shear layers shed off the strut edges. Some distance downstream of the wake, the diffusion combustion as well as the premixed combustion could be found with vigorous heat release in the second region. Specifically, diffusion combustion mainly occurs around the outer edge of the shear layer while premixed combustion dominates near the inner edge of the shear layer. Although a large amount of heat is released in the second region, the high-temperature zone is quite narrow because of the high speed flow and the small residence time that limit the mixing between the hot combustion products and the cold air passing through the combustor. In the third region, turbulent mixing and lean post-combustion take place featured with significant heat
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28335
Fig. 5 e Contours of temperature, heat release rate, and flame index.
transfer. It corresponds to the broadened high-temperature zone with weak heat release. Both diffusion combustion and premixed combustion could be observed in the third region. However, diffusion combustion dominates around the edges of the vortex structures and premixed combustion occurs in the cores of the vortex structures. The profiles of the flame index at x ¼ 70, 100, 150, 200, 250, and 280 mm are plotted in Fig. 6. At the early stage where x ¼ 70 mm, Findex is almost negative since diffusion is the dominating physics. A little downstream distance at x ¼ 100 mm, Findex has negative values as well as positive values with large peak magnitudes. It indicates that vigorous chemical reactions take place in both diffusion combustion mode and premixed combustion mode. However, Findex ¼ 0 in the central part of the profile, which means that vigorous combustion does not occur in the extremely fuel-rich zone. The mixing and reacting layer has a width of about 6 mm consisting of a 3.2 mm diffusion combustion layer and a 2.8 mm premixed combustion layer. Farther downstream, negative and positive values of Findex could be always observed indicating that turbulent combustion occurs in multiple modes. With the increasing downstream distance, the flame spreads in width with less intensity as the profiles of Findex broaden with small peak values. Fig. 7 shows the scatter plot of heat release rate with respect to flame index colored by temperature at different locations to offer another view of the reacting flow. At the early stage where x ¼ 70 mm, the heat release rate is extremely small and the overall temperature is quite low.
Sufficient heat release is observed some distance downstream of the wake. At x ¼ 100 mm, the plot of HRR with respect to Findex presents the significant feature with two peaks near Findex z 4 and Findexz4, respectively. It means that chemical reactions take place vigorously and release a large amount of heat in both diffusion and premixed combustion modes. But the overall temperature of the diffusion combustion zone is much lower than that of the premixed combustion zone. This is because the diffusion combustion zone is closely connected to the cold surrounding air, which is also seen in Fig. 6. It is interesting to note that the high-temperature zone corresponds to relatively small magnitudes of HRR and Findex, rather than maximums of HRR and Findex. In other words, both heat release and heat transfer determines the temperature distribution of the supersonic reacting flow. With the increasing downstream distance, both HRR and the magnitude of Findex decrease due to the consumption of combustible mixtures, while the overall temperature increases because of heat transfer and energy exchange in the turbulent flow. Besides, the scatter plot shifts a little from left (negative Findex) to right (positive Findex) and large HRR corresponds to positive Findex. It shows that premixed combustion makes more contributions to the heat release in the downstream. In order to further evaluate the heat release in the supersonic reacting flow, the three-dimensional surfaces of mixture fraction (z), flame index (Findex), and heat release rate (HRR) colored by temperature (T) at different locations are displayed in Fig. 8. It is interesting to note the evolution of the flow field in the new space. At x ¼ 70 mm, as discussed before, Findex is
28336
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 6 e Distributions of the flame index in y-direction at different locations.
Fig. 7 e Scatter plots of heat release rate vs. flame index colored by temperature at different locations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28337
Fig. 8 e Distributions of heat release rate in z-Findex space colored by temperature at different locations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
almost negative and HRR is very small since sufficient mixing and combustion do not occur until some distance downstream of the wake. The value of mixture fraction (z) varies from 0 (pure airstream) to 1 (pure fuel jet). A relatively high temperature region with medium value of z could be observed, which indicates that weak reactions are induced in the shear layer between the fuel jet and the airstream. This makes preparations for the following intensive combustion and keeps the flame from blowing off in the high speed flow. At the location where x ¼ 100 mm, the heat is released in a small range of mixture fraction with two combustion modes. With the increasing downstream distance, ‘the ranges of z, HRR, and Findex decrease gradually. It should also be noticed that the premixed combustion releases a little more heat than the diffusion combustion does. That is to say, in the far downstream the weak combustion takes place mainly in premixed combustion in terms of heat release. In order to separate the premixed combustion mode from the diffusion mode and to investigate their contributions to heat release qualitatively as well as quantitatively, the premixed flame index Fp and the diffusion flame index Fd based on the Findex are defined: 8 Findex jFindex j > > < Fd ¼ 2 > F þ jFindex j > index : Fp ¼ 2
(5)
The value of Fd varies from zero to negative ones while the value of Fp ranges between zero and positive ones. In addition,
the diffusion flame filter and the premixed flame filter are defined as: 8 Fd > > > fd ¼ < Findex > Fp > > : fp ¼ Findex
(6)
Both fd and fp only have two values: 0 or 1. fd is 1 only for the diffusion combustion zone while it is 0 for the other region. On the contrary, fp is 1 only for the premixed combustion zone while it is 0 for the other region. The two quantities fd and fp are supposed to offer relevant estimates of the respective weights of the premixed and diffusion contributions. With the help of the combustion mode filters fd and fp, one can easily distinguish the heat released by diffusion combustion from the heat released by premixed combustion for the reacting flow field by using the following equation:
HRRd ¼ fd HRR HRRp ¼ fp HRR
(7)
As a consequence, Fig. 9(a) shows the contours of the diffusion flame index (Fd) and the premixed flame index (Fp). Correspondingly, Fig. 9(b) offers vivid pictures of the heat release rate of diffusion combustion (HRRd) and the heat release rate of premixed combustion (HRRp). It is notable that the diffusion combustion zone is a little larger than that of the premixed combustion region while premixed combustion makes more contributions to heat release than the diffusion
28338
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 9 e Contours of (a) the diffusion flame index Fd and the premixed flame index Fp; (b) the heat release rate of diffusion combustion HRRd and the heat release rate of premixed combustion HRRp. combustion, which should be further investigated quantitatively. We use the following equations to calculate the diffusion combustion area and the premixed combustion area at a certain cross section: Z 8 < Ad ¼ fd dA Z : Ap ¼ fp dA
(8)
And Eq. (9) is used to calculate the relevant area ratios: 8 > > > < zd ¼ > > > : zp ¼
Ad Ad þ Ap Ap Ad þ Ap
(9)
Similarly, the heat release rates resulting from diffusion combustion or premixed combustion at a certain cross section could be quantitatively estimated by: Z 8 < Qd ¼ HRRd dA Z : Qp ¼ HRRp dA
(10)
And the contribution coefficient is introduced to quantify the contributions to the heat release by the two distinct combustion modes: 8 > Qd > > > hd ¼ < Qd þ Qp > Qp > > > : hp ¼ Q þ Q d p
increases significantly peaking at x z 130 mm, and then it goes down dramatically. Another small peak could be observed at x z 200 mm. Then it continues to decrease gradually along the channel length. However, hd becomes smaller than hp, which means that premixed combustion contributes to heat release greatly. For the simulated 3D configuration in the present study, we find that R R and f dV= ðfd þfp ÞdV ¼ 70:4% R R d HRRd dV= ðHRRd þHRRp ÞdV ¼ 33:3% that. In other words, only 33.3% of heat is released by diffusion combustion that takes place in 70.4% of the whole reacting zone. It indicates that although the volume of the diffusion combustion is larger than that of the premixed combustion, premixed combustion mode is dominant in the present model scramjet engine since its overall contribution coefficient to heat release is 66.7%. A notable feature in Fig. 10 is that the combustion area starts to decreases at the very location x z 100 mm where the shock wave interacts with the shear layer, which is also confirmed in Figs. 3e4. This is understandable due to the compression effect associated with shocks. In addition, the baroclinic effect, which is the key point of the RichimyerMeshkov instability [48], also plays an important role in the shock/shear-layer interaction. The vorticity equation could be derived by taking the curl of the momentum equation: dU 1 1 ðU , VÞU þ ðV , UÞU ¼ V F þ 2 ðVr VpÞ þ V ðnDUÞ þ V dt r 3 ½nVðV , UÞ (12)
(11)
The parameters hd and hp are expected to quantitatively evaluate premixed and diffusion contributions to heat release in the supersonic reacting flow. Some additional analysis are offered by looking at the time-averaged profiles in Fig. 10 and Fig. 11, respectively. It is obvious that the combustion area is increasing along the channel length with the development of the shear layer. The diffusion combustion area is always larger than the area of premixed combustion. But things become a little complex for the distribution of the heat release rate shown in Fig. 11. At the first stage (67 mm < x < 90 mm), chemical reactions are induced mostly in the diffusion combustion mode since hd is larger than hp, though both Qd and Qp are extremely small. After that, the relative heat release rate
The term Vr Vp makes significant contributions to the vorticity disturbance since it is a main source term of vorticity in supersonic flows [49]. The magnitude contours of the Vr V p are presented in Fig. 12. When the shock wave impinges on the shear layer, large kVr Vpk could be observed in the following regions. It indicates that the non-aligned gradients of density and pressure contribute to vortex generation and mixing enhancement. As a consequence, in Fig. 11 the heat release rate is greatly enhanced to some extent despite of the decrease of the combustion area. However, it shows that the interaction between the shock wave and the shear layer has more significant impact on the heat release rate resulting from premixed combustion. When the shock waves impinge on the shear layer, they direct the airstream vertically toward the fuel to increase the air entrainment rate. The adverse pressure gradient caused by the shocks could elongate the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28339
Fig. 10 e Time-averaged profiles of (a) combustion area of different modes versus the chamber length; and (b) area ratio of different combustion modes versus the chamber length.
Fig. 11 e Time-averaged profiles of (a) heat release rate versus the chamber length resulting from different combustion mode; and (b) contribution coefficient of different combustion mode versus the chamber length.
Fig. 12 e Contours of the kVr Vpk. local recirculation zones. Moreover, additional vorticity is induced locally by the shocks owing to baroclinic effects, which enhances the turbulent mixing and the chemical reactions [50]. The shock wave could also induce a local temperature increase due to compression, which is beneficial to ignite the hydrogen/air mixture [51]. As a result, the heat release rate, especially for the one caused by premixed combustion, is greatly enhanced with significant peaks, which is observed in Fig. 11. This has positive effect on improving flame stability in the supersonic flows. The similar trend could be also found in the second interaction region (x z 190 mm) where the combustion area decreases a little and the heat
release rate is enhanced with a small peak value since the shock waves are relatively weak and the amounts of the reactants are small.
Conclusion In the present study, a model scramjet engine in which the 1.0 Ma hydrogen jet mixes and reacts with the 2.0 Ma surrounding airstream, has been investigated by large eddy simulation (LES) based on OpenFOAM. The calculated results agree well with the experimental data, which demonstrates
28340
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
the reasonability of the employed numerical methods and computational strategies. The flame structure is investigated with a focus on the relationship between combustion mode and heat release in the supersonic reacting flow. The premixed flame index and the diffusion flame index are defined based on the classical flame index, which are supposed to discriminate the diffusion combustion mode from the premixed combustion mode. The flame filters are used accordingly to evaluate the contributions to the heat release by different combustion modes qualitatively as well as quantitatively. Results show that the heat is released from a combination of diffusion combustion mode and premixed combustion mode in the scramjet engine. Local mode transition occurs during the flame propagation affected by shocks. Diffusion combustion is dominant during the ignition stage with very small heat release rate. With the increasing downstream distance, premixed combustion plays a more and more important role in the supersonic reacting flow as the shear layer grows. When the shocks impinge on the mixing and reacting layer, the combustion area reduces a little owing to the compression effect associated with shocks. However, the heat release rate peaks in the region where shocks intersect with the shear layer. This is because shock waves could increase the air entrainment rate by directing the airflow toward the fuel jet and enhance the mixing rate by inducing additional vorticity due to baroclinic effects, which is good for flame-holding in the supersonic flow. Although the fuel and airstream are injected into the combustor separately, 66.7% of the heat is released by premixed combustion while only 33.3% of the heat is released by diffusion combustion. Thus the premixed combustion mode is dominant in the model scramjet engine in terms of its contributions to heat release.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
Acknowledgments This work is financially supported by the National Natural Science Foundation of China through grants 51706185.
[19]
references
[20]
[1] Segal C. The scramjet engine processes and characteristics. New York, USA: Cambridge University Press; 2009. p. 127e8. [2] Tian Y, Yang S, Le J, Su T, Yue M, Zhong F, Tian X. Investigation of combustion and flame stabilization modes in a hydrogen fueled scramjet combustor. Int J Hydrogen Energy 2016;41:19218e30. [3] Choubey G, Deuarajan Y, Huang W, Mehar K, Tiwari M, Pandey K. Recent advances in cavity-based scramjet enginea brief review. Int J Hydrogen Energy 2019;44:13895e909. [4] Kimmel R, Adamczak D, Borg M, Jewell J, Juliano T, Stanfield S, Berger K. First and fifth hypersonic international flight research experimentation's flight and ground tests. J Spacecr Rocket 2019;56:421e31. [5] Smart M, Hass N, Paull A. Flight data analysis of the HyShot 2 scramjet flight experiment. AIAA J 2006;44:2366e75. [6] Patton CH, Wignall TJ, Edwards JR, Echekki T. LES model assessment for high speed combustion. 2016. p. 1937. AIAA Paper. [7] Liu C, Wang Z, Wang H, Sun M, Li P. Large eddy simulation of cavity-stabilized hydrogen combustion in a diverging
[21]
[22]
[23]
[24] [25]
[26]
[27]
supersonic combustor. Int J Hydrogen Energy 2017;42:28918e31. Koo H, Donde P, Raman V. A quadrature-based LES/ transported probability density function approach for modeling supersonic combustion. Proc Combust Inst 2011;33:2203e10. Fureby C, Chapuis M, Fedina E, et al. CFD analysis of the HyShot II scramjet combustor. Proc Combust Inst 2011;33:2399e405. Watanabe J, Kouchi J, Takita TK, et al. Large-eddy simulation of jet in supersonic crossflow with different injectant species. AIAA J 2012;50(2):2765e78. Liu B, He G, Qin F, An J, Wang S, Shi L. Investigation of influence of detailed chemical kinetics mechanisms for hydrogen on supersonic combustion using large eddy simulation. Int J Hydrogen Energy 2019;44:5007e19. Gong C, Jangi M, Bai X, Liang J, Sun M. Large eddy simulation of hydrogen combustion in supersonic flows using an Eulerian stochastic fields method. Int J Hydrogen Energy 2017;42:1264e75. Chung SH. Stabilization, propagation and instability of tribrachial triple flames. Proc Combust Inst 2007;31:877e92. Huang Z, He G, Qin F, et al. Large eddy simulation of combustion characteristics in a kerosene fueled rocketbased combined-cycle engine combustor. Acta Astronaut 2016;127:326e34. Tabet F, Sarh B, Goekalp I. Turbulent non-premixed hydrogen-air flame structure in the pressure range of 1-10 atm. Int J Hydrogen Energy 2011;36:15838e50. Cabra R, Myhrvold T, Chen JY, et al. Simultaneous laser Raman-Rayleigh-LIF measurements and numerical modeling results of a lifted turbulent H2/N2 jet flame in a vitiated coflow. Proc Combust Inst 2002;29:1881e8. Wei H, Shang Y, Cai J, Pan M, Shu G, Chen R. Numerical study on transition of hydrogen/air flame triggered by autoignition under effect of pressure wave in an enclosed space. Int J Hydrogen Energy 2017;42:16877e86. Su LK, Sun OS, Mungal MG. Experimental investigation of stabilization mechanisms in turbulent, lifted jet diffusion flames. Combust Flame 2006;144:494e512. Yang Y, Wang Z, Sun M, et al. Numerical and experimental study on flame structure characteristics in a supersonic combustor with dual-cavity. Acta Astronaut 2015;117:376e89. Mizobuchi Y, Rachibana S, Shinio J, Ogawa S, Takeno T. A numerical analysis of the structure of a turbulent hydrogen jet lifted flame. Proc Combust Inst 2002;29:2009e15. Ma S, Zhong F, Zhang X. Numerical study on supersonic combustion of hydrogen and its mixture with Ethylene and methane with strut injection. Int J Hydrogen Energy 2018;43:7591e9. Barnes FW, Segal C. Cavity-based flameholding for chemically-reacting supersonic flows. Prog Aerosp Sci 2015;76:24e41. Boivin P, Dauptain A, Jimenez C, Cuenot B. Simulation of a supersonic hydrogen-air autoignition-stabilized flame using reduced chemistry. Combust Flame 2012;159:1779e90. Mastorakos E. Ignition of turbulent non-premixed flames. Prog Energy Combust Sci 2009;35:57e97. Yamashita H, Shimada M, Takeno T. A numerical study on flame stability at the transition point of jet diffusion flames. Proc Combust Inst 1996;26:27e34. Choi J, Han S, Kim K, Yang V. High resolution numerical study on the coaxial supersonic turbulent flame structures. 2014. p. 3745. AIAA Paper. Dinesh K, Jiang X, Oijen J. Hydrogen-enriched non-premixed jet flames: analysis of the flame surface, flame normal, flame
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
[28] [29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
index and Wobbe index. Int J Hydrogen Energy 2014;39:6753e63. Poinsot T, Veynante D. Theoretical and numerical combustion. USA: R. T. Edwards; 2005. p. 84e6. Mameri A, Tabet F. Numerical investigation of counter-flow diffusion flame of biogas-hydrogen blends: effects of biogas composition, hydrogen enrichment and scalar dissipation rate on flame structure and emissions. Int J Hydrogen Energy 2016;41:2011e22. Zhao ZY, Yoo CS, Richardson ES, et al. Chemical explosive mode analysis for a turbulent lifted ethylene jet flame in highly-heated coflow. Combust Flame 2012;159:265e74. Wang L, Jiang Y, Pan L, Xia Y, Qiu R. Lagrangian investigation and chemical explosive mode analysis of extinction and reignition in H-2/CO/N-2 syngas non-premixed flame. Int J Hydrogen Energy 2016;41:4820e30. An J, Jiang Y, Ye M, Qiu R. One-dimensional turbulence simulations and chemical explosive mode analysis for flame suppression mechanism of hydrogen/air flames. Int J Hydrogen Energy 2013;38:7528e38. Wang H, Wang Z, Sun M, Wu H. Combustion modes of hydrogen jet combustion in a cavity-based supersonic combustor. Int J Hydrogen Energy 2013;38:12078e89. W. Waidmann, F. Alff, M. Bohm, et al., Supersonic combustion of hydrogen/air in a SCRAMJET combustion chamber, IAF-94-S.4.429. Oevermann M. Numerical investigation of turbulent hydrogen combustion in a SCRAMJET using flamelet modeling. Aero Sci Technol 2000;4:463e80. Wu J, Wang Z, Bai X, et al. The hybrid RANS/LES of partially premixed supersonic combustion using G/Z flamelet model. Acta Astronaut 2016;127:375e83. Zhang Z, Cui G, Xu C. Theory and application of large eddy simulation. Beijing, China: Tsinghua University Press; 2008. Chaps. 2-3. Wang Z, Sun M. Supersonic turbulent flow, combustion modeling and large eddy simulation. Beijing, China: Science Press; 2013. p. 1e13.
28341
[39] Yoshizawa A, Horiuti K. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. J Phys Soc Jpn 1985;54(8):2834e9. [40] Menon S, Yeung PK, Kim WW. Effect of subgrid models of the computed interscale energy transfer in isotropic turbulence. Comput Fluids 1996;25(2):165e80. [41] Nakayama A, Vengadesan SN. On the influence of numerical schemes and subgrid-stress models on large eddy simulation of turbulent flow past a square cylinder. Int J Numer Methods Fluids 2002;38(3):227e53. [42] Marinov NM, Westbrook CK, Pitz WJ. Detailed and global chemical kinetics model for hydrogen, 8th International Symposium on Transport Properties. 1995. p. 1e29. [43] Fureby C, Fedina F, Tegner J. A computational study of supersonic combustion behind a wedge-shaped flameholder. Shock Waves 2014;24:41e50. [44] Berglund M, Fedina E, Fureby C, et al. Finite rate chemistry large-eddy simulation of self-ignition in a supersonic combustion ramjet. AIAA J 2010;48(3):540e50. [45] OpenFOAM: OpenCFD Ltd. Available from: www.openfoam. com. [46] Harren A. High resolution schemes for hyperbolic conservation law. J Comput Phys 1997;135:260e78. [47] Luo K, Jin T, Lu S, et al. DNS analysis of a three-dimensional supersonic turbulent lifted jet flame. Fuel 2013;108:691e8. [48] Brouillette M. The Richtmyer-Meshkov instability. Annu Rev Fluid Mech 2002;34:445e68. [49] Yan Y, Chen C, Liu P, et al. Study on shock wave-vortex ring interaction by the micro vortex generator controlled ramp flow with turbulent inflow. Aero Sci Technol 2013;30:226e31. [50] Huh H, Driscoll JF. Shock-wave-enhancement of the mixing and the stability limits of supersonic hydrogen-air jet flames. Proc Combust Inst 1996;26:2933e9. [51] Moule Y, Sabelnikov V, Mura A. Highly resolved numerical simulation of combustion in supersonic hydrogeneair coflowing jets. Combust Flame 2014;161:2647e68.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation on combustion mode and heat release in a model scramjet engine affected by shocks Duo Zhang a, Donggang Cao b, Guoqiang He a, Bing Liu a, Fei Qin a,* a
Science and Technology on Combustion, Internal Flow and Thermal-structure Laboratory, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, PR China b Faculty of Aerospace Engineering, Technion Israel Institute of Technology, Haifa, 3200002, Israel
highlights A model scramjet engine is investigated using Large Eddy Simulation. The heat release rate of premixed/diffusion combustion mode is analyzed. A flame filter is conducted to evaluate the contributions to heat release. The influence of combustion modes on heat release rate is assessed.
article info
abstract
Article history:
A model scramjet engine in which the 1.0 Ma hydrogen jet mixes and reacts with the 2.0 Ma
Received 20 July 2019
surrounding airstream is investigated using large eddy simulation. The flame structure is
Received in revised form
analyzed with a focus on the relationship between premixed/diffusion combustion mode
5 September 2019
and heat release in the supersonic reacting flow. The flame filter is used to evaluate the
Accepted 9 September 2019
contributions to heat release rate by different combustion modes qualitatively and quan-
Available online 30 September 2019
titatively. Results show that the heat is released from a combination of premixed combustion mode and diffusion combustion mode even when the fuel and airstream are
Keywords:
injected into the combustor separately. Local mode-transition occurs as the supersonic jet
Large eddy simulation
flame propagates and interacts with shocks. The diffusion combustion mode dominates
Scramjet engine
during the ignition stage and the premixed combustion becomes dominant during the
Combustion mode
intensive combustion region. When the shock wave impinges on the flame, the combus-
Heat release
tion area decreases a little due to the compression effects of the shock. However, the heat release rate is significantly improved in the interaction region since the shock could increase the air entrainment rate by directing the airflow toward the fuel jet and enhance the mixing rate by inducing vorticity due to baroclinic effects, which is good for flame stabilization in the supersonic flow. For the present case, 33.3% of the heat is released by diffusion combustion and 66.7% of the heat is released by premixed combustion. Thus the premixed combustion mode is dominant in terms of its contributions to heat release in the model scramjet engine. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (F. Qin). https://doi.org/10.1016/j.ijhydene.2019.09.063 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Nomenclature A Cc, Ck Dm E fd fp Fd Findex Fp h HRR HRRd HRRp k Ma Mm p q Q T uj Vj,m Ym D m n r zd zp hd hp tij um U ~ sgs
area constants mixture diffusivity energy diffusion flame filter premixed flame filter diffusion flame index using the logarithmic function flame index using the logarithmic function premixed flame index using the logarithmic function enthalpy heat release rate heat release rate of diffusion combustion heat release rate of premixed combustion kinetic energy Mach number the molecular weight of the mth species pressure heat flux second invariant of the velocity gradient tensor temperature velocity in j-direction diffusion velocity in j-direction of the mth species mass fraction of the mth species local grid size dynamic viscosity kinematic viscosity density diffusion combustion contribution coefficient to combustion area premixed combustion contribution coefficient to combustion area diffusion combustion contribution coefficient to heat release rate premixed combustion contribution coefficient to heat release rate viscous stress tensor production mass rate of the mth species the antisymmetric part of the velocity gradient tensor filter Favre average sub-grid scale quantity
Introduction Supersonic combustion has obtained increasing attention due to its application to scramjet engines, which are promising candidates for the future air-breathing propulsion systems [1,2]. The successful development of performing engines for the scramjet-powered vehicles would depend, to a large extent, on the sound understanding of supersonic
28331
combustion. Up to now, remarkable achievements have been made in the field of supersonic combustion [3], which has strongly supported the success of several flight tests [4,5]. However, the present knowledge about the detailed mechanism of supersonic combustion process is not deep and wide enough to support further development of advanced scramjet and combined cycle engines in future. With the rapid progress in computing capabilities, large eddy simulation (LES) has become a more dominant method for numerical studies on turbulent combustion in recent years [6,7]. The LES approach applied for supersonic combustion studies reveal insight physics and improve overall prediction accuracy by capturing eddies that play fundamental roles in mixing and combustion [8]. With LES methodology, the instantaneous three dimensional vortices and flame structures are visualized and characterized in detail by many researchers [9e12]. For more in-depth understanding of the high-speed turbulent combustion, flame stabilization and combustion mode are analyzed. Explanations of the stabilization mechanisms are proposed based on premixed and nonpremixed flames [13e15], auto-ignition [16,17], and turbulence-flame interactions [18,19]. However, it is still a big challenge to analyze the mechanism of flame stabilization in the supersonic flows because the instantaneous stabilization position fluctuates rapidly [20e22]. Moreover, the nonpremixed combustion, partially-premixed combustion, premixed combustion and auto-ignition could contribute simultaneously to flame stabilization [14,23]. Analyzing combustion modes is an important issue, which motivates the development of analysis methods and tools. Temperature or an individual species concentration (OH, HO2) has been employed for the detection of critical features such as ignition, extinction, and flame fronts in traditional flame diagnostics [24]. Flame index is often employed to identify non-premixed and premixed combustion modes [25e27]. The scalar dissipation rate based on the mixture fraction is also extensively used to study the turbulent combustion [28,29]. More recently, chemical explosive mode analysis (CEMA) has been extended and employed to identify the flame structure and stabilization mechanism [30e32]. These methods are expected to offer a glance of the turbulent flow, fuel-air mixing and combustion. Identification of flame structure and combustion modes remains a hot subject for high-speed propulsion systems that are actively studied. It has become clear that the true stabilization picture of the jet flame involves a compromise between fully premixed and non-premixed combustion as been addressed by these methods. However, the links and interactions between different combustion modes haven't been fully understood as the flame propagates unsteadily. This is especially true for the supersonic combustion in scramjet engines [33]. When the fuel is injected into the chamber, the combustible mixture is formed leading to the consequent chemical reactions and heat release. Due to the high flow speed and the short residence time in the combustor of a scramjet, both combustion mode and heat release vary along the channel length as flame propagates downstream. It is necessary to find out the distributions of different combustion modes and their relationships with the heat release in the supersonic flow within a finite length combustor. Furthermore, quantitative study should be
28332
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
further conducted to investigate the contributions to heat release by different combustion modes, though the combustion regimes have been qualitatively distinguished. In the present study, the mixing and combustion processes between the hydrogen jet at 1.0 Ma and the co-flow airstream at 2.0 Ma in a scramjet engine model are investigated using large eddy simulation together with a partially stirred reactor (PaSR) combustion model and a 27-step H2-air reaction mechanism. Comparisons are made between experimental data and calculation profiles to validate the accuracy of the LES results which are further used to identify the flame structure and combustion modes. The premixed flame index and diffusion flame index are derived from the traditional flame index to separate premixed combustion region from the diffusion combustion zone. The flame filters are also defined to calculate the heat release rate by different combustion modes. Then the focus of the present study is placed on the qualitative and quantitative assessment on the contributions to heat release by premixed combustion and non-premixed combustion in the supersonic reacting flow by introducing the contribution coefficient.
Model scramjet engine The present study is based on a geometry configuration that is experimentally investigated at the German Aerospace Center (DLR). It is featured with a rectilinear combustion chamber with a slanted upper wall and a wedge-shaped flame-holder at the base of which hydrogen is injected into the supersonic surrounding airstream [34e36]. A schematic of the scramjet experimental facility is shown in Fig. 1. The combustor consists of a one-sided divergent channel with a 3 angle to compensate for the expansion of the boundary layer. The base cross section has a height of 50 mm and a width of 40 mm, which is connected to a Laval nozzle. The preheated air is expanded through the nozzle and flows into the combustion chamber at 2.0 Ma. The hydrogen jet enters the combustion section from the base of the wedge with an angle of 12 . The fuel is injected parallel to the air stream at the sonic speed using the fuel nozzle. After being expanded from the Laval nozzle, the supersonic air stream enters the combustor at p ¼ 0.1 MPa and T ¼ 340 K, whereas the hydrogen is injected at p ¼ 0.1 MPa and T ¼ 250 K. Combustion is initiated by a spark in a hydrogen tube with a small amount of oxygen. The periodicity in the span-wise direction is imposed since three fuel injection holes are used in the computational configuration. All coordinates of the present study are relative to a coordinate system where the tip of the wedge has the coordinates
x ¼ 35 mm and y ¼ 25 mm, and the lower wall of the flow channel has the coordinate y ¼ 0 mm.
Governing equations and numerical methods The governing equations for the reactive flow are the balance equations of mass, momentum, energy, and species. In LES, all variables are decomposed into resolved and unresolved (subgrid) components by a spatial filter so thatf ¼ f~ þ f ' , where f~ ¼ r f =r is the Favre-filtered variable, and the LES governing equations can be expressed as [37,38]: 8 vr v > ~j ¼ 0 þ ru > > vt vx > j > > > > > > v v > > ~j þ pdij tij þ tsgs ~i Þ þ ~i u ¼0 ru > ðru ij > < vt vxj i > > v ~ v h ~ sgs > > ~j þ q~j u ~i tij þ Hsgs ðrEÞ þ ðrE þ pÞu ¼0 þ sj > j > vt vxj > > > > > > > > : v ðrY ~ m Þ þ v rY ~mu ~mV ~ j;m þ Y sgs þ qsgs ¼ u_ m ~j rY j;m j;m vt vxj
(1)
Here, r is the density, (ui)i¼1,2,3 is the velocity vector in Cartesian coordinates, p is the pressure, Ym is the mass fraction for the mth species, and u_ m is the production mass rate of the mth species. The total energy of the system is the sum of the internal energy and the kinetic energy. As a result, the filtered total energy is given as the sum of the filtered internal energy, the resolved kinetic energy, and the subgrid kinetic energy. The filtered viscous stress tensor t ij is approximated as: 8 > ~ij 1S~kk dij > t ¼ 2m S > ij < 3 > ~j ~ i vu 1 vu > > : S~ij ¼ þ 2 vxj vxi
(2)
The one equation eddy model is used to calculate the subgrid stress tensor with the following expressions [39e41]: 8 2 sgs > tij ¼ 2nk S~ij þ ksgs dij > > > 3 > > > < pffiffiffiffiffiffiffiffi sgs nk ¼ Ck k D > > > sgs sgs 3=2 > > ~i k vk v sgs v nk vksgs > sgs vu > : ~j k u þ þ Cc ¼ tij vxj vxj sk vxj vt vxj D
(3)
For H2-air combustion, the 27-step reactions chemical mechanism is employed [42], and the PaSR combustion model is adopted to close the LES governing equations for reacting flows [43,44]. The LES equations are solved by the code from
Fig. 1 e Geometry of the model scramjet engine (mm).
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
OpenFOAM, which is based on unstructured collocated finite volume method using Gauss theorem [45]. The density-based solver rhoReactingFoam is used with a second-order CrankNicholson time-integration scheme. The TVD (Total Variation Diminishing) compatible flux limiter is used, and the diffusive fluxes are reconstructed using central differencing of the inner derivatives [46]. The CFL number is less than 0.3, which corresponds to a physical time step at the order of 1 108 s. All variables are prescribed at inflow boundaries with Dirichlet conditions. Neumann conditions are used at outflow boundary where all variables are extrapolated from the interior ones. At fixed walls, the nonslip conditions are applied. Three grids with approximately 6 million (Grid_1), 12 million (Grid_2), and 19 million (Grid_3) cells are used for the simulations. Local refinement of the computational grids has been performed with a great attention. The grids are clustered towards the walls as well as in the wake region and the shear layer region to resolve the mixing and chemical reactions.
Results and discussion The rig has been experimentally investigated with a wide range of measurements, including CARS measurements of the temperature, LDV and PIV measurements of the velocity et al. [34,35,43]. Comparisons between the experimental data and the numerical results using three different grids are made to validate the simulation methods involved in the present study. Fig. 2(a) presents the time-averaged temperature profiles as well as CARS-measured data at different stream-wise locations. The hydrogen is injected into the surrounding airstream resulting in the combustible mixture. At the first location where x ¼ 78 mm, a local temperature minimum in the middle of the chamber together with two temperature maxima at the boarder of the jet could be observed in the figure. It indicates that chemical reactions start to occur at the interface between the hydrogen jet and the airstream, but only a small amount of heat is released due to limited mixing. At the location x ¼ 125 mm, vigorous combustion takes place releasing a large amount of heat in a narrow central region. It is featured with a sharp peak since there are large gradients around the mixing and reacting layer. With the increase of downstream distance, the shear layer grows and the flame spreads widely. Farther downstream where x ¼ 233 mm, the
28333
combustion intensity weakens due to the consumption of reactants, leading to a small peak value in the profiles. However, with the mass and heat transfer in the turbulent flow, the high temperature zone expands and the temperature profiles become wider compared to the profiles at x ¼ 125 mm. Fig. 2(b) shows the velocity profiles with the experimental data at different locations. Note that the fuel is injected at the base of the strut (x ¼ 67 mm) at sonic speed. Just a little downstream distance from the strut at x ¼ 78 mm, strong reverse velocity is observed on each side of the fuel jets because of the recirculation zones formed at the base of the strut, which is helpful to enhance mixing and to hold flame. The mass, momentum, and energy are exchanged between the fuel jet and the airstream along the channel length with the development of the shear layer. The profiles at x ¼ 125 mm have a relatively small minimum-peak in the middle as the recirculation region gradually shrinks. At the downstream location where x ¼ 207 mm, the core flow is accelerated in the divergent chamber with a similar magnitude of velocity to the outer flow. Thus the profiles become relatively flat at this location. In order to visualize the flow field, Fig. 3 shows the isosurface of the second invariant of the velocity gradient (Qcriterion) colored by heat release rate (HRR) with the contours of density gradient magnitude. And Fig. 4 presents the isosurface of the vorticity colored by temperature with the contours of Mach number. When the supersonic air flow encounters the wedge-shaped strut that leads to the convergence of the channel, an oblique shock is formed at the tip of the wedge due to the compression effect. The induced shocks reflect off the upper and lower chamber walls and interact with the shear layer where mixing and chemical reactions take place. Relatively weak expansion fans and the following recompression shocks could also be observed at the upper and lower corners of the wedge. A slight asymmetry is noticed due to the divergent combustor and the nature of turbulence. Furthermore, the recirculation regions are found just downstream of the strut base featured with low speed. This is good for mixing and flame-holding in the scramjet engine. A shear layer is formed between the fuel jet and the airstream. Initially the shear layer is relatively flat and then it becomes pronounced and distorted. With the development of the shear layer, the stream-wise vortex interacts with the span-wise vortex resulting in the complex patterns with three
Fig. 2 e Comparison between simulation results and the experimental data [35] at different locations: (a) temperature and (b) velocity.
28334
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 3 e Iso-surface of the Q-criterion colored by heat release rate with the contours of density gradient magnitude. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4 e Iso-surface of the vorticity colored by temperature with the contours of Mach number. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
dimensional features. The shear layer grows with increasing downstream distance due to vortex stretching, baroclinic torque, heat release, volumetric expansion, and diffusion. And the vortex structures eventually develop into longitudinal vortices that dominate in the far flow field. When the hydrogen mixes and reacts with the surrounding air stream, diffusion, convection, and chemical reactions take place simultaneously. Combustion occurs in multiple modes including premixed combustion and diffusion (non-premixed) combustion depending on the local mixing status. The flame index, which is defined as the degree of alignment of the fuel and the oxidizer gradients FI ¼ VYF ,VYO , has been a useful measure to distinguish the local premixed or diffusion flame [25]. In the premixed flame, the gradients of fuel and oxidizer are aligned so that the rapid consumption of the reactants across the flame results in a positive value of the flame index. On the contrary, the gradients of fuel and oxidizer oppose one another in the non-premixed or diffusion flame. Therefore, the positive FI represents the premixed combustion mode while the negative FI indicates the diffusion combustion mode in the jet flame. In order to avoid getting too small or too large values, the flame index is combined with a logarithm function as [47]:
Findex ¼
FI log ðjFIj þ 1Þ jFIj þ 1 10
(4)
The contours of flame index, temperature, and heat release rate are presented in Fig. 5. It suggests that the supersonic reacting flow could be thoroughly divided into three regions. The first region is just down the strut where the hydrogen jets discharge in the wake of the flame holder and mix with the surrounding air. Diffusion combustion with small heat release rates is observed in the shear layers shed off the strut edges. Some distance downstream of the wake, the diffusion combustion as well as the premixed combustion could be found with vigorous heat release in the second region. Specifically, diffusion combustion mainly occurs around the outer edge of the shear layer while premixed combustion dominates near the inner edge of the shear layer. Although a large amount of heat is released in the second region, the high-temperature zone is quite narrow because of the high speed flow and the small residence time that limit the mixing between the hot combustion products and the cold air passing through the combustor. In the third region, turbulent mixing and lean post-combustion take place featured with significant heat
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28335
Fig. 5 e Contours of temperature, heat release rate, and flame index.
transfer. It corresponds to the broadened high-temperature zone with weak heat release. Both diffusion combustion and premixed combustion could be observed in the third region. However, diffusion combustion dominates around the edges of the vortex structures and premixed combustion occurs in the cores of the vortex structures. The profiles of the flame index at x ¼ 70, 100, 150, 200, 250, and 280 mm are plotted in Fig. 6. At the early stage where x ¼ 70 mm, Findex is almost negative since diffusion is the dominating physics. A little downstream distance at x ¼ 100 mm, Findex has negative values as well as positive values with large peak magnitudes. It indicates that vigorous chemical reactions take place in both diffusion combustion mode and premixed combustion mode. However, Findex ¼ 0 in the central part of the profile, which means that vigorous combustion does not occur in the extremely fuel-rich zone. The mixing and reacting layer has a width of about 6 mm consisting of a 3.2 mm diffusion combustion layer and a 2.8 mm premixed combustion layer. Farther downstream, negative and positive values of Findex could be always observed indicating that turbulent combustion occurs in multiple modes. With the increasing downstream distance, the flame spreads in width with less intensity as the profiles of Findex broaden with small peak values. Fig. 7 shows the scatter plot of heat release rate with respect to flame index colored by temperature at different locations to offer another view of the reacting flow. At the early stage where x ¼ 70 mm, the heat release rate is extremely small and the overall temperature is quite low.
Sufficient heat release is observed some distance downstream of the wake. At x ¼ 100 mm, the plot of HRR with respect to Findex presents the significant feature with two peaks near Findex z 4 and Findexz4, respectively. It means that chemical reactions take place vigorously and release a large amount of heat in both diffusion and premixed combustion modes. But the overall temperature of the diffusion combustion zone is much lower than that of the premixed combustion zone. This is because the diffusion combustion zone is closely connected to the cold surrounding air, which is also seen in Fig. 6. It is interesting to note that the high-temperature zone corresponds to relatively small magnitudes of HRR and Findex, rather than maximums of HRR and Findex. In other words, both heat release and heat transfer determines the temperature distribution of the supersonic reacting flow. With the increasing downstream distance, both HRR and the magnitude of Findex decrease due to the consumption of combustible mixtures, while the overall temperature increases because of heat transfer and energy exchange in the turbulent flow. Besides, the scatter plot shifts a little from left (negative Findex) to right (positive Findex) and large HRR corresponds to positive Findex. It shows that premixed combustion makes more contributions to the heat release in the downstream. In order to further evaluate the heat release in the supersonic reacting flow, the three-dimensional surfaces of mixture fraction (z), flame index (Findex), and heat release rate (HRR) colored by temperature (T) at different locations are displayed in Fig. 8. It is interesting to note the evolution of the flow field in the new space. At x ¼ 70 mm, as discussed before, Findex is
28336
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 6 e Distributions of the flame index in y-direction at different locations.
Fig. 7 e Scatter plots of heat release rate vs. flame index colored by temperature at different locations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28337
Fig. 8 e Distributions of heat release rate in z-Findex space colored by temperature at different locations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
almost negative and HRR is very small since sufficient mixing and combustion do not occur until some distance downstream of the wake. The value of mixture fraction (z) varies from 0 (pure airstream) to 1 (pure fuel jet). A relatively high temperature region with medium value of z could be observed, which indicates that weak reactions are induced in the shear layer between the fuel jet and the airstream. This makes preparations for the following intensive combustion and keeps the flame from blowing off in the high speed flow. At the location where x ¼ 100 mm, the heat is released in a small range of mixture fraction with two combustion modes. With the increasing downstream distance, ‘the ranges of z, HRR, and Findex decrease gradually. It should also be noticed that the premixed combustion releases a little more heat than the diffusion combustion does. That is to say, in the far downstream the weak combustion takes place mainly in premixed combustion in terms of heat release. In order to separate the premixed combustion mode from the diffusion mode and to investigate their contributions to heat release qualitatively as well as quantitatively, the premixed flame index Fp and the diffusion flame index Fd based on the Findex are defined: 8 Findex jFindex j > > < Fd ¼ 2 > F þ jFindex j > index : Fp ¼ 2
(5)
The value of Fd varies from zero to negative ones while the value of Fp ranges between zero and positive ones. In addition,
the diffusion flame filter and the premixed flame filter are defined as: 8 Fd > > > fd ¼ < Findex > Fp > > : fp ¼ Findex
(6)
Both fd and fp only have two values: 0 or 1. fd is 1 only for the diffusion combustion zone while it is 0 for the other region. On the contrary, fp is 1 only for the premixed combustion zone while it is 0 for the other region. The two quantities fd and fp are supposed to offer relevant estimates of the respective weights of the premixed and diffusion contributions. With the help of the combustion mode filters fd and fp, one can easily distinguish the heat released by diffusion combustion from the heat released by premixed combustion for the reacting flow field by using the following equation:
HRRd ¼ fd HRR HRRp ¼ fp HRR
(7)
As a consequence, Fig. 9(a) shows the contours of the diffusion flame index (Fd) and the premixed flame index (Fp). Correspondingly, Fig. 9(b) offers vivid pictures of the heat release rate of diffusion combustion (HRRd) and the heat release rate of premixed combustion (HRRp). It is notable that the diffusion combustion zone is a little larger than that of the premixed combustion region while premixed combustion makes more contributions to heat release than the diffusion
28338
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
Fig. 9 e Contours of (a) the diffusion flame index Fd and the premixed flame index Fp; (b) the heat release rate of diffusion combustion HRRd and the heat release rate of premixed combustion HRRp. combustion, which should be further investigated quantitatively. We use the following equations to calculate the diffusion combustion area and the premixed combustion area at a certain cross section: Z 8 < Ad ¼ fd dA Z : Ap ¼ fp dA
(8)
And Eq. (9) is used to calculate the relevant area ratios: 8 > > > < zd ¼ > > > : zp ¼
Ad Ad þ Ap Ap Ad þ Ap
(9)
Similarly, the heat release rates resulting from diffusion combustion or premixed combustion at a certain cross section could be quantitatively estimated by: Z 8 < Qd ¼ HRRd dA Z : Qp ¼ HRRp dA
(10)
And the contribution coefficient is introduced to quantify the contributions to the heat release by the two distinct combustion modes: 8 > Qd > > > hd ¼ < Qd þ Qp > Qp > > > : hp ¼ Q þ Q d p
increases significantly peaking at x z 130 mm, and then it goes down dramatically. Another small peak could be observed at x z 200 mm. Then it continues to decrease gradually along the channel length. However, hd becomes smaller than hp, which means that premixed combustion contributes to heat release greatly. For the simulated 3D configuration in the present study, we find that R R and f dV= ðfd þfp ÞdV ¼ 70:4% R R d HRRd dV= ðHRRd þHRRp ÞdV ¼ 33:3% that. In other words, only 33.3% of heat is released by diffusion combustion that takes place in 70.4% of the whole reacting zone. It indicates that although the volume of the diffusion combustion is larger than that of the premixed combustion, premixed combustion mode is dominant in the present model scramjet engine since its overall contribution coefficient to heat release is 66.7%. A notable feature in Fig. 10 is that the combustion area starts to decreases at the very location x z 100 mm where the shock wave interacts with the shear layer, which is also confirmed in Figs. 3e4. This is understandable due to the compression effect associated with shocks. In addition, the baroclinic effect, which is the key point of the RichimyerMeshkov instability [48], also plays an important role in the shock/shear-layer interaction. The vorticity equation could be derived by taking the curl of the momentum equation: dU 1 1 ðU , VÞU þ ðV , UÞU ¼ V F þ 2 ðVr VpÞ þ V ðnDUÞ þ V dt r 3 ½nVðV , UÞ (12)
(11)
The parameters hd and hp are expected to quantitatively evaluate premixed and diffusion contributions to heat release in the supersonic reacting flow. Some additional analysis are offered by looking at the time-averaged profiles in Fig. 10 and Fig. 11, respectively. It is obvious that the combustion area is increasing along the channel length with the development of the shear layer. The diffusion combustion area is always larger than the area of premixed combustion. But things become a little complex for the distribution of the heat release rate shown in Fig. 11. At the first stage (67 mm < x < 90 mm), chemical reactions are induced mostly in the diffusion combustion mode since hd is larger than hp, though both Qd and Qp are extremely small. After that, the relative heat release rate
The term Vr Vp makes significant contributions to the vorticity disturbance since it is a main source term of vorticity in supersonic flows [49]. The magnitude contours of the Vr V p are presented in Fig. 12. When the shock wave impinges on the shear layer, large kVr Vpk could be observed in the following regions. It indicates that the non-aligned gradients of density and pressure contribute to vortex generation and mixing enhancement. As a consequence, in Fig. 11 the heat release rate is greatly enhanced to some extent despite of the decrease of the combustion area. However, it shows that the interaction between the shock wave and the shear layer has more significant impact on the heat release rate resulting from premixed combustion. When the shock waves impinge on the shear layer, they direct the airstream vertically toward the fuel to increase the air entrainment rate. The adverse pressure gradient caused by the shocks could elongate the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
28339
Fig. 10 e Time-averaged profiles of (a) combustion area of different modes versus the chamber length; and (b) area ratio of different combustion modes versus the chamber length.
Fig. 11 e Time-averaged profiles of (a) heat release rate versus the chamber length resulting from different combustion mode; and (b) contribution coefficient of different combustion mode versus the chamber length.
Fig. 12 e Contours of the kVr Vpk. local recirculation zones. Moreover, additional vorticity is induced locally by the shocks owing to baroclinic effects, which enhances the turbulent mixing and the chemical reactions [50]. The shock wave could also induce a local temperature increase due to compression, which is beneficial to ignite the hydrogen/air mixture [51]. As a result, the heat release rate, especially for the one caused by premixed combustion, is greatly enhanced with significant peaks, which is observed in Fig. 11. This has positive effect on improving flame stability in the supersonic flows. The similar trend could be also found in the second interaction region (x z 190 mm) where the combustion area decreases a little and the heat
release rate is enhanced with a small peak value since the shock waves are relatively weak and the amounts of the reactants are small.
Conclusion In the present study, a model scramjet engine in which the 1.0 Ma hydrogen jet mixes and reacts with the 2.0 Ma surrounding airstream, has been investigated by large eddy simulation (LES) based on OpenFOAM. The calculated results agree well with the experimental data, which demonstrates
28340
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
the reasonability of the employed numerical methods and computational strategies. The flame structure is investigated with a focus on the relationship between combustion mode and heat release in the supersonic reacting flow. The premixed flame index and the diffusion flame index are defined based on the classical flame index, which are supposed to discriminate the diffusion combustion mode from the premixed combustion mode. The flame filters are used accordingly to evaluate the contributions to the heat release by different combustion modes qualitatively as well as quantitatively. Results show that the heat is released from a combination of diffusion combustion mode and premixed combustion mode in the scramjet engine. Local mode transition occurs during the flame propagation affected by shocks. Diffusion combustion is dominant during the ignition stage with very small heat release rate. With the increasing downstream distance, premixed combustion plays a more and more important role in the supersonic reacting flow as the shear layer grows. When the shocks impinge on the mixing and reacting layer, the combustion area reduces a little owing to the compression effect associated with shocks. However, the heat release rate peaks in the region where shocks intersect with the shear layer. This is because shock waves could increase the air entrainment rate by directing the airflow toward the fuel jet and enhance the mixing rate by inducing additional vorticity due to baroclinic effects, which is good for flame-holding in the supersonic flow. Although the fuel and airstream are injected into the combustor separately, 66.7% of the heat is released by premixed combustion while only 33.3% of the heat is released by diffusion combustion. Thus the premixed combustion mode is dominant in the model scramjet engine in terms of its contributions to heat release.
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
Acknowledgments This work is financially supported by the National Natural Science Foundation of China through grants 51706185.
[19]
references
[20]
[1] Segal C. The scramjet engine processes and characteristics. New York, USA: Cambridge University Press; 2009. p. 127e8. [2] Tian Y, Yang S, Le J, Su T, Yue M, Zhong F, Tian X. Investigation of combustion and flame stabilization modes in a hydrogen fueled scramjet combustor. Int J Hydrogen Energy 2016;41:19218e30. [3] Choubey G, Deuarajan Y, Huang W, Mehar K, Tiwari M, Pandey K. Recent advances in cavity-based scramjet enginea brief review. Int J Hydrogen Energy 2019;44:13895e909. [4] Kimmel R, Adamczak D, Borg M, Jewell J, Juliano T, Stanfield S, Berger K. First and fifth hypersonic international flight research experimentation's flight and ground tests. J Spacecr Rocket 2019;56:421e31. [5] Smart M, Hass N, Paull A. Flight data analysis of the HyShot 2 scramjet flight experiment. AIAA J 2006;44:2366e75. [6] Patton CH, Wignall TJ, Edwards JR, Echekki T. LES model assessment for high speed combustion. 2016. p. 1937. AIAA Paper. [7] Liu C, Wang Z, Wang H, Sun M, Li P. Large eddy simulation of cavity-stabilized hydrogen combustion in a diverging
[21]
[22]
[23]
[24] [25]
[26]
[27]
supersonic combustor. Int J Hydrogen Energy 2017;42:28918e31. Koo H, Donde P, Raman V. A quadrature-based LES/ transported probability density function approach for modeling supersonic combustion. Proc Combust Inst 2011;33:2203e10. Fureby C, Chapuis M, Fedina E, et al. CFD analysis of the HyShot II scramjet combustor. Proc Combust Inst 2011;33:2399e405. Watanabe J, Kouchi J, Takita TK, et al. Large-eddy simulation of jet in supersonic crossflow with different injectant species. AIAA J 2012;50(2):2765e78. Liu B, He G, Qin F, An J, Wang S, Shi L. Investigation of influence of detailed chemical kinetics mechanisms for hydrogen on supersonic combustion using large eddy simulation. Int J Hydrogen Energy 2019;44:5007e19. Gong C, Jangi M, Bai X, Liang J, Sun M. Large eddy simulation of hydrogen combustion in supersonic flows using an Eulerian stochastic fields method. Int J Hydrogen Energy 2017;42:1264e75. Chung SH. Stabilization, propagation and instability of tribrachial triple flames. Proc Combust Inst 2007;31:877e92. Huang Z, He G, Qin F, et al. Large eddy simulation of combustion characteristics in a kerosene fueled rocketbased combined-cycle engine combustor. Acta Astronaut 2016;127:326e34. Tabet F, Sarh B, Goekalp I. Turbulent non-premixed hydrogen-air flame structure in the pressure range of 1-10 atm. Int J Hydrogen Energy 2011;36:15838e50. Cabra R, Myhrvold T, Chen JY, et al. Simultaneous laser Raman-Rayleigh-LIF measurements and numerical modeling results of a lifted turbulent H2/N2 jet flame in a vitiated coflow. Proc Combust Inst 2002;29:1881e8. Wei H, Shang Y, Cai J, Pan M, Shu G, Chen R. Numerical study on transition of hydrogen/air flame triggered by autoignition under effect of pressure wave in an enclosed space. Int J Hydrogen Energy 2017;42:16877e86. Su LK, Sun OS, Mungal MG. Experimental investigation of stabilization mechanisms in turbulent, lifted jet diffusion flames. Combust Flame 2006;144:494e512. Yang Y, Wang Z, Sun M, et al. Numerical and experimental study on flame structure characteristics in a supersonic combustor with dual-cavity. Acta Astronaut 2015;117:376e89. Mizobuchi Y, Rachibana S, Shinio J, Ogawa S, Takeno T. A numerical analysis of the structure of a turbulent hydrogen jet lifted flame. Proc Combust Inst 2002;29:2009e15. Ma S, Zhong F, Zhang X. Numerical study on supersonic combustion of hydrogen and its mixture with Ethylene and methane with strut injection. Int J Hydrogen Energy 2018;43:7591e9. Barnes FW, Segal C. Cavity-based flameholding for chemically-reacting supersonic flows. Prog Aerosp Sci 2015;76:24e41. Boivin P, Dauptain A, Jimenez C, Cuenot B. Simulation of a supersonic hydrogen-air autoignition-stabilized flame using reduced chemistry. Combust Flame 2012;159:1779e90. Mastorakos E. Ignition of turbulent non-premixed flames. Prog Energy Combust Sci 2009;35:57e97. Yamashita H, Shimada M, Takeno T. A numerical study on flame stability at the transition point of jet diffusion flames. Proc Combust Inst 1996;26:27e34. Choi J, Han S, Kim K, Yang V. High resolution numerical study on the coaxial supersonic turbulent flame structures. 2014. p. 3745. AIAA Paper. Dinesh K, Jiang X, Oijen J. Hydrogen-enriched non-premixed jet flames: analysis of the flame surface, flame normal, flame
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 8 3 3 0 e2 8 3 4 1
[28] [29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
index and Wobbe index. Int J Hydrogen Energy 2014;39:6753e63. Poinsot T, Veynante D. Theoretical and numerical combustion. USA: R. T. Edwards; 2005. p. 84e6. Mameri A, Tabet F. Numerical investigation of counter-flow diffusion flame of biogas-hydrogen blends: effects of biogas composition, hydrogen enrichment and scalar dissipation rate on flame structure and emissions. Int J Hydrogen Energy 2016;41:2011e22. Zhao ZY, Yoo CS, Richardson ES, et al. Chemical explosive mode analysis for a turbulent lifted ethylene jet flame in highly-heated coflow. Combust Flame 2012;159:265e74. Wang L, Jiang Y, Pan L, Xia Y, Qiu R. Lagrangian investigation and chemical explosive mode analysis of extinction and reignition in H-2/CO/N-2 syngas non-premixed flame. Int J Hydrogen Energy 2016;41:4820e30. An J, Jiang Y, Ye M, Qiu R. One-dimensional turbulence simulations and chemical explosive mode analysis for flame suppression mechanism of hydrogen/air flames. Int J Hydrogen Energy 2013;38:7528e38. Wang H, Wang Z, Sun M, Wu H. Combustion modes of hydrogen jet combustion in a cavity-based supersonic combustor. Int J Hydrogen Energy 2013;38:12078e89. W. Waidmann, F. Alff, M. Bohm, et al., Supersonic combustion of hydrogen/air in a SCRAMJET combustion chamber, IAF-94-S.4.429. Oevermann M. Numerical investigation of turbulent hydrogen combustion in a SCRAMJET using flamelet modeling. Aero Sci Technol 2000;4:463e80. Wu J, Wang Z, Bai X, et al. The hybrid RANS/LES of partially premixed supersonic combustion using G/Z flamelet model. Acta Astronaut 2016;127:375e83. Zhang Z, Cui G, Xu C. Theory and application of large eddy simulation. Beijing, China: Tsinghua University Press; 2008. Chaps. 2-3. Wang Z, Sun M. Supersonic turbulent flow, combustion modeling and large eddy simulation. Beijing, China: Science Press; 2013. p. 1e13.
28341
[39] Yoshizawa A, Horiuti K. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. J Phys Soc Jpn 1985;54(8):2834e9. [40] Menon S, Yeung PK, Kim WW. Effect of subgrid models of the computed interscale energy transfer in isotropic turbulence. Comput Fluids 1996;25(2):165e80. [41] Nakayama A, Vengadesan SN. On the influence of numerical schemes and subgrid-stress models on large eddy simulation of turbulent flow past a square cylinder. Int J Numer Methods Fluids 2002;38(3):227e53. [42] Marinov NM, Westbrook CK, Pitz WJ. Detailed and global chemical kinetics model for hydrogen, 8th International Symposium on Transport Properties. 1995. p. 1e29. [43] Fureby C, Fedina F, Tegner J. A computational study of supersonic combustion behind a wedge-shaped flameholder. Shock Waves 2014;24:41e50. [44] Berglund M, Fedina E, Fureby C, et al. Finite rate chemistry large-eddy simulation of self-ignition in a supersonic combustion ramjet. AIAA J 2010;48(3):540e50. [45] OpenFOAM: OpenCFD Ltd. Available from: www.openfoam. com. [46] Harren A. High resolution schemes for hyperbolic conservation law. J Comput Phys 1997;135:260e78. [47] Luo K, Jin T, Lu S, et al. DNS analysis of a three-dimensional supersonic turbulent lifted jet flame. Fuel 2013;108:691e8. [48] Brouillette M. The Richtmyer-Meshkov instability. Annu Rev Fluid Mech 2002;34:445e68. [49] Yan Y, Chen C, Liu P, et al. Study on shock wave-vortex ring interaction by the micro vortex generator controlled ramp flow with turbulent inflow. Aero Sci Technol 2013;30:226e31. [50] Huh H, Driscoll JF. Shock-wave-enhancement of the mixing and the stability limits of supersonic hydrogen-air jet flames. Proc Combust Inst 1996;26:2933e9. [51] Moule Y, Sabelnikov V, Mura A. Highly resolved numerical simulation of combustion in supersonic hydrogeneair coflowing jets. Combust Flame 2014;161:2647e68.