- Email: [email protected]
carbon dioxide gases
Accepted Manuscript Study on flame-vortex interaction in a spark ignition engine fueled with methane/ carbon dioxide gases Xin Zhang, Tao Wang, Jian Xu, Shizhuo Zheng, Xiaosen Hou PII:
S1743-9671(15)30474-8
DOI:
10.1016/j.joei.2016.09.005
Reference:
JOEI 272
To appear in:
Journal of the Energy Institute
Received Date: 25 December 2015 Revised Date:
20 September 2016
Accepted Date: 26 September 2016
Please cite this article as: X. Zhang, T. Wang, J. Xu, S. Zheng, X. Hou, Study on flame-vortex interaction in a spark ignition engine fueled with methane/carbon dioxide gases, Journal of the Energy Institute (2016), doi: 10.1016/j.joei.2016.09.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Study on flame-vortex interaction in a spark ignition engine fueled with methane/carbon dioxide gases
Xin Zhang, Tao Wang*, Jian Xu, Shizhuo Zheng, Xiaosen Hou Department of Power Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, PR China
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Abstract A numerical study on the in-cylinder flame-vortex interaction of gaseous spark ignited engine fueled with methane/carbon dioxide is carried out by means of large-eddy method. Evolution of in-cylinder turbulence in charge phase and flame-vortex interaction during combustion process are analyzed in great detail. It's found out that the large scale coherent structures are transformed into homogeneous small scale vortexes during the intake and compression stroke. The strong vortex cores are generated by interaction between flame and in-cylinder background turbulence. Those generated vortex cores wrinkle flame surface and augment turbulent flame speed. The contra-rotation between the two vortexes of vortex-pair in the unburned area results in the appearance of large scale flame wrinkles, which is because the vortex-pair movement leads to the local entrainment and hence stretch of the flame surface. With the increase of volume fraction of carbon dioxide in the gases, the turbulent flame speed is decreased, the effect of vortex pair on the flame structure is weakened, and the level of the flame wrinkling is decreased correspondingly. Keywords: IC engine, methane/carbon dioxide, flame-vortex interaction, Large-eddy simulation 1. Introduction
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In recent years, the natural gas has been known as the high quality gaseous fuel. However, with the increasingly prominence of the energy crisis, several gaseous fuels such as biogas are becoming the research focus of new alternative energy fuels. The concentration of methane in these fuels is relatively lower and non-hydrocarbon gases are with a higher level in general. The biogas is composed by 40%-60% methane, 40%-60% carbon dioxide [1]. The value of biogas is lower compared with the natural gas. One attractive feature of biogas is that it can be produced close to the consumption points and hence is ideal for decentralized power generation in remote rural areas. The biogas is more suitable for the spark ignited (SI) engine with a high compression ratio because it has an extremely low energy density, low flame velocity and not so wide flammability limits on account of its high carbon dioxide content [2]. The challenges of using these gases as the engine fuel are the lower heat release rate and the unstable combustion, which lead to much lower engine efficiency and higher cyclic variation. The combustion of biogas in engine is much more like a combination of larger portion of EGR and natural gas. Low laminar flame speed is the crucial factor. Therefore, some experimental studies struggled to augment turbulent flame propagation through adding hydrogen in order to improve power output and performance [3][4] However, combustion stability is still a problem there. How to improve the combustion stability of the biogas fueled engine is of great significance for the clean fuel engine development. The inherent factors for combustion stability should be researched. Based on the research of the SI engine cyclic variation causes and the influence factors, Ramos et al. [5] proposed that small scale turbulent structures and their impact on the mixing process of the reactants lead to the growth of the unstable flame kernel, while the large scale turbulent structures affect the surface area of the flame front. Multi-cycle simulations of IC engines using large-eddy simulation become popular because of huge advancements in parallel computing. Vermorel [6] and *
Corresponding author. Department of Power Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, PR China Tel.: +8601051688404 E-mail address: [email protected] (Tao Wang).
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Richard [7] conducted multi-cycle simulations of single spark ignition engine with coherent flame model. More advanced combustion model then was used to capture the flame [8]. These works expect to clarify the root causes of cycle-to-cycle variations. According to their studies, variations of turbulence within engine, as well as flame-turbulence interaction, might play a dominant role. In the research area of flame-turbulence interaction, studies of flame-vortex interaction might be a great branch. The vortex movement, the turbulent fluctuation and the velocity gradient on the flame front distorted and wrinkled the flame surface. Therefore, the flame propagation speed and the flame front structure are of large differences between the engine cycles, which could be the main reason of the engine cyclic variation. In order to deeply understand the mechanism of cyclic variation in gaseous fueled engine, it is necessary to study the interaction between the turbulent vortex and flame front. The flame-vortex interaction mainly includes two patterns. One is that the central axis of the vortex parallel to the flame surface, the other one is that the central axis of the vortex perpendicular to the flame surface. The reality is often the combination of both [9]. For the former one, Poinsot et al. [10] studied the flame-vortex interaction by using numerical methods so as to estimate the local quenching conditions of the turbulent premixed flames. Roberts et al. [ 11 ] conducted an experimental research on the role of the flame-vortex interaction in the quenching process using OH laser-induced fluorescence spectrometry. Mueller et al. [12] measured the velocity field of the vortexes with three different vorticity strength and exam the decay, regeneration of the vortexes during the flame-vortex interaction. Patnaik and Kailasanath [13] simulated the effect of the vortex ring on the methane/air flame. The results show that the local flame quenching tents to occur at the leading edge of the vortex ring. For the latter situation, it is generally suggested that the flame propagation velocity equals to the maximum peripheral velocity of the vortex. The research results of Asato et al. [14] indicated that if a vortex ring is filled with premixed gas, the flame will move in two different directions along the vortex ring after ignition. The flame propagation velocity is proportional to the maximum peripheral velocity of the vortex. An unsteady two-dimensional numerical simulation was conducted by Ishizuka et al. [15]. The result shows that after passing through a weak vortex pair, the flame surface wrinkle gradually declines and a pair of counter-clockwise rotated vorticity field is produced. The consistent conclusion was obtained in the experimental research of Mueller et al. [12]. As flame interact with a moderate intensity vortex pair, a mushroom-shaped flame front is formed in the beginning. Then a capsule-shaped flame zone appears gradually in the unburnt area. Despite the vortex pair continues decay, it is surround by the closed flame front. Recently, large-eddy method was applied to do research on flame-vortex interaction. Valeria et al. has conducted large-eddy simulation of transient premixed flame-vortex interactions in gas explosions, in which mainly grid effects were studies in great detail. [16][17]. Impact of chemistry models on flame-vortex interaction were covered.[18]. From the works mentioned above, main fundamental studies of flame-vortex interaction were conducted and engine-like conditions, even real engine configuration, were rare. So some scholars have done some researches about flame-turbulence interaction in engine-like condition. For instance, [19] combined direct numerical simulation with reduced chemistry to simulate turbulence-kernel interaction under gas-fueled engine conditions. A length scale defined as the ratio of turbulent length scale to kernel diameter was used to identify regimes of turbulence-kernel interaction. Three different interaction regimes are identified and analyzed-kernel breakup regime, kernel deformation regime and kernel convection regime. Therefore, flame-vortex is pretty crucial factor. Currently, the study on the flame-vortex interaction of the engine combustion is rare. The in-cylinder flame-vortex interaction is not only restricted by the flow pattern of the turbulent field which is influenced by the intake process, but also limited by the heat release which is decided by the components of the gas blends. In order to have a comprehensive understanding of the turbulent flame development in engine combustion, large-eddy simulation of the turbulent combustion in an engine fueled with methane/carbon dioxide was carried out in this paper. Flame-vortex interaction was analyzed.
ACCEPTED MANUSCRIPT 2. Large-eddy Simulation Combustion Modelling 2.1 Governing Equations and Turbulent Model
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The irregular flow in the engine is the turbulence. The Large eddy simulation is used to model the in-cylinder turbulent flow and the vortex movement. In this paper, the reactive flow equations are filtered as follow [20]: ∂ρ + ∇ ⋅ ( ρ u% ) = 0 (1) ∂t ∂ρ u% + ∇ ⋅ ( ρ u% ⊗ u% ) = −∇p% + ∇ ⋅ (S + τ ) (2) ∂t ∂ρ h% + ∇ ⋅ ( ρ u% h% ) = ∇ ⋅ (− pu% + S% + h − bh ) (3) ∂t ∂ρ Y%i + ∇ ⋅ ( ρ u% Y%i ) = ∇ ⋅ ( ji − b i ) + w& i (4) ∂t in which - and ~ denotes filtered and Favre filtered operations. ρ is the density, u the velocity，
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p the pressure, S the viscous stress tensor, h the enthalpy, h the heat flux vector，Yi ， ji , w& i , the mass fraction, mass diffusion and reaction rate of species i, τ = ρ (u% ⊗ u% − u ⊗ u) , b = ρ (uY − u% Y% ) ，and i
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b h = ρ (uh − u% h% ) the unresolved transport sub-grid terms. The linear viscous for the fuel mixture, % , h% ≈ κ∇T% and j ≈ D ∇Y% , Fourier heat conduction and Fickian diffusion are assumed as S ≈ 2 µ D D
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% is the deviatoric part of D % = 0.5* (∇u% + ∇u% T ) .The mixture heat conductivity, mixture in which D D diffusion coefficient and mixture dynamic viscosity are calculated using the Cantera
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thermodynamics and transport packages. Since non-equilibrium conditions commonly occur in free shear layers, boundary layers and wall domains, the Sub-grid scale (SGS) model chosen in this study is one-equation turbulent energy model. Based on the eddy-viscosity concept, a transport equation of the sub-grid scale kinetic energy on which the eddy viscosity depends is solved
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additionally. Through subtracting the filtered momentum equation from the corresponding non-filtered one, the relation of the fluctuating component of velocity u′ can be obtained. The one-equation turbulent energy model can be derived from multiplying the above result by the
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sub-grid velocity vector [21], ∂K + ∇ ⋅ ( Ku ) − ∇ ⋅ [(ν + ν sgs )∇K ] − ε = − τ : D (5) ∂t Where the K is the SGS kinetic energy, the τ is the SGS stress tensor, the D is the large-scale strain rate tensor, the ν sgs is the SGS eddy-viscosity, model constant Ck = 0.094 and Ce = 1.048 , the ε is the dissipation rate, 1 τ − tr ( τ ) = −2ν sgs D (6) 3 1 D = (∆u + ∆uT ) (7) 2 ν = C K1/ 2∆ (8) sgs k
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(9)
One-equation models [22] are good at providing a more accurate time scale for defining the velocity scale independently and have the advantage of modeling transitional flows and large scale unsteady flows. In particular, it is more suitable to treat the flows in the engine geometry. Eddy-viscosity based models have the drawback from the assumption of the isotropy in the unresolved scales. This problem can be reduced by the mesh refinement.
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2.2 Partially Stirred Combustion Model
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Turbulence and chemistry interaction model described in the partially stirred reactor model (PaSR Model) for the combustion in a reactor has been proposed to account for the effects of mixture imperfections on chemical reaction rates [23]. It is a sequential process where mixing is followed by chemical reactions and the rates of the individual steps are equal. The source term of the species transportation equation can be expressed as: (10) in which, k is the reacting sub-grid volume fraction. The high exothermicity and volumetric expansion happen in the small structures distributed among the fine structure vortices. The reacting flow is divided into fine structures (*), responsible for mixing and chemical reactions, which provide a high temperature to the surrounding fluid (0). k characterizes the turbulence effects on the chemistry. According to [24], it is a function of the turbulent mixing time and the chemical reaction time. τc 1 ′ = H (t , tmix ) κ= τ mix (11) ′ τ c + τ mix 2 H (t , tmix ) is the harmonic mean. τ c is the chemical time scale. The micro-mixing time τ mix is a important variable in PaSR model whose definition is quite controversial. Chomiak and Karlsson [23] define it in a form of similar to the Kolmogorov time definition by replacing the molecular viscosity by the turbulent viscosity. 2 ν lν t 1/ 2 k ) = (2 Cµ τ k )1/ 2 (12) τ mix = (
ε
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According to Golovitchev and Chomiak [24], the model is given a quality of the SGS approach by adding the minimal scale resolved on the grid in the definition. τ mix = ∆ 2/3ε −1/3 (13)
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In this paper, τ mix is defined based on a phenomenological model [25], in which the micro-mixing time is partly decided by the micro fractal structure of the turbulence. 6
τ mix = τ d = l02 / ( Re1+ D ν ) F
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in which τ d is the viscous diffusion time, l0 is the initial length scale of the eddy, ν is the molecular viscosity, Re is the Reynolds number and DF is the fractal dimension of the turbulent field. In general, the micro-mixing occurs below the resolvable scale. Then the eddy length scale and the molecular viscosity are derived as follow. ∞
∞
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1/ ∆
lSGS = ∫ dkk −1 E (k ) / ∫ dkE (k ) = ∆
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ν SGS = ∫ dkk −1[k −1 E (k )]1/ 2 = ò1/3∆ 4/3
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in which, ∆ is minimum resolvable scale, E (k ) = Cò2/3 k −5/3 is the energy spectrum of the Kolmogorov scale. Finally, the micro-mixing time scale is obtained.
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2 DF −5 1+ DF 2
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Table 1: Reactions for 2-step reduced mechanism 2S-CM2-JB mechanism A Ea 5.1E14 3.5E4 CH4+1.5O2=>CO+2H2O 5.1E8 1.2E4 CO+0.5O2<=>CO2
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Reaction No. 1 2
7 + DF
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Accurate prediction of the combustion temperatures and flame structures require the detailed reaction mechanisms. For methane-air combustion, the GRI-3.0 mechanism which involves 53 species and 325 reactions is suggested. But in the LES-combustion case, those mechanisms are often too expensive to handle. In this paper, the 2S-CM2-JB mechanism [26] modified from the 2S-CM2 mechanism [27] is chosen to complete the chemical reaction modeling for the combustion of methane/carbon dioxide gas, which is a reduced two step chemical kinetic mechanism as shown in Tab.1. The progress variable b is defined through the mass fraction of the species. YH2 O + YCO2 + YEGR b = 1− (18) YFuel→H 2O+CO2 + YH 2O + YCO2 − YEGR YEGR is mass fraction of previous burnt product and YFuel→ H2 O+CO2 refers to mass fraction of burnt product under the condition that unburnt mixture is completely burnt. At the start of charge phase, in the cylinder, initial mass fractions of CO2 and H2O are set. The sub-grid flame surface wrinkling factor Ξ is given by the Weller combustion model [28]. The flame surface wrinkling ∑ is the flame surface area of the unit volume, which is calculated as below. ∑ = Ξ ∇b (19)
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2.3 AKTIM-LES Spark Ignition Model
The AKTIM-LES spark ignition model [29] is used here. The electric spark length lspk is given by the electrical circuit equations in the AKTIM (Arc and Kernel Tracking Ignition) model [30]. A few nanoseconds after the spark timing t spk an electric spark is formed. A critical ignition energy is
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set and an initial burned gases mass mbign is is deposited once the electrical energy is larger than the critical one. The volume of the initial burned mass is defined as a cylindrical unit with a radius of 2δ L and length lspk :
mbign =< ρu lspk 4πδ L2 >
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Cign ( x, tign ) = Cinit exp(−0.6−2 x − xspk ∆% −2 )
where constant Cinit satisfies
∫ρ C b
ign
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dV = mign , ρb is the burned gases density and xspk the spark plug
location. Then, the ignition energy added is distribute rbign = (3(4π )−1 ∫ Cign dV )1/3 d according to the value of Cign on each ignition cells. The flame kernel is assumed to be spherical, its radius rbign can be defined as: rbign = (3(4π )−1 ∫ Cign dV )1/3 (22)
3. Mesh Managements and Numerical Methods 3.1 Mesh managements Multi-dimensional simulation of internal combustion engines involves physical modeling and
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geometrical dynamic mesh handling [ 31 ]. For the geometry and mesh handling aspect, the combustion chamber, the manifolds and valves of an IC engine often have very complex shapes. The movements of the piston and the valves which lead to both geometry and topological changes require more developed dynamic mesh motion techniques [32]. Two main technical topics for handling the unstructured mesh in internal combustion engine modeling are mesh motion and topological changes. IC engine simulations involve moving boundaries such as the valves and the piston. For prescribing solution-dependent motion more easily, a second-order FEM solver is used to solve the mesh motion equation. Every polyhedral cell is split into tetrahedra and this will introduce additional points in the cell centers and faces. The point velocity can be obtained from the motion equation: ∇ ⋅ (γ∇U p ) = 0
(23)
3.2 Discretization Scheme
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in which γ is the diffusion coefficient, U p is the point velocity. Variety of γ can be used to control different kinds of mesh motion. Mesh quality is destroyed under the extreme deformation of boundary. The approaches involving topological changes require higher skills to generate quite fine meshes which is tough for complex engine geometries. One of these approaches uses attach/detach boundaries, cell layer addition/removal and sliding mesh interfaces to preserve the high quality of the dynamic mesh by changing the connectivity of the mesh and the numbers of cells. Another approach which is called the mesquite mesh optimization solver [33]. It requires the mesh to be constituted by the tetrahedrons. The slip patches with their moving directions and fixed length scale patches are specified first for the motion solver. Through checking and improving the mesh quality by a series of optimization algorithms, the meshes are added and removed by merging and dividing the tetrahedrons. The Smoothing interval is set to control the frequency of the mesh refinement. This approach has the advantage that unstructured engine geometry can be easily meshed by the tetrahedrons and the high quality of mesh refinement can be obtained during the dynamic movement. In this paper, A method is proposed to couple both the polyhedron vertex movement algorithm and the Mesquite algorithm. The former one is used when the mesh quality is quite fine while the latter is used to reconnect and smooth the mesh as the quality cannot meet the requirement. The time interval for the mesh refinement in set as 10 CA. The advantage of this coupling method is to improve the running efficiency and assure the mesh quality at the same time.
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As the computational platform, the C++ library OpenFOAM whose discretization is based on Gauss theorem is used in this study. For low Mach number flows in IC engine, a semi-implicit code based on a second order accurate Crank-Nicholson time integration scheme and a PISO procedure utilizing a Rhie-Chow interpolation for the cell centered data storage structure is used. The convective fluxes are reconstructed by a monotonicity preserving scheme constituted with one second order linear reconstruction, one first order upwind reconstruction and one non-linear flux limiter [20]. The flux limiter is used to switch between the flux reconstruction schemes. The diffusion term and the sub-grid fluxes are split into orthogonal and non-orthogonal parts to minimize the non-orthogonal errors. Central difference approximation and gradient face interpolation codes use collocated cell-centered variable arrangement. A variable time step corresponding to a Courant number of 0.2 is set to keep the computational accuracy and stability [34].
3.3 Initial and Boundary Conditions Table 2: Temperature boundary condition Walls Temperature(K) Piston 540 Liner 480
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500 600 375
4. Engine parameters and operation conditions
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At the inlet section, mass flow rates and temperature profiles are imposed. The Han-Reitz wall heat transfer model [35] is used in this study, in which the influence of the gas density of the boundary layer and the turbulent Prandtl number are considered. The initial field data including the fractions of the exhaust gases are taken from a simulation result of the 2D engine multi-cycles modelling. The initial fields of the inlet part and the cylinder part are treated by the setFields function in OpenFOAM, which is good at setting the non-uniform initial fields. Tab.2 shows the temperature assigned on the wall boundaries. Each temperature value is estimated on the basis of experimental data in [36]. The simulation begins at 12 °CA ATDC (Intake Valve Open Timing), pressure and temperature conditions inside cylinder and inlet duct are defined from previous RANS simulation. Boundary conditions for species fractions, the turbulent kinetic energy and dissipation rate are set to be zero gradient. The no-slip condition is used for the velocity at the walls.
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The prototype of the simulation is the ZS1100M series single-cylinder which is a four-stroke gas engine with port fuel injection system. The engine specifications and operating conditions are given in Tab.3. The testing engine is equipped with the electronic control system developed by the engine lab of Beijing Jiaotong University. Electronic throttle is used in order to change the engine load adjustment from quality into quantity. Intake port injection is controlled by ECU which could be beneficial to obtain the accurate air-fuel ratio. The engine that we studied might be applied in power generation, where engine operates at a fixed load and rotational speed. In this case, total flux or absolute mass of charge keep constant. However, composition of biogas varies in different seasons, especially volume fraction of carbon dioxide. In addition, using these fuels in IC engines might lead to unstable combustion and lower heat release rate. Therefore, motivation of this paper is to study how different combinations of carbon dioxide and methane, which simulate biogas, affect the flame-vortex interaction in engine.
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Table 3: Engine Specifications Engine Items Engine type Single cylinder 4-stroke Bore(mm) 100 Stroke(mm) 115 Con. Rod length(mm) 210 Displacement (cm3/cyl) 930 Compression Ratio 10.2 IEMP (MPa) 0.8 Normal Speed (r/min) 2000 Normal Power (kW) 10
The engine operates at a speed of 1500 r/min, a throttle opening of 30% and stoichiometric ratio condition. The spark ignition timing is set at 18°CA BTDC. The engine is fueled with gas blends of methane and carbon dioxide in which the volume fractions of carbon dioxide are 10%, 20%, 30% and 40%, respectively. Detailed information can be found in Tab.4. We deduce that variation of composition might be the cause of unstable combustion. Table 4: Calorific value and density of methane/carbon dioxide gases (273K, 101.325kPa) Fuel No. CH4/CO2 Mass fraction Volume caloric value Density Volume fraction % CH4/CO2/O2/N2 (MJ.m-3) (kg.m-3) Fuel 1 90/10 4.2/1.3/22.1/72.4 31.46 0.83 Fuel 2 80/20 3.4/2.1/22.1/72.4 27.97 0.96 Fuel 3 70/30 2.5/3.0/22.1/72.4 24.47 1.08
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The comparison of the experiment data and the LES modeling result of the in-cylinder pressure are shown in Fig.1. As illustrated in the figure, the experiment and modelling pressure curves match well during the compression stroke. There are tiny differences in the combustion stage. It is mainly because the thoroughly description of the chemical reaction is difficult for the reduced two steps mechanism. That leads to the slower flame propagation and smaller pressure rise rate. The work efficiency during the expansion phase is lower as well. This phenomenon is obvious in the curve of Fuel 1. However, with the volume fraction of carbon dioxide in the gases increases (such as Fuel 3), the gap between the modeling and experiment data is reduced.
5. Results and Discussion
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Figure 1. Comparison of LES modeling and experiment results for in-cylinder pressure
5.1 Evolution of in-cylinder turbulent flow
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In order to study the in-cylinder flame-vortex interaction, it is necessary to investigate the movement of the turbulent flow and the distribution of the vortex in the engine. Since the turbulent flow is notably time varying and strongly chaotic, large amount of vortexes with different length and time scales are transported simultaneously. By far, there have been several approaches for the identification of a vortex [37][38][39]. Lust [40] supposed a vortex is a multitude of material particles rotating around a common center. Chong [38] proposed a vortex is a region of complex eigenvalues of ∇U . In this section, the coherent structures in turbulent flows of the engine is identified by Q criterion proposed by Hunt et al. The Q criterion identifies vortices as flow regions with positive second invariant of the velocity gradient tensor: Q =( W 2 - S 2 ) /2 , in which W and S are the skew-symmetric and symmetric parts of ∇U , respectively. The iso-surface of a certain value of Q is chosen to inspect the generation, development, fragmentation and dissipation of the vortexes. As depicted in Fig.2, the iso-surface of Q=1.0 × 106 s −2 can catch the evolution of coherent structure fairly clear. Figure 2a-Figure 2b shows that at the early stage of the intake stroke (30-60°CA ATDC), a strong shear flow is formed in the cylinder as the gas mixture travels through the intake valve. A reflux is produced at the bottom of the valve, causing lots of the large scale vortexes fulfilled in the cylinder. When the piston moves downward (90-120°CA ATDC) in Fig.2c-Fig.2d, the fresh charge continuously flows into the cylinder and mixes with the former vortex structures with the increase of the valve lift, which leads to the vortexes spreading all over the whole space of the cylinder. Figure 2e-Figure 2f shows that at the late stage of the intake stroke
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(150-180°CA ATDC), the strength of the overall flow field reduces, the former large-scale vortexes are constantly stretched, deformed and broken into small vortexes. Therefore the coherent structures with higher strength are clearly illustrated during the valve closing stage (210-230°CA ATDC) in Fig.2g-Fig.2h. Figure 2i-Figure 2j shows that at the early stage of the compression stroke (240-270°CA ATDC), the large scale vortexes are further broken down and dissipated. A squeeze flow is obviously emerged near the clearance of the combustion chamber during the late stage of the compression stroke (330-330°CA ATDC) in Fig.2k-Fig.2l. The squeeze flow spreads to the chamber interior space which speeds up the homogenization of the turbulent flow field in the cylinder.
(b) 60°CA ATDC
(e) 150°CA ATDC
(f) 180°CA ATDC
(c) 90°CA ATDC
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(a) 30°CA ATDC
(d) 120°CA ATDC
(h) 230°CA ATDC
(k) 300°CA ATDC
(l) 330°CA ATDC
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(g) 210°CA ATDC
(i) 240°CA ATDC
(j) 270°CA ATDC
Figure 2. Vortex field in engine cylinder during charging and compression stage. (Contour of Q=1.0 × 10 magnitude is m.s-1
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s ) Unit of U
5.2 Analysis of flame-vortex interaction 5.2.1Flame-vortex interaction Since the turbulent flame propagates from a flame kernel to the whole cylinder during the fast burning period of a SI engine, it is significant to investigate the flame-vortex interaction in this time
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period. Within SI engine, flame presents flamelet regime which means that flame is very thin and turbulence plays a role in wrinkling the flame front. Although it is not convincible that turbulence is completely composed of large amounts of vortices, it does make sense that analysis of flame-vortex interaction is conducted through studying interaction between flame surface and those vortices whose spatial scales are larger than that of flame front. A minimum vortex scale of analysis in this paper is laminar flame thickness. For the purpose of better understanding the flame-vortex interaction of the engine combustion, as shown in Fig.3a, three transverse slices with fixed positions are selected for the further analysis. The red spot highlighted in Fig.3b is the position of the spark ignition site. The ignition site is located at the eccentric position in the cylinder.
Figure 3. Position of selected slices and ignition site
In this section, the λ2 criterion which is proposed by Jeong [37] is applied to identify the vortex core during the flame propagation. A vortex core is an area with intensive vorticity inside the vortex, which rotates as a rigid body. λ2 is the second largest eigenvalue of W 2 + S 2 ,which satisfies the following formula:
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DS 1 + W.W + S.S −ν∇ 2S = − ∇∇p (23) ρ Dt in which, the unsteady rotation effect DS / Dt and the viscous effectν∇ 2S both have influence on the pressure gradient field. The term W.W + S.S is the only factor that decides if the local minimum pressure is led by the existence of the vortex. According to Jeong [37], the vortex core is detected as two of the three eigenvalues of the tensor W.W + S.S are negative. Meanwhile, since the tensor is symmetric, the three eigenvalues require the condition λ1 ≥ λ2 ≥ λ3 to be real. Therefore, The region of negative λ2 represents the existence of the vortex core and the larger is the magnitude of
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negative λ2 , the greater is the vortex strength. Figure 4 shows the iso-surface of λ2 = −1×107 during the flame propagation. Because the velocity of the flame propagation is faster than the one of the local gas flow, the relative motion between the flame and the flow field will generate new turbulent vortexes. The strength of the new generated vortexes is often larger than that of vortexes from the background flow field. The color legend in Fig.4 indicates the value of progress variable b . For the value of b on the iso-surface of λ2 is between 0 and 1, it means the new generated vortexes are located in the region near the flame front. As the flame spread forward, the generated vortex continues to dissipate and the new one is appeared with the changing of the flame front location.
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Figure 4. Iso-surface of λ2 during flame propagation (Fuel 1, λ2
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Figure 5 shows temperature distribution and that of vortex core near the flame front on three slices at TDC. The solid black lines indicate the position of the flame front highlighted by b = 0.3 and the solid red line represents T = 1000 K . The region between solid red line and black line is defined as preheated zone because temperature is below 1000K uniformly outsider this preheated zone. It is shown in Fig.5a-Fig.5c, the flame front is highly wrinkled and absolutely not a normal cycle. Many vortices appear within the preheated zone. Furthermore, the new generated vortex core with larger strength locates in the region where the flame surface wrinkling is higher as well. Especially, the vortex core often appears near the position where the flame surface raised toward the unburnt area. For example, the region around the point (0,-2.8) in Fig.5a, the point (-0.5,-1.5) in Fig.5b and the point (-2,2.5) in Fig.5c. The flame surface in these regions tend to be entrained or stretched by the new generated vortexes. These effects will lead to an increase of the flame propagation speed. Figure 6 is the scatter diagram of the mean flame wrinkling Σ and the mean turbulent flame velocity St versus the mean λ2 on the flame front, respectively. It is shown in Fig.6a that with the
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increase of the magnitude of mean λ2 the mean flame surface wrinkling increases. The flame surface wrinkling is quite helpful to extend the contact area between the flame surface and the vortex field and thus more prone to the production of the new vortex cores. On the other side, the new vortexes will raise the flame surface wrinkling level. Because slice 3 is close to the bottom of the combustion chamber, the flame propagation is spatially influenced by the bottom wall to some extent and the flame surface is over distorted by the coupling effect of the local turbulence and the chamber structure. Thus the mean flame surface wrinkling on slice 3 is higher than those on slice 1 and slice 2 as λ2 < −1× 107 . Figure 6b shows that with the increase of the magnitude of mean λ2 , the mean turbulent flame speed increases. It indicates that the vortex with higher strength contributes to the fast burning of the turbulent flame. This law is more obvious for the flame surface on slice 2 since it is conducive to the fully development of the flame. Therefore, with flame propagating, interaction between gas preheating effect and in-cylinder background turbulence produces many vortex cores within preheated zone. These generated vortex cores will wrinkle the flame surface and augment turbulent flame speed. Fundamentally, most wrinkled flame positions are located around those vortex cores with high strength.
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Figure 5. Temperature distribution Top and Distribution of vortex core near the flame front on three slices at TDC (Fuel 1)
Figure 6. Flame parameters versus mean λ2 on the flame front, (a) mean flame wrinkling, (b )mean turbulent flame velocity St
5.2.2 Effect of vortex-pair on flame front During interaction between flame and vortex core, a particular phenomenon happens when two adjacent vortex cores have opposite directions, namely vortex-pair. Figure 7 shows the evolution of the in-cylinder flame-vortex pair interaction of the engine combustion. The sign of the vorticity on behalf of the rotation direction of the vortex, where positive is for a vortex of counterclockwise rotation and negative is for the opposite case. As shown in the figure, there is always another vortex of the contrary-rotation direction around one vortex to make them a vortex-pair. In order to investigate the effects of the vortex-pair movement on the formation of the flame front structure, the situation on three slices at two crank angle are analyzed. Figure 7a-Figure 7c shows that at the early stage of the flame propagation (355°CA ATDC), the flame propagation speed is relatively slower,
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coupled with the lack of large scale and high strength vortex-pair in the local region, there is no obvious wrinkles on the flame surface. Figure 7d-Figure 7e shows that as the flame front spread forward (360°CA ATDC), the flame surface area increases, the effects of the vortex-pair on the flame surface enlarge. In addition, the contrary rotation of the two vortexes in the vortex-pair leads to the entrainment of the local flame surface to the center of the vortex-pair or the stretch along the outside border of the vortex-pair, thus the flame surface wrinkles are formed. Meanwhile, the flame surface absorbs the original vortexes as traveling through the vortex-pair in the unburnt area. The large scale vortexes are broken down into small ones, which makes the turbulent field of the burnt area more uniform. For studying the flame-vortex-pair interaction in detail, the slice 2 is taken as an example. As depicted in Fig.7b, a typical vortex-pair is constituted by the two vortexes whose rotation centers are at the points (-1,-0.5) and (-2,-0.5). While the flame front moving toward that front vortex-pair, the flame surface part between the two vortexes is dragged into the unburnt area, the part at the outer ring of the vortex-pair is entrained into the burnt area. Consequently, the flame surface wrinkle is generated significantly in the region near the point (-1,-1.5).
Figure 7. Evolution of flame-vortex pair interaction of engine combustion.(Fuel 1)
5.3 Effect of carbon dioxide on flame-interaction
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Figure 8 shows the effect of engine fueled with different methane/carbon dioxide gases on flame structures on slice 2 while the progress variable b is reaching 0.15. As shown in Fig.8a-Fig.8b, as gas mixture is diluted with much more CO2, the effects of the vortex-pair movement on the flame structure are weakened in the same background turbulent field. Owing to the dilution effect of CO2, the combustion process slows down and the cylinder volume under the same progress variable b increases. The concentration of the vortex field and the vortex strength decrease as well. For example, in the region near the point (1,-1) in Fig.8a, a flame surface wrinkle towards the burnt area is clearly raised due to the local vortex-pair movement. The flame surface wrinkle at the same place in Fig.8b is still distinct while the vortex strength in the background turbulent is reduced. However, the wrinkle in Fig.8c is attenuated apparently compared to the one in Fig.8a and the wrinkle in Fig.8d is almost disappeared as a result of moderate flame-vortex-pair interaction. The similar situation is demonstrated in the region near the point (0,1) on the slice 3.
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Figure 8. Effect of engine fueled with different methane/carbon dioxide gases on flame structures. (Slice 2, b = 0.15)
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Figure 9 is the scatter diagram of the vorticity magnitude ω and the flame surface wrinkling Σ versus the crank angle when engine is fueled with different methane/carbon dioxide gases. As shown in the Fig.9a, when the engine is fueled with Fuel1, Fuel 2, Fuel 3 and Fuel 4, the peak of the mean vorticity magnitudes are 4495 s-1, 3100 s-1, 2271 s-1 and 2190 s-1, the corresponding crank angles of the mean vorticity magnitude are 364.2°CA ATDC, 365.5°CA ATDC, 368.2°CA ATDC and 378.6°CA ATDC, respectively. It conveys that with the increase of the volume fraction of the carbon dioxide, the mean vorticity magnitude decreases, the corresponding time of the peak value is postponed. Figure 9b shows that with the increase of the carbon dioxide volume fraction in the gases, the crank angle when the flame reaching the same surface wrinkling is delayed. For example, the situation of Fuel 1 advances about 16 CA than that of Fuel 4, when the flame surface wrinkling reaches 400m-1.
Figure 9. Flame and flow parameters versus crank angle when engine is fueled with different methane/carbon dioxide gases, (a) Mean vorticity magnitude
ω
, (b) mean flame surface wrinkling Σ
6. Conclusion In this study, the large-eddy simulation is used to investigate the in-cylinder flame-vortex interaction when spark ignition engine is fueled by methane/carbon dioxide. The conclusions are acquired as follow.
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During the flame propagation, the large strength vortex cores often locate in the regions where the flame surface wrinkling is higher and the crests of the flame wrinkles raise toward the unburnt area. The flame surface in these regions tend to be entrained or stretched by the new generated vortexes. These effects will lead to an increase of the flame propagation speed. Those generated vortex cores around the flame front is a consequence of interaction between flame and in-cylinder background turbulence.
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With the increase of the flame surface area, the effects of the vortex-pair on the flame surface enlarge. The contrary rotation of the two vortexes in the vortex-pair leads to the entrainment of the local flame surface to the center of the vortex-pair or the stretch along the outside border of the vortex-pair. Thus the flame surface wrinkles are formed. At the same time, the flame surface absorbs the original vortexes as traveling through the vortex-pair in the unburnt area. The large scale vortexes are broken down into small ones, which makes the turbulent field of the burnt area more uniform. With the increase of the volume fraction of the inert gas carbon dioxide in the gas mixtures, the effects of the vortex-pair movement on the flame structure are weakened. The combustion process slows down and the cylinder volume under the same progress variable b increases. The concentration of the vortex field and the vortex strength decrease. 7. Acknowledgement
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This work was financially supported by the National Natural Science Foundation of China (Grant No. 51376020).
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[1] X. Zhang, C. Li, J. Xu, Journal of Energy Institute 83(1), 12, 2010 [2] E. Porpatham, A. Ramesh, International Journal of Hydrogen Energy 32(12), 2057, 2007 [3] Erjiang Hu, Zuohua Huang, Bing Liu, Jianjun Zheng, Xiaolei Gu, Bin Huang, International Journal of Hydrogen Energy,34(1):528-539, 2009 [4] Erjiang Hu, Zuohua Huang, Bing Liu, Jianjun Zheng, Xiaolei Gu, International Journal of Hydrogen Energy, 34(2): 1035-1044, 2009 [5] J.I. Ramos, Internal Combustion Engine Modeling, Hemisphere Publishing Corporation, 1989 [6] V. O., R.S.C.O.A.C.B. A., SAE Paper, 2007-01-0151 [7] S. Richard, O. Colin, O. Vermorel, Benkenida, C. Angelberger, D. Veynante, Proceedings of the Combustion Institute 31, 3059, 2007 [8] O. Vermorel, S. Richard, O. Colin, Combustion and Flame 156(8), 1525, 2009 [9] S. Kadowaki, T. Hasegawa, Progress in Energy and Combustion Science 31, 193, 2005 [10] T. Poinsot, D. Veynante, S. Candel, Journal of Fluid Mechanics 228, 561, 1991 [11] W.L. Roberts, J.F. Driscoll, M.C. Drake, J.W. Ratcli_e, Proceeding of the Combustion Institute 24, 169, 1992 [12] C.J. Mueller, J.F. Driscoll, D.L. Reuss, M.C. Drake, M.E. Rosalik, Combustion and Flame 112, 342, 1998 [13] G. Patnaik, K. Kailasanath, Proceeding of the Combustion Institute 27, 711, 1998 [14] K. Asato, H.W.T. Hiruma, Y. Takeuchi, Combustion and Flame 110, 418, 1997 [15] S. Ishizuka, T. Murakami, T. Hamasaki, K. Koumura, R. Hasegawa, Combustion and Flame 113, 542, 1998 [16] Valeria DiSarli, Almerinda Di Benedetto, GennaroRusso, Chemical Engineering Science, 71:539-551,2012 [17] Valeria DiSarli, Almerinda Di Benedetto, GennaroRusso, Chemical Engineering Science, 51(22):7704-7712,2012 [18] Lapointe Simon, Bobbitt Brock, Blanquart Guillaume, Proceedings of the combustion Institute, 35:1033-1040, 2015
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[19] R. H, A. J, Fuel 103, 1090, 2013 [20] M. Chapuis, C. Fureby, E. Fedina, N. Alin, J. Tegn´er, Les modeling of combustion applications using openfoam. Tech. rep., Defense Security Systems Technology, The Swedish Defense Research Agency - FOI, Stockholm,Sweden (2010). V European Conference on Computational Fluid Dynamics, Lisbon, Portugal, Jun 14-17, 2010 [21] A. Yoshizawa, K.Horiuti, Journal of the Physical Society of Japan 54(8), 2834,1985 [22] U.Schumann, Phys.Fluids, 1977 [23] J. Chomiak, A. Karlsson, Symposium (International) on Combustion 26(2), 2557, 1996 [24] V.I. Golovitchev, J. Chomiak, Numerical modeling of high temperature air ”flameless” combustion. Tech. rep., Chalmers University of Technology, Goteborg,Sweden (2001). The 4th International Symposium on High Temperature Air Combustion and Gasification, Rome, Italy, Nov 26-30, 2004 [25] U. Frisch, P. Sulem, M. Nelkin, Journal of Fluid Mechanics 87, 719, 1978 [26] J. Bibrzycki, T. Poinsot, Reduced chemical kinetic mechanism for methane combustion in o2/n2 and o2/co2 atmosphere. Tech. rep., CERFACS, 2010 [27] G. Boudier, Methane/air flame with 2-step chemistry: 2s ch4 cm2. Tech. rep., CERFACS, 2007 [28] H. Weller, The development of a new flame area combustion model using conditional averaging. Tech. rep., Department of Mechanical Engineering, Imperial College of Science Technology and Medicine, 1993 [29] O. Colin, K. Tru_n, Proceedings of the Combustion Institute 33(2), 3097, 2011 [30] J.M. Duclos, O. Colin, Arc and kernel tracking ignition model for 3d spark ignition engine calculations. Tech. rep., Institut Francais du P´etrole, Rueil-Malmaison, France (2001). International Conference on Modeling and Diagnostics for Advanced Engine Systems (COMODIA 2001),Nagoya, Japan,2001 [31] T. Lucchini, G. D'Errico, F. Brusiani, G.M. Bianchi, A _nite-element based mesh motion technique for internal combustion engine simulations. Tech. rep., Politecnico di Milano,Milano, Italy. 7th International Conference on Modeling and Diagnostics for Advanced Engine Systems (COMODIA 2008), Sapporo, Japan, Jul 28-31, 2008 [32] H. Jasak, H.G. Weller, N. Nordin, Tech. Rep. 2004-01-0110, Nabla Ltd, Salfords,United Kingdom (2004). SAE 2004 World Congress and Exhibition (SAE 2004), Detroit, MI, USA, Mar 08, 2004 [33] M. Brewer, L.F. Diachin, P. Knupp, T. Leurent, D. Melander, in 12th International Meshing Roundtable, Sandia National Laboratories report SAND 2003-3030P, 2003 [34] H. Jasak, Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine, 1996 [35] M. Jia, M. Xie, Journal of Automobile Engineering 221(D4), 465, 2007 [36] G.M. Bianchi, F. Brusiani, L. Postrioti, C. Grimaldi, M. Marcacci, L. Carmignani, in SAE paper, 2006-32-0022 [37] J. Jeong, F. Hussain, Journal of Fluid Mechanics 285, 69, 1995 [38] M.S. Chong, A.E. Perry, B.J. Cantwell, Physics of Fluids A 2, 765, 1990 [39] M.V. Melander, F. Hussain, Physics of Fluids A 5, 1992, 1993 [40] H.J. Lugt, The dilemma of defining a vortex. In Recent Developments in theoretical and experimental fluid mechanics, Springer, 1979
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Highlights (1) Vortex development in charge and compression stoke is analyzed. (2) Large strength vortex cores are located at regions with high flame wrinkles. (3)Vortex-pair leads to flame wrinkles through entrainment of flame front. (4)Large-scale vortices break up into small-scale ones across flame front. (5)Addition of carbon dioxide weakens effects of vortex-pair on flame.
S1743-9671(15)30474-8
DOI:
10.1016/j.joei.2016.09.005
Reference:
JOEI 272
To appear in:
Journal of the Energy Institute
Received Date: 25 December 2015 Revised Date:
20 September 2016
Accepted Date: 26 September 2016
Please cite this article as: X. Zhang, T. Wang, J. Xu, S. Zheng, X. Hou, Study on flame-vortex interaction in a spark ignition engine fueled with methane/carbon dioxide gases, Journal of the Energy Institute (2016), doi: 10.1016/j.joei.2016.09.005. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Study on flame-vortex interaction in a spark ignition engine fueled with methane/carbon dioxide gases
Xin Zhang, Tao Wang*, Jian Xu, Shizhuo Zheng, Xiaosen Hou Department of Power Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, PR China
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Abstract A numerical study on the in-cylinder flame-vortex interaction of gaseous spark ignited engine fueled with methane/carbon dioxide is carried out by means of large-eddy method. Evolution of in-cylinder turbulence in charge phase and flame-vortex interaction during combustion process are analyzed in great detail. It's found out that the large scale coherent structures are transformed into homogeneous small scale vortexes during the intake and compression stroke. The strong vortex cores are generated by interaction between flame and in-cylinder background turbulence. Those generated vortex cores wrinkle flame surface and augment turbulent flame speed. The contra-rotation between the two vortexes of vortex-pair in the unburned area results in the appearance of large scale flame wrinkles, which is because the vortex-pair movement leads to the local entrainment and hence stretch of the flame surface. With the increase of volume fraction of carbon dioxide in the gases, the turbulent flame speed is decreased, the effect of vortex pair on the flame structure is weakened, and the level of the flame wrinkling is decreased correspondingly. Keywords: IC engine, methane/carbon dioxide, flame-vortex interaction, Large-eddy simulation 1. Introduction
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In recent years, the natural gas has been known as the high quality gaseous fuel. However, with the increasingly prominence of the energy crisis, several gaseous fuels such as biogas are becoming the research focus of new alternative energy fuels. The concentration of methane in these fuels is relatively lower and non-hydrocarbon gases are with a higher level in general. The biogas is composed by 40%-60% methane, 40%-60% carbon dioxide [1]. The value of biogas is lower compared with the natural gas. One attractive feature of biogas is that it can be produced close to the consumption points and hence is ideal for decentralized power generation in remote rural areas. The biogas is more suitable for the spark ignited (SI) engine with a high compression ratio because it has an extremely low energy density, low flame velocity and not so wide flammability limits on account of its high carbon dioxide content [2]. The challenges of using these gases as the engine fuel are the lower heat release rate and the unstable combustion, which lead to much lower engine efficiency and higher cyclic variation. The combustion of biogas in engine is much more like a combination of larger portion of EGR and natural gas. Low laminar flame speed is the crucial factor. Therefore, some experimental studies struggled to augment turbulent flame propagation through adding hydrogen in order to improve power output and performance [3][4] However, combustion stability is still a problem there. How to improve the combustion stability of the biogas fueled engine is of great significance for the clean fuel engine development. The inherent factors for combustion stability should be researched. Based on the research of the SI engine cyclic variation causes and the influence factors, Ramos et al. [5] proposed that small scale turbulent structures and their impact on the mixing process of the reactants lead to the growth of the unstable flame kernel, while the large scale turbulent structures affect the surface area of the flame front. Multi-cycle simulations of IC engines using large-eddy simulation become popular because of huge advancements in parallel computing. Vermorel [6] and *
Corresponding author. Department of Power Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, PR China Tel.: +8601051688404 E-mail address: [email protected] (Tao Wang).
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Richard [7] conducted multi-cycle simulations of single spark ignition engine with coherent flame model. More advanced combustion model then was used to capture the flame [8]. These works expect to clarify the root causes of cycle-to-cycle variations. According to their studies, variations of turbulence within engine, as well as flame-turbulence interaction, might play a dominant role. In the research area of flame-turbulence interaction, studies of flame-vortex interaction might be a great branch. The vortex movement, the turbulent fluctuation and the velocity gradient on the flame front distorted and wrinkled the flame surface. Therefore, the flame propagation speed and the flame front structure are of large differences between the engine cycles, which could be the main reason of the engine cyclic variation. In order to deeply understand the mechanism of cyclic variation in gaseous fueled engine, it is necessary to study the interaction between the turbulent vortex and flame front. The flame-vortex interaction mainly includes two patterns. One is that the central axis of the vortex parallel to the flame surface, the other one is that the central axis of the vortex perpendicular to the flame surface. The reality is often the combination of both [9]. For the former one, Poinsot et al. [10] studied the flame-vortex interaction by using numerical methods so as to estimate the local quenching conditions of the turbulent premixed flames. Roberts et al. [ 11 ] conducted an experimental research on the role of the flame-vortex interaction in the quenching process using OH laser-induced fluorescence spectrometry. Mueller et al. [12] measured the velocity field of the vortexes with three different vorticity strength and exam the decay, regeneration of the vortexes during the flame-vortex interaction. Patnaik and Kailasanath [13] simulated the effect of the vortex ring on the methane/air flame. The results show that the local flame quenching tents to occur at the leading edge of the vortex ring. For the latter situation, it is generally suggested that the flame propagation velocity equals to the maximum peripheral velocity of the vortex. The research results of Asato et al. [14] indicated that if a vortex ring is filled with premixed gas, the flame will move in two different directions along the vortex ring after ignition. The flame propagation velocity is proportional to the maximum peripheral velocity of the vortex. An unsteady two-dimensional numerical simulation was conducted by Ishizuka et al. [15]. The result shows that after passing through a weak vortex pair, the flame surface wrinkle gradually declines and a pair of counter-clockwise rotated vorticity field is produced. The consistent conclusion was obtained in the experimental research of Mueller et al. [12]. As flame interact with a moderate intensity vortex pair, a mushroom-shaped flame front is formed in the beginning. Then a capsule-shaped flame zone appears gradually in the unburnt area. Despite the vortex pair continues decay, it is surround by the closed flame front. Recently, large-eddy method was applied to do research on flame-vortex interaction. Valeria et al. has conducted large-eddy simulation of transient premixed flame-vortex interactions in gas explosions, in which mainly grid effects were studies in great detail. [16][17]. Impact of chemistry models on flame-vortex interaction were covered.[18]. From the works mentioned above, main fundamental studies of flame-vortex interaction were conducted and engine-like conditions, even real engine configuration, were rare. So some scholars have done some researches about flame-turbulence interaction in engine-like condition. For instance, [19] combined direct numerical simulation with reduced chemistry to simulate turbulence-kernel interaction under gas-fueled engine conditions. A length scale defined as the ratio of turbulent length scale to kernel diameter was used to identify regimes of turbulence-kernel interaction. Three different interaction regimes are identified and analyzed-kernel breakup regime, kernel deformation regime and kernel convection regime. Therefore, flame-vortex is pretty crucial factor. Currently, the study on the flame-vortex interaction of the engine combustion is rare. The in-cylinder flame-vortex interaction is not only restricted by the flow pattern of the turbulent field which is influenced by the intake process, but also limited by the heat release which is decided by the components of the gas blends. In order to have a comprehensive understanding of the turbulent flame development in engine combustion, large-eddy simulation of the turbulent combustion in an engine fueled with methane/carbon dioxide was carried out in this paper. Flame-vortex interaction was analyzed.
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The irregular flow in the engine is the turbulence. The Large eddy simulation is used to model the in-cylinder turbulent flow and the vortex movement. In this paper, the reactive flow equations are filtered as follow [20]: ∂ρ + ∇ ⋅ ( ρ u% ) = 0 (1) ∂t ∂ρ u% + ∇ ⋅ ( ρ u% ⊗ u% ) = −∇p% + ∇ ⋅ (S + τ ) (2) ∂t ∂ρ h% + ∇ ⋅ ( ρ u% h% ) = ∇ ⋅ (− pu% + S% + h − bh ) (3) ∂t ∂ρ Y%i + ∇ ⋅ ( ρ u% Y%i ) = ∇ ⋅ ( ji − b i ) + w& i (4) ∂t in which - and ~ denotes filtered and Favre filtered operations. ρ is the density, u the velocity，
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p the pressure, S the viscous stress tensor, h the enthalpy, h the heat flux vector，Yi ， ji , w& i , the mass fraction, mass diffusion and reaction rate of species i, τ = ρ (u% ⊗ u% − u ⊗ u) , b = ρ (uY − u% Y% ) ，and i
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b h = ρ (uh − u% h% ) the unresolved transport sub-grid terms. The linear viscous for the fuel mixture, % , h% ≈ κ∇T% and j ≈ D ∇Y% , Fourier heat conduction and Fickian diffusion are assumed as S ≈ 2 µ D D
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% is the deviatoric part of D % = 0.5* (∇u% + ∇u% T ) .The mixture heat conductivity, mixture in which D D diffusion coefficient and mixture dynamic viscosity are calculated using the Cantera
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thermodynamics and transport packages. Since non-equilibrium conditions commonly occur in free shear layers, boundary layers and wall domains, the Sub-grid scale (SGS) model chosen in this study is one-equation turbulent energy model. Based on the eddy-viscosity concept, a transport equation of the sub-grid scale kinetic energy on which the eddy viscosity depends is solved
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additionally. Through subtracting the filtered momentum equation from the corresponding non-filtered one, the relation of the fluctuating component of velocity u′ can be obtained. The one-equation turbulent energy model can be derived from multiplying the above result by the
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sub-grid velocity vector [21], ∂K + ∇ ⋅ ( Ku ) − ∇ ⋅ [(ν + ν sgs )∇K ] − ε = − τ : D (5) ∂t Where the K is the SGS kinetic energy, the τ is the SGS stress tensor, the D is the large-scale strain rate tensor, the ν sgs is the SGS eddy-viscosity, model constant Ck = 0.094 and Ce = 1.048 , the ε is the dissipation rate, 1 τ − tr ( τ ) = −2ν sgs D (6) 3 1 D = (∆u + ∆uT ) (7) 2 ν = C K1/ 2∆ (8) sgs k
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One-equation models [22] are good at providing a more accurate time scale for defining the velocity scale independently and have the advantage of modeling transitional flows and large scale unsteady flows. In particular, it is more suitable to treat the flows in the engine geometry. Eddy-viscosity based models have the drawback from the assumption of the isotropy in the unresolved scales. This problem can be reduced by the mesh refinement.
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2.2 Partially Stirred Combustion Model
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Turbulence and chemistry interaction model described in the partially stirred reactor model (PaSR Model) for the combustion in a reactor has been proposed to account for the effects of mixture imperfections on chemical reaction rates [23]. It is a sequential process where mixing is followed by chemical reactions and the rates of the individual steps are equal. The source term of the species transportation equation can be expressed as: (10) in which, k is the reacting sub-grid volume fraction. The high exothermicity and volumetric expansion happen in the small structures distributed among the fine structure vortices. The reacting flow is divided into fine structures (*), responsible for mixing and chemical reactions, which provide a high temperature to the surrounding fluid (0). k characterizes the turbulence effects on the chemistry. According to [24], it is a function of the turbulent mixing time and the chemical reaction time. τc 1 ′ = H (t , tmix ) κ= τ mix (11) ′ τ c + τ mix 2 H (t , tmix ) is the harmonic mean. τ c is the chemical time scale. The micro-mixing time τ mix is a important variable in PaSR model whose definition is quite controversial. Chomiak and Karlsson [23] define it in a form of similar to the Kolmogorov time definition by replacing the molecular viscosity by the turbulent viscosity. 2 ν lν t 1/ 2 k ) = (2 Cµ τ k )1/ 2 (12) τ mix = (
ε
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In this paper, τ mix is defined based on a phenomenological model [25], in which the micro-mixing time is partly decided by the micro fractal structure of the turbulence. 6
τ mix = τ d = l02 / ( Re1+ D ν ) F
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in which τ d is the viscous diffusion time, l0 is the initial length scale of the eddy, ν is the molecular viscosity, Re is the Reynolds number and DF is the fractal dimension of the turbulent field. In general, the micro-mixing occurs below the resolvable scale. Then the eddy length scale and the molecular viscosity are derived as follow. ∞
∞
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ν SGS = ∫ dkk −1[k −1 E (k )]1/ 2 = ò1/3∆ 4/3
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in which, ∆ is minimum resolvable scale, E (k ) = Cò2/3 k −5/3 is the energy spectrum of the Kolmogorov scale. Finally, the micro-mixing time scale is obtained.
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(17)
Table 1: Reactions for 2-step reduced mechanism 2S-CM2-JB mechanism A Ea 5.1E14 3.5E4 CH4+1.5O2=>CO+2H2O 5.1E8 1.2E4 CO+0.5O2<=>CO2
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Reaction No. 1 2
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Accurate prediction of the combustion temperatures and flame structures require the detailed reaction mechanisms. For methane-air combustion, the GRI-3.0 mechanism which involves 53 species and 325 reactions is suggested. But in the LES-combustion case, those mechanisms are often too expensive to handle. In this paper, the 2S-CM2-JB mechanism [26] modified from the 2S-CM2 mechanism [27] is chosen to complete the chemical reaction modeling for the combustion of methane/carbon dioxide gas, which is a reduced two step chemical kinetic mechanism as shown in Tab.1. The progress variable b is defined through the mass fraction of the species. YH2 O + YCO2 + YEGR b = 1− (18) YFuel→H 2O+CO2 + YH 2O + YCO2 − YEGR YEGR is mass fraction of previous burnt product and YFuel→ H2 O+CO2 refers to mass fraction of burnt product under the condition that unburnt mixture is completely burnt. At the start of charge phase, in the cylinder, initial mass fractions of CO2 and H2O are set. The sub-grid flame surface wrinkling factor Ξ is given by the Weller combustion model [28]. The flame surface wrinkling ∑ is the flame surface area of the unit volume, which is calculated as below. ∑ = Ξ ∇b (19)
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2.3 AKTIM-LES Spark Ignition Model
The AKTIM-LES spark ignition model [29] is used here. The electric spark length lspk is given by the electrical circuit equations in the AKTIM (Arc and Kernel Tracking Ignition) model [30]. A few nanoseconds after the spark timing t spk an electric spark is formed. A critical ignition energy is
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set and an initial burned gases mass mbign is is deposited once the electrical energy is larger than the critical one. The volume of the initial burned mass is defined as a cylindrical unit with a radius of 2δ L and length lspk :
mbign =< ρu lspk 4πδ L2 >
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Cign ( x, tign ) = Cinit exp(−0.6−2 x − xspk ∆% −2 )
where constant Cinit satisfies
∫ρ C b
ign
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dV = mign , ρb is the burned gases density and xspk the spark plug
location. Then, the ignition energy added is distribute rbign = (3(4π )−1 ∫ Cign dV )1/3 d according to the value of Cign on each ignition cells. The flame kernel is assumed to be spherical, its radius rbign can be defined as: rbign = (3(4π )−1 ∫ Cign dV )1/3 (22)
3. Mesh Managements and Numerical Methods 3.1 Mesh managements Multi-dimensional simulation of internal combustion engines involves physical modeling and
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geometrical dynamic mesh handling [ 31 ]. For the geometry and mesh handling aspect, the combustion chamber, the manifolds and valves of an IC engine often have very complex shapes. The movements of the piston and the valves which lead to both geometry and topological changes require more developed dynamic mesh motion techniques [32]. Two main technical topics for handling the unstructured mesh in internal combustion engine modeling are mesh motion and topological changes. IC engine simulations involve moving boundaries such as the valves and the piston. For prescribing solution-dependent motion more easily, a second-order FEM solver is used to solve the mesh motion equation. Every polyhedral cell is split into tetrahedra and this will introduce additional points in the cell centers and faces. The point velocity can be obtained from the motion equation: ∇ ⋅ (γ∇U p ) = 0
(23)
3.2 Discretization Scheme
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in which γ is the diffusion coefficient, U p is the point velocity. Variety of γ can be used to control different kinds of mesh motion. Mesh quality is destroyed under the extreme deformation of boundary. The approaches involving topological changes require higher skills to generate quite fine meshes which is tough for complex engine geometries. One of these approaches uses attach/detach boundaries, cell layer addition/removal and sliding mesh interfaces to preserve the high quality of the dynamic mesh by changing the connectivity of the mesh and the numbers of cells. Another approach which is called the mesquite mesh optimization solver [33]. It requires the mesh to be constituted by the tetrahedrons. The slip patches with their moving directions and fixed length scale patches are specified first for the motion solver. Through checking and improving the mesh quality by a series of optimization algorithms, the meshes are added and removed by merging and dividing the tetrahedrons. The Smoothing interval is set to control the frequency of the mesh refinement. This approach has the advantage that unstructured engine geometry can be easily meshed by the tetrahedrons and the high quality of mesh refinement can be obtained during the dynamic movement. In this paper, A method is proposed to couple both the polyhedron vertex movement algorithm and the Mesquite algorithm. The former one is used when the mesh quality is quite fine while the latter is used to reconnect and smooth the mesh as the quality cannot meet the requirement. The time interval for the mesh refinement in set as 10 CA. The advantage of this coupling method is to improve the running efficiency and assure the mesh quality at the same time.
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As the computational platform, the C++ library OpenFOAM whose discretization is based on Gauss theorem is used in this study. For low Mach number flows in IC engine, a semi-implicit code based on a second order accurate Crank-Nicholson time integration scheme and a PISO procedure utilizing a Rhie-Chow interpolation for the cell centered data storage structure is used. The convective fluxes are reconstructed by a monotonicity preserving scheme constituted with one second order linear reconstruction, one first order upwind reconstruction and one non-linear flux limiter [20]. The flux limiter is used to switch between the flux reconstruction schemes. The diffusion term and the sub-grid fluxes are split into orthogonal and non-orthogonal parts to minimize the non-orthogonal errors. Central difference approximation and gradient face interpolation codes use collocated cell-centered variable arrangement. A variable time step corresponding to a Courant number of 0.2 is set to keep the computational accuracy and stability [34].
3.3 Initial and Boundary Conditions Table 2: Temperature boundary condition Walls Temperature(K) Piston 540 Liner 480
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500 600 375
4. Engine parameters and operation conditions
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At the inlet section, mass flow rates and temperature profiles are imposed. The Han-Reitz wall heat transfer model [35] is used in this study, in which the influence of the gas density of the boundary layer and the turbulent Prandtl number are considered. The initial field data including the fractions of the exhaust gases are taken from a simulation result of the 2D engine multi-cycles modelling. The initial fields of the inlet part and the cylinder part are treated by the setFields function in OpenFOAM, which is good at setting the non-uniform initial fields. Tab.2 shows the temperature assigned on the wall boundaries. Each temperature value is estimated on the basis of experimental data in [36]. The simulation begins at 12 °CA ATDC (Intake Valve Open Timing), pressure and temperature conditions inside cylinder and inlet duct are defined from previous RANS simulation. Boundary conditions for species fractions, the turbulent kinetic energy and dissipation rate are set to be zero gradient. The no-slip condition is used for the velocity at the walls.
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The prototype of the simulation is the ZS1100M series single-cylinder which is a four-stroke gas engine with port fuel injection system. The engine specifications and operating conditions are given in Tab.3. The testing engine is equipped with the electronic control system developed by the engine lab of Beijing Jiaotong University. Electronic throttle is used in order to change the engine load adjustment from quality into quantity. Intake port injection is controlled by ECU which could be beneficial to obtain the accurate air-fuel ratio. The engine that we studied might be applied in power generation, where engine operates at a fixed load and rotational speed. In this case, total flux or absolute mass of charge keep constant. However, composition of biogas varies in different seasons, especially volume fraction of carbon dioxide. In addition, using these fuels in IC engines might lead to unstable combustion and lower heat release rate. Therefore, motivation of this paper is to study how different combinations of carbon dioxide and methane, which simulate biogas, affect the flame-vortex interaction in engine.
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Table 3: Engine Specifications Engine Items Engine type Single cylinder 4-stroke Bore(mm) 100 Stroke(mm) 115 Con. Rod length(mm) 210 Displacement (cm3/cyl) 930 Compression Ratio 10.2 IEMP (MPa) 0.8 Normal Speed (r/min) 2000 Normal Power (kW) 10
The engine operates at a speed of 1500 r/min, a throttle opening of 30% and stoichiometric ratio condition. The spark ignition timing is set at 18°CA BTDC. The engine is fueled with gas blends of methane and carbon dioxide in which the volume fractions of carbon dioxide are 10%, 20%, 30% and 40%, respectively. Detailed information can be found in Tab.4. We deduce that variation of composition might be the cause of unstable combustion. Table 4: Calorific value and density of methane/carbon dioxide gases (273K, 101.325kPa) Fuel No. CH4/CO2 Mass fraction Volume caloric value Density Volume fraction % CH4/CO2/O2/N2 (MJ.m-3) (kg.m-3) Fuel 1 90/10 4.2/1.3/22.1/72.4 31.46 0.83 Fuel 2 80/20 3.4/2.1/22.1/72.4 27.97 0.96 Fuel 3 70/30 2.5/3.0/22.1/72.4 24.47 1.08
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The comparison of the experiment data and the LES modeling result of the in-cylinder pressure are shown in Fig.1. As illustrated in the figure, the experiment and modelling pressure curves match well during the compression stroke. There are tiny differences in the combustion stage. It is mainly because the thoroughly description of the chemical reaction is difficult for the reduced two steps mechanism. That leads to the slower flame propagation and smaller pressure rise rate. The work efficiency during the expansion phase is lower as well. This phenomenon is obvious in the curve of Fuel 1. However, with the volume fraction of carbon dioxide in the gases increases (such as Fuel 3), the gap between the modeling and experiment data is reduced.
5. Results and Discussion
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Figure 1. Comparison of LES modeling and experiment results for in-cylinder pressure
5.1 Evolution of in-cylinder turbulent flow
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In order to study the in-cylinder flame-vortex interaction, it is necessary to investigate the movement of the turbulent flow and the distribution of the vortex in the engine. Since the turbulent flow is notably time varying and strongly chaotic, large amount of vortexes with different length and time scales are transported simultaneously. By far, there have been several approaches for the identification of a vortex [37][38][39]. Lust [40] supposed a vortex is a multitude of material particles rotating around a common center. Chong [38] proposed a vortex is a region of complex eigenvalues of ∇U . In this section, the coherent structures in turbulent flows of the engine is identified by Q criterion proposed by Hunt et al. The Q criterion identifies vortices as flow regions with positive second invariant of the velocity gradient tensor: Q =( W 2 - S 2 ) /2 , in which W and S are the skew-symmetric and symmetric parts of ∇U , respectively. The iso-surface of a certain value of Q is chosen to inspect the generation, development, fragmentation and dissipation of the vortexes. As depicted in Fig.2, the iso-surface of Q=1.0 × 106 s −2 can catch the evolution of coherent structure fairly clear. Figure 2a-Figure 2b shows that at the early stage of the intake stroke (30-60°CA ATDC), a strong shear flow is formed in the cylinder as the gas mixture travels through the intake valve. A reflux is produced at the bottom of the valve, causing lots of the large scale vortexes fulfilled in the cylinder. When the piston moves downward (90-120°CA ATDC) in Fig.2c-Fig.2d, the fresh charge continuously flows into the cylinder and mixes with the former vortex structures with the increase of the valve lift, which leads to the vortexes spreading all over the whole space of the cylinder. Figure 2e-Figure 2f shows that at the late stage of the intake stroke
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(150-180°CA ATDC), the strength of the overall flow field reduces, the former large-scale vortexes are constantly stretched, deformed and broken into small vortexes. Therefore the coherent structures with higher strength are clearly illustrated during the valve closing stage (210-230°CA ATDC) in Fig.2g-Fig.2h. Figure 2i-Figure 2j shows that at the early stage of the compression stroke (240-270°CA ATDC), the large scale vortexes are further broken down and dissipated. A squeeze flow is obviously emerged near the clearance of the combustion chamber during the late stage of the compression stroke (330-330°CA ATDC) in Fig.2k-Fig.2l. The squeeze flow spreads to the chamber interior space which speeds up the homogenization of the turbulent flow field in the cylinder.
(b) 60°CA ATDC
(e) 150°CA ATDC
(f) 180°CA ATDC
(c) 90°CA ATDC
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(a) 30°CA ATDC
(d) 120°CA ATDC
(h) 230°CA ATDC
(k) 300°CA ATDC
(l) 330°CA ATDC
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(g) 210°CA ATDC
(i) 240°CA ATDC
(j) 270°CA ATDC
Figure 2. Vortex field in engine cylinder during charging and compression stage. (Contour of Q=1.0 × 10 magnitude is m.s-1
6 −2
s ) Unit of U
5.2 Analysis of flame-vortex interaction 5.2.1Flame-vortex interaction Since the turbulent flame propagates from a flame kernel to the whole cylinder during the fast burning period of a SI engine, it is significant to investigate the flame-vortex interaction in this time
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period. Within SI engine, flame presents flamelet regime which means that flame is very thin and turbulence plays a role in wrinkling the flame front. Although it is not convincible that turbulence is completely composed of large amounts of vortices, it does make sense that analysis of flame-vortex interaction is conducted through studying interaction between flame surface and those vortices whose spatial scales are larger than that of flame front. A minimum vortex scale of analysis in this paper is laminar flame thickness. For the purpose of better understanding the flame-vortex interaction of the engine combustion, as shown in Fig.3a, three transverse slices with fixed positions are selected for the further analysis. The red spot highlighted in Fig.3b is the position of the spark ignition site. The ignition site is located at the eccentric position in the cylinder.
Figure 3. Position of selected slices and ignition site
In this section, the λ2 criterion which is proposed by Jeong [37] is applied to identify the vortex core during the flame propagation. A vortex core is an area with intensive vorticity inside the vortex, which rotates as a rigid body. λ2 is the second largest eigenvalue of W 2 + S 2 ,which satisfies the following formula:
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DS 1 + W.W + S.S −ν∇ 2S = − ∇∇p (23) ρ Dt in which, the unsteady rotation effect DS / Dt and the viscous effectν∇ 2S both have influence on the pressure gradient field. The term W.W + S.S is the only factor that decides if the local minimum pressure is led by the existence of the vortex. According to Jeong [37], the vortex core is detected as two of the three eigenvalues of the tensor W.W + S.S are negative. Meanwhile, since the tensor is symmetric, the three eigenvalues require the condition λ1 ≥ λ2 ≥ λ3 to be real. Therefore, The region of negative λ2 represents the existence of the vortex core and the larger is the magnitude of
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negative λ2 , the greater is the vortex strength. Figure 4 shows the iso-surface of λ2 = −1×107 during the flame propagation. Because the velocity of the flame propagation is faster than the one of the local gas flow, the relative motion between the flame and the flow field will generate new turbulent vortexes. The strength of the new generated vortexes is often larger than that of vortexes from the background flow field. The color legend in Fig.4 indicates the value of progress variable b . For the value of b on the iso-surface of λ2 is between 0 and 1, it means the new generated vortexes are located in the region near the flame front. As the flame spread forward, the generated vortex continues to dissipate and the new one is appeared with the changing of the flame front location.
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Figure 4. Iso-surface of λ2 during flame propagation (Fuel 1, λ2
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Figure 5 shows temperature distribution and that of vortex core near the flame front on three slices at TDC. The solid black lines indicate the position of the flame front highlighted by b = 0.3 and the solid red line represents T = 1000 K . The region between solid red line and black line is defined as preheated zone because temperature is below 1000K uniformly outsider this preheated zone. It is shown in Fig.5a-Fig.5c, the flame front is highly wrinkled and absolutely not a normal cycle. Many vortices appear within the preheated zone. Furthermore, the new generated vortex core with larger strength locates in the region where the flame surface wrinkling is higher as well. Especially, the vortex core often appears near the position where the flame surface raised toward the unburnt area. For example, the region around the point (0,-2.8) in Fig.5a, the point (-0.5,-1.5) in Fig.5b and the point (-2,2.5) in Fig.5c. The flame surface in these regions tend to be entrained or stretched by the new generated vortexes. These effects will lead to an increase of the flame propagation speed. Figure 6 is the scatter diagram of the mean flame wrinkling Σ and the mean turbulent flame velocity St versus the mean λ2 on the flame front, respectively. It is shown in Fig.6a that with the
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increase of the magnitude of mean λ2 the mean flame surface wrinkling increases. The flame surface wrinkling is quite helpful to extend the contact area between the flame surface and the vortex field and thus more prone to the production of the new vortex cores. On the other side, the new vortexes will raise the flame surface wrinkling level. Because slice 3 is close to the bottom of the combustion chamber, the flame propagation is spatially influenced by the bottom wall to some extent and the flame surface is over distorted by the coupling effect of the local turbulence and the chamber structure. Thus the mean flame surface wrinkling on slice 3 is higher than those on slice 1 and slice 2 as λ2 < −1× 107 . Figure 6b shows that with the increase of the magnitude of mean λ2 , the mean turbulent flame speed increases. It indicates that the vortex with higher strength contributes to the fast burning of the turbulent flame. This law is more obvious for the flame surface on slice 2 since it is conducive to the fully development of the flame. Therefore, with flame propagating, interaction between gas preheating effect and in-cylinder background turbulence produces many vortex cores within preheated zone. These generated vortex cores will wrinkle the flame surface and augment turbulent flame speed. Fundamentally, most wrinkled flame positions are located around those vortex cores with high strength.
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Figure 5. Temperature distribution Top and Distribution of vortex core near the flame front on three slices at TDC (Fuel 1)
Figure 6. Flame parameters versus mean λ2 on the flame front, (a) mean flame wrinkling, (b )mean turbulent flame velocity St
5.2.2 Effect of vortex-pair on flame front During interaction between flame and vortex core, a particular phenomenon happens when two adjacent vortex cores have opposite directions, namely vortex-pair. Figure 7 shows the evolution of the in-cylinder flame-vortex pair interaction of the engine combustion. The sign of the vorticity on behalf of the rotation direction of the vortex, where positive is for a vortex of counterclockwise rotation and negative is for the opposite case. As shown in the figure, there is always another vortex of the contrary-rotation direction around one vortex to make them a vortex-pair. In order to investigate the effects of the vortex-pair movement on the formation of the flame front structure, the situation on three slices at two crank angle are analyzed. Figure 7a-Figure 7c shows that at the early stage of the flame propagation (355°CA ATDC), the flame propagation speed is relatively slower,
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coupled with the lack of large scale and high strength vortex-pair in the local region, there is no obvious wrinkles on the flame surface. Figure 7d-Figure 7e shows that as the flame front spread forward (360°CA ATDC), the flame surface area increases, the effects of the vortex-pair on the flame surface enlarge. In addition, the contrary rotation of the two vortexes in the vortex-pair leads to the entrainment of the local flame surface to the center of the vortex-pair or the stretch along the outside border of the vortex-pair, thus the flame surface wrinkles are formed. Meanwhile, the flame surface absorbs the original vortexes as traveling through the vortex-pair in the unburnt area. The large scale vortexes are broken down into small ones, which makes the turbulent field of the burnt area more uniform. For studying the flame-vortex-pair interaction in detail, the slice 2 is taken as an example. As depicted in Fig.7b, a typical vortex-pair is constituted by the two vortexes whose rotation centers are at the points (-1,-0.5) and (-2,-0.5). While the flame front moving toward that front vortex-pair, the flame surface part between the two vortexes is dragged into the unburnt area, the part at the outer ring of the vortex-pair is entrained into the burnt area. Consequently, the flame surface wrinkle is generated significantly in the region near the point (-1,-1.5).
Figure 7. Evolution of flame-vortex pair interaction of engine combustion.(Fuel 1)
5.3 Effect of carbon dioxide on flame-interaction
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Figure 8 shows the effect of engine fueled with different methane/carbon dioxide gases on flame structures on slice 2 while the progress variable b is reaching 0.15. As shown in Fig.8a-Fig.8b, as gas mixture is diluted with much more CO2, the effects of the vortex-pair movement on the flame structure are weakened in the same background turbulent field. Owing to the dilution effect of CO2, the combustion process slows down and the cylinder volume under the same progress variable b increases. The concentration of the vortex field and the vortex strength decrease as well. For example, in the region near the point (1,-1) in Fig.8a, a flame surface wrinkle towards the burnt area is clearly raised due to the local vortex-pair movement. The flame surface wrinkle at the same place in Fig.8b is still distinct while the vortex strength in the background turbulent is reduced. However, the wrinkle in Fig.8c is attenuated apparently compared to the one in Fig.8a and the wrinkle in Fig.8d is almost disappeared as a result of moderate flame-vortex-pair interaction. The similar situation is demonstrated in the region near the point (0,1) on the slice 3.
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Figure 8. Effect of engine fueled with different methane/carbon dioxide gases on flame structures. (Slice 2, b = 0.15)
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Figure 9 is the scatter diagram of the vorticity magnitude ω and the flame surface wrinkling Σ versus the crank angle when engine is fueled with different methane/carbon dioxide gases. As shown in the Fig.9a, when the engine is fueled with Fuel1, Fuel 2, Fuel 3 and Fuel 4, the peak of the mean vorticity magnitudes are 4495 s-1, 3100 s-1, 2271 s-1 and 2190 s-1, the corresponding crank angles of the mean vorticity magnitude are 364.2°CA ATDC, 365.5°CA ATDC, 368.2°CA ATDC and 378.6°CA ATDC, respectively. It conveys that with the increase of the volume fraction of the carbon dioxide, the mean vorticity magnitude decreases, the corresponding time of the peak value is postponed. Figure 9b shows that with the increase of the carbon dioxide volume fraction in the gases, the crank angle when the flame reaching the same surface wrinkling is delayed. For example, the situation of Fuel 1 advances about 16 CA than that of Fuel 4, when the flame surface wrinkling reaches 400m-1.
Figure 9. Flame and flow parameters versus crank angle when engine is fueled with different methane/carbon dioxide gases, (a) Mean vorticity magnitude
ω
, (b) mean flame surface wrinkling Σ
6. Conclusion In this study, the large-eddy simulation is used to investigate the in-cylinder flame-vortex interaction when spark ignition engine is fueled by methane/carbon dioxide. The conclusions are acquired as follow.
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During the flame propagation, the large strength vortex cores often locate in the regions where the flame surface wrinkling is higher and the crests of the flame wrinkles raise toward the unburnt area. The flame surface in these regions tend to be entrained or stretched by the new generated vortexes. These effects will lead to an increase of the flame propagation speed. Those generated vortex cores around the flame front is a consequence of interaction between flame and in-cylinder background turbulence.
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With the increase of the flame surface area, the effects of the vortex-pair on the flame surface enlarge. The contrary rotation of the two vortexes in the vortex-pair leads to the entrainment of the local flame surface to the center of the vortex-pair or the stretch along the outside border of the vortex-pair. Thus the flame surface wrinkles are formed. At the same time, the flame surface absorbs the original vortexes as traveling through the vortex-pair in the unburnt area. The large scale vortexes are broken down into small ones, which makes the turbulent field of the burnt area more uniform. With the increase of the volume fraction of the inert gas carbon dioxide in the gas mixtures, the effects of the vortex-pair movement on the flame structure are weakened. The combustion process slows down and the cylinder volume under the same progress variable b increases. The concentration of the vortex field and the vortex strength decrease. 7. Acknowledgement
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This work was financially supported by the National Natural Science Foundation of China (Grant No. 51376020).
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[1] X. Zhang, C. Li, J. Xu, Journal of Energy Institute 83(1), 12, 2010 [2] E. Porpatham, A. Ramesh, International Journal of Hydrogen Energy 32(12), 2057, 2007 [3] Erjiang Hu, Zuohua Huang, Bing Liu, Jianjun Zheng, Xiaolei Gu, Bin Huang, International Journal of Hydrogen Energy,34(1):528-539, 2009 [4] Erjiang Hu, Zuohua Huang, Bing Liu, Jianjun Zheng, Xiaolei Gu, International Journal of Hydrogen Energy, 34(2): 1035-1044, 2009 [5] J.I. Ramos, Internal Combustion Engine Modeling, Hemisphere Publishing Corporation, 1989 [6] V. O., R.S.C.O.A.C.B. A., SAE Paper, 2007-01-0151 [7] S. Richard, O. Colin, O. Vermorel, Benkenida, C. Angelberger, D. Veynante, Proceedings of the Combustion Institute 31, 3059, 2007 [8] O. Vermorel, S. Richard, O. Colin, Combustion and Flame 156(8), 1525, 2009 [9] S. Kadowaki, T. Hasegawa, Progress in Energy and Combustion Science 31, 193, 2005 [10] T. Poinsot, D. Veynante, S. Candel, Journal of Fluid Mechanics 228, 561, 1991 [11] W.L. Roberts, J.F. Driscoll, M.C. Drake, J.W. Ratcli_e, Proceeding of the Combustion Institute 24, 169, 1992 [12] C.J. Mueller, J.F. Driscoll, D.L. Reuss, M.C. Drake, M.E. Rosalik, Combustion and Flame 112, 342, 1998 [13] G. Patnaik, K. Kailasanath, Proceeding of the Combustion Institute 27, 711, 1998 [14] K. Asato, H.W.T. Hiruma, Y. Takeuchi, Combustion and Flame 110, 418, 1997 [15] S. Ishizuka, T. Murakami, T. Hamasaki, K. Koumura, R. Hasegawa, Combustion and Flame 113, 542, 1998 [16] Valeria DiSarli, Almerinda Di Benedetto, GennaroRusso, Chemical Engineering Science, 71:539-551,2012 [17] Valeria DiSarli, Almerinda Di Benedetto, GennaroRusso, Chemical Engineering Science, 51(22):7704-7712,2012 [18] Lapointe Simon, Bobbitt Brock, Blanquart Guillaume, Proceedings of the combustion Institute, 35:1033-1040, 2015
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[19] R. H, A. J, Fuel 103, 1090, 2013 [20] M. Chapuis, C. Fureby, E. Fedina, N. Alin, J. Tegn´er, Les modeling of combustion applications using openfoam. Tech. rep., Defense Security Systems Technology, The Swedish Defense Research Agency - FOI, Stockholm,Sweden (2010). V European Conference on Computational Fluid Dynamics, Lisbon, Portugal, Jun 14-17, 2010 [21] A. Yoshizawa, K.Horiuti, Journal of the Physical Society of Japan 54(8), 2834,1985 [22] U.Schumann, Phys.Fluids, 1977 [23] J. Chomiak, A. Karlsson, Symposium (International) on Combustion 26(2), 2557, 1996 [24] V.I. Golovitchev, J. Chomiak, Numerical modeling of high temperature air ”flameless” combustion. Tech. rep., Chalmers University of Technology, Goteborg,Sweden (2001). The 4th International Symposium on High Temperature Air Combustion and Gasification, Rome, Italy, Nov 26-30, 2004 [25] U. Frisch, P. Sulem, M. Nelkin, Journal of Fluid Mechanics 87, 719, 1978 [26] J. Bibrzycki, T. Poinsot, Reduced chemical kinetic mechanism for methane combustion in o2/n2 and o2/co2 atmosphere. Tech. rep., CERFACS, 2010 [27] G. Boudier, Methane/air flame with 2-step chemistry: 2s ch4 cm2. Tech. rep., CERFACS, 2007 [28] H. Weller, The development of a new flame area combustion model using conditional averaging. Tech. rep., Department of Mechanical Engineering, Imperial College of Science Technology and Medicine, 1993 [29] O. Colin, K. Tru_n, Proceedings of the Combustion Institute 33(2), 3097, 2011 [30] J.M. Duclos, O. Colin, Arc and kernel tracking ignition model for 3d spark ignition engine calculations. Tech. rep., Institut Francais du P´etrole, Rueil-Malmaison, France (2001). International Conference on Modeling and Diagnostics for Advanced Engine Systems (COMODIA 2001),Nagoya, Japan,2001 [31] T. Lucchini, G. D'Errico, F. Brusiani, G.M. Bianchi, A _nite-element based mesh motion technique for internal combustion engine simulations. Tech. rep., Politecnico di Milano,Milano, Italy. 7th International Conference on Modeling and Diagnostics for Advanced Engine Systems (COMODIA 2008), Sapporo, Japan, Jul 28-31, 2008 [32] H. Jasak, H.G. Weller, N. Nordin, Tech. Rep. 2004-01-0110, Nabla Ltd, Salfords,United Kingdom (2004). SAE 2004 World Congress and Exhibition (SAE 2004), Detroit, MI, USA, Mar 08, 2004 [33] M. Brewer, L.F. Diachin, P. Knupp, T. Leurent, D. Melander, in 12th International Meshing Roundtable, Sandia National Laboratories report SAND 2003-3030P, 2003 [34] H. Jasak, Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine, 1996 [35] M. Jia, M. Xie, Journal of Automobile Engineering 221(D4), 465, 2007 [36] G.M. Bianchi, F. Brusiani, L. Postrioti, C. Grimaldi, M. Marcacci, L. Carmignani, in SAE paper, 2006-32-0022 [37] J. Jeong, F. Hussain, Journal of Fluid Mechanics 285, 69, 1995 [38] M.S. Chong, A.E. Perry, B.J. Cantwell, Physics of Fluids A 2, 765, 1990 [39] M.V. Melander, F. Hussain, Physics of Fluids A 5, 1992, 1993 [40] H.J. Lugt, The dilemma of defining a vortex. In Recent Developments in theoretical and experimental fluid mechanics, Springer, 1979
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Highlights (1) Vortex development in charge and compression stoke is analyzed. (2) Large strength vortex cores are located at regions with high flame wrinkles. (3)Vortex-pair leads to flame wrinkles through entrainment of flame front. (4)Large-scale vortices break up into small-scale ones across flame front. (5)Addition of carbon dioxide weakens effects of vortex-pair on flame.