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Pore-scale Simulation of Hydrogen-Air Premixed Combustion Process in Randomly Packed Beds Linsong Jiang, Hongsheng Liu, Dan Wu, Jiansheng Wang, Mao-Zhao Xie, and Minli Bai Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02020 • Publication Date (Web): 10 Oct 2017 Downloaded from http://pubs.acs.org on October 11, 2017
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Pore-scale Simulation of Hydrogen-Air Premixed Combustion Process in Randomly Packed Beds JIANG Linsong1,2, LIU Hongsheng1,2*, WU Dan3, WANG Jiansheng2, XIE Mao-Zhao1, BAI Minli1 1. Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, 116024, Dalian, China; 2. Key Laboratory of Medium-Low Temperature Thermal Energy Efficient Utilization of Ministry of Education Department of Thermal Energy Engineering, School of Mechanical Engineering, Tianjin University 3. The 760th Research Institute of China Shipbuilding Industry Corporation,116013, Dalian, China * Corresponding author: LIU Hongsheng School of Energy and Power Engineering Dalian University of Technology Dalian, 116024, China Fax: +86-411-84708460 Email:
[email protected] Abstract Real geometric structures of randomly packed beds are modeled using discrete element software LIGGGHTS. The pore scale computational region are screened and chosen with non-extreme local distortion, porosity and other structural parameters, and in this region the distribution of spherical walls of pellets are representative and typical. Wall-Adapting Local Eddy-Viscosity (WALE) model and EBU-Arrhenius combustion model are used to simulate ignition process in a closed cavity and the calculated results are compared with the direct simulation results. It shows that turbulence model and combustion model used in this work are basically reasonable. Then the propagation of the Hydrogen-Air premixed flame and the interaction of flame with turbulence in the porous and non-porous structures during ignition process are simulated and analyzed. Results show that the temperature propagating velocity in the porous structure is higher than that in the non-porous one, and the porous structure can make the temperature field more uniform; in porous structure, at initial ignition stage temperature gradient is relatively high, and at the following time points, the top temperature gradients gradually decline and keep stable, and the distances between adjacent temperature gradient tops have no obvious changes with passage of time, and the flame propagation is faster in the porous structure. In the region near the ignition point, the vorticity in the porous structure is lower than that in the non-porous structure, in the region away from the ignition point, the vorticity in the porous structure is higher. In addition, the interaction of the flame and turbulence is quantitatively described by the Karlovitz number, and the flame regimes at different time are identified. Results show that the ignition process in porous structure experiences two turbulent flame regimes: corrugated flamelets regime and thin reaction regime, and mainly in the thin reaction zone; in the non-porous structure two turbulent flame regimes are experienced too, thin reaction regime and corrugated flamelets regime, and mainly in corrugated flamelets zone.
Keywords: Randomly packed beds; Real geometric structures; Karlovitz number; flame modals; interaction of the flame and turbulence 1. Introduction
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In recent years, with the deepening awareness of technology of combustion in porous media, some scholars have tried to use this technology to the gas turbine, internal combustion engine and the production of fuel cell1-5. In the study of combustion in porous media, the premixed flame research plays an important role. The investigation on premixed flame in porous media can be traced back to the bringing forward of the concept of super enthalpy flame6, and great achievements have been made in theoretical, experimental7-9 and numerical10-12 research of low-velocity (or laminar) filtration premixed combustion literature13-21 made comprehensive review of this type of combustion, compared with the low-velocity filtration premixed combustion. At present, study on high-velocity (or turbulent) premixed filtration combustion is scarce. According to theoretical analysis, Lim and Matthews22 proposed a single equation k-epsilon model based on the fact that the maximum turbulent eddy scale is confined to pores scale, the model assumes that the main effect of the turbulence in porous media is to improve the transport property of scalar in the pore. Based on the experimental data, Dobrego and Chornyi23 presented a theoretical analysis of the similarity between turbulent premixed combustion and turbulent filtered premixed combustion. De Lemos24, 25 applied the double decomposition method to the construction of turbulent filtration combustion model, and obtained an expression for the fuel consumption rate in the turbulent premixed combustion model, by spatial filtering and time averaging the single-step overall reaction mechanism of methane. Theoretical analysis and numerical simulation of adiabatic premixed flame in porous media were carried out by Pereira et al.26-28. Based on the asymptotic solutions of adiabatic premixed combustion by Pereira, Kokubun et al.29 analyzed the effects of the stretch ratio on temperature and combustibility of extremely lean flames under low equivalence ratio impinging jet condition. The results showed that, when the porosity and the heat loss are low, and the interphase heat transfer is stronger, compared with the flat flame, the slight stretching of the flame is more helpful to improve the stability of the flame. Okuyama et al.30 used the high-speed photography to measure the characteristics of flame in the packed bed under high pressure (0.1~1 MPa), obtained empirical relationships between flame speed and pressure, diameter of pellets, coherent anti-Stokes Raman spectra (CARS) has been used to measure the temperature and concentration distribution of methane-air premixed flame in porous structure under different velocity (5~130 cm/s) by Weikl et al.31, the experimental results showed that when the equivalence ratio equal to 1 the thickness of the premixed flame (about 5.5mm) is larger than the average pore size (4.23 mm). From the above literature it can be noticed that Reynolds-averaged turbulence model is mainly adopted in the research of porous medium combustion process, although this model has good applicability on calculating the macro parameters in the combustion process, but can not predict details of flame structure and propagation effectively. In recent years, the large eddy simulation(LES) of turbulent combustion has developed rapidly, and the key point is to establish turbulent combustion model and subgrid scale turbulence model suitable for small scale fluctuation. Park et al.32 used the Smagorinsky subgrid scale turbulence model and G equation flame model to simulate turbulent combustion process, and the results agree with the experimental result qualitatively, but there was a large gap between them in quantitative analysis. Charlette et al33, 34 proposed a turbulent flame velocity model under subgrid scale based on the concept of flame surface density, and the simulation was verified by DNS results. Masri et al.35 used the dynamic Germano model and the laminar flamelet model to simulate the deflagration flames by LES, and used PIV (Particle Image Velocimetry) and PLIF (planar laser induced fluorescence) to measure flame propagation velocity and flame front structure, overpressure value, and carried out a detailed comparison with simulation results, the results showed that simulation results can reflect the characteristic of actual turbulent flame. Molkov et al.36 applied LES to numerical study on the hydrogen-air premixed deflagration, used progress variable equation and turbulent premixed combustion model proposed by
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Yokhots36 to simulate the dynamic propagation characteristics of premixed flame fronts, the study found that for the deflagration in free space, the turbulence phenomena during flame propagation is mainly caused by the flame front. Based on the Charlette model, Sarli et al.37-41 presented a large eddy simulation on the methane-air deflagration in the semi closed vessels with built-in obstacles, and conducted experiments on flame flow using the PIV (Particle Image Velocimetry), numerical results were compared with the experimental results, showing that the LES results satisfactorily reflect the space and time distribution of flame shape, front, propagation velocity and overpressure and vortex field. In addition, Sarli et al.42 also carried out a large eddy simulation of the interaction between flame and turbulent vortex in turbulent premixed deflagration, and the effect of grid size on the accuracy was also discussed. M Bi et al.43 simulated the methane-air premixed deflagration in cylindrical pipe with Large Length-diameter Ratio by a LES turbulence model, and the length-diameter ratio(L/D) is 6~10.35, the results showed that the deflagration flame shape is greatly affected by the vessel wall in Large Length-diameter Ratio cylindrical pipe, the vortex behind the flame front is the main reason for the change of flame shape and propagation velocity. Gubba et al.44 and Ibrahim et al.45 carried out simulations on the propane-air premixed deflagration flame in continuous barrier container by LES, and used FSD (Flame surface density) model and DFSD (Dynamic Flame Surface Density) model to calculate the subgrid combustion rate, the simulation results showed a good agreement with the experimental results, the simulation results also showed that the overpressure, flame propagation velocity and the chemical reaction rate are directly affected by the number and distance of the obstacles. Considering the influences of transient overpressure and sudden change in temperature caused by turbulent flow and flame front on turbulent combustion rate, Xiao et al.46 conducted a large eddy simulation of hydrogen-air premixed deflagration tulip flame, used Multi-phenomena Premixed Combustion Model proposed by Ulser University, provided a effective method to further research the tulip flame formation mechanism, front, pressure wave and the interaction with turbulence. Wang et al.47 used DFSD model to simulate the development of turbulent premixed flame kernel during spark ignition process in internal combustion engine, the simulation results are in good agreement with experimental data in a certain range of ignition parameters. Based on the dynamic Smagorinsky-Lilly subgrid model and the flame surface density combustion model proposed by Boger48, Johansen et al.49 researched the acceleration process of methane-air premixed flame at the initial deflagration stage in 3-D barrier pipe, and predicted the process of deflagration flame transiting from laminar to turbulent in the Thin Reaction Zone. Through the above literature survey we can seen that it is rare to investigate the combustion process in real geometry packed beds by LES method. There are great differences between real packed beds and ordered ones, and with the LES method the evolution and distribution of flame surface in the complex space can be calculated correctly and described clearly. Moreover, numerical simulation and analysis on the combustion characteristics and turbulence-flame interaction in the pore-scale computational domain of random packed beds is one of the most challenging tasks in the combustion area, and to the best knowledge of the authors there is no relevant research has been yet reported in the literature in this respect. Therefore, the objective of this work is to construct a model for the real geometries of packed beds and use turbulence and combustion model to predict temperature and vorticity distribution, flame surface and modals evolution, flame-turbulence interaction in porous structure, and compare them with non-porous structure. The focus of this work is put on the simulation and analysis of the premixed combustion process in the porous and non-porous structure with Wall-Adapting Local Eddy-Viscosity (WALE) model and EBU-Arrhenius combustion model. To examine the accuracy of the structure model, turbulence model and combustion model used in this method, the computed local porosity, the flame shape features in each period and maximum heat flux are compared with experimental and DNS data. Then we have screened and chosen the pore scale computational region with non extreme local distortion, porosity and other structural parameters in which the
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distribution of spherical walls are representative and typical. Moreover, the changing of temperature, temperature gradient, vorticity distributions and flame surface in the porous structure with time are investigated, and compared with non-porous structure. Moreover, by the Karlovitz number propsed by Pitsch et al50. for the large eddy simulation of premixed turbulent combustion, the interaction of the flame and turbulence is quantitatively described, and in the turbulent flame regime diagram improved by Pitsch et al50, the flame regimes at different time in porous and non-porous structures are identified. 2. Physical models and computational method 2.1. Geometrical and Physical Models In this paper, we used the discrete element software LIGGGHTS51 to built a geometrical model for randomly packed beds and due to the ultra-realistic for packing process in our code, the model is much close to the actual packing structure in nature. During the stacking process, a cluster of particles are initially randomly located at the top of the packed zone and allowed to fall down under the gravity. In addition, the density, surface roughness, hardness and other particle characteristic parameters should be given in the program, and are consistent with the real material of the pellets. Based on the type of the spheres, a series of collision formulas considering various interactions and forces are selected. The trajectory and the position of each pellet after collision are calculated through the stochastic statistical equations51. At last, after a pellet has dropped down and collisions are completed, different from example outlined by V. Frishfelds52 the position with the lowest local potential energy will be selected as its final position, this step in practice is equivalent to compact pellets after packing. By above procedure, a randomly formed packed structure with 3mm radius of pellets are shown in Figure 1.
(a)
(c)
Fig.1. Computational domain: (a) structured packed bed (b) Local non-porous structure (c) Local porous structure
In this work, the development of hydrogen combustion in the meso-scale computational domain with porous and non-porous structure is simulated by a LES model, the physical models are displayed in figure 2. In order to further analyze the details of flame propagation at the early stages of combustion, and save the calculation time of LES, a spherical closed cavity with a radius of 10mm is considered as the computational field of non-porous structure case(figure 1(b)), in the case with porous structure, we cut the spherical cavity
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with the same radius from the packed bed and obtained the computational field (figure 1(c)). For initial conditions, the preheating temperature, the wall temperature, the equivalence ratio and the initial pressure are set to 700 K, 450 K, 1.0 and 0.1 MPa, respectively, and a spherical high temperature region in the geometric center is used to ignition, can obtain the ignition source in close to the quasi-laminar state. The initial distribution of species is assumed to be uniform. For the boundary conditions, isothermal and no-slip conditions given by the Navier–Stokes characteristic boundary condition (NSCBC)53,54 are imposed on the walls and the wall surfaces are supposed to be chemically inert. Boundary conditions for all species mass fractions are the Neumann ones, i.e. zero gradients. 2.2. Computational method In this method, the temperature in the reaction region changed violently, the gas in the computational domain should be regarded as ideal gas, and the thermal radiation and heat conduction within the solid particles are not considered, because of that the reaction time of this research is on 10-4s scale, in such a short time, we neglected heat exchange with solid. In general, LES control equations of compressible turbulent flow can be obtained by filtering the N-S and other equations, however, by the direct filtration of compressible N-S equations, very complex resolved scale turbulence equations will be produced, so in this work, we used the Favre filtering method to obtain the compressible LES control equations: The Soret effect, the Dufour effect and pressure gradient diffusion are assumed to be negligible. The detailed kinetic mechanism55 including 6 reactive species (H2, O2, O, H, OH and H2O) and 7 elementary reactions is used for the hydrogen-air reaction.
∂ρ ∂ ( ρ u%i ) + =0 ∂t ∂xi ∂ ( ρ u%i ) ∂ ( ρ u%i u% j ) ∂ ∂p ∂σ% ij + −2 + µSGS S%ij = − ∂t ∂x j ∂x j ∂xi ∂x j
( ) + ∂ ( ρ u% h% ) −
∂ ρ h%
i
∂ µ SGS CP ∂T% ∂ ∂T% = λ + ωT ∂x j PrSGS ∂xi ∂xi ∂xi
∂t
∂x j
∂ ρ Y%C
) + ∂ ( ρ u% Y% ) −
(
∂t
i C
∂x j
∂ ∂x j
µ SGS ∂Y%C ∂ ∂Y%C = ρD + RC ∂xi ScSGS ∂x j ∂xi p = ρ RT%
(1)
(2)
(3)
(4) (5)
u x where, ρ , P, T, t and i are density, pressure, temperature, time and velocity in i direction, i is rectangular coordinate parameter,
σ ij
is viscous stress tensor, h is enthalpy,
λ is thermal conductivity, ωT is the chemical
reaction heat, RC is the burning rate of chemical species C, D is diffusion coefficient, superscript "-" and "~" represent physical space filtering and Favre filtering, respectively. The Subgrid stress, subgrid species flux and subgrid enthalpy flux are closed by subgrid turbulence model, the subgrid Prandtl number PrSGS and subgrid Schmidt number ScSGS were 0.737.
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2.2.1 Subgrid stress model The Wall-Adapting Local Eddy-Viscosity (WALE) model is used to close the subgrid scale stress tensor. In the WALE model, the subgrid viscosity is defined as:
µ S G S = ρ L 2S where, the subgrid mixing length
( S ij S ij ) 5
2
2
+ ( S ijd S ijd ) 5
4
(6)
LS and Sijd are defined as:
d LS = min(κ d , CwV 1 3 ) ， Sij =
where,
( S ijd S ijd ) 3
1 2 1 ( gij + g 2ji ) − δ ij g kk2 ， g ij = ∂u i 2 3 ∂x j
κ , d and V are the Von Carmen constant, the minimum distance from the grid to the wall and grid
volumes, respectively,
Cw is the WALE constant, equal to 0.325 here.
We can see that, compared with traditional Smagorinsky-Lilly model, the WALE model is based on the square of velocity gradient tensor, so in the region close to the wall, relatively accurate results of eddy viscosity can be obtained without using a dynamic model; the other advantage over the Smagorinsky-Lilly model is that, using WALE model the value of turbulent viscosity in the case of the laminar flow is zero, which makes the calculation on the laminar flow zone properly disposed, however when using the Smagorinsky-Lilly model the turbulent viscosity in the laminar region is not zero, this is simply not true. 2.2.2 Combustion model The EBU-Arrhenius combustion model is used to determine the burning rate RC of species C :
RC = min( RCA , RCT ) where,
RCA
is the reaction rate of chemical species C in the Arrhenius reaction,
(7)
RCT
is the turbulent reaction
rate of C under the limit of chemical mixture in the eddy dissipation model, there is no need to repeat the Arrhenius reaction, and only gave the definition of eddy dissipation model: −1 RCT = min(vC′ M C Aρτ sgs min( R
where,
M C is the molar mass of species C, g/mol,
Y YR −1 ∑ P P ), vC′ M C AB ρτ sgs ) vR′ M R vC′′ M C
(8)
YP is the mass fraction of any product; YR is the mass
fraction of any reactant; A and B are empirical constants and take the values of 4 and 0.5, respectively; −1 τ sgs = 2Sij S ji
is the time scale of subgrid mixing rate, s-1; Grid and model validation 3.1. Grid independence test
Sij
is the tensor of strain rate , s-1.
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Fig.2. Sketch map of grid distribution (a) Porous structure (b) Non-porous structure
In order to solve the problem of generating hexahedral mesh in the whole computational domain, due to the high spatial distortion in the porous media, the equations are spatially discreted in the cell-vertex finite volume scheme into hexahedral cells and a small quantity of polyhedral cells, as shown in figure 2. In the LES, the diffusion under subgrid-scale was decreased with the mesh refining, and in the combustion the results of large eddy simulation vary with the mesh, with decreasing grid scale and time steps the numerical diffusion could be far less than the Reynolds average, providing results that are more accurate and closer to DNS, so the grid independence test involved in usual numerical calculation is not applicable for this method. The grid size is 0.2mm, considering that the LES has a strict demand for grids, especially near rigid walls, we used the boundary layer grid to make the y+ to meet the requirement of staying under 1 during the combustion process, in the structure of porous media the total number of grid is 281397, in non-porous medium structure grid number id 583799 (figure 2). Due to the stochastic structure, high pressure gradient appears in some regions, so the pressure was calculated by the PRESTO! algorithm, and for the mass, momentum, energy and component equations the QUICK scheme with three order accuracy was used. It was verified that a convergence criterion of residual error of 10-6, could meet the accuracy requirement. 3.2. Model verification Considering that there are no relative experimental studies yet, we verified the combustion method and structural characteristics separately, the above mentioned large eddy model and combustion model are used to simulate the ignition process under the conditions described by Yenerdag et al56, and the calculated results were comparied with the direct simulation results of Yenerdag et al56 to verify the models.
(a1)
(a2)
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(b2)
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(b3)
Fig.3. Temporal development of the flame surface for the small vessela: (a1)at the 96us, DNS, (a2)at the 150us, DNS, (a3)at the 240us, DNS, (b1)at the 96us, LES, (b2)at the 150us, LES, (b3)at the 240us, LES.
Figure 3 shows the change of flame surface with time in a cubic container, in which fig.(a1), fig.(a2) and fig(a3) are DNS results of Yenerdag et al56 at 96 us, 150us and 240us, and fig.(b1), fig.(b2) and fig(b3) are LES results in this work at the same times respectively, comparing figure 3(a1), (b1), we can see that at 96us after ignition, the flame surface become wrinkled due to expansion and effect of turbulence. From figure 3 (a2), (b2) it can be observed that, at the 150us, the flame continues to expand and contact with the top and bottom walls of constant temperature(450℃) , the shape of the flame became wide and flat; from figure 3 (a3), (b3) it can be observed that, at the 240us, due to the influence by the top and bottom low temperature walls, and also due to the reactant depletion in the container center region, the flame changes from circular flat shape into annular shape. Overall, the simulation results are consistent with direct numerical simulation(DNS) results of each period at each time points, the flame shape features also agree with the characteristics of each period, but compared with the DNS results, the flame front surface wrinkles in this simulation are coarser and the number of the wrinkles is less, this is because the grid size in this work is larger than that used in the DNS, making some subgrid scale eddies in the simulation can not be distinguished, which results in the difference in the wrinkle shape. Considering that in the simulation of this work the turbulence intensity in porous and non-porous media is relatively low, the gridsize in this simulation can meet the needs of following research.
Fig.4. The maximum wall heat flux on the lower wall as function of mean pressure
Figure 4 shows the maximum wall heat flux on the lower wall(simple maximum heat flux) changing with the mean pressure in the vessels (simple mean pressure). It can be observed that there are several differences between the results of this simulation and the DNS of Yenerdag, First, at the initial ignition stage56, in the DNS
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the value of maximum heat flux increases continuously, while the mean pressure is almost unchanged keeping at one bar pressure, while in this simulation the the mean pressure is also rising, this is because that in our simulation the combustion mechanism is more simple, and at the initial ignition stage the combustion reaction is a finite-rate reaction, so the simplified mechanism brings errors. Second, when the mean pressure ranges from 1.5atm to 3atm, the maximum heat flux is higher than that in the DNS, this is because this period is the rapid combustion period, in this period turbulence dominates the reaction, and in this method, the subgrid size of the LES is five times as large as the grid size in the DNS, this brings some errors. Third, in the region where the maximum heat flux decreased, the curve of our simulation declined steeper than the DNS, this is because this region is extinguish stage56, and the combustion models in our work is only applicable to the initial ignition stage and propagation stage, and in the later simulation, the extinguish stage is also not involved, this part of the models will be improved in future studies. In summary, the simulation results show the same general trend with the DNS, and in the propagation stage, the maximum heat flux varies linearly with the mean pressure, which agrees with the basic character described in the literature56, and the overall relative error is less than 5%, hence, the turbulence model and combustion model we used are basically reasonable under this conditions, and can be used to predict the turbulent flow and flame shape in closed cavity under similar conditions.
Fig.5 Variations of mean porosity (r=3mm)
Furthermore, in order to verify the stochastic structural model in porosity prediction, the radius of the calculation domain are divided into 100 equal parts, then 100 coaxial cylindrical sections are obtained, mean porosity inside each section is calculated, and the calculated results are compared with the experimental data in the literature57. From figure 5, we can see that the simulation results are in good agreement with the experimental data, the amplitudes of fluctuates are almost equal, relative errors were less than 6% in the whole computational domain, and the maximum error of the porosity in the calculation area is 0.056, appears at about R=24mm. The results also showed that in the region far away from cylinder wall (R
