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air combustion in a mesoscale divergent porous media combustor
international journal of hydrogen energy xxx (xxxx) xxx
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Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor Peng Qian, Minghou Liu*, Xinlong Li, Fubo Xie, Zizhen Huang, Chengyuan Luo, Xiugen Zhu Department of Thermal Science and Energy Engineering, University of Science and Technology of China (USTC), Hefei, Anhui, 230027, PR China
highlights A divergent channel is proposed to improve the performance of the MTPV system. The divergent channel promotes the blowout limit by 186%. A smaller wall thermal conductivity is recommended.
article info
abstract
Article history:
To improve flammability and radiation efficiency, a divergent porous media combustor is
Received 13 September 2019
proposed and numerically studied. The local thermal non-equilibrium model is used to
Received in revised form
consider the temperature difference between gas and solid matrix. Effects of equivalence
11 December 2019
ratio, the wall thermal conductivity, solid matrix thermal conductivity, and divergent ratio
Accepted 12 December 2019
on combustion characteristics, radiation efficiency, and flammability limits are studied.
Available online xxx
The results show that the divergent channel extends the blowout limit by 186% and obtains a maximum radiation efficiency of 29.3%, increased by 70% compared with the straight
Keywords:
channel. A smaller wall thermal conductivity is recommended considering the flamma-
Porous media combustion
bility range and radiation efficiency. A careful choice of solid matrix thermal conductivity
Micro-combustor
and the divergent ratio is suggested to balance their opposing effects on the radiation ef-
Micro thermophotovoltaic system
ficiency and the flammability.
Flammability limit
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Excess enthalpy combustion Radiation efficiency
* Corresponding author. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 445 Huangshan Road, Hefei, Anhui, 230027, PR China. E-mail addresses: [email protected] (P. Qian), [email protected] (M. Liu), [email protected] (X. Li), 15162118062@ 163.com (F. Xie), [email protected] (Z. Huang), [email protected] (C. Luo), [email protected] (X. Zhu). https://doi.org/10.1016/j.ijhydene.2019.12.094 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Introduction The fast depletion of fossil fuel and environmental pollution brings about the energy crisis, which is an urgent problem needed to be solved in the 21st century. Seeking an efficient, reliable, and compact energy source has given birth to the development of micro-/meso-power generators, one of which is the micro-/meso-thermophotovoltaic (MTPV) system [1,2]. Typical MTPV systems are driven by thermal power, especially the combustion because the energy density of hydrocarbon fuels is 20e50 times higher than the most advanced Li-ion concept based electrochemical batteries [3,4]. Compared with hydrocarbon fuels, hydrogen is the cleanest and the most promising fuel in an MTPV system driven by combustion because of its higher energy density and lower pollution. In a typical MTPV system, the combustor itself functions as the emitter [5]. However, as the combustor volume decreases, along with the increased energy density, one of the most common and salient problems is heat loss, resulting in unstable flames [6]. Various methods are proposed to achieve stable micro-/meso-scale combustion. On one hand, there has been a great effort on flame stabilization in micro-/mesocombustors including backward-facing step [7e10], wall cavity [11e13], divergent channel [14], bluff-body [15e18], catalytic combustion [19e21], non-circular channel [22], ribs [23,24], etc. Yang et al. [25] found that the divergent channel was beneficial to flame stabilization because its expanding section slows down the flow and increases the time for residence and heat transfer. On the other hand, higher temperatures and radiation efficiencies that can be obtained by heat recirculation techniques are of great value in MTPV systems [26]. A common way to implement the heat recirculation is multi-channels such as Swiss-roll combustor [27], double-channel combustor [28], four-channel combustor [29,30]. The heat recirculation through the wall was proved to be able to achieve higher wall temperatures [28] and extend flammability limits [31]. Another effective way is to insert porous media. The porous media combustion (PMC) concept was first demonstrated analytically by Takeno and Sato [32]. The results showed that inserting porous media into the flame zone enhances heat recirculation and preheats the incoming fresh gas, which leads to higher combustion temperature, wider dynamic range, and less fuel consumption. Hence, it is beneficial to integrate PMC into MTPV because of its higher temperatures as compared to free-flame combustion [33]. Research related to micro-/meso-scale PMC emerged in recent years. Li et al. [34,35] conducted experiment and simulation studies of premixed hydrogen/air combustion in a planar micro-combustor and pointed out that a porous microcombustor gives a higher wall temperature and a lower flame temperature than a free-flame counterpart. Channel height [36] and the difference between the partially and fully filled porous combustors [37] were examined by Wang et al. Bani et al. [38] combined TPV and PMC to estimate the effect of hydrogen/air equivalence ratio, effective thermal conductivity, and inlet velocity on wall temperature distribution. The experiment produced electricity power of 1.703 W. In addition, it indicated that the radiation efficiency is important in MTPV
system. Comprehensive review papers such as Refs [26,39,40] outlined the fundamentals and applications of TPV systems. The above literature review shows that there are many ways to improve the performance of the MTPV system based on the free-flame combustor. Compared with the free-flame counterpart, the PMC combustor processes higher wall temperatures, which is advantageous for the performance improvement of the MTPV system. Nonetheless, the increase of inlet velocity and the decrease of equivalence ratio or porosity lead to flame moving downstream and even blowout [35], causing uneven wall temperatures, low radiation efficiencies, and narrow flammability range. Therefore, the flame stabilization is imperative in the MTPV system based on PMC in order to take advantage of the higher wall temperatures. So far as the authors know, little research devotes to improve radiation efficiency and to extend flammability by varying channel cross-section areas in the PMC field, whereas it functions in the free-flame counterpart [14,25]. In the present work, a planar divergent channel is proposed to address the problem of narrow flammability range and low radiation efficiency in the straight channel, inspired by successful implements in the field of free-flame combustors. The planar configuration is adopted since it is more suitable for thermophotovoltaic cells array than tubes [41]. Hydrogen/air mixture is the fuel because of high heat value and low pollution. Effects of equivalence ratio, inlet velocity, wall thermal conductivity, solid matrix thermal conductivity, and divergent ratio on radiation efficiency and flammability limits are studied. Also, the combustion characteristics of porous media combustion in the divergent channel are investigated. This work develops a numerical method to accurately simulate the flame characteristics and to predict radiation efficiency for a better understanding of porous media combustion in the divergent channel, benefiting the design of future MTPV systems.
Physical and numerical modeling Physical model The geometric model adopted in the present study is shown schematically in Fig. 1. The combustor is mainly featured by a channel filled with inert porous media (steel mesh). The total length (L) of this channel is 21 mm. The height of the inlet and outlet are Hin (1 mm) and Hout (4 mm) respectively. A solid region with a thickness (t) of 0.5 mm is wrapped around porous media to form a divergent channel. Flange with a thickness of 0.5 mm and a height of 6.5 mm to connect other components in the experiment is also considered in numerical simulation. This similar configuration is adopted from Ref. [35] and the experiment results from Ref. [35] are compared with the simulation results in this paper. Premixed hydrogen/air is introduced into the channel and ignited inside the channel to release chemical energy. Part of the released heat is emitted through the combustor wall by radiation and convection. The rest of the heat is lost with the exhaust. Additional properties of the inert porous media are provided in Table 1.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Fig. 1 e Physical model. where p is the pressure of the gas mixture and m is the viscosity. Energy equation in the wall solid zone:
Table 1 e Properties of applied porous media. Property Fiber width (ds) Characteristic path length of the light quantum (l0) Emissivity of the solid matrix (εs ) Solid matrix conductivity (ks)
Unit
Value
m m
1.14 10e4 l0 ¼ εds =ð1 εÞ
e W/m$K
0.8 15
Governing equations Combustion is a complex phenomenon coupled with fluid flow, chemical reaction, and heat transfer. The following assumptions are adopted to simplify calculations. (1) The porous media combustor is symmetric and a 2D laminar steady model is applied. The aspect ratio of 10 is also adopted in the experiment [34,35], which indicates 2D symmetric treatment is reasonable [15,42]. A simple computation revealed that the flow remains laminar for inlet velocities of up to 21 m/s [43]. The maximum inlet velocity in the present study is 20 m/s; (2) Gas radiation is not considered. Radiation between solid porous matrix is considered by effective thermal conductivity [44,45]; (3) Catalytic effects are negligible [46]; (4) The flow speed is sufficiently low that the gas mixture is incompressible [46]; Governing equations are expressed as follows by applying the above assumptions. Continuity equation: v ¼0 V , εrg !
mixture. rg is the density of the gas mixture. Momentum equation:
(3)
where kw and Tw is the thermal conductivity and the temperature of the wall, respectively. The local thermal equilibrium (LTE) model [34,38,43] is the most convenient model and widely used in the study of porous media combustion to simulate the temperature field. However, it is not quite accurate due to the neglect of the heat transfer between gas and solid matrix. In the present study, the local thermal non-equilibrium (LTNE) model is adopted as shown in Eq. (4) and Eq. (5). Energy equation in the gas phase: X X ! v Tg þ rg εYi V i cg VTg ¼ εV , kg VTg ε ui hi Wi V , εcg rg ! þ hv Ts Tg
i
i
(4)
where cg is the heat capacity of the gas mixture. kg is the gas mixture thermal conductivity. Tg is the gas mixture temperature. hi is the enthalpy of species i. Di;m is the mass diffusivity of species i. Yi is the mass fraction of species i. ui is the molar production rate of species i. Wi is the relative molecular mass of species i. Energy equation in the porous solid matrix phase: V , ks;eff VTs þ hv Tg Ts ¼ 0
where kg is the thermal conductivity of the gas mixture. Ts is
hv ¼
2ð1 εÞNukg 2
ds
Nu ¼ 1 þ
4ð1 εÞ 1 þ ð1 εÞ0:5 Re0:6 Pr1=3 ε 2
(6)
And the effective thermal conductivity of solid matrix ks;eff considering solid-solid radiation is expressed as [48]: ks;eff ¼ ð1 εÞks þ krad
(2)
(5)
the solid matrix temperature. The volumetric heat transfer coefficient hv coupling the gas and solid matrix energy equations is determined by Ref. [47]:
(1)
where ε represents the porosity of porous media and it is 0.6 in the following investigation except for the grid independence and data validation section. ! v is the velocity vector of the gas
vÞ V , εrg ! v! v ¼ εVp þ mV2 ðε!
V , ðkw VTw Þ ¼ 0
krad ¼
16sεs l0 T3s 3
(7)
Species transport equation:
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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! V , εrg ! v Yi ¼ V, εrg VYi V i þ εui Wi
Solution method (8)
! where Yi is the local mass fraction of species i. V i is the diffusion velocity [46]. The k th chemical reaction is of the general form: i X
0
vik xi 4
i¼1
i X
00
vik xi
(9)
i¼1
where xi is symbol denoting species i. The molar production rate of species i is: ! i i i Y Y X 00 0 h0ik h0 0ik ui ¼ ½xi krk ½xi vik vik kfk i¼1
i¼1
(10)
i¼1
The forward and backward rate constants are: Ei kfk ¼ Ai Tbgk exp Rc Tg
(11)
Er br krk ¼ Ari Tgi exp i Rc Tg
(12)
A CHEMKIN mechanism comprising 10 species and 21 elementary reversible reactions [49] is applied in the present study to simulate the gas-phase reaction. This CHEMKIN format mechanism and related thermophysical data provide preexponential factor (Ai ), temperature exponent (bk ), activation energy (Ei ), rate exponent (h0ik , h}ik ), stoichiometric coefficient (n0ik , n}ik ) for the calculation of the forward rate constant, the backward constant and the molar production rate of certain species. All the variables in governing equations are SI units.
The above equations are implemented using the software Fluent 6.3. The SIMPLE algorithm [52] was adopted to solve the pressure-velocity coupling momentum equation. UDFs (User Defined Functions) are utilized to represent the volumetric convective heat transfer coefficient (hv, Eq. (6)) and the effective thermal conductivity (ks,eff, Eq. (7)) in the LTNE model (Eq. (4)(5)). A UDS (User Defined Scalar) is used to consider the energy equation (Eq. (5)) for the solid porous matrix. The finite volume method (FVM) is used to discretize the governing equations. During the iterative calculation, the convergence criterion of the energy equation is 106, and the convergence criterion of other equations is 103. The initial temperature in the porous media region is set to 1600 K in order to ignite combustion.
Grid independence and data validation To demonstrate the numerical algorithm reliability and validity, a detailed grid independence test and data validation are carried out. The mesh independence test is examined by dividing the computation region into uniform finite volume elements. To this end, four sets of meshes are chosen to inspect grid independence. The equivalence ratio and porosity
Boundary conditions At the inlet (x ¼ 0), the uniform velocity profile is set because the difference introduced by the uniform and fully developed velocity profile was proved to be insignificant and can be neglected [50]. The gas mixture temperature is 300 K while the mass fraction of hydrogen and air are prescribed according to equivalence ratio. vx ¼ vin ; vy ¼ 0; Yi ¼ Yi;in ; Tg ¼ Tin ¼ 300K
(13)
At the outlet (x ¼ 21 mm), the pressure outlet condition [35] is applied. A fixed atmospheric pressure (pa ¼ 101325 Pa) is set to the outlet. vT vv vYi ¼ 0; ¼ 0; ¼ 0; p ¼ pa vx vx vx
(14)
On the outer wall: qw ¼ hc ðTw Ta Þ þ εw s T4w T4a
(15)
where Ta is the ambient temperature (300 K). Heat loss through radiation and convection at the outer wall are taken into account. The emissivity of the wall is estimated to be εw ¼ 0.9. s ¼ 5.67 108W/m2$K4 is the Stefan-Boltzmann constant. hc is the natural convective heat transfer coefficient and is estimated to be 15 W/m2$K according to Ref. [51]. In addition, the velocity slip at the gas-wall interface was found to be negligible [50]. Therefore, a non-slip boundary condition is considered for the gas-wall interface.
Fig. 2 e Grid independence, (a) gas temperature, (b) solid matrix and outer wall temperature.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 3 e Mesh pattern.
of these tests are 0.8 and 0.88, respectively, which is the same as Ref [35]. The results are shown in Fig. 2. Gas temperature, solid temperature along the symmetry axis and outer wall temperature distribution are the criterion to identify reasonable mesh. As can be seen from Figs. 2 and 58500 cells (solid lines in Fig. 2) are adequate enough to represent combustion inside the porous media while more cells do not introduce any significant difference in terms of temperature distribution. The mesh pattern is shown in Fig. 3. The wall region is divided into 25000 elements. The flange region is divided into 7250 elements and the porous region is divided into 26250 elements. The outer wall temperature distribution is compared with experimental results from Ref. [35]. As is shown in Fig. 4 The maximum relative error is smaller than 5% and simulation results follow the same trend as the experiment results, which confirm the data validity of the simulation. In summary, the present numerical algorithm and boundary conditions are reasonable to simulate porous media combustion.
Fig. 4 e Wall temperature of simulation and experiment.
5
Fig. 5 e Gas and solid matrix temperature distribution along the axis of symmetry.
Results and discussion Excess enthalpy combustion PMC is characterized by excess enthalpy combustion. In this section, PMC inside the divergent channel and the straight channel are investigated to identify excess enthalpy combustion. Gas and solid temperature distribution along the axis of symmetry are obtained and plotted in Fig. 5. In the divergent and the straight channel, kw ¼ ks ¼ 15 W/m$K, ε ¼ 0.6, f ¼ 0.6, vin ¼ 3 m/s. The porous media channel is divided into the preheat region, where gas temperature is higher than solid temperature, and the combustion region, where gas temperature is lower than solid temperature. The heat released from the combustion region recirculated to the preheat region by conduction and radiation to preheat the gas mixture. The inter-phase thermal non-equilibrium is responsible for the excess enthalpy combustion and heat recirculation [53], which is not represented by the LTE model. Hence, the LTNE model is applied for the nature of porous media combustion and heat recirculation analysis in the following sections. Additionally, it was shown that the LTNE model can predict the essential features including burning velocity and temperature distribution [46] of the flames. The temperature difference between solid and gas is also represented in Fig. 5. The adiabatic flame temperature of hydrogen/air mixture with an equivalence ratio of 0.6 is 1800 K [54]. Excess enthalpy combustion is the combustion of which the maximum flame temperature is higher than the adiabatic flame temperature. It can be seen from Fig. 5 that the maximum temperature of the gas mixture is slightly lower than the adiabatic flame temperature because of non-adiabatic wall boundary conditions, which indicates that excess enthalpy combustion does not take place. The mean wall temperature of the divergent channel (980 K) is 28.6% higher than that of the straight channel (762 K), which is the reason for the higher radiation efficiency of the divergent channel under vin ¼ 3 m/s in Fig. 14. It is worth noticing that the temperature difference between gas and solid near the inlet region is larger in divergent
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Fig. 6 e Combustion regions, EECR (excess enthalpy combustion regime) and RCR (regular combustion regime).
channel than that in straight channel. The reason is that the flame front is near the inlet in divergent channel, preheating inlet gas mixture effectively. Combustion situations of f ¼ 0.4,0.6,0.8 in the divergent channel are inspected and divided into two regimesdexcess enthalpy combustion regime (EECR) and regular combustion regime (RCR), according to the difference between the maximum combustion temperature and the adiabatic flame temperature. The results are shown in Fig. 6. Each pentagram in Fig. 6 represents the condition of a certain equivalence ratio and inlet velocity. It can be seen that all situations of f ¼ 0.8 are not the excess enthalpy combustion and all situations of f ¼ 0.4 are the excess enthalpy combustion. For f ¼ 0.6, the excess enthalpy combustion takes place when the inlet velocity is higher than 5 m/s. In order to disclose the reason for this observation, heat loss ratio (hloss ), preheat efficiency (hpre ), and net heat recirculation efficiency (hnet ) are defined to quantify the heat recirculation: Ph hloss ¼
i
Fig. 7 e Effects of equivalence ratio and inlet velocity on the net heat recirculation efficiency.
enthalpy combustion cannot exist under a high equivalence ratio (f ¼ 0.8, Fig. 6) and happens when equivalence ratio is smaller (f ¼ 0.4 and f ¼ 0.6, Fig. 6) or inlet velocity is higher (vin 5 m/s under f ¼ 0.6, Fig. 6).
Fundamental flame characteristics: flame position and burning velocity Flame position along the axis of symmetry is determined at the position where the mass fraction of H radical is the largest. Stabilization of the flame front occurs when the superficial gas velocity vs ¼ εv equals the burning velocity Sp in the porous medium [55], where ε is the macroscopic porosity and v is the gas-phase velocity. Burning velocities of different operating conditions are identified according to this definition. In this paper, the burning velocities are evaluated at the symmetry axis.
i εw s T4w;i T4a;i þ hc Tw;i Ta;i DSi
Prec ¼ hpre ¼ Pth
m_ fuel LHV
(16)
P hv;i DVi Ts;i Tg;i i
hnet ¼ hpre hloss
m_ fuel LHV
(17)
(18)
where DSi is the surface area of the meshed surface unit. LHV is the lower heat value of hydrogen gas (1.2 108 J/kg). Preheat efficiency (hpre ) is the ratio of total heat recirculated (Prec ) to the preheat region and thermal power input (Pth ). i is the indicator of the meshed cell. hv;i is the volumetric heat transfer coefficient of the meshed cell i. DVi is the volume of the meshed cell i. Ts;i and Tg;i are the solid matrix and gas temperature of the meshed cell i. m_ fuel is the mass flow rate of hydrogen gas. It can be seen from Fig. 7 that the net heat recirculation efficiency decreases with the increase of equivalence ratio but increases against the inlet velocity, which is the reason why the excess
Fig. 8 e Effects of inlet velocity and equivalence ratio on the flame position.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 8 shows the effects of equivalence ratio on the flame position versus inlet velocity. It indicates that PMC for f ¼ 0.8 has the widest flammability range while it is the least narrow for f ¼ 0.4. Self-sustain combustion can exist even under the inlet velocity as low as 0.5 m/s. The lowest inlet velocity is a little higher than the one obtained (~0.2 m/s) by Li et al. [35], which can be attributed to the porosity difference between the present study and the latter. This comparison indicates that the extinction limit can be reduced by the increase of porosity. As shown in Fig. 8, a higher inlet velocity makes flame stabilize downstream while a larger equivalence ratio makes flame stabilize upstream, which confirms the findings of Refs. [35,46]. In fact, higher inlet velocities lead to higher advection velocities that move flame downstream [35]. As for the effect of equivalence ratio, for instance, the mixture with f ¼ 0.4 gives downstream flame position due to its higher ignition temperature and less heat release [34]. The effects of inlet velocity and equivalence ratio on the burning velocity are illustrated in Fig. 9. The burning velocity increases with the increase of inlet velocity and equivalence ratio. Li et al. [34] attributed the reason for this observation to chemical kinetics. In other words, a higher inlet velocity or equivalence ratio means more thermal power input and more heat release, resulting in a higher flame temperature that increases the burning velocity of the mixture according to the Arrhenius equation (Eq. (11)).
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Fig. 10 e Flammability limits. blowout limits are identified for f ¼ 0.4,0.6,0.8. As shown in Fig. 10, it is obvious that the stable combustion region of the divergent channel is much wider than that of the straight channel. As for f ¼ 0.6 and f ¼ 0.8, the blowout limits are significantly extended by 167% and 186% respectively compared with the divergent channel while the extinction
Flammability limits One particular advantage of PMC is the extended flammability limits compared with free-flame combustion. Terminologically, for certain equivalence ratio, flammability limits consist of two limits, the extinction limit, which means gas mixture could not react under low velocities, and the blowout limit, which shows that inlet velocity is such high that flame would be blown out of the combustor [56]. Flammability range or stable combustion region is the distance between those two limits. A comparison between the traditional straight channel and the divergent channel is made. Extinction limits and
Fig. 9 e Effects of inlet velocity and equivalence ratio on the burning velocity.
Fig. 11 e (a) Velocity magnitude along the symmetry axis, (b) contour of radical H in the straight porous media channel, (c) contour of radical H in the divergent porous media channel (half of the channel is shown).
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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limits of these two channels remain almost the same. It is worth mentioning that combustion cannot be maintained for the straight channel when f ¼ 0.4. The preheat efficiency and the flow field provide some insight into the extended blowout limits. Taking the case of f ¼ 0.6 vin ¼ 3 m/s for example, Pth ¼ 3787 W, Prec ¼ 1423 W, hpre ¼ 37.6% when the channel is straight and Pth ¼ 3787 W, Prec ¼ 1694 W, hpre ¼ 44.7% when the channel is divergent. It can be concluded from the above computation that the divergent channel extends blowout limits through improving the preheat efficiency. The distribution of velocity magnitude along the symmetry axis and radical H contours when f ¼ 0.6 vin ¼ 3 m/s are illustrated in Fig. 11. Radical H can be seen as an indicator of the flame front [57]. Fig. 11a shows that the flame inside porous media stabilizes at the position where the velocity gradient is the largest while divergent channel makes this position closer to the inlet, which illustrates that divergent channel is able to sustain combustion under higher inlet velocities as compared to the straight channel. As can be seen from Fig. 11b and c, the flame has a reversed “C” shape, which is the same as the flame shape in a typical free-flame microchannel [25,58]. However, the flame is “C” shape [59] in a micro-fibrous porous media tube with a diameter of 8 mm and our previous study [60] showed that the flame is flat in 20 mm macro-channel filled with alumina foams under adiabatic conditions. It may be concluded that the flame shape is related to length scale and thermal conditions, which requires further investigation in the future. In the divergent channel, the flame is flatter near the symmetric axis than the one inside the straight channel due to more uniform velocity distribution along the y-direction. The effects of the wall and solid matrix thermal conductivity on flammability limits are investigated. Dolomite (kw ¼ 1.75 W/m$K), steel (kw ¼ 15 W/m$K), and aluminum (kw ¼ 202 W/m$K) are selected to make a comparison among different wall thermal conductivities. Steel (ks ¼ 15 W/m$K), nickel (ks ¼ 97.7 W/m$K), and aluminum (ks ¼ 202 W/m$K) are selected to observe the effect of solid matrix thermal
Fig. 12 e Effects of equivalence ratio on the radiation efficiency.
conductivity on the flammability limits. The results are shown in Table 2 and Table 3. It can be seen from Table 2 that the wall thermal conductivity has little influence on blowout limits while a large wall thermal conductivity narrows flammability
Table 2 e Effect of wall thermal conductivity on flammability limits (ks ¼ 15 W/m·K, f ¼ 0.6). Wall thermal conductivity (W/m$K) 1.75 15 202
Extinction limit (m/s)
Blowout limit (m/s)
1 1 2
8 8 8
Table 3 e Effect of solid matrix thermal conductivity on flammability limits (kw ¼ 15 W/m·K, f ¼ 0.6). Solid matrix thermal conductivity (W/m$K) 15 97.7 202
Extinction limit (m/s)
Blowout limit (m/s)
1 2 3
8 16 20
Fig. 13 e Effects of (a) wall thermal conductivity and (b) solid matrix conductivity on the radiation efficiency.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
range in terms of extinction limits. Wang et al. [37] pointed out that the flame extinction is mainly dependent on the heat loss from the flame root that increases with the increase of wall thermal conductivity and decreases with the increase of inlet velocity. As a consequence, the extinction limit under a higher wall thermal conductivity is increased. Table 3 illustrates that both the extinction and blowout limits increase with the increase of solid matrix thermal conductivity. Meanwhile, the flammability range becomes wider. In fact, the preheat efficiency increases when solid matrix thermal conductivity increases [35]. Increased solid matrix thermal conductivity leads to the increase of effective thermal conductivity (ks;eff ) that enhances heat exchange between gas and solid in the preheat region, which promotes flammability.
Radiation efficiency Radiation efficiency is an important parameter and is widely applied to characterize the performance of MTPV systems [22,61e64]. Here, in the present investigation, the radiation efficiency is defined as the ratio of the wall radiation power (Prad ) and thermal power input (Pth ), which can be expressed as follows. Prad ¼ hrad ¼ Pth
P εw sT4w;i DSi i
m_ fuel LHV
(19)
where DSi is the meshed unit surface area of the wall. The effects of equivalence ratio, thermal conductivity, inlet velocity, and geometry configuration on the radiation efficiency are studied in detail. Fig. 12 shows the radiation efficiency of different inlet velocities when f ¼ 0.4,0.6,0.8. It can be found that f ¼ 0.4 has the
9
lowest radiation efficiency and the radiation efficiency decreases due to the fact that flame stabilizes downstream when inlet velocity is increased, which is shown in Fig. 8. As for f ¼ 0.6 and f ¼ 0.8, the radiation efficiency undertakes a slight increase before decrease while inlet velocity is increasing. The reason for the slight increase is that the flame stabilizes near the inlet and a large amount of heat is lost by the radiation through the flange when inlet velocity is slow. Overall, the radiation efficiency increases with the decrease of inlet velocity or the increase of equivalence ratio and the maximum radiation efficiency (25.6%) is achieved when f ¼ 0.8, vin ¼ 4 m/ s. Similarly, Pan et al. [45] and Bani et al. [38] pointed out that the radiation efficiency is the maximum when f ¼ 0.8 while the temperature of the wall is the highest with f ¼ 1.0 in the straight channel. The effects of the wall and solid matrix thermal conductivity on the radiation efficiency are shown in Fig. 13. It is obvious that the radiation efficiency is significantly affected by the flange when inlet velocity is lower than 3 m/s. From Fig. 13a, it can be found that increased wall thermal conductivity has a negative effect on the radiation efficiency. In fact, flame temperature decreases with increased wall thermal conductivity because more heat is lost by the flange. Thus, less heat radiates through the emitter wall. Combining the results in Table 2 and Fig. 13, it can be concluded that increased wall thermal conductivity decreases the radiation efficiency and flammability range. Therefore, a smaller wall thermal conductivity is preferred in design. For instance, the maximum radiation efficiency can be further increased from 25.4% to 29.2% when the wall thermal conductivity is decreased from 15 W/m$K to 1.75 W/m$K. The increase of solid matrix thermal conductivity increases the heat loss from flame and decreases flame
Fig. 14 e Effect of the divergence ratio on the radiation efficiency. Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Table 4 e Effect of the divergence ratio on the flammability limits. Divergent ratio Extinction limit (m/s) Blowout limit (m/s) 1 2 3 4
2 2 2 1
3 5 7 8
temperature [35]. For this reason, the radiation efficiency decreases when solid matrix thermal conductivity increases, which can be seen from Fig. 13b. When inlet velocity surpasses 5 m/s, the radiation efficiency of ks ¼ 15 W/m$K decreases sharply because the flame stabilizes near the outlet. However, increased solid matrix thermal conductivity improves flammability. As a result, there is a trade-off between the radiation efficiency and flammability range considering the implement of solid matrix thermal conductivity. The effect of geometry configuration is studied in terms of the divergence ratio (DR), which is defined as the ratio of the height of inlet (Hinlet ≡ 1 mm) and outlet (Houtlet ). DR ¼
Houtlet Hinlet
(20)
The results are shown in Fig. 14 and Table 4. It is obvious that the radiation efficiency decreases with the increase of DR. An increased DR brings about a wider flammability range and a lower radiation efficiency. For DR ¼ 1 vin ¼ 3 m/s, DR ¼ 2 vin ¼ 5 m/s, and DR ¼ 3 vin ¼ 6 m/s, 7 m/s, the radiation efficiency is extremely low because the flame stabilizes near the outlet. It can be seen from the contours in Fig. 14 that flame stabilizes upstream with the increase of DR. This is the reason why increased DR widens flammability range, as listed in Table 4. Compared with the straight channel (DR ¼ 1), the divergent channel (DR ¼ 2) obtains a maximum radiation efficiency of 29.3%, increased by 70% when vin ¼ 3 m/s. Overall, the divergent channel shows better performance considering the flammability range. However, a large DR makes flame stabilize upstream, leading to more heat losses through the flange. As a result, the maximum radiation efficiency drops from 29.3% to 25.4% when the DR is increased from 2 to 4. Therefore, a trade-off between the flammability range and the radiation efficiency must be made to determine a desired DR. Moreover, Li et al. [65] mentioned that only the photons with energy higher than the material band-gap are useful for the TPV converter. A common way is to make an estimated PV cell efficiency (constant, 15.4%) [11,66,67]. A more detailed estimation would be the one that considers the unique absorption characteristic (external quantum efficiency, etc. [40]) of a certain PV cell regarding the radiation spectrum of the emitter, which could be a future investigation topic.
Conclusions The present study proposed a divergent channel configuration to stabilize flame and to improve radiation efficiency. Premixed hydrogen/air combustion in porous media was numerically studied to manifest the proposed method. The numerical model was well validated by comparison with the
experimental data of measured wall temperature. Excess enthalpy combustion, flame position, burning velocity, flammability limit, geometry configuration, and radiation efficiency were investigated. The following conclusions can be drawn from the present investigation. (1) It is found that the equivalence ratio and inlet velocity determine the excess enthalpy combustion by changing the net heat recirculation efficiency. The excess enthalpy combustion is hard to maintain under a high equivalence ratio of 0.8; (2) A high inlet velocity makes flame stabilize downstream and a larger equivalence ratio makes flame stabilize upstream. Burning velocity increases with the increase of inlet velocity or equivalence ratio; (3) The divergent channel extends the blowout limit by 167% and 186% when f ¼ 0.6 and f ¼ 0.8 compared with the straight channel because of the enhanced preheat effect and the flow field. (4) The radiation efficiency of the divergent channel increases with the increase of equivalence ratio within 0.4e0.8, which is consistent with the experimental result in the straight channel; (5) There is a trade-off between the radiation efficiency and flammability range considering the implement of solid matrix thermal conductivity or the divergent ratio (DR). A larger solid matrix thermal conductivity or DR decreases radiation efficiency but extends flammability range significantly. On the other hand, a smaller wall thermal conductivity is preferred concerning the flammability range and radiation efficiency. The maximum radiation efficiency obtained in the divergent channel (DR ¼ 2) is 29.3%, increased by 70% than that in the straight channel.
Acknowledgments This work was supported by the National Key R&D Program of China [2018YFB1900602] and the National Natural Science Foundation of China [NSFC Grant No.11372302] and the Supercomputing Center of University of Science and Technology of China.
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Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor Peng Qian, Minghou Liu*, Xinlong Li, Fubo Xie, Zizhen Huang, Chengyuan Luo, Xiugen Zhu Department of Thermal Science and Energy Engineering, University of Science and Technology of China (USTC), Hefei, Anhui, 230027, PR China
highlights A divergent channel is proposed to improve the performance of the MTPV system. The divergent channel promotes the blowout limit by 186%. A smaller wall thermal conductivity is recommended.
article info
abstract
Article history:
To improve flammability and radiation efficiency, a divergent porous media combustor is
Received 13 September 2019
proposed and numerically studied. The local thermal non-equilibrium model is used to
Received in revised form
consider the temperature difference between gas and solid matrix. Effects of equivalence
11 December 2019
ratio, the wall thermal conductivity, solid matrix thermal conductivity, and divergent ratio
Accepted 12 December 2019
on combustion characteristics, radiation efficiency, and flammability limits are studied.
Available online xxx
The results show that the divergent channel extends the blowout limit by 186% and obtains a maximum radiation efficiency of 29.3%, increased by 70% compared with the straight
Keywords:
channel. A smaller wall thermal conductivity is recommended considering the flamma-
Porous media combustion
bility range and radiation efficiency. A careful choice of solid matrix thermal conductivity
Micro-combustor
and the divergent ratio is suggested to balance their opposing effects on the radiation ef-
Micro thermophotovoltaic system
ficiency and the flammability.
Flammability limit
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Excess enthalpy combustion Radiation efficiency
* Corresponding author. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 445 Huangshan Road, Hefei, Anhui, 230027, PR China. E-mail addresses: [email protected] (P. Qian), [email protected] (M. Liu), [email protected] (X. Li), 15162118062@ 163.com (F. Xie), [email protected] (Z. Huang), [email protected] (C. Luo), [email protected] (X. Zhu). https://doi.org/10.1016/j.ijhydene.2019.12.094 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Introduction The fast depletion of fossil fuel and environmental pollution brings about the energy crisis, which is an urgent problem needed to be solved in the 21st century. Seeking an efficient, reliable, and compact energy source has given birth to the development of micro-/meso-power generators, one of which is the micro-/meso-thermophotovoltaic (MTPV) system [1,2]. Typical MTPV systems are driven by thermal power, especially the combustion because the energy density of hydrocarbon fuels is 20e50 times higher than the most advanced Li-ion concept based electrochemical batteries [3,4]. Compared with hydrocarbon fuels, hydrogen is the cleanest and the most promising fuel in an MTPV system driven by combustion because of its higher energy density and lower pollution. In a typical MTPV system, the combustor itself functions as the emitter [5]. However, as the combustor volume decreases, along with the increased energy density, one of the most common and salient problems is heat loss, resulting in unstable flames [6]. Various methods are proposed to achieve stable micro-/meso-scale combustion. On one hand, there has been a great effort on flame stabilization in micro-/mesocombustors including backward-facing step [7e10], wall cavity [11e13], divergent channel [14], bluff-body [15e18], catalytic combustion [19e21], non-circular channel [22], ribs [23,24], etc. Yang et al. [25] found that the divergent channel was beneficial to flame stabilization because its expanding section slows down the flow and increases the time for residence and heat transfer. On the other hand, higher temperatures and radiation efficiencies that can be obtained by heat recirculation techniques are of great value in MTPV systems [26]. A common way to implement the heat recirculation is multi-channels such as Swiss-roll combustor [27], double-channel combustor [28], four-channel combustor [29,30]. The heat recirculation through the wall was proved to be able to achieve higher wall temperatures [28] and extend flammability limits [31]. Another effective way is to insert porous media. The porous media combustion (PMC) concept was first demonstrated analytically by Takeno and Sato [32]. The results showed that inserting porous media into the flame zone enhances heat recirculation and preheats the incoming fresh gas, which leads to higher combustion temperature, wider dynamic range, and less fuel consumption. Hence, it is beneficial to integrate PMC into MTPV because of its higher temperatures as compared to free-flame combustion [33]. Research related to micro-/meso-scale PMC emerged in recent years. Li et al. [34,35] conducted experiment and simulation studies of premixed hydrogen/air combustion in a planar micro-combustor and pointed out that a porous microcombustor gives a higher wall temperature and a lower flame temperature than a free-flame counterpart. Channel height [36] and the difference between the partially and fully filled porous combustors [37] were examined by Wang et al. Bani et al. [38] combined TPV and PMC to estimate the effect of hydrogen/air equivalence ratio, effective thermal conductivity, and inlet velocity on wall temperature distribution. The experiment produced electricity power of 1.703 W. In addition, it indicated that the radiation efficiency is important in MTPV
system. Comprehensive review papers such as Refs [26,39,40] outlined the fundamentals and applications of TPV systems. The above literature review shows that there are many ways to improve the performance of the MTPV system based on the free-flame combustor. Compared with the free-flame counterpart, the PMC combustor processes higher wall temperatures, which is advantageous for the performance improvement of the MTPV system. Nonetheless, the increase of inlet velocity and the decrease of equivalence ratio or porosity lead to flame moving downstream and even blowout [35], causing uneven wall temperatures, low radiation efficiencies, and narrow flammability range. Therefore, the flame stabilization is imperative in the MTPV system based on PMC in order to take advantage of the higher wall temperatures. So far as the authors know, little research devotes to improve radiation efficiency and to extend flammability by varying channel cross-section areas in the PMC field, whereas it functions in the free-flame counterpart [14,25]. In the present work, a planar divergent channel is proposed to address the problem of narrow flammability range and low radiation efficiency in the straight channel, inspired by successful implements in the field of free-flame combustors. The planar configuration is adopted since it is more suitable for thermophotovoltaic cells array than tubes [41]. Hydrogen/air mixture is the fuel because of high heat value and low pollution. Effects of equivalence ratio, inlet velocity, wall thermal conductivity, solid matrix thermal conductivity, and divergent ratio on radiation efficiency and flammability limits are studied. Also, the combustion characteristics of porous media combustion in the divergent channel are investigated. This work develops a numerical method to accurately simulate the flame characteristics and to predict radiation efficiency for a better understanding of porous media combustion in the divergent channel, benefiting the design of future MTPV systems.
Physical and numerical modeling Physical model The geometric model adopted in the present study is shown schematically in Fig. 1. The combustor is mainly featured by a channel filled with inert porous media (steel mesh). The total length (L) of this channel is 21 mm. The height of the inlet and outlet are Hin (1 mm) and Hout (4 mm) respectively. A solid region with a thickness (t) of 0.5 mm is wrapped around porous media to form a divergent channel. Flange with a thickness of 0.5 mm and a height of 6.5 mm to connect other components in the experiment is also considered in numerical simulation. This similar configuration is adopted from Ref. [35] and the experiment results from Ref. [35] are compared with the simulation results in this paper. Premixed hydrogen/air is introduced into the channel and ignited inside the channel to release chemical energy. Part of the released heat is emitted through the combustor wall by radiation and convection. The rest of the heat is lost with the exhaust. Additional properties of the inert porous media are provided in Table 1.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Fig. 1 e Physical model. where p is the pressure of the gas mixture and m is the viscosity. Energy equation in the wall solid zone:
Table 1 e Properties of applied porous media. Property Fiber width (ds) Characteristic path length of the light quantum (l0) Emissivity of the solid matrix (εs ) Solid matrix conductivity (ks)
Unit
Value
m m
1.14 10e4 l0 ¼ εds =ð1 εÞ
e W/m$K
0.8 15
Governing equations Combustion is a complex phenomenon coupled with fluid flow, chemical reaction, and heat transfer. The following assumptions are adopted to simplify calculations. (1) The porous media combustor is symmetric and a 2D laminar steady model is applied. The aspect ratio of 10 is also adopted in the experiment [34,35], which indicates 2D symmetric treatment is reasonable [15,42]. A simple computation revealed that the flow remains laminar for inlet velocities of up to 21 m/s [43]. The maximum inlet velocity in the present study is 20 m/s; (2) Gas radiation is not considered. Radiation between solid porous matrix is considered by effective thermal conductivity [44,45]; (3) Catalytic effects are negligible [46]; (4) The flow speed is sufficiently low that the gas mixture is incompressible [46]; Governing equations are expressed as follows by applying the above assumptions. Continuity equation: v ¼0 V , εrg !
mixture. rg is the density of the gas mixture. Momentum equation:
(3)
where kw and Tw is the thermal conductivity and the temperature of the wall, respectively. The local thermal equilibrium (LTE) model [34,38,43] is the most convenient model and widely used in the study of porous media combustion to simulate the temperature field. However, it is not quite accurate due to the neglect of the heat transfer between gas and solid matrix. In the present study, the local thermal non-equilibrium (LTNE) model is adopted as shown in Eq. (4) and Eq. (5). Energy equation in the gas phase: X X ! v Tg þ rg εYi V i cg VTg ¼ εV , kg VTg ε ui hi Wi V , εcg rg ! þ hv Ts Tg
i
i
(4)
where cg is the heat capacity of the gas mixture. kg is the gas mixture thermal conductivity. Tg is the gas mixture temperature. hi is the enthalpy of species i. Di;m is the mass diffusivity of species i. Yi is the mass fraction of species i. ui is the molar production rate of species i. Wi is the relative molecular mass of species i. Energy equation in the porous solid matrix phase: V , ks;eff VTs þ hv Tg Ts ¼ 0
where kg is the thermal conductivity of the gas mixture. Ts is
hv ¼
2ð1 εÞNukg 2
ds
Nu ¼ 1 þ
4ð1 εÞ 1 þ ð1 εÞ0:5 Re0:6 Pr1=3 ε 2
(6)
And the effective thermal conductivity of solid matrix ks;eff considering solid-solid radiation is expressed as [48]: ks;eff ¼ ð1 εÞks þ krad
(2)
(5)
the solid matrix temperature. The volumetric heat transfer coefficient hv coupling the gas and solid matrix energy equations is determined by Ref. [47]:
(1)
where ε represents the porosity of porous media and it is 0.6 in the following investigation except for the grid independence and data validation section. ! v is the velocity vector of the gas
vÞ V , εrg ! v! v ¼ εVp þ mV2 ðε!
V , ðkw VTw Þ ¼ 0
krad ¼
16sεs l0 T3s 3
(7)
Species transport equation:
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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! V , εrg ! v Yi ¼ V, εrg VYi V i þ εui Wi
Solution method (8)
! where Yi is the local mass fraction of species i. V i is the diffusion velocity [46]. The k th chemical reaction is of the general form: i X
0
vik xi 4
i¼1
i X
00
vik xi
(9)
i¼1
where xi is symbol denoting species i. The molar production rate of species i is: ! i i i Y Y X 00 0 h0ik h0 0ik ui ¼ ½xi krk ½xi vik vik kfk i¼1
i¼1
(10)
i¼1
The forward and backward rate constants are: Ei kfk ¼ Ai Tbgk exp Rc Tg
(11)
Er br krk ¼ Ari Tgi exp i Rc Tg
(12)
A CHEMKIN mechanism comprising 10 species and 21 elementary reversible reactions [49] is applied in the present study to simulate the gas-phase reaction. This CHEMKIN format mechanism and related thermophysical data provide preexponential factor (Ai ), temperature exponent (bk ), activation energy (Ei ), rate exponent (h0ik , h}ik ), stoichiometric coefficient (n0ik , n}ik ) for the calculation of the forward rate constant, the backward constant and the molar production rate of certain species. All the variables in governing equations are SI units.
The above equations are implemented using the software Fluent 6.3. The SIMPLE algorithm [52] was adopted to solve the pressure-velocity coupling momentum equation. UDFs (User Defined Functions) are utilized to represent the volumetric convective heat transfer coefficient (hv, Eq. (6)) and the effective thermal conductivity (ks,eff, Eq. (7)) in the LTNE model (Eq. (4)(5)). A UDS (User Defined Scalar) is used to consider the energy equation (Eq. (5)) for the solid porous matrix. The finite volume method (FVM) is used to discretize the governing equations. During the iterative calculation, the convergence criterion of the energy equation is 106, and the convergence criterion of other equations is 103. The initial temperature in the porous media region is set to 1600 K in order to ignite combustion.
Grid independence and data validation To demonstrate the numerical algorithm reliability and validity, a detailed grid independence test and data validation are carried out. The mesh independence test is examined by dividing the computation region into uniform finite volume elements. To this end, four sets of meshes are chosen to inspect grid independence. The equivalence ratio and porosity
Boundary conditions At the inlet (x ¼ 0), the uniform velocity profile is set because the difference introduced by the uniform and fully developed velocity profile was proved to be insignificant and can be neglected [50]. The gas mixture temperature is 300 K while the mass fraction of hydrogen and air are prescribed according to equivalence ratio. vx ¼ vin ; vy ¼ 0; Yi ¼ Yi;in ; Tg ¼ Tin ¼ 300K
(13)
At the outlet (x ¼ 21 mm), the pressure outlet condition [35] is applied. A fixed atmospheric pressure (pa ¼ 101325 Pa) is set to the outlet. vT vv vYi ¼ 0; ¼ 0; ¼ 0; p ¼ pa vx vx vx
(14)
On the outer wall: qw ¼ hc ðTw Ta Þ þ εw s T4w T4a
(15)
where Ta is the ambient temperature (300 K). Heat loss through radiation and convection at the outer wall are taken into account. The emissivity of the wall is estimated to be εw ¼ 0.9. s ¼ 5.67 108W/m2$K4 is the Stefan-Boltzmann constant. hc is the natural convective heat transfer coefficient and is estimated to be 15 W/m2$K according to Ref. [51]. In addition, the velocity slip at the gas-wall interface was found to be negligible [50]. Therefore, a non-slip boundary condition is considered for the gas-wall interface.
Fig. 2 e Grid independence, (a) gas temperature, (b) solid matrix and outer wall temperature.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 3 e Mesh pattern.
of these tests are 0.8 and 0.88, respectively, which is the same as Ref [35]. The results are shown in Fig. 2. Gas temperature, solid temperature along the symmetry axis and outer wall temperature distribution are the criterion to identify reasonable mesh. As can be seen from Figs. 2 and 58500 cells (solid lines in Fig. 2) are adequate enough to represent combustion inside the porous media while more cells do not introduce any significant difference in terms of temperature distribution. The mesh pattern is shown in Fig. 3. The wall region is divided into 25000 elements. The flange region is divided into 7250 elements and the porous region is divided into 26250 elements. The outer wall temperature distribution is compared with experimental results from Ref. [35]. As is shown in Fig. 4 The maximum relative error is smaller than 5% and simulation results follow the same trend as the experiment results, which confirm the data validity of the simulation. In summary, the present numerical algorithm and boundary conditions are reasonable to simulate porous media combustion.
Fig. 4 e Wall temperature of simulation and experiment.
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Fig. 5 e Gas and solid matrix temperature distribution along the axis of symmetry.
Results and discussion Excess enthalpy combustion PMC is characterized by excess enthalpy combustion. In this section, PMC inside the divergent channel and the straight channel are investigated to identify excess enthalpy combustion. Gas and solid temperature distribution along the axis of symmetry are obtained and plotted in Fig. 5. In the divergent and the straight channel, kw ¼ ks ¼ 15 W/m$K, ε ¼ 0.6, f ¼ 0.6, vin ¼ 3 m/s. The porous media channel is divided into the preheat region, where gas temperature is higher than solid temperature, and the combustion region, where gas temperature is lower than solid temperature. The heat released from the combustion region recirculated to the preheat region by conduction and radiation to preheat the gas mixture. The inter-phase thermal non-equilibrium is responsible for the excess enthalpy combustion and heat recirculation [53], which is not represented by the LTE model. Hence, the LTNE model is applied for the nature of porous media combustion and heat recirculation analysis in the following sections. Additionally, it was shown that the LTNE model can predict the essential features including burning velocity and temperature distribution [46] of the flames. The temperature difference between solid and gas is also represented in Fig. 5. The adiabatic flame temperature of hydrogen/air mixture with an equivalence ratio of 0.6 is 1800 K [54]. Excess enthalpy combustion is the combustion of which the maximum flame temperature is higher than the adiabatic flame temperature. It can be seen from Fig. 5 that the maximum temperature of the gas mixture is slightly lower than the adiabatic flame temperature because of non-adiabatic wall boundary conditions, which indicates that excess enthalpy combustion does not take place. The mean wall temperature of the divergent channel (980 K) is 28.6% higher than that of the straight channel (762 K), which is the reason for the higher radiation efficiency of the divergent channel under vin ¼ 3 m/s in Fig. 14. It is worth noticing that the temperature difference between gas and solid near the inlet region is larger in divergent
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Fig. 6 e Combustion regions, EECR (excess enthalpy combustion regime) and RCR (regular combustion regime).
channel than that in straight channel. The reason is that the flame front is near the inlet in divergent channel, preheating inlet gas mixture effectively. Combustion situations of f ¼ 0.4,0.6,0.8 in the divergent channel are inspected and divided into two regimesdexcess enthalpy combustion regime (EECR) and regular combustion regime (RCR), according to the difference between the maximum combustion temperature and the adiabatic flame temperature. The results are shown in Fig. 6. Each pentagram in Fig. 6 represents the condition of a certain equivalence ratio and inlet velocity. It can be seen that all situations of f ¼ 0.8 are not the excess enthalpy combustion and all situations of f ¼ 0.4 are the excess enthalpy combustion. For f ¼ 0.6, the excess enthalpy combustion takes place when the inlet velocity is higher than 5 m/s. In order to disclose the reason for this observation, heat loss ratio (hloss ), preheat efficiency (hpre ), and net heat recirculation efficiency (hnet ) are defined to quantify the heat recirculation: Ph hloss ¼
i
Fig. 7 e Effects of equivalence ratio and inlet velocity on the net heat recirculation efficiency.
enthalpy combustion cannot exist under a high equivalence ratio (f ¼ 0.8, Fig. 6) and happens when equivalence ratio is smaller (f ¼ 0.4 and f ¼ 0.6, Fig. 6) or inlet velocity is higher (vin 5 m/s under f ¼ 0.6, Fig. 6).
Fundamental flame characteristics: flame position and burning velocity Flame position along the axis of symmetry is determined at the position where the mass fraction of H radical is the largest. Stabilization of the flame front occurs when the superficial gas velocity vs ¼ εv equals the burning velocity Sp in the porous medium [55], where ε is the macroscopic porosity and v is the gas-phase velocity. Burning velocities of different operating conditions are identified according to this definition. In this paper, the burning velocities are evaluated at the symmetry axis.
i εw s T4w;i T4a;i þ hc Tw;i Ta;i DSi
Prec ¼ hpre ¼ Pth
m_ fuel LHV
(16)
P hv;i DVi Ts;i Tg;i i
hnet ¼ hpre hloss
m_ fuel LHV
(17)
(18)
where DSi is the surface area of the meshed surface unit. LHV is the lower heat value of hydrogen gas (1.2 108 J/kg). Preheat efficiency (hpre ) is the ratio of total heat recirculated (Prec ) to the preheat region and thermal power input (Pth ). i is the indicator of the meshed cell. hv;i is the volumetric heat transfer coefficient of the meshed cell i. DVi is the volume of the meshed cell i. Ts;i and Tg;i are the solid matrix and gas temperature of the meshed cell i. m_ fuel is the mass flow rate of hydrogen gas. It can be seen from Fig. 7 that the net heat recirculation efficiency decreases with the increase of equivalence ratio but increases against the inlet velocity, which is the reason why the excess
Fig. 8 e Effects of inlet velocity and equivalence ratio on the flame position.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
Fig. 8 shows the effects of equivalence ratio on the flame position versus inlet velocity. It indicates that PMC for f ¼ 0.8 has the widest flammability range while it is the least narrow for f ¼ 0.4. Self-sustain combustion can exist even under the inlet velocity as low as 0.5 m/s. The lowest inlet velocity is a little higher than the one obtained (~0.2 m/s) by Li et al. [35], which can be attributed to the porosity difference between the present study and the latter. This comparison indicates that the extinction limit can be reduced by the increase of porosity. As shown in Fig. 8, a higher inlet velocity makes flame stabilize downstream while a larger equivalence ratio makes flame stabilize upstream, which confirms the findings of Refs. [35,46]. In fact, higher inlet velocities lead to higher advection velocities that move flame downstream [35]. As for the effect of equivalence ratio, for instance, the mixture with f ¼ 0.4 gives downstream flame position due to its higher ignition temperature and less heat release [34]. The effects of inlet velocity and equivalence ratio on the burning velocity are illustrated in Fig. 9. The burning velocity increases with the increase of inlet velocity and equivalence ratio. Li et al. [34] attributed the reason for this observation to chemical kinetics. In other words, a higher inlet velocity or equivalence ratio means more thermal power input and more heat release, resulting in a higher flame temperature that increases the burning velocity of the mixture according to the Arrhenius equation (Eq. (11)).
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Fig. 10 e Flammability limits. blowout limits are identified for f ¼ 0.4,0.6,0.8. As shown in Fig. 10, it is obvious that the stable combustion region of the divergent channel is much wider than that of the straight channel. As for f ¼ 0.6 and f ¼ 0.8, the blowout limits are significantly extended by 167% and 186% respectively compared with the divergent channel while the extinction
Flammability limits One particular advantage of PMC is the extended flammability limits compared with free-flame combustion. Terminologically, for certain equivalence ratio, flammability limits consist of two limits, the extinction limit, which means gas mixture could not react under low velocities, and the blowout limit, which shows that inlet velocity is such high that flame would be blown out of the combustor [56]. Flammability range or stable combustion region is the distance between those two limits. A comparison between the traditional straight channel and the divergent channel is made. Extinction limits and
Fig. 9 e Effects of inlet velocity and equivalence ratio on the burning velocity.
Fig. 11 e (a) Velocity magnitude along the symmetry axis, (b) contour of radical H in the straight porous media channel, (c) contour of radical H in the divergent porous media channel (half of the channel is shown).
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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limits of these two channels remain almost the same. It is worth mentioning that combustion cannot be maintained for the straight channel when f ¼ 0.4. The preheat efficiency and the flow field provide some insight into the extended blowout limits. Taking the case of f ¼ 0.6 vin ¼ 3 m/s for example, Pth ¼ 3787 W, Prec ¼ 1423 W, hpre ¼ 37.6% when the channel is straight and Pth ¼ 3787 W, Prec ¼ 1694 W, hpre ¼ 44.7% when the channel is divergent. It can be concluded from the above computation that the divergent channel extends blowout limits through improving the preheat efficiency. The distribution of velocity magnitude along the symmetry axis and radical H contours when f ¼ 0.6 vin ¼ 3 m/s are illustrated in Fig. 11. Radical H can be seen as an indicator of the flame front [57]. Fig. 11a shows that the flame inside porous media stabilizes at the position where the velocity gradient is the largest while divergent channel makes this position closer to the inlet, which illustrates that divergent channel is able to sustain combustion under higher inlet velocities as compared to the straight channel. As can be seen from Fig. 11b and c, the flame has a reversed “C” shape, which is the same as the flame shape in a typical free-flame microchannel [25,58]. However, the flame is “C” shape [59] in a micro-fibrous porous media tube with a diameter of 8 mm and our previous study [60] showed that the flame is flat in 20 mm macro-channel filled with alumina foams under adiabatic conditions. It may be concluded that the flame shape is related to length scale and thermal conditions, which requires further investigation in the future. In the divergent channel, the flame is flatter near the symmetric axis than the one inside the straight channel due to more uniform velocity distribution along the y-direction. The effects of the wall and solid matrix thermal conductivity on flammability limits are investigated. Dolomite (kw ¼ 1.75 W/m$K), steel (kw ¼ 15 W/m$K), and aluminum (kw ¼ 202 W/m$K) are selected to make a comparison among different wall thermal conductivities. Steel (ks ¼ 15 W/m$K), nickel (ks ¼ 97.7 W/m$K), and aluminum (ks ¼ 202 W/m$K) are selected to observe the effect of solid matrix thermal
Fig. 12 e Effects of equivalence ratio on the radiation efficiency.
conductivity on the flammability limits. The results are shown in Table 2 and Table 3. It can be seen from Table 2 that the wall thermal conductivity has little influence on blowout limits while a large wall thermal conductivity narrows flammability
Table 2 e Effect of wall thermal conductivity on flammability limits (ks ¼ 15 W/m·K, f ¼ 0.6). Wall thermal conductivity (W/m$K) 1.75 15 202
Extinction limit (m/s)
Blowout limit (m/s)
1 1 2
8 8 8
Table 3 e Effect of solid matrix thermal conductivity on flammability limits (kw ¼ 15 W/m·K, f ¼ 0.6). Solid matrix thermal conductivity (W/m$K) 15 97.7 202
Extinction limit (m/s)
Blowout limit (m/s)
1 2 3
8 16 20
Fig. 13 e Effects of (a) wall thermal conductivity and (b) solid matrix conductivity on the radiation efficiency.
Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
international journal of hydrogen energy xxx (xxxx) xxx
range in terms of extinction limits. Wang et al. [37] pointed out that the flame extinction is mainly dependent on the heat loss from the flame root that increases with the increase of wall thermal conductivity and decreases with the increase of inlet velocity. As a consequence, the extinction limit under a higher wall thermal conductivity is increased. Table 3 illustrates that both the extinction and blowout limits increase with the increase of solid matrix thermal conductivity. Meanwhile, the flammability range becomes wider. In fact, the preheat efficiency increases when solid matrix thermal conductivity increases [35]. Increased solid matrix thermal conductivity leads to the increase of effective thermal conductivity (ks;eff ) that enhances heat exchange between gas and solid in the preheat region, which promotes flammability.
Radiation efficiency Radiation efficiency is an important parameter and is widely applied to characterize the performance of MTPV systems [22,61e64]. Here, in the present investigation, the radiation efficiency is defined as the ratio of the wall radiation power (Prad ) and thermal power input (Pth ), which can be expressed as follows. Prad ¼ hrad ¼ Pth
P εw sT4w;i DSi i
m_ fuel LHV
(19)
where DSi is the meshed unit surface area of the wall. The effects of equivalence ratio, thermal conductivity, inlet velocity, and geometry configuration on the radiation efficiency are studied in detail. Fig. 12 shows the radiation efficiency of different inlet velocities when f ¼ 0.4,0.6,0.8. It can be found that f ¼ 0.4 has the
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lowest radiation efficiency and the radiation efficiency decreases due to the fact that flame stabilizes downstream when inlet velocity is increased, which is shown in Fig. 8. As for f ¼ 0.6 and f ¼ 0.8, the radiation efficiency undertakes a slight increase before decrease while inlet velocity is increasing. The reason for the slight increase is that the flame stabilizes near the inlet and a large amount of heat is lost by the radiation through the flange when inlet velocity is slow. Overall, the radiation efficiency increases with the decrease of inlet velocity or the increase of equivalence ratio and the maximum radiation efficiency (25.6%) is achieved when f ¼ 0.8, vin ¼ 4 m/ s. Similarly, Pan et al. [45] and Bani et al. [38] pointed out that the radiation efficiency is the maximum when f ¼ 0.8 while the temperature of the wall is the highest with f ¼ 1.0 in the straight channel. The effects of the wall and solid matrix thermal conductivity on the radiation efficiency are shown in Fig. 13. It is obvious that the radiation efficiency is significantly affected by the flange when inlet velocity is lower than 3 m/s. From Fig. 13a, it can be found that increased wall thermal conductivity has a negative effect on the radiation efficiency. In fact, flame temperature decreases with increased wall thermal conductivity because more heat is lost by the flange. Thus, less heat radiates through the emitter wall. Combining the results in Table 2 and Fig. 13, it can be concluded that increased wall thermal conductivity decreases the radiation efficiency and flammability range. Therefore, a smaller wall thermal conductivity is preferred in design. For instance, the maximum radiation efficiency can be further increased from 25.4% to 29.2% when the wall thermal conductivity is decreased from 15 W/m$K to 1.75 W/m$K. The increase of solid matrix thermal conductivity increases the heat loss from flame and decreases flame
Fig. 14 e Effect of the divergence ratio on the radiation efficiency. Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Table 4 e Effect of the divergence ratio on the flammability limits. Divergent ratio Extinction limit (m/s) Blowout limit (m/s) 1 2 3 4
2 2 2 1
3 5 7 8
temperature [35]. For this reason, the radiation efficiency decreases when solid matrix thermal conductivity increases, which can be seen from Fig. 13b. When inlet velocity surpasses 5 m/s, the radiation efficiency of ks ¼ 15 W/m$K decreases sharply because the flame stabilizes near the outlet. However, increased solid matrix thermal conductivity improves flammability. As a result, there is a trade-off between the radiation efficiency and flammability range considering the implement of solid matrix thermal conductivity. The effect of geometry configuration is studied in terms of the divergence ratio (DR), which is defined as the ratio of the height of inlet (Hinlet ≡ 1 mm) and outlet (Houtlet ). DR ¼
Houtlet Hinlet
(20)
The results are shown in Fig. 14 and Table 4. It is obvious that the radiation efficiency decreases with the increase of DR. An increased DR brings about a wider flammability range and a lower radiation efficiency. For DR ¼ 1 vin ¼ 3 m/s, DR ¼ 2 vin ¼ 5 m/s, and DR ¼ 3 vin ¼ 6 m/s, 7 m/s, the radiation efficiency is extremely low because the flame stabilizes near the outlet. It can be seen from the contours in Fig. 14 that flame stabilizes upstream with the increase of DR. This is the reason why increased DR widens flammability range, as listed in Table 4. Compared with the straight channel (DR ¼ 1), the divergent channel (DR ¼ 2) obtains a maximum radiation efficiency of 29.3%, increased by 70% when vin ¼ 3 m/s. Overall, the divergent channel shows better performance considering the flammability range. However, a large DR makes flame stabilize upstream, leading to more heat losses through the flange. As a result, the maximum radiation efficiency drops from 29.3% to 25.4% when the DR is increased from 2 to 4. Therefore, a trade-off between the flammability range and the radiation efficiency must be made to determine a desired DR. Moreover, Li et al. [65] mentioned that only the photons with energy higher than the material band-gap are useful for the TPV converter. A common way is to make an estimated PV cell efficiency (constant, 15.4%) [11,66,67]. A more detailed estimation would be the one that considers the unique absorption characteristic (external quantum efficiency, etc. [40]) of a certain PV cell regarding the radiation spectrum of the emitter, which could be a future investigation topic.
Conclusions The present study proposed a divergent channel configuration to stabilize flame and to improve radiation efficiency. Premixed hydrogen/air combustion in porous media was numerically studied to manifest the proposed method. The numerical model was well validated by comparison with the
experimental data of measured wall temperature. Excess enthalpy combustion, flame position, burning velocity, flammability limit, geometry configuration, and radiation efficiency were investigated. The following conclusions can be drawn from the present investigation. (1) It is found that the equivalence ratio and inlet velocity determine the excess enthalpy combustion by changing the net heat recirculation efficiency. The excess enthalpy combustion is hard to maintain under a high equivalence ratio of 0.8; (2) A high inlet velocity makes flame stabilize downstream and a larger equivalence ratio makes flame stabilize upstream. Burning velocity increases with the increase of inlet velocity or equivalence ratio; (3) The divergent channel extends the blowout limit by 167% and 186% when f ¼ 0.6 and f ¼ 0.8 compared with the straight channel because of the enhanced preheat effect and the flow field. (4) The radiation efficiency of the divergent channel increases with the increase of equivalence ratio within 0.4e0.8, which is consistent with the experimental result in the straight channel; (5) There is a trade-off between the radiation efficiency and flammability range considering the implement of solid matrix thermal conductivity or the divergent ratio (DR). A larger solid matrix thermal conductivity or DR decreases radiation efficiency but extends flammability range significantly. On the other hand, a smaller wall thermal conductivity is preferred concerning the flammability range and radiation efficiency. The maximum radiation efficiency obtained in the divergent channel (DR ¼ 2) is 29.3%, increased by 70% than that in the straight channel.
Acknowledgments This work was supported by the National Key R&D Program of China [2018YFB1900602] and the National Natural Science Foundation of China [NSFC Grant No.11372302] and the Supercomputing Center of University of Science and Technology of China.
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Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094
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Please cite this article as: Qian P et al., Combustion characteristics and radiation performance of premixed hydrogen/air combustion in a mesoscale divergent porous media combustor, International Journal of Hydrogen Energy, https://doi.org/10.1016/ j.ijhydene.2019.12.094