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Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities
Accepted Manuscript Title: Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities Authors: Aiwu Fan, Ying Xiang, Wei Yang, Linhong Li PII: DOI: Reference:
S0255-2701(18)30551-8 https://doi.org/10.1016/j.cep.2018.06.014 CEP 7316
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
10-5-2018 14-6-2018 19-6-2018
Please cite this article as: Fan A, Xiang Y, Yang W, Li L, Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities, Chemical Engineering and Processing - Process Intensification (2018), https://doi.org/10.1016/j.cep.2018.06.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities
Aiwu Fan*, Ying Xiang, Wei Yang, Linhong Li
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Technology, Wuhan 430074, China
Corresponding author:
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E-mail: [email protected]
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Fax: +86-27-87540724
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1037 Luoyu Road, Wuhan 430074, China
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Prof. Aiwu Fan
Phone: +86-27-87542618
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State Key Laboratory of Coal Combustion, Huazhong University of Science and
Graphical abstract
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Combustion efficiency of lean H2/O2/N2 flames can be notably improved by helium dilution because of the intensifications of chemical reactions and heat release at the tip of H2/O2/He
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flames. As a result, the flame tip opening phenomenon is suppressed and combustion completeness is significantly promoted.
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Highlights
Combustion efficiency of lean H2 flames can be notably enhanced by helium dilution.
Flame temperature increases greatly due to a smaller heat capacity of helium.
The effective Lewis number of the gaseous mixture with helium dilution is raised.
Stretch effect at the tip of H2/O2/He flames is weaker compared to H2/O2/N2 flames.
Reaction rate and heat release rate at the tip of H2/O2/He flames is intensified.
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Abstract
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For very lean H2/air flames in a micro-combustor with cavity flame holders, the
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combustion efficiency decreases rapidly at sufficiently high inlet velocity due to the occurrence of "flame tip opening". To suppress this undesirable phenomenon, we used helium (He) to replace nitrogen (N2) as dilution in the oxidant. Numerical simulation was conducted under an equivalence ratio of 0.4 for both N2 and He dilutions. The results show that the combustion efficiency is greatly improved, remaining above 98%
at 32 m/s in the case of He dilution. The analysis reveals that several reasons are responsible for these results. Firstly, the heat capacity of He is smaller than N2, which leads to a higher temperature level of the gaseous mixture in reaction zone. Second, the effective Lewis number of the H2/O2/He mixture is larger than that of the
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H2/O2/N2 mixture. Thirdly, the magnitude of stretch rate at the flame tip for He dilution is less than the N2 counterpart. The combined effects of three aspects result in
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intensified reaction rate and heat release rate at the flame tip. As a consequence, the
flame tip opening phenomenon can be significantly suppressed and combustion
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efficiency be notably increased.
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Keywords: micro combustor; combustion efficiency; helium dilution; Lewis number;
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stretch rate
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1. Introduction
Combustion in micro reactors is an emerging area which has attracted extensive
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attentions in past decades. The main merit of a micro combustor is that this device can
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provide a considerably higher power density compared to conventional batteries [1]. However, flame stabilization under a reduced scale remains a daunting task because
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of the increased heat loss ratio and reduced residence time [2-7]. Researchers have spent a lot of efforts to enhance flame stability in miniaturized
combustors. Thermal interactions between the flame and combustor walls significantly affect the flame stability [8]. Thus, thermal management is most frequently used for flame stabilization in small combustors. The “Swiss roll”
configuration can effectively improve combustion performance of micro combustors [9, 10] via heat recirculation. Kang and Veeraragavan [11] made a micro combustor with thermally orthotropic material, which has broadened flammability limits due to enhanced heat recirculation and reduced heat loss. Wan et al. [12, 13] proposed a
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micro combustor with preheating channels and a plate flame holder, demonstrating that lean methane/air mixtures can be burned even below the conventional
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flammability limit. SiC foam was employed in a micro modular combustor by Yang et al. [14]. They found that porous foam is helpful to form a high and uniform distribution.
Standing
waves
can
be
achieved
in
a
planar
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temperature
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micro-combustor partially filled with porous media [15]. Stationary flames emerge
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over a wide operational range in mesoscale channels filled with fibrous porous media
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[16-18] for both premixed and non-premixed combustions. Zuo et al. [19] improved
micro TPV devices.
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the thermal performance of a micro combustor with double counterflow channels for
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Moreover, catalytic combustion is an effective measure to attenuate the
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radical-quenching effect of the wall surfaces. Li et al. [20] numerically studied the effects of catalyst segmentation and wall cavities on CH4/O2 flames in micro-combustors. Zhang et al. [21] investigated the effects of convex cavity structure,
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position and number on methane conversion and extinction limit through catalytic combustion in a micro-channel. Yan et al. [22] explored catalytic combustion characteristics of a meso-scale combustor with preheating channels. They found that combustion efficiency increases by approximately 9% in this combustor compared to
that without heat recirculation. To anchor flame in micro combustors, forming a recirculation zone or low velocity zone is another effective approach. The flame stability in micro combustors was improved by fabricating one or multiple backward facing steps in the walls [23,
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24]. E et al. [25] examined the impacts of inlet pressure and found that the highest energy conversion efficiency and exergy efficiency were both obtained at an
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atmospheric pressure. Baigmohammadi [26] investigated the effects of mixture flow rate, equivalence ratio, oxygen enhancement, and geometrical parameters on the
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stability of premixed propane-air flames meso-scale combustors with a step. Rich
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flame dynamics were observed in their experiment. Various bluff bodies were used as
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flame holders in small combustors which can notably expand flame blow-off limit
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[27-31]. Meso-scale combustors with dual cavities in the walls can also obtain a large
mixtures [32, 33].
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blow-off limit that is several times the corresponding burning velocities of incoming
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Although flame stability can be significantly promoted in the presence of wall
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cavities, the combustion efficiency of lean H2/air flames decreases quickly at sufficiently high inlet velocity [34]. It is revealed that the incomplete combustion is owing to the emergence of “flame tip opening”. This phenomenon was also reported
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by Brambilla et al. [35] in lean H2/CO/air flames in mesoscale channels. Many factors, such as wall thermal conductivey, surface emissivity, cavity depth, initial temperature and pressure, and oxygen concentration [36-41], can affect the occurrence of flame tip opening in micro combustors. It is well understood that flame tip opening is
essentially local extinction that always happens in stretched premixed flames with a sub-unity effective Lewis number [42, 43]. A large number of studies have demonstrated that using helium (He) as dilution can raise the effective Lewis number and increase the laminar burning velocity of the mixture [44]. Therefore, in the
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present study we are dedicated to numerically investigating the effect of helium dilution on the combustion efficiency of H2 flames in a micro-combustor with wall
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cavities. 2. Numerical methods
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2.1 Geometric model
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The schematic of the micro-combustor with double cavities is shown in Fig. 1. The
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gap distance (W1), length (L0) and width (W0) of the channel are respectively 1 mm,
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10 mm and 18 mm. The distance (L1) from the combustor entrance to the vertical wall
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of the cavity is 3 mm, while the length (L2) and depth (W2) of the cavity are 3 mm and 1 mm, respectively. The acute angle (θ) between the ramped cavity wall and interior
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wall is 45°. The wall thickness (W3) is 2 mm.
Fig. 1.
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2.2 Mathematical model In this work, H2 is used as the fuel, and the oxidant is mixed by 21% O2 and 79% N2 or 79% He. First, we estimate the value of Knudsen number, Kn=Lg/Lc, where Lg is the mean free path of the gas and Lc is the characteristic scale of the combustor. For both
H2 and O2, the orders of magnitude of Kn are approximately 10-5. According to [45], if the Knudsen number is less than 10-3, the Navier-Stokes equations are still applicable. Because heat recirculation via the channel walls has a significant impact on the flame tip opening phenomenon [36], heat conduction in the solid walls is considered in the
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computation. A two-dimensional, steady-state model is employed to reduce the computational cost because the aspect ratio (W0/W1) of the micro combustor is very
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large (10:1). 2.3 Computation scheme
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Similar to our previous experiments, quartz is selected as the solid material. The
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density (ρ), thermal conductivity (λs), specific heat capacity (cp) and surface
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emissivity () for quartz glass are 2650 kg/m3, 1.05 W/(mK), 750 J/(kg·K) and 0.92,
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respectively [46]. The mixture equivalence ratios are held at = 0.4. The gaseous
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mixture is treated as an ideal gas and its specific heat, viscosity and thermal conductivity are computed from a mass-fraction-weighted average of the species’
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properties. The detailed chemistry reported by Li et al. [47] was employed to model
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the combustion of H2. It involves 13 species and 19 reversible elementary reactions. The results have been verified to be independent of employed mechanisms [41]. The thermodynamic and transport properties of the gaseous species are imported from the
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CHEMKIN databases [48]. The boundary conditions are explained as follows: 1) At the inlet: uniform concentration and velocity profiles are imposed; The inlet temperature (Tin) is 300 K.
2) At the outlet: Neumann boundary condition with zero gradients is given. 3) At the inner surfaces: The effect of interior surface to surface radiation is considered using the discrete ordinates (DO) model [34]. 4) At the exterior surfaces: both heat losses via radiation and natural convection are
q o h o T w , o T T w , o T 4
4
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taken into account and the total heat loss rate is calculated through Eq. (1):
(1)
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where ho is the natural convection heat transfer coefficient (～20 W/(m2 K) [49], T∞ is
the ambient temperature (300 K), Tw,o is the outer wall temperature, is the emissivity
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of the solid surface (0.92), and σ is the Stephan-Boltzmann constant with a value of
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5.67×10-8 W/(m2 K4).
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The grid independency was checked by comparing the results of three different grid
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systems, i.e., Δx=Δy=10 μm, 15 μm and 20 μm. The condition of = 0.4, Vin= 8 m/s
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with N2 dilution was chosen as an example. The profiles of gas temperature and mass fraction of H2 along the centerline of the micro-combustor are plotted in Fig. 2. The
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differences between these numerical results are negligible. Therefore, the cell size of
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Δx=Δy= 20 μm is considered to be fine enough to obtain accurate prediction. Further refinement of the grid system was conducted in the cavity region and the total cell numbers are 138033 in the final computation. The local grid system in the vicinity of
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upper cavity is illustrated in Fig. 3.
Fig. 2.
Fig. 3.
The commonly used computational fluid dynamics (CFD) software FLUENT 6.3 [50] was applied to solve the mass, momentum, energy and species conservation
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equations. The second-order upwind scheme was used to discretize the mathematical model, and the “SIMPLE” algorithm was employed to solve the coupling of pressure
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and velocity. To initiate the chain reactions of lean mixture, an initial temperature of
2000 K was imposed on the fluid zone. This is a frequently adopted strategy in
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combustion simulation applying CFD software. The convergence criteria were set to
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be 1.0×10−6 for the residuals of all variables.
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2.4 Model validation
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In a previous work [34], we validated the accuracy of the numerical model and
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computing scheme by comparing predicted and measured values of exhaust gas temperatures at various inlet velocities, as presented in Fig. 4. It’s noted that the
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largest and smallest relative errors are 10.3% (at Vin= 8 m/s) and 4.43% (Vin= 26 m/s),
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respectively. This is because the Reynolds number will be increased with the increase in the inlet velocity. Therefore, the prediction accuracy by using a turbulence model will be higher at large inlet velocities. This verifies that the results of present study are
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reliable.
Fig. 4.
3 Results and discussion 3.1 Combustion efficiency Here, we define the combustion efficiency as, C out C in
(2)
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c 1
where Cin and Cout are fuel mass fractions at the inlet and outlet of the
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micro-combustor, respectively. For comparison, the variations of combustion efficiency with inlet velocity are plotted in Fig. 5 for both N2 and He dilutions. It is seen from Fig. 5 that in the N2 atmosphere, combustion efficiency decreases rapidly
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with an increasing inlet velocity. For example, the combustion efficiency under N2
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dilution drops to 78.0% at Vin= 32 m/s. In contrast, when N2 is replaced by He, the
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combustion efficiency still remains above 98.2% at very high inlet velocities. This confirms that replacing N2 with He is an extremely effective way to improve the
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combustion efficiency of lean H2 flames in the micro-cavity combustor.
Fig. 5
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The distributions of H2 mole fraction under N2 and He dilutions are presented in
Fig. 6 for the case of Vin= 24 m/s. Meanwhile, the centerline profiles of H2 mole
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fraction are plotted in Fig. 7. These two pictures clearly demonstrate that when the dilution is N2, the fuel is not completely burnt at the flame tip and leaks out from the combustor exit. This is attributed to the occurrence of flame tip opening, which is a frequently observed phenomenon in lean flames suffering from intense stretch effect. However, for the He dilution case, the fuel concentration starts to decrease earlier and
much faster (Fig. 7). As a result, H2 is almost fully consumed in a much shorter distance.
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Fig. 6.
Fig. 7.
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3.2 Analysis and Discussion
First, we took the case of 16 m/s to examine the third body effect of helium. The combustion efficiencies were 98.99% and 90.09% respectively when the third body
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effect was considered and not considered, which demonstrated that the third body
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effect was negligible on the combustion efficiency. In the following sections, the
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effect of helium will be analyzed from other aspects. 3.2.1 Effect of He dilution on temperature level, effective Lewis number and
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stretch rate
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The original differences between He and N2 are their thermophysical properties, such as density and specific heat. These may lead to derived differences in combustion
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characteristics including flame temperature, elementary reaction rates, total heat release rate, flame height, stretch rate, and so on. In the following, we will discuss
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about these aspects in more details, where the inlet velocity of 24 m/s is chosen as an example. It is known that the heat capacity (ρcp) of He and N2 are 0.845 kJ/(m3·K) and 1.181 kJ/(m3·K), respectively. Namely, the former is only 72% of the latter. Because the dilution takes up a large volume fraction of the gaseous mixture, the heat capacity
of the mixture is largely determined by that of the dilution. Therefore, the gaseous mixture can be raised up to a much higher temperature level in the case of He dilution even if the total heat release amounts are assumed to be the same (Actually, as will be seen in Fig. 10, the total heat release under He dilution is larger than that of N2). To
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confirm this, the centerline gas temperature profile is plotted in Fig. 8. It is noted that the gas temperature rises up to 1540 K for the He dilution case, which is about 523 K
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higher than the N2 scenario. Accordingly, the wall temperature will also be raised to a higher level, which can improve the heat recirculation effect through convection heat
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exchange between the upstream inner wall and incoming fresh mixture. Our
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calculation shows that the heat recirculation ratio is increased from 2.89% to 3.55%
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when the dilution gas is changed from nitrogen to helium. Thus, it can be expected
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that elementary reactions could be intensified according to the Arrhenius law.
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Fig. 8.
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Another difference that the dilution might bring about is the effective Lewis number of the mixture, Leeff, which is defined as a weighted average of the Lewis number of oxidizer, LeO, and fuel, LeF. In the present work, the mixture is a fuel lean
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one, whose Leeff can be calculated through Eq. (3) [42, 43], Le eff
~ Le O ( 1 ) Le ~ 2
F
(3)
~
1
(4)
Here the Zel’dovich number. The effective Lewis numbers for the mixtures of =
0.4 with He and N2 dilutions are 0.60 and 0.57, respectively. Namely, the effective Lewis number of the mixture is increased when N2 is replaced by He. It is well known that the Lewis number effect is also termed as "differential diffusion effect", which implies that if the Lewis number is apart from unity, the balance between thermal
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diffusion and mass diffusion cannot be reached. As a result, reaction intensity in the flame front will be weakened. This is one of the most significant factors responsible
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for the "flame tip opening phenomenon". Although the difference between the effective Lewis numbers of these two cases are not that large, it might have significant
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effect on the occurrence of "flame tip opening" for near-limit combustion condition.
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The stretch effect is also an important factor that affects the flame structure,
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propagation and extinction [51]. For a stationary flat flame, the stretch rate is mainly
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determined by the tangential velocity gradient and flame curvature. To compute the
expressed in Eq. (5).
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stretch rate of a general flame shape, Candel and Poinsot [52] developed a formula, as
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a n u n u n n
(5)
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Here, n is the unit normal vector of the element pointing toward the unburned gas and u is the flow velocity at the flame surface. The first and second terms on the right hand side of Eq. (5) respectively represent the contributions of flow non-uniformity
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and flame curvature to the total stretch rate. In the present study, u can be read from numerical results and n can be derived by assuming the flame front to be a parabola [39]. For comparison, the stretch rates at flame tips are calculated for He and N2 atmospheres. The specific values are 5.93×106 and 6.39×106 for He and N2,
respectively. This implies that the flame tip suffers from a weaker stretch effect in the He atmosphere, which can lead to a larger burning velocity. We calculated the laminar burning velocities at = 0.4 in He and N2 environments, which are 1.10 m/s and 0.33 m/s, respectively. Obviously, the laminar burning velocity in He environment is much
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greater than that with N2 dilution. 3.2.2 Effects of He dilution on elementary reaction rates and total heat release
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rate
To investigate the influence of dilution on combustion reaction, we draw the
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Arrhenius rate of each elementary reaction at the flame tip in Fig. 9. According to Li
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[47], the elementary reactions are divided into four groups. It is seen from Fig. 9 that
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most of the elementary reactions have a bigger reaction rate under He atmosphere. In
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these elementary reactions, the H2/O2 chain reactions (R1–R4), R8 and R9 have great
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effect on the overall reaction. On the one hand, these six reactions play an important role in combustion. On the other hand, the Arrhenius rates of these reactions show
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bigger difference for different dilutions. For example, the reaction rate of R-3 is 310%
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larger for He than N2. The overall reaction rates are 13.8 and 53.3 kmol/m3·s for N2 and He dilutions, respectively, which confirms that the whole reaction process can be
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accelerated by replacing N2 with He. Fig. 9.
The total heat release rate (HRR) can show the reaction intensity intuitionally. Fig. 10 illustrates the centerline profiles of HRR, which clearly indicate that in the He
dilution case, the HRR peak value is greater than the N2 dilution counterpart. This implies that under He atmosphere, the overall reaction rate is higher. Moreover, according to the peak HRR positions, the H2/O2/He flame front is located more upstream, indicating that replacing N2 with He could shorten the flame height and
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reduce the stretch rate at the flame tip (refer to Fig. 8). In summary, for He dilution, the reaction rate and heat release rate at the flame tip is notably intensified, as a
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consequence, the flame tip opening phenomenon can be diminished and combustion
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efficiency is remarkably improved.
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Fig. 10.
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4. Conclusions
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Combustion of lean H2/O2/N2 and H2/O2/He mixtures in a micro-reactor with wall cavities were investigated numerically. It is shown that for H2/O2/N2 flames, "flame
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tip opening" occurs at high inlet velocities, which leads to a sharp decrease in the
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combustion efficiency. However, the combustion efficiency can be remarkably improved when the dilution is changed to helium. Theoretical analysis reveals that the underlying mechanisms lie in three aspects. In the first place, helium has a smaller
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heat capacity compared to nitrogen, which leads to a higher flame temperature. Moreover, the effective Lewis number of H2/O2/He mixture is greater than that of H2/O2/N2 mixture. Furthermore, the stretch effect at flame tip with He dilution is weaker than the N2 dilution counterpart. These three aspects act together and lead to
larger reaction rate and heat release rate at the flame tip, which alleviates the flame tip opening phenomenon and makes a high combustion efficiency achievable. Acknowledgements This work was supported by the National Natural Science Foundation of China under
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the Grant Number: 51576084.
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analysis on the blow-off limits of premixed CH4/air flames in a mesoscale bluff-body combustor, Energy 113 (2016) 193-203. [32] J.L. Wan, A.W. Fan, Y. Liu, H. Yao, W. Liu, Experimental investigation and
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numerical analysis on flame stabilization of CH4/air mixture in a mesoscale channel with wall cavities, Combust. Flame 162 (2015) 1035-1045.
[33] J.L. Wan, A.W. Fan, H. Yao, W. Liu, Effect of pressure on the blow-off limits of premixed CH4/air flames in a mesoscale cavity-combustor, Energy 91 (2015) 102-109. [34] J.L. Wan, A.W. Fan, H. Yao, W. Liu, A numerical investigation on combustion
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characteristics of H2/air mixture in a micro-combustor with wall cavities, Int J Hydrogen Energy 39 (2014) 8138-8146.
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[38] W. Yang, Y. Xiang, A.W. Fan, H. Yao, Effect of the cavity depth on the
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combustion efficiency of lean H2/air flames in a micro combustor with dual cavities, Int. J. Hydrogen Energy 42 (2017) 14312-14320. [39] W. Yang, A.W. Fan, H. Yao, Effect of inlet temperature on combustion efficiency
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of lean H2/air mixtures in a micro-combustor with wall cavities, Appl. Therm. Eng. 107 (2016) 837-843. [40] W. Yang, A.W. Fan, H. Yao, W. Liu, Effect of reduced pressures on the combustion efficiency of lean H2/air flames in a micro cavity-combustor, Int. J.
Hydrogen Energy 41 (2016) 1535-15361. [41] W. Yang, L.H. Li, A.W. Fan, H. Yao, Effect of oxygen enrichment on combustion efficiency of lean H2/N2/O2 flames in a micro cavity-combustor, Chem. Eng. Process.: Process Intensif. 127 (2018) 50–57.
[43] M. Matalon, Flame dynamics, Proc. Combust. Inst. 32 (2009) 57-82.
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[42] C.K. Law, Combustion physics, New York: Cambridge University Press; 2006.
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[44] B. Galmiche, F. Halter, F. Foucher, P. Dagaut, Effects of dilution on laminar burning velocity of premixed methane/air flames, Energy Fuels 25 (2011) 948-954.
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[45] A. Beskok, G.E. Karniadakis, A model for flows in channels, pipes, and ducts at
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micro and nano scales, Microscale Therm. Eng. 3 (1999) 43-77.
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[46] Q.F. Ma, R.S. Fang, L.C. Xiang, Handbook of thermo-physical properties,
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Bejing: China Agricultural Machinery Press; 1986 (in Chinese).
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[47] J. Li, Z.W. Zhao, A. Kazakov, F.L. Dryer, An updated comprehensive kinetic model of hydrogen combustion, Int. J. Chem. Kinet. 36 (2004) 1-10.
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[48] CHEMKIN-PRO Release 15101, Reaction Design Inc, San Diego, CA, 2010.
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[49] J.P. Holman, Heat transfer, 9th ed. New York: McGraw-Hill; 2002. [50] Fluent 6.3 user’s Guide, Lebanon, New Hampshire: Fluent Inc, 2006. [51] CK. Law, Dynamics of stretched flames. Symposium (International) on Combust.
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22 (1989)1381-1402. [52] S.M. Candel, T.J. Poinsot, Flame stretch and the balance equation for the flame area, Combust. Sci. Tech. 70 (1990) 1-15.
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Fig. 1. Schematic diagram and coordinates of the micro-combustor with wall cavities:
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(a) longitudinal cross section, (b) transverse cross section.
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Fig. 2. Centerline profiles of gas temperature and H2 mass fraction for different grid
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resolutions under = 0.4, Vin= 8 m/s and N2 dilution.
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Fig. 3. Demonstration of the grid system near the upper cavity.
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Fig. 4. Comparison between predicted and measured exhaust gas temperature [34].
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Fig. 5. Variations of combustion efficiency with inlet velocity for N2 and He dilutions.
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Fig. 6. H2 mole fraction distributions for N2 and He dilutions at Vin= 24 m/s.
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Fig. 7. Centerline profiles of H2 mole fraction for N2 and He dilutions at Vin= 24 m/s.
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m/s.
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Fig. 8. Centerline profiles of gaseous temperature for N2 and He dilutions at Vin= 24
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(b)
(d)
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(c)
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(a)
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Fig. 9. Elementary reaction rates of at the flame tip for N2 and He dilutions at Vin= 24
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m/s: (a) H2/O2 chain reactions, (b) H2/O2 dissociation/recombination reactions, (c)
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formation and consumption of HO2, (d) formation and consumption of H2O2.
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Fig. 10. Centerline profiles of total heat release rate for N2 and He dilutions at Vin= 24
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m/s.
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Figure Captions List
Fig. 1. Schematic diagram and coordinates of the micro-combustor with wall cavities: (a) longitudinal cross section, (b) transverse cross section.
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Fig. 2. Centerline profiles of gas temperature and H2 mass fraction for different grid resolutions under = 0.4, Vin= 8 m/s and N2 dilution. Fig. 3. Demonstration of the grid system near the upper cavity. Fig. 4. Comparison between predicted and measured exhaust gas temperature[34].
Fig. 5. Variations of combustion efficiency with inlet velocity for N2 and He dilutions. Fig. 6. H2 mole fraction distributions for N2 and He dilutions at Vin= 24 m/s. Fig. 7. Centerline profiles of H2 mole fraction for N2 and He dilutions at Vin= 24 m/s. Fig. 8. Centerline profiles of gaseous temperature for N2 and He dilutions at Vin= 24
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m/s. Fig. 9. Elementary reaction rates of at the flame tip for N2 and He dilutions at Vin= 24
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m/s: (a) H2/O2 chain reactions, (b) H2/O2 dissociation/recombination reactions, (c) formation and consumption of HO2, (d) formation and consumption of H2O2.
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Fig. 10. Centerline profiles of total heat release rate for N2 and He dilutions at Vin= 24
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m/s.
S0255-2701(18)30551-8 https://doi.org/10.1016/j.cep.2018.06.014 CEP 7316
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
10-5-2018 14-6-2018 19-6-2018
Please cite this article as: Fan A, Xiang Y, Yang W, Li L, Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities, Chemical Engineering and Processing - Process Intensification (2018), https://doi.org/10.1016/j.cep.2018.06.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Enhancement of hydrogen combustion efficiency by helium dilution in a micro-combustor with wall cavities
Aiwu Fan*, Ying Xiang, Wei Yang, Linhong Li
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Technology, Wuhan 430074, China
Corresponding author:
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E-mail: [email protected]
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Fax: +86-27-87540724
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1037 Luoyu Road, Wuhan 430074, China
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Prof. Aiwu Fan
Phone: +86-27-87542618
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State Key Laboratory of Coal Combustion, Huazhong University of Science and
Graphical abstract
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Combustion efficiency of lean H2/O2/N2 flames can be notably improved by helium dilution because of the intensifications of chemical reactions and heat release at the tip of H2/O2/He
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flames. As a result, the flame tip opening phenomenon is suppressed and combustion completeness is significantly promoted.
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Highlights
Combustion efficiency of lean H2 flames can be notably enhanced by helium dilution.
Flame temperature increases greatly due to a smaller heat capacity of helium.
The effective Lewis number of the gaseous mixture with helium dilution is raised.
Stretch effect at the tip of H2/O2/He flames is weaker compared to H2/O2/N2 flames.
Reaction rate and heat release rate at the tip of H2/O2/He flames is intensified.
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Abstract
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For very lean H2/air flames in a micro-combustor with cavity flame holders, the
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combustion efficiency decreases rapidly at sufficiently high inlet velocity due to the occurrence of "flame tip opening". To suppress this undesirable phenomenon, we used helium (He) to replace nitrogen (N2) as dilution in the oxidant. Numerical simulation was conducted under an equivalence ratio of 0.4 for both N2 and He dilutions. The results show that the combustion efficiency is greatly improved, remaining above 98%
at 32 m/s in the case of He dilution. The analysis reveals that several reasons are responsible for these results. Firstly, the heat capacity of He is smaller than N2, which leads to a higher temperature level of the gaseous mixture in reaction zone. Second, the effective Lewis number of the H2/O2/He mixture is larger than that of the
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H2/O2/N2 mixture. Thirdly, the magnitude of stretch rate at the flame tip for He dilution is less than the N2 counterpart. The combined effects of three aspects result in
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intensified reaction rate and heat release rate at the flame tip. As a consequence, the
flame tip opening phenomenon can be significantly suppressed and combustion
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efficiency be notably increased.
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Keywords: micro combustor; combustion efficiency; helium dilution; Lewis number;
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stretch rate
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1. Introduction
Combustion in micro reactors is an emerging area which has attracted extensive
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attentions in past decades. The main merit of a micro combustor is that this device can
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provide a considerably higher power density compared to conventional batteries [1]. However, flame stabilization under a reduced scale remains a daunting task because
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of the increased heat loss ratio and reduced residence time [2-7]. Researchers have spent a lot of efforts to enhance flame stability in miniaturized
combustors. Thermal interactions between the flame and combustor walls significantly affect the flame stability [8]. Thus, thermal management is most frequently used for flame stabilization in small combustors. The “Swiss roll”
configuration can effectively improve combustion performance of micro combustors [9, 10] via heat recirculation. Kang and Veeraragavan [11] made a micro combustor with thermally orthotropic material, which has broadened flammability limits due to enhanced heat recirculation and reduced heat loss. Wan et al. [12, 13] proposed a
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micro combustor with preheating channels and a plate flame holder, demonstrating that lean methane/air mixtures can be burned even below the conventional
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flammability limit. SiC foam was employed in a micro modular combustor by Yang et al. [14]. They found that porous foam is helpful to form a high and uniform distribution.
Standing
waves
can
be
achieved
in
a
planar
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temperature
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micro-combustor partially filled with porous media [15]. Stationary flames emerge
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over a wide operational range in mesoscale channels filled with fibrous porous media
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[16-18] for both premixed and non-premixed combustions. Zuo et al. [19] improved
micro TPV devices.
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the thermal performance of a micro combustor with double counterflow channels for
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Moreover, catalytic combustion is an effective measure to attenuate the
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radical-quenching effect of the wall surfaces. Li et al. [20] numerically studied the effects of catalyst segmentation and wall cavities on CH4/O2 flames in micro-combustors. Zhang et al. [21] investigated the effects of convex cavity structure,
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position and number on methane conversion and extinction limit through catalytic combustion in a micro-channel. Yan et al. [22] explored catalytic combustion characteristics of a meso-scale combustor with preheating channels. They found that combustion efficiency increases by approximately 9% in this combustor compared to
that without heat recirculation. To anchor flame in micro combustors, forming a recirculation zone or low velocity zone is another effective approach. The flame stability in micro combustors was improved by fabricating one or multiple backward facing steps in the walls [23,
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24]. E et al. [25] examined the impacts of inlet pressure and found that the highest energy conversion efficiency and exergy efficiency were both obtained at an
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atmospheric pressure. Baigmohammadi [26] investigated the effects of mixture flow rate, equivalence ratio, oxygen enhancement, and geometrical parameters on the
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stability of premixed propane-air flames meso-scale combustors with a step. Rich
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flame dynamics were observed in their experiment. Various bluff bodies were used as
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flame holders in small combustors which can notably expand flame blow-off limit
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[27-31]. Meso-scale combustors with dual cavities in the walls can also obtain a large
mixtures [32, 33].
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blow-off limit that is several times the corresponding burning velocities of incoming
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Although flame stability can be significantly promoted in the presence of wall
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cavities, the combustion efficiency of lean H2/air flames decreases quickly at sufficiently high inlet velocity [34]. It is revealed that the incomplete combustion is owing to the emergence of “flame tip opening”. This phenomenon was also reported
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by Brambilla et al. [35] in lean H2/CO/air flames in mesoscale channels. Many factors, such as wall thermal conductivey, surface emissivity, cavity depth, initial temperature and pressure, and oxygen concentration [36-41], can affect the occurrence of flame tip opening in micro combustors. It is well understood that flame tip opening is
essentially local extinction that always happens in stretched premixed flames with a sub-unity effective Lewis number [42, 43]. A large number of studies have demonstrated that using helium (He) as dilution can raise the effective Lewis number and increase the laminar burning velocity of the mixture [44]. Therefore, in the
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present study we are dedicated to numerically investigating the effect of helium dilution on the combustion efficiency of H2 flames in a micro-combustor with wall
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cavities. 2. Numerical methods
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2.1 Geometric model
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The schematic of the micro-combustor with double cavities is shown in Fig. 1. The
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gap distance (W1), length (L0) and width (W0) of the channel are respectively 1 mm,
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10 mm and 18 mm. The distance (L1) from the combustor entrance to the vertical wall
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of the cavity is 3 mm, while the length (L2) and depth (W2) of the cavity are 3 mm and 1 mm, respectively. The acute angle (θ) between the ramped cavity wall and interior
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wall is 45°. The wall thickness (W3) is 2 mm.
Fig. 1.
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2.2 Mathematical model In this work, H2 is used as the fuel, and the oxidant is mixed by 21% O2 and 79% N2 or 79% He. First, we estimate the value of Knudsen number, Kn=Lg/Lc, where Lg is the mean free path of the gas and Lc is the characteristic scale of the combustor. For both
H2 and O2, the orders of magnitude of Kn are approximately 10-5. According to [45], if the Knudsen number is less than 10-3, the Navier-Stokes equations are still applicable. Because heat recirculation via the channel walls has a significant impact on the flame tip opening phenomenon [36], heat conduction in the solid walls is considered in the
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computation. A two-dimensional, steady-state model is employed to reduce the computational cost because the aspect ratio (W0/W1) of the micro combustor is very
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large (10:1). 2.3 Computation scheme
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Similar to our previous experiments, quartz is selected as the solid material. The
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density (ρ), thermal conductivity (λs), specific heat capacity (cp) and surface
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emissivity () for quartz glass are 2650 kg/m3, 1.05 W/(mK), 750 J/(kg·K) and 0.92,
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respectively [46]. The mixture equivalence ratios are held at = 0.4. The gaseous
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mixture is treated as an ideal gas and its specific heat, viscosity and thermal conductivity are computed from a mass-fraction-weighted average of the species’
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properties. The detailed chemistry reported by Li et al. [47] was employed to model
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the combustion of H2. It involves 13 species and 19 reversible elementary reactions. The results have been verified to be independent of employed mechanisms [41]. The thermodynamic and transport properties of the gaseous species are imported from the
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CHEMKIN databases [48]. The boundary conditions are explained as follows: 1) At the inlet: uniform concentration and velocity profiles are imposed; The inlet temperature (Tin) is 300 K.
2) At the outlet: Neumann boundary condition with zero gradients is given. 3) At the inner surfaces: The effect of interior surface to surface radiation is considered using the discrete ordinates (DO) model [34]. 4) At the exterior surfaces: both heat losses via radiation and natural convection are
q o h o T w , o T T w , o T 4
4
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taken into account and the total heat loss rate is calculated through Eq. (1):
(1)
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where ho is the natural convection heat transfer coefficient (～20 W/(m2 K) [49], T∞ is
the ambient temperature (300 K), Tw,o is the outer wall temperature, is the emissivity
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of the solid surface (0.92), and σ is the Stephan-Boltzmann constant with a value of
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5.67×10-8 W/(m2 K4).
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The grid independency was checked by comparing the results of three different grid
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systems, i.e., Δx=Δy=10 μm, 15 μm and 20 μm. The condition of = 0.4, Vin= 8 m/s
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with N2 dilution was chosen as an example. The profiles of gas temperature and mass fraction of H2 along the centerline of the micro-combustor are plotted in Fig. 2. The
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differences between these numerical results are negligible. Therefore, the cell size of
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Δx=Δy= 20 μm is considered to be fine enough to obtain accurate prediction. Further refinement of the grid system was conducted in the cavity region and the total cell numbers are 138033 in the final computation. The local grid system in the vicinity of
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upper cavity is illustrated in Fig. 3.
Fig. 2.
Fig. 3.
The commonly used computational fluid dynamics (CFD) software FLUENT 6.3 [50] was applied to solve the mass, momentum, energy and species conservation
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equations. The second-order upwind scheme was used to discretize the mathematical model, and the “SIMPLE” algorithm was employed to solve the coupling of pressure
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and velocity. To initiate the chain reactions of lean mixture, an initial temperature of
2000 K was imposed on the fluid zone. This is a frequently adopted strategy in
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combustion simulation applying CFD software. The convergence criteria were set to
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be 1.0×10−6 for the residuals of all variables.
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2.4 Model validation
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In a previous work [34], we validated the accuracy of the numerical model and
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computing scheme by comparing predicted and measured values of exhaust gas temperatures at various inlet velocities, as presented in Fig. 4. It’s noted that the
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largest and smallest relative errors are 10.3% (at Vin= 8 m/s) and 4.43% (Vin= 26 m/s),
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respectively. This is because the Reynolds number will be increased with the increase in the inlet velocity. Therefore, the prediction accuracy by using a turbulence model will be higher at large inlet velocities. This verifies that the results of present study are
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reliable.
Fig. 4.
3 Results and discussion 3.1 Combustion efficiency Here, we define the combustion efficiency as, C out C in
(2)
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c 1
where Cin and Cout are fuel mass fractions at the inlet and outlet of the
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micro-combustor, respectively. For comparison, the variations of combustion efficiency with inlet velocity are plotted in Fig. 5 for both N2 and He dilutions. It is seen from Fig. 5 that in the N2 atmosphere, combustion efficiency decreases rapidly
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with an increasing inlet velocity. For example, the combustion efficiency under N2
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dilution drops to 78.0% at Vin= 32 m/s. In contrast, when N2 is replaced by He, the
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combustion efficiency still remains above 98.2% at very high inlet velocities. This confirms that replacing N2 with He is an extremely effective way to improve the
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combustion efficiency of lean H2 flames in the micro-cavity combustor.
Fig. 5
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The distributions of H2 mole fraction under N2 and He dilutions are presented in
Fig. 6 for the case of Vin= 24 m/s. Meanwhile, the centerline profiles of H2 mole
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fraction are plotted in Fig. 7. These two pictures clearly demonstrate that when the dilution is N2, the fuel is not completely burnt at the flame tip and leaks out from the combustor exit. This is attributed to the occurrence of flame tip opening, which is a frequently observed phenomenon in lean flames suffering from intense stretch effect. However, for the He dilution case, the fuel concentration starts to decrease earlier and
much faster (Fig. 7). As a result, H2 is almost fully consumed in a much shorter distance.
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Fig. 6.
Fig. 7.
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3.2 Analysis and Discussion
First, we took the case of 16 m/s to examine the third body effect of helium. The combustion efficiencies were 98.99% and 90.09% respectively when the third body
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effect was considered and not considered, which demonstrated that the third body
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effect was negligible on the combustion efficiency. In the following sections, the
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effect of helium will be analyzed from other aspects. 3.2.1 Effect of He dilution on temperature level, effective Lewis number and
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stretch rate
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The original differences between He and N2 are their thermophysical properties, such as density and specific heat. These may lead to derived differences in combustion
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characteristics including flame temperature, elementary reaction rates, total heat release rate, flame height, stretch rate, and so on. In the following, we will discuss
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about these aspects in more details, where the inlet velocity of 24 m/s is chosen as an example. It is known that the heat capacity (ρcp) of He and N2 are 0.845 kJ/(m3·K) and 1.181 kJ/(m3·K), respectively. Namely, the former is only 72% of the latter. Because the dilution takes up a large volume fraction of the gaseous mixture, the heat capacity
of the mixture is largely determined by that of the dilution. Therefore, the gaseous mixture can be raised up to a much higher temperature level in the case of He dilution even if the total heat release amounts are assumed to be the same (Actually, as will be seen in Fig. 10, the total heat release under He dilution is larger than that of N2). To
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confirm this, the centerline gas temperature profile is plotted in Fig. 8. It is noted that the gas temperature rises up to 1540 K for the He dilution case, which is about 523 K
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higher than the N2 scenario. Accordingly, the wall temperature will also be raised to a higher level, which can improve the heat recirculation effect through convection heat
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exchange between the upstream inner wall and incoming fresh mixture. Our
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calculation shows that the heat recirculation ratio is increased from 2.89% to 3.55%
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when the dilution gas is changed from nitrogen to helium. Thus, it can be expected
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that elementary reactions could be intensified according to the Arrhenius law.
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Fig. 8.
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Another difference that the dilution might bring about is the effective Lewis number of the mixture, Leeff, which is defined as a weighted average of the Lewis number of oxidizer, LeO, and fuel, LeF. In the present work, the mixture is a fuel lean
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one, whose Leeff can be calculated through Eq. (3) [42, 43], Le eff
~ Le O ( 1 ) Le ~ 2
F
(3)
~
1
(4)
Here the Zel’dovich number. The effective Lewis numbers for the mixtures of =
0.4 with He and N2 dilutions are 0.60 and 0.57, respectively. Namely, the effective Lewis number of the mixture is increased when N2 is replaced by He. It is well known that the Lewis number effect is also termed as "differential diffusion effect", which implies that if the Lewis number is apart from unity, the balance between thermal
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diffusion and mass diffusion cannot be reached. As a result, reaction intensity in the flame front will be weakened. This is one of the most significant factors responsible
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for the "flame tip opening phenomenon". Although the difference between the effective Lewis numbers of these two cases are not that large, it might have significant
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effect on the occurrence of "flame tip opening" for near-limit combustion condition.
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The stretch effect is also an important factor that affects the flame structure,
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propagation and extinction [51]. For a stationary flat flame, the stretch rate is mainly
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determined by the tangential velocity gradient and flame curvature. To compute the
expressed in Eq. (5).
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stretch rate of a general flame shape, Candel and Poinsot [52] developed a formula, as
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a n u n u n n
(5)
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Here, n is the unit normal vector of the element pointing toward the unburned gas and u is the flow velocity at the flame surface. The first and second terms on the right hand side of Eq. (5) respectively represent the contributions of flow non-uniformity
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and flame curvature to the total stretch rate. In the present study, u can be read from numerical results and n can be derived by assuming the flame front to be a parabola [39]. For comparison, the stretch rates at flame tips are calculated for He and N2 atmospheres. The specific values are 5.93×106 and 6.39×106 for He and N2,
respectively. This implies that the flame tip suffers from a weaker stretch effect in the He atmosphere, which can lead to a larger burning velocity. We calculated the laminar burning velocities at = 0.4 in He and N2 environments, which are 1.10 m/s and 0.33 m/s, respectively. Obviously, the laminar burning velocity in He environment is much
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greater than that with N2 dilution. 3.2.2 Effects of He dilution on elementary reaction rates and total heat release
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rate
To investigate the influence of dilution on combustion reaction, we draw the
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Arrhenius rate of each elementary reaction at the flame tip in Fig. 9. According to Li
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[47], the elementary reactions are divided into four groups. It is seen from Fig. 9 that
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most of the elementary reactions have a bigger reaction rate under He atmosphere. In
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these elementary reactions, the H2/O2 chain reactions (R1–R4), R8 and R9 have great
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effect on the overall reaction. On the one hand, these six reactions play an important role in combustion. On the other hand, the Arrhenius rates of these reactions show
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bigger difference for different dilutions. For example, the reaction rate of R-3 is 310%
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larger for He than N2. The overall reaction rates are 13.8 and 53.3 kmol/m3·s for N2 and He dilutions, respectively, which confirms that the whole reaction process can be
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accelerated by replacing N2 with He. Fig. 9.
The total heat release rate (HRR) can show the reaction intensity intuitionally. Fig. 10 illustrates the centerline profiles of HRR, which clearly indicate that in the He
dilution case, the HRR peak value is greater than the N2 dilution counterpart. This implies that under He atmosphere, the overall reaction rate is higher. Moreover, according to the peak HRR positions, the H2/O2/He flame front is located more upstream, indicating that replacing N2 with He could shorten the flame height and
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reduce the stretch rate at the flame tip (refer to Fig. 8). In summary, for He dilution, the reaction rate and heat release rate at the flame tip is notably intensified, as a
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consequence, the flame tip opening phenomenon can be diminished and combustion
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efficiency is remarkably improved.
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Fig. 10.
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4. Conclusions
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Combustion of lean H2/O2/N2 and H2/O2/He mixtures in a micro-reactor with wall cavities were investigated numerically. It is shown that for H2/O2/N2 flames, "flame
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tip opening" occurs at high inlet velocities, which leads to a sharp decrease in the
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combustion efficiency. However, the combustion efficiency can be remarkably improved when the dilution is changed to helium. Theoretical analysis reveals that the underlying mechanisms lie in three aspects. In the first place, helium has a smaller
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heat capacity compared to nitrogen, which leads to a higher flame temperature. Moreover, the effective Lewis number of H2/O2/He mixture is greater than that of H2/O2/N2 mixture. Furthermore, the stretch effect at flame tip with He dilution is weaker than the N2 dilution counterpart. These three aspects act together and lead to
larger reaction rate and heat release rate at the flame tip, which alleviates the flame tip opening phenomenon and makes a high combustion efficiency achievable. Acknowledgements This work was supported by the National Natural Science Foundation of China under
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the Grant Number: 51576084.
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Fig. 1. Schematic diagram and coordinates of the micro-combustor with wall cavities:
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(a) longitudinal cross section, (b) transverse cross section.
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Fig. 2. Centerline profiles of gas temperature and H2 mass fraction for different grid
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resolutions under = 0.4, Vin= 8 m/s and N2 dilution.
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Fig. 3. Demonstration of the grid system near the upper cavity.
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Fig. 4. Comparison between predicted and measured exhaust gas temperature [34].
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Fig. 5. Variations of combustion efficiency with inlet velocity for N2 and He dilutions.
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Fig. 6. H2 mole fraction distributions for N2 and He dilutions at Vin= 24 m/s.
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Fig. 7. Centerline profiles of H2 mole fraction for N2 and He dilutions at Vin= 24 m/s.
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m/s.
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Fig. 8. Centerline profiles of gaseous temperature for N2 and He dilutions at Vin= 24
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(b)
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(a)
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Fig. 9. Elementary reaction rates of at the flame tip for N2 and He dilutions at Vin= 24
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m/s: (a) H2/O2 chain reactions, (b) H2/O2 dissociation/recombination reactions, (c)
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formation and consumption of HO2, (d) formation and consumption of H2O2.
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Fig. 10. Centerline profiles of total heat release rate for N2 and He dilutions at Vin= 24
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m/s.
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Figure Captions List
Fig. 1. Schematic diagram and coordinates of the micro-combustor with wall cavities: (a) longitudinal cross section, (b) transverse cross section.
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Fig. 2. Centerline profiles of gas temperature and H2 mass fraction for different grid resolutions under = 0.4, Vin= 8 m/s and N2 dilution. Fig. 3. Demonstration of the grid system near the upper cavity. Fig. 4. Comparison between predicted and measured exhaust gas temperature[34].
Fig. 5. Variations of combustion efficiency with inlet velocity for N2 and He dilutions. Fig. 6. H2 mole fraction distributions for N2 and He dilutions at Vin= 24 m/s. Fig. 7. Centerline profiles of H2 mole fraction for N2 and He dilutions at Vin= 24 m/s. Fig. 8. Centerline profiles of gaseous temperature for N2 and He dilutions at Vin= 24
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m/s. Fig. 9. Elementary reaction rates of at the flame tip for N2 and He dilutions at Vin= 24
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m/s: (a) H2/O2 chain reactions, (b) H2/O2 dissociation/recombination reactions, (c) formation and consumption of HO2, (d) formation and consumption of H2O2.
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Fig. 10. Centerline profiles of total heat release rate for N2 and He dilutions at Vin= 24
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m/s.