Heat recirculating reactors: Fundamental research and applications

Progress in Energy and Combustion Science 72 (2019) 32–58

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Progress in Energy and Combustion Science journal homepage: www.elsevier.com/locate/pecs

Heat recirculating reactors: Fundamental research and applications Janet L. Ellzey∗, Erica L. Belmont, Colin H. Smith a b c

University of Texas at Austin, Walker Department of Mechanical Engineering, 204 E. Dean Keeton St., Stop C2200, Austin, TX 78712, United States University of Wyoming, Department of Mechanical Engineering, Dept. 3295, 1000 E. University Avenue Laramie, WY 82071 Vector Launch, 15261 Connector Ln., Huntington Beach, CA 92649-1117

a r t i c l e

i n f o

Article history: Received 9 May 2018 Accepted 30 December 2018

Keywords: Heat recirculating reactor Superadiabatic Excess enthalpy Porous reactor Lean combustion Rich combustion

a b s t r a c t Worldwide emphasis on fuel efficiency, low emissions, and use of low-quality fuels such as biogas continues to drive the development of combustors that operate over a wider range of fuel/air ratios and with higher burning velocities than their conventional counterparts. Enhancement of reaction rates is required to increase burning velocities and widen fuel/air operating ranges over values achievable in conventional combustors, and extensive research over the last few decades has shown that transferring heat in a reactor from hot combustion products to incoming reactants can accomplish this enhancement without external energy addition. These reactors, called heat recirculating reactors, use various geometries and flow strategies to optimize the heat transfer. In this paper, research on heat recirculating reactors is reviewed with an emphasis on the most important designs and applications. The basic characteristics of a heat recirculating reactor are encompassed in a simple configuration: a flame stabilized in a tube with high thermal conductivity. More complex designs that have evolved to further optimize heat transfer and recirculation are then described, including porous reactors with or without flame stabilization and channel reactors consisting of parallel tubes or slots. Advanced designs introduce additional means of heat transfer, such as transverse heat transfer from hot products through channel walls to incoming reactants, thereby leading to the counter-flow channel reactor. The flexibility of heat recirculating reactors to operate on a variety of fuels and over wide operating ranges has led to many applications including fuel reformers, radiant heaters and thermal oxidizers, and important work on these applications is reviewed. Finally, future research directions are discussed. © 2019 Elsevier Ltd. All rights reserved.

Contents 1.

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3.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Fundamental principle of heat recirculating reactors. 1.2. Important parameters for design and performance. . 1.3. Operating regimes of heat recirculating reactors . . . . 1.4. Scope of this review. . . . . . . . . . . . . . . . . . . . . . . . . . . Unidirectional flow reactors. . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Operating principle of unidirectional flow reactor. . . 2.2. Unidirectional reactor designs. . . . . . . . . . . . . . . . . . . 2.2.1. Reactors with self-stabilizing flames . . . . . . . 2.2.2. Reactors with flame stabilization . . . . . . . . . 2.2.3. Filtration reactors . . . . . . . . . . . . . . . . . . . . . . Steady state counter-flow reactors . . . . . . . . . . . . . . . . . . . . 3.1. Operating principle of counter-flow reactors . . . . . . . 3.2. Counter-flow reactor designs . . . . . . . . . . . . . . . . . . . 3.2.1. Folded channel reactor . . . . . . . . . . . . . . . . . . 3.2.2. Swiss roll combustors. . . . . . . . . . . . . . . . . . .

Corresponding author. E-mail address: [email protected] (J.L. Ellzey).

https://doi.org/10.1016/j.pecs.2018.12.001 0360-1285/© 2019 Elsevier Ltd. All rights reserved.

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3.2.3. Counter-flow channels . . . . . Applications of heat recirculating reactors . 4.1. Lean combustion . . . . . . . . . . . . . . . . 4.2. Radiant heating . . . . . . . . . . . . . . . . . 4.3. Thermoelectric power generation . . . 4.4. Fuel reforming . . . . . . . . . . . . . . . . . . 5. Conclusions and future work. . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.

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1. Introduction The importance of heat transfer to premixed combustion is firmly established in both theory and practice, often defining the nature of the combustion process or whether it will occur at all. This basic principle was established by Mallard and Le Chatelier [1] who proposed that self-sustaining combustion of a premixed fuel/air reactant mixture was achieved by the transfer of heat from the flame zone such that the unburned mixture was brought up to the ignition temperature. Their groundbreaking work resulted in a simple expression showing that burning rate, or flame speed, is positively related to thermal diffusivity. In this simple model of a laminar flame, the thermal diffusivity of the gas, which determines the gas phase heat transfer, is set by the particular fuel/oxidizer mixture and cannot be altered to enhance flame characteristics. The reaction rate, however, can be changed by heat transfer into or out of a reactant mixture, thereby increasing or decreasing the reactant temperature and altering the reaction rate. As a result, the flammability limits of the reactant mixture can be broadened or narrowed [2–4]. Explosion limits are also a function of heat transfer; an explosion is produced when heat transfer raises the temperature of a fuel/oxidizer mixture such that heat release from runaway exothermic reactions is greater than heat loss. Heat transfer also plays a critical role in flame quenching when heat loss from the reaction zone overwhelms heat release, thus resulting in extinguishment of the chemical reactions [5]. These fundamental theories demonstrate that heat transfer into and out of the reaction zone has the potential for profound effects on combustion characteristics. Enhancing heat transfer from hot combustion gases to lower temperature reactants can be achieved by exposing the combustion gases to solid surfaces, which provide an effective conductive and radiative pathway to transfer heat from hot combustion products to relatively cold reactants. This idea has given rise to heat recirculating reactors, which are purposely designed to use solid surfaces to enhance the heat transfer from the reaction zone to the unburned reactants [6,7].

1.1. Fundamental principle of heat recirculating reactors The basic principle behind heat recirculating reactors is that energy is recycled from the flame to the reactants to increase the reactant temperature such that reactions will proceed at enhanced rates, without any energy addition from an external source. One of the interesting features of heat recirculating reactors is the possibility that maximum temperatures may exceed those predicted by chemical equilibrium [6]. This gave rise to the terms superadiabatic or excess enthalpy combustion and presented the possibility of two other distinct but related phenomena: stable combustion of fuels at equivalence ratios significantly beyond conventional flammability limits [6–8], and flame speeds that exceed the laminar flame speed. It is important to note that the terms superadiabatic or excess enthalpy refer to local quantities, i.e. the maximum peak temperature or enthalpy may exceed that of an adiabatic flame without heat recirculation, but the overall energy balance as restricted by the first law remains unchanged.

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The impact of heat addition varies according to the equivalence ratio of the mixture, as shown in Fig. 1. At equivalence ratios well within the conventional flammability limits (Regime I), heat addition is not necessary for combustion stability although it may enhance the burning rate. As the mixture approaches the lean or rich flammability limit (Regime II), the flame becomes less stable, which is unsuitable in practical applications, and these mixtures benefit from heat addition to enhance flame stability. Beyond the flammability limits, a flame is not self-sustaining because the exothermic reactions cannot overcome heat losses (Regime III). Heat addition in this regime must produce reaction temperatures above the temperature predicted by equilibrium (superadiabatic temperatures) in order for combustion to be sustained. Heat recirculating reactors may operate within the conventional flammability limits or beyond these limits, in the ultra-lean or ultra-rich regimes. Reactors operating in each of these equivalence ratio regimes have different applications as described in Fig. 2, which shows a distribution of the adiabatic and constant pressure equilibrium products for methane/air at different equivalence ratios calculated using Cantera [9]. Combustors may operate near stoichiometry where thermal energy output per unit of reactant mixture is maximized and major products include carbon dioxide (CO2 ) and water (H2 O). There are practical advantages to operating near the lean flammability limit for low emissions of both carbon monoxide (CO) and nitric oxide (NO). Thermal oxidizers, which have applications in emissions control, operate beyond the lean flammability limit in the ultra-lean regime where significant amounts of oxygen (O2 ) and nitrogen (N2 ) are in the reactants and only trace amounts of fuel are available. The ultimate goal of a lean-burning reactor is robust operation in terms of operating range while minimizing emissions such as NO, CO and unburned hydrocarbons (UHC). On the rich side of stoichiometry, near and beyond the rich flammability limit, the reactor is a fuel reformer and converts the fuel to syngas consisting of CO, hydrogen (H2 ), and other products. Since performance is driven by heat transfer rather than catalytic reactions, heat recirculating reactors tend to be fuel flexible, operating similarly with different fuels and insensitive to fuel impurities. 1.2. Important parameters for design and performance Heat recirculating reactors are based on the concept of an embedded flame, i.e. the flame is stabilized within and not at the surface of the reactor. This characteristic distinguishes these reactors from those in which combustion takes place at the exit of a tube and places a number of limits on design and operating parameters, described by the Damköhler number (Da), quenching Peclet number (Peq ), dimensionless heat loss ratio (H˜ ), and Reynolds number (Re)

Da = P eq = H˜ =

τf L/U = τc τc SL dq

α

hE AE hI AI

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J.L. Ellzey, E.L. Belmont and C.H. Smith / Progress in Energy and Combustion Science 72 (2019) 32–58

Fig. 1. Flame stability as a function of equivalence ratio and effect of heat addition.

Fig. 2. Adiabatic, constant pressure equilibrium products of methane/air mixtures as a function of equivalence ratio.

Re =

U dp

v

where τ f and τ c are the residence and chemical times scales, respectively; L and U are the reactor length and inlet velocity, respectively; SL , dq and α are the laminar flame speed, quenching diameter, and thermal diffusivity, respectively; hE is the convective heat transfer coefficient between the external surface and the environment and hI is the convective heat transfer coefficient between internal surfaces and the gas; AE and AI are the external and internal areas for heat transfer, respectively; and dp and v are the pore diameter or channel height and the kinematic viscosity of the gas, respectively. Gas residence time, dependent upon reactor length and reactant velocity, is highly influential in whether an embedded flame can be sustained in a reactor. The required reactor length and maximum reactant velocity is suggested by Da, as an embedded flame is able to exist when its chemical reaction time is smaller than the reac-

tor residence time (Da 1). There is no minimum reactor length L for infinitely fast kinetics (Da = ∞), so it is important to consider finite rate kinetics when developing a reactor design; for example, accommodation of finite rate kinetics is critical for fuel reforming where relatively slow reactions are significant contributors to the production of hydrogen (Section 4.4). Limits on reactant velocity are reflected in Re limits, which define the stability characteristics of the reactor; at low Re heat losses overwhelm heat release and the flame extinguishes, and at high Re the flame blows off due to insufficient residence time (Da1) [10]. Re also specifies the flow regime; heat recirculating reactors generally operate either in the laminar regime or the transitional regime, where modeling of turbulence becomes important [11]. The pore diameter or channel height is an important parameter for embedded flames because the solid surfaces can lead to quenching of the flames, as described by Peq . With typical quenching distances on the order of millimeters and flame speeds of 10–50 cm/s depending on equivalence ratio, typical Peq values for

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35

Fig. 3. Characteristics of heat recirculating reactors for operation in different regimes.

flames in tubes or channels are in the range of 10 to 60 [12,13] and provide guidance on minimum length scales for reactor design. Peq is also relevant for flame stabilization in porous media burners; it has been shown that quenching occurs when a flame interacts with a cold porous medium if Peq < ∼ 65 [14], so flame stabilization within porous media can be achieved at the interface of two sections of porous media with different characteristic length scales as in a two-section burner (Section 2.2.2) As for all combustion devices, heat losses substantially affect operating limits. Solid surfaces provide a means of internal heat recirculation but also provide pathways for heat loss to the environment at the external boundaries. The balance between external losses and internal recirculation highlights a challenge of heat recirculating reactor design and operation, which is to maintain the ratio H˜ as small as possible. The defining characteristic of internal heat recirculation is achieved through convective heat transfer between gas and solid phases, conduction within the solid and radiation between solid surfaces. The relative roles of convection and conduction in sustaining embedded flames can be characterized by a Biot number

B=

hI Lc ks

where ks is the solid conductivity and Lc is a characteristic length scale for a given reactor geometry (e.g. Lc has been given as 2L2 /t for a counter-flowing reactor, where L is the channel length and t is the wall thickness [15]). B has different implications for different designs. For a reactor with counterflowing channels, the main mode of heat transfer is through the walls and transverse to the flow direction, and streamwise conduction is less important, or even detrimental, so a maximized value of B is optimal. For example, a counterflow reactor with infinitely thin walls dividing the channels would have B → ∞. For a reactor with co-flowing channels, however, the only means of heat transfer upstream is through axial conduction and radiation and subsequent solid-to-gas heat transfer, so a finite value of B is necessary for optimal performance. Performance of the heat recirculating reactors is characterized by the non-dimensional temperature, T˜ and velocity, U˜

T˜ =

Tmax Tad

U˜ =

U SL

where Tmax and Tad are the local maximum temperature in the reactor and the adiabatic flame temperature for the reactant mixture, respectively. These two parameters describe the enhancement of the combustion process over that of an adiabatic premixed laminar

flame; values of nondimensional temperature and velocity greater than unity indicate superadiabatic or enhanced combustion. For example, T˜ has been predicted and measured at 2.3 for a filtration reactor operating on a methane/air mixture with an equivalence ratio of 0.15 [16,17]. Similarly, U˜ gives a measure of burning velocity relative to the adiabatic laminar flame speed for a specific fuel/oxidizer mixture. This ratio is a measure of the burning rate enhancement over that of a conventional laminar flame and is typically in the range of 2 to 5, though these values are still significantly lower than turbulent flames speeds with enhancements of over 20 times the laminar flame speed [18]. 1.3. Operating regimes of heat recirculating reactors In early work, Jones et al. [7] proposed many different concepts to enhance the heat recirculation in a reactor. Most of the research since then, however, has focused on a few major designs which are dominated by different flow and heat transfer processes (Fig. 3). One of the simplest designs is a reactor made of twosections of porous media, a bundle of tubes, or parallel channels. Heat is recirculated by axial conduction through the solid and radiation between solid surfaces, and the operating range is in moderate equivalence ratios. Filtration reactors, typically a single section of porous media, are more complex in that the reaction front propagates relative to the solid. In a frame of reference fixed to a downstream-propagating reaction front, the hot solid moves into the reaction zone and is an additional mode of heat recirculation as described by Babkin [19]. These reactors are capable of operation at moderate-to-extreme rich and lean equivalence ratios. In contrast to these reactors, which utilize unidirectional flow and heat transfer, a third type of reactor is the counter-flow reactor in which the gas flows in opposite directions in neighboring channels. In counter-flow reactors, there is an additional mechanism of transverse heat transfer through the walls. These reactors are capable of operation near and beyond flammability limits. In this paper, we focus on these major designs, the principles of operation, and applications. 1.4. Scope of this review Many review articles on heat recirculating reactors have been published, the first in 1995 by Howell et al. [20], which provided an overview of work in porous media combustion. Since then, more specific reviews have focused on lean combustion in porous reactors [21], production of syngas [22], practical applications [23,24], microcombustion [25], modeling of porous media combustion [26], and combustion of liquid fuels in porous reac-

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Fig. 5. Gas and solid temperatures for axial flow reactor showing heat recirculation.

Fig. 4. Heat transfer processes in a unidirectional flow reactor.

tors [27]. In this review, the area of investigation is broadened to consider porous media reactors as well as other non-catalytic heat recirculating designs and a variety of applications. The important underlying mechanisms of major reactor designs based on general flow and heat transfer characteristics, applications of these reactors with comparisons between reactor types, and studies published since the last review articles on this topic are discussed. 2. Unidirectional flow reactors In a unidirectional flow reactor, the bulk flow of the gas is in one direction and the solid surfaces provide conduction and radiation pathways for heat transfer upstream from hot products to cold reactants (Fig. 4). Solids, especially porous media such as packed beds or reticulated foams, generate axial and transverse dispersion of mass and energy through the open-cell structure, which is another heat transfer enhancement pathway [28,29]. 2.1. Operating principle of unidirectional flow reactor The fundamental principle of unidirectional reactors is that the heat release produces a locally high temperature in the gas that is greater than that of the surrounding solid (Fig. 5). Heat is transferred from the gas to the solid and subsequently upstream through conduction and solid-to-solid radiation, producing an upstream solid temperature that is greater than the surrounding gas. Heat is then transferred from the solid to the gas, thereby preheating it without any external addition of energy. The basic concept of a unidirectional heat recirculating reactor can be demonstrated by a one-dimensional model of a flame in a single tube with convective internal and external boundary conditions as well as axial conductive heat transfer through the wall. Critical insights gained from one-dimensional studies, and confirmed by experimental studies, include the observation that burning speeds greater than the adiabatic laminar flame speed predicted by one-dimensional laminar flame theory can be achieved, flammability limits can be extended, and combustion can be sustained at tube diameters less than the classical quenching distance [30,31]. Additional insights gained from these models highlight the impact of wall properties and heat loss on stability of near-limit flames. Thus, one-dimensional modeling captures many of the fundamental aspects of heat recirculating reactors.

Additional important insights into flame stabilization have been gained by two-dimensional modeling of combustion in tubes. Notably, the burning rates of a flame in a tube were investigated by Gauthier et al. [32,33] who developed a two-dimensional model using the Navier–Stokes equations for low Mach number reacting flows including the effects of solid conduction and solid-to-gas heat transfer. Their results showed burning rate enhancement is attributed to two factors: increased flame surface area over that of a one-dimensional flame and preheating of the incoming gases. Their calculations of flame surface area as a function of non-dimensional inlet velocity, Uin , equivalent to U˜ defined in Section 1.2, for various non-dimensional tube diameters is shown in Fig. 6a. These computations represent an idealized case of combustion and heat recirculation because external heat loss, which could significantly reduce flame velocities, was not included. For small inflow velocities (Uin < 1), the non-dimensional flame areas are all close to one, indicating that those flames are nearly flat. As inlet velocity increases, the surface area increases. Larger diameter tubes show a stronger effect with a tube of 2.46 times the quenching distance exhibiting flame areas up to six times those of a flat flame. The dimensionless burning velocity per unit area, Uf , as a function of inlet velocity is shown in Fig. 6(b). At a value of Uf = 1, the flame velocity per unit of flame area is the same as that for a onedimensional flame. For large diameter tubes ( dd = 2.46), Uf is close q

to one for all inlet velocities indicating that the increase in burning velocity, Uin , is due to the increase in flame area rather than due to enhanced reaction rate brought about by preheating. For smaller diameter tubes, the flame velocity per unit area is as high as 2 times that for a flat laminar flame. In these tubes, heat recirculation due to the solid walls is an important factor in enhancing the burning velocity. Both conduction and solid-to-solid radiation are important contributors to heat transfer in a heat-recirculating tube reactor [34]. Hackert et al. [12] included both solid conduction and radiation in two-dimensional simulations of a flame in a radially insulated cylindrical tube of diameter 1.1 mm. Fig. 7 shows predictions of the effect of solid conductivity and emissivity on the burning rate of a methane/air mixture with an equivalence ratio of 0.6. Increasing W the conductivity from 5 to 15 mK resulted in a greater than 50% increase in burning rate. Increasing the emissivity had a more modest effect, particularly for values greater than 0.1. Radiation exiting the tube, important for applications to radiant heating, is similarly sensitive to conductivity and emissivity. To better understand flame stabilization in burners like these, some researchers have investigated flame stabilization and dy-

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37

Fig. 6. Computational predictions of (a) dimensionless flame area, Af /ACS , and (b) dimensionless burning velocity per unit flame area, Uf , as a function of inlet velocity nondimensionalized by flame speed, Uin , for a stoichiometric flame in an adiabatic tube, with inlet gas temperature and wall temperature of 900 K and wall thickness equal to half of tube radius. Af = flame surface area, ACS = cross-sectional tube area, dq = quenching diameter, Ub = burning velocity (Reprinted from Gauthier et al. [32] with permission of Elsevier).

Fig. 7. Computational predictions of burning rate and radiant output fraction vs. (a) solid conductivity, k, and (b) solid emissivity, ε , for methane/air flame in radially insulated 1.1 mm diameter tube with wall thickness 0.17 mm at equivalence ratio of 0.6 with flame located at x/L = 1/4. For comparison, the calculated laminar flame speed at 0.6 is ∼15 cm/s (Reprinted from Hackert et al. [12] with permission of Elsevier).

namics in heated channels with length scales on the order of or smaller than the quenching distance [25,35–37]. Various dynamic and steady phenomena have been observed [25,38,39] and predicted by models [36,40–42], including the complex phenomena of FREI (flames with repetitive extinction and ignition). As described by Nakamura et al. [36], FREI was observed when reactants flowed through a small heated channel; when a sufficiently high gas temperature was reached, combustion initiated and the flame propagated in both directions until extinction, and then the process restarted as fresh reactants flowed through the heated channel. In addition to FREI, researchers have reported a variety of other stable and unstable flame types such as cool flames, pulsating flames, stable symmetric and asymmetric flames, and mixed modes of these flame types [37]. Though the surfaces of the reactors were heated externally in these experiments and models, in contrast to heatrecirculating reactors which have no external heat addition, the flame behavior observed can take place in heat-recirculating reactors since many of these devices are composed of channels or pores with dimensions on the order of the quenching distance and with an axial temperature gradient. An example is the oscillatory behavior in a two-section heat recirculating reactor (Section 2.2.2) described by Vogel and Ellzey [43]. At the extreme operating conditions for this reactor, the reaction zone propagated upstream into the cold porous solid and extinguished at the interface between the highly porous downstream solid and a less porous solid upstream as heat losses overcame heat release. After the reaction extinguished, fresh reactants filtered through the hot solid and reignited, beginning the process again, and an analogy with FREI behavior in heated channels [44] was noted.

Fig. 8. Different unidirectional reactor designs (a) parallel tubes or channels (b) single section porous medium (c) two-section porous media.

2.2. Unidirectional reactor designs Practical designs of unidirectional reactors include multiple tubes with either solid walls or an open pore structure. These solid geometries are generically referred to as porous media. Fig. 8 shows the various unidirectional flow reactor designs that have been studied, including a bundle of tubes or stacked channels, a single section of open-cell porous media, or two sections of porous media stacked one on the other.

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Fig. 9. Measured and computed temperatures in a slit in a honeycomb burner as a function of length for propane/air at equivalence ratio of 0.55 and an inlet velocity twice the laminar flame speed. T = gas temperature; Ts = solid temperature; r = ratio of mass flow to that for a conventional laminar flame, Xf = flame position (Reprinted from Min and Shin [50] with permission of Elsevier).

2.2.1. Reactors with self-stabilizing flames Reactors such as those shown in Fig. 8(a) and (b), consisting of a single section of channels or reticulated media, do not have internal flame arrestors. Consequently, the flame stabilizes at the point where the burning velocity balances the incoming flow, resulting in different flame locations for different operating conditions. Weak flames will tend to stabilize nearer the center of the burner where radiative losses out the exit are smaller and stronger flames will stabilize closer to the exit [45]. A single section reactor was explored theoretically by Takeno et al. [46,47] who predicted burning velocities much greater than the laminar flame speed and extended flammability limits. Subsequent experimental work confirmed the attainment of high burning rates as well as stable combustion beyond the lean flammability limit [48]. These effects were attributed to the enhanced axial conduction provided by the porous media that recirculated heat from the flame zone to the incoming mixture. Later modeling studies showed the importance of solid radiation [49]. Similar to the results of earlier research [47,48], Hackert et al. [12] concluded that the dominant heat transfer mechanism was axial conduction. An example of a well-characterized unidirectional reactor is the ceramic honeycomb combustor studied by Min and Shin [50]. Their combustor was 76 mm in diameter with a cell density of 400 square cells per square inch, a cell hydraulic diameter of 1.1 mm, and an overall porosity of 75%. In comparison to random porous matrices, the geometry of this combustor was simple and welldefined honeycomb which made it amenable to theoretical analysis. Experimental results showed U˜ up to 4.5, and a modest extension of the lean flammability limit. Though experimental data for separate gas and solid temperatures are not often presented for these burners due to the difficulty of measurement, Min and Shin obtained gas and solid temperatures by cutting a slit of 1.1 mm in the axial direction of the burner and measuring the solid temperature in the cell next to the slit (Fig. 9). The measured profiles show the fundamental characteristics of a heat recirculating reactor: a peak gas temperature greater than the adiabatic flame temperature (T˜ ≈ 1.15), downstream gas temperature greater than the solid temperature, and upstream solid temperature greater than the gas temperature. Computations, which included heat losses to the environment, showed good agreement with experiment. Similarly, Schoegl and Ellzey [45] confirmed these essential characteristics using a simplified analytical model of combustion in parallel channels.

Fig. 10. Computed isotherms for a flame in a 13-channel parallel plate burner including external heat losses. Flow is from left to right. Plate separation is 0.55 mm and wall thickness is 0.17 mm. The upstream isotherm is 400 K and the far downstream isotherm is 1450 K. Maximum isotherm is 1800 K. Predicted burning speed is 62.8 cm/s at equivalence of 0.6 for methane/air compared to ∼12 cm/s for laminar flame speed using same simplified chemistry (Reprinted from Hackert et al. [12] with permission of Elsevier).

Min and Shin [50] also examined soot lines formed in the burner to determine flame location and curvature. The center of the flames that were stabilized entirely within the burner were one-dimensional except near the wall where heat losses resulted in curvature. Further details of the flame shape were elucidated by the numerical modeling of this burner by Hackert et al. [12]. In cases where heat losses to the exterior were included, the individual flames stabilized at different locations along the tube. Fig. 10 shows the results of a simulation of 13 parallel plate channels with a separation of 0.55 mm and wall thickness of 0.17 mm. For channels near the exterior, there is more external radial heat loss and the flame stabilizes closer to the center where there is less radiative heat loss from the ends of the channels. These results show that the flames are two-dimensional on two different scales: the individual flames within the channels are elongated and the overall flame in the burner is curved, which indicates heat loss via transfer in the transverse direction from the inner tubes where heat losses are minimum to the outer tubes where heat loss is maximum. The relationships between heat recirculation, heat loss, flashback and blowoff for a large-aspect ratio microreactor partially filled with a porous medium were studied by Li et al. [51]. The stability limits (blowoff and flashback) were described for lean mixtures of H2 and air in terms of the ratio of preheating to heat loss, which was calculated using the heat transfer in the location upstream of the reaction zone and within the reaction zone defined as the region bounded by the 5% and 95% H2 contours. Stable reaction was observed for an equivalence ratio down to 0.35 when the ratio of preheating to heat loss was the maximum calculated value of 9, and the ratio of preheating to heat loss increased with decreasing equivalence ratio. The results of this study illustrate the importance of low H˜ for stable combustion of mixtures with equivalence ratios far from stoichiometry. 2.2.2. Reactors with flame stabilization Early papers on combustion in channel reactors led to significant work in the research and development of reactors filled with porous media. One obstacle to practical utility of these burners was the tendency of the flame to propagate slowly through the porous medium. Consequently, significant work has focused on holding the flame in a fixed position or region. With this idea in mind, Hsu et al. [52] proposed a new design consisting of two sections of porous media: an upstream section with small pores through which the flame could not propagate followed by a section with larger pores in which conductive and radiative heat transfer re-

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Fig. 11. Measured temperature vs. distance over a range of inlet velocities for a two-section porous burner operating on methane/air at an equivalence ratio of 0.65. For comparison, the adiabatic laminar flame speed at 0.65 is 15.7 cm/s (Adapted from Mathis and Ellzey [55]).

circulated energy (Fig. 8(c)). Both experimental and computational research has confirmed that this design is successful at stabilizing the flame at or near the interface between the two sections [53– 58]. In these designs, the upstream section has pores sizes such that d < dq and Pe < Peq which halts potential upstream propagation and stabilizes combustion in the downstream section. Fig. 11 shows the temperature profiles at various operating conditions for a burner consisting of two sections of reticulated ceramic foam: an upstream section with 23.6 pores per centimeter (ppcm) followed by a downstream section with 3.9 ppcm [55]. The interface between the two sections is at x = 5 cm, and the results clearly show the effectiveness of the small pores at stabilizing the flame over a range of inlet velocities from 15 to 75 cm/s, corresponding to firing rates of 313 and 1563 kW , respectively. These results demonstrate m2 a significant enhancement in burning speed achieved over the adiabatic laminar flame speed of 15.7 cm/s at an equivalence ratio of 0.65, with a maximum U˜ of more than 4.5 at the highest tested operating condition reported. Unlike some other heat recirculating reactors, the maximum temperatures in a two-section reactor are at most only modestly greater than the adiabatic flame temperature. Despite the enhancement in burning rate observed in Fig. 11, the maximum temperature is less than the adiabatic flame temperature of ∼1750 K for an equivalence ratio of 0.65. Similar results of enhanced burning rates with temperature below the adiabatic value (Fig. 12) were found by Brenner et al. [56] who conducted experiments and computations including heat losses. For comparison, the adiabatic flame temperature for methane/air at an equivalence ratio of 0.90 is ∼2130 K. At a fixed equivalence ratio, the firing rate is increased by increasing the inlet speed of the fuel/air mixture. At high firing rates, the relative losses to the surroundings are less and the maximum temperature is close to but still less than the adiabatic flame temperature. Conversion of the firing rates to velocities show burning rate enhancement of greater than 6.5 at an equivalence ratio of 0.67. Barra and Ellzey [53] modeled the two-section burner of Smucker and Ellzey [54] consisting of reticulated foam with upstream and downstream pore densities of 60 and 10 ppi, respectively. Their one-dimensional model included full kinetics, solid and gas conduction, solid-to-solid radiation, and interfacial heat transfer. Assuming no radial heat losses, the maximum temperatures were 5% greater than the adiabatic flame temperature at an equivalence ratio of 0.55, and 5% less at an equivalence ratio of 0.90. Although maximum temperatures in the two-section burner do not typically exceed those predicted by equilibrium by a large

Fig. 12. Temperature vs. equivalence at two firing rates for a two-section porous burner operating on methane/air (Reprinted from Brenner et al. [56] with permission of Elsevier).

Fig. 13. Operating range of two-section burner operating on propane/air. Adapted from Smucker and Ellzey [54].

amount, superadiabatic performance is often attributed to this design due to the burning speeds, which can be significantly greater than the laminar flame speed, as noted above. Using the model developed by Barra et al. [58], Smucker and Ellzey [54] compared the experimental and computational operating limits of a two-section burner operating on propane (Fig. 13). The laminar flame speed is lower than any of the flow velocity limits shown for operation in the porous burner. At the upper experimental limit measured at equivalence ratio of 0.65, the burning velocity is more than 7 times the laminar flame speed at that condition. Since temperature measurements do not indicate superadiabatic values, other factors must influence the burning rate. Barra and Ellzey [53] showed computationally that there was effective heat recirculation from the flame zone upstream to the preheat zone in a two-section burner consisting of reticulated foams even without significant superadiabatic temperatures. Using results of their numerical model, they predicted that as much as 25% of the energy release was recirculated. In addition, an important characteristic of flow in a reticulated foam is fluid dispersion arising from the tortuous path a fluid particle must follow through the interconnected pores. With a similar model, Henneke [59] showed that dispersion significantly affects the maximum stable burning velocity in a reactor of reticulated foam with 3.9 pores per cm and a methane/air mixture of equivalence ratio 0.7. Using two different correlations from the literature for axial dispersion, the maximum burning ve-

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Fig. 14. Measured velocity vs. pore density (in pores per inch, or ppi) for methane/air flame at an equivalence ratio of 0.6 in 50 mm burner consisting of upstream section of 3 mm packed balls followed by downstream section of ceramic foam with different pore densities (10 ppi = 3.9 ppcm; 30 ppi = 11.8 ppcm). For comparison, laminar flame speed of methane/air at equivalence ratio 0.6 is 11.7 cm/s (Reprinted from Gao et al. [61] with permission of Elsevier).

locity increased by approximately 20%, or 68% over the value predicted with no dispersion. It is important to note that the models are one-dimensional using volume-averaged techniques and so the details of the intra-pore flow and flame shape are not captured. Further investigation of these characteristics might provide important insights into the performance of two-section burners. The development of the two-section design has continued to evolve with a focus on various materials and pore characteristics [55,60,61]. The pore density has a significant effect on the stable operating range as shown in Fig. 14. Larger pore density, or smaller pores, in the downstream section quench the flame more readily and therefore limit the operating range. This is consistent with quenching studies on flames in tubes [33,34]. The maximum velocity of 70 cm/s represents a burning rate enhancement U˜ of ∼6. Two-section porous reactors have been shown to operate effectively on a wide variety of fuels including conventional gaseous fuels such as methane and propane [54,62,63], liquid fuels [27,64,65], and unconventional fuels like syngas [66] and biogas [67]. This fuel flexibility is an advantage of using heat recirculation to enhance reaction rates as compared to catalysts which often have restrictions on operating conditions, fuel chemistry and fuel quality. In addition to the two-section burner, other designs have been proposed to stabilize the flame in a fixed region [22,24,68]. Notably, several researchers have designed reactors in which the porous section was tapered such that the flow velocity decreased with the wider cross-sectional area, effectively extending the operating range [69,70]. Recently Song et al. [71] built a reactor with porous media in an annular geometry which stabilized lean mixtures over a wide range of conditions. The tapered geometry, the annular geometry and the two-section geometry were recently compared experimentally and computationally by Bedoya et al. [72]. Based on their experimental results, the tapered geometry demonstrated the best performance in terms of operation beyond the lean flammability limit and maximum burning enhancement U˜ of ∼10 as compared to ∼5 and ∼3 for the two-section and radial burners, respectively. 2.2.3. Filtration reactors A single-section porous reactor in which the reaction zone propagates is called a filtration reactor. This design contrasts with the two-section reactor in which an intentional design feature is the stabilization of the flame in a fixed position within the reactor.

Fig. 15. Heat transfer processes in filtration combustion.

Though a reaction zone in a filtration reactor can remain in a fixed position, the location is not stable; changes in flow rate or mixture composition will cause the reaction zone to propagate relative to the solid. The inherently transient nature of filtration combustion sets it apart from the other heat-recirculating reactors, which can operate indefinitely. The complex heat transfer processes are described in Fig. 15, which shows a generic filtration reactor. After an initial startup period, a reaction zone establishes within the porous solid. The downstream solid is hot from combustion products and the upstream solid is cool from incoming reactants. Heat transfers upstream from the reaction zone by solid conduction and radiation, and reactants are preheated by the solid as they near the reaction zone. This heat transfer mechanism is shared with axial flow reactors in which the reaction zone does not propagate. In a filtration reactor, however, the reaction zone is not constrained, and propagation relative to the solid provides an additional heat transfer mechanism that is not present in other types of heatrecirculating reactors in which the reaction zone is stabilized [19]. If the flow velocity is greater than the burning velocity, the combustion front propagates downstream into the hot solid, and heat is transferred from the solid to the gas. If the flow velocity is less than the burning velocity, then the reaction zone propagates upstream into the cold solid, and heat is transferred from the gas to the solid. As described by Babkin [19], the transient operation can take many forms, which are generally described by the propagation speed of the reaction zone, uo , within the porous medium: a low-velocity regime (uo ∼ =10 − 4 m/s), a high-velocity regime (uo ∼ =10 m/s), a sound velocity regime (uo ∼ =102 m/s), a lowvelocity detonation (uo = 800 − 1500 m/s) and a normal detonation with losses (uo = 1500 − 2000 m/s). The differences between these regimes have been well-characterized [14,19,73] along with transition between the regimes [74,75]. Studies on the various regimes and the controlling parameters show that the principle factor that determines the behavior is the magnitude of the thermal interaction between the porous solid and the gases [75]. The highvelocity, sound velocity and detonation regimes will occur when the porous medium has relatively large pores (pores with scales greater than the flame thickness); the flame propagates with limited interaction with the solid. Alternatively, a reactor with pores of the scale of the reaction zone or smaller will support lowvelocity reaction zone propagation where the thermal interaction between the solid and the gas is large, and this review focuses on low-velocity regime filtration combustion.

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Fig. 16. Nonreacting and reacting fronts in porous media (a) thermal front in inert gas propagating at velocity ut (b) combustion front of reacting mixture propagating at velocity uw .

A critical relationship between propagation velocity and thermal energy in filtration combustion in the low-velocity regime can be understood by comparing a thermal front and a combustion front propagating in a porous medium (Fig. 16). If an inert gas is introduced into a porous medium and flows from left to right with an initial single impulse of thermal energy, the gas and solid temperature will change as a function of time as shown in Fig. 16(a); the maximum temperature decreases as the front propagates downstream, but the total energy remains constant until energy begins to exit the system at Time = 3. The rate of propagation and the shape of the temperature profile depends on the gas and solid properties and the inlet velocity of the incoming gas. Fig. 16(b) shows the gas temperature for an exothermic reacting gas flowing through a porous medium; in this case the maximum temperature does not decrease as it propagates, and thermal energy increases over time [76] as described by Zhdanok and Kennedy [16]. The direction of propagation is inherently linked to other characteristics of the combustion front such as maximum temperature. The theoretical analysis by Zhdanok and Kennedy [16] showed that the maximum gas temperature increase T is described by

T = 

Tad 1−

uw ut



where Tad is the temperature increase across an adiabatic combustion front, and uw and ut are the velocities of the combustion front and a thermal front, respectively, as shown in Fig. 16. The temperature increase may be significantly greater than that due to adiabatic combustion when uw is less than ut but close in magnitude so that the thermal and combustion fronts shown in Fig. 16 are nearly aligned. According to Zhdanok’s theory, superadiabatic temperatures only occur when the combustion front is propagating in the same direction as the flow (co-currently). The analysis also indicates that if uw and ut are of opposite signs, indicating that the combustion front and thermal front are moving away from each other, then T is less than the adiabatic temperature rise; this is called subadiabatic combustion. At the unique condition of uw = 0 (stationary front), the temperature increase is that predicted from an adiabatic calculation. In this case the reaction rate exactly balances the rate of reactants flowing into the reaction zone. When the equivalence ratio increases or decreases, the reaction rate and flame speed of the mixture increase or decrease accordingly; if the inlet velocity is maintained and the flame speed decreases, the re-

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action zone will propagate downstream, and if the flame speed increases, the reaction zone will propagate upstream. Almost all modeling and experiments have indicated that the reaction zone is stationary for a unique velocity at each equivalence ratio, however some papers have reported the observation [77] and prediction [78,79] of “anchoring regimes” where the reaction zone is stationary over a range of velocities in micro-fibrous porous media with ceramic fibers 4 μm in diameter. Hydrodynamic changes to the shape and therefore area of the reaction zone are proposed as the reason for anchoring, though further investigation is warranted (see discussion on modeling below). In addition, some observations of oscillating reaction zones have been reported [44,68]. Advanced two-dimensional and potentially three-dimensional modeling is required to understand the full range of the transient behavior of filtration combustion. The propagation of the reaction zone can be observed experimentally by temperature measurement (Fig. 17) and by photograph (Fig. 18). Downstream and upstream propagation rates in low-velocity-regime filtration combustion have been observed to reach ∼1 cm/s, and stable combustion can be achieved with gas flow velocities on the order of 10–100 cm/s. According to theory [74], the direction and magnitude of the propagation velocity depends on many parameters including porous medium characteristics, reactant composition (including diluents), equivalence ratio and inlet velocity, and multiple researchers have described experimental observations of these complex relationships [16,17,80,81]. In many experiments with filtration reactors, instability of the propagating reaction zone has been observed; the shape of the reaction zone changes or the reaction zone breaks into fragments as shown in Figs. 19 and 20, respectively. As noted by Minaev et al. [82], the operation of a practical reactor would be difficult or impossible with an unstable reaction zone. Vainshtein first attempted to explain this instability by creating a theoretical model that included both hydrodynamic and thermal instability sources [83]. Vainshtein showed that propagating reaction zones are more stable when the reaction front propagates upstream relative to the solid porous media rather than downstream as has been observed in many experiments. Later, Minaev reported on experiments and modeling undertaken to further understand observations of stable upstream-propagating reaction zones and unstable downstreampropagating reaction zones [82]. In addition to confirming the stability of upstream propagating fronts relative to downstream propagating fronts using a hydrodynamic model, Minaev found critical reactor diameters (for cylindrical reactors) under which instability would not be observed. Dobrego et al. [84] performed experiments and created a two-dimensional numerical simulation to provide simple expressions for the size of the reaction zone inclination, a measure of reaction zone instability. The inclination size and growth rate were found to increase with the reactor diameter and reaction front velocity. Kakutkina [85] found criteria for the production of fragmented reaction zones, and recent work has shown that even small inhomogeneity in initial preheating of the solid will produce flame instability [86]. Filtration combustion has been demonstrated for both liquid and gaseous fuels, and a typical experimental reactor is an insulated cylindrical tube filled with a porous medium. Porous materials include aluminum oxide spheres [89], silicon carbide grains [90], metal balls [19], ceramic foams [91] or sand, as was described in one of the earliest works published in English literature on gaseous filtration combustion [68]. The effects of porous media material and pore size on low-velocity filtration combustion has been studied by multiple researchers [68,92,93]. De Soete [68] experimented with a reaction front submerged in sand grains with varying diameters. Minimum grain sizes for supporting a stable combustion zone were found by comparing the chain branching probability with the chain breaking probability, which increases

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Fig. 17. Temperature measurements of a propagating filtration combustion reaction zone for methane/air in a 76 mm diameter cylindrical reactor packed with 5.6 mm alumina beads with an air-to-fuel ratio of 62.2 and an inlet velocity of 43 cm/s. Curves show the reaction zone location moving from left to right at approximately 0.02 cm/s (Reprinted from Zhdanok and Kennedy [16] with permission from Elsevier).

Fig. 18. Photograph showing propagation of reaction zone in gaseous filtration combustion of methane and air with an air-to-fuel ratio of 37 and an inlet velocity of 43 cm/s. The reactor was a 76 mm diameter cylinder filled with 5.6 mm diameter alumina beads. The reaction zone propagates from the bottom to the top as time increases from left to right at ∼0.02 cm/s (Reprinted from Zhdanok and Kennedy [16] with permission of Elsevier).

with increasing solid surface area. The grain sizes varied from 0.045 mm to 0.14 mm, and stable combustion was achieved in all grain sizes. The production of syngas from methane as a function of porous media size and type was studied by Gavrilyuk et al. [93] who made cylindrical reactors with beds of various pellets: Al2 O3 cylinders, Al2 O3 spheres of 6 and 3 mm diameters, ZrO2 granules and SiO2 pieces, and they found that the generation of hydrogen was insensitive to the type of material used in their study. In contrast, Fay et al. [92] found differences in hydrogen produc-

Fig. 19. Photographs showing reaction zone distortion in downstream-propagating reaction zone of methane and air with an inlet velocity of 0.42 m/s. Numbers on the x-axis indicate time in minutes. The reactor was a 0.4 m tall cylinder packed with 3 mm diameter alumina beads (Reprinted from Shi et al. [87] with permission of Elsevier).

tion from methane between a bed of Al2 O3 spheres and reticulated ceramic, noting that Gavrilyuk et al. did not observe temperatures high enough for the steam reforming reaction to proceed at high rates. In the Fay et al. study, which compared packed beds (porosity of ∼40%) with reticulated ceramics (porosity of ∼85%) in terms of generating syngas from methane, the reticulated ceramic reactor generated more hydrogen, which was attributed to higher tem-

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Fig. 20. Photograph showing fragmented reaction zone in H2 /air filtration combustion with 6.8% H2 concentration and an inlet velocity of 1.3 m/s. The reactor was a 76 mm diameter cylinder with 5.6 mm diameter beads (Reprinted from Saveliev et al. [88] with permission of Elsevier).

peratures (and therefore faster reaction rate and higher Da) in the steam reforming region downstream of the primary reaction zone. These results, along with the lower pressure drop across a more porous solid, indicate that reticulated ceramics are preferable to a

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packed bed for fuel reforming, though reticulated ceramics have a propensity for cracking and fast reaction zone propagation, which are undesirable traits for practical application. The propagating front in filtration combustion produces a practical difficulty: the reactor cannot be operated indefinitely. In order to move past this limitation, some groups have developed reactors in which the direction of propagation is reversed periodically. These reactors have been termed reciprocal flow reactors [94] or reactors with reciprocating superadiabatic combustion in porous media [95]. In a superadiabatic reciprocal flow reactor, combustion is initiated, and operating conditions are selected that produce a downstream-propagating reaction zone. When the reaction zone nears one end of the porous medium, the flow is reversed, and the reaction zone propagates in the reverse direction. Repeating this procedure results in pseudo-steady operation. The basic design and description of the physical parameters are shown in Fig. 21 for a reactor used to generate electricity when coupled with a thermoelectric device. The concept was introduced in the literature by Hanamura et al. [95] with the objective of developing a practical device for the destruction of paint vapors. This original numerical study was followed by experiments with the intended applications of radiative heating or generating electrical power by coupling a reciprocal flow reactor with a thermoelectric device [96], experiments and modeling on the conversion of ultra-rich mixtures of methane/air to syngas [97], and a numerical study of integrating the reciprocal flow reactor with a heat exchanger for process heating [98]. Other methods of reaction zone stabilization are possible, such as variation of the flow area in the flow direction [68,99], but if the reaction zone is stationary relative to the solid, then the key heat transfer mechanism of filtration combustion, relative motion of the hot solid, is lost, and the reactor operates as a unidirectional flow reactor with a consequent reduction in operating range.

Fig. 21. Schematic describing reciprocal flow reactor (Reprinted from Hoffmann et al. [96] with permission of Elsevier).

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One of the more significant experimental advances that has been made in recent history is experimentation with a wider variety of fuels, particularly for the purpose of producing syngas [22]. Many early studies focused on gaseous fuels such as hydrogen and methane [62,68,74,97,100] while liquid fuels have been tested in more recent work [27]. Smith et al. demonstrated the conversion of wet and dry ethanol [101] and jet fuel and butanol [102] to syngas using a filtration reactor of alumina spheres. Recently liquified petroleum gas, diesel fuel, and heavy fuel oil were converted to syngas in a filtration reactor [103]. Vaporization, mixing and delivery of the reactants to the porous medium are the principle difficulties in working with liquid fuels, and these issues are discussed in depth by Mujeebu [27]. Filtration combustion was first described as a reaction zone propagating through a porous solid fuel [104,105], and some workers have used solid fuels in conjunction with gaseous fuels in a hybrid filtration reactor. In this type of reactor a porous bed is formed by mixing inert material with solid fuel such as wood pellets [106] or coal [107]. A mixture of fuel and oxidizer flows through the bed, and the oxidizer consumes both the gaseous and solid fuels. Further investigation on burning solid fuels included the gasification of coal dust with water addition [108]. Since the beginning of research in this field, numerical and analytical studies have provided insights into the theory and operation of filtration combustion. Babkin et al. [74] reported an analytical model that included finite-rate heat transfer between the gas and the solid (a two-temperature model), and showed predictions of superadiabatic and subadiabatic temperatures that agreed well with their experimental data. In further modeling work, the effect of heat loss was included, and the predictions of this model were compared with experimental data where the heat loss was varied by using reactors of varying tube diameters and thicknesses [109]. These analytical models as well as early finite-difference numerical models [95,100] generally employed one-step global reactions instead of full chemical kinetic models, which were first included in filtration combustion models by Henneke and Ellzey [17] and Kennedy et al. [110]. Many modeling studies since then have employed full chemical kinetic models [101,111], which enable investigation of the chemical structure of the reaction zone and the prediction of product species. Since filtration reactors enable the burning of mixtures far outside the conventional flammability limits, chemical kinetics models are sometimes used beyond the range of equivalence ratios for which they have been validated. GRI 1.2 produced accurate predictions of hydrogen and carbon monoxide for rich methane combustion [110], but numerical predictions for more complex fuels like heptane and ethanol [101,111] have not shown adequate agreement with experiments at very high equivalence ratios as can be seen in Fig. 22. Most modeling of filtration combustion has treated the solid heuristically [17] or as a continuum with effective properties derived from volume-averaging [87,112] with some exceptions [12,79,113–115]. Recently, Sirotkin et al. [78] developed a model of filtration combustion in which the porous media was modeled in two dimensions with discrete pores (Fig. 23). The conditions for which the front was not propagating, which they referred to as the flame anchoring regime, were studied specifically. Their main finding was that they observed and predicted reaction zone propagation velocities of zero over a range of inlet velocities at a given equivalence ratio (for equivalence ratios greater than ∼0.6), though no mechanistic reason was given for the observation. The prediction of a range of flame-anchored states was consistent with their own experimental observations [116], but this result is in contrast to results from similar experiments, in which standing waves were observed for unique equivalence ratios at a given inlet velocity [110] and models with continuous porous media, which showed a unique inlet velocity for a zero-velocity reaction zone

Fig. 22. Hydrogen and carbon monoxide yields from rich filtration combustion of ethanol and air as a function of equivalence ratio with an inlet velocity of 20 cm/s. The reactor was a 5.5 cm diameter cylinder filled with 3 mm diameter alumina beads. Open markers are computational results, closed markers are experimental results and lines are equilibrium calculations (Reprinted from Smith et al. [101] with permission of Elsevier).

at a given equivalence ratio [74]. A two-dimensional model by Fursenko [79] also predicted flame anchoring, which was observed in experiments on filtration combustion in micro-fibrous media, i.e. media with ceramic fibers 4 μm in diameter [77]. Fursenko explained the flame anchoring as a consequence of hydrodynamic instability, which distorts the flame front and thus the burning area. The change in flame front shape and area allows for an anchored flame over a range of flow rates since a flame will anchor whenever the flow velocity matches the burning velocity. It is reasonable to find a range of flame-anchored inlet velocities in a twodimensional non-uniform model like Sirotkin’s because the flame shape and area varies in the flow direction, and the condition of matching flow velocity to flame speed can be met when flames stabilize in different locations. It is also important to consider that the model included many simplifications, such as a single step reaction, adiabatic boundaries and the calculation of the velocity field independent of the solution of the energy equation, each of which could have effects on stability [12,41]. Further refinement of multidimensional and discrete models will enhance the understanding of the complex and unique phenomenon of propagating reaction zones in filtration combustion. 3. Steady state counter-flow reactors In early work on a unidirectional reactor, Kotani and Takeno [48] observed that performance was improved when the exhaust flow was directed around the external walls of the reactor, thus providing an additional means of heat transfer. They referred to this as external heat transfer, as compared to internal heat transfer associated with the embedded solid matrix. This formed the basic idea of another type of reactor, referred to here generally as the counter-flow reactor, in which internal heat transfer is enhanced as compared to an axial flow reactor via transverse heat transfer from combustion products across channel walls. 3.1. Operating principle of counter-flow reactors The fundamental processes of a counter-flow reactor are illustrated for two channels with counter-flowing fluids in Fig. 24. Cold reactants enter the channel and heat is transferred through the wall separating the two channels. In addition, heat is transferred internally through wall conduction and radiation from the

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Fig. 23. Image of porous media structure used in non-continuum 2D modeling of filtration combustion. Flow is left to right, and color indicates gas velocity in porous structure with porosity = 0.74 and U0 = 20 cm/s (Reprinted from Sirotkin et al. [78] with permission of Elsevier).

Fig. 24. Heat transfer processes in counter-flowing channels.

hot zone surrounding the flame upstream to colder walls which then transfer energy to the cold reactants. Several studies have developed the theoretical basis for counter-flow heat recirculating reactors, including the importance of conductive and internal convective heat transfer on heat recirculation and the impact of external convective heat losses on flame stability and operating range [15]. The ability of flames to self-regulate their positions in adjacent channels in response to operating conditions is a key feature of counter-flow reactors; this, and the criterion of relative flame position for stability, have been demonstrated through theoretical analyses [116,117]. Later, the theoretical analysis of Kurdyumov and Matalon [118] demonstrated the importance of transverse

heat transfer; namely that an increase in the surface area of a separating wall between cold reactants and hot products increases heat exchange, thereby enhancing the burning speed and sustaining combustion at higher reactant flow rates as compared to adiabatic conditions (increased U˜ ). This increased area for transverse heat exchange, along with the insulating effect of adjacent channels against external heat loss [12], are significant distinctions between counter-flow and unidirectional reactors, which rely solely on axial heat transfer, and single channel reactors, which consist solely of outside walls which are prone to heat loss. These differences translate to a much broader range of flame stabilization in terms of equivalence ratio and burning rates [15].

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Fig. 25. Different counter-flow reactor designs: (a) folded channel, (b) dual folded channel, (c) spiral, and (d) counter-flow channel.

3.2. Counter-flow reactor designs Counter-flow reactors offer a number of advantages over unidirectional flow reactors; for example, counter-flow reactors can be designed to be compact for portable applications. Large external surface area-to-volume ratios at small scales can lead to significant external heat loss, however, which can cause instability in microscale combustors [117]. Thus, counter-flow reactor designs seek to incorporate large internal surface areas for heat recirculation while minimizing external surface area for heat loss (i.e. small H˜ designs). A number of counter-flow reactors have been devised which harness the improved heat transfer characteristics of small-scale channels to effectively recirculate heat while also reducing external wall area where heat loss occurs. Examples of these geometries are illustrated in Fig. 25. The folded and dual folded channel reactors are continuous channels formed in a U-shape (Fig. 25(a) and (b), respectively). The spiral reactor is similar in concept to the folded channel, except that the counter-flowing channels are rolled together with reactants flowing in the outside channel and products produced at the center flowing out of the neighboring channel (Fig. 25(c)). The counter-flow channel reactor consists of straight channels with counter-flowing fluid in neighboring channels (Fig. 25(d)). 3.2.1. Folded channel reactor Perhaps the simplest counter-flow geometry is a folded channel, sometimes referred to as a U-shaped or bent channel (Fig. 25(a)) in which reactants enter one channel and flow around a bend where combustion occurs. Combustion products then flow into the adjacent channel and exit the other side of the reactor. Variations on the simple folded reactor have included dual folded channels on both sides of the inlet tube in a planar configuration or utilized a cylindrical design to surround the inlet tube with an annular tube (Fig. 25(b)). The objective of these variants on the folded channel is to increase heat recirculation from product gases to reactant gases while shielding the preheated reactants from heat loss to the surroundings. Heat is transferred from hot combustion products through the inner wall of the bent channel to preheat the incoming reactants, and the other walls are exterior walls through which heat loss or external heating can occur. An early model was developed of such counter-flow heat recirculating combustors that

included transverse heat transfer from product to reactant gases through a thermally thin wall via convection on both sides of the wall, combustion in a well-stirred reactor at the end of the reactor, ambient losses and axial heat conduction through the wall in the streamwise direction [15]. The critical role of heat loss in reactor stability was highlighted by the relatively modest dimensionless heat loss ratio (H˜ ) of 0.05 which resulted in significant decrease in reactor temperature. This model of a folded reactor was compared to that of a single tube with a flame stabilized at the exit of the tube with heat recirculation occurring via conduction along the axial direction of the tube. The flame at the exit of the tube required a higher minimum fuel concentration for stable operation as compared to the counter-current configuration for a range of Biot number (B), (Fig. 26). Results also showed that axial conduction has a significant impact on the operating limits of counter-flow combustors by providing an avenue for heat redistribution from the combustion zone areas of the reactor where losses to ambient occur. As B decreases, the relative importance of solid conduction increases and heat is less effectively recirculated into the mixture, preventing stable combustion. Another mathematical model examined a U-shaped combustor with insulated outer walls and showed that the dividing wall between the two sides of the channel effectively acted as a heat sink, removing heat from combustion products, and a heat source, heating the incoming gas, thereby permitting the stabilization of methane/air flames below the standard condition lean flammability limit [119]. Experimental studies have compared the performance of straight and folded channels and demonstrated improved performance, in terms of extended stable reactant flow rates and equivalence ratios, when counter-current heat recirculation was implemented [120,121]. An experimental investigation of methane/air by Maruta et al. [38] used external heating of a folded reactor, which allowed for heat recirculation independent of heat release by combustion, to substantially broaden flammability limits and stable inlet velocity operating range as compared to a straight channel. Consistent with work on other reactors, the authors concluded that heat recirculation enables stable combustion beyond standard condition flammability limits and at reactant flow rates above the adiabatic flame speed, and that the folded geometry enhances these effects.

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Fig. 26. Effect of mass flux (M) on required minimum temperature rise required for stable combustion (࢞T), where a higher temperature rise means a higher minimum fuel concentration, at the extinction limit from a numerical study of (a) a conductive-tube combustor and (b) a counter-current combustor for variation in the Biot number (B) (Reprinted from Mujeebu et al. [15] with permission of Elsevier).

Fig. 27. Numerical simulations show the effect of wall thermal conductivity on methane/air flame stability, as indicated by the critical heat loss coefficient above which combustion cannot be sustained. Results are shown for a single channel reactor and a dual-folded channel (“Heat recirculating”) reactor in which the center channel is encased by two exhaust channels (Reprinted from Chen et al. [122] with permission of Elsevier).

The impact of materials on stability of combustion in a folded channel reactor has been studied for various designs, and these studies have shown that wall thermal conductivity plays a key role in flame stability. Fig. 27 shows the critical external heat loss coefficient, above which combustion cannot be sustained due to excessive convective and radiative heat losses, evaluated in numerical simulations for a single channel combustor and a dual-folded channel combustor, in which the center channel is encased in two exhaust channels, for a range of wall thermal conductivities [122]. The folded combustor sustains combustion at higher critical heat loss coefficients than the single channel, except at high wall thermal conductivities where no additional significant advantage over axial wall conduction was offered by the additional transverse heat recirculation in the folded reactor. At low wall thermal conductivities, the single channel did not achieve sufficient heat recirculation via axial conduction alone to sustain combustion against significant heat losses. An experimental study of folded channel reactors by Lee et al. [123] supports these findings, as lower thermal conductivity quartz combustors supported wider flammability limits than stainless steel combustors, which was attributed to the ability to achieve higher local temperatures for effective heat recirculation. 3.2.2. Swiss roll combustors A variation on the folded channel is the spiral channel or Swiss roll combustor (Fig. 25(c)) [8]. As a result of the spiral geometry,

Fig. 28. Experimentally measured minimum reactant inlet velocities required for stable combustion of propane in Swiss roll combustors with a range of geometries (W – wide combustion chamber and shallow channels, S – narrow combustion chamber and shallow channels, D – narrow combustion chamber and deep channels) and construction materials (all reactors constructed of stainless steel except two S-type reactors have quartz caps with and without insulation – Sq and Si, respectively) (Reprinted from Kim et al. [126] with permission of Elsevier).

there is a significantly larger ratio of internal heat transfer area to external heat loss area (smaller H˜ ) as compared to folded reactors [124]. A number of experimental and modeling studies have been undertaken to understand the performance of Swiss roll combustors. Results have shown two extinction regimes: one at high flow rates and Re where insufficient residence time for combustion leads to blow-off of the flame, and another at low flow rates and Re where external heat losses exceed the heat release rate; in fact, these two modes of extinction are critical for all small-scale reactors and are observed in many heat recirculating reactor studies [125]. An experimental study by Kim et al. [126] of multiple Swiss roll combustors with varying channel and combustion chamber geometries and constructed of multiple materials examined the minimum inlet velocities at which each combustor supported stable combustion over a wide range of propane equivalence ratios. The results of that study, summarized in Fig. 28, show that minimum velocities ranged from near to well above the maximum laminar burning velocities of propane, which is approximately 0.44 m/s. Blow-off was not observed over the range of inlet velocities tested in this study. Experimental testing and three-dimensional modeling of Swiss roll combustors have been conducted to guide combustor design and operating conditions [124,127]. Comparison of a three-

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serted in the combustion chamber showed higher reactant velocity blow-off limits and lower heat loss as compared to quartz and SiC reactors (high ε ). This increased stability was attributed to lower external radiative losses induced by stainless steel as compared to other materials. These findings are consistent with the modeling work of Hackert et al. [12] who showed that increased emissivity led not only to increased burning rate via heat recirculation but also increased radiant fraction (i.e. heat loss) in a honeycombtype reactor structure; notably, the model of Hackert et al. did not account for radial losses from the reactor which could affect the impact of radiative heat transfer on burning rate if increased heat losses were incurred along the length of the reactor. In summary, the effect of radiative heat transfer is not only additional heat recirculation but also the redistribution of heat, similar to the effect of axial conduction along reactor walls, which can increase external losses and reduce reactor stability.

Fig. 29. Numerical temperature profiles, non-dimensionalized by adiabatic flame temperature, are shown for flames in adjacent (upper and lower) channels of a counter-flow channel reactor with and without heat recirculation (χ = 0.002 and χ = 0.0, respectively) at a flame separation distance (L) of zero and a given normalized flame concentration (YF ) and external heat loss scale (κ ) (Reprinted from Ju et al. [117] with permission of Elsevier).

dimensional model and experimental results showed excellent agreement with a two-dimensional model that incorporated a volumetric sink term into the energy equation for external losses; this similarity was attributed to a minimal temperature gradient along the height of each channel within the combustor. The threedimensional results also showed the importance of turbulence in damping out Dean vortices that form when a turbulence model is included [127]. A two-dimensional representation of an element of the Swiss roll combustor near the center section was achieved by modeling a folded channel that had adiabatic walls except near the turn in the channel where heat exchange was permitted, and showed that the flame stabilized in or near the turn in the channel, analogous to the center section of the Swiss roll combustor [118]. The effects of materials on flame stability in a Swiss roll reactor are similar to those observed in folded channel studies: high thermal conductivity walls are detrimental to flame stability because of the increased heat loss incurred by the reactor. An experimental study by Vijayan and Gupta [128] examined the construction of Swiss roll combustors from steel, aluminum and ceramics and found that the metal combustors were not able to sustain propane/air flames without external heating because of the high thermal conductivity of the material, which produced a low B for the reactor. The extinction induced by high thermal conductivity materials was also observed when a high thermal conductivity viewing window was installed on the reactor in place of quartz. A two-dimensional numerical model has shown similar results in which the fuel mole fraction of lean propane/air mixtures at extinction decreased significantly with decrease in thermal conductivity [11]. The benefits observed from decreasing thermal conductivity do not extend to the limit at zero conductivity, however, because wall conduction is required for heat recirculation; therefore, optimum reactor material properties which produce the widest possible operating range can be found for a given reactor geometry [10]. Additionally, low emissivity materials have been shown to be required for ultra-lean combustion in the Swiss roll combustor [129]. A numerical study by Fan et al. [130] highlighted the importance of material emissivity in addition to thermal conductivity, as a stainless steel Swiss roll combustor (low ε ) with a bluff body in-

3.2.3. Counter-flow channels A variation on the folded geometry is the counter-flow channel reactor in which isolated streams flow in opposing directions in neighboring channels (Fig. 25(d)). Heat is transferred between these channels in a similar way to the folded reactor except each channel contains reactants, a combustion zone and combustion products. The combustion products in each channel heat reactants in one adjacent channel or multiple adjacent channels depending on the geometry of the reactor. Heat transfer is dominated by convective heat transfer between the solid walls and the gases in such reactors due to the use of thin and highly conductive separating walls between the channels. One-dimensional models have been developed which capture this transverse heat transfer to study the dynamics of the flames in a two-channel counter-flow geometry [116,117,131]. Fursenko et al. [131] used a one-dimensional model to study the stabilization location of flames in a counter-flow reactor in response to changes in reactant velocity and heat loss. Results showed that the separation distance between flames decreased with increase in gas velocity and increase in heat loss. Ju and Choi also conducted one-dimensional modeling to study the stabilization of methane flames below their flammability limit in a two-channel reactor Ju and Choi [117]. External heat losses were shown to be influential in flame stability and could lead to extinction, in contrast to the model results of Ronney [15] which revealed no extinction limit at low mass fluxes in the absence of streamwise conduction in the separating wall. While Ronney’s model demonstrated the potentially significant impact of axial conduction along a separating wall on extinction in a parallel channel reactor via heat redistribution and subsequent loss, the use of a well-stirred reactor (WSR) did not capture the effects of flame thickness and thermal diffusion on external heat loss. Ju and Choi did include these effects and demonstrated that external heat loss is sufficient to quench flames, even without heat conduction along the inner wall. Thus, between these two modeling studies, the critical importance of heat loss, whether directly via external losses or indirectly via heat distribution within the channel and subsequent external losses, has been demonstrated. Fig. 29 shows the temperature distributions of flames in two adjacent channels for different levels of heat transfer intensity between channels, or heat recirculation; a scale factor (χ ) was used to artificially vary the rate of convective heat transfer to the walls, calculated using Newton’s Law of Cooling, for which larger values of χ indicate higher rates of heat transfer and recirculation [117]. The presence of heat recirculation (χ = 0.002) created a significant convective preheating zone ahead of the convective-diffusive zone of the flame observed with and without heat recirculation (χ = 0.0). Additionally, the impact of heat recirculation on peak temperature can be observed in the results, with subadiabatic peak flame temperatures (T˜ , denoted by T in Fig. 30, less than unity) produced without heat recircula-

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Fig. 30. Numerical results show the variation of flame temperature (Tf ) and flame speed (U), both normalized by adiabatic values, and heat loss at the extinction limit with variation in heat transfer intensity in a counter-current reactor for a given fuel concentration and a flame separation distance of zero (Reprinted from Ju et al. [117] with permission of Elsevier).

Fig. 32. The dependence of maximum flame separation distance on equivalence ratio in a counter-flow channel reactor shown by numerical simulations for a range of heat transfer intensities (χ ) at the critical external heat loss scale where extinguishment occurs (κ c ) (Reprinted from Ju et al. [117] with permission of Elsevier).

tion due to external heat losses, and superadiabatic temperatures (T˜ > 1) produced with heat recirculation. The impact of heat recirculation intensity on extinction limit flame speed and temperature, as well as critical heat loss level at extinction, were quantified and results are shown in Fig. 30. As heat transfer intensity was increased from χ = 0.0 (no convective heat transfer) to χ = 1.0 (convective heat transfer equal to that calculated for fully developed internal flow), the flame temperature increased by approximately 75% of its adiabatic value while flame speed increased dramatically to greater than 6 times its adiabatic value (U˜ = 6) and the heat loss at the extinction limit (κ ) increased to 38 times the natural convection heat loss. Thus, the ability of heat recirculation to extend combustion stability by counteracting external loss-induced extinction was demonstrated. Furthermore, an increase in throughput was achieved relative to a reactor without heat recirculation. The results of Ju and Choi [117] also demonstrated that the flame separation distances change in response to changes in heat loss and recirculation. A one-dimensional model was constructed

which approximated a two-channel geometry, neglecting the thermal conductivity along the channel walls. This model was used to evaluate the range of heat loss, mixture composition and reactant velocity over which flame stabilization could be achieved. Analytical and experimental results showed that reaction zones were stationary only if the flame fronts are positioned at positive separation distances, upstream of the location of the flame fronts in the adjacent channels; once the flame fronts pass each other, the configuration is no longer stable [117]. Similar results were presented in other studies of folded channels, for which a flame position before the bend in the channel constitutes a stable flame [116,123] as illustrated in Fig. 31. Fig. 32 shows the maximum flame separation distance for different values of heat transfer intensities over a range of lean equivalence ratios at and below the lean flammability limit of methane in a counter-flow channel reactor. The flames can freely propagate in the channel at and above the lean flammability limit as they do not require heat recirculation to stabilize, making control of flame position within the channel difficult. Below the flammability limit,

Fig. 31. Stable and unstable flame positions for (a) a counter-flow (b) folded reactors.

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Fig. 33. The impact of variation in (a) equivalence ratio, (b) inlet temperature, (c) non-dimensional axial conduction (κ ), and (d) non-dimensional gas/wall heat transfer (μ) on stable methane/air flame position as determined from numerical simulations for a counter-flow channel reactor over a range of reactant flow rates (Reprinted from Schoegl and Ellzey [45] with permission of Elsevier).

two flame separation distances are shown: one positive and one negative. The positive, stable separation distances were found to decrease as the reactant mixture became leaner, as an increase in heat recirculation is needed to increase the flame speed of leaner mixtures and permit stabilization. Conversely, less heat recirculation and increase in flame speed were needed for higher equivalence ratios to stabilize at a given reactant flow rate, leading to an increase in flame separation distance. The importance of transverse interfacial heat transfer as the dominant heat transfer mode in counter-flow reactors has been elucidated in one- and two-dimensional models of counter-flow reactors of finite lengths [45,132,133]. A one-dimensional analytical model was developed by Schoegl and Ellzey [45] to study and compare co-flow and counter-flow configurations in finite length channels; finite length channels allowed for more substantial loss of enthalpy via hot products exiting the reactor as compared to infinite length channels, which allow sufficient time for equilibration of temperature between exiting products and entering reactants in adjacent channels. The impacts of equivalence ratio, reactor geometry and heat transfer parameters on axial flame position over a range of flow rates were examined, some results of which are shown in Fig. 33 for variations in equivalence ratio (ϕ ), inlet temperature (T0 ), axial conduction and gas/wall heat transfer. Notably, a wide range of equivalence ratios beyond the upper flammability limit of methane could be stabilized, although the stable position and flow rate ranges narrowed as equivalence ratio increased due to the need for increased heat recirculation for a stabilized flame to be achieved. Also noteworthy, stability was shown to be more sensitive to increases in gas/wall heat transfer as compared to axial

conduction, indicating that transverse heat transfer between gases and dividing walls is the dominant heat transfer mechanism in the counter-flow reactor. For comparison, the same model was adapted to a co-flow or unidirectional configuration, which was found to be dominated by axial conduction and interfacial heat transfer and had a far more limited stable operating range. A two-dimensional model of a finite length counter-flow reactor was developed by Belmont et al. [132] to study the impact of variation in height and length of reactor channels. Results showed that heat recirculation was more effective at smaller channel heights, supporting the deduction of a significant impact of transverse interfacial heat transfer in other studies. The concepts developed in the models for combustion in counter-flow combustors have been implemented in experimental studies of ultra-rich [134–136] and ultra-lean [137,138] methane, propane and heptane combustion using four-channel counter-flow reactors with opposing flow in adjacent channels. These studies confirmed key characteristics of heat recirculating counterflow combustors that were elucidated by modeling studies, including sub-limit flame stabilization, superadiabatic temperatures, and self-regulation of flame positions within the channels. Stable operating points were achieved for all tested fuels beyond their respective upper and lower flammability limits and at temperatures above their adiabatic flame temperatures, confirming that superadiabatic operation was achieved by heat recirculation through the channel walls. Models of counter-flow reactors have indicated that, for meso-scale combustors, external heat loss remains highly influential on flame stabilization and peak temperatures despite the insulating effects of adjacent channels. Counteracting external

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Fig. 34. Peak counter-flow channel reactor wall temperatures (Tw ) compared to adiabatic flame temperature (Tad ), and unburned hydrocarbon (UHC) emissions, experimentally measured for combustion of ultra-lean methane (CH4 ), propane (C3 H8 ) and heptane (C7 H16 ) at ϕ = 0.44 for methane and ϕ = 0.41 for propane and heptane (Reprinted from Belmont and Ellzey [138] with permission of Elsevier).

heat losses are the rates of heat release and internal heat transfer within the combustor channels, and the balance between these heat transfer rates determines the level of superadiabatic operation achieved in the channels [132]. The significant impact of flow rate on peak temperatures within the channels was observed in experimental studies of counter-flow channel reactors. Peak channel wall temperatures and unburned hydrocarbons measured for ultra-lean combustion are shown in Fig. 34 for three different fuels. Peak wall temperatures were observed to increase from subadiabatic to superadiabatic with an increase in reactant velocity, although model results indicate that gas temperatures were significantly higher than wall temperatures, suggesting superadiabatic conditions at all velocities [132,133]. Similar results were observed in studies of ultra-rich combustion as well. The observed trend shows that the increased volumetric heat release associated with increased velocity is relatively more important than external heat loss resulting in higher reactor temperatures. Additionally, the impact of these temperatures on the extent of fuel conversion was shown to be substantial, such as the observed increase in unburned hydrocarbons at lower reactant velocities and peak temperatures in studies of ultra-lean combustion [137,138].

dition of an equivalence ratio of 0.026, with a filtration reactor and the Swiss roll reactor also operating at very low equivalence ratios (0.1 and 0.15, respectively). For rich conditions, the two-section reactor and reciprocal flow reactors were operated at the highest equivalence ratios of 9.0 and 8.0, respectively. Such comparisons can be informative, but it is important to interpret any comparisons with the understanding that operating at the most extreme equivalence ratio or burning velocity was not necessarily a study goal and so the limits of stable operation might not have been evaluated. Laminar flame speeds for typical hydrocarbons at nearstoichiometric conditions are ∼40 cm/s, with the flame speed decreasing as the equivalence ratio deviates significantly from stoichiometry. For both lean and rich conditions, burning rates far exceeding the laminar flame speeds were achieved. The highest burning rates were demonstrated in the Swiss roll reactor, which achieved a burning velocity of ∼500 cm/s with lean methane/air mixtures. Applications of heat-recirculating reactors are considered at various scales, including micro- and meso-scales for portable applications as reviewed by Ju and Maruta [25] and larger scales for fuel reforming [22]. In this section, a summary of recent work done in each of the various major application categories is reviewed.

4. Applications of heat recirculating reactors 4.1. Lean combustion The ability of heat-recirculating reactors to burn mixtures outside the conventional flammability limits and at burning rates far exceeding the adiabatic laminar flame speed at standard conditions opens up a wide range of applications [7]. Stable combustion of lean and ultra-lean reactants provides a pathway to increase fuel efficiency and destroy low levels of contaminants. The high radiant output of solid surfaces is useful for industrial heating applications and electricity generation through thermoelectric and thermophotovoltaic generation. Finally, ultra-rich combustion can produce syngas, which is useful as a fuel or chemical input to other processes such as fuel cells. These applications depend on the range of equivalence ratios that can be stably burned and burning velocities that can be achieved in these reactors; a selection from the literature is shown in Table 1. As Table 1 indicates, stable burning at equivalence ratios that are nearly 5 times the rich flammability limit [97] and 5% of the lean flammability limit [96] have been achieved. For lean operation the reciprocal flow reactor was operated at the most extreme con-

One of the principle applications of heat-recirculating reactors is to burn fuels as lean as possible. A survey of the literature shows very lean operation with a variety of fuels and reactors [21]. The reactors generally achieving the leanest operating conditions are spiral and filtration reactors, though the filtration reactors cannot operate indefinitely, as discussed, unless they are designed as reciprocal flow reactors. Significant research has focused on the two-section reactor as a low emissions combustor. Keramiotis et al. [65] conducted a study on a two-section burner consisting of a layer of Al2 O3 followed by a 3.9 ppcm layer of SiSiC foam. As shown in Fig. 35, CO emissions are more sensitive to thermal load than NOx emissions are at a fixed equivalence ratio. The results also illustrate the advantage of operating at very lean conditions. The emissions of both CO and NOx roughly double between λ of 1.4 and 1.2 (equivalence ratios of 0.71 and 0.83). This wide variation illustrates the need to carefully consider burner operating conditions such that emissions

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J.L. Ellzey, E.L. Belmont and C.H. Smith / Progress in Energy and Combustion Science 72 (2019) 32–58 Table 1 Experimental demonstrations of ultra-lean and ultra-rich combustion in heat recirculating reactors. In some cases, values are approximate. Reactor type

Fuel

Lower or upper fuel flammability limit

Min. or Max. φ

Max. inlet velocity (cm/s) at min. or max. φ

Counter-flow [134] Counter-flow [136] Swiss-roll [125] Two- section porous media [139] Filtration [101] Filtration [110] Reciprocal flow reactor [97] Counter-flow [138] Counter-flow [138] Counter-flow [137] Swiss-roll [125] Swiss-roll [7] Filtration [16] 2-section porous media [52] Reciprocal flow reactor [96] Bank of tubes [48] Filtration [140]

Methane Heptane Propane Methanol Ethanol Methane Methane Propane Heptane Methane Propane Methane Methane Methane Methane Methane Natural gas

1.67 3.77 2.7 4.1 2.8 1.67 1.67 0.56 0.58 0.52 0.51 0.52 0.52 0.52 0.52 0.52 ∼0.52

2.5 3.9 4 9 5 2.75 8 0.27 0.27 0.28 0.18 0.1 0.15 0.41 0.026 0.32 0.09

125 50 0.81 15 20 50 100 100 100 100 3.86 ∼500 43 11 32 28 40

Fig. 35. Measured emissions of CO and NOx vs. thermal load from a two-section burner; λ = 1.2, 1.4, 1.6 correspond to equivalence ratios of 0.83, 0.71, 0.63 (Reprinted from Keramiotis et al. [65] with permission of Elsevier).

are appropriate for a desired application. The fuel flexibility of this burner is demonstrated by stable operation with two different fuels, methane and liquefied petroleum gas, and by the similarity of the emissions profiles at similar conditions. Filtration reactors have been used to burn very lean mixtures of fuel and oxidizer, making them appropriate as thermal oxidizers. Hoffman et al. [96] successfully operated a reciprocal flow reactor on methane/air at an equivalence ratio of 0.026. The system was shown to be effective at oxidizing very small amounts of volatile organic compounds (VOCs), and was further studied numerically to find the relationships between the lowest flammability limit (lean combustion limit) and reactor parameters, noting that porous media particle size was the most important parameter [141]. A unique application of lean combustion for pollutant destruction was described by Chen and Ronney [127]. Their small Swiss roll reactor, which burned mixtures of propane and air at equivalence ratios as low as ∼0.1 [125], was proposed for integration with a gas mask to destroy chemical or biological agents; if noxious agents could be burned sufficiently lean, the CO2 level in the exhaust would be breathable.

motivated studies of the two-section burner as a radiant heater [57,62,63,142,143]. In Fig. 36, radiant efficiency, defined as the percentage of the energy in the fuel emitted as radiation, is shown for different downstream porous media, referred to as the flame support layer. The thickness of the flame support layer does not appear to significantly affect the radiant efficiency in contrast to the pore density (ppc). Increasing the pore density, which results in an increase of optical thickness, significantly decreases the radiant output. The magnitudes of heat transfer to the environment by radiative and convective modes have been quantified in a study of small scale Swiss roll combustors designed to be used as heaters [126]. Fig. 37(a) summarizes the experimentally measured mean combustor temperature over a range of mean velocities for a variety of combustor geometries and shows a positive dependence of temperature on mean velocities or firing rate. Fig. 37(b) compares calculated natural convective and radiative heat loss over the range of experimentally measured combustor temperatures and shows that radiative heat transfer dominates for combustors constructed of high emissivity materials. Furthermore, comparison of Fig. 37(a) and (b) indicates that heat transfer to surroundings is directly dependent on inlet velocity.

4.2. Radiant heating 4.3. Thermoelectric power generation The hot porous medium is a very effective radiant emitter that can be used to generate radiant heating from gaseous fuels such as methane, which have low sooting tendencies and therefore would not otherwise be useful for radiant heating. This characteristic

Heat-recirculating reactors are unique in their ability to generate and sustain high temperatures from lean reactant mixtures, as demonstrated by their use as radiant heaters. This has led some

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Fig. 36. Measured radiant efficiency vs. firing rate for two-section porous burner operating on methane/air (ppc = pore per centimeter) (Reprinted from Mital et al. [63] with permission of Elsevier).

researchers to investigate their use in generating power with thermoelectric devices, which operate most efficiently with large temperature differences [25,96,144–146]. This potential was evaluated by Weinberg [145] in a theoretical analysis of three different heat exchanger/thermoelectric converter configurations. He found, for the most practical of the configurations, that the maximum possible system efficiency could be as high as 22.6%, which is a 58% improvement over a design with no heat recirculation, thus demonstrating the potential of this approach. Thermoelectric generators have been coupled to porous media combustors [146] and reciprocal flow filtration reactor [95,96], with results generally showing higher thermoelectric power output with increased combustor temperature. Efficiencies, varying from experimental values of less than 0.2% [23] to modeling values of >5% [147], were far from the maximums predicted by Weinberg. A combined heat-recirculating combustor and thermoelectric converter concept using a folded channel combustor was shown to theoretically achieve a nearly 60% increase in system efficiency by preheating as compared to a

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combustor-converter without heat recirculation [148]. The practical production of electrical power from thermoelectric devices still faces significant hurdles: the thermoelectric generator efficiency is generally low (∼10 − 15%), and system level efficiency is even lower [149,150]; the standard material (Bi2 Te3 ) for thermoelectric power generation cannot operate above ∼ 200 ◦ C [151], so the development of materials that can operate at high temperatures is an active research area [150–152]; lastly, system-level design, including the minimization of heat losses and the design and integration of hot and cold side heat exchangers, remains challenging and costly [145,150,152]. An alternative to coupling of combustors and thermoelectric generators is the use of thermophotovoltaics with combustors. A thermophotovoltaic generally consists of three components: a heat source, an emitter and photovoltaic cells. When a combustor is integrated into a thermophotovoltaic system, the combustor wall can serve as the emitter. Heat recirculating reactors have been shown to be favorable for use in thermophotovoltaic systems because of the high and uniform wall temperatures that can be achieved. Studies have examined single and two-section porous media and counter-flow combustors, and found operating conditions and geometry to significantly impact system performance, largely through combustor wall temperature magnitude and distribution uniformity [153–155]. One numerical and experimental study of such a system utilized a tubular combustor with and without a heat recuperator, where the heat recuperator was the addition of an axisymmetric outer quartz cylinder to form a folded counter-flow tubular combustor [156]. Results of the study showed that reactor temperature and electrical power generation were increased with the counter-flow configuration as compared to the unidirectional combustor. 4.4. Fuel reforming The ability to combust rich and ultra-rich fuel mixtures in heat recirculating reactors provides opportunities to reform gaseous and liquid fuels into hydrogen- and carbon monoxide-rich syngas. The production of syngas is desirable for a number of applications, including the subsequent combustion of the syngas as a cleaner burning fuel than the original hydrocarbon. Rich combustion in porous media reactors was reviewed in 2010 [99] and in 2016 [22]. These reviews detailed studies where many heat recirculating reactor types were used to convert various fuels to syngas and hydrogen. A selection of hydrogen and carbon monoxide production for various reactors and fuels is shown in Table 2.

Fig. 37. The relationships between (a) experimentally measured mean temperature and mean velocity and (b) calculated mean temperature and heat transfer to surroundings (heat loss) for a variety of experimentally examined Swiss roll combustor geometries (designated by W, Sq, S, Si and D) and material emissivities (ε ) operating on stoichiometric propane (Reprinted from Kim et al. [126] with permission of Elsevier).

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J.L. Ellzey, E.L. Belmont and C.H. Smith / Progress in Energy and Combustion Science 72 (2019) 32–58 Table 2 Examples of hydrogen and carbon monoxide production in heat-recirculating reactors. Values without asterisks were reported by the cited papers. Values with asterisks were calculated where possible using a carbon balance (if carbon-containing species with non-negligible concentrations were not reported, then the yields are artificially high). Reactor type

Fuel

φ /inlet velocity (cm/s)

H2 yield (%)/H2 conc. (%)

CO yield (%)/CO conc. (%)

Counter-flow [134] Counter-flow [135] Counter-flow [136] 2-section porous media [139] 2-section porous media [139] Filtration [101] Filtration [102] Filtration [102] Filtration [110] Reciprocal flow [97] Conical porous media (reactants preheated to 550 °C) [112]

Methane Propane Heptane Methane Octane Ethanol Jet fuel Butanol Methane Methane Methane

2.4/125 2.2/125 2.9/125 1.85/5.5e-3 g/s fuel 3.25/1.5 e-2 g/s 3/20 3.2/34 2.5/30 2.38/25 4/80 2.4/1520 kW/m2

53∗ /18 52∗ /17 NA/14 43∗ /12 36∗ /11 48/NA 42/NA 45/NA 50/16 65/NA 57∗ /20

82∗ /14 74∗ /18 NA/16 78/11 63∗ /17 64/NA 52/NA 72/NA 72∗ /13 75/NA 74∗ /13

Hydrogen yields are near 50%, while CO yields are generally closer to 75%, and those yields are consistent with exhaust gas concentrations of ∼20% H2 and ∼15% CO. Many authors have compared their experimental results with both equilibrium calculations and various reactor models. Generally, the models show adequate prediction of concentrations and yields for moderately rich equivalence ratios and do not agree as well with experiments at higher equivalence ratios. This is also true for equilibrium calculations, which overpredict hydrogen concentrations at high equivalence ratios (Fig. 22), indicating that finite-rate kinetics are important. Because of this, key parameters related to finite rate kinetics have been studied in detail [97,157,158]. Studies on fuel reforming kinetics have indicated that hydrogen production occurs in both the primary reaction zone and downstream in which the relatively slow steam-reforming reaction (Cn Hm + nH2 O → (n + m 2 )H2 + nCO) and water gas shift reaction (CO + H2 O → H2 + CO2 ) take place. AlHamamre [157] showed that above ∼1300 K, the hydrogen mole fraction after long times (>10,0 0 0 s) was ∼0.25 and insensitive to temperature, but reaching ∼0.25 required ∼10 0 0 s when the temperature was 1400 K and only ∼0.1 seconds when the temperature was 1900 K using a zero-dimensional kinetics model. These findings indicate that a sufficiently large Da in the post-flame region must be obtained for maximum production of hydrogen, so the parameters affecting Da (length, flow velocity and temperature) must be considered in reactor design. The possibility of converting water to hydrogen via the steam reforming and water gas shift reactions has also led researchers to investigate the enhancement of hydrogen production by adding water to the reactants [99,101,159,160] as is done with catalytic steam reforming [161]. Dobrego et al. numerically [159] and Araya et al. experimentally [160] studied the addition of water to the reactants in noncatalytic reforming in heat recirculating reactors, finding that water addition substantially improved hydrogen yields, with Araya reporting 98% hydrogen conversion efficiency for methane (where the hydrogen in water is not counted in the denominator of the conversion efficiency calculation). A similar idea was tested by Smith et al. [101] who converted wet ethanol to syngas in a filtration reactor. Wet ethanol is ethanol that has not been fully dehydrated by energy-intensive separation processes, so a systems-level energy savings was demonstrated by converting wet ethanol, rather than dry ethanol, to hydrogen. Besides raw production efficiency, other practical considerations are important when comparing reactors for hydrogen production. Filtration reactors can operate at the most extreme conditions but require flow reversal for pseudo-steady operation. Hydrogen production generally increases with equivalence ratio up to a certain point, generally near the rich flammability limit, and then decreases [101]; therefore, reactors without propagating fronts that operate at more moderate equivalence ratios can be used for fuel reforming though potentially having suboptimal hydrogen produc-

tion. Another important consideration when reforming heavy fuels is soot formation [60,162] and reactor clogging, which depend on operating conditions and reactor design. Parallel channel reactors can require periodic burning off of carbon deposits [135], and total reactor clogging has been observed in filtration reactors [102]. Butanol and jet fuel were converted [102] to syngas and hydrogen in a filtration media reactor, but it was noted that soot buildup clogged the reactor when burning jet fuel, and for this reason the tested equivalence ratios were limited to 3.58. Experiments with externally-preheated reactants have shown, promisingly, that the soot point can be shifted rich with preheat [157].

5. Conclusions and future work Heat transfer into and out of reactants has a significant impact on combustion phenomena due primarily to the strong temperature dependence of chemical kinetics. Research on the coupling of heat transfer and combustion has provided great insights into the major combustion phenomena of flame stability, flammability limits, and burning rates. In the last few decades, significant effort has focused on managing the heat transfer in reactors such that it enhances all of these phenomena. The resulting heat recirculating reactors have wider flammability limits, higher burning rates, and greater flame stability than those of a conventional premixed laminar flame. These greater operating ranges have provided opportunities for novel reactors that may be thermal oxidizers to eliminate trace VOCs, fuel reformers to convert hydrocarbons to syngas, or lean reactors for low emission operations. Further development of this important technology requires advancement in several areas. The nature of heat recirculating reactors is that they are characterized by small channels and/or tight bends, making fabrication difficult. New fabrication methods, such as additive manufacturing (AM), would create possibilities for both research and manufacture of novel reactors. At the current time, AM has not been applied extensively to devices which have the harsh thermal and chemical conditions of a reactor, particularly when the flame is impinging on the solid surface. Laser sintering, one AM technique, allows the use of ceramics or metal infilled ceramics which would greatly expand the temperature limits over conventional materials [163]. Though not restricted to AM, topology optimization, which is a method for computational optimization of geometry, has been applied to fluid systems [164,165]. Topology optimization algorithms produce geometries that are often ill-suited for traditional manufacturing processes, so the development of AM for high-temperature reacting systems presents an opportunity for the design of optimal geometries. In the future, these algorithms can be used to search for optimal heat-recirculating reactor chamber geometry for the purposes of expanding operating range, increasing firing rate or increasing target species production as in the case of fuel reforming.

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AM also opens up possibilities to tailor the material properties such as conductivity to enhance or diminish heat transfer in a particular direction or to vary the conductivity in a single material as has been achieved with gradient alloys of titanium, stainless steel, invar and inconel [166], which could be useful for flame stabilization or other forms of control. This idea has been explored by Veeraragavan [167] who developed a two-dimensional computational model that permitted different axial and transverse wall solid conductivities. The results indicate that by controlling the conductivities, the operating range of the reactor may be tailored to different specifications. Recently, Sobhani et al. [168] developed a onedimensional model of a two-section reactor with topology gradation such that the interface had spatially graded properties rather than a discontinuity. An experimental reactor consisted of sections of stacked ceramic foams. Experimental and computational results agreed qualitatively and showed that the reactor with the graded interface had a larger stable operating range than the one with a discrete interface. These results provide further evidence that AM is a promising tool for development of novel reactors. Since the heat-recirculating reactors described in this review require high interaction between the gas phase and solid phase, the length scales (for example, pore diameter and channel widths) are often small in order to accommodate high rates of heat transfer, and the reaction zones are submerged within the pores, limiting access for measurement [169]. This is especially true for combustion in porous media; detailed understanding of the intra-pore flame characteristics is still lacking due to the challenges of making measurements in the combined solid and gas environments. Knowledge of flame shape and thickness would provide important insights into burning rate enhancement and flame stabilization, two critical characteristics for practical designs. Since temperature and temperature difference are the driving forces behind combustion and heat transfer, greater understanding would allow optimization of existing designs and provide guidance for new concepts. Thermocouple and probe measurements are often limited by the size and location of the measurement point; pore sizes must be greater than thermocouple bead size, and many surfaces must be passed through if the location is not at the outer surface of a porous medium. Some careful attempts at measuring the difference between the gas and solid phase temperatures in pores have been made [169,170] with useful results, but more work is needed. Imaging techniques, such as x-ray computed tomography [171] and LIF [172], show promise to provide greater detail and advance our understanding as they are applied to more types of heat recirculating reactors. Detailed multi-dimensional modeling of heat recirculating reactors has been limited by inherent characteristics of large time scales in the solid and short time scales in the gas. Differences between one-dimensional and two-dimensional models show the importance of accurately representing the detailed character of the flow within these reactors [127]. Chemical kinetics schemes are typically not optimized, or perhaps not validated at all, at extreme equivalence ratios that are of interest to designers of thermal oxidizers and fuel reformers. In particular, reduced schemes which make computations more tractable, are rarely validated beyond conventional limits. Three-dimensional modeling which would reveal the spatial variations in temperature and concentrations would be useful for design and optimization, but the computational requirements for these simulations are prohibitive [78]. Heat recirculating reactors are often envisioned as parts of larger systems. Examples include a fuel reformer coupled with a fuel cell to produce electrical power [102], a stable and efficient heat source for thermoelectric [146] or thermophotovoltaic power generation, and a radiant heater for manufacturing and material processing [21]. As described previously, much of the basic theory of heat recirculating reactors is understood. Models of varying

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