Volumetric Heat Loss Research Articles

INFLUENCE OF UPSTREAM VERSUS DOWNSTREAM HEAT LOSSON THE STRUCTURE AND STABILITY OF PLANAR PREMIXED BURNER-STABILIZED FLAMES

The asymptotic structure and diffusional-thermal instability of a planar premixed burner-stabilized flame suffering either upstream or downstream volumetric heat loss with a rate described by a linear dependence on temperature is studied using activation-energy asymptotics. A brief review of the results for a flame without volumetric heat loss is presented. The results are compared to those obtained recently for a flame suffering combined upstream/downstream volumetric heat loss. For the structure, the analysis predicts that the expressions for the burning rate and the specific heat loss rate to the burner are not identical, unlike that shown for the freely propagating flame with volumetric heat loss. This is in agreement with earlier investigations of a flame suffering the three separate heat loss modes studied using thin-flame theory. Also in agreement with these earlier studies, the analysis predicts that the downstream heat loss mode is larger in magnitude than the upstream heat loss mode. For the diffusional-thermal instability, the analysis demonstrates that for the linear stability model considered, the effects of upstream and downstream heat loss appear in additive form. For fixed mass flux and volumetric heat loss intensity, it is found that the downstream heat loss mode is more effective than the upstream heat loss mode in promoting flame instability. These results are similar to those of the freely propagating flame with volumetric heat loss. A flame diagram dependent on the thermochemical data and volumetric heat loss mode is produced, which illustrates the stable flame region and the predicted extinction limits for low to medium values of the mass flux. It is found that at high mass flux no extinguishment point may be identified.

Propagation rates of nonpremixed edge flames

The propagation rates ( U edge ) of nonpremixed ignition (advancing) fronts and extinction (retreating) edge flames were measured as a function of global strain rate ( σ), jet spacing ( d), mixture strength, stoichiometric mixture fraction ( Z st ), and Lewis number (Le) using a counterflow slot-jet burner in which edge flames propagated along its long dimension. Electrical heaters at both ends of the slot “anchored” the flames, allowing conditions resulting in negative values of U edge to be studied by triggering local extinction of anchored flames with an N 2 jet. Results are presented in terms of the effects of a dimensionless flame thickness ( ε) related to σ and a dimensionless heat loss ( κ) on a scaled U edge . Propagation rates were markedly enhanced/retarded in mixtures with low/high Le. Propagation rates and extinction conditions were highly asymmetric with respect to Z st = 0.5 despite the symmetry of flame location; mixtures with Z st greater/less than 0.5 behaved like stronger/weaker mixtures, apparently due to the relative locations of the radical production zone and maximum temperature zone for varying Z st . Two extinction limits were identified, corresponding to a high- σ strain-induced limit that was strongly dependent on Le but nearly independent of κ and a low- σ heat-loss-induced limit that was strongly dependent on κ but not Le. Most experimental findings were in good agreement with theoretical predictions; however, unlike predictions, “tailless” triple flames were not observed; instead standard triple flames and “short length” edge flames were found, and only for a very narrow range of experimental conditions. This is proposed to be due to the difference between the volumetric heat loss presumed in the models and the conductive transfer to the jet exits that dominates heat loss in the experiments.

Study of the premixed flame model with heat losses The existence of two solutions

We study the existence of planar flames, in the case of a single-step chemical reaction with volumetric heat losses, with a general reaction term. We prove that for all positive Lewis numbers, and for small values of the heat loss rate parameter, two distinct solutions exist. We also give upper bounds for the flame speed and for the heat loss rate parameter. Moreover, we explicitly compute a lower bound for the unburned gases after reaction.

05/01195 Performance analysis and optimum criteria of an irreversible Braysson heat engine

Nonadiabatic heterogeneous flame propagation and extinction in self-propagating high-temperature synthesis (SHS) are analyzed based on a premixed mode of propagation for the bulk flame supported by the nonpremixed reaction of dispersed nonmetals in the liquid metal. The formulation allows for volumetric heat loss throughout the bulk flame, finite-rate Arrhenius reaction at the particle surface, and temperaturesensitive Arrhenius mass diffusion in the liquid. Results show that, subsequent to melting of the metal, the flame structure consists of a relatively thin diffusion-consumption/convection zone followed by a relatively thick convection-loss zone, that the flame propagation rate decreases with increasing heat loss, that at a critical heat-loss rate the flame extinguishes as indicated by the characteristic turning-point behavior, that the surface reaction is diffusion limited such that the nonlinear, temperature-sensitive nature of the system is actually a consequence of the Arrhenius mass diffusion, and that extinction is sensitively affected by the mixture ratio, the degree of dilution, the initial temperature of the compact, and the size of the nonmetal particles. An explicit expression is derived for the normalized mass burning rate, which exhibits the characteristic turning point and shows that extinction occurs when this value is reduced to e−1/2, which is the same as that for the nonadiabatic gaseous premixed flame. It is further shown that the theoretical results agree well with available experimental data, indicating that the present formulation captures the essential features of the nonadiabatic heterogeneous SHS processes and its potential for extension to describe other SHS phenomena.

Effect of Lewis number on flame propagation through vortical flows

The premixed gas flame spreading through an array of large-scale vortices is studied numerically. It is found that the flame speed is a nonmonotonic function of the stirring intensity. At sufficiently low Lewis numbers ( Le < 1 ) the system becomes bistable with a hysteretic transition between possible propagation modes. In the presence of volumetric heat losses the stirring invariably promotes extinction (reduces the flammability limits), provided Le > 1 . At Le < 1 this holds only for sufficiently strong stirring, whereas moderate stirring actually expands the flammability limits. At Le > 1 the deficient reactant is fully consumed up to the very quenching point. At Le < 1 , prior to the total extinction, part of the deficient reactant escapes the reaction zone and remains unconsumed.

Existence de deux solutions du type front progressif pour un modèle de combustion avec pertes de chaleur

This Note deals with the existence of planar flames, in the case of a single-step chemical reaction with volumetric heat losses. We prove the existence of two distinct solutions, for small values of the heat loss rate parameter. We also give upper bounds for the flame speed and for the heat loss rate parameter. To cite this article: L. Roques, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The role of radiative losses in self-extinguishing and self-wrinkling flames

We have developed a general theory of non-adiabatic premixed flames that is valid for flames of arbitrary shape that fully accounts for the hydrodynamic and diffusive-thermal processes, and incorporates the effects of volumetric heat losses. The model is used to describe aspects of experimentally observed phenomena of self-extinguishing (SEFs) and self-wrinkling flames (SWFs), in which radiative heat losses play an important role. SEFs are spherical flames that propagate considerable distances in sub-limit conditions before suddenly extinguishing. Our results capture many aspects of this phenomenon including an explicit determination of flame size and propagation speed at quenching. SWFs are hydrodynamically unstable flames in which cells spontaneously appear on the flame surface once the flame reaches a critical size. Our results yield expressions of the critical flame size at the onset of wrinkling and expected cell size beyond the stability threshold. The various possible burning regimes are mapped out in parameter space.

A numerical analysis of initiation of polymerization waves

Frontal polymerization is a process of converting a monomer into a polymer by means of a self-propagating, thermal reaction wave. We study initiation of polymerization waves by a heat source. A five-species reaction model is considered with a focus on the evolution of two of these species and the temperature of the mixture. We conduct independent numerical analyses of two experimental configurations. The first of these consists of a mixture of monomer and initiator (a catalytic agent) placed in a test tube and a constant high temperature imposed at one end of the tube. Here, we identify four parameters whose values are determined by the rate of initiator decomposition, amount of volumetric heat loss, amount of heat produced by chemical conversion, and initial mixture temperature. We present a marginal initiation criterion as a relation between these parameters. The second experimental configuration considered here involves placing a test tube filled with a monomer and initiator mixture into a hot thermostatic oil bath. Asakur et al. recently reported that they had observed the formation of a reaction front in the center of a mixture under these conditions. We offer a simple mathematical model of this experiment and the results of numerical simulations based on this model. We show that the model proposed here captures a phenomenon observed in experiment, namely, that for a given bath temperature, there is a minimal tube radius necessary for a reaction front to be initiated. Our results further confirm that the frontal polymerization observed in such experiments can occur via a thermal mechanism.

Characteristics of premixed flame in microcombustors with different diameters

Microcombustors with diameters of 2 and 6 mm are studied. The effect of the diameter on the transverse profiles of velocity, temperature and species mass fraction, as well as the axial volumetric heat loss and the wall shear stress were simulated and analyzed. The results show that there is a flat region on the transverse profiles for the 6 mm microcombustor. However, there is no flat region on the profiles for the 2 mm microcombustor. The non-flat structure reflects the wall effects. In addition, both the volumetric heat loss and the wall shear stress increase with decreasing the diameter.

Heterogeneous flame propagation in the self-propagating, high-temperature, synthesis (SHS) process in multi-layer foils: theory and experimental comparisons

A theory for heterogeneous flame propagation in the self-propagating, high-temperature synthesis (SHS) process that proceeds in multi-layer foils consisting of alternating layers of constituents has been formulated, describing a pre-mixed mode of bulk flame propagation supported by a non-pre-mixed reaction that proceeds at the layer surface of a constituent with higher melting point. The formulation allows for volumetric heat loss throughout the bulk flame, a finite-rate Arrhenius reaction at the layer surface, and temperature-sensitive, Arrhenius mass diffusion in the liquid phase. Results show that the burning velocity is inversely proportional to the layer thickness of the constituent with higher melting point; that the burning velocity decreases with increasing heat loss; that at a critical heat-loss rate, the SHS flame extinguishes, as indicated by the characteristic turning-point behavior; that extinction is sensitively affected by the mixture ratio, initial temperature, layer thickness of the constituent with higher melting point, etc.; that the surface reaction is partly or mainly reaction-controlled when the layer is a few nano-meters thick; that effects of the inter-mixed region produced by inter-facial mixing during deposition can be examined by regarding its components as reaction products that play the role of a diluent; and that the critical layer-thickness that the SHS flame ceases to propagate corresponds to the limit of flammability with respect to dilution. It is further shown that the analytical results agree with available experimental data in the literature, indicating that the present formulation captures the essential features of the non-adiabatic, heterogeneous SHS process that self-propagates in multi-layer foils.

An Asymptotic Model of Nonadiabatic Catalytic Flames in Stagnation-Point Flow

A formal asymptotic model is derived for a nonadiabatic catalytic flame in stagnation-point flow. In the present context, the premixed reaction in the bulk gas is augmented by a surface catalytic reaction on the stagnation plane, where conductive heat losses are allowed to occur. In addition, the thermal effects of a finite-volume combustor are accounted for by allowing for volumetric heat losses from the bulk gas. The analysis exploits the near-equidiffusional limit corresponding to near-unity Lewis numbers, and yields a general nonsteady nonplanar model for the reactionless outer flow subject to boundary conditions that reflect both surface catalysis and distributed chemical reaction in a thin boundary layer. For the case of steady planar combustion, the surface-temperature response indicates the possibility of multiple solution branches, which are shown to be linearly stable, and a corresponding extension of the extinction limit that demonstrates how the presence of a surface catalyst can counterbalance the extinguishing effects of heat loss and stretch in nonadiabatic strained flames. The present model is particularly relevant for small-volume combustors, where the increased surface-to-volume ratio can lead to extinction of the nonadiabatic flame in the absence of a catalyst.

The thick flame asymptotic limit and Damköhler's hypothesis

We derive analytical expressions for the burning rate of a flame propagating in a prescribed steady parallel flow whose scale is much smaller than the laminar flame thickness.In this specific context, the asymptotic results can be viewed as an analytical test of Damköhler's hypothesis relating to the influence of the small scales in the flow on the flame; the increase in the effective diffusion processes is described. The results are not restricted to the adiabaticequidiffusional case, which is treated first, but address also the influence of non-unit Lewis numbers and volumetric heat losses. In particular, it is shown that non-unit Lewis numbereffects become insignificant in the asymptotic limit considered. It is also shown that the dependence of the effective propagation speed on the flow is the same as in the adiabatic equidiffusional case, provided it is scaled with the speed of the planar non-adiabatic flame.

Effect of volumetric heat loss on triple-flame propagation

We present a numerical study of the effect of volumetric heat loss on the propagation of triple flames in the strained mixing layer formed between two opposed streams of fuel and air. The propagation speed of the triple flame is computed for a wide range of values of two non-dimensional parameters: a normalized flame thickness ε , proportional to the square root of the strain rate, and a heat-loss parameter κ . It is shown that, for relatively small values of κ , the propagation speed U is decreased by heat loss, and its dependence on ε is similar to the adiabatic case, known in the literature: in particular, a monotonic decrease in the speed from positive to negative values is observed as ε is increased. However, for κ larger than a critical value, this monotonic behavior is lost. It is shown that the more complex behavior obtained is mainly associated with the fact that, in the presence of heat loss, the trailing planar diffusion flame is extinguished both for sufficiently large and sufficiently small values of the strain rate. Moreover, for sufficiently small values of ε , the dependence of U on κ is similar to that of the non-adiabatic planar premixed flame, with total extinction occurring for a finite positive value of U . On the other hand, for larger values of ε , negative speeds, corresponding to extinction fronts, appear before total extinction is brought about by an increase in κ . A summary of the main results is provided by delimiting the different combustion regimes observed in the κ-ε plane.

Radiation losses as a driving mechanism for flame oscillations

In this paper, we describe the behavior of an edge flame in the mixing layer of two coflowing streams, one of fuel and the other of oxidizer, established at the mouth of a cylindrical injector. The edge flame is stabilized by conductive losses to the rim of the injector and a diffusion flame is trailing behind, either converging to the centerline of the cylinder or extending outward in the oxidizer region. The objective is to determine whether radiative losses alone can drive the edge of the flame to oscillate back and forth, a behavior that has been observed in various experimental configurations. The assumption-of-unity Lewis numbers is adopted to avoid differential-diffusion effects that are known to promote oscillations. Steady and unsteady calculations are reported within a diffusive-thermal approximation, but with finite-rate chemistry. We show that, in the presence of volumetric heat losses, the edge of the flame is stabilized at a larger distance from the rim than in their absence. Furthermore, when the intensity of radiation losses is sufficiently low, the edge remains stationary. When radiative losses become excessive, the edge undergoes sustained oscillations, moving back and forth with a well-defined frequency and amplitude.

Instability of burner-stabilized flames with volumetric heat loss

Behavior of the planar, burner-stabilized premixed flame that suffers volumetric heat loss, with its rate described by a linear function of temperature, is analyzed by activation energy asymptotics. Both its steady burning characteristics and its diffusional-thermal flame-front instability are investigated. The effect of volumetric heat loss is found to slow down the reaction so that the flame moves away from the burner. Consequently, the heat transfer from the flame to the burner is reduced and the flame temperature is increased. By continuously increasing the intensity of volumetric heat loss, the flame eventually is detached from the burner and becomes freely propagating. The stability analysis then reveals that the volumetric heat loss renders the flame to be less stable, similar to what is known for the freely propagating flame. The increase in the flame temperature has only a weak effect to stabilize the flame. It is primarily to compensate the decrease in the burning rate that is induced by the volumetric heat loss. In addition, the volumetric heat loss has a stronger impact on the reduction of stability for flames with a lower burner supply rate, that also is the burning rate. A critical burner supply rate exists, below which the flame turns absolutely unstable before detaching from the burner so that the freely propagating limit cannot be reached by increasing the intensity of volumetric heat loss. This study further supports the existence of the dual flame behavior experimentally observed by Spalding and Yumlu in that there exist two flame speeds for a heat transfer rate to the burner because stable flame exists, even for relatively small burner supply rates, when the volumetric heat loss is weak.

The onset of oscillations in diffusion flames

We present a theoretical study aimed at understanding the basic mechanisms responsible for the onset of oscillations in diffusion flames. A simple one-dimensional configuration is considered with one reactant supplied in a uniform stream and the other diffusing against the stream. The analysis allows for unequal non-unity Lewis numbers as well as for incomplete combustion. It is found that oscillations are possible when the Damköhler number is sufficiently small, namely at near-extinction conditions. They occur when the reactant diffusing against the stream is more completely consumed and the corresponding Lewis number is sufficiently large (typically larger than one). The conditions also require the Lewis number of the reactant supplied in the stream to be within a certain range (typically also larger than one). In accord with experimental results the onset of oscillations is found to be sensitive to stoichiometric conditions (or mixture strength) and to the temperature differential between the supply conditions. The effect of volumetric heat losses was also studied and it is shown that increased heat losses enhance the onset of instabilities. Predicted oscillations are of low frequency, typically 1-6 Hz for the range of Lewis numbers and mixture strengths used in experiments. (Some figures in this article are in colour only in the electronic version; see www.iop.org)

On the nonlinear response of stretched premixed flames

The nonlinear response of stretched premixed flames was studied analytically and computationally, with emphasis on the turning point behavior associated with flame extinction. Extending our previous study of the weakly stretched flames exhibiting linear responses, expressions for the nonlinear flame response were derived by using an integral method. For adiabatic flames, the extinction stretch rates were determined by using the global flame parameters extracted from the linear flame response. The predicted flame responses were then compared with computed results for counterflow and inwardly propagating spherical flames, and reasonably good agreements were obtained. The agreement was further improved by taking into account the increase of the effective activation energy with decreasing flame temperature as the flame approaches the extinction state. For nonadiabatic flames, the effect of volumetric heat loss was investigated via the one-dimensional planar flame subject to radiation loss, while the effect of conductive loss was studied via the counterflow flame against an isothermal wall. The formulation holds potential utility in predicting quantitatively accurate flame responses and in its implementation in the modeling of turbulent combustion.

A Simple Model of a Spray Diffusion Flame: Effects of Heat Loss and Differential Diffusion

In this study we examine theoretically the structure of a simple one-dimensional spray diffusion flame. The analysis is carried out along two complementary routes: an asymptotic approach, that treats the limiting behaviors of fast vaporization followed by fast chemical reaction and illustrates the various physical mechanisms involved in the complex multi-phase field, and a numerical approach that validates and extends the solution to arbitrary parameter values. The results emphasize the importance of heat and mass transfer rates, the supply conditions, the droplet loading, the size distribution of the droplets in the spray and the effects of volumetric heat loss. Particular attention is given to the conditions for flame extinguishment and those effects that may promote or delay extinction.

Effects of heat loss on the SHS flame propagation

Effects of heat loss on the flame propagation in the Self-propagating High-temperature Synthesis (SHS) are examined with a heterogeneous theory based on the premixed mode of the bulk flame propagation supported by the non-premixed reaction of dispersed non-metal particles in the liquid metal. This formulation allows for volumetric heat loss throughout the bulk flame, finite rate Arrhenius reaction at the particle surface and temperature-sensitive Arrhenius mass diffusion in the liquid. The results show that the burning velocity decreases with increasing heat loss, that at a critical heat-loss rate the flame extinguishes as indicated by the turning-point behavior, and that the extinction is sensitively affected by the mixture ratio, the degree of dilution, the initial temperature of the compact, the size of the non-metal particles and the size of the compact. It is further shown that the theoretical results agree well with available experimental data, indicating that the present formulation captures the essential feature of the non-adiabatic heterogeneous SHS process.

Self‐Propagating High‐Temperature Synthesis Flammable Range and Dominant Parameters for Synthesizing Several Ceramics and Intermetallic Compounds under Heat‐Loss Condition

Extensive comparisons have been conducted between experimental and theoretical results for the nonadiabatic self‐propagating high‐temperature synthesis combustion characteristics of many solid‐solid systems subjected to volumetric heat loss. The nonadiabatic flame propagation theory‐which describes the premixed mode of bulk flame propagation supported by the nonpremixed reaction of dispersed nonmetal (or higher‐melting‐point metal) particles in the liquid metal, with finite‐rate reaction at the particle surface and temperature‐sensitive Arrhenius‐type condensed‐phase mass diffusivity‐is used to compare with experimental results with heat loss. Systems examined are ceramics (TiC, TiB2, and ZrB2) and intermetallic compounds (NiAl, TiCo, and TiNi). By using a consistent set of physicochemical parameters for these systems, satisfactory quantitative agreement is demonstrated for the flammable range (defined in terms of the mixture ratio, degree of dilution, particle size, and/or compact diameter.