Non-reacting Case Research Articles

Numerical investigation of liquid methanol evaporation and oxy-combustion inside a button-cell ITM reactor

A numerical study is conducted to investigate the performance of a button-cell LNO-ITM reactor utilizing the soot-free oxygenated liquid methanol under oxy-combustion condition. The Euler-Lagrange approach is utilized to solve discrete phase model. Taylor analogy breakup (TAB) model is used due to its convenience with the cases of low injection speed. A plain orifice atomizer is used for fuel atomization and CO2 is used as sweep gas. A semi-empirical oxygen permeation model (ABn model) is validated with the available experimental data and is, then, applied in the present model. Over a wide range of inlet fuel concentrations, the results showed increase in oxygen permeation flux of about five times in cases of reacting conditions as compared to the cases of non-reacting cases. The results showed high oxygen permeation flux at low inlet fuel concentrations due to the improvement in the oxygen to fuel ratio toward the stoichiometric conditions. At inlet gas temperatures of 1223K, 1123K, 1023K and 923K, the combustion temperature approached 1423K, 1347K, 1284K and 1231K, respectively, indicating an average combustion efficiency of 43% at moderate inlet gas temperatures. High fuel concentration at low inlet sweep flow resulted in high oxygen flux and high combustion temperature.

Sparse-Lagrangian MMC simulations of an n-dodecane jet at engine-relevant conditions

Simulations are presented for the engine combustion network (ECN) n-dodecane spray A using the sparse-Lagrangian multiple mapping conditioning model for the reactive scalar field coupled with a large eddy simulation for the flow (MMC-LES). This is the first application of the MMC-LES to both transient and engine conditions and, in line with earlier simulations of the ECN flames, the fuel injection is modelled as a gas-jet. The model is evaluated initially for a baseline non-reacting case with ambient temperature of 900 K. Results for vapour penetration lengths and the radial profiles of mixture fraction show good agreement with experiments. The model is then applied to reacting cases, featuring transient ignition and combustion with a lifted flame base. A 106-species chemistry mechanism is employed. Simulations are performed at various ambient temperatures (800–1100 K) and various volume fractions of ambient oxygen (13–21%) that correspond to conditions in both conventional and advanced diesel engines. The trend towards decreasing ignition delay time and lift-off length with increasing ambient temperature and oxygen is predicted well. The quantitative agreement between the computed and experimental ignition delay times is satisfactory. The accuracy of lift-off length predictions is less accurate but comparable to the existing literature. Better results are obtained at the conditions with lower ambient temperatures and oxygen concentrations. This outcome is explored with a detailed analysis of heat release and scalar dissipation rates under various ambient temperature conditions. It is revealed that at high ambient temperatures, flame stabilisation occurs in a region with significant turbulence–chemistry interactions and close to the nozzle exit where the liquid phase would be expected to influence the flame.

Impact of confinement on flowfield of swirl flow burners

Swirlers are commonly used in gas turbine combustors as they provide recirculation zones and reduce axial velocity for enhanced flame stability. Swirl provides hot gas recirculation zone at front end of the combustor for enhanced mixing between hot reactive species and the freshly introduced mixture. In this paper, the impact of confinement on a swirl assisted combustion was investigated with focus on the flowfield under unconfined and confined conditions. The features of the flowfield were characterized under both isothermal and reacting conditions. Experimental results showed that for the unconfined cases, the flowfield exhibited the traditional central toroidal recirculation zone. Upon confinement, this zone shortened and also widened with increased velocity fluctuations across the combustor. Increase in the Reynolds number further enhanced the recirculation zone and increased the velocity magnitudes and turbulence. For reacting conditions, minimal recirculation was noticed for the unconfined flame. The recirculation zone was significantly enlarged upon confinement (compared to the non-reacting case) and with increase in Reynolds number. In general, the fluctuating velocity was found to be higher in the confined case compared to the unconfined case, and even higher at increased Reynolds number.

A stochastic breakup model for Large Eddy Simulation of a turbulent two-phase reactive flow

The current work presents numerical investigations of model burner in which a non-swirling air-assisted methanol spray is injected using a pressure-swirl atomiser. A stochastic breakup model is formulated in the context of Large Eddy Simulation (LES) and validated by detailed comparisons of the results with measurements. An excellent agreement is achieved for the non-reactive case in terms of the dispersion of the spray, the mean droplet distributions and the time-averaged spray velocities. The transported probability density function (pdf) equation/Eulerian stochastic field method are used to represent the interaction of turbulence and chemistry while the gas phase reaction of the methanol/air spray flame is described by a reduced reaction mechanism involving 18 chemical species and 84 elementary steps. The sub-grid scale (sgs) chemistry model in conjunction with the formulated breakup model are found to capture the influence of the flame on droplet dynamics together with the formation of a double reaction zone typically resulting from a polydisperse spray to a good accuracy.

An analysis of the structure of an n-dodecane spray flame using TPDF modelling

With a view to understanding ignition and combustion behaviours in diesel engines, this study investigates several aspects of ignition and combustion of an n-dodecane spray in a high pressure, high temperature chamber, known as Spray A, using data resulting from modelling using the transported probability density function (TPDF) method. The model has been validated comprehensively with good to excellent agreement in our previous work against all available experimental data including for mixture-fraction and velocity fields in non-reacting cases, and flame lift-off length and ignition delay in reacting cases. This good agreement encourages further investigation of the numerical model results to help understand the structure of this flame, which serves to complement the experimental information that is available, which is very limited due to the difficult experimental conditions in which this flame exists. For example, quantitative experimental measurements of local mixture-fraction, temperature, velocity gradients, etc. are not yet possible in reacting cases. Analysis of the model results shows that two-stage ignition is found to occur across the ambient temperature conditions considered: the first stage is rapidly initiated on the lean side where temperatures are high and sequentially moves to richer, cooler conditions. The first stage is extremely resilient to turbulence, occurring in a region of very low Damköhler number. The second stage of ignition occurs first in rich mixtures in a region behind the head of the fuel jet where mixture gradients are low, and appears to be influenced strongly by turbulence. Relative to a homogeneous reactor, it is delayed on the lean side but advanced on the rich side, suggesting entrainment and mixing from the early igniting lean regions into richer mixtures is an important moderator of the ignition process. The second-stage ignition front propagates at very high velocities initially, suggesting it is a sequential ignition moving according to gradients of ignition delay and/or residence time. The flame stabilises however on the lean side in a region of much lower velocity, where turbulent velocity fluctuations are sufficiently high such that turbulent transport influences the propagation. It stabilises in a region of low Damköhler number which implies that a competition of chemistry versus micro-mixing might also be involved in stabilisation. The stabilisation mechanism is investigated by an analysis of the transport budgets, showing the flame is stabilised by autoignition but moderated by turbulent diffusion. Further analysis of the flame index supports this stabilisation mechanism, and demonstrates the simultaneous existence of non-premixed and premixed combustion modes in the same flame. Analysis of the flow fields also reveals that local entrainment and dilatation are important flow features near the flame base.

Large-eddy simulation of flow and combustion dynamics in a lean partially premixed swirling combustor

A lean partially premixed swirling combustor was studied by resolving the complete flow path from the swirl vanes to the chamber outlet with large-eddy simulation (LES). The flow and combustion dynamics for non-reacting and reacting situations was analysed, where the intrinsic effects of swirl vanes and counter flows on the vortex formation, vorticity distribution for non-reacting cases were examined. A modified flame index was introduced to identify the flame regime during the partially premixed combustion. The combustion instability phenomenon was examined by applying Fourier spectra analysis. Several scalar variables were monitored to investigate the combustion dynamics at different operating conditions. The effects of swirl number, equivalence ratio and nitrogen dilution on combustion dynamics and NOx emissions were found to be significant.

Experimental study of the inverse diffusion flame using high repetition rate OH/acetone PLIF and PIV

Most previous work on inverse diffusion flames (IDFs) has focused on laminar IDF emissions and the soot formation characteristics. Here, we investigate the characteristics and structure of methane IDFs using high speed planar laser-induced fluorescence (PLIF) images of OH, particle image velocimetry (PIV), and acetone PLIF imaging for non-reacting cases. First, the flame appearance was investigated with fixed methane loading (mass flux) but with varying airflow rates, yielding a central air jet Reynolds number (Re) of 1,000 to 6,000 (when blow-off occurs). Next, it was investigated a fixed central air jet Re of 4500, but with varied methane mass flux such that the global equivalence ratio spanned 0.5 to 4. It was observed that at Re smaller than 2000, the inner air jet promotes the establishment of an inverse diffusion flame surrounded by a normal diffusion flame. However, when the Re was increased to 2500, two distinct zones became apparent in the flame, a lower entrainment zone and an upper mixing and combustion zone. 10kHz OH-PLIF images, and 2D PIV allow the identification of the fate and spatial flame structure. Many flame features were identified and further analyzed using simple but effective image processing methods, where three types of structure in all the flames investigated here: flame holes or breaks; closures; and growing kernels. Insights about the rate of evolution of these features, the dynamics of local extinction, and the sequence of events that lead to re-ignition are reported here. In the lower entrainment zone, the occurrence of the flame break events is counterbalanced by closure events, and the edge propagation appears to control the rate at which the flame holes and closures propagate. The rate of propagation of holes was found to be statistically faster than the rate of closure. As the flames approach blow-off, flame kernels become the main mechanism for flame re-ignition further downstream. The simultaneous OH-PLIF/Stereo PIV measurements indicate that the individual breaks events could be correlated to local vortical flow structure and strain rates fields. The detailed measurements provide a more complete understanding of IDF flame characteristics and structure than was previously possible.

Direct numerical simulation on supersonic turbulent reacting and non-reacting spray jet in heated coflow

Comparative studies of three-dimensional spatially-developing supersonic turbulent spray reactive and non-reactive flows have been conducted by direct numerical simulations. The gas-droplet flow system has been captured with the hybrid Eulerian–Lagrangian approach. High-resolution bandwidth-optimized weighted essentially non-oscillatory (WENO) scheme of spatial discretization and total variation diminishing Runge–Kutta temporal integration are used to capture the compressible turbulent flow. The flow motions of droplets are tracked in the Lagrangian frame. Arrhenius-type finite-rate chemistry is employed for the chemical reaction. The decay of the mean axial velocity at the centerline has been found much slower for the reacting case. The half-width of the spreading reacting jet is larger than the non-reacting case. The velocity of droplet has been found to be increased compared with the droplet at the same position in non-reacting flow. Heat release mainly occurs in the subsonic region. Premixed and diffusion modes are found to coexist in the present flame. Heat release contributed by premixed flame to the total heat release occupies more than 50% and peaks at 71.4% downstream of the flame. Combustion also affects the turbulent intensity of the flow field. Reynolds stress has been found to be slightly larger in the mixing layer with intense heat release. The fluctuation of temperature, mixture fraction has been found to be amplified significantly in the reacting flow.

Large eddy simulation of a piston–cylinder assembly: The sensitivity of the in-cylinder flow field for residual intake and in-cylinder velocity structures

Large eddy simulation (LES) in an axisymmetric piston–cylinder geometry was carried out using three LES approaches: (1) Smagorinsky subgrid scale model, (2) implicit LES, and (3) scale selective discretisation (SSD). In addition to the LES subgrid scale model sensitivity study, two additional simulations were carried out in order to understand the roles of the intake and the in-cylinder residual turbulence to the flow statistics. Altogether 12 cycles were computed for each simulation on a grid with 5 million cells and requiring over a month of wall-clock time per simulation on a supercomputer. Analysis of velocity statistics revealed that the results were not very sensitive to the LES model type. However, the residual turbulence was noted to have a clear impact on the velocity statistics. In particular, the simulations revealed that removing the residual turbulence from the intake region at the top-dead-centre has a clear impact on the overall velocity statistics. In many cases the cycle-to-cycle variation (CCV) increased. In a respective numerical test, where only the in-cylinder turbulence was removed at top-dead-centre, weaker sensitivity was observed. In addition, the CCV relative to the mean velocity was in some cases as high as 30% even in such a non-reactive case. The present study complements previous studies on the same set-up by investigating the sensitivity of three LES models on flow statistics, quantifying CCV using three different LES approaches in the standard set-up, and assessing the role of residual turbulence on the flow statistics via modified flow cases.

Impact of numerics on the predictive capabilities of reacting flow LES

Combustors in modern aerospace propulsion systems are highly optimized devices and further enhancements to their performance will require advanced predictive modeling techniques. The LES approach has potential to be such a technique, but demonstration of its true predictive capability remains a challenge. In this paper, a methodical study is performed to assess the impact of numerical error on the predictive capabilities of LES and to distinguish it from error arising from physical modeling. Four codes are employed to simulate the bluff body stabilized flame experiment of Volvo Flygmotor AB. The physical models (governing equations and sub-grid models) are kept identical between the codes so that the physical modeling error is the same. For the same reason, computational grids are also kept identical since the sub-grid models are grid dependent. Results indicate that all codes produce a very similar solution for the non-reacting flow in terms of large scale unsteady vortex shedding behavior, mean profiles and second order turbulence statistics, on a suitably refined grid. This solution is also very close to the experimentally observed behavior of the flow. In contrast, for the reacting case, solutions from the various codes exhibit significant differences when analyzed under the same metrics and with similar or even finer grid resolution than that used for the non-reacting case. These differences are large enough to change the macroscopic behavior of the flow, e.g. some codes predict symmetric vortex shedding while others predict asymmetric shedding and some codes show strong recirculation zones while others show stagnant regions behind the bluff body. It is also shown that none of the solutions truly predicts the experimentally observed flow. Given that the physical sub-grid models and computational grids are the same in all the simulations, the inconsistency between results points to a significant impact of numerical methods and, hence, numerical error. The need for mitigation of this impact is highlighted, along with the need for metrics detailing how LES should be applied to reacting flows. It is suggested that both of these issues should be the focus of future work.

Experimental and numerical analysis of oxy-fuel combustion in a porous plate reactor

The present work focuses on studying experimentally and numerically the oxy-fuel combustion characteristics inside a porous plate reactor towards the application of oxy-combustion carbon capture technology. Initially, non-reactive flow experiments are performed to analyze the permeation rate of oxygen in order to obtain the desired stoichiometric ratios. A numerical model is developed for non-reactive and reactive flow cases. The model is validated against the presently recorded experimental data for the non-reacting flow cases, and it is validated against the available literature data for oxy-fuel combustion for the reacting flow cases. A modified two-step oxy-combustion reaction kinetics model for methane is implemented in the present model. Simulations are performed over wide range of operating oxidizer ratios (O2/CO2 ratio), from OR = 0.2 to OR = 0.4, and over wide range of equivalence ratios, from φ = 0.7 to φ = 1.0. The flame length was decreased as a result of the increase of the oxidizer ratio. Effects of CO2 recirculation amount on the oxy-combustion flame stability are examined. A reduction in combustion temperature and increase in flame fluctuations are encountered while increasing CO2 concentration inside the reactor. At high equivalence ratio, the combustion temperature and flame stability are improved. At low equivalence ratio, the flame length is increased, and the flame was moved towards the reactor center line. Copyright © 2015 John Wiley & Sons, Ltd.

Role of the pore fluid in crack propagation in glass

We investigate pore fluid effects due to surface energy variation or due to chemical corrosion in cracked glass. Both effects have been documented through experimental tests on cracked borosilicate glass samples. Creep tests have been performed to investigate the slow crack propagation behavior. We compared the dry case (saturated with argon gas), the nonreactive water saturated case (commercial mineralized water), and the distilled and deionized water saturated case (pure water). Chemical corrosion effects have been observed and evidenced from pH and water composition evolution of the pure water. Then, the comparison of the dry case, the mineral water saturated case, and the corrosion case allow to (i) evidence the mechanical effect of the presence of a pore fluid and (ii) show also the chemical effect of a glass dissolution. Both effects enhance subcritical crack propagation.

Modelling n-dodecane spray and combustion with the transported probability density function method

An n-dodecane spray in temperature and pressure conditions typical of diesel engines, known as Spray A, is modelled by the transported probability density function (TPDF) method coupled with a time-dependent Reynolds-averaged k–∊ turbulence model and a Lagrangian discrete phase model of the liquid spray. To establish a baseline for comparisons, non-reacting cases are first studied. Good results are obtained for the vapour penetration, the mean and variance of fuel mixture fraction, and velocity profiles, with variations in ambient density and injection pressure. These comparisons are more extensive than previous studies due to new experimental data being available. Reacting cases are then investigated for a number of ambient conditions and injection parameters, employing a reduced chemical kinetic model. The chemical mechanism incorporates an OH∗ sub-mechanism (Hall and Petersen, 2006) which enables a direct comparison with experimental measurements of the lift-off length that are based on OH∗ chemiluminescence. To assess the importance of interactions between turbulence and chemistry, the results from the PDF model are compared to the measurements and to those from a well-mixed model that ignores turbulent fluctuations. Variations of ambient temperature, ambient oxygen concentration, ambient density, and injection pressure are considered. In all cases the PDF model with the EMST mixing model and Cϕ=1.5 shows an excellent agreement with the experimental lift-off length and presents improved results compared with the well-mixed model. Ignition delay is however over-predicted by both the PDF method and well-mixed models. Available shock tube data suggests that this may be due to the chemical kinetic model over-predicting ignition delay at higher pressures.

Large-eddy Simulation of Flow and Combustion Dynamics in a Lean Partially-premixed Swirling Combustor

Abstract A lean partially premixed swirling combustor is studied by resolving the complete flow path from the swirl vanes to the chamber outlet with large-eddy simulation (LES). Flow and combustion dynamics for non-reacting and reacting situations are analysed. The influence of Reynolds number on the vorticity distribution and vortex rings formation for non-reacting cases is examined. A modified flame index is introduced to identify the flame regime during the partially premixed combustion. The combustion instability phenomenon is detected by applying Fourier spectra analysis. Several scalar variables are monitored to investigate the combustion dynamics at different operating conditions. The effects of swirl number, equivalence ratio and nitrogen dilution on combustion dynamics are studied in detail.

Optical diagnostics of fuel–air mixing and vortex formation in a cavity combustor

The current work reports optical diagnostic measurements of fuel–air mixing and vortex structure in a single cavity trapped vortex combustor (TVC). Specifically, the mixture fraction using acetone PLIF technique in the non-reacting flow, and PIV measurements in the reacting flow are reported for the first time in trapped vortex combustors. The fuel–air momentum flux ratio, where the air momentum corresponds to that entering the cavity through a specially-incorporated flow guide vane, is used to characterize the mixing. The acetone PLIF experiments show that at high momentum flux ratios, the fuel–air mixing in the cavity is very minimal and is enhanced as the momentum flux ratio reduces, due to a favourable vortex formation in the cavity. Stoichiometric mixture fraction surfaces show that the mixing causes the reaction surfaces to shift from non-premixed to partially-premixed stratified mixtures. PIV measurements conducted in the non-reacting flow in the cavity further reinforce this observation. The scalar dissipation rates of mixture fraction were compared with the contours of RMS of fluctuating velocity and showed very good agreement. The regions of maximum mixing are observed to be along the fuel air interface. Reacting flow PIV measurements which differ substantially from the non-reacting cases primarily because of the heat release from combustion and the resulting gas expansion show that the vortex is displaced from the centre of the cavity towards the guide vane. Overall, the measurements show interesting features of the flow including the presence of the dual cavity structure and lead to a clear understanding of the underlying physics of the cavity flow highlighting the importance of the fuel–air momentum ratio parameter.

Reactive scalar field near the turbulent/non-turbulent interface in a planar jet with a second-order chemical reaction

The reactive scalar field near the turbulent/non-turbulent (T/NT) interface is analyzed using a direct numerical simulation (DNS) of a planar jet with an isothermal second-order chemical reaction A + B → P. Reactants A and B are supplied from the jet and ambient flows, respectively. The DNS of the reactive jet is performed for Damköhler numbers Da = 0.1, 1, and 10. A visualization of the T/NT interface shows that most of the product P is contained in the turbulent region. The conditional mean concentrations of the reactive species change sharply near the T/NT interface. The width of the jump in the conditional mean concentration is almost independent of the chemical species and the Damköhler number. For the slow reaction (Da = 0.1), the conditional average of the chemical production rate gradually increases from the non-turbulent region toward the turbulent region. In contrast, the conditional average of the production rate for Da = 1 and 10 has a large peak value slightly inside the T/NT interface. The chemical reaction near the T/NT interface strongly depends on the interface orientation. The reactant A is deficient near the T/NT interface. The production rate is large near the interface toward which the deficient reactant A is frequently transported by the velocity fields. The transport due to the velocity relative to the interface movement strongly depends on the relationship between the interface geometry and the mean flow field. The dependence of the chemical reaction on the interface orientation becomes strong as Da increases. When the interface propagates toward the non-turbulent region, the reactant A and product P are contained in the turbulent region although the molecular diffusion and reaction contribute to the increase in the concentrations of A (non-reactive case) and P in the non-turbulent region. In contrast, the interface propagation toward the turbulent region leaves the fluids containing A and P in the non-turbulent region.

Simulation of Dilute Acetone Spray Flames with LES-CMC Using Two Conditional Moments

Large-eddy simulations (LES) have been coupled with a conditional moment closure (CMC) method for the computation of a series of turbulent spray flames. An earlier study by Ukai et al. (Proc. Combust. Inst. 34(1),1643–1650, 2013) gave reasonable results for the prediction of temperature and velocity profiles, but some limitations of the method became apparent. These limitations are primarily related to the upper limit in mixture fraction space. In order to enhance the applicability of the LES-CMC model, this paper proposes a two-conditional moment approach to account for the existence of pre-evaporated fuel by introducing two sets of conditional moments based on different mixture fractions. The two-conditional moment approach is first tested for a non-reacting test case. The results indicate that the spray evaporation induces relatively large conditional fluctuations within a CMC cell, and one set of conditional moments might not be sufficient. The upper limit of the mixture fraction space is dynamically selected for the solution of the second set of conditional moments, and the corresponding CMC solution in a CFD cell is estimated by interpolation between the two conditional moments weighted by the amount of vapour emitted within the domain. The cell-filtered value is given by integration of the conditional moment across mixture fraction space using a bounded β-FDF for the distribution of the scalar. As a result, the fuel concentration profiles given by LES and the two-conditional moment approach are shown to agree well. Then, the two-conditional moment approach is applied to four different flame configurations. The comparison of LES cell quantities and conditionally averaged moments indicates that the two sets of conditional moments are necessary for accurate predictions in zones where gas phase mixture fraction is significantly increased by droplet evaporation within the computational domain. The unconditional temperature profiles clearly show that the new approach improves the predictions of mean temperature especially along the centerline. Also, the better predictions of the temperature field improve the accuracy of the predicted mean axial droplet velocities. Overall, good agreement with the experimental results is found for all four cases, and the methodology is shown to be applicable to flames with a relatively wide range of fuel vapour concentrations.

LES of Premixed Methane Flame Impinging on the Wall Using Non-adiabatic Flamelet Generated Manifold (FGM) Approach

In this paper LES of flame wall interaction using a non-adiabatic FGM approach is reported for a premixed methane fuel jet impinging on a spherical disk. Nitrogen is used as co-flow in order to avoid the interaction with the surrounding air and combustion. The flow field is described by means of the Smagorinsky model with Germano procedure for SGS stresses. The SGS scalar flux in scalar transport equations is modeled by the linear eddy diffusivity model. Two aspects are especially addressed in this paper. First focus is on the grid resolution required near the wall without including a special wall-adapted SGS modeling in reacting configurations. The second aspect is devoted to the integration of the near wall kinetic effects into the FGM framework. The results for the flow field, mixing and combustion properties are presented and analyzed in terms of grid resolution, Reynolds number (in reacting and non-reacting case) and adiabaticity. Comparisons with available experimental data show satisfactory agreement. An outline of the thermal and flow boundary layer analysis is subsequently provided.

Numerical study of flame/vortex interactions in 2-D Trapped Vortex Combustor

The interactions between flame and vortex in a 2-D Trapped Vortex Combustor are investigated by simulating the Reynolds Averaged Navier Stokes (RANS) equations, for the following five cases namely (i) non-reacting (base) case, (ii) post-vortex ignition without premixing, (iii) post-vortex ignition with premixing, (iv) pre-vortex ignition without premixing and (v) pre-vortex ignition with premixing. For the post-vortex ignition without premixing case, the reactants are mixed well in the cavity resulting in a stable ?C? shaped flame along the vortex edge. Further, there is insignificant change in the vorticity due to chemical reactions. In contrast, for the pre-vortex ignition case (no premixing); the flame gets stabilized at the interface of two counter rotating vortices resulting in reduced reaction rates. There is a noticeable change in the location and size of the primary vortex as compared to case (ii). When the mainstream air is premixed with fuel, there is a further reduction in the reaction rates and thus structure of cavity flame gets altered significantly for case (v). Pilot flame established for cases (ii) and (iii) are well shielded from main flow and hence the flame structure and reaction rates do not change appreciably. Hence, it is expected that cases (ii) and (iii) can perform well over a wide range of operating conditions.

Rayleigh–Bénard instability generated by a diffusion flame

AbstractWe investigate the Rayleigh–Bénard convection problem within the context of a diffusion flame formed in a horizontal channel where the fuel and oxidizer concentrations are prescribed at the porous walls. This problem seems to have received no attention in the literature. When formulated in the low-Mach-number approximation the model depends on two main non-dimensional parameters, the Rayleigh number and the Damköhler number, which govern gravitational strength and reaction speed respectively. In the steady state the system admits a planar diffusion flame solution; the aim is to find the critical Rayleigh number at which this solution becomes unstable to infinitesimal perturbations. In the Boussinesq approximation, a linear stability analysis reduces the system to a matrix equation with a solution comparable to that of the well-studied non-reactive case of Rayleigh–Bénard convection with a hot lower boundary. The planar Burke–Schumann diffusion flame, which has been previously considered unconditionally stable in studies disregarding gravity, is shown to become unstable when the Rayleigh number exceeds a critical value. A numerical treatment is performed to test the effects of compressibility and finite chemistry on the stability of the system. For weak values of the thermal expansion coefficient $\alpha $, the numerical results show strong agreement with those of the linear stability analysis. It is found that as $\alpha $ increases to a more realistic value the system becomes considerably more stable, and also exhibits hysteresis at the onset of instability. Finally, a reduction in the Damköhler number is found to decrease the stability of the system.