Reference natural gas flames at nominally autoignitive engine-relevant conditions

Laminar natural gas flames are investigated at engine-relevant thermochemical conditions where the ignition delay time τ is short due to very high ambient temperatures and pressures. At these conditions, it is not possible to measure or calculate well-defined values for the laminar flame speed s_l, laminar flame thickness δ_l, and laminar flame time scale ${\tau }_l={\delta }_l/s_l$ due to the explosive thermochemical state. Here, the corresponding reference values, s_R, δ_R, and ${\tau }_R={\delta }_R/s_R,$ that account for the effects of autoignition, are numerically estimated to investigate the enhancement of flame propagation, and the competition with autoignition that arises under nominally autoignitive conditions (characterised here by the number τ/τ_R). Large values of τ/τ_R indicate that autoignition is unimportant, values near or below unity indicate that flame propagation is not possible, and intermediate values indicate that a combination of both flame propagation and autoignition may be important, depending upon factors such as device geometry, turbulence, stratification, et cetera. The reference quantities are presented for a wide range of temperatures, equivalence ratios, pressures, and hydrogen concentrations, which includes conditions relevant to stationary gas turbine reheat burners and boosted spark ignition engines. It is demonstrated that the transition from flame propagation to autoignition is only dependent on residence time, when the results are non-dimensionalised by the reference values. The temporal evolution of the reference values are also reported for a modelled boosted SI engine. It is shown that the nominally autoignitive conditions enhance flame propagation, which may be an ameliorating factor for the onset of engine knock. The calculations are performed using a recently-developed, detailed 177 species mechanism for C0–C3 chemistry that is derived from theoretical chemistry and is suitable for a wide range of thermochemical conditions as it is not tuned or optimised for a particular operating condition.     

Wall-impinging laminar premixed n-dodecane flames under autoignitive conditions

Laminar one-dimensional (1D) flames in a stagnation flow stabilised at a wall are used to study flame–wall interaction under diesel engine conditions. The thermochemical conditions correspond to that of the Engine Combustion Network (ECN) Spray A reference case. A range of inflow velocities is considered, where the lowest inflow velocity is chosen such that the flame is detached from the inlet. The presence of a wall is shown to have a significant impact on the flame structure and emission formation. The 1D flame and homogeneous reactor results exhibit two distinct reaction zones due to low- and high-temperature chemistry (LTC and HTC, respectively). The burner-stabilised flames are overall dominated by autoignition for all inflow velocities. For the impinging jet flames, the response of the LTC reaction zone follows closely that of the burner-stabilised flames up to relatively high inflow velocities. The HTC reaction zone, however, deviates strongly from the burner-stabilised flames, already at low inflow velocities and quenches at high inflow velocities. A budget analysis revealed a strong contribution from diffusion in the HTC reaction zone, resulting in an increasing importance of deflagrative combustion as opposed to autoignition. This trend was attributed to enhanced strain rates at higher inlet velocity leading to higher gradients. Wall heat transfer was also investigated. The highest wall heat transfer rates were observed for mixtures between $\Phi =1.0$ and $\Phi =1.5$ and for inlet velocities just below the quenching limit. This was attributed jointly to the higher peak product temperatures for these mixtures and to their enhanced resilience to quenching under strain which leads to higher temperature gradients at the wall just before quenching. NO formation was studied. The highest NO formation was observed near $\Phi =1.0,$ though the response to strain rate was different for stoichiometric and rich mixtures, which was attributed to differing NO formation pathways.     

Burning characteristics of candle flames in sub-atmospheric pressures: An experimental study and scaling analysis

Burning characteristics (mass burning rate, natural convection boundary layer thickness, flame height and dark zone height) of laminar diffusion flames produced by a candle at sub-atmospheric pressures in the range of P_∞?=?50–100?kPa were experimentally studied in a reduced-pressure chamber; such data are not reported to date. Scaling analysis was performed to interpret the pressure dependence. The new experimental findings for candle flames in the sub-atmospheric pressures were well interpreted by the proposed scaling laws: (1) the mass burning rate was higher for a candle with larger wick length, and it increased with increasing ambient pressure, a stagnant layer B-number model based on natural convection boundary (flame boundary layer thickness) was developed to scale the mass burning rate of candle flames at various pressures; (2) the flame boundary layer thickness was wider in lower pressure and can be well represented by a natural convection boundary layer solution; (3) flame height was higher for a candle with larger wick length, meanwhile the ratio of flame height to burning rate was independent of pressure; (4) the flame dark zone height representing a soot formation length scale changes little with pressure, meanwhile its ratio to the total flame height is scaled with pressure by $P_{\infty }^{?1/2}/L_{w,e}^{3/4}$ (L_w,e is effective wick length inside flame). This work provided new experimental data and scaling laws of candle flame behaviors in sub-atmospheric pressures, which provided information for future characterization and soot modeling for diffusion flames associated with melting and evaporation processes of solid fuels.     

Ignition by moving hot spheres in H2-O2-N2 environments

A combined experimental and numerical study was carried out to investigate thermal ignition by millimeter size ($d=6$ mm) moving hot spheres in H₂-O₂-N₂ environments over a range of equivalence ratios. The mixtures investigated were diluted with N₂ to keep their laminar flame speed constant and comparable to the sphere fall velocity (2.4 m/s) at time of contact with the reactive mixture. The ignition thresholds (and confidence intervals) were found by applying a logistic regression to the data and were observed to increase from lean ($\Phi =0.39$; T_sphere = 963 K) to rich ($\Phi =1.35$; T_sphere = 1007 K) conditions. Experimental temperature fields of the gas surrounding the hot sphere during an ignition event were, for the first time, extracted using interferometry and compared against simulated fields. Numerical predictions of the ignition thresholds were within 2% of the experimental values and captured the experimentally observed increasing trend between lean and rich conditions. The effect of stoichiometry and dilution on the observed variation in ignition threshold was explained using 0-D constant pressure delay time computations.     

Experimental study on downward/opposed flame spread and extinction over electric wires in partial gravity environments

Downward/opposed flame spread over laboratory wire samples under varied gravity conditions were investigated in the range from 0 G to 1 G. Reduced gravity experiments are conducted by parabolic flights of an airplane. Limiting oxygen concentrations (LOCs) and flame spread rates ($V_{\mathrm{f}}$) are obtained as a function of gravity level, with oxygen concentration, forced flow velocity, and wire characteristics such as insulation thickness and core material as experimental variables. The samples used in this study consist of low-density polyethylene (LDPE) insulation over metallic cores. Copper (Cu) and nickel-chrome (NiCr) were selected as core materials. It is found that the effect of gravity on the insulation flammability varies with the thermal conductivity of the wire core; the LOCs of the Cu sample are less affected by gravity, while those of the NiCr sample decrease with decreasing gravity level. On the other hand, $V_{\mathrm{f}}$ increase monotonically with increasing gravity level in the Cu sample, while $V_{\mathrm{f}}$ of the NiCr sample show a peak value under the low gravity conditions. It is suggested that these differences in the response of LOCs and $V_{\mathrm{f}}$ to the gravity level due to the difference in core materials are controlled by the fuel concentration in the reaction zone, which is a function of $V_{\mathrm{f}}$. It is also found that the molten LDPE produced during the flame spread process shows unique behaviors depending on the gravity levels and wire characteristics. Some characteristics of the dynamic motion of the molten LDPE during the flame spread process, such as deformation and dripping, are also summarized in this paper. The experimental data obtained in this study provide useful information on the flammability of materials in a partial gravity environment and will serve as a database for fire safety design in future space exploration.     

Dynamics of FREI with/without cool flame interaction

The interactions between cool flames and flames with repetitive extinction and ignition (FREI) of stoichiometric n-heptane/air mixture were studied using a micro flow reactor with a controlled temperature profile from 373 to 1300 K. Two different flame dynamics with and without cool flames were observed in reactors with inner diameters $d_{\text{inner}}$ of 1 and 2 mm. Cool flames and FREI are spatially separated at $d_{\text{inner}}=$ 1 mm, whereas interactions between cool flames and FREI are observed at $d_{\text{inner}}=$ 2 mm. At $d_{\text{inner}}=$ 1 mm, the brightness intensity from cool flames depends on the inlet velocity ($u_{\text{inlet}}$). Approximately above $u_{\text{inlet}}=$ 10 cm/s, the brightness intensity from cool flames decreases with increasing inlet velocity, despite a large amount of mixture input. This is because before low temperature ignition occurs under higher inlet velocity conditions, the mixture archives temperature where negative temperature coefficient is dominant. Reaction front propagation speed of FREI decreases monotonically due to heat loss because the extinction points of FREI are located in higher temperatures than the cool flame region. At $d_{\text{inner}}=$ 2 mm, the acceleration of the reaction front in the cool flame region is confirmed experimentally, as predicted in our previous two-dimensional numerical simulations. Additionally, the instantaneous reaction front speed after autoignition is analyzed at $d_{\text{inner}}=$ 1 mm. The instantaneous reaction front speed decreases as the time from extinction to ignition $t_{\text{ex}\_\text{ig}}$ becomes longer because a moderate mixing zone of reactants and products is formed.     

Combustion properties of H2/N2/O2/steam mixtures

The present work reports new experimental and numerical results of the combustion properties of hydrogen based mixtures diluted by nitrogen and steam. Spherical expanding flames have been studied in a spherical bomb over a large domain of equivalence ratios, initial temperatures and dilutions at an initial pressure of 100 kPa (T_ini = 296, 363, 413 K; N₂/O₂ = 3.76, 5.67, 9; %Steam = 0, 20, 30). From these experiments, the laminar flame speed $S_L^0$, the Markstein length L’, the activation energy Ea and the Zel'dovich β number have been determined. These parameters were also simulated using COSILAB^® in order to verify the validity of the Mével et al. [1] detailed kinetic mechanism. Other parameters as the laminar flame thickness δ and the effective Lewis number Le_eff were also simulated. These new results aim at providing an extended database that will be very useful in the hydrogen combustion hazard assessment for nuclear reactor power plant new design.     

Numerical study of the ignition behavior of a post-discharge kernel in a turbulent stratified crossflow

Ensuring robust ignition is critical for the operability of aeronautical gas-turbine combustors. For ignition to be successful, an important aspect is the ability of the hot gas generated by the spark discharge to initiate combustion reactions, leading to the formation of a self-sustained ignition kernel. This study focuses on this phenomena by performing simulations of kernel ignition in a crossflow configuration that was characterized experimentally. First, inert simulations are performed to identify numerical parameters correctly reproducing the kernel ejection from the ignition cavity, which is here modeled as a pulsed jet. In particular, the kernel diameter and the transit time of the kernel to the reacting mixture are matched with measurements. Considering stochastic perturbations of the ejection velocity of the ignition kernel, the variability of the kernel transit time is also reproduced by the simulations. Subsequently, simulations of a series of ignition sequences are performed with varying equivalence ratio of the fuel-air mixture in the crossflow. The numerical results are shown to reproduce the ignition failure that occurs for the leanest equivalence ratio ($?=0.6$). For higher equivalence ratios, the simulations are shown to capture the sensitivity of the ignition to the equivalence ratio, and the kernel successfully transitions into a propagating flame. Significant stochastic dispersion of the ignition strength is observed, which relates to the variability of the transit time of the kernel to the reactive mixture. An analysis of the structure of the ignition kernel also highlights the transition towards a self-propagating flame for successful ignition conditions.     

Application of a multiple mapping conditioning mixing model to ECN Spray A

The engine combustion network (ECN) Spray A is modelled using the Reynolds-averaged Navier–Stokes-transported probability density function (RANS-TPDF) approach to validate the application of a new multiple mapping conditioning (MMC) mixing model to multiphase reactive flows. The composition TPDF equations are solved using a Lagrangian stochastic approach and the spray is modelled with a discrete particle approach. The model is first validated under non-reacting conditions (at 900 K) using experimental mixture-fraction data. Reactive simulations are then performed for three different ambient temperatures (800, 900, 1100 K) and oxygen concentrations (13, 15, 21%) at an ambient density of 22.8 kg/m³. The MMC mixing model is compared with the interaction by exchange with the mean (IEM) mixing model. The ignition delay predictions are not sensitive to the mixing model and are predicted well by both the mixing models under all the tested ambient conditions. The IEM model overpredicts the flame lift-off length (FLOL) at high temperature and high oxygen conditions with a mixing constant $C_{?}=2$. The MMC model with $C_{?}=2$ and a target correlation coefficient $r_t=0.935$ between the mixture fraction and a reference variable used to condition mixing predicts good FLOL under all the conditions except 800 K. It is demonstrated that the lift-off length is controllable by changing the target correlation coefficient, while C_? and therefore the mixing fields are held fixed. In comparison to the MMC model, the IEM model predicts a higher variance of temperature conditioned on mixture fraction near the flame base owing to its lacking the property of localness. The mixing distance between the notional TPDF particles in the composition space is also higher with the IEM model and it is demonstrated that by changing r_t, different levels of mixing locality can be achieved.     

Impact of non-ideal transport modeling on supercritical flow simulation

The simulation of a supercritical fluid flow requires sophisticated models for real gas thermodynamic and non-ideal phenomena. They both are presently addressed through the simulation of a non-reacting and reacting high pressure H₂/O₂ splitter-plate configuration. In particular, the diffusion velocity of species is evaluated through the gradient of chemical potential (${\mathbf{d}}_l^{\text{NI}}=X_l{\left(?{\mu }_l\right)}_T$) expressed with the Peng–Robinson equation of state, or with the classical low-pressure approach ${\mathbf{d}}_l^{\mathrm{I}}=?X_l,$ which only uses the gradient of the lth species molar fraction, X_l. In addition, the high pressure binary diffusion coefficients are estimated by the correction of Kurochkin et al. or with the Takahashi approach. The results for the non-reaction case are consistent with the literature for mean and rms values using ${\mathbf{d}}_l^{\mathrm{I}}$. The use of ${\mathbf{d}}_l^{\text{NI}}$ has a limited impact but the temperature profiles become steeper. In the reactive case, the two approaches lead to a difference of 50 K on the average temperature just downstream of the injector and about 100 K further downstream. A non-ideal transport is then required for the modeling of supercritical flow simulation.     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters $a,c$ and k, are illustrated.