The Application of a Laminar Flamelet Model to Confined Explosion Hazards

The majority of computational studies of confined explosion hazards apply simple and inaccurate combustion models, requiring adhoc corrections to obtain realistic flame shapes and often predicting an order of magnitude error in the overpressures. This work describes the application of a laminar flamelet model to a series of two-dimensional test cases. The model is computationally efficient applying an algebraic expression to calculate the flame surface area, an empirical correlation for the laminar flame speed and a novel unstructured, solution adaptive numerical grid system which allows important features of the solution to be resolved close to the flame. Accurate flame shapes are predicted, the correct burning rate is predicted near the walls, and an improvement in the predicted overpressures is obtained. However, in these fully turbulent calculations the overpressures are still too high and the flame arrival times too low, indicating the need for a model for the early laminar burning phase. Due to the computational expense, it is unrealistic to model a laminar flame in the complex geometries involved and therefore a pragmatic approach is employed which constrains the flame to propagate at the laminar flame speed. Transition to turbulent burning occurs at a specified turbulent Reynolds number. With the laminar phase model included, the predicted flame arrival times increase significantly, but are still too low. However, this has no significant effect on the overpressures, which are predicted accurately for a baffled channel test case where rapid transition occurs once the flame reaches the first pair of baffles. In a channel with obstacles on the centreline, transition is more gradual and the accuracy of the predicted overpressures is reduced. However, although the accuracy is still less than desirable in some cases, it is much better than the order of magnitude error previously expected. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling of a Bluff-Body Nonpremixed Flame using a Coupled Radiation/Flamelet Combustion Model

A coupled radiation/flamelet combustion modelling technique is applied to the simulation of a bluff-body flame. Radiation heat transfer is incorporated into the laminar flamelet model for turbulent combustion through the enthalpy defect. A new method is developed for generating flamelet library with enthalpy defect. The radiation within the flame is modelled using a raytracing approach based on the discrete transfer method. The predicted results are compared with the reported experimental data. Comparison shows that the effects of radiative heat transferr on the temperature and major species are small for the flame considered. However, a significant improvement in the prediction of OH is achieved when radiation heat transfer is included. This revised version was published online in July 2006 with corrections to the Cover Date.     

Efficient Thermo-Chemistry Tabulation for Non-Premixed Combustion at High-Pressure Conditions

Propellant injection and turbulent combustion in high-pressure engines is often dominated by real-gas effects. However, previous studies suggested that the departure of the fluid properties from an ideal gas behavior has only a limited effect on the laminar flame structure. This is due to the fact that chemical reactions take place in the flame zone where the temperature is sufficiently high and molecular interactions are negligible, i.e., the ideal gas assumption is valid. On the other hand, various experimental and numerical studies of injection processes at high-pressure conditions demonstrated that real-gas effects can have a strong impact on the turbulent flow. Mixing is influenced by the rapid change of fluid properties. In this work, we exploit the gap in the fidelity of the thermodynamics model needed to describe the laminar flame structure and that needed to describe the turbulent flow field. We then propose a new real-gas flamelet model with increased numerical performance. The computational cost of the new formulation is not significantly higher than that of an ideal gas simulation. The performance of the method is analyzed and the error that is introduced by our assumptions is assessed by comparison to more complete modeling. Finally, the method is used to simulate a turbulent jet flame emanating from a coaxial injector at supercritical pressure and cryogenic oxidizer temperature. The results are compared with experimental OH^? images giving evidence of the suitability of the present method.     

Direct measurement of mixture fraction in reacting flow using Rayleigh scattering

The mixture fraction variable, , is very useful in describing reaction zone structure in nonpremixed flames. Extinction limits and turbulent mixing are often described as a function of this variable. Experimental evaluation of is critical for improving our understanding of the influence of turbulent mixing on the chemistry process. Heretofore, the evaluation of mixture fraction in combusting flow required multiple simultaneous concentration measurements. In this paper we present a fuel designed to permit measurements of mixture fraction by Rayleigh scattering technique only. A Rayleigh intensity/mixture fraction correspondence has been obtained experimentally in a laminar coflow flame. The influence of strain rate and differential diffusion effects have been investigated using laminar counterflow diffusion flame and shifting equilibrium chemistry models. The results obtained from comparisons between experiments and these models are very encouraging and suggest that the Rayleigh/mixture fraction correspondence established is valid under both the turbulent mixing and laminar strained flamelet combustion regimes.     

Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.     

Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.     

Numerical Simulation of Delft-Jet-in-Hot-Coflow (DJHC) Flames Using the Eddy Dissipation Concept Model for Turbulence–Chemistry Interaction

In this paper, we report results of a numerical investigation of turbulent natural gas combustion for a jet in a coflow of lean combustion products in the Delft-Jet-in-Hot-Coflow (DJHC) burner which emulates MILD (Moderate and Intense Low Oxygen Dilution) combustion behavior. The focus is on assessing the performance of the Eddy Dissipation Concept (EDC) model in combination with two-equation turbulence models and chemical kinetic schemes for about 20 species (Correa mechanism and DRM19 mechanism) by comparing predictions with experimental measurements. We study two different flame conditions corresponding to two different oxygen levels (7.6% and 10.9% by mass) in the hot coflow, and for two jet Reynolds number (Re = 4,100 and Re = 8,800). The mean velocity and turbulent kinetic energy predicted by different turbulence models are in good agreement with data without exhibiting large differences among the model predictions. The realizable k-ε model exhibits better performance in the prediction of entrainment. The EDC combustion model predicts too early ignition leading to a peak in the radial mean temperature profile at too low axial distance. However the model correctly predicts the experimentally observed decreasing trend of lift-off height with jet Reynolds number. A detailed analysis of the mean reaction rate of the EDC model is made and as possible cause for the deviations between model predictions and experiments a low turbulent Reynolds number effect is identified. Using modified EDC model constants prediction of too early ignition can be avoided. The results are weakly sensitive to the sub-model for laminar viscosity and laminar diffusion fluxes.     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Level‐set based flamelet approach for simulating turbulent lifted jet flame

The present study focuses on numerically investigating the flame structure, flame liftoff, and stabilization in a lifted turbulent H₂/N₂ jet flame with a vitiated coflow. To realistically represent the turbulent partially premixed nature in the flow region between nozzle exit and flame base, the level‐set approach coupled with the conserved scalar flamelet model has been applied. The unstructured‐grid level‐set approach has been developed to allow the geometric flexibility and computational efficiency for the solution of the physically and geometrically complex reacting flows. The pressure–velocity coupling is handled by the multiple pressure‐correction method. The predicted flame pattern is in good conformity with the measured one. In terms of the liftoff height, the agreement between prediction and experiment is quite good. Even if there are noticeable deviations in a certain region, the predicted profiles for the overall flame structure agree reasonably well with the experimental data. These numerical results indicate that the present level‐set‐based flamelet approach in conjunction with the unstructured‐grid finite‐volume method is capable of realistically predicting the essential features and precise structure of the turbulent‐lifted jet flame with computational efficiency. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical and experimental study of two turbulent opposed plane jets

The turbulent interaction between two opposed plane jets separated by a distance H is experimentally studied by using a PIV (Particle Image Velocimetry) method and numerically investigated by means of a finite volume code. Two turbulence models have been tested: the standard k-ɛ model and a second-order model. The validation of the numerical study was performed by comparing the results with experimental data obtained for the case of two interacting opposed jets at ambient temperature (isothermal case). The effect of the angle of inclination of the jets is studied. Conclusions of the validation are then used to study the interaction between two jets, one being maintained at ambient temperature whereas the other is heated. Results show that the stagnation point moves towards the heated jet. It is shown that the heating induces a stabilizing effect on the flow.     

Incompressible flows with combustion simulated by a preconditioning method using multigrid acceleration and MUSCL reconstruction

A numerical algorithm for the steady state solution of three‐dimensional incompressible flows is presented. A preconditioned time marching scheme is applied to the conservative form of the governing equations. The preconditioning matrix multiplies the time derivatives of the system and circumvents the eigenvalue‐caused stiffness at low speed. The formulation is suitable for constant density flows and for flows where the density depends on non‐passive scalars, such as in low‐speed combustion applications. The k–ε model accounts for turbulent transport effects. A cell‐centred finite volume formulation with a Runge–Kutta time stepping scheme for the primitive variables is used. Second‐order spatial accuracy is achieved by developing for the preconditioned system an approximate Riemann solver with MUSCL reconstruction. A multi‐grid technique coupled with local time stepping and implicit residual smoothing is used to accelerate the convergence to the steady state solution. The convergence behaviour and the validation of the predicted solutions are examined for laminar and turbulent constant density flows and for a turbulent non‐premixed flame simulated by a presumed probability density function (PDF) model. Copyright © 2001 John Wiley & Sons, Ltd.     

密闭空间可燃气体爆炸超压预测

为避免密闭空间内可燃预混气体爆炸事故造成的伤害，对其进行较为准确的爆炸超压预测是抗爆设计和日常安全管理的关键。结合已有文献实验数据，利用光滑层流火焰传播理论模型建立了爆炸超压模型；对比发现，当体积较大时，光滑层流火焰传播理论模型存在较大的误差。较大体积密闭空间爆炸火焰传播过程中的不稳定性造成火焰前锋面褶皱并引起湍流燃烧，导致火焰前锋面表面积大幅增加，且在火焰传播过程中表现出自相似分形特征。依据褶皱及湍流火焰传播过程中的自相似分形特征，基于分形燃烧理论和相关经验数据，进一步建立了考虑可燃预混气体爆炸火焰褶皱及湍流火焰传播的爆炸超压预测模型，并与实验所得结果进行了对比。结果表明:当密闭空间体积较大时，利用褶皱及湍流火焰传播理论建立的爆炸超压模型进行峰值压力估算时，两种工况下实验所得和理论计算所得相对误差分别为10.4%和11.1%，较光滑层流火焰传播理论爆炸超压模型相比，误差分别减少了72.3%和50.6%。本文所建立理论模型与实验所得结果具有较好的一致性，在一定程度上可满足结构抗爆设计或日常安全管理的需要。     

Experimental and numerical study of the ignition of hydrogen-air mixtures by a localized stationary hot surface

The ignition of hydrogen-air mixtures by a stationary hot glow plug has been experimentally investigated using two-color pyrometry and interferometry. The ignition process was characterized by the surface temperature at ignition, as well as by the location where the initial flame kernel was formed. The experimental results indicate that: (i) the ignition temperature threshold is a function of equivalence ratio; (ii) the ignition location is a function of the rate at which the glow plug is heated because high heating rates favor non-uniform heating. As a result, ignition occurs on the side rather than near the top face of the glow plug. Comparison with two-dimensional numerical simulations exhibits discrepancies in terms of the temperature threshold value and dependence on equivalence ratio. Simulations performed imposing a non-uniform surface temperature show that a temperature difference between the side and the top of the glow plug as low as 12.5 to 25 K resulted in side ignition for hydrogen-air mixtures. The effect of surface chemistry was estimated numerically by imposing a boundary condition of zero species concentration for intermediate species, H and HO₂, at the hot surface, which increased the ignition threshold by up to 50 K for an initial H₂ concentration of 70%. The present study shows that surface temperature non-uniformity, heterogeneous chemistry and reaction model used, could influence the experimentally reported and numerically predicted ignition threshold as well as the location of ignition.     

Effects of Differential Diffusion on Predicted Autoignition Delay Times Inspired by H2/N2 Jet Flames in a Vitiated Coflow Using the Linear Eddy Model

Mixing and chemistry interactions in a H₂/N₂ jet flame into a vitiated coflow are considered key factors affecting autoignition. A 1-D numerical model under laminar flow condition first is simulated to reveal the effects of fuel species, pressure, and coflow properties on the autoignition with and without the consideration of preferential diffusion among species. Proper laminar reference autoignition delays are proposed and examined for different diffusion models. Next, the reference autoignition delays defined from laminar simulations are investigated in an example turbulent flow using the Linear Eddy Model (LEM). LEM is used to model the effect of turbulent mixing on autoignition, where we specifically investigate if the effect of turbulence on autoignition can be classified in two regimes, which are dependent on a proper reference laminar autoignition delay and turbulence time scale. The trend of the effect of differential diffusion on autoignition versus turbulence Reynolds is simulated and analyzed, and several tentative conclusions are drawn.     

LES of Low to High Turbulent Combustion in an Elevated Pressure Environment

A subgrid scale flame surface density combustion model for the Large Eddy Simulation (LES) of premixed combustion is derived and validated. The model is based on fractal characteristics of the flame surface, assuming a self similar wrinkling of the flame between smallest and largest wrinkling length scales. Experimental and direct numerical simulation databases as well as theoretical models are used to derive a model for the fractal parameters, namely the cut-off lengths and the fractal dimension suitable in the LES context. The combustion model is designed with the intent to simulate low as well as high Reynolds number premixed turbulent flame propagation and with a focus on correct scaling with pressure. The combustion model is validated by simulations of turbulent Bunsen flames with methane and propane fuel at pressure levels between 0.1 MPa and 2 MPa and at turbulence levels of $0 < u^{\prime }/s_{L}^{0} < 11$ , conditions typical for spark ignition engines. The predicted turbulent flame speed is in a very good agreement with the experimental data and a smooth transition from resolved flame wrinkling to fully modelled, nearly subgrid-only wrinkling is realized. Evaluating the influence of mesh resolution shows a predicted mean flame surface and turbulent flame speed independent of mesh resolution for cases with 9–86 % resolved flame surface. Additional simulations of a highly turbulent jet flame at 0.1 MPa and 0.5 MPa and the comparison with experimental data in terms of flame shape, velocity field and turbulent fluctuations validates the model also at conditions typical for gas turbines.     

Direct Numerical Simulations of Premixed Turbulent Flames with Reduced Chemistry: Validation and Flamelet Analysis

Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the thin reaction zone regime and in the broken reaction zone regime are performed. The flamelet-generated manifold method is used in order to deal with detailed reaction kinetics. The computational results are analyzed by using an extended flame stretch theory. It is investigated whether this theory is able to describe the influence of flame stretch and curvature on the local burning velocity of the flame. It is found that if the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is well predicted. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate. The influence of using a reduced chemistry model is investigated by comparing flamelet simulations with reduced and detailed chemistry.     

Flame Surface Density in Turbulent Premixed V-Flame with Buoyancy

A fractional step numerical model is established for turbulent premixed combustion with buoyancy. The flame front propagation is described by the level-set method. Simulated results without buoyancy have been previously validated with available experimental data on a premixed V-flame. A new formula is presented to fit the flame surface density with respect to the reaction progress variable in a turbulent premixed V-flame. By numerical simulations, dynamical behaviour of the flame under the interaction of turbulence, exothermicity and buoyancy are investigated.     

Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re_max = 1,920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are here compared with experimental results of previous investigators. Predictions of the flow regime on present oscillating flow conditions are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-ε turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-ε model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.     

Numerical Study of Turbulent Jet Ignition in a Lean Premixed Configuration

Direct numerical simulations (DNS) of a hot combustion product jet interacting with a lean premixed hydrogen-air coflow are conducted to fundamentally investigate turbulent jet ignition (TJI) in a three-dimensional configuration. TJI is an efficient method for initiating and controlling combustion in ultra-lean combustion systems. Fully compressible gas dynamics and species equations are solved with high order finite difference methods. The hydrogen-air reaction is simulated with a reliable detailed chemical kinetics mechanism. The physical processes involved in the TJI-assisted combustion are investigated by considering the flame heat release, temperature, species concentrations, vorticity, and Baroclinc torque. The complex turbulent flame and flow structures are delineated in three main: i) hot product jet, ii) burned-mixed, and iii) flame zones. In the TJI-assisted combustion, the flow structures and the flame features such as flame speed, temperature, and species distribution are found to be quite different than those in “standard” turbulent premixed combustion due to the existence of a high energy turbulent hot product jet. The flow structures and statistics are also found to be different than those normally seen in non-isothermal non-reacting jets.