Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.     

A Fully Implicit, Compact Finite Difference Method for the Numerical Solution of Unsteady Laminar Flames

Forced laminar diffusion flames form an important class of problems that can help to bridge the significant gap between steady laminar flames in simple burner configurations and the turbulent flames found in many practical combustors. Such flames offer a much wider range of interactions between convection, diffusion, and chemical reaction than can be examined under steady-state conditions, and yet detailed simulations of them should be feasible without having to resort to “modeling” any of the relevant physics, above all without having prematurely to reduce the large kinetic mechanisms typical of hydrocarbon fuels. Nevertheless, the computation of time-dependent laminar diffusion flames with conventional numerical methods is hindered by technical challenges that, while not new, are more troublesome to surmount than in the calculation of otherwise similar, unforced flames. First, the intricate spatiotemporal coupling between fluid dynamics and combustion thermochemistry ensures that spurious numerical diffusion or spatial under-resolution of the mixing process at any stage of the computation can lead to inaccurate prediction of flame characteristics for the remainder thereof. Second, relatively long simulated flow times and extremely short chemical time scales make many standard time integration algorithms impractical on all but the largest parallel computer clusters. This paper introduces a new numerical approach for time-varying laminar flames that addresses these challenges through the use of high order compact finite difference schemes within a robust, fully implicit solver based on a Jacobian-free Newton–Krylov method. The capabilities of this implicit-compact solver are demonstrated on a periodically forced axisymmetric laminar jet diffusion flame with one-step Arrhenius chemistry, and the results are compared to those of a conventional low order finite difference solver.     

Turbulent Combustion of Hydrogen–CO Mixtures

Laminar and turbulent burning velocities were measured in a closed-volume fan-stirred vessel for H₂–CO mixtures using two independent methods of flame definition. It has been shown that the unsteady flame development is an important factor and it needs to be taken into account for comparison of the burning rates obtained in different experiments. For the atmospheric pressure flames, the mixtures with faster laminar flame velocities burnt faster in turbulent flow despite the fact that the lean flames exhibit cellular structures. However, even a modest increase of the initial pressure promotes strongly cellularity and causes a significant acceleration of a lean laminar flame. The same lean flame burns faster in turbulent flow as well and this increase in the rate of combustion is greater that can be deduced from variation of the molecular heat diffusivity and laminar flame speed.     

流体黏性对输流管道运动方程及临界流速的影响

考虑实际流体黏性引起的管内流速非均匀分布,针对层流和两种不同的湍流流态,对理想流体情况下输流管道运动方程中的离心力项进行了修正,得到的修正系数分别为1.333(圆管层流)、1.020(光滑管壁圆管湍流)和1.037～1.055(粗糙管壁圆管湍流).根据修正后的运动方程得到的上述3种情况下的发散失稳临界流速比理想流体流动情况下依次分别低13.4%,1.0%和1.8%～2.6%.流体黏性对输流管道运动方程及临界流速的影响只与流态有关,雷诺数决定流态,而黏性系数通过雷诺数间接起作用.     

Large Eddy simulation for engineering applications

In the field of fluid engineering, controlling turbulent flows remains a crucial problem. This paper presents a basis of numerical methods and turbulence models for the large Eddy simulation. Simulation results include the unsteady analyses of complex flows, such as the vortex dynamics of turbulent jets subject to inlet perturbations and the reacting flow with flame propagation in a gas–turbine combustor flow. Applications employing large Eddy simulation are emerging as one of the most important aspects of the “Frontier Simulation Software for Industrial Science” project for the next generation of fluid dynamic design and development.     

Analysis of fluid flow in constricted tubes and ducts using body-fitted non-staggered grids

A finite volume method for the calculation of laminar and turbulent fluid flows inside constricted tubes and ducts is described. The selected finite volume method is based on curvilinear non-orthogonal co-ordinates (body-fitted co-ordinates) and a non-staggered grid arrangement. The grids are either generated by transfinite interpolation or an elliptic grid generator. The method is employed for calculation of laminar flows through a tube, a converging-diverging duct and different constricted tubes by both a two- and a three-dimensional computer program. In addition, turbulent flow through an axisymmetric constricted tube is calculated. Both the power law scheme and the second-order upwind scheme are used. The calculated results are compared with the experimental data and with other numerical solutions.     

Flow stability analysis and excitation using pulsating jets

Classical flow stability applied to transition from laminar to turbulent flow may also describe the behavior of vorticity fluctuations created by a pulsating jet placed along a solid boundary. A numerical laminar flow experiment involving a pulsating jet placed along the surface of a duct with flow separation downstream, resulted in eliminating most part of the separated flow region. Applying the same approach to a turbulent flow, it was possible to develop a turbulent stability flow formulation and apply successfully turbulent pulsating jet flow separation control. To cite this article: D. Skamnakis, K. Papailiou, C. R. Mecanique 333 (2005).     

Bluff-body Thermal Property and Initial State Effects on a Laminar Premixed Flame Anchoring Pattern

Bluff-body stabilized laminar flames remain at the root of many industrial applications. Such a simple flame arrangement although steady results from complex chemical, flow mixing as well as solid body thermal interactions that are still today misunderstood. Numerically, accurate predictions of such non linear problems require Conjugate Heat Transfer (CHT) approaches that are seldom because of the need for complex fluid flow solvers as well as multi-physics coupling strategies that are computationally expensive and difficult to master. Such numerical tools however provide access to fundamental elements otherwise inaccessible. Relying on Direct Numerical Simulation (DNS) CHT based predictions, the following work underlines several key features of importance to predict and understand square bluff-body stabilized flames. In the case of fluid only predictions, where the bluff-body wall temperature is fixed and assumed constant, three possible flame topologies are obtained and respectively qualified as anchored, lifted and bowed flames. Out of these three stable flow solutions, only two topologies are found physically possible whenever computed in a CHT context. Furthermore, depending on the solid material and the initial solution, the non linear CHT problem exhibits multiple solutions highlighting the complex coupling that can arise. As evidenced by these simple flame problems, such a behavior higlights the potential difficulties of predicting flame wall interaction problems where coupling schemes and turbulent closures / modeling will be required.     

Method of Lines for Transient Flow Fields

A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available in the literature. The predicted flow fields were found to be in favorable agreement with those available in the literature for laminar channel flow with sudden expansion and turbulent channel flow with Re=6600. The code was then applied to the prediction of the highly turbulent flow field in the inlet flue of a heat recovery steam generator (HRSG). The predicted flow field was found to display the same trend with the experimental findings and numerical solutions reported previously for a turbulent diverging duct. As the code uses the MOL approach in conjunction with (i) an intelligent higher-order spatial discretization scheme, (ii) a parabolic algorithm for pressure, and (iii) an elliptic grid generator using a body-fitted coordinate system for complex geometries, it provides an efficient algorithm for future direct numerical simulation (DNS) applications in complex rectangular geometries.     

A Combined Experimental and Numerical Study of Laminar and Turbulent Non-piloted Oxy-fuel Jet Flames Using a Direct Comparison of the Rayleigh Signal

In the present study laminar and turbulent oxy-fuel jet flames are investigated both experimentally and numerically with emphasis on the direct comparison of the Rayleigh signal. The Rayleigh signal was measured for both flame setups, correcting for background light appropriately. Two downstream regions were recorded for the laminar flame and three for the turbulent flame. Equivalently, the signal was processed numerically based on the numerical species data and temperature. The laminar flame was used for validating the procedure of processing the Rayleigh signal. Both the numerical species data and the temperature are known from detailed simulations, so a predicted Rayleigh signal can easily be obtained. Further, the influence of the choice of the kinetic mechanism, radiation and diffusion model was investigated. In contrast, in the turbulent Large Eddy Simulation, the Rayleigh signal has to be computed using an appropriate turbulence-chemistry interaction model in order to obtain the Reynolds-filtered Rayleigh signal which is of non-linear nature. In the present investigation, the Rayleigh signal was incorporated in the flamelet/progress variable approach. The statistics of the experimental and numerical Rayleigh signal were then compared. The proposed procedure of directly comparing the experimental and predicted Rayleigh signal was shown to be advantageous in model validation especially in turbulent flame configurations. The procedure enables accurate model validation across an entire 2D field of view whilst using a realistic fuel-oxidizer combination and reducing experimental complexity.     

Role of Buoyancy on Instabilities and Structure of Transitional Gas Jet Diffusion Flames

Transitional jet diffusion flames provide the link between dynamics of laminar and turbulent flames. In this study, instabilities and their interaction with the flow structure are explored in a transitional jet diffusion flame, with focus on isolating buoyancy effects. Experiments are conducted in hydrogen flames with fuel jet Reynolds number of up to 2,200 and average jet velocity of up to 54 m/s. Since the fuel jet is laminar at the injector exit, the transition from laminar to turbulent flame occurs by the hydrodynamic instabilities in the shear layer of fuel jet. The instabilities and the flow structures are visualized and quantified by the rainbow schlieren deflectometry technique coupled with a high-speed imaging system. The schlieren images acquired at 2,000 frames per second allowed exposure time of 23 μs with spatial resolution of 0.4 mm. Results identify a hitherto unknown secondary instability in the flame surface, provide explanation for the observed intermittency in the breakpoint length, show coherent vortical structures downstream of the flame breakpoint, and illustrate gradual breakdown of coherent structures into small-scale random structures in the far field turbulent region.     

New Directions in Advanced Modeling and in Situ Measurements Near Reacting Surfaces

Multidimensional numerical modeling and in situ spatially-resolved measurements of gas-phase thermoscalars over the catalyst boundary layer have fostered fundamental investigation of the heterogeneous and homogeneous chemical reaction pathways and their coupling at realistic operating conditions. The methodology for validating catalytic and gas-phase reaction mechanisms is firstly outlined for industrially-relevant fuels. Combination of advanced modeling and in situ near-wall species and velocity measurements is then used to address the intricate interplay between interphase fluid transport (laminar or turbulent) and hetero-/homogeneous kinetics. Controlling parameters of this interplay are the homogeneous ignition chemistry, flame propagation characteristics, competition between the catalytic and gaseous pathways for fuel consumption, diffusional imbalance of the limiting reactant, flow laminarization due to heat transfer from the hot catalytic walls, and fuel leakage through the gaseous reaction zone. Dynamic reactor operation and intrinsic flame dynamics driven by interactions between homogeneous kinetics and catalytic walls are outlined using detailed transient simulation. It is shown that the presence of catalytic reactions moderates flame instabilities. Future directions for transient modeling and for temporally-resolved in situ near-wall measurements are finally summarized.     

Large-Scale Turbulent Vortical Structures inside a Sudden Expansion Cylinder Chamber

A large eddy simulation (LES) is performed for turbulent flow around a bluff body inside a sudden expansion cylinder chamber, a configuration which resembles a premixed gas turbine combustor. To promote turbulent mixing and to accommodate flame stability, a flame holder is installed inside the combustion chamber. The Smagorinsky model and the Lagrangian dynamic subgrid-scale model are employed and tested. The calculated Reynolds number is 5,000 based on the bulk velocity and the diameter of inlet pipe. The simulation code is constructed by using a general coordinate system based on the physical contravariant velocity components. The predicted turbulent statistics are evaluated by comparing with the laser-doppler velocimetry (LDV) measurement data. The agreement of LES with the experimental data is shown to be satisfactory. Emphasis is placed on the time-dependent evolutions of turbulent vortical structures behind the flame holder. The numerical flow visualizations depict the behavior of large-scale vortices. The turbulent behavior behind the flame holder is analyzed by visualizing the sectional views of vortical structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

SENSITIVITY ANALYSIS AND OPTIMIZATION OF COUPLED THERMAL AND FLOW PROBLEMS WITH APPLICATIONS TO CONTRACTION DESIGN

The finite element method and the Newton–Raphson solution algorithm are combined to solve the momentum, mass and energy conservation equations for coupled flow problems. Design sensitivities for a generalised response function with respect to design parameters which describe shape, material property and load data are evaluated via the direct differentiation method. The efficiently computed sensitivities are verified by comparison with computationally intensive, finite difference sensitivity approximations. The design sensitivities are then used in a numerical optimization algorithm to minimize the pressure drop in flow through contractions. Both laminar and turbulent flows are considered. In the turbulent flow problems the time-averaged momentum and mass conservati on equations are solved using a mixing length turbulence model.     

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.     

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.     

An embedded boundary framework for compressible turbulent flow and fluid–structure computations on structured and unstructured grids

The finite volume method with exact two‐phase Riemann problems (FIVER) is a two‐faceted computational method for compressible multi‐material (fluid–fluid, fluid–structure, and multi‐fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi‐phase flow problems, FIVER is a Godunov‐type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two‐phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi‐material computations on nonbody‐fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second‐order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)‐based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time‐dependent distance to the wall because it is required by many RANS‐based turbulence models. The second algorithm addresses the robust and accurate computation of the flow‐induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter‐rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A‐18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Problem of Deceleration of a Supersonic Conducting Channel Flow by a Magnetic Field

Problems of the deceleration of a supersonic conducting flow by a magnetic field are investigated. A conducting gas flow in a circular tube is considered in the presence of an axisymmetric magnetic field induced by a unit current loop or solenoid of finite length. The analysis is carried out on the basis of both the Euler equations (inviscid gas) and the complete system of Navier-Stokes equations for laminar viscous gas flow and turbulent flow using a one-parameter turbulence model. The numerical simulation is based on an implicit relaxation finite-difference scheme which is a modification of the Godunov method. The total pressure losses are determined for various values of the magnetohydrodynamic (MHD) interaction, the initial Mach number, and different magnetic field geometries and it is shown that the irreversible losses are significant in MHD supersonic flow deceleration.