A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis

The principal component analysis (PCA) is used to analyze the high dimensional chemistry data of laminar premixed/stratified flames under strain effects. The first few principal components (PCs), which have larger contribution ratios, are chosen as the tabulated scalars to build the look-up chemistry table. Prior tests show that the strained premixed flame structure can be well reconstructed. To highlight the physical meanings of the tabulated scalars in the stratified flames, a modified PCA method is developed, where the mixture fraction is used to replace one of the PCs with the highest correlation coefficient with a mixture fraction. The other two tabulated scalars are then modified with the Schmidt orthogonalization. The modified tabulated scalars not only have clear physical meanings, but also contain passive scalars. The PCA method has good commonality, and can be extended for building the thermo-chemistry table including strain rate effects when different fuels are used.     

3D Numerical Simulation of a Laminar Experimental SWQ Burner with Tabulated Chemistry

Flame-wall interaction (FWI) plays an important role in enclosed combustion systems. For avoiding the complexity of close to reality combustors, in this study an atmospheric premixed V-shaped flame interacting with an isothermal cold wall in a side wall quenching (SWQ) configuration is investigated. A stoichiometric methane/air mixture is used as fuel. A three-dimensional (3D) numerical simulation, which resolves all flow structures is combined with a tabulated chemistry approach (flamelet generated manifold, FGM). Results are compared with experimental data and two-dimensional simulations. The FGM approach is a suitable trade-off between computationally expensive detailed chemistry simulations and over simplified single step mechanisms. 2D simulations are used to investigate the influence of the uncertainty of the wall temperature, to show that the resolution in 3D is sufficient and that the influence of the flame thickening on the wall heat fluxes can be determined. Our results show that the 3D FGM approach is in close agreement to experimentally obtained flow and temperature fields. The dimensionless wall heat flux and Péclet number matches the expected values of 0.16 and 7, respectively. However, during FWI the measured CO mole fractions are not reproduced accurately showing that the transported variables in the present approach of tabulated chemistry do not recover premixed flame structures near walls.     

Flow Physics of a Bluff-Body Swirl Stabilized Flame and their Prediction by Means of a Joint Eulerian Stochastic Field and Tabulated Chemistry Approach

In the frame of this work a transported joint scalar probability density function (PDF) method is combined with the flamelet generated manifolds (FGM) tabulated chemistry approach for large eddy simulation (LES) modeling of a three-dimensional turbulent premixed swirl burner. This strategy accounts for the turbulence-chemistry interaction at reasonable computational costs. At the same time, it allows the usage of detailed chemistry mechanisms for the creation of the chemical database. The simulation results obtained are comparatively assessed along with complementary measurements. Furthermore, transient and time-averaged data are used to provide insight into the flow physics of the bluff-body swirl stabilized flame considered. The sensitivity of the results to different modeling approaches regarding the predicted flame shape and its dynamics is also investigated, where the implemented approach is compared with the well-established artificially thickened flame (ATF) combustion model. Consequently, the investigation conducted in this work aims to provide a complete picture on the ability of the proposed combustion model to reproduce the flow conditions within complex bluff-body swirl stabilized flames.     

Effects of the Local Flow Topologies Upon the Structure of a Premixed Methane-air Turbulent Jet Flame

Local flow topologies have been identified and their interactions with the iso-scalar surfaces geometries have been investigated using the results of a three-dimensional direct numerical simulation (DNS) of a turbulent premixed methane-air flame in a piloted Bunsen burner configuration with tabulated chemistry. The universal teardrop shape of the joint probability density function (jpdf) of the second and third invariants of the velocity-gradient tensor disappears in the different flame regions under study. A ‘canonical’ vortex, which affects the fine-scale structure of the turbulent premixed flame, has been identified and analyzed at three times, differing by increments of the order of the Kolmogorov time micro-scale.     

Assessment of the Dynamic SGS Wrinkling Combustion Modeling Using the Thickened Flame Approach Coupled with FGM Tabulated Detailed Chemistry

The dynamic power-law wrinkling model proposed by Charlette et al. is coupled with Flamelet Generated Manifolds (FGM) tabulated chemistry combined with an artificially thickened flame model (ATF) for large eddy simulation. The dynamic formulation is similar to the “Germano” procedure and uses Taylor series based Gaussian filter. Thereby, the power-law wrinkling model parameter is considered to have both temporal and spatial dependency. Series of simulations are conducted for a lean premixed turbulent flame, using both dynamic and non-dynamic versions of the wrinkling model under different grid levels. The simulation results applying the non-dynamic wrinkling model show different behavior for each particular flame resolution, where none of the simulations could deliver the correct flame statistics, such as flame height. The dynamic version of the power-law wrinkling model improves the results independently of the flame resolution, as a consequence of the conservation of the total flame surface.     

An investigation on multilayer shape memory polymers under finite bending through nonlinear thermo-visco-hyperelasticity

This study presents a semi-analytical solution to describe the behavior of shape memory polymers(SMPs) based on the nonlinear thermo-visco-hyperelasticity which originates from the concepts of internal state variables and rational thermodynamics. This method is developed for the finite bending of multilayers in a dual-shape memory effect(SME) cycle. The layer number and layering order are investigated for two different SMPs and a hyperelastic material. In addition to the semi-analytical solution...     

A Two-Dimensional Tabulated Flamelet Combustion Model for Furnace Applications

A new tabulated chemistry approach for representing turbulent combustion in industrial furnaces is presented. This model is based on the tabulation of two dimensional diffusion flamelets to account for ternary mixtures between fuel, oxidant and burned gases which are integrated over probability density functions. To avoid excessive CPU time for the table generation, the calculation of the two dimensional flamelets is performed using the method proposed in the ADF-PCM (Approximated Diffusion Flame - Presumed Conditional Moment) approach: only the equation for the progress variable is solved, instead of the equations for all species. The progress variable reaction rate is given by a table of homogeneous reactors using the DHR model (Diluted Homogeneous Reactor) proposed by Locci et al. These approximated diffusion flames are first compared to exact diffusion flames computed using the flamelet equations and the chemistry for all species. The resulting model, called A2DF (Approximate 2 Dimensional Flamelet) is then applied to the RANS (Reynolds Averaged Navier-Stokes) simulations of Sandia Flames D and F, showing a good agreement with experimental measurements. Finally, this model is applied to the flameless and conventional combustion cases of the burner of Verissimo et al., showing a correct agreement for temperature and species predictions.     

On Fokker–Planck Equations for Turbulent Reacting Flows. Part 1. Probability Density Function for Reynolds-Averaged Navier–Stokes Equations

The accurate treatment of finite-rate chemistry is possible by the application of stochastic turbulence models which generalize Reynolds-averaged Navier–Stokes equations. Usually, one considers linear stochastic equations. In this way, fluctuations are generated by uncorrelated forces and relax with a frequency that is independent of the actual fluctuation. It has been proved that such linear equations are well appropriate to simulate near-equilibrium flows. However, the inapplicability or unfeasibility of other methods also results in a need for stochastic methods for more complex flow simulations. Their construction requires an extension of the simple mechanism of linear stochastic equations. Two ways to perform this are investigated here. The first way is the construction of a stochastic model for velocities where the relaxation frequency depends on the actual fluctuation. This is a requirement to involve relevant mixing variations due to large-scale flow structures. The stochastic model developed is applied to the simulation of convective boundary layer turbulence. Comparisons with the results of measurements provide evidence for its good performance and the advantages compared to existing methods. The second way presented here is the construction of scalar equations which involve memory effects regarding to both the stochastic forcing and relaxation of fluctuations. This allows to overcome shortcomings of existing stochastic methods. The model predictions are shown to be in excellent agreement with the results of the direct numerical simulation of scalar mixing in stationary, homogeneous and isotropic turbulence. The consideration of memory effects is found to be essential to simulate correctly the evolution of scalar fields within the first stage of mixing.     

Anti-plane fracture of a functionally graded material strip

This paper considers the anti-plane (or mode III) crack problem in a functionally graded material strip. The shear modulus of the strip is considered for a class of functional forms for which the equilibrium equation has an analytical solution. The problem is solved by means of singular integral equation technique. Both a single crack and a series of collinear cracks are studied. The results are tabulated and plotted to show the effect of the material nonhomogeneity and crack location on the stress intensity factors.     

Large Eddy Simulation of a Polydisperse Ethanol Spray Flame

Ethanol is identified as an interesting alternative fuel. In this regards, the predictive capability of combustion Large Eddy Simulation approach coupled to Lagrangian droplet dynamic model to retrieve the turbulent droplet dispersion, droplet size distribution, spray evolution and combustion properties is investigated in this paper for an ethanol spray flame. Following the Eulerian-Lagrangian approach with a fully two way coupling, the Favre-filtered low Mach number Navier-Stokes equations are solved on structured grids with dynamic sub-grid scale models to describe the turbulent carrier gas phase. Droplets are injected in polydisperse manner and generated in time dependent boundary conditions. They evaporate to form an air-fuel mixture that yields spray flame. Part of the ethanol droplets evaporates within the prevaporization area before reaching the combustion zone, making the flame to burn in a partially premixed regime. The chemistry is described by a tabulated detailed chemistry based on the flamelet generated manifold approach. The fuel, ethanol, is modeled by a detailed reaction mechanism consisting of 56 species and 351 reversible reactions. The simulation results including excess gas temperature, droplet velocities and corresponding fluctuations, droplet mean diameters and spray volume flux at different distances from the exit plane show good agreement with experimental data. Analysis of combustion spray features allows gaining a deep insight into the two-phase flow process ongoing.     

LES Modeling of the Impact of Heat Losses and Differential Diffusion on Turbulent Stratified Flame Propagation: Application to the TU Darmstadt Stratified Flame

Common combustion chambers often exhibit turbulent flames propagating in partially-premixed mixtures. This propagation is generally governed by aerodynamics, unsteady mixing and chemical processes and may also be affected by conductive heat losses when the reactive zone develops close to the burner lips. The Filtered TAbulated Chemistry for Large Eddy Simulation (F-TACLES) model has been recently developed to include tabulated chemistry in Large Eddy Simulation (LES) of adiabatic stratified flames in flamelet regimes. The present article proposes a modeling approach to account for both differential diffusion and non-adiabatic effects on flame consumption speed following the F-TACLES formalism. The adiabatic F-TACLES model is first detailed using a generalized formalism for diffusive fluxes allowing either to account for differential diffusion or not. The F-TACLES model is then extended to non-adiabatic situations. A correction factor based on the non-adiabatic consumption rate is introduced to recover a realistic filtered flame consumption speed. The objective is here to tackle flame stabilization mechanisms when heat losses affect the reaction zone. The proposed approach is validated through the simulation of the unconfined stratified turbulent jet flame TSF-A for which stabilization process is affected by heat losses. Five simulations are performed for both adiabatic and non-adiabatic flow conditions comparing unity Lewis number and complex diffusion assumptions. The adiabatic F-TACLES model predicts a flame anchored at the burner lip disagreeing with experimental data. The non-adiabatic simulation exhibits local extinction due to heat losses near the burner exit. The flame is then lifted improving the comparison with experiments. Results also show a significant impact of molecular diffusion model on both mean flame consumption rate and angle.     

Simulation of shock-initiated ignition

The scenario of detonative ignition in shocked mixture is significant because it is a contributor to deflagration to detonation transition, for example following shock reflections. However, even in one dimension, simulation of ignition between a contact surface or a flame and a shock moving into a combustible mixture is difficult because of the singular nature of the initial conditions. Initially, as the shock starts moving into reactive mixture, the region filled with reactive mixture has zero thickness. On a fixed grid, the number of grid points between the shock and the contact surface increases as the shock moves away from the latter. Due to initial lack of resolution in the region of interest, staircasing may occur, whereby the resulting plots consist of jumps between few values a few grid points, and these numerical artifacts are amplified by the chemistry which is very sensitive to temperature, leading to unreliable results. The formulation is transformed, replacing time and space by time and space over time as the independent variables. This frame of reference corresponds to the self-similar formulation in which the non-reactive problem remains stationary, and the initial conditions are well-resolved. Additionally, a solution obtained from short time perturbation is used as initial condition, at a time still short enough for the perturbation to be very accurate, but long enough so that there is sufficient resolution. The numerical solution to the transformed problem is obtained using an essentially non-oscillatory algorithm, which is adequate not only for the early part of the process, but also for the latter part, when chemistry leads to appearance of a shock and eventually a detonation wave is formed. A validation study was performed and the results were compared with the literature, for single step Arrhenius chemistry. The method and its implementation were found to be effective. Results are presented for values of activation energy ranging from mild to stiff.     

A finite element model for shape memory alloys considering thermomechanical couplings at large strains

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension–compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment.     

Heat loss calculation in thermal simulation

An appraisal is presented for four different methods that are usually incorporated in thermal simulators to estimate the rate of heat loss to surroundings. The methods are the analytical solution using a superposition theorem, the analytical solution using a numerical approximation to the convolution integral, the semi-analytical solution, and the numerical solution. This appraisal includes expressing the equations in a form that can be incorporated into a fully implicit simulator, computer programming complexity, and the computer CPU time and memory storage requirements. A steam flood problem is used for the comparison, and the gas recovery, oil recovery, and heat loss performances for a reservoir in one and two dimensions are presented. It is found that the numerical solution is sensitive to grid size in the overburden, the semi-analytical solution is the simplest to program but its prediction is the least accurate, the analytical solution is the most expensive, whereas the analytical-numerical solution combines both accuracy and acceptable storage requirements, and therefore, it is recommended for use in thermal simulation.     

The influences of both offset and mass moment of inertia of a tip mass on the dynamics of a centrifugally stiffened visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that they have to be included in the modeling process.     

Rigorous upscaling of the reactive flow with finite kinetics and under dominant Péclet number

We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Péclet and Damköhler numbers. We suppose Péclet numbers corresponding to Taylor’s dispersion regime. The two main results of the paper are the following. First, using the anisotropic perturbation technique, we derive rigorously an effective model for the enhanced diffusion. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. Error estimates for the approximation of the physical solution by the upscaled one are presented in the energy norms. Presence of an initial time boundary layer allows only a global error estimate in L ² with respect to space and time. We use the Laplace’s transform in time to get optimal estimates. Second, we explicit the retardation and memory effects of the adsorption/desorption reactions on the dispersive characteristics and show their importance. The chemistry influences directly the characteristic diffusion width.     

On the comparison of the solutions obtained by using two different transform methods for the second problem of Stokes for Newtonian fluids

The unsteady flow over a plane wall which is initially at rest and the plate begins suddenly to oscillate in own plane is considered. The solution subject to the boundary and initial conditions is obtained by applying to the governing equation the Laplace transform method or Fourier transform method. A comparison of the solutions obtained by two transform methods for flow considered is given. It is shown that the solution obtained by the Laplace transform method or Fourier transform method is the sum of the steady-state and the transient parts. The transient parts are found in terms of definite integrands whose integrals are oscillatory functions. Therefore, the transient parts are expressed in terms of the tabulated functions.     

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

This paper describes a nonlinear, three‐dimensional spectral collocation method for the simulation of the incompressible Navier–Stokes equations under the Boussinesq approximation, motivated by geophysical and environmental flows. These flows are driven by the interaction of stratified fluid with topography, which this model accurately accounts for by using a mapped coordinate system. The spectral collocation method is implemented with both a Fourier trigonometric expansion and the Chebyshev polynomials, as appropriate for the domain boundary conditions. The coordinate mapping prohibits the use of existing, fast solution methods that rely on the separation of variables, so a preconditioner based on the approximate solution of a corresponding finite‐difference problem with geometric multigrid is used. The model is parallelized with the Message Passing Interface library, and it runs effectively on shared and distributed‐memory systems. Copyright © 2013 John Wiley & Sons, Ltd.