Effects of combined dimension reduction and tabulation on the simulations of a turbulent premixed flame using a large-eddy simulation/probability density function method

A turbulent lean-premixed propane–air flame stabilised by a triangular cylinder as a flame-holder is simulated to assess the accuracy and computational efficiency of combined dimension reduction and tabulation of chemistry. The computational condition matches the Volvo rig experiments. For the reactive simulation, the Lagrangian Large-Eddy Simulation/Probability Density Function (LES/PDF) formulation is used. A novel two-way coupling approach between LES and PDF is applied to obtain resolved density to reduce its statistical fluctuations. Composition mixing is evaluated by the modified Interaction-by-Exchange with the Mean (IEM) model. A baseline case uses In Situ Adaptive Tabulation (ISAT) to calculate chemical reactions efficiently. Its results demonstrate good agreement with the experimental measurements in turbulence statistics, temperature, and minor species mass fractions. For dimension reduction, 11 and 16 represented species are chosen and a variant of Rate Controlled Constrained Equilibrium (RCCE) is applied in conjunction with ISAT to each case. All the quantities in the comparison are indistinguishable from the baseline results using ISAT only. The combined use of RCCE/ISAT reduces the computational time for chemical reaction by more than 50%. However, for the current turbulent premixed flame, chemical reaction takes only a minor portion of the overall computational cost, in contrast to non-premixed flame simulations using LES/PDF, presumably due to the restricted manifold of purely premixed flame in the composition space. Instead, composition mixing is the major contributor to cost reduction since the mean-drift term, which is computationally expensive, is computed for the reduced representation. Overall, a reduction of more than 15% in the computational cost is obtained.     

A study of the rate-controlled constrained-equilibrium dimension reduction method and its different implementations

The Rate-Controlled Constrained-Equilibrium (RCCE) method is a thermodynamic based dimension reduction method which enables representation of chemistry involving n _s species in terms of fewer n _r constraints. Here we focus on the application of the RCCE method to Lagrangian particle probability density function based computations. In these computations, at every reaction fractional step, given the initial particle composition (represented using RCCE), we need to compute the reaction mapping, i.e. the particle composition at the end of the time step. In this work we study three different implementations of RCCE for computing this reaction mapping, and compare their relative accuracy and efficiency. These implementations include: (1) RCCE/TIFS (Trajectory In Full Space): this involves solving a system of n _s rate-equations for all the species in the full composition space to obtain the reaction mapping. The other two implementations obtain the reaction mapping by solving a reduced system of n _r rate-equations obtained by projecting the n _s rate-equations for species evaluated in the full space onto the constrained subspace. These implementations include (2) RCCE: this is the classical implementation of RCCE which uses a direct projection of the rate-equations for species onto the constrained subspace; and (3) RCCE/RAMP (Reaction-mixing Attracting Manifold Projector): this is a new implementation introduced here which uses an alternative projector obtained using the RAMP approach. We test these three implementations of RCCE for methane/air premixed combustion in the partially-stirred reactor with chemistry represented using the n _s=31 species GRI-Mech 1.2 mechanism with n _r=13 to 19 constraints. We show that: (a) the classical RCCE implementation involves an inaccurate projector which yields large errors (over 50%) in the reaction mapping; (b) both RCCE/RAMP and RCCE/TIFS approaches yield significantly lower errors (less than 2%); and (c) overall the RCCE/TIFS approach is the most accurate, efficient (by orders of magnitude) and robust implementation.     

Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane–air and iso-octane–air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.     

The extension of the ILDM concept to reaction–diffusion manifolds

In the present work, the method of simplifying chemical kinetics based on Intrinsic Low-Dimensional Manifolds (ILDMs) is modified to deal with the coupling of reaction and diffusion processes. Several problems of the ILDM method are overcome by a relaxation to an invariant system manifold (Reaction–Diffusion Manifold – REDIM). This relaxation process is governed by a multidimensional parabolic partial differential equation system, where, as an initial solution, an extended ILDM is used. Furthermore, a method for the solution and tabulation of the manifold is proposed in terms of generalized coordinates, with a subsequent procedure for the integration of the reduced system on the found manifold. This modification of the ILDM significantly improves the performance of the concept and allows us to extend its area of applicability. Illustrative comparative calculations of detailed and reduced models of flat laminar flames verify the approach.     

On the role of pressure in elasto-inertial turbulence

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.     

Waveguide Dye Solution Lasers

Since the development of first lasers the possibility of light amplificatior and oscillation in waveguide structures has been investigated. Waveguide lasers have been constructed using a variety of lasing materials, either solid, gaseous, or liquid.