On the non-equilibrium models for subfilter scalar variance in large eddy simulation of turbulent mixing and combustion

A combustion model based on the flame surface density (FSD) concept is developed and implemented for large eddy simulation of turbulent nonpremixed combustion of wood pyrolysis gas and air. In this model, the filtered reaction rate ω̇̄α of species α is estimated as the product of the consumption rate per unit surface area ṁα and the filtered FSD Σ̄. This approach is attractive since it decouples the chemical problem from the description of the turbulence combustion interaction. The filtered FSD is modeled as the product of the conditional filtered gradient of mixture fraction and the filtered probability density function. This approach is validated from direct numerical simulation (DNS) using spatial filtering operation. Results show that the proposed FSD model provides a good description for the filtered reaction rate of wood pyrolysis gas. Temperature predicted by large eddy simulation agrees well with that filtered from DNS data.

A data-driven subgrid scale model in Large Eddy Simulation of turbulent premixed combustion

Combustion is a natural phenomenon. It happens in forest, automotive engine and gas cooker. In Computational Fluid Dynamics (CFD), the combustion phenomenon complies with a set of partial differential equations. According to the resolution scale, from big to small, the simulation methods in combustion are Reynolds Averaged Navior Stokes method (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). Combustion model research in RANS and LES was, is and will still be a hot topic. In this chapter, an Algebraic Sub-grid Scale turbulent Combustion Model (ASSCM) for LES is brought forward. Then this model is applied to a partly diffusion jet flame and a premixed flame, after that, the database of the LES simulation results is used to test a RANS turbulent combustion model closure idea. Finally, a DNS by spectral method (Xu et al, 1996) in channel flow is carried on with consideration of buoyancy effects, and the database of the DNS simulation results is used to study RANS and LES turbulent combustion models.

Large Eddy Simulation (LES) of the lab-scale methane fire plumes investigated experimentally by McCaffrey is performed using the steady laminar flamelet/presumed beta filtered density function model on grids of different resolution ranging from the Taylor length scale to about six times the Kolmogorov length scale. This work focuses on investigating existing subgrid (SGS) mixing models for mixture fraction variance prediction. Three different models based on the local equilibrium assumption, the variance transport equation (VTE) and the second moment transport equation (STE) are assessed. In the non-equilibrium modelling (VTE and STE), the scalar dissipation rate is modelled with an algebraic expression involving an SGS mixing time-scale. The comparison of the solutions is based on the convergence properties of LES statistics for mixture fraction, temperature and axial velocity with respect to the filter width. The simulations show that the equilibrium algebraic model is not suitable for purely buoyant flows. On the other hand, simulations performed with the transport models show that grids coarser than 1 cm cannot resolve adequately the natural laminar instability near the edge of the plume that governs the formation of large-scale vortex and, therefore, underestimate the mixing process, especially in the lower part of the continuous flame. For grid resolutions finer than 1 cm, the STE model is less sensitive to grid refinement than the VTE formulation and differences between the two models are reduced with grid refinement. The STE model predicts also a stronger mixing, resulting in a slightly larger lateral expansion of the fire plume. Predicted solutions by the two models are in quantitative agreement with the experimental data in terms of axial temperature, velocity and temperature fluctuations.

Modeling and discretization errors in large eddy simulations of hydrodynamic and magnetohydrodynamic channel flows

The complex interactions among turbulence, combustion and spray in liquid-fuel burners are modeled and simulated via a new two-phase Lagrangian-Eulerian-Lagrangian large eddy simulation (LES) methodology. In this methodology, the spray is modeled with a Lagrangian mathematical/computational method which allows two-way mass, momentum and energy coupling between phases. The subgrid gas-liquid combustion is based on the two-phase filtered mass density function (FMDF) that has several advantages over “conventional” two-phase combustion models. The LES/FMDF is employed in conjunction with non-equilibrium reaction and droplet models. Simulations of turbulent combustion in a spray-controlled double-swirl burner are conducted via LES/FMDF. The generated results are used for better understanding of spray combustion in realistic turbulent flow configurations. The effects of spray angle, mass loading ratio, fuel type, droplet size distribution, wall and inflow/outflow conditions on the flow and combustion are investigated. The LES/FMDF predictions are shown to be consistent with the experimental results.

A dynamic SGS combustion model based on fractal characteristics of turbulent premixed flames

A subgrid scale model for large eddy simulations of turbulent premixed combustion is developed and validated. The approach is based on the concept of artificially thickened flames, keeping constant the laminar flame speed sl0. This thickening is simply achieved by decreasing the pre-exponential factor of the chemical Arrhenius law whereas the molecular diffusion is enhanced. When the flame is thickened, the combustion–turbulence interaction is affected and must be modeled. This point is investigated here using direct numerical simulations of flame–vortex interactions and an efficiency function E is introduced to incorporate thickening effects in the subgrid scale model. The input parameters in E are related to the subgrid scale turbulence (velocity and length scales). An efficient approach, based on similarity assumptions, is developed to extract these quantities from the resolved velocity field. A specific operator is developed to exclude the dilatational part of the velocity field from the estimation of turbulent fluctuations. The combustion model is then implemented in a compressible parallel finite volume–element solver able to handle hybrid grids to simulate a lateral injections combustor (LIC). Results are in agreement with the available experimental data.

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

Implementation of a dynamic thickened flame model for large eddy simulations of turbulent premixed combustion

Analysis of turbulent flows is one of the most difficult and challenging topics in physical sciences because of the nonlinearity of the governing equations, which is manifested by a large range of length and time scales. Resolution of this large range of scales is difficult to address using both experimental and numerical means. This problem is further exacerbated in turbulent reacting flows due to the nonlinearity of the temperature dependence of burning rate in typical combustion processes. Moreover, the interaction of flow and chemistry in turbulent premixed combustion (where reactants are homogeneously mixed prior to the combustion process) necessitates simultaneous measurements of fluid velocity and flame propagation in three dimensions with adequate spatial resolution. Such an experimental analysis is either impossible in most configurations or extremely expensive to carry out. The advances in high-performance computing have made it possible to carry out three-dimensional Direct Numerical Simulations (DNS) of turbulent premixed combustion by resolving all the relevant length and time scales of turbulent reacting flows without any recourse to physical approximations. The cost of DNS for non-reacting flows is immense where one only has to resolve the Kolmogorov scale, and it is more expensive for premixed combustion because it requires additional resolution of the internal flame structure. It can be shown that for simulating homogeneous non-reacting turbulence the number of grid points varies with Reynolds number as \( Re_{t}^{9/4} \), where \( Re_{t} \) is the large-scale turbulent Reynolds number, which is why DNS is limited by computer capacity and the application of DNS remains limited to research problems in simple configurations for moderate turbulent Reynolds numbers. However, the data obtained from DNS circumvents the aforementioned limitations of experimental data and can be considered as an equivalent to experimental data with a spatial resolution up to the Kolmogorov length scale (i.e. the smallest significant length scale of turbulence). Although DNS does not require turbulence and combustion modelling (and thus avoids physical inaccuracies associated with them), the chemical aspect of premixed combustion is often simplified for the sake of computational economy in order to conduct a detailed parametric analysis. The simplification of chemistry and the specification of ‘soft’ boundary conditions often significantly affect the results and determine the aspects which can be analysed using DNS data. In spite of these constraints, DNS data can be explicitly Reynolds-averaged/filtered to extract the ‘exact’ behaviour of the unclosed terms in the Reynolds-averaged/ filtered transport equations of momentum, energy and species. This makes it possible to compare the predictions of existing models with respect to the ‘exact’ unclosed terms extracted from DNS data and propose either model modifications or new models, wherever necessary, in the light of physical insights obtained from DNS data. Thus, even though the DNS of premixed combustion remains mostly limited to canonical configurations, the physical insights obtained from it contribute significantly to the development of the high-fidelity models for Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulations (LES), which are used for engineering calculations for designing industrial burners. As an example, this chapter will illustrate how DNS data can contribute to the model development for the Reynolds flux of sensible enthalpy in head-on quenching of statistically planar turbulent premixed flames by an inert isothermal wall.

The subgrid-scale (SGS) modeling in large-eddy simulation (LES) which accounts for the effect of unsteadiness and nonequilibrium state in the SGS is considered. Unsteadiness is incorporated by considering the spectral evolution in the forced homogeneous isotropic turbulence using the transport equation for the SGS energy. As for the unfiltered spectrum, perturbative expansion of the Kovasnay spectral model about the Kolmogorov −5/3 energy spectrum which constitutes a base equilibrium state in the inertial subrange, yields the extra components with −7/3 and −9/3 powers. It is shown that these spectra are actually extracted in the direct numerical simulation (DNS) data and these components govern the unsteady energy transfer. As for the SGS real-space representation of the spectral model, we consider the SGS one-equation model. The perturbation expansion is applied to the one-equation model by setting the base SGS energy as the standard Smagorinsky model, which assumes the equilibrium state in the SGS and its spectral counterpart is the Kolmogorov −5/3 spectrum. The solution yields the terms whose spectral counterparts are the components with −7/3 and −9/3 powers. These additional terms are induced by temporal variations of the base SGS energy. In the temporal variations of the grid-scale energy, SGS energy, SGS production term, and SGS dissipation which are obtained by applying the filter to the DNS data, it is shown that these quantities lag in time in this order. This time-lag is not realized in the standard Smagorinsky model and the one-equation model because the SGS dissipation is defined so that it instantaneously adjusts to the SGS energy. In the one-equation model, the direction of the energy cascade in the initial period is opposite to that obtained in the DNS data. To retrieve correct time-lag and direction of energy transfer, we relax this instantaneous adjustment and propose the nonequilibrium Smagorinsky model. In this nonequilibrium model, the SGS energy incurred by the −7/3 spectrum is added to the base Smagorinsky energy. Assessment in actual LES shows that the time-lag predicted using the standard Smagorinsky and the one-equation models is inaccurate, whereas good agreement with the DNS data is achieved in the nonequilibrium Smagorinsky model. Extraction of the grid-scale nonequilibrium energy spectrum yields the −7/3 and −9/3 components in addition to the base −5/3 spectrum. In the nonequilibrium Smagorinsky model, continuation of the grid-scale spectra into the SGS is established for the −5/3 and −7/3 components. As a result, the unsteady energy transfer is more accurately predicted, whereas the standard Smagorinsky model does not have the SGS counterpart for the −7/3 component. Feasibility of employing the eddy-viscosity approximation to account for the transfer in the period in which −9/3 spectrum prevails is discussed.

This paper presents a systematic investigation of large eddy simulation (LES) and subgrid scale (SGS) modeling with application to transcritical and supercritical turbulent mixing and combustion. There remains uncertainty about the validity of extending the LES formalism developed for low-pressure, ideal-gas flows to simulations of high-pressure real-fluid flows. To address this concern, we reexamine the LES theoretical framework and the underlying assumptions in the context of real-fluid mixing and combustion. Two-dimensional direct numerical simulations of nonreacting and reacting mixing layers of gaseous methane and liquid oxygen in the thermodynamically transcritical and supercritical fluid regimes are performed. The computed results are used to evaluate the exact terms in the LES governing equations and associated SGS models. Order of magnitude analysis of the exact filtered and subgrid terms in the LES equations and a priori analysis of the simplifications are performed at different filter widths. It is shown that several of these approximations do not hold for supercritical turbulent mixing. Subgrid scale terms, which are neglected in the LES framework for ideal-gas flows, become significant in magnitude compared to the other leading terms in the governing equations. In particular, the subgrid term arising from the filtering of the real-fluid equation of state is shown to be important.

Subfilter scalar variance is a critical indicator of small scale mixing in large eddy simulation (LES) of turbulent combustion and is an important parameter of conserved scalar based combustion models. Realistic combustion models have a highly nonlinear dependence on the conserved scalar, making the prediction of flow thermochemistry sensitive to errors in subfilter variance modeling, including errors due to numerical discretization. Large numerical errors can result from the use of grid-based filtering and the resulting under-resolution of the smallest filtered scales, which are a key to variance modeling. Hence, the development of variance models should take into account this sensitivity to numerical discretization. In this work, a novel coupled direct numerical simulation (DNS)-LES a posteriori method is used to study the role of discretization errors in variance prediction for the two most widely used types of models: algebraic dynamic models and transport equation-based models. Algebraic models are found to be ill-suited to discretization due to their dependence on filtered scalar gradient values. Additionally, the use of dynamic modeling procedures enhances their sensitivity to filtered scalar errors. The accuracy of transport equation models primarily rests on the accuracy of the scalar dissipation rate closure with numerical error having a secondary effect. The influence of dissipation rate modeling error is investigated using the unique information provided by the combined DNS-LES simulation method. Overall, transport equation models are found to offer a more powerful approach to variance modeling due to more complete model physics and reduced effects of discretization error.

Reynolds number dependence of mixing in a lock-exchange system from direct numerical and large eddy simulations