Significant progress has been made on the model development for simulating turbulent reacting flows. As a consequence, we are currently in a position where key-physical aspects of fairly complex combustion processes are well understood at a qualitative and -- in many cases -- also at a quantitative level. Examples are the prediction of temperature and major species, statistically stationary flames, gas-phase combustion, turbulent transport, and turbulence/flame coupling. However, current challenges lie in capturing transient processes and stability boundaries, minor species and emissions, multiphase flows and phase-transition, as well as multidimensional flame/flow interactions that may involve flame curvature effects, stratification, partially premixing, or flame-wall interaction. With this, the question arises what steps need to be taken to elevate the current state of modeling capabilities in order to address these deficiencies? This paper seeks to address this question. We begin by reviewing the current state of combustion model approaches, our quest for improving existing models, the separation of errors arising from numerical discretization and physical models, and ideas on model evaluations. We then proceed by examining concepts on quantitative model evaluations, requirements on predictability, quantities of interest, and cost/accuracy trade-offs. We close by introducing recent concepts that assimilate time-resolved measurements into numerical simulations for state estimation, model evaluation, and parameter determination.
We study turbulent diffusion of chemically reacting gaseous admixtures in a developed turbulence. In our previous study [Phys. Rev. Lett. {\bf 80}, 69 (1998)] using a path-integral approach for a delta-correlated in time random velocity field, we demonstrated a strong modification of turbulent transport in fluid flows with chemical reactions or phase transitions. In the present study we use the spectral tau approximation, that is valid for large Reynolds and Peclet numbers, and show that turbulent diffusion of the reacting species can be strongly depleted by a large factor that is the ratio of…
The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously (Phys. Rev. E {\bf 90}, 053001, 2014) is generalized for large yet finite Reynolds numbers, and the dependence of turbulent diffusion coefficient versus two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales) is obtained. Three-dimensional direct numerical simulations (DNS) of a finite thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are per…
Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are challenging to model, and accurate closures for the unresolved terms in large eddy simulations of such flows are difficult to obtain. In this study, we investigate the use of artificial neural networks for modelling an important unclosed term namely the unresolved stress tensor, in a highly demanding turbulent and reacting flow, which additionally includes …
The concept of local isotropy in a chemically reacting turbulent wall-jet flow is addressed using direct numerical simulation (DNS) data. Different DNS databases with isothermal and exothermic reactions are examined. The chemical reaction and heat release effects on the turbulent velocity, passive scalar and reactive species fields are studied using their probability density functions (PDF) and higher order moments for velocities and scalar fields, as well as their gradients. With the aid of the anisotropy invariant maps for the Reynolds stress tensor the heat release effects on the anisotropy…
Super-resolution of turbulent reacting flows on complex meshes using graph neural networks
FLAME Laboratory, Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru, 560012, India（印度科学研究院流体动力学与能源实验室，班加罗尔）；CAPS Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland（苏黎世联邦理工学院机械与过程工程实验室，苏黎世）；Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, 52425, Germany（尤利希超算中心，尤利希）
A study of a reacting boundary layer flow with heat transfer at conditions typical for configurations at elevated pressures has been performed using a set of direct numerical simulations. Effects of wall temperatures are investigated, representative for cooled walls of gas turbines and sub-scale rocket engines operating with hydrocarbon as fuels. The results show that exothermic chemical reactions induced by the low-enthalpy in the boundary layer take place predominantly in the logarthimic sub-layer. The majority of the heat release is attributed to the exothermic recombination of OH and CO to…
In the application of the combustion models based on low-dimensional manifolds (for instance flamelet models) to large-eddy simulation (LES) of reactive turbulent flows, the modeling simplifications of the combustion process is a critical source of uncertainty in addition to those due to the turbulent closure model and numerical discretization. The ability to quantitatively assess this uncertainty in absence of the reference result is vital to the reliable and predictive simulations of practical combustion devices.In the present study, the Pareto-efficient combustion (PEC) framework is extende…
The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasi-adiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully-developed turbulent conditions using a five-species, chemically-reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inle…
Large eddy simulation (LES) has become the de-facto computational tool for modeling complex reacting flows, especially in gas turbine applications. However, readily usable general-purpose LES codes for complex geometries are typically academic or proprietary/commercial in nature. The objective of this work is to develop and disseminate an open source LES tool for low-Mach number turbulent combustion using the OpenFOAM framework. In particular, a collocated-mesh approach suited for unstructured grid formulation is provided. Unlike other fluid dynamics models, LES accuracy is intricately linked …
A new compact active turbulence generator is developed, tested, and characterized, which extends the capabilities of such generators used in turbulent premixed combustion research. The generator is composed of two blades that resemble the shape of two bow-ties. Hot-wire anemometry and high-speed imaging are performed to characterize the non-reacting flow produced by the generator and the blades dynamics, respectively. Two mean bulk flow velocities of 5.0 and 7.0 m/s are examined. For comparison purposes, in addition to the developed generator, tests are also performed for a free jet as well as…
In this work, methods for the evaluation of LES-quality and LES-accuracy are presented, which include the Lyapunov exponent for the analysis of short-time predictability of LES-calculation and the Wasserstein metric for the quantitative assessment of simulation results. Both methods are derived and evaluated in application to the Volvo test case. Both the non-reacting and reacting cases are calculated. For the non- reacting cases, good agreement with the experimental data is achieved by solvers at high numerical resolution. The reacting cases are more challenging due to the small length scale …
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. The operator splitting is based on the Simpler balanced splitting method, which is constructed with improved stability properties and reduced computational cost. The method is shown to be capable of stable and accurate prediction of ignition and extinction for reaction-diffusion systems near critical conditions. The ROK4E scheme is desig…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters (Turbulent Combustion, 2000) and based on work by Corrsin (JFM, vol. 11, p.407-416) beyond single-component transport phenomena and involving nonlinear reaction…
Turbulent mixing is a physical process of fundamental importance in high-speed premixed flames. This mixing results in enhanced transport of temperature and chemical scalars, leading to potentially large changes in flame structure and dynamics. To understand turbulent mixing in non-reacting flows, a number of classical theories have been proposed to describe the scaling and statistics of dispersing fluid particle pairs, including predictions of the effective, or turbulent, eddy diffusivity. Here we examine the validity of these classical theories through the study of fluid particle pair disper…
A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；Computational Science Center, National Renewable Energy Laboratory（美国国家可再生能源实验室计算科学中心）
Accurate simulations of high-pressure transcritical fuel sprays are essential for the design and optimization of next-generation gas turbines, internal combustion engines, and liquid propellant rocket engines. Most important and challenging is the accurate modelling of complex real-gas effects in high-pressure environments, especially the hybrid subcritical-to-supercritical mode of evaporation during the mixing of fuel and oxidizer. In this paper, we present a novel modeling framework for high-fidelity simulations of reacting and non-reacting transcritical fuel sprays. In this method, the high…
This paper experimentally analyzes the simultaneous influence of heat release and coherent vortex structures on the transfer of kinetic energy across scales around the laminar flame thickness $δ^0_\mathrm{L}$ in a turbulent premixed swirl flame and a non-reacting swirl flow. High-resolution tomographic particle image velocimetry and formaldehyde planar laser induced fluorescence measurements are used to obtain 3D velocity fields and estimates of the progress variable and density fields. The kinetic energy transfer across a filter scale of $Δ= 1.5 δ^0_\mathrm{L}$ was then quantified using physi…
Nonpremixed turbulent reacting flows are intrinsically difficult to model due to the strong coupling between turbulent motions and reaction. The large amount of heat released by a typical hydrocarbon flame leads to significant modifications of the thermodynamic variables and the molecular transport coefficients and thus alters the fluid dynamics. Additionally, in nonpremixed combustion, the flame has a complex spatial structure. Localized expansions and contractions occur, enhancing the dilatational motions. Therefore, the compressibility of the flow and the heat release are intimately related…
This study performs a linear analysis of a turbulent reacting methane-air jet flame, with the goal of predicting the response of the reacting flow to upstream acoustic actuation. Accounting for heat release fluctuations is a vital component when investigating thermoacoustic instabilities and flame noise in a linearized framework. Unlike previous studies this work develops and applies an active flame approach, meaning the heat release oscillations of the flame resulting from the acoustic fluctuations are taken into account. To yield an active flame approach in the linear framework, a combustion…
Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct…
Université Libre de Bruxelles（布鲁塞尔自由大学（法语区））；École polytechnique de Bruxelles（布鲁塞尔理工学院）；Vrije Universiteit Brussel（布鲁塞尔自由大学（荷兰语区））；Politecnico di Milano（米兰理工大学）
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and computer models. The performance of these tools is enhanced if all the prior knowledge and the physical constraints are embodied. In other words, the scientific method must be adapted to bring machine learning into the picture, and make the best use of the massive amount of data we have produced, thanks to the advances in numerical computing. The present chapte…
The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremel…
We propose a predictive model of the turbulent burning velocity $S_T$ in homogeneous isotropic turbulence (HIT) based on Lagrangian statistics of propagating surfaces. The propagating surfaces with a constant displacement speed are initially arranged on a plane, and they evolve in non-reacting HIT, behaving like the propagation of a planar premixed flame front. The universal constants in the model of $S_T$ characterize the enhancement of area growth of premixed flames by turbulence, and they are determined by Lagrangian statistics of propagating surfaces. The flame area is then modelled by the…
We develop predictive formulas for friction resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress nonuniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes as triangles and regular polygons. The analysis also suggests that a new effective diameter should be used in more general cases, yielding corrections of a few percent to friction estimates based on the traditional hydraulic diameter. Fair but consistent predictive improvement is shown for du…
(Abridged) A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully-resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damköhler numbers Da = 0.1-6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. 1) Turbulent flame speed develops pulsations with the …
We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of the convective terms in the Navier-Stokes equations relies on a robust energy-preserving numerical flux, and numerical diffusion inherited from the AUSM scheme is added limited to the vicinity of shock waves, or wherever spurious numerical oscillations are sensed. The solver is capable of conserving the total kinetic energy in the inviscid limit, and it bears…
This paper describes the numerical simulation of the NASA Langley Research Center supersonic H2 -Air combustion chamber performed using two approaches to model the presumed probability density function (PDF) in the flamelet progress variable (FPV) framework. The first one is a standard FPV model, built presuming the functional shape of the PDFs of the mixture fraction, Z, and of the progress parameter, Λ. In order to enhance the prediction capabilities of such a model in high-speed reacting flows, a second approach is proposed employing the statistically most likely distribution (SMLD) techcni…
A joint experimental and numerical investigation of turbulent flame front anchoring at externally heated walls is presented. The phenomenon is examined for lean hydrogen/air mixtures in a novel burner design, which comprises a cylindrical burning chamber converging into a glass pipe as well as a wall heating assembly at their intersection. The transparent part allows for optical OH* chemiluminescence measurements serving as a basis for numerical validation. For a comprehensive numerical evaluation the effect of heat loss on different hydrogen/air chemical reaction mechanisms is reviewed in a p…
Distributed combustion, often associated with the low-oxygen condition, offers ultra-low NOX emission. However, it was recently achieved without combustion air dilution or internal flue gas recirculation, using a distinct approach called Mixture Temperature-Controlled combustion. Here, the fuel-air stream is cooled at the inlet to delay ignition and hence foster homogeneous mixture formation. The aim of this numerical study aims to understand the operation of this combustion concept better and present a robust framework for distributed combustion modeling in a parameter range where such operat…
The present work reports on LES of turbulent reacting flow of the Delft-Jet-in-Hot-Coflow (DJHC) burner, emulating MILD combustion, with transported PDF based combustion models using ANSYS FLUENT 13.0. Two different eddy viscosity models for LES (Dynamic Smagorinsky and Kinetic Energy Transport) along with two solution approaches for PDF transport equation, i.e. Eulerian and Lagrangian, have been used in the present study. Moreover, the effects of chemical kinetics and the micro-mixing models have also been investigated for two different fuel jet Reynolds number (Re = 4,100 and Re = 8,800). Th…
Presumed probability density function (PDF) and transported PDF methods are commonly applied to model the turbulence chemistry interaction in turbulent reacting flows. However, little focus has been given to the turbulence chemistry interaction PDF closure for flame-wall interaction. In this study, a quasi-DNS of a turbulent premixed, stoichiometric methane-air flame ignited in a fully developed turbulent channel flow undergoing side-wall quenching is investigated. The objective of this study is twofold. First, the joint PDF of the progress variable and enthalpy that needs to be accounted for …
Flamelet Progress Variable (FPV) combustion models allow the evaluation of all thermo chemical quantities in a reacting flow by computing only the mixture fraction Z and a progress variable C. When using such a method to predict a turbulent combustion in conjunction with a turbulence model, a probability density function (PDF) is required to evaluate statistical averages (e.g., Favre average) of chemical quantities. The choice of the PDF is a compromise between computational costs and accuracy level. The aim of this paper is to investigate the influence of the PDF choice and its modeling aspec…
Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the bou…
We investigate and model pressure effects on the turbulent burning velocity over a wide range of pressures and turbulence intensities with the direct numerical simulation (DNS) of statistically planar turbulent premixed flames for lean hydrogen/air mixture. DNS results indicate that the stretch factor has an impact on the turbulent burning velocity and flame surface area at elevated pressures. In particular, the enhanced stretch factor at high pressures increases the ratio of turbulent and laminar burning velocities, diminishing the "bending" effect. Based on a good consistency between turbule…
Direct numerical simulations (DNS) of turbulent channel flows up to $Re_τ \approx 1000$ are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber-frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber-frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping…
The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic reconstruction against experimental data. The method is derived and generalized for turbulent reacting flows, and applied to validation tests involving the Sydney piloted jet flame. It is shown that the Wasserstein metric is an effective validation tool that extends to multiple scalar quantities, providing an objective and quantitative evaluation of model deficien…
