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Methods of Numerical Integration

Combustion is a reactive oxidation process that releases energy bound in chemical compounds used as fuels─energy that is needed for power generation, transportation, heating, and industrial purposes. Because of greenhouse gas and local pollutant emissions associated with fossil fuels, combustion science and applications are challenged to abandon conventional pathways and to adapt toward the demand of future carbon neutrality. For the design of efficient, low-emission processes, understanding the details of the relevant chemical transformations is essential. Comprehensive knowledge gained from decades of fossil-fuel combustion research includes general principles for establishing and validating reaction mechanisms and process models, relying on both theory and experiments with a suite of analytic monitoring and sensing techniques. Such knowledge can be advantageously applied and extended to configure, analyze, and control new systems using different, nonfossil, potentially zero-carbon fuels. Understanding the impact of combustion and its links with chemistry needs some background. The introduction therefore combines information on exemplary cultural and technological achievements using combustion and on nature and effects of combustion emissions. Subsequently, the methodology of combustion chemistry research is described. A major part is devoted to fuels, followed by a discussion of selected combustion applications, illustrating the chemical information needed for the future.

Combustion, Chemistry, and Carbon Neutrality.

While the accuracy of chemical kinetic mechanisms continues to improve, these mechanisms are still models with, sometimes considerable, uncertainty. In order to rigorously validate turbulent combustion simulations against experimental data, this uncertainty must be separated from deficiencies in the turbulent combustion model itself. In this work, a method is developed for quantifying the uncertainty in turbulent flame simulations due to input uncertainty in the chemical mechanism. Here the method is developed for Large Eddy Simulation (LES) combined with a steady flamelet model. Rather than a brute force probabilistic approach in which hundreds or thousands of LES runs are required to compute statistics of outputs of interest, the method takes advantage of the actual algorithm employed with the steady flamelet model. First, the high-dimensional uncertainty in the chemical kinetics is propagated through the flamelet equations, and the resulting lower-dimensional joint distribution of the temperature, species mass fractions, and other derived quantities is used as a stochastic equation of state in the LES. Since only a few “active” quantities are needed to evolve the LES governing equations, efficient non-intrusive stochastic collocation is used to propagate the uncertainty in the density, requiring only a few LES runs. This process captures the uncertainty in the flow field induced by the uncertainty in the chemical kinetic rates. The remaining uncertainty in “passive” quantities, that is, quantities needed only for post-processing such as the temperature and species mass fractions, is computed with random sampling during the LES runs. The uncertainty quantification algorithm is demonstrated with Sandia flame D, and it is shown that the uncertainty in the simulation results caused by uncertainties in the kinetic rates is sufficiently large to account for the discrepancies with the experimental measurements. The implication is that the turbulent combustion model cannot be fairly assessed with such a large uncertainty.

Chemical kinetic uncertainty quantification for large eddy simulation of turbulent nonpremixed combustion

Non-Intrusive Uncertainty Quantification in the simulation of turbulent spray combustion using Polynomial Chaos Expansion: A case study

pdf/an-implicit-high-order-k-exact-finite-volume-approach-on-3ee251xv1q.pdf

An implicit high-order k-exact finite-volume approach on vertex-centered unstructured grids for incompressible flows

Large Eddy Simulation of Turbulent Ethanol Spray Flames under MILD conditions using a Finite Rate Chemistry Combustion Model


 Computational Fluid Dynamics are widely used as a design tool for a variety of thermo-fluid systems. Advantages of those numerical approaches are clearly the fairly detailed degree of valuable data at low computational costs, when RANS (Reynolds Averaged Navier Stokes) methods are used in the system design process.
 In this work, a combustion system operated at elevated pressure conditions is re-designed with CFD RANS methods. The combustor is operated with liquid fuel and is positioned between an upstream recuperation and a downstream turbine section. System design is carried out on the basis of a commercially available C30 configuration from the Capstone® Turbine Corporation. The micro turbine produces 30kW of electrical power and is therefore highly suited for micro gas turbine related applications.
 In the design process, as presented in the paper, several modifications are carried out. The system recuperation is changed, thus inflow modifications are given. Recuperation was explicitly simulated and is used as a combustor inflow boundary condition. The system is then analyzed and modified in terms of air splits in order to achieve certain combustion characteristics. Optimization is carried out for combustor air splits and turbine inlet temperature profile conditions are significantly improved. Reacting multi-phase simulations are used in order to characterize flow field and combustion. Further on, conjugated heat transfer is taken into account in order to characterize temperature distribution in the combustor. Additionally, combustor residence times are determined. It is demonstrated that the pursued methods and procedures are computationally cheap but at the same time highly suited and sufficient for thorough combustion system development.

A Re-Design Study Based on a High Pressure Cyclonic Combustor Operated With Liquid Fuel

\n As an alternative to the commonly used swirl burners in micro gas turbines (MGT), the FLOX®-based combustion concept promises great potential for the nitric oxide emission reduction and increased fuel flexibility. Previous research on FLOX®-based MGT combustors mainly addressed gaseous fuels and there is limited knowledge available on liquid fuel FLOX®-based MGT combustors. Despite having to deal with a new set of challenges while utilizing liquid fuel in the burner, first steps are taken to gain more information on the influencing operational parameters. In this regard, a FLOX®-based liquid fuel burner is developed to fit into a newly designed combustor for the Capstone C30 MGT. The C30 combustor operates with three burners arranged tangentially to an annular combustion chamber and provides a total thermal power of 115 kW. In this work, operational properties of merely one of the three C30 liquid fuel burners are investigated and the rest of the two burners are emulated in form of hot cross–flow. As for the liquid burners, the experiments are conducted with three geometrically different single–nozzle burners at atmospheric pressure. The studied FLOX®-based burners consist of an air nozzle with a coaxially arranged fuel pressure atomizer. The cross–flow is realized by utilizing a 20–nozzle FLOX®-based natural gas combustor. Measurements include visualization of the reaction zone and analysis of the exhaust gas emissions. By detecting the hydroxyl radical chemiluminescence (OH*-CL) emissions, the position of the heat release zone within the combustion chamber is attained. Correspondingly, the flame height above burner and the flame length are calculated. The investigated design parameters include air preheat temperature up to 733 K, equivalence ratio, burner geometry, and thermal power. The work presented in this paper aims to deepen the understanding of the design parameter interactions involved within the single–nozzle liquid–FLOX®-based burners. The cross–flow is set at a constant operating point to take the influence of the circulating hot gases on the flame into account. Through variation of thermal power the effect of liquid fuel preparation, i.e., atomization, evaporation, and mixing on combustion properties and exhaust gas emissions are examined. Analyses of measurements of different burner configurations are shown. The results show that the burners with the medium diameter consistently performed remarkably at different flame temperatures and thermal powers. The lowest NOx and CO emissions for the medium diameter burner lied between 5–7 ppm and 8–10 ppm, respectively. The collected data sets can be used for the validation of numerical simulations as well.

Experimental Investigation of the Combustion Behavior of Single-Nozzle Liquid-FLOX®-Based Burners on an Atmospheric Test Rig

Non-intrusive uncertainty quantification methods mostly rely on space filling sampling of the simulation model over the parameter space of input uncertainties. However, this direct sampling approach is costly for complex applications such as reacting multiphase flows or spray combustion due to the high computational demand. A common strategy is therefore the approximation of the high fidelity simulation via a suitable surrogate model. Thus, only sparse sampling of the actual simulation model over the considered parameter space is required for the generation of surrogate model training data. This paper examines the feasibility of different methods for the construction of surrogate models for spray combustion applications with a high dimension of input parameters and multiple output Quantities of Interest (QoI). Therefore, the Delft Spray in Hot Coflow flame is investigated by means of reacting multiphase simulations. In this testcase, main input uncertainties arise from the specification of a spray boundary condition replacing the need to model the primary atomization of the fuel injector. Radial profiles of temperature over the flame zone are considered as QoIs. Different sampling methods such as Central Composite Design (CCD), Latin Hypercube Sampling (LHS) and a low discrepancy Sobol sequence are used for the derivation of surrogate model training data. A second order polynomial approximation, Multivariate Adaptive Regression Splines (MARS) and Gaussian Process based Kriging (GP) are selected as surrogate models. The effect of combined sampling strategy and choice of surrogate model on surrogate model quality is determined through local and global cross validation as well as hold out validation against additional simulation data. An efficient and reliable approach is found in the combination of Sobol sequence sampling plan and GP surrogate model. Finally, the application of the constructed surrogate models in an uncertainty quantification of the testcase considered is demonstrated.

/pdf/towards-affordable-uncertainty-quantification-in-the-5896buiytv.pdf

Towards affordable Uncertainty Quantification in the Simulation of Turbulent Spray Combustion via Surrogate Modeling

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