Matthias Ihme

Modeling of radiation and nitric oxide formation in turbulent nonpremixed flames using a flamelet/progress variable formulation

A model for the prediction of the nitric oxide (NO) formation in turbulent nonpremixed flames is proposed. Since the NO formation has a strong temperature sensitivity, the accurate prediction of the flame temperature under the consideration of radiative heat losses is required. The first part of the paper addresses the extension of a flamelet-based combustion model to account for radiative heat loss effects by introducing enthalpy as an additional parameter. A transport equation for enthalpy is solved, and the radiative sink term in this equation is obtained from unsteady flamelet solutions. The model is applied to a large-eddy simulation (LES) of Sandia flame D, and the importance of the interaction between turbulence and radiation on temperature and mixture fraction is investigated. Based on the radiative flamelet formulation, a consistent model for the prediction of NO formation is developed in the second part of the paper. In this model, an additional transport equation for the NO mass fraction is sol...

Short Note: Regularization of reaction progress variable for application to flamelet-based combustion models

Many combustion models that are based on the flamelet paradigm employ a reaction progress variable. While such a progress variable is well defined for one-step reaction kinetics, this is typically not the case for complex chemical mechanisms. Consequently, several expressions for a progress variable have been utilized. In this paper a formal method for the generation of a reaction progress variable is proposed that is optimal with respect to a set of constraints. The potential of the method is demonstrated in applications to partially premixed and diffusion flames, and the extension to premixed combustion is discussed. It is shown that the proposed method can lead to significant improvements in the definition of an optimal progress variable over conventional formulations, essentially eliminating the expert knowledge previously required in identifying such quantities.

Reduced-Order Modeling of Turbulent Reacting Flows with Application to Ramjets and Scramjets

DOI: 10.2514/1.50272 A new engine model has been developed for applications requiring run times shorter than a few seconds, such as design optimization or control evaluation. A reduced-order model for mixing and combustion has been developed that is based on nondimensional scaling of turbulent jets in crossflow and tabulated presumed probability distribution function flamelet chemistry. The three-dimensional information from these models is then integrated across cross-sectional planes so that a one-dimensional profile of the reaction rate of each species can be established. Finally, the one-dimensional conservation equations are integrated along the downstream axial direction and the longitudinal evolution of the flow can be computed. The reduced-order model accurately simulates real-gas effects such as dissociation, recombination, and finite rate chemistry for geometries for which the main flow is nearly onedimensional. Thus, this approach may be applied to any flowpath in which this is the case; ramjets, scramjets, and rockets are good candidates. Comparisons to computational fluid dynamics solutions and experimental data were conducted to determine the validity of this approach. I. Introduction T HIS work addresses the need for an improved control-oriented model of a dual-mode ramjet/scramjet propulsion system. Improvements are needed to include more realistic estimates of the losses of the propulsion efficiency due to shock wave interactions in the inlet, as well as due to gas dissociation and incomplete combustion in the combustor section. One problem is that previous lowerorder propulsion models [1–3] do not include the losses due to multiple shock interactions, gas dissociation, and incomplete combustioncausedby finiteratechemistry.Thisisaseriousproblem, because the main advantage of ascramjet engine over a ramjet isthat the scramjet reduces losses due to internal shock waves and gas dissociation [4]. That is, the scramjet eliminates the need for strong internalshockwavestodeceleratethegastosubsonicconditionsand maintains lower static temperatures than a ramjet, which reduces the dissociation losses. The present effort addresses previous shortcomings by including both of these types of losses into a code called MASIV. MASIV consists of several reduced-order models (ROMs). One is an inlet ROM that computes losses due to multiple shock/ expansion wave interactions; this ROM is described elsewhere [5]. The other is a fuel/air mixing/combustion ROM that is the focus of the present paper. MASIV has been incorporated into a larger hypersonic vehicle (HSV) code, which is available without charge and without International Traffic in Arms Regulations restrictions. Sincecomputational fluiddynamics(CFD)codestakemanyhours to reach solutions for reacting flows, they are difficult to apply to problems in which a large number of solutions are required. A tool that can solve these configurations in a short time to acceptable accuracyishighlydesirableforcontrolanddesignapplications,such

An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows

Abstract A finite-volume method is developed for simulating the mixing of turbulent flows at transcritical conditions. Spurious pressure oscillations associated with fully conservative formulations are addressed by extending a double-flux model to real-fluid equations of state. An entropy-stable formulation that combines high-order non-dissipative and low-order dissipative finite-volume schemes is proposed to preserve the physical realizability of numerical solutions across large density gradients. Convexity conditions and constraints on the application of the cubic state equation to transcritical flows are investigated, and conservation properties relevant to the double-flux model are examined. The resulting method is applied to a series of test cases to demonstrate the capability in simulations of problems that are relevant for multi-species transcritical real-fluid flows.

An Unsteady/Flamelet Progress Variable Method for LES of Nonpremixed Turbulent Combustion

An unsteady flamelet/progress variable model has been developed and formulated as an extension of the steady flamelet/progress variable model. For this model, a large number of unsteady laminar flamelet simulations is performed for various conditions, and solutions are recorded as function of time. From this, a flamelet library is generated, which provides the filtered quantities of all scalar values as function of the filtered mixture fraction, the mixture fraction sub-filter variance, the filtered reaction progress variable, and the filtered scalar dissipation rate. The model has been implemented in an LES code. Simulations have been performed for a confined swirl burner using the unsteady flamelet/progress variable model. The results are compared with experimental data for velocities and velocity fluctuations, temperature, CO2, and CO mole fractions. The results agree reasonably well with the experiments for all quantities. In particular, CO is predicted with good accuracy.

Large Eddy Simulation of Shear Coaxial Rocket Injector: Real Fluid Effects

The implementation and verification of real-fluid effects towards the high-fidelity large eddy simulation of rocket combustors is reported. The non-ideal fluid behavior is modeled using a cubic Peng-Robinson equation of state; a thermodynamically consistent approach is used to convert conserved into primitive variables. The viscosity is estimated by Chung et al.’s method in the supercritical gas phase. In the transcritical liquid phase, a simple, accurate and efficient method to estimate the viscosity as a function of temperature and pressure is proposed. The highly non-linear coupling of the primitive thermodynamic variables requires special consideration in regions of high-density gradients to avoid spurious numerical oscillations. The characterization of the non-linearity of the equation of state identifies the regions of high sensitivity. In these regions, small relative changes in the pressure lead to significant changes in density and/or temperature, therefore, numerical instabilities tend to be amplified in these regions. To avoid non-physical oscillations, a first-order and second-order essentially non-oscillatory (ENO) schemes are locally applied to the flux computation on the faces identified with a dual-threshold relative density sensor. The evaluation of the sensor and capabilities of the non-oscillatory schemes on canonical test cases are presented. Finally, these schemes are used to model two canonical cases.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock–fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

Generation of optimal artificial neural networks using a pattern search algorithm: Application to approximation of chemical systems

A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization. When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function, and the connectivity among neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrates equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully connected feedforward network having four nonlinear hidden layers and 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 500 grid point discretization of the parameter space.

Analysis of Different Sound Source Formulations to Simulate Combustion Generated Noise Using a Hybrid LES/APE-RF Method

Combustion noise and sound source mechanisms of the DLR-A flame are investigated. A hybrid large-eddy simulation/computational aeracoustics (LES/CAA) approach is employed. In the first step of the hybrid analysis the flamelet/progress variable (FPV) model is employed as combustion model followed by the acoustic simulation in the second step using the acoustic perturbation equations for reacting flows (APE-RF). The flamelet/progress variable database has been extended in terms of acoustic source terms. The analysis of the acoustic field of low MACH number reacting flows induced by the thermoacoustic sources such as the unsteady heat release leads to a very stiff problem formulation, since the related sources require highly resolved regions in the source area, which restricts the possible time step. To simulate combustion generated noise using such a hybrid approach, a suitable source description has to be used, which preferably satisfies two requirements, i.e, to efficiently and accurately predict the generated sound field, while the source term can be easily evaluated from the LES. Using the source term, which is expressed via the scaled partial time derivative of the density, the acoustic field can be reproduced best up to a maximum Strouhal number of StD = 2. However, this source formulation requires a rigorous constraint at the interface of the hybrid approach to avoid spurious noise due to artificial acceleration caused by interpolation. To be more precise, the convection speed of density inhomogeneities has to be preserved during interpolation. A compromise between efficiency and accuracy can be achieved using the source formulation expressed via the scaled material derivative of the density, since by definition this formulation does not describe the convection of density inhomogeneities.

On the Generation of Direct Combustion Noise in Turbulent Non-Premixed Flames

Generation of combustion noise in an unconfined turbulent non-premixed flame is investigated. For this, a model is developed, combining Lighthills acoustic analogy with a flamelet-based combustion model to consistently express all thermochemical quantities by a set of reduced scalars. The model is applied in a large-eddy simulation, and the acoustic pressure in the far field is obtained from an integral solution. Three relevant acoustic source terms with different source characteristics and Mach number scaling are identified. The spatial distribution and spectral characteristics of the acoustic sources are analyzed, and it is shown that the acoustic source due to chemical reaction is the main noise contributor, and is located in the upper part of the flame. Contributions from the acoustic sources due to Reynolds stresses and fluctuating mass flux are found to be virtually insignificant at low frequencies. Discrepancies in the prediction of high-frequency sound pressure level in the jet forward direction were analyzed and are attributed to high-frequency acoustic refraction effects due to variations in sound speed. The directivity exhibits a weak directionality in the 30° forward direction, and some phase cancellation between individual acoustic sources is evident.