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In this paper, asymptotic multiple-scale methods are used to formulate a mathematically consistent set of thermo-acoustic equations in the low-Mach number limit for linear stability analysis. The resulting sets of nonlinear equations for hydrodynamics and acoustics are two-way coupled. The coupling strength depends on which multiple scales are used. The double-time-double-space (2T-2S), double-time-single-space (2T-1S) and single-time-double-space (1T-2S) limits are revisited, derived and linearized. It is shown that only the 1T-2S limit produces a two-way coupled linearized system. Therefore this limit is adopted and implemented in a finite-element solver. The methodology is applied to a coaxial jet combustor. By using an adjoint method and introducing the intrinsic sensitivity, (i) the interaction between the acoustic and hydrodynamic subsystems is calculated and (ii) the role of the global acceleration term, which is the coupling term from the acoustics to the hydrodynamics, is analyzed. For the confined coaxial jet diffusion flame studied here, (i) the growth rate of the thermo-acoustic oscillations is found to be more sensitive to small changes in the hydrodynamic field around the flame and (ii) increasing the global acceleration term is found to be stabilizing in agreement with the Rayleigh Criterion.

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Knock is a major bottleneck to achieving higher thermal efficiency in spark-ignited (SI) engines. The overall tendency to knock is highly dependent on fuel anti-knock quality as well as engine operating conditions. It is, therefore, critical to gain a better understanding of fuel-engine interactions in order to develop robust knock mitigation strategies. In the present work, a numerical model based on three-dimensional (3-D) computational fluid dynamics (CFD) was developed to capture knock in a Cooperative Fuel Research (CFR) engine. For combustion modeling, a hybrid approach incorporating the G-equation model to track turbulent flame propagation, and a homogeneous reactor multizone model to predict end-gas auto-ignition ahead of the flame front and post-flame oxidation in the burned zone, was employed. In addition, a novel methodology was implemented wherein a laminar flame speed lookup table generated a priori from a chemical kinetic mechanism could be used to provide flame speed as an input to the G-equation model, instead of using conventional empirical correlations. Multi-cycle Reynolds-Averaged Navier Stokes (RANS) simulations were performed for two different spark timings (STs) corresponding to non-knocking and knocking conditions, with other operating conditions kept the same as those of a standard Research Octane Number (RON) test. Iso-octane was considered as the fuel for the numerical study. Two different reduced kinetic mechanisms were employed to describe end-gas auto-ignition chemistry and to generate the flame speed lookup table. Experimental data, including intake/exhaust boundary conditions, was provided by a spark timing sweep study conducted in an in-house CFR engine. Moreover, cylinder wall/valve/port surface temperatures and residual gas fraction (RGF) were estimated using a well-calibrated onedimensional (1-D) model. On the other hand, a novel methodology was also developed to analyze experimental data for the knocking case and identify the most representative cycle. For the non-knocking case, a good agreement was found between experiment and CFD simulation, with respect to cycle-averaged values of 10% burn point (CA10), 50% burn point (CA50) and peak pressure magnitude/location. The virtual CFR engine model was also demonstrated to be capable of predicting average knock characteristics for the knocking case, such as knock point, knock intensity and energy of resonance, with good accuracy.

The selection of an appropriate combustion model for the numerical prediction of reacting flows remains an outstanding issue. Often, expert knowledge or experimental data is required to make an informed decision in selecting a suitable model. Furthermore, the computational cost that is associated with the application of certain combustion models introduces another constraint in the selection process. By addressing these issues, the objective of this work is to develop a Pareto-efficient combustion (PEC) framework for application to complex chemically reacting flows under consideration of user-specific input about quantities of interest, desired simulation accuracy and computational cost, and a set of combustion models. PEC utilizes a Pareto efficiency, and introduces a manifold drift term as a measure for determining the adequacy of using a certain combustion-manifold model to predict selected quantities of interest. Since underlying model assumptions are encoded in the manifold, PEC restricts the application of submodels within its intended use. Further, the proposed approach for evaluating the manifold drift provides a rigorous method for combining different combustion models-as long as they can be described by a manifold. As such, this formulation represents a general description for the selection of combustion models, thereby overcoming potential limitations of flame-topology indicators and regime-specific combustion models. The capability of the PEC-framework is demonstrated in application to a tribrachial flame. By considering combustion models from the class of reaction-transport manifolds (inert mixing, equilibrium, flamelet/progress variable, and flame-prolongation in ILDM) and chemistry manifolds (using detailed and skeletal mechanisms), it is shown that PEC locally adapts the submodel fidelity within the user-defined threshold for selected quantities of interest. A parametric analysis is conducted to illustrate the dynamic range of the PEC-framework in accommodating Pareto-efficient submodel arrangements.

I. Introduction The current design of gas-turbine (GT) systems is driven by the need for increased powerdensities, improved fuel-efficiencies, and reduced life cycle costs and environmental impact. Computational techniques have the potential for providing valuable information for the design of GT combustion systems, if adequate models are available. Over recent years, remarkable progress has been made in the development of high-fidelity combustion models and numerical techniques for turbulent reacting flows. In particular, the LES technique has been demonstrated to provide considerably improved predictions for scalar mixing processes compared to Reynolds-averaged Navier-Stokes (RANS) approaches. This improved predictive capability is attributed to the fact that in LES the energy-containing and large-scale coherent structures are fully resolved, and only effects of numerically unresolved turbulent scales require modeling. These small scales, however, are more homogeneous so that more universal closure models can be utilized. Over recent years, different LES combustion models have been developed, including level-set formulations, 1-7 conditional moment closure models, 8-12 thickened flamelet models, 13-15 transported PDF methods, 16-18 and flamelet-based combustion models. 19-24 However, these models have been largely developed and validated in the context of canonical and geometrically unconfined flame-configurations, such as jetflames or simple dump-combustors. Furthermore, LES-calculations in complex burner-configuration that are relevant to realistic gas-turbine combustor and operating conditions have so far not been fully utilized. This shortcoming can be attributed to the following reasons: (i) Absence of highfidelity computational models that can accurately describe the turbulent combustion processes and coupling between turbulence, reaction chemistry, and scalar mixing; (ii) Lack of experimental data to enable comprehensive model-validation; (iii) Geometric complexity and construction of geometry-conform meshes for complex combustor geometries; (iv) Highly transient combustion regime, topologic asymmetry, and flow-field sensitivity and solution-dependence on grid-resolution and numerical accuracy; and (v) Computational complexity and necessary requirements for accurately resolving relevant spatio-temporal scales. Apart from very few exceptions, LES-calculations of gas-turbine combustors have so far been performed under drastically simplified conditions, limited or no comparison with experimental data, and by employing significant simplifications in the description of the combustion model (i.e., utilizing one-step reaction chemistry, ambient operating conditions, and restriction to gaseous fuel combustion).