Yee Chee See

An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods

This manuscript is concerned with the detection of shock discontinuities in the solution of conservation laws for high-order discontinuous Galerkin methods. A shock detector based on the entropy residual is proposed to distinguish smooth and non-smooth parts of the solution. The numerical analysis shows that the proposed entropy residual converges if the true solution is smooth and sufficiently regularized in space and time. To precisely localize discontinuities of different natures, an approach is developed that dynamically sets the threshold on the detection function, such that the detection criterion retains its sensitivity to the characteristics of the local solution. The implementation is conducted in an entropy-bounded discontinuous Galerkin framework, and numerical tests confirm the convergence property of the entropy-residual formulation and the effectiveness of the thresholding procedure. This shock detector is combined with an artificial viscosity scheme for shock stabilization. Comparison with other detectors is performed to demonstrate the excellent performance of the entropy-residual based shock detector for a wide range of problems on regular and triangular grids.

Large-Eddy Simulation of a Turbulent Lifted Flame in a Vitiated Co-Flow

Large-eddy simulation (LES) of a lifted flame in a vitiated co-flow has been performed using an unsteady flamelet/progress variable (UFPV) model. This model is an extension to the steady flamelet/progress variable approach, and describes the transient autoignition process of the lifted flame through the unsteady flamelet model. The particular advantage of this model is that it eliminates the flamelet time scale, and all thermochemical quantities are parameterized by mixture fraction, reaction progress parameter, and stoichiometric scalar dissipation rate. For application to LES, a presumed probability density function closure is employed, in which a beta-distribution is used for the mixture fraction, a statistically most-likely distribution is employed for the reaction progress parameter, and the distribution of the stoichiometric scalar dissipation rate is modeled by a Dirac delta function. Compared to the steady flamelet/progress variable model, predictions from the UFPV model show significant improvements, and the spatial evolution of the flame ignition process and lift-off height is in good agreement with experimental data. Flow field structure, statistical results, and scatter data are compared with experimental data, and potential improvements of the model are discussed.

LES Investigation of Flow Field Sensitivity in a Gas Turbine Model Combustor

Large eddy simulation (LES) is a computational method that has the potential to enable the prediction of turbulent reacting flows in gas turbine combustors. However, flows in these complex combustor environments represent modeling challenges. Specifically, the vortex breakdown dynamics of swirling flows exhibit sensitivities to upstream and downstream conditions. Compounded by this is the added complexity of modern combustors, feature several geometrically-complex swirl generators. In the present work, a mesh sensitivity study is performed by considering a dual swirl gas turbine model combustor, which is studied at non-reacting flows conditions. By utilizing pure hexahedral meshes in the LES calculations, we are able to obtain results that show both grid convergence and agreement with experimental measurements. However, we also find that LES predictions of the flow field in this combustor can be highly dependent on the mesh type utilized for the simulations. Mesh refinement in crucial regions of the combustor was found to be insufficient to improve the simulation accuracy, and may – under certain circumstances – even worsen the modeling results. A parametric investigation of the mass flow rate split between the two swirlers only leads to the identification of a partial cause, which could be attributed to the presence of a subcritical bifurcation in the flow-field behavior.

Jet Noise Receptivity to Nozzle-upstream Perturbations in Compressible Heated Jets

E ects of nozzle-upstream entropy perturbations on the acoustic radiation from heated jets are investigated. For this, a model problem is considered, in which a gas-turbine combustor discharges reaction products through a converging nozzle into the ambient environment. The turbulent reacting ow eld in the combustor is computed using large-eddy simulation (LES), and the unsteady oweld at the combustor exit is extracted to provide realistic in ow conditions to the jetow simulation. To study the indirect coupling process, arising from the interaction of the combustion-generated entropy uctuations with the adverse pressure gradient through the nozzle, a linearized Euler formulation is employed. Parametric studies are performed to investigate e ects of frequency and amplitude of the nozzle-upstream entropy perturbations on the jet instability and the jet noise directivity. Simulation results show that the directivity is dependent on the perturbation frequency. Excitation near the preferred shear-layer instability leads to strong acoustic radiation in the 45 forward direction, and the radiation angle decreases with decreasing excitation frequency.

A general and robust high-order numerical framework for shock-capturing: entropy-bounding, shock detection and artificial viscosity

A high-order shock-capturing framework is presented, that includes three key components, namely entropybounding, shock detection and artificial viscosity. The discontinuous Galerkin scheme is used to provide the discretization foundation, although the entire methodology is applicable to any discontinuous scheme. In this framework, entropy-bounding guarantees the numerical robustness by completely avoiding the appearance of non-physical quantities. An entropy-residual based shock detector is developed, which is able to accurately locate discontinuities. Building on the first two components, artificial viscosity is introduced locally to reduce spurious oscillations. By conducting Fourier analysis, a algebraic relation for the artificial viscosity is derived, which is linked to the eigen-spetrum of the numerical discretization. The resulting numerical framework offers a good balance between shock-capturing and computational efficiency for explicit time integration. Several test cases are conducted to confirm the benefits of using this method.

Large-Eddy Simulation of a Gas Turbine Model Combustor

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, conditional moment closure models, thickened flamelet models, transported PDF methods, and flamelet-based combustion models. 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).

A Fidelity Adaptive Modeling Framework for Combustion Systems Based on Model Trust-Region

In numerical predictions of turbulent reacting flows, the selection of a particular combustion model remains an area where there is no well-established systematic procedures. Often, expert knowledge and even experimental measurements are required to make an informed decision on the particular choice of a combustion model. Furthermore, the computational cost that is associated with a combustion model is another constraint in the selection process. To date, there has yet to be a general high fidelity combustion model that is computationally tractable for a large class of realistic combustion devices. In this work, a fidelity adaptive modeling (FAM) framework for combustion problems is developed to alleviate some of these issues. With minimal user input, this modeling framework is designed to automatically utilize the most appropriate combustion model locally in reacting flow simulations. This framework is demonstrated in an application to steady tribrachial flame, representing a challenging test case to single-regime reaction-diffusion manifold models. By utilizing reaction-diffusion manifold models in regions where they are accurate for a user-defined threshold, simulations with the FAM approach are able to reproduce results comparable to the detailed chemistry simulation. ∗Research Assistant, Center for Turbulence Research, Stanford University, AIAA Member. †Research Assistant, Flow Physics and Computational Engineering, Stanford University, AIAA Member. ‡Professor, Center for Turbulence Research, Stanford University, AIAA Member.

Linear Stability Analysis of a Non-premixed Buoyant Jet Flame

Non-premixed combustion systems are susceptible to hydrodynamic and diusivethermal instabilities. These instabilities are of practical interest as they can assist in enhancing scalar mixing and turbulent transition. Linear stability theory has been used in the past to characterize the response of non-premixed ames to per

LES Modeling of a Turbulent Lifted Flame in a Vitiated Co-flow Using an Unsteady Flamelet/Progress Variable Formulation

In this work, an unsteady flamelet/progress variable (UFPV) model is applied in large-eddy simulation of a lifted methane/air flame in a vitiated co-flow. In this burner configuration, the flame is stabilized by autoignition. This ignition mode is of particular relevance to a number of practical applications, including furnaces, internal combustion engines, and flame stabilization in augmentors.

Characterization and Sensitivity Analysis of a Turbulent Diffusion Flame in Diluted Hot Coflow

Large-eddy simulation of a jet flame in a hot diluted coflow has been performed. The burner under consideration was operated in the moderate and intense low oxygen dilution (MILD) combustion regime, and utilizes a three-stream feed system to supply fuel, diluted coflow, and air to the burner (Dally, B. B., Karpetis, A. N., and Barlow, R. S., Proc. Combust. Inst., Vol. 29, 2002, pp. 1147–1154). The reduced oxygen concentration in the coflow decreases the reactivity of the mixture, and, in turn, increases the sensitivity of the flame to variations in mixture composition and inflow conditions at the burner inlet. This work addresses both issues, namely the modeling of a three-stream burner system and the characterization of the sensitivity of the burner to variations in inflow and scalar boundary conditions. In the first part of this paper, a flamelet-based combustion model is extended to account for variations in the composition of the oxidizer stream. To this end, a scalar quantity, representing the oxidizer split, is introduced, and all thermochemical quantities are represented in terms of two conserved scalars and a reaction progress variable. The second part of this paper investigates the sensitivity of the flame structure to variations in scalar inflow boundary conditions. LES calculations with nominal boundary conditions and boundary conditions determined from experimental data are prescribed for all scalar quantities. Results show that the selection of the inflow conditions not only affects the nozzle-near region of the flame, but also leads to significant variations in the upper part of the flame. Reasons for this sensitivity are attributed to the population of the flamelet state-space and are further analyzed in the paper.