James J. Riley

A laminar flamelet approach to subgrid-scale chemistry in turbulent flows

Abstract A method is presented whereby filtered chemical species may be modeled in large eddy simulations (LES) of nonpremixed, turbulent combustion. The model is based on the concept of laminar flamelets, and assumes that a filtered mixture-fraction, as well as its subgrid-scale variance and filtered dissipation rate, are known at each grid cell of an LES. The model makes use of the subgrid-scale or “large-eddy” probability density function of the mixture-fraction, which is assumed to follow a beta-distribution. Also, an assumed functional form for the scalar dissipation rate is employed. The model is evaluated by filtering data from direct numerical simulations (DNS) of homogeneous, isotropic, decaying turbulence. Results show that the model, termed the large-eddy, laminar flamelet model (LELFM), is reasonably accurate and that the accuracy improves with increasing Damkohler number.

Subgrid-scale modeling for turbulent reacting flows

The Large Eddy Simulation of non-premixed, turbulent, reacting flows is addressed. A new subgrid-scale chemistry model, previously proposed for incompressible, isothermal flows, is extended to the case of compressible combustion with multi-step, Arrhenius-rate reactions. The chemistry model predicts filtered chemical species concentrations and filtered reaction rates in a turbulent flow. It accounts for finite-rate chemistry by invoking the laminar flamelet approximation and employs an assumed form for the subgrid or “Large Eddy” Probability Density Function (LEPDF) of a mixture-fraction. It also uses an assumed counterflow form for the local scalar dissipation rate. Inputs to the chemistry model are the Favre-filtered mixture-fraction, its subgrid-scale variance, and filtered dissipation rate. The model is evaluated using (256) 3 point Direct Numerical Simulations of incompressible, nonisothermal decaying turbulence with a single-step reaction. Results indicate that, as the activation temperature is increased, the accuracy of the model degrades in an absolute sense but improves relative to an equilibrium chemistry assumption. Finally, it is also demonstrated that the assumed Beta distribution for the LEPDF yields reasonably accurate results for low (realistic) stoichiometric values of the mixture-fraction.

Direct numerical simulation of laboratory experiments in isotropic turbulence

Massively parallel computers are now large enough to support accurate direct numerical simulations (DNSs) of laboratory experiments on isotropic turbulence, providing researchers with a full description of the flow field as a function of space and time. The high accuracy of the simulations is demonstrated by their agreement with the underlying laboratory experiment and on checks of numerical accuracy. In order to simulate the experiments, requirements for the largest and smallest length scales computed must be met. Furthermore, an iterative technique is developed in order to initialize the larger length scales in the flow. Using these methods, DNS is shown to accurately simulate isotropic turbulence decay experiments such as those of Comte-Bellot and Corrsin [J. Fluid Mech. 48, 273 (1971)].

Instability of internal waves near a critical level

Abstract The three-dimensional stability problem is investigated for a family of velocity and density profiles similar in form to those expected for large-amplitude internal gravity waves near a critical level. These profiles exhibit regions of high shear and stable stratification alternating with regions of weak shear and unstable stratification. Analytical solutions are given for inviscid, neutral modes that are similar to those found under neutral conditions with stable stratification. Neutral modes form closed streamline patterns centered at locations of maximal shear, and are not strongly influenced by nearby regions of unstable stratification. Unstable modes are computed numerically. It is shown that the instability mechanism for these wave-like flows fundamentally three-dimensional in character and exhibits both shear and convective dynamics. For flows with parameter values below the neutral curves, unstable modes oriented in the streamwise direction undergo shear instability, while modes oriented orthogonally are convectively unstable. In addition to their intrinsic physical relevance, the results of this study have important implications for the physics and the numerical modeling of breaking internal gravity waves. Two-dimensional models will bias the breaking dynamics by eliminating the possibility for convection oriented in the transverse plane.

Investigation of Modeling for Non-Premixed Turbulent Combustion

A method for predicting filtered chemical species concentrations and filtered reaction rates in Large-Eddy Simulations of non-premixed, non-isothermal, turbulent reacting flows has been demonstrated to be quite accurate for higher Damköhler numbers. This subgrid-scale model is based on flamelet theory and uses presumed forms for both the dissipation rate and subgrid-scale probability density function of a conserved scalar. Inputs to the model are the chemistry rates, the Favre-filtered scalar, and its subgrid-scale variance and filtered dissipation rate. In this paper, models for the filtered dissipation rate and subgrid-scale variance are evaluated by filtering data from 5123-point Direct Numerical Simulations of a single-step, isothermal reaction developing in the isotropic, incompressible, decaying turbulence field of Comte-Bellot and Corrsin. Both the subgrid-scale variance and the filtered dissipation rate models (the ”sub-models”) are found to be reasonably accurate. The effect of the errors introduced by the sub-models on the overall model is found to be small, and the overall model is shown to accurately predict the spatial average of the filtered species concentrations over a wide range of times.

The Premixed Conditional Moment Closure Method Applied to Idealized Lean Premixed Gas Turbine Combustors

This paper presents the premixed conditional moment closure (CMC) method as a new tool for modeling turbulent premixed combustion with detailed chemistry. By using conditional averages the CMC method can more accurately model the affects of the turbulent fluctuations of the temperature on the reaction rates. This provides an improved means of solving a major problem with traditional turbulent reacting flow models, namely how to close the reaction rate source term. Combined with a commercial CFD code this model provides insight into the emission formation pathways with reasonable runtimes. Results using the full GRI2.11 methane kinetic mechanism are compared to experimental data for a backward-facing step burning premixed methane. This model holds promise as a design tool for lean premixed gas turbine combustors.

A Lagrangian study of scalar diffusion in isotropic turbulence with chemical reaction

Direct numerical simulations are performed of a single-step, nonpremixed, Arrhenius-type reaction developing in isotropic, incompressible, decaying turbulence, for conditions where flame extinction and re-ignition occur. The Lagrangian characteristics of scalar diffusion, information necessary for modeling approaches such as some implementations of probability density function (PDF) methods, are investigated by tracking fluid particles. Focusing on the mixture fraction and temperature as the scalar variables of interest, fluid particles are characterized as continuously burning or noncontinuously burning based upon their recent time history, and noncontinuously burning particles are further characterized based upon their initial regions relative to the flame zone. The behavior of the mixture fraction and temperature fields is contrasted for the different types of particles characterized. Significant differences among these characterized particles are found, for example, in the unclosed conditional expecta...

Review of Large-Eddy Simulation of Non-Premixed Turbulent Combustion

Recent developments in the methodology of large-eddy simulation applied to turbulent, reacting flows are reviewed, with specific emphasis on mixture-fraction-based approaches to nonpremixed reactions. Some typical results are presented, and the potential use of the methodology in applications and the future outlook are discussed.

Re-examining the thermal mixing layer with numerical simulations

The question of whether a temperature mixing layer evolves in a self-similar manner is of importance in developing and validating theories about scalar mixing. The simplicity of the flow encourages the thought that it is self-similar, but several laboratory experiments at moderate Peclet numbers have found inconsistencies with self-similar behavior. The experimentalists are limited, however, by the length of the wind tunnels and by difficulties in aligning the virtual origins of the scalar and velocity fields. Direct numerical simulations virtually eliminate both these problems, and large-eddy simulations add the ability to study an approximation to the case of an infinite Peclet number. These two simulation techniques are used in this paper to show that the mixing layer at a moderate Peclet number very nearly evolves with a single length and time scale, and that behavior consistent with self-similarity is observed in the case of an infinite Peclet number. In addition, the results show that direct numerical simulations can accurately reproduce the data from wind tunnel experiments downstream of a turbulence grid, and that large-eddy simulations are a valuable research tool for studying the large-scale characteristics of mixing.

Hemodynamic Conditions in a Failing Peripheral Artery Bypass Graft

OBJECTIVEnThe mechanisms of restenosis in autogenous vein bypass grafts placed for peripheral artery disease are not completely understood. We investigated the role of hemodynamic stress in a case study of a revised bypass graft that failed due to restenosis.nnnMETHODSnThe morphology of the lumen was reconstructed from a custom three-dimensional ultrasound system. Scans were taken at 1, 6, and 16 months after a patch angioplasty procedure. Computational hemodynamic simulations of the patient-specific model provided the blood flow features and the hemodynamic stresses on the vessel wall at the three times studied.nnnRESULTSnThe vessel was initially free of any detectable lesions, but a 60% diameter-reducing stenosis developed during the 16-month study interval. As determined from the simulations, chaotic and recirculating flow occurred downstream of the stenosis due to the sudden widening of the lumen at the patch location. Curvature and a sudden increase in the lumen cross-sectional area induced these flow features that are hypothesized to be conducive to intimal hyperplasia. Favorable agreement was found between simulation results and in vivo Doppler ultrasound velocity measurements.nnnCONCLUSIONSnTransitional and chaotic flow occurs at the site of the revision, inducing a complex pattern of wall shear as computed with the hemodynamic simulations. This supports the hypothesis that the hemodynamic stresses in the revised segment, produced by the coupling of vessel geometry and chaotic flow, led to the intimal hyperplasia and restenosis of the graft.