M. S. Anand

Calculations of Premixed Turbulent Flames by PDF Methods

Idealized premixed turbulent flames are studied using probability density function (pdf) methods. A modeled transport equation for the joint pdf of velocity and the reaction progress variable is solved by a Monte Carlo method. Detailed calculations of flame properties and flow statistics, including the flame speed, the scalar flux, the turbulence intensities, the kinetic energy budget and conditional statistics are presented for different density ratios. Results are compared with the limited available experimental data and the calculations based on the Bray-Moss-Libby (BML) model. Compared to the BML model, the present pdf approach has several advantages: fewer processes have to be modeled, more information can be extracted from the solution, and the method is directly applicable to multidimensional flames.

In Situ Detailed Chemistry Calculations in Combustor Flow Analyses

In the numerical simulation of turbulent reacting flows, the high computational cost of integrating the reaction equations precludes the inclusion of detailed chemistry schemes, therefore reduced reaction mechanisms have been the more popular route for describing combustion chemistry, albeit at the loss of generality. The in situ adaptive tabulation scheme (ISAT) has significantly alleviated this problem by facilitating the efficient integration of the reaction equations via a unique combination of direct integration and dynamic creation of a look-up table, thus allowing for the implementation of detailed chemistry schemes in turbulent reacting flow calculations. In the present paper, the probability density function (PDF) method for turbulent combustion modeling is combined with the ISAT in a combustor design system, and calculations of a piloted jet diffusion flame and a low-emissions premixed gas turbine combustor are performed. It is demonstrated that the results are in good agreement with experimental data and computations of practical turbulent reacting flows with detailed chemistry schemes are affordable.

A PDF Method for Turbulent Recirculating Flows

A novel approach for the application of probability density function (PDF) methods to multidimensional turbulent recirculating flows is presented. The method is applicable to turbulent recirculating and reacting flows such as in gas turbine combustors. The method is based on a judicious combination of the conventional finite-volume technique for the solution of the Reynolds-averaged equations and the Monte Carlo technique for the solution of the transport equation for the veloCity-scalar joint PDF. An important aspect of the approach is that the use of conventional turbulence closure models is avoided. The method is applied to the flow over a backward-facing step investigated experimentally by Pronchick and Kline [1]. The results predicted using the present approach are in good agreement with data.

Calculations of Swirl Combustors Using Joint Velocity-Scalar Probability Density Function Method

Calculations are reported for recirculating swirling reacting flows using a joint velocity-scalar probability density function (PDF) method. The PDF method offers signiflcant advantages over conventional finite volume, Reynolds-average-based methods, especially for the computation of turbulent reacting flows. The PDF calculations reported here are based on a newly developed solution algorithm for elliptic flows, and on newly developed models for turbulent frequency and velocity that are simpler than those used in previously reported PDF calculations. Calculations are performed for two different gas-turbine-like swirl combustor flows for which detailed measurements are available. The computed results are in good agreement with experimental data.

The Lagrangian PDF Transport Method for Simulations of Gas Turbine Combustor Flows

Probability density function (PDF) transport methods are increasingly used in simulations of gas turbine combustors. One of the main advantages of the PDF transport method is that the crucial turbulence-chemistry interaction is accurately accounted for. Due to its large dimensionality, the PDF transport equation is solved using one of two Monte-Carlo methods – the Eulerian (or node-based) method and the Lagrangian method. Studies on the Eulerian method show that a large number of particles per cell is necessary for accurate simulations. In the present study, the Lagrangian method is developed for the simulation of actual gas turbine combustors. The key technologies developed are a robust particle tracking algorithm and a variable time-step algorithm to accelerate the convergence of the flow. The accuracy of the Lagrangian method is evaluated by applying it to several combustor configurations. A model combustor and two production combustors are studied. The predicted exit temperature profiles are in excellent agreement with rig data. Simulations show that even with 10 particles per cell, accurate results are obtained. The study shows that the Lagrangian Monte-Carlo PDF method can be reliably used in simulations of practical gas turbine combustors. INTRODUCTION With increasing emphasis on accurate CFD predictions of the flow in gas turbine combustors, there is greater need to develop advanced models. Predicting the combusting flow in gas turbine combustors is a complex task due to the strong role played by turbulence-chemistry interactions. The traditional approach to modeling these interactions via the eddy-dissipation model or the presumed PDF model has met with limited success. In light of this, the PDF transport method is a promising alternative to modeling turbulent-chemistry interactions. Several Copyright  2002 by Rolls-Royce Corporation and Cornell University. Published by AIAA, Inc., with permission. studies have shown that this method can accurately predict turbulent flames, even flames close to extinction. There have been several studies of PDF methods in axisymmetric reacting flow configurations. However, studies in three-dimensional flow configurations have been limited due to the difficulty of solving the PDF transport equation in complex three-dimensional flows. In the present study, the joint PDF of scalars (or composition) is considered, as opposed to the more comprehensive and computationally intensive velocity-scalar-dissipation PDF method. The PDF transport equation is a hyperdimensional equation and is generally solved using Monte-Carlo methods. In Monte-Carlo methods, an ensemble of particles represents the joint PDF of scalars. The transport of these particles in physical and compositional space mimics the solution of the transport equation. In the Eulerian Monte-Carlo method, all the particles in a cell are located at the cell-center. The transport of these particles is determined by cell-face fluxes, computed from the flowsolver. An accompanying study on the application of the Eulerian method for gas turbine combustors showed that a large number of particles per cell is required for accurate simulations. Studies in 2D flows have shown that for a given accuracy level, the Lagrangian Monte-Carlo scheme is cheaper than the Eulerian scheme. In the Lagrangian Monte-Carlo method, particles are randomly distributed in the computational domain and are associated with the cell that they are in at a given instant of time. The implementation of the Lagrangian method is significantly more complex than the Eulerian method; hence, there have been few applications of the Lagrangian method to complex three-dimensional flows. The main difficulty in the method is the accurate tracking of particles and conservative implementation of various submodels. In the present study, the Lagrangian method has been developed for the simulation of the flow in gas turbine combustor configurations. The key technologies developed in the method are a robust particle tracking algorithm, accurate treatment of boundary conditions, and a conservative 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 7-10 July 2002, Indianapolis, Indiana AIAA 2002-4017 Copyright

Calculation of a Premixed Swirl Combustor Using the PDF Method

The evolution probability density function (PDF) method provides a framework for the simulation of both diffusion and premixed turbulent flames. With this method, the chemical reaction rates are treated without approximation. In contrast, the conventional Reynolds-average methods need to model the mean reaction rates in turbulent flame calculations. In addition, conventional methods require special models for premixed flames that are developed under restrictive assumptions and rely on ad hoc expressions for the rate of reaction progress. The present work demonstrates the capability of the PDF method in realistic combustor design calculations. A lean premixed flame swirl combustor is simulated using the scalar PDF method, and the results are compared with experimental data. It is shown that the PDF method can correctly predict the turbulent flame speed and location of the flame. The ability of the PDF method to handle finite-rate complex chemistry of any number of reaction steps makes it an ideal candidate for emissions predictions in low emission combustor designs.Copyright

An unconditionally-stable central differencing scheme for high Reynolds number flows

The central difference scheme (CDS) is a second order accurate scheme which is free of numerical diffusion (in the second order sense) and is simple to implement: However, for grid Peclet numbers larger than 2, the CDS leads to over- and undershoots and is unstable. The present paper describes a method, called CONDIF, which retains the essential nature of the CDS but eliminates the over- and under-shoots. It leads to unconditionally positive coefficients and, in the limit, approaches the CDS for all values of grid Peclet numbers. The CONDIF modifies the CDS by introducing a controlled amount of numerical diffusion based on the local gradients. In the worst case the scheme yields results similar to those of the hybrid scheme. This paper reports the results obtained from CONDIF for a number of test problems which have been widely used for comparative study of numerical schemes in the published literature. For most of these problems, the CONDIF results are significantly more accurate than the hybrid scheme at high Peclet numbers. In particular, the CONDIF scheme depicts much lower level of numerical diffusion than the hybrid scheme even when the Peclet number is very high and the flow is at large angles to the grid.

pdf calculations for swirl combustors

Calculations are reported for recirculating swirling reacting flows using the joint velocity-scalar probability density function (pdf) method. The pdf method offers significant advantages over conventional finite-volume, Reynolds-average based methods, especially for the computation of turbulent reacting flows. The pdf calculations reported here are based on a newly developed solution algorithm for elliptic flows, and on newly developed models for turbulent frequency and velocity that are simpler than those used in previously reported pdf calculations. Calculations are performed for two different gas-turbine-like swirl combustor flows for which detailed measurements are available. The computed results are in good agreement with experimental data. (Author)