Givi, P
1993
Binary Scalar Mixing and Reaction in Homogeneous Turbulence: Some Linear Eddy Model Results
Frankel, S.H.; Madnia, C.K.; McMurtry, P.A. and Givi, P.
Energy & Fuels, 7 (6):827-834, 1993. Funded by National Science Foundation, Office of Naval Research, and ACERC.
The Linear Eddy Model (LEM) of Kerstine is used to simulate the mechanism of scalar mixing from an initial binary state in incompressible, homogeneous turbulence. The simulated results are used to measure the limiting rate of mean reactant conversion in a chemical reaction of the type F + rO --> (1 + r) Products under isothermal and nonpremixed conditions. The objective of the simulations is to access the performance of the closed form analytical expressions obtained by Madnia et al., based on the Amplitude Mapping Closure for the evaluation of the mean reactant conversion rate. This assessment is made for various flow conditions with different asymptotic statistical behavior.
Linear Eddy Modeling of Reactant Conversion and Selectivity in Turbulent Flows
Frankel, S.H.; McMurtry, P.A. and Givi, P.
Presented at the APS Division of Fluid Dynamics Conference, Albuquerque, NM, November 1993. Funded by the National Science Foundation and ACERC.
The Linear Eddy Model (LEM) is utilized for statistical predictions of stationary, homogeneous turbulent flows under the influence of isothermal chemical reactions. Nonpremixed reacting systems are considered with two reaction mechanisms: A binary, irreversible single-step reaction of the type A + B --> P, and the series-parallel reaction A + B --> R, A + R --> P. For both systems, the influence of various flow parameters on the rate of reactant conversion is elucidated. For the second reaction scheme, the effects of the flow parameters on the "selectivity" are also investigated. The trends portrayed by LEM are shown to be in accord with those produced by Direct Numerical Simulation (DNS) at moderate values of the Reynolds number, the Schmidt number and the Damköhler number. The advantage of LEM is its capability to extend the parameter range well beyond that currently attainable by DNS. The LEM generated results for a wide range of Schmidt and Damköhler numbers are presented and their effects on the chemical selectivity are discussed. These results are also used to examine the performance of some of the existing closures for the modeling of selectivity. It is shown that none of the closures considered are capable of reproducing LEM results accurately. In view of the agreement of LEM predictions with DNS results and the previous success of the model in reproducing known statistical features of scalar mixing, the use of the model is recommended for statistical modeling and analyses of chemically reacting turbulent flows.
1992
Direct Numerical Simulations of a Reacting Turbulent Mixing Layer by a Pseudospectral-Spectral Element Method
McMurtry, P.A. and Givi, P.
Chapter 14, Finite Element Methods in Fluids, 8:355, 1992. Funded by National Science Foundation, NASA Lewis Research Center and ACERC.
The purpose of this chapter is to describe the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Some of the important experimental and numerical studies that have been directed at investigating the development, evolution, and mixing characteristics of shear flows are reviewed. These works provide a framework for subsequent discussions on the formulation of the spectral-element method. The mathematical formulation of the physical configuration of the spatially developing reacting mixing layer, together with a rather detailed presentation on the application of the spectral-element for the numerical simulation of mixing layers is given. Results from two- and three-dimensional calculations of chemically reacting mixing layers are discussed. Finally, conclusion and speculation for future related work are given.
Spectral Simulations of Reacting Turbulent Flows
McMurtry, P.A. and Givi, P.
AIAA Progress in Engineering Series, 135:257-301, 1992. Funded by National Science Foundation, NASA Lewis Research Center and ACERC.
The Navier-Stokes equations, along with appropriate conservation equations of energy and chemical species, are generally accepted to provide an "exact" model for most turbulent combustion phenomena of interest. Unfortunately, the complexity of these equations prohibits both their analytic and numerical solutions except under idealized conditions. To provide engineering tools to predict the performance of turbulent combustion systems, it is necessary to resort to approximate analyses in which the effects of turbulence are not treated exactly, but are incorporated by means of turbulence models.
An overview of spectral methods is given, together with a discussion of their implementation in the numerical solution of fluid transport. Various classifications of spectral methods and their convergence properties are described. The "spectral element" method, which constitutes a new category of spectral approximations, is also presented. Its flexibility in dealing with complex flow geometries is highlighted. A review of the recent applications of spectral methods to reacting flow problems is also given. Emphasis is placed primarily on the interpretation of the physical phenomena captured by spectral simulations of reactive flows. There is some mention of spectral simulations of the turbulent mixing of a passive scalar, but only where an explicit connection to chemical reactions has been made. We conclude with an evaluation for the benefits and limitations of spectral methods, and some speculation of their contributions for turbulent combustion research in the future.
1990
Spectral Simulations of Reacting Turbulent Flows
McMurtry, P.A. and Givi, P.
AIAA Progress in Engineering Series, Oran, E. and Boris, J., Editors., 1990 (In press). Funded by ACERC and NASA Lewis Research Center.
The Navier-Stokes equations, along with appropriate conservation equations of energy and chemical species, are generally accepted to provide an "exact" model for most turbulent combustion phenomena of interest. Unfortunately, the complexity of these equations prohibits both their analytic and numerical solutions except under idealized conditions. To provide engineering tools to predict the performance of turbulent combustion systems, it is necessary to resort to approximate analyses in which the effects of turbulence are not treated exactly, but are incorporated by means of turbulence models.
An overview of spectral methods is given, together with a discussion of their implementation in the numerical solution of fluid transport. Various classifications of spectral methods and their convergence properties are described. The "spectral element" method, which constitutes a new category of spectral approximations, is also presented. Its flexibility in dealing with complex flow geometries is highlighted.
A review of the recent applications of spectral methods to reacting flow problems is also given. Emphasis is placed primarily on the interpretation of the physical phenomena captured by spectral simulations of reactive flows. There is some mention of spectral simulations of the turbulent mixing of a passive scalar, but only where an explicit connection to chemical reactions has been made. We conclude with an evaluation for the benefits and limitations of spectral methods, and some speculation of their contributions for turbulent combustion research in the future.
1988
Direct Numerical Simulations of Mixing and Reaction in a Non-Premixed Homogeneous Turbulent Flow
McMurtry, P.A. and Givi, P.
To appear in Combustion and Flame, 1988. Funded by Air Force Office of Scientific Research.
Direct numerical simulations have been performed to study the mechanisms of mixing and chemical reaction in a three-dimensional, homogeneous turbulent flow under the influence of the reaction of the type A + B = Products. The results are used to examine the applicability of Toors hypotheses [1] and also to determine the range of validity of various coalescence/dispersion (C/D) turbulence models that have been used previously to model the effects of turbulent mixing in such flows [2]. The results of numerical simulations indicate that the probability density function (PDF) of a conserved Shvab-Zeldovich scalar quantity, characterizing the mixing process, evolves from an initial double-delta distribution to an asymptotic shape that can be approximated by a Gaussian distribution. During this evolution, the PDF cannot be characterized by its first two moments; therefore, the application of Toor's hypothesis is not appropriate for the prediction of such flows. The results further indicate that the initial stages of mixing are well represented by the Dopazo-O'Brien C/D model, whereas, at intermediate times, the results obtained by DNS fall between those obtained by the two closures of Dopazo and O'Brien [3] and Janicka et al. [4], and deviate the most from those of Curl [5]. Therefore, a C/D model between the two closures of Dopazo-O'Brien and Janicka et al. is expected to result in favorable comparison with our data. The final stages of mixing are not well predicted by any of the C/D closures in that none of the models is capable of predicting a Gaussian asymptotic PDF for the Shavab-Zeldovich scalar variable. The results of our numerical simulations may be used to generate a C/D model (or models) that can predict all the stages of mixing accurately.
Direct Numerical Simulations of the PDFs of a Passive Scalar in a Forced Mixing Layer
Givi, P. and McMurtry, P.A.
Combust. Sci. and Tech., 57, 141-147, 1988. 7 pgs. Funded by Air Force Office of Scientific Research.
The probability density functions of a passive scalar quantity are calculated in a perturbed mixing layer by means of direct numerical simulations. The results indicate that the two-dimensional rollup of the unsteady shear layer, and the pairing process in particular, contributes greatly to the generation of the predominant peak of the PDFs within the mixing region.
Givi, P
1993
Binary Scalar Mixing and Reaction in Homogeneous Turbulence: Some Linear Eddy Model Results
Frankel, S.H.; Madnia, C.K.; McMurtry, P.A. and Givi, P.
Energy & Fuels, 7 (6):827-834, 1993. Funded by National Science Foundation, Office of Naval Research, and ACERC.
The Linear Eddy Model (LEM) of Kerstine is used to simulate the mechanism of scalar mixing from an initial binary state in incompressible, homogeneous turbulence. The simulated results are used to measure the limiting rate of mean reactant conversion in a chemical reaction of the type F + rO --> (1 + r) Products under isothermal and nonpremixed conditions. The objective of the simulations is to access the performance of the closed form analytical expressions obtained by Madnia et al., based on the Amplitude Mapping Closure for the evaluation of the mean reactant conversion rate. This assessment is made for various flow conditions with different asymptotic statistical behavior.
Linear Eddy Modeling of Reactant Conversion and Selectivity in Turbulent Flows
Frankel, S.H.; McMurtry, P.A. and Givi, P.
Presented at the APS Division of Fluid Dynamics Conference, Albuquerque, NM, November 1993. Funded by the National Science Foundation and ACERC.
The Linear Eddy Model (LEM) is utilized for statistical predictions of stationary, homogeneous turbulent flows under the influence of isothermal chemical reactions. Nonpremixed reacting systems are considered with two reaction mechanisms: A binary, irreversible single-step reaction of the type A + B --> P, and the series-parallel reaction A + B --> R, A + R --> P. For both systems, the influence of various flow parameters on the rate of reactant conversion is elucidated. For the second reaction scheme, the effects of the flow parameters on the "selectivity" are also investigated. The trends portrayed by LEM are shown to be in accord with those produced by Direct Numerical Simulation (DNS) at moderate values of the Reynolds number, the Schmidt number and the Damköhler number. The advantage of LEM is its capability to extend the parameter range well beyond that currently attainable by DNS. The LEM generated results for a wide range of Schmidt and Damköhler numbers are presented and their effects on the chemical selectivity are discussed. These results are also used to examine the performance of some of the existing closures for the modeling of selectivity. It is shown that none of the closures considered are capable of reproducing LEM results accurately. In view of the agreement of LEM predictions with DNS results and the previous success of the model in reproducing known statistical features of scalar mixing, the use of the model is recommended for statistical modeling and analyses of chemically reacting turbulent flows.
1992
Direct Numerical Simulations of a Reacting Turbulent Mixing Layer by a Pseudospectral-Spectral Element Method
McMurtry, P.A. and Givi, P.
Chapter 14, Finite Element Methods in Fluids, 8:355, 1992. Funded by National Science Foundation, NASA Lewis Research Center and ACERC.
The purpose of this chapter is to describe the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Some of the important experimental and numerical studies that have been directed at investigating the development, evolution, and mixing characteristics of shear flows are reviewed. These works provide a framework for subsequent discussions on the formulation of the spectral-element method. The mathematical formulation of the physical configuration of the spatially developing reacting mixing layer, together with a rather detailed presentation on the application of the spectral-element for the numerical simulation of mixing layers is given. Results from two- and three-dimensional calculations of chemically reacting mixing layers are discussed. Finally, conclusion and speculation for future related work are given.
Spectral Simulations of Reacting Turbulent Flows
McMurtry, P.A. and Givi, P.
AIAA Progress in Engineering Series, 135:257-301, 1992. Funded by National Science Foundation, NASA Lewis Research Center and ACERC.
The Navier-Stokes equations, along with appropriate conservation equations of energy and chemical species, are generally accepted to provide an "exact" model for most turbulent combustion phenomena of interest. Unfortunately, the complexity of these equations prohibits both their analytic and numerical solutions except under idealized conditions. To provide engineering tools to predict the performance of turbulent combustion systems, it is necessary to resort to approximate analyses in which the effects of turbulence are not treated exactly, but are incorporated by means of turbulence models.
An overview of spectral methods is given, together with a discussion of their implementation in the numerical solution of fluid transport. Various classifications of spectral methods and their convergence properties are described. The "spectral element" method, which constitutes a new category of spectral approximations, is also presented. Its flexibility in dealing with complex flow geometries is highlighted. A review of the recent applications of spectral methods to reacting flow problems is also given. Emphasis is placed primarily on the interpretation of the physical phenomena captured by spectral simulations of reactive flows. There is some mention of spectral simulations of the turbulent mixing of a passive scalar, but only where an explicit connection to chemical reactions has been made. We conclude with an evaluation for the benefits and limitations of spectral methods, and some speculation of their contributions for turbulent combustion research in the future.
1990
Spectral Simulations of Reacting Turbulent Flows
McMurtry, P.A. and Givi, P.
AIAA Progress in Engineering Series, Oran, E. and Boris, J., Editors., 1990 (In press). Funded by ACERC and NASA Lewis Research Center.
The Navier-Stokes equations, along with appropriate conservation equations of energy and chemical species, are generally accepted to provide an "exact" model for most turbulent combustion phenomena of interest. Unfortunately, the complexity of these equations prohibits both their analytic and numerical solutions except under idealized conditions. To provide engineering tools to predict the performance of turbulent combustion systems, it is necessary to resort to approximate analyses in which the effects of turbulence are not treated exactly, but are incorporated by means of turbulence models.
An overview of spectral methods is given, together with a discussion of their implementation in the numerical solution of fluid transport. Various classifications of spectral methods and their convergence properties are described. The "spectral element" method, which constitutes a new category of spectral approximations, is also presented. Its flexibility in dealing with complex flow geometries is highlighted.
A review of the recent applications of spectral methods to reacting flow problems is also given. Emphasis is placed primarily on the interpretation of the physical phenomena captured by spectral simulations of reactive flows. There is some mention of spectral simulations of the turbulent mixing of a passive scalar, but only where an explicit connection to chemical reactions has been made. We conclude with an evaluation for the benefits and limitations of spectral methods, and some speculation of their contributions for turbulent combustion research in the future.
1988
Direct Numerical Simulations of Mixing and Reaction in a Non-Premixed Homogeneous Turbulent Flow
McMurtry, P.A. and Givi, P.
To appear in Combustion and Flame, 1988. Funded by Air Force Office of Scientific Research.
Direct numerical simulations have been performed to study the mechanisms of mixing and chemical reaction in a three-dimensional, homogeneous turbulent flow under the influence of the reaction of the type A + B = Products. The results are used to examine the applicability of Toors hypotheses [1] and also to determine the range of validity of various coalescence/dispersion (C/D) turbulence models that have been used previously to model the effects of turbulent mixing in such flows [2]. The results of numerical simulations indicate that the probability density function (PDF) of a conserved Shvab-Zeldovich scalar quantity, characterizing the mixing process, evolves from an initial double-delta distribution to an asymptotic shape that can be approximated by a Gaussian distribution. During this evolution, the PDF cannot be characterized by its first two moments; therefore, the application of Toor's hypothesis is not appropriate for the prediction of such flows. The results further indicate that the initial stages of mixing are well represented by the Dopazo-O'Brien C/D model, whereas, at intermediate times, the results obtained by DNS fall between those obtained by the two closures of Dopazo and O'Brien [3] and Janicka et al. [4], and deviate the most from those of Curl [5]. Therefore, a C/D model between the two closures of Dopazo-O'Brien and Janicka et al. is expected to result in favorable comparison with our data. The final stages of mixing are not well predicted by any of the C/D closures in that none of the models is capable of predicting a Gaussian asymptotic PDF for the Shavab-Zeldovich scalar variable. The results of our numerical simulations may be used to generate a C/D model (or models) that can predict all the stages of mixing accurately.
Direct Numerical Simulations of the PDFs of a Passive Scalar in a Forced Mixing Layer
Givi, P. and McMurtry, P.A.
Combust. Sci. and Tech., 57, 141-147, 1988. 7 pgs. Funded by Air Force Office of Scientific Research.
The probability density functions of a passive scalar quantity are calculated in a perturbed mixing layer by means of direct numerical simulations. The results indicate that the two-dimensional rollup of the unsteady shear layer, and the pairing process in particular, contributes greatly to the generation of the predominant peak of the PDFs within the mixing region.