Kerstein, AR
1997
Mixing Mechanisms in Turbulent Pipe Flow
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Phys. Fluids, 9(3):717-23(1997). Funded by ACERC and National Science Foundation.
An experimental investigation of passive scalar mixing in turbulent pipe flow is carried out using a new non-intrusive scalar initialization technique. The measurements support a recently predicted similarity scaling of concentration spectra in flows that are unbounded in one direction. Reflecting this scaling, the scalar variance exhibits a power-law rather than exponential decay, indicating that the traditional plug-flow reactor picture of turbulent pipe-flow mixing omits key physical mechanisms.
1994
Long-Tailed Probability Distributions in Turbulent-Pipe-Flow Mixing
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Physical Review E, 56(2):1753-758(1997). Funded by ACERC and National Science Foundation.
Exponential-tailed scalar probability density functions (PDF's) are obtained by high-pass filtering scalar concentration time series measured in turbulent pipe flow. This behavior reflects the scale separation of scalar and velocity fluctuations that develops in this flow, such that the low-wave-number scalar fluctuations act as and imposed scalar gradient stirred by finer-scale wall-generated shear. This observation broadens the class of flows in which long-tailed scalar PDF's are anticipated to occur.
Effects of Turbulence Length-Scale Distribution on Scalar Mixing in Homogeneous Turbulent Flow
Cremer, M.A.; McMurtry, P.A. and Kerstein, A.R.
Physics of Fluids, 6:2143, 1994. Funded by ACERC and US Department of Energy.
The linear eddy-mixing model is used to study effects of the turbulence length-scale distribution on the transient evolution of a passive scalar in a statistically steady homogeneous turbulent flow. Model simulations are carried out using both wide-band length-scale distributions reflecting high-Reynolds-number scaling, and narrow-band (in effect, low-Reynolds-number) distributions. The two cases are found to exhibit qualitative differences in mixing behavior. These differences are interpreted mechanistically. The narrow-band case yields the best agreement with published direct numerical simulation results, suggesting that those results are, in effect, low-Reynolds, number results not readily extrapolated to high-Reynolds-number mixing.
Low-Wave-Number Statistics of Randomly Advected Passive Scalars
Kerstein, A.R. and McMurtry, P.A.
Physical Review E, 50:2057, 1993. Funded by ACERC, National Science Foundation and US Department of Energy.
A heuristic analysis of the decay of a passive scalar field, subject to statistically steady random advection, predicts two low-wave-number spectral scaling regimes analogous to the similarity states previously identified by Chasnov. Consequences of their predicted coexistence in a single flow are examined. The analysis is limited to the idealized case of narrow band advection. To complement the analysis, and to extend the predictions to physically more realistic advection processes, advection diffusion is simulated using a one-dimensional stochastic model. An experimental test of the predictions is proposed.
Prediction of NOx Production in a Turbulent Hydrogen-Air Jet Flame
Menon, S.; McMurtry, P.A.; Kerstein, A.R. and Chen, J.
AIAA Journal of Propulsion and Power, 10:161-168, 1994. Funded by ACERC, NASA and US Department of Energy.
A major concern in the numerical study of turbulent nonpremixed flames is the accurate prediction of trace species. The production of pollutants such as NOx during unsteady combustion needs to be understood and predicted accurately so that the design of the next generation's combustion systems can meet the forthcoming stricter environmental restrictions. Numerical studies using steady-state methods cannot account for the unsteady phenomena in the mixing region, and therefore, fail to accurately predict the NOx production that could occur. A novel unsteady mixing model is demonstrated here that accounts for all the length scales associated with mixing and molecular diffusion processes. Finite-rate kinetics in the form of a reduced mechanism have been used to study hydrogen-air nonpremixed jet flames. NOx production in these jet flames was also predicted. Comparisons with experimental data and PDF calculations show good agreement, thereby, providing validation of the mixing model.
Mean-Field Theories of Random Advection
Kerstein, A.R. and McMurtry, P.A.
Physical Review, E, 49:474-482, 1994. Funded by ACERC, National Science Foundation and US Department of Energy.
Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir to derive the phenomenological model of Pumir, Shraiman, and Siggia governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.
1993
Linear Eddy Modeling of Turbulent Combustion
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Energy & Fuels, 7, (6):817-826, 1993. Funded by National Science Foundation and ACERC.
The use of the linear eddy mixing model in application to reacting flows is discussed for several different combustion geometries. The unique feature of this model is the explicit distinction made among the various physical processes (convection, diffusion, and reaction) at all scales of the flow. This is achieved by resolving all relevant scales of motion through a reduced, one-dimensional statistical description of the scalar field in a linear domain. The advantages of this modeling approach over other conventional modeling approaches are pointed out. Applications to both "stand-alone" formulations and subgrid formulations for use in large eddy simulation (LES) are discussed.
Mean-Field Theories of Random Advection
Kerstein, A.R. and McMurtry, P.A.
Physical Review, E, 1993 (in press). Funded by US Department of Energy, National Science Foundation and ACERC.
Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir to derive the phenomenological model of Pumir, Shraiman, and Siggia governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.
Linear Eddy Simulations of Mixing in a Homogeneous Turbulent Flow
McMurtry, P.A.; Gansuage, T.C.; Kerstein, A.R. and Krueger, S.K.
Physics of Fluids A., 5 (4):1023 - 1034, 1993. (Also presented at the Thirteenth Symposium on Turbulence, Rolla, MI, September 1992.) Funded by US Department of Energy and ACERC.
The linear eddy-mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics.
Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.
A Linear Eddy Subgrid Model for Turbulent Combustion: Application to Premixed Combustion
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
AIAA 31st Annual Aerospace Sciences Meeting, 93-0107, Reno, NV, January 1993. Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
Accurate treatment of turbulent mixing processes is among the most important unsolved problems in developing numerical predictive schemes for reacting flows and propulsion systems. In this paper, the development and implementation of a new subgrid modeling approach to treat turbulent mixing and chemical reactions is described. The model is applicable to both nonreacting and reacting flows, with and without heat release. In addition, the same subgrid model with some minor changes is applicable to both nonpremixed and premixed reacting flows. The application of the subgrid model to simulate thin premixed flame propagation in a turbulent media is demonstrated in this paper.
1992
A Linear Eddy Mixing Model for a Large Eddy Simulation of Turbulent Combustion
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
Linear Eddy Mixing of Complex Engineering and Geophysical Flows, 1992 (in press). Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
To improve predictive capabilities for modern combustion processes, sophisticated models that faithfully represent the physics of turbulent mixing and reaction are required. Models that are presently used to study combustion systems, such as those based on gradient diffusion assumptions, omit important aspects of the subgrid mixing process. More sophisticated methods based on probability density function (PDF) transport equations treat the reaction process exactly, but the molecular mixing submodels that are employed are not fully satisfactory. Although the utility of these models should not be overlooked, there is clearly a need to develop alternative methods for calculating turbulent mixing processes.
In modeling the scalar mixing process, one encounters difficulties not present in modeling momentum transport. These difficulties can be primarily attributed to the interactions among turbulent stirring, molecular diffusion, and chemical reaction at the smallest scales of the flow. A reliable model of subgrid mixing and reaction should therefore include and distinguish among these distinctly different physical processes. To accomplish this, it appears that a comprehensive description of the scalar microfield is needed. This is fundamentally different from momentum transport modeling, in which the main influence of the small scales is to provide dissipation for the large-scale structures. Thus, while the effect of subgrid stresses on the momentum transport can be reasonably treated with various eddy viscosity models, a similar characterization of the subgrid scalar field in terms of an eddy diffusivity is neither sufficient nor correct, since an accurate description of the small-scale dynamics is critical to the overall mixing and the combustion process. As a result of these features of the turbulent mixing process, progress in the development of subgrid mixing models for us in large eddy simulation (LES) has been limited.
These fundamental issues are relevant to both the solution of the Reynolds-averaged flow field (where only the mean motion is of interest) and the solution of the unsteady flow field simulated using LES techniques. In this chapter, the development of a subgrid modeling approach specifically directed at scalar mixing is addressed. The model is based on Kerstein's (1988, 1991) linear eddy model. The emphasis here is placed on premixed combustion applications, although the general formulation has also been applied to turbulent diffusion flames (McMurtry et al., 1991, 1992).
A New Unsteady Mixing Model to Predict NOx Production During Rapid Mixing in a Dual-Stage Combustor
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
AAIA Journal of Jet Propulsion and Power, 1992 (in press). (Also presented at the AIAA Annual Aerospace Sciences Meeting, Reno, NV, January 1992). Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
An advanced gas turbine engine to power supersonic transport aircraft is currently under study. In addition to high combustion efficiency requirements, environmental concerns have placed stringent restrictions on the pollutant emissions from these engines. A dual-stage combustor with the potential for minimizing pollutants such as NOx emissions is undergoing experimental evaluation. A major technical issue in the design of this combustor is how to rapidly mix the hot, fuel-rich primary stage product with the secondary diluent air to obtain a fuel-lean mixture for combustion in the secondary stage. Numerical design studies using steady-state methods cannot account for the unsteady phenomena in the mixing region. Therefore, to evaluate the effect of unsteady mixing and combustion processes, a novel unsteady mixing model is demonstrated here. This model has been used in a stand-alone mode to study mixing and combustion in hydrogen-air nonpremixed jet flames. NOx production in these jet flames was also predicted. Comparison of the computed results with experimental data shows good agreement thereby providing validation of the mixing model. This mixing model has been developed so that it can also be implemented within steady-state prediction codes and thus, may eventually provide an improved engineering design analysis tool.
Linear Eddy Simulations of Mixing in a Homogeneous Turbulent Flow
McMurtry, P.A.; Gansuage, T.C. and Kerstein, A.R.
Physics of Fluids A., 1992 (in press). (Also presented at the Thirteenth Symposium on Turbulence, Rolla, MI, September 1992). Funded by US Department of Energy, Office of Naval Research and ACERC.
The linear eddy-mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics. Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.
Effects of Turbulence Length Scale Distribution on Scalar Mixing in Homogeneous Turbulent Flow
McMurtry, P.A.; Cremer, M. and Kerstein, A.R.
APS Division of Fluid Dynamics, Tallahassee, FL, November 1992. Funded by US Department of Energy and ACERC.
The linear eddy-mixing model is used to study effects of the turbulence length scale distribution on the transient evolution of a passive scalar in a statistically steady, homogeneous turbulent flow. Model simulations are carried out using length-scale distributions that are respectively wide-banded and narrow-banded, representing mixing at high and low Reynolds number. The two cases found to exhibit qualitative differences in mixing behavior. The low Reynolds number linear eddy results exhibit behaviors not seen in DNS studies, such as trimodal transient scalar pdf's. It is found that asymptotically non-Gaussian scalar pdf's may be obtained both for high and low Reynolds number cases.
The sensitivity of mixing behavior to flow bandwidth is interpreted mechanistically. In particular, a geometrical representation of scalar fields in turbulence based on a lamellar picture is shown to exhibit analogous sensitivity to bandwidth. Under assumptions corresponding to narrow-band mixing, this "Clipped laminar profile" representation reproduces the pdf evolution previously obtained using mapping closure. Thus, the mapping closure solution as well as the DNS is found to be narrow-band in character. This interference is consistent with the absence of length-scale considerations in the mapping closure analysis, and with the good agreement of the mapping closure solution with DNS results.
A Linear Eddy Subgrid Model for Turbulent Reacting Flows: Application to Hydrogen-Air Combustion
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, Sydney, Australia, July 1992. (Also presented at the APS Division of Fluid Dynamics, Tallahasee, Fl, November 1992 and the AIAA Annual Aerospace Sciences Meeting, Reno, NV, Janaury 1992.) Funded by U.S. Department of Energy, NASA Lewis Research Center and ACERC.
A new sub-grid mixing model for use in large eddy simulations of turbulent combustion is presented and applied to a hydrogen-air diffusion flame. The sub-grid model is based on Kerstein's Linear Eddy Model (Comb. Sci. Tech. 60, 391, 1988), which reduces the description of the scalar field to a locally one-dimensional representation. The formulation involves performing separate linear eddy calculations in each cell to describe the small-scale scalar mixing and reaction process. Convective transport across grid surfaces is accomplished by "splicing" events by which linear eddy elements are copied to and from neighboring grid cells based on the grid-resolved velocity field.
The model is first used to predict the mixing of a conserved scalar in a turbulent shear flow. The model correctly predicts the behavior of the pdf of the scalar field. In particular, it displays a non-marching peak at the preferred mixture fraction as the shear layer is traversed. It is then illustrated how a reduced chemical mechanism can be implemented within the linear eddy subgrid model formulation. The model is used to predict NO formation in a hydrogen-air diffusion flame using a reduced chemical mechanism involving nine reactive scalars.
1991
A Linear Eddy Subgrid Model for Turbulent Mixing and Reaction
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Fourth International Conference on Numerical Combustion, St. Petersburg, FL, November 1991. Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
A new subgrid modeling technique is described for use in large eddy simulations of turbulent mixing and reaction. In particular, a model for mixing and chemical reactions at the subgrid level is developed based on the Kerstein's linear eddy approach. A unique feature of this model is the separate treatment of turbulent convection and molecular diffusion over all length-scales of the flow. This distinction, which is not retained in existing mixing models, is critical for predicting the small scale mixing process and capturing Schmidt number dependency and the effects of finite rate reaction.
1990
Chemical Percolation Model for Devolatilization: 2. Temperature and Heating Rate Effects on Product Yields
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Energy & Fuels, 4 (54), 1990. Funded by Pittsburgh Energy Technology Center, US Department of Energy, National Science Foundation and ACERC.
The chemical percolation devolatilization (CPD) model previously developed to describe the devolatilization behavior of rapidly heated coal was based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe generation of finite tar clusters as labile bonds are cleaved in the infinite coal lattice. The model is used here to describe effects of heating rate and temperature on tar and gas release from coal. Coefficients for the net rate of competition between char formation and side-chain formation are generated from heated screen data performed at five different heating rates. The model also compares well with heated screen data obtained at 1000 K/s and different hold times at the final temperature as well as with data from entrained-flow reactors obtained at higher heating rates (104 K/s) where particle temperatures have been measured. Results indicate that the CPD model predictions yield good agreement with published data for a wide range of coals and particle heating rates.
A Chemical Percolation Model of Coal Devolatilization: 3. Direct Use of C-13 NMR Data to Predict Effects of Coal Type
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J.; Solum, M.S. and Grant, D.M.
Polycyclic Aromatic Compounds, 1:251-264, 1990. Funded by Gas Research Institute and ACERC.
The chemical percolation devolatilization (CPD) model describes the devolatilization behavior of rapidly heated coal based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe the generation of tar precursors of finite size based on the number of cleaved labile bonds in the infinite coal lattice. The chemical percolation devolatilization model described here includes treatment of vapor-liquid equilibrium and a cross-linking mechanism. The cross-linking mechanism permits reattachment of metaplast to the infinite char matrix. A generalized vapor pressure correlation for high molecular weight hydrocarbons, such as coal tar, is proposed based on data from coal liquids. Coal-independent kinetic parameters are employed. Coal-dependent chemical structure coefficients for the CPD model are taken directly from C-13 NMR measurements, with the exception of one empirical parameter representing the population of char bridges in the parent coal. This is in contrast to the previous and common practice of adjusting input coefficients to precisely match measured tar and total volatiles yields. The CPD model successfully predicts the effects of pressure on tar and total volatiles yields observed in heated grid experiments for both bituminous coal and for lignite. Predicted tar molecular weights are consistent with size-exclusion chromatography (SEC) data and field ionization mass spectrometry (FIMS) data. Predictions of average molecular weights of aromatic clusters as a function of coal type agree with corresponding data from NMR analyses of parent coals. The direct use of chemical structure data as a function of coal type helps justify the model on a mechanistic rather than an empirical basis.
1989
Chemical Percolation Model for Devolatilization: II. Temperature and Heating Rate Effects on Product Yields
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Accepted for publication by Energy & Fuels, 1989. Funded by US Department of Energy and ACERC (National Science Foundation and Associates and Affiliates).
The CPD model previously developed to describe the devolatilization behavior of rapidly heated coal was based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe generation of finite tar clusters as labile bonds are cleaved in the infinite coal lattice. The model is used here to describe effects of heating rate and temperature on tar and gas release from coal. Coefficients for the net rate of competition between char formation and side chain formation are generated from heated screen data performed at five different heating rates. The model also compares well with heated screen data obtained at 1000 K/s and different hold times at the final temperature as well as with data from entrained flow reactors obtained at higher heating rates (104 K/s) where particle temperatures have been measured. Results indicate that the CPD model predictions yield good agreement with published data for a wide range of coals and particle heating rates.
A Chemical Percolation Model for Devolatilization: Temperature and Heating Rate Effects
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Fuel Div. Preprint, 34 (4), 1272-1279, 198th ACS National Meeting, Miami, 1989. Funded by US Department of Energy and ACERC (National Science Foundation and Associates and Affiliates).
It is well known that the yield of volatile matter obtained from a pulverized coal is dependent upon the temperature history of the particle. However, the effect of heating rate on volatiles yield is difficult to study independently of final temperature. For example, the volatile yields obtained in an entrained flow reactor study by Kobayashi, et al. increase with both temperature and heating rate, but the independent contribution of heating rate could not be assessed. Heated screen experiments were developed to study devolatilization behavior at different heating rates independently from the final particle temperature. The data of Anthony and Howard show little increase in volatiles yield when particles are heated to the same final temperature on a heated screen at different heating rates. In a more recent study, Gibbins-Matham and Kandiyoti show evidence for small increases in the volatiles yield from a Pittsburgh #8 coal as the heating rate is increased from 1 K/s to 1000 K/s on a heated screen. Coal samples were heated at 5 different heating rates to a final temperature of 700ºC and held for 30 s. Experiments were repeated several times in order to ensure accuracy of the data. The total volatiles yield increases from 41.5% at 1 K/s to 46.8% at 1000 K/s, a relative increase in yield of 13%. This increase in yield with increase in heating rate is small, but is larger than associated experimental errors.
The chemical percolation devolatilization (CPD) model was developed as a means to describe coal devolatilization behavior based upon the chemical structure of the patent coal. Some of the input parameters for this model are obtained from NMR characterizations of the parent coal. Percolation statistics are used to describe the probability of generating finite tar fragments from the infinite coal matrix. Pyrolysis yields of tar, gas, and char for three different types of coal are described using a single set of kinetic parameters: only chemical structure parameters are changed for the different coals. The initial description of the CPD model allowed for a temperature dependence of the competition between side chain formation and char formation. However, this option was not exercised in the initial study in order to demonstrate general utility of the model for one set of devolatilization data on three coals collected over a narrow range of temperatures and heating rates. In the present work, the Gibbins-Matham and Kandiyoti data are used to determine additional coefficients for the CPD model that accurately predict the changes in char and tar yield as a function of heating rate.
1988
A Chemical Model of Coal Devolatilization Using Percolation Lattice Statistics
Grant, D.M.; Pugmire, R.J.; Fletcher, T.H. and Kerstein, A.R.
ACS Div. of Fuel Chemistry, 33, (2), 322-332, 1988. 10 pgs. Funded by ACERC (National Science Foundation and Associates and Affiliates).
We have developed a model for coal devolatilization that incorporates the diversity of coal structure in such a way that the analytical data obtained from solid state NMR provides the initial input data. Using experimentally determined kinetic rate parameters, it is possible to fit the gas, tar and char production of a lignite and high volatile bituminous coal. We have employed percolation theory to provide analytical expressions for the lattice statistics required in devolatilization modeling. The percolation theory allows one to avoid the more time-consuming Monte Carlo technique with no loss of generality or important statistical features. Percolation theory analytically describes the size distribution of finite clusters of sites joined by intact bridges but isolated from all remaining sites by broken bridges. The theory specifies a critical bridge population, depending only on the site coordination number, above which infinite arrays will coexist with clusters of finite size. It is a simple matter to adapt the structural features of percolation theory to both the tar and gas obtained in coal pyrolysis. The infinite arrays of percolation theory are interpreted as the macroscopic lattice of unreacted coal and/or char while the relatively small tar molecules may be identified with the fine clusters of percolation theory. The details of the model will be discussed together with the results obtained in modeling devolatilization behavior of coals of various ranks.
Kerstein, AR
1997
Mixing Mechanisms in Turbulent Pipe Flow
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Phys. Fluids, 9(3):717-23(1997). Funded by ACERC and National Science Foundation.
An experimental investigation of passive scalar mixing in turbulent pipe flow is carried out using a new non-intrusive scalar initialization technique. The measurements support a recently predicted similarity scaling of concentration spectra in flows that are unbounded in one direction. Reflecting this scaling, the scalar variance exhibits a power-law rather than exponential decay, indicating that the traditional plug-flow reactor picture of turbulent pipe-flow mixing omits key physical mechanisms.
1994
Long-Tailed Probability Distributions in Turbulent-Pipe-Flow Mixing
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Physical Review E, 56(2):1753-758(1997). Funded by ACERC and National Science Foundation.
Exponential-tailed scalar probability density functions (PDF's) are obtained by high-pass filtering scalar concentration time series measured in turbulent pipe flow. This behavior reflects the scale separation of scalar and velocity fluctuations that develops in this flow, such that the low-wave-number scalar fluctuations act as and imposed scalar gradient stirred by finer-scale wall-generated shear. This observation broadens the class of flows in which long-tailed scalar PDF's are anticipated to occur.
Effects of Turbulence Length-Scale Distribution on Scalar Mixing in Homogeneous Turbulent Flow
Cremer, M.A.; McMurtry, P.A. and Kerstein, A.R.
Physics of Fluids, 6:2143, 1994. Funded by ACERC and US Department of Energy.
The linear eddy-mixing model is used to study effects of the turbulence length-scale distribution on the transient evolution of a passive scalar in a statistically steady homogeneous turbulent flow. Model simulations are carried out using both wide-band length-scale distributions reflecting high-Reynolds-number scaling, and narrow-band (in effect, low-Reynolds-number) distributions. The two cases are found to exhibit qualitative differences in mixing behavior. These differences are interpreted mechanistically. The narrow-band case yields the best agreement with published direct numerical simulation results, suggesting that those results are, in effect, low-Reynolds, number results not readily extrapolated to high-Reynolds-number mixing.
Low-Wave-Number Statistics of Randomly Advected Passive Scalars
Kerstein, A.R. and McMurtry, P.A.
Physical Review E, 50:2057, 1993. Funded by ACERC, National Science Foundation and US Department of Energy.
A heuristic analysis of the decay of a passive scalar field, subject to statistically steady random advection, predicts two low-wave-number spectral scaling regimes analogous to the similarity states previously identified by Chasnov. Consequences of their predicted coexistence in a single flow are examined. The analysis is limited to the idealized case of narrow band advection. To complement the analysis, and to extend the predictions to physically more realistic advection processes, advection diffusion is simulated using a one-dimensional stochastic model. An experimental test of the predictions is proposed.
Prediction of NOx Production in a Turbulent Hydrogen-Air Jet Flame
Menon, S.; McMurtry, P.A.; Kerstein, A.R. and Chen, J.
AIAA Journal of Propulsion and Power, 10:161-168, 1994. Funded by ACERC, NASA and US Department of Energy.
A major concern in the numerical study of turbulent nonpremixed flames is the accurate prediction of trace species. The production of pollutants such as NOx during unsteady combustion needs to be understood and predicted accurately so that the design of the next generation's combustion systems can meet the forthcoming stricter environmental restrictions. Numerical studies using steady-state methods cannot account for the unsteady phenomena in the mixing region, and therefore, fail to accurately predict the NOx production that could occur. A novel unsteady mixing model is demonstrated here that accounts for all the length scales associated with mixing and molecular diffusion processes. Finite-rate kinetics in the form of a reduced mechanism have been used to study hydrogen-air nonpremixed jet flames. NOx production in these jet flames was also predicted. Comparisons with experimental data and PDF calculations show good agreement, thereby, providing validation of the mixing model.
Mean-Field Theories of Random Advection
Kerstein, A.R. and McMurtry, P.A.
Physical Review, E, 49:474-482, 1994. Funded by ACERC, National Science Foundation and US Department of Energy.
Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir to derive the phenomenological model of Pumir, Shraiman, and Siggia governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.
1993
Linear Eddy Modeling of Turbulent Combustion
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Energy & Fuels, 7, (6):817-826, 1993. Funded by National Science Foundation and ACERC.
The use of the linear eddy mixing model in application to reacting flows is discussed for several different combustion geometries. The unique feature of this model is the explicit distinction made among the various physical processes (convection, diffusion, and reaction) at all scales of the flow. This is achieved by resolving all relevant scales of motion through a reduced, one-dimensional statistical description of the scalar field in a linear domain. The advantages of this modeling approach over other conventional modeling approaches are pointed out. Applications to both "stand-alone" formulations and subgrid formulations for use in large eddy simulation (LES) are discussed.
Mean-Field Theories of Random Advection
Kerstein, A.R. and McMurtry, P.A.
Physical Review, E, 1993 (in press). Funded by US Department of Energy, National Science Foundation and ACERC.
Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir to derive the phenomenological model of Pumir, Shraiman, and Siggia governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.
Linear Eddy Simulations of Mixing in a Homogeneous Turbulent Flow
McMurtry, P.A.; Gansuage, T.C.; Kerstein, A.R. and Krueger, S.K.
Physics of Fluids A., 5 (4):1023 - 1034, 1993. (Also presented at the Thirteenth Symposium on Turbulence, Rolla, MI, September 1992.) Funded by US Department of Energy and ACERC.
The linear eddy-mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics.
Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.
A Linear Eddy Subgrid Model for Turbulent Combustion: Application to Premixed Combustion
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
AIAA 31st Annual Aerospace Sciences Meeting, 93-0107, Reno, NV, January 1993. Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
Accurate treatment of turbulent mixing processes is among the most important unsolved problems in developing numerical predictive schemes for reacting flows and propulsion systems. In this paper, the development and implementation of a new subgrid modeling approach to treat turbulent mixing and chemical reactions is described. The model is applicable to both nonreacting and reacting flows, with and without heat release. In addition, the same subgrid model with some minor changes is applicable to both nonpremixed and premixed reacting flows. The application of the subgrid model to simulate thin premixed flame propagation in a turbulent media is demonstrated in this paper.
1992
A Linear Eddy Mixing Model for a Large Eddy Simulation of Turbulent Combustion
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
Linear Eddy Mixing of Complex Engineering and Geophysical Flows, 1992 (in press). Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
To improve predictive capabilities for modern combustion processes, sophisticated models that faithfully represent the physics of turbulent mixing and reaction are required. Models that are presently used to study combustion systems, such as those based on gradient diffusion assumptions, omit important aspects of the subgrid mixing process. More sophisticated methods based on probability density function (PDF) transport equations treat the reaction process exactly, but the molecular mixing submodels that are employed are not fully satisfactory. Although the utility of these models should not be overlooked, there is clearly a need to develop alternative methods for calculating turbulent mixing processes.
In modeling the scalar mixing process, one encounters difficulties not present in modeling momentum transport. These difficulties can be primarily attributed to the interactions among turbulent stirring, molecular diffusion, and chemical reaction at the smallest scales of the flow. A reliable model of subgrid mixing and reaction should therefore include and distinguish among these distinctly different physical processes. To accomplish this, it appears that a comprehensive description of the scalar microfield is needed. This is fundamentally different from momentum transport modeling, in which the main influence of the small scales is to provide dissipation for the large-scale structures. Thus, while the effect of subgrid stresses on the momentum transport can be reasonably treated with various eddy viscosity models, a similar characterization of the subgrid scalar field in terms of an eddy diffusivity is neither sufficient nor correct, since an accurate description of the small-scale dynamics is critical to the overall mixing and the combustion process. As a result of these features of the turbulent mixing process, progress in the development of subgrid mixing models for us in large eddy simulation (LES) has been limited.
These fundamental issues are relevant to both the solution of the Reynolds-averaged flow field (where only the mean motion is of interest) and the solution of the unsteady flow field simulated using LES techniques. In this chapter, the development of a subgrid modeling approach specifically directed at scalar mixing is addressed. The model is based on Kerstein's (1988, 1991) linear eddy model. The emphasis here is placed on premixed combustion applications, although the general formulation has also been applied to turbulent diffusion flames (McMurtry et al., 1991, 1992).
A New Unsteady Mixing Model to Predict NOx Production During Rapid Mixing in a Dual-Stage Combustor
Menon, S.; McMurtry, P.A. and Kerstein, A.R.
AAIA Journal of Jet Propulsion and Power, 1992 (in press). (Also presented at the AIAA Annual Aerospace Sciences Meeting, Reno, NV, January 1992). Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
An advanced gas turbine engine to power supersonic transport aircraft is currently under study. In addition to high combustion efficiency requirements, environmental concerns have placed stringent restrictions on the pollutant emissions from these engines. A dual-stage combustor with the potential for minimizing pollutants such as NOx emissions is undergoing experimental evaluation. A major technical issue in the design of this combustor is how to rapidly mix the hot, fuel-rich primary stage product with the secondary diluent air to obtain a fuel-lean mixture for combustion in the secondary stage. Numerical design studies using steady-state methods cannot account for the unsteady phenomena in the mixing region. Therefore, to evaluate the effect of unsteady mixing and combustion processes, a novel unsteady mixing model is demonstrated here. This model has been used in a stand-alone mode to study mixing and combustion in hydrogen-air nonpremixed jet flames. NOx production in these jet flames was also predicted. Comparison of the computed results with experimental data shows good agreement thereby providing validation of the mixing model. This mixing model has been developed so that it can also be implemented within steady-state prediction codes and thus, may eventually provide an improved engineering design analysis tool.
Linear Eddy Simulations of Mixing in a Homogeneous Turbulent Flow
McMurtry, P.A.; Gansuage, T.C. and Kerstein, A.R.
Physics of Fluids A., 1992 (in press). (Also presented at the Thirteenth Symposium on Turbulence, Rolla, MI, September 1992). Funded by US Department of Energy, Office of Naval Research and ACERC.
The linear eddy-mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics. Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.
Effects of Turbulence Length Scale Distribution on Scalar Mixing in Homogeneous Turbulent Flow
McMurtry, P.A.; Cremer, M. and Kerstein, A.R.
APS Division of Fluid Dynamics, Tallahassee, FL, November 1992. Funded by US Department of Energy and ACERC.
The linear eddy-mixing model is used to study effects of the turbulence length scale distribution on the transient evolution of a passive scalar in a statistically steady, homogeneous turbulent flow. Model simulations are carried out using length-scale distributions that are respectively wide-banded and narrow-banded, representing mixing at high and low Reynolds number. The two cases found to exhibit qualitative differences in mixing behavior. The low Reynolds number linear eddy results exhibit behaviors not seen in DNS studies, such as trimodal transient scalar pdf's. It is found that asymptotically non-Gaussian scalar pdf's may be obtained both for high and low Reynolds number cases.
The sensitivity of mixing behavior to flow bandwidth is interpreted mechanistically. In particular, a geometrical representation of scalar fields in turbulence based on a lamellar picture is shown to exhibit analogous sensitivity to bandwidth. Under assumptions corresponding to narrow-band mixing, this "Clipped laminar profile" representation reproduces the pdf evolution previously obtained using mapping closure. Thus, the mapping closure solution as well as the DNS is found to be narrow-band in character. This interference is consistent with the absence of length-scale considerations in the mapping closure analysis, and with the good agreement of the mapping closure solution with DNS results.
A Linear Eddy Subgrid Model for Turbulent Reacting Flows: Application to Hydrogen-Air Combustion
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, Sydney, Australia, July 1992. (Also presented at the APS Division of Fluid Dynamics, Tallahasee, Fl, November 1992 and the AIAA Annual Aerospace Sciences Meeting, Reno, NV, Janaury 1992.) Funded by U.S. Department of Energy, NASA Lewis Research Center and ACERC.
A new sub-grid mixing model for use in large eddy simulations of turbulent combustion is presented and applied to a hydrogen-air diffusion flame. The sub-grid model is based on Kerstein's Linear Eddy Model (Comb. Sci. Tech. 60, 391, 1988), which reduces the description of the scalar field to a locally one-dimensional representation. The formulation involves performing separate linear eddy calculations in each cell to describe the small-scale scalar mixing and reaction process. Convective transport across grid surfaces is accomplished by "splicing" events by which linear eddy elements are copied to and from neighboring grid cells based on the grid-resolved velocity field.
The model is first used to predict the mixing of a conserved scalar in a turbulent shear flow. The model correctly predicts the behavior of the pdf of the scalar field. In particular, it displays a non-marching peak at the preferred mixture fraction as the shear layer is traversed. It is then illustrated how a reduced chemical mechanism can be implemented within the linear eddy subgrid model formulation. The model is used to predict NO formation in a hydrogen-air diffusion flame using a reduced chemical mechanism involving nine reactive scalars.
1991
A Linear Eddy Subgrid Model for Turbulent Mixing and Reaction
McMurtry, P.A.; Menon, S. and Kerstein, A.R.
Fourth International Conference on Numerical Combustion, St. Petersburg, FL, November 1991. Funded by US Department of Energy, NASA Lewis Research Center and ACERC.
A new subgrid modeling technique is described for use in large eddy simulations of turbulent mixing and reaction. In particular, a model for mixing and chemical reactions at the subgrid level is developed based on the Kerstein's linear eddy approach. A unique feature of this model is the separate treatment of turbulent convection and molecular diffusion over all length-scales of the flow. This distinction, which is not retained in existing mixing models, is critical for predicting the small scale mixing process and capturing Schmidt number dependency and the effects of finite rate reaction.
1990
Chemical Percolation Model for Devolatilization: 2. Temperature and Heating Rate Effects on Product Yields
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Energy & Fuels, 4 (54), 1990. Funded by Pittsburgh Energy Technology Center, US Department of Energy, National Science Foundation and ACERC.
The chemical percolation devolatilization (CPD) model previously developed to describe the devolatilization behavior of rapidly heated coal was based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe generation of finite tar clusters as labile bonds are cleaved in the infinite coal lattice. The model is used here to describe effects of heating rate and temperature on tar and gas release from coal. Coefficients for the net rate of competition between char formation and side-chain formation are generated from heated screen data performed at five different heating rates. The model also compares well with heated screen data obtained at 1000 K/s and different hold times at the final temperature as well as with data from entrained-flow reactors obtained at higher heating rates (104 K/s) where particle temperatures have been measured. Results indicate that the CPD model predictions yield good agreement with published data for a wide range of coals and particle heating rates.
A Chemical Percolation Model of Coal Devolatilization: 3. Direct Use of C-13 NMR Data to Predict Effects of Coal Type
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J.; Solum, M.S. and Grant, D.M.
Polycyclic Aromatic Compounds, 1:251-264, 1990. Funded by Gas Research Institute and ACERC.
The chemical percolation devolatilization (CPD) model describes the devolatilization behavior of rapidly heated coal based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe the generation of tar precursors of finite size based on the number of cleaved labile bonds in the infinite coal lattice. The chemical percolation devolatilization model described here includes treatment of vapor-liquid equilibrium and a cross-linking mechanism. The cross-linking mechanism permits reattachment of metaplast to the infinite char matrix. A generalized vapor pressure correlation for high molecular weight hydrocarbons, such as coal tar, is proposed based on data from coal liquids. Coal-independent kinetic parameters are employed. Coal-dependent chemical structure coefficients for the CPD model are taken directly from C-13 NMR measurements, with the exception of one empirical parameter representing the population of char bridges in the parent coal. This is in contrast to the previous and common practice of adjusting input coefficients to precisely match measured tar and total volatiles yields. The CPD model successfully predicts the effects of pressure on tar and total volatiles yields observed in heated grid experiments for both bituminous coal and for lignite. Predicted tar molecular weights are consistent with size-exclusion chromatography (SEC) data and field ionization mass spectrometry (FIMS) data. Predictions of average molecular weights of aromatic clusters as a function of coal type agree with corresponding data from NMR analyses of parent coals. The direct use of chemical structure data as a function of coal type helps justify the model on a mechanistic rather than an empirical basis.
1989
Chemical Percolation Model for Devolatilization: II. Temperature and Heating Rate Effects on Product Yields
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Accepted for publication by Energy & Fuels, 1989. Funded by US Department of Energy and ACERC (National Science Foundation and Associates and Affiliates).
The CPD model previously developed to describe the devolatilization behavior of rapidly heated coal was based on the chemical structure of the parent coal. Percolation lattice statistics are employed to describe generation of finite tar clusters as labile bonds are cleaved in the infinite coal lattice. The model is used here to describe effects of heating rate and temperature on tar and gas release from coal. Coefficients for the net rate of competition between char formation and side chain formation are generated from heated screen data performed at five different heating rates. The model also compares well with heated screen data obtained at 1000 K/s and different hold times at the final temperature as well as with data from entrained flow reactors obtained at higher heating rates (104 K/s) where particle temperatures have been measured. Results indicate that the CPD model predictions yield good agreement with published data for a wide range of coals and particle heating rates.
A Chemical Percolation Model for Devolatilization: Temperature and Heating Rate Effects
Fletcher, T.H.; Kerstein, A.R.; Pugmire, R.J. and Grant, D.M.
Fuel Div. Preprint, 34 (4), 1272-1279, 198th ACS National Meeting, Miami, 1989. Funded by US Department of Energy and ACERC (National Science Foundation and Associates and Affiliates).
It is well known that the yield of volatile matter obtained from a pulverized coal is dependent upon the temperature history of the particle. However, the effect of heating rate on volatiles yield is difficult to study independently of final temperature. For example, the volatile yields obtained in an entrained flow reactor study by Kobayashi, et al. increase with both temperature and heating rate, but the independent contribution of heating rate could not be assessed. Heated screen experiments were developed to study devolatilization behavior at different heating rates independently from the final particle temperature. The data of Anthony and Howard show little increase in volatiles yield when particles are heated to the same final temperature on a heated screen at different heating rates. In a more recent study, Gibbins-Matham and Kandiyoti show evidence for small increases in the volatiles yield from a Pittsburgh #8 coal as the heating rate is increased from 1 K/s to 1000 K/s on a heated screen. Coal samples were heated at 5 different heating rates to a final temperature of 700ºC and held for 30 s. Experiments were repeated several times in order to ensure accuracy of the data. The total volatiles yield increases from 41.5% at 1 K/s to 46.8% at 1000 K/s, a relative increase in yield of 13%. This increase in yield with increase in heating rate is small, but is larger than associated experimental errors.
The chemical percolation devolatilization (CPD) model was developed as a means to describe coal devolatilization behavior based upon the chemical structure of the patent coal. Some of the input parameters for this model are obtained from NMR characterizations of the parent coal. Percolation statistics are used to describe the probability of generating finite tar fragments from the infinite coal matrix. Pyrolysis yields of tar, gas, and char for three different types of coal are described using a single set of kinetic parameters: only chemical structure parameters are changed for the different coals. The initial description of the CPD model allowed for a temperature dependence of the competition between side chain formation and char formation. However, this option was not exercised in the initial study in order to demonstrate general utility of the model for one set of devolatilization data on three coals collected over a narrow range of temperatures and heating rates. In the present work, the Gibbins-Matham and Kandiyoti data are used to determine additional coefficients for the CPD model that accurately predict the changes in char and tar yield as a function of heating rate.
1988
A Chemical Model of Coal Devolatilization Using Percolation Lattice Statistics
Grant, D.M.; Pugmire, R.J.; Fletcher, T.H. and Kerstein, A.R.
ACS Div. of Fuel Chemistry, 33, (2), 322-332, 1988. 10 pgs. Funded by ACERC (National Science Foundation and Associates and Affiliates).
We have developed a model for coal devolatilization that incorporates the diversity of coal structure in such a way that the analytical data obtained from solid state NMR provides the initial input data. Using experimentally determined kinetic rate parameters, it is possible to fit the gas, tar and char production of a lignite and high volatile bituminous coal. We have employed percolation theory to provide analytical expressions for the lattice statistics required in devolatilization modeling. The percolation theory allows one to avoid the more time-consuming Monte Carlo technique with no loss of generality or important statistical features. Percolation theory analytically describes the size distribution of finite clusters of sites joined by intact bridges but isolated from all remaining sites by broken bridges. The theory specifies a critical bridge population, depending only on the site coordination number, above which infinite arrays will coexist with clusters of finite size. It is a simple matter to adapt the structural features of percolation theory to both the tar and gas obtained in coal pyrolysis. The infinite arrays of percolation theory are interpreted as the macroscopic lattice of unreacted coal and/or char while the relatively small tar molecules may be identified with the fine clusters of percolation theory. The details of the model will be discussed together with the results obtained in modeling devolatilization behavior of coals of various ranks.