McMurtry, PA
1997
A Model of Turbulent Mixing and Reaction for H2-Air Combustion
Cremer, M.A. and McMurtry, P.A.
Propulsion and Power, (in press), 1997. Funded by ACERC and National Science Foundation.
A one-dimensional stochastic turbulent mixing model is formulated for application to a constant diameter, cylindrical combustion geometry. Simulations are performed to study effects of turbulence and non-equilibrium chemistry on NO formation in a cylindrically confined H2-air jet. Effects of secondary air injectors, combustion tube diameter, flow rate, and equivalence ratio on NO formation are presented over a range of these parameters. It is illustrated that variations of these parameters can lead to reduced NO production by increasing the turbulence levels and through minimization of residence times in stoichiometric regions where NO production is greatest. Application of these results to the development of new burner concepts is addressed.
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.
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.
1996
Use of Caged Fluorescent Dyes for the Study of Turbulent Passive Scalar Mixing
Guilkey, J.E.; Gee, K.R.; McMurtry, P.A. and Klewicki, J.C.
Experiments and Fluids, 21:237-242, 1996. Funded by National Science Foundation.
The non-intrusive initialization of flow field with distinct spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by "uncaging" the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced florescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.
Modeling Entrainment and Fine-Scale Mixing in Cumulus Clouds
Krueger, S.K.; Su, C. and McMurtry, P.A.
J. Atmos. Sci, (in press), 1996. Funded by National Science Foundation and Office of Naval Research.
The model used by Krueger (1993) to study entrainment and mixing of thermodynamic properties in the stratus-topped boundary layer has been extended to study these processes in cumulus clouds. The new model, called the "explicit mixing parcel model" (EMPM), represents the fine-scale internal structure of a rising thermal in a cumulus cloud using 1D domain. The internal structure evolves in the EMPM as a consequence of a sequence of discrete entrainment events and an explicit representation of turbulent mixing based on Kerstein's (1988) linear eddy model. In this version of the EMPM, a simple parameterization is used to determine the local condensation or evaporation rates. However, the EMPM can incorporate a droplet growth model to allow prediction of droplet spectra evolution.
The EMPM was used to predict the characteristics of Hawaiian cumulus clouds observed by RAGA, et. Al. (1990). All of these quantities required by the EMPM, except for the entrained blob size were obtained form the observations. Profiles of in-cloud mean and variances of thermodynamic properties calculated by the EMPM for entrained blob sized of 50 m, 100 m, and 200 m and by a parcel model with instantaneous mixing were compared to those both mixing representations, but the observed mean liquid water mixing ratio and buoyancy profiles and all of the observed variance profiles are better reproduced by the EMPM. The measurements were not accurate enough to allow further conclusions regarding the entrained blob size.
Additional results from the EMPM suggest that the characteristic entrained blob size may be more precisely determined from aircraft measurements of the clear-air segment size distribution. The model results also demonstrate that the fine-scale structure represented by the EMPM's 1D domain can be directly compared to high-frequency aircraft measurements.
Mixing Mechanisms in Turbulent Pipe Flow
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Physics of Fluids, (in press), 1996. Funded by 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
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reacting Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
ASME Journal of Heat Transfer, 116:761-764, 1994. Funded by ACERC.
The understanding of turbulent reacting flows, which are characterized by the Navier-Stokes equations along with conservation equations of mass and energy, is one of the most challenging fields of engineering science. Various theoretical models based on simplifying assumptions have been developed to predict the behavior of such flows. In some of the models proposed, the problem of modeling the mean reaction rate is exchanged for the problem of describing a scalar dissipation function. Thus the scalar dissipation, which describes the destruction of the fluctuations of a passive scalar at the finest scales existing in a given flow, is an important parameter in modeling turbulent reacting flows.
The objective of this work is to present the statistics of dissipation of a conserved scalar from the DNS of a turbulent reacting shear layer. Since experimental data on the statistics of temperature dissipation in a reacting shear layer of jet flame is readily available, a comparison of this data with the DNS results will also be made.
The Structure of Premixed Flames in Isotropic and Shear Driven Turbulent Flows
Smith, T.M.; Menon, S. and McMurtry, P.A.
Proceedings of the 32nd Aerospace Sciences Meeting, Reno, NV, January 1994. Funded by ACERC and NASA.
The characteristic properties of constant density premixed flames in turbulent flows are analyzed using the results of direct simulations. A thin flame model is used to simulate the propagation of the flame sheet in both decaying isotropic turbulent flow and temporal mixing layers with three-dimensional instability. The study so far has focused on characterizing the geometry of the flame surface that evolves in different types of turbulent fields. The curvature of the flame surface and the strain field in the plane of the flame has been determined and the results show that the most probable shape of the scalar structure in three-dimensional flow fields is cylindrical (i.e. two-dimensional), in both isotropic turbulence and turbulent mixing layers. This agrees with the results of Ashurst, who showed that in constant energy systems, the flame sheet tends to align itself in the direction of the most compressive strain and attain a cylindrical shape. The preferential two-dimensional nature of the flame structure seen in different types of turbulent flows suggests that realistic premixed combustion studies could be carried out using two-dimensional simulations. However, conventional simulation of the propagating thin flames is still subject to some uncertainty since the flame is much thinner than the grid resolution, and thus, cannot be resolved properly. This problem has been addressed in a new 'subgrid' flame propagation model that simulates the flame evolution within each of the grid cells. This new model has shown potential for reproducing many characteristics of the premixed flame structure. However, before such a model can be used for simulating realistic reacting flows it must be demonstrated that the small-scale statistics of the flame structure are reproduced correctly as seen in the direct simulations. Therefore, the statistical data obtained from the subgrid approach will be compared to momentum transport. Based on the preliminary results obtained so far, it is expected that the new subgrid approach will not only reproduce geometrical properties such as the flame curvature and the effect of strain, as seen in the direct simulations, but also will give additional higher order statistical information such as, the time evolution of the flame brush thickness and flame crossing frequency that is difficult to obtain using conventional direct simulations.
1993
Turbulent Reacting Flows
McMurtry, P.A. and Queiroz, M.
Chapter 7, Fundamentals of Coal Combustion: For Clean and Efficient Use, (L.D. Smoot, ed.), Elsevier Science Publishers, The Netherlands, 1993. Funded by ACERC.
This chapter summarizes current technologies and developments for treating reacting turbulent flows. Accurately predicting the effects of turbulence on combustion processes ranks among the most challenging problems in the engineering sciences. Since most combustion occurs in a turbulent environment, effects of turbulence must be treated in a realistic manner in any predictive method. In addition to the effects of turbulence on the chemical species transport, density changes resulting from exothermic chemical reactions can alter the structure and development of the flow field. As such, the fluid mechanics, thermodynamics, and chemistry are strongly coupled, making the description of the turbulent combustion process extremely difficult. Moreover, other complications often arise. Among these are the effects of multiple phases, an inherent aspect of entrained solids and liquids. This chapter illustrates some of the characteristics of turbulent flows and outlines some of the methods used to treat turbulence in reacting flows, while pointing out the need for improved capabilities in this field of study. First, general background on turbulent flows is provided. The most popular approaches used to model turbulence in reactive systems for engineering applications are discussed, along with a few newly introduced techniques. Some of the complications that arise in multi-phase turbulent flow are also discussed. More computationally intensive numerical approaches, used primarily in fundamental research applications, are presented. These methods include Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). Direct simulation results for simplified flow configurations are discussed in light of the information they have provided concerning the physics of turbulent reacting flows.
Thrust Area 4 Research Program: Turbulent, Reacting Fluid Mechanics and Heat Transfer
McMurtry, P.A. and Queiroz, M.
Energy & Fuels, 7 (6):814-816, 1993. Funded by ACERC.
Two of the main reasons for poor turbulence model performance are the lack of understanding of the basic physical mechanisms acting in turbulent reaction flows and a lack of reliable data needed to "tune" model parameters. In addition, the physical complexity of the turbulent mixing process does not lend itself easily to packaged models. There is a need for true innovations and new approaches to treat the turbulence in reacting flows. The work in this thrust area consists of a combination of experiments and numerical studies aimed at (1) directly improving the performance and extending the generality of comprehensive combustion computer codes; (2) developing new approaches to modeling turbulent flows; and (3) conducting fundamental research to improve our understanding of the physical processes acting in turbulent reacting flows and heat transfer. The key products anticipated from the research in this thrust area include (1) new turbulent mixing models that can be incorporated in comprehensive predictive codes for turbulent combustion processes; (2) documented experimental data on planar sprays and particle dynamics in turbulent flows; (3) documented experimental data on radiation properties in multiphase combustion applications; (4) model improvements in the ACERC computer codes to handle spray flames and pulverized particles; (5) three-dimensional radiation submodels for incorporation into the comprehensive code; and (6) fundamental data on the mechanisms of turbulent mixing and reaction.
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.
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reacting Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
ASME Journal of Heat Transfer, 1993 (in press). Funded by ACERC.
The understanding of turbulent reacting flows, which are characterized by the Navier-Stokes equations along with conservation equations of mass and energy, is one of the most challenging fields of engineering science. Various theoretical models based on simplifying assumptions have been developed to predict the behavior of such flows. In some of the models proposed, the problem of modeling the mean reaction rate is exchanged for the problem of describing a scalar dissipation function. Thus the scalar dissipation, which describes the destruction of the fluctuations of a passive scalar at the finest scales existing in a given flow, is an important parameter in modeling turbulent reacting flows.
The objective of this work is to present the statistics of dissipation of a conserved scalar from the DNS of a turbulent reacting shear layer. Since experimental data on the statistics of temperature dissipation in a reacting shear layer of jet flame is readily available, a comparison of this data with the DNS results will also be made.
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.
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reaction Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
Heat Transfer in Fire and Combustion Systems, 223:97-103, 1992. (Also presented at the ASME National Heat Transfer Conference, San Diego, CA, August 1992). Funded by ACERC.
Data from a three-dimensional numerical simulations for a binary single step chemical reaction in a temporally developing turbulent shear layer were used to study the dissipation statistics of a conserved scalar as well as of temperature. Two specific chemical reaction cases were considered: isothermal reaction and chemical reaction with moderate heat release. The average and rms profiles of the mixture fraction dissipation are presented. The study indicated that in both cases the mixture fraction dissipation is related to the reaction rate. The temperature dissipation was found to be lognormally distributed in a region where there was significant chemical reaction. Also features of the temperature dissipation compare qualitatively well with experimental results reported in the literature.
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.
A Study of Favre Averaging Turbulent Flows with Chemical Reaction
Chen, C; Riley, J.J. and McMurtry, P.A.
Combustion and Flame, 87:257-277, 1992. Funded by Office of Naval Research and ACERC.
This article presents an investigation of the Favre averaging method for turbulent flows with chemical reaction. A set of data from direct numerical simulations of a chemically reacting turbulent mixing layer is employed. Favre-averaged quantities are compared directly with their corresponding Reynolds-averaged values. The gradient transport assumptions in the kappa-epsilon model in Favre-averaged form are also tested. Finally the transport equations for the Reynolds stress and scalar flux of the chemical product are studied term by term. Some Favre-averaged quantities such as u, ˜c, and ˜k are very similar numerically to their Reynolds-averaged values. Other Favre-averaged quantities, however, like ˜e, ˜p, ˜u, and ˜v, are significantly different from their Reynolds-averaged values. The gradient transport models generally work rather well when the mixing layer is in a naturally developing turbulent state, although some important weaknesses are noted. Some significant effects of pressure on they Reynolds stress and scalar flux are exhibited.
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.
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.
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
The Effect of Heat Release on Various Statistical Properties of a Reacting Shear Layer
Son, S.F.; McMurtry, P.A; and Queiroz, M.
Combustion and Flame, 85:51-67, 1991. Funded by ACERC.
Three-dimensional direct numerical simulations were used to study the effect of heat release from a binary, single-step chemical reaction on the statistical properties of a temporally developing turbulent mixing layer. Various statistical moments, probability density functions, power spectral densities, and autocorrelations of a conserved scalar, and the velocity field are presented. Scalar-velocity and pressure-velocity correlations, and joint probability density functions, which are extremely difficult to measure experimentally, were also calculated from the simulations. Many features of the calculated statistics compare qualitatively well with results reported from related experimental studies. Significant changes in the vortex structure occur with moderate heat release, resulting in more diffuse vortices than in the isothermal simulation. Consequently, slower rotation rates of the coherent structures occur with moderate heat release. This effect has previously been shown to be caused by the baroclinic torques and thermal expansion in the mixing layer. The statistics in this study reflect these changes in the vortex structure due to moderate heat release.
A Study of Favre Averaging Turbulent Flows with Chemical Reaction
Chen, C; Riley, J.J.; and McMurtry, P.A.
Combustion and Flame, 1991 (in press). Funded by ACERC.
This article presents an investigation of the Favre averaging method for turbulent flows with chemical reaction. A set of data from direct numerical simulations of a chemically reacting turbulent mixing layer is employed. Favre-averaged quantities are compared directly with their corresponding Reynolds-averaged values. The gradient transport assumptions in the k - model in Favre-averaged form are also tested. Finally the transport equations for the Reynolds stress and scalar flux of the chemical product are studied term by term. Some Favre-averaged quantities such as are very similar numerically to their Reynolds-averaged values. Other Favre-averaged quantities, however, like and , are significantly different from their Reynolds-averaged values. The gradient transport models generally work rather well when the mixing layer is in a naturally developing turbulent state, although some important weaknesses are noted. Some significant effects of pressure on they Reynolds stress and scalar flux are exhibited.
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
The Effect of Heat Release on Various Statistical Properties of a Reacting Shear Layer
Son, S.F.; McMurtry, P.A. and Queiroz, M.
Combustion and Flame, 1990 (In press). Funded by ACERC.
Three-dimensional direct numerical simulations were used to study the effect of heat release from a binary, single-step chemical reaction on the statistical properties of a temporally developing turbulent mixing layer. Various statistical moments, probability density functions, power spectral densities, and autocorrelations of a conserved scalar, and the velocity field are presented. Scalar-velocity and pressure-velocity correlations, and joint probability density functions, which are extremely difficult to measure experimentally, were also calculated from the simulations. Many features of the calculated statistics compare qualitatively well with results reported from related experimental studies. Significant changes in the vortex structure occur with moderate heat release, resulting in more diffuse vortices than in the isothermal simulation. Consequently, slower rotation rates of the coherent structures occur with moderate heat release. This effect has previously been shown to be caused by the baroclinic torques and thermal expansion in the mixing layer. The statistics in this study reflect these changes in the vortex structure due to moderate heat release.
Direct Numerical Simulation of a Planar Shear Layer Using the Spectral-Compact Finite Difference Technique
Clarksean, R. and McMurtry, P.A.
AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, Paper 90-1495, Seattle, Washington, 1990. Funded by ACERC and Environmental Protection Agency.
A numerical algorithm is presented for studying mixing processes in turbulent flows. The approach is a combination of the spectral method and the compact finite difference technique. The compact method is fourth order accurate in space and has good phase error characteristics. In addition, the compact finite difference technique is easily implemented on variable grids. The fourth order accuracy is only degraded to order 2.4 accuracy on large aspect ratio grids (6:1) for the two-dimensional advection equation. The application of this method is illustrated by performing direct numerical simulations of a spatially developing mixing layer. The evolving flow field is visualized by contour plots of vorticity magnitude and the scalar field. These figures show the shedding and pairing of vortices similar to previously conducted experimental work. The three-dimensional results show secondary structures developing, which enhance the mixing process. The structure of the three-dimensional flow field is similar to that observed experimentally, illustrating the ability of this hybrid scheme to accurately simulate the unsteady development of incompressible flows.
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.
1989
Flame Generation of Vorticity; Vortex Dipoles from Monopoles
Ashurst, W.T. and McMurtry, P.A.
Comb. Sci, and Tech., 66, 17-37, 1989. Funded by US Department of Energy.
Numerical simulation of premixed flame propagation through a two-dimensional vorticity distribution exhibits the coupling between combustion heat release and fluid dynamics. Effects of both thermal expansion and vorticity generation via baroclinic torques are considered. The rotational part of the velocity field is described by discrete vorticity. The irrotational velocity, given by a velocity potential, is determined by a Poisson equation where the chemical reaction determines the spatial distribution of volume expansion. The transport of a single reacting scalar is computed on an Eulerian mesh with a small-Mach number flow assumption so that the density gradient is nonzero only within the reaction zone. The vector cross product of density gradient and pressure gradient defines the baroclinic generation of vorticity. With a single initial vortical region - the monopole interacting with a premixed flame - the baroclinic effects produce opposite circulation, and, thus, creates a dipole configuration. We use the dipole description in a loose sense, because in some solutions the two signs of vorticity are spatially intermingled. However, in comparison to the monopole, the "dipole" solution has stronger local velocity fluctuations but weaker long-range velocities. Thus, the turbulence in the burnt gas is more intense with smaller length scales than the configuration before the flame-vortex interaction.
Mixing and Reaction in Turbulent Shear Flows: Direct Numerical Simulation
McMurtry, P.A.
1st International Congress. on Tox. Comb., Los Angeles, California, 1989. Funded by ACERC (National Science Foundation and Associates and Affiliates).
Results from numerical simulations of chemically reacting, turbulent mixing layers are presented. Effects of turbulent mixing, chemical heat release, and chemical nonequilibrium are discussed. Effects of chemical heat release in turbulent mixing layers are shown to result in lower chemical formation rates than similar isothermal reactions. A study of the flow in terms of vorticity dynamics and linear stability indicates that the large-scale characteristic vortex structures of mixing layers are inhibited by heat release. Phenomena resulting from chemical nonequilibrium are also presented. In agreement with previous analytic studies, incomplete combustion and flame quenching is shown to result when local diffusion time scales are lowered to those of characteristic chemical time scales. The statistical description of the scalar dissipation is the most important parameter describing the turbulence-chemical nonequilibrium interactions. An understanding of these phenomena is crucial for efficient and complete combustion in turbulent shear flows. On going research activities and suggestions for future work are presented.
1988-1986
Effects of Heat Release on the Large-Scale Structure in Turbulent Mixing Layers
McMurtry, P.A.; Riley, J.J. and Metcalfe, R.W.
To appear in Journal of Fluid Mechanics, 1988. Funded by NASA Lewis Research Center and Office of Naval Research.
The effects of chemical heat release on the large-scale structure in a chemically reacting, turbulent mixing layer are investigated using direct numerical simulations. Three-dimensional, time-dependent simulations are performed for a binary, single-step chemical reaction occurring across a temporally developing turbulent mixing layer. It is found that moderate heat release slows the development of the large-scale structures and shifts their wavelengths to larger scales. The resulting entrainment of reactants is reduced, decreasing the overall chemical product formation rate. The simulation results are interpreted in terms of turbulence energetics, vorticity dynamics, and stability theory. The baroclinic torque and thermal expansion in the mixing layer produce changes in the flame vortex structure that result in more diffuse vortices than in the large-scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques.
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.
The Use of Direct Numerical Simulation in the Study of Turbulent Chemically-Reacting Flows
Riley, J.J. and McMurtry, P.A.
To appear in Analysis of Reacting Flows, Springer-Verlag, 1988. Funded by NASA Lewis Research Center, Office of Naval Research, University of Washington, and US Office of Basic Energy Sciences.
At the present time the role of direct numerical simulation as applied to turbulent, chemically reacting flows is twofold; to understand the physical processes involved, and to develop and test theories. In this paper we present and example of the former. We employ full turbulence simulations to study the effects of chemical heat release on the large-scale structures in turbulent mixing layers. This work not only aids in understanding this phenomenon, but also gives insight into strengths and limitations of the methodology.
We find, in agreement with previous laboratory experiments, the heat release is observed to lower the rate at which the mixing layer grows and to reduce the rate at which chemical products are formed. The baroclinic torque and thermal expansion in the mixing layer are shown to produce changes in the flame vortex structure the act to produce more diffuse vortices than in the constant density case, resulting in lower rotation rates of the large scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques. The density reductions also lower the generation rates of turbulent kinetic energy and the turbulent shear stresses, resulting in less turbulent mixing of fluid elements.
Calculations of the energy in the various wave numbers shows that the heat release has a stabilizing effect on the growth rates of individual modes. A linear stability analysis of a simplified model problem confirms this, showing that low-density fluid in the mixing region will result in a shift in the frequency of the unstable modes to lower wave numbers (longer wavelengths). The growth rates of the unstable modes decrease, contributing to the slower growth of the mixing layer.
Finally, we find that this methodology can be confidently applied for Reynolds numbers less than several hundred and for Damkohler numbers less than about ten. With some modification it is possible to treat the infinite Damkohler number case using a conserved scalar.
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.
Direct Numerical Simulations of a Reacting Mixing Layer with Chemical Heat Release
McMurtry, P.A.; Metcalfe, R.W.; Jou, W.H. and Riley, J.J.
AIAA Journal, 24, (6), 962, 1986. Funded by NASA Lewis Research Center.
To study the coupling between chemical heat release and fluid dynamics, we have performed direct numerical simulations of a two-dimensional mixing layer undergoing a simple single-step chemical reaction with heat release. The reaction is function only of the species concentrations and does not depend on temperature. We have treated the fully compressible equations, as well as an approximate set of equations that is asymptotically valid for low Mach number flows. These latter equations have the computational advantage that high-frequency acoustic waves have been filtered out, allowing much larger time steps to be taken in the numerical solution procedure. A derivation of these equations along with an outline of the numerical solution technique is given. Simulation results indicate that the rate of chemical product formed, the thickness of the mixing layer, and the dynamics are studied to analyze and interpret some effects of heat release on the fluid motion.
McMurtry, PA
1997
A Model of Turbulent Mixing and Reaction for H2-Air Combustion
Cremer, M.A. and McMurtry, P.A.
Propulsion and Power, (in press), 1997. Funded by ACERC and National Science Foundation.
A one-dimensional stochastic turbulent mixing model is formulated for application to a constant diameter, cylindrical combustion geometry. Simulations are performed to study effects of turbulence and non-equilibrium chemistry on NO formation in a cylindrically confined H2-air jet. Effects of secondary air injectors, combustion tube diameter, flow rate, and equivalence ratio on NO formation are presented over a range of these parameters. It is illustrated that variations of these parameters can lead to reduced NO production by increasing the turbulence levels and through minimization of residence times in stoichiometric regions where NO production is greatest. Application of these results to the development of new burner concepts is addressed.
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.
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.
1996
Use of Caged Fluorescent Dyes for the Study of Turbulent Passive Scalar Mixing
Guilkey, J.E.; Gee, K.R.; McMurtry, P.A. and Klewicki, J.C.
Experiments and Fluids, 21:237-242, 1996. Funded by National Science Foundation.
The non-intrusive initialization of flow field with distinct spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by "uncaging" the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced florescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.
Modeling Entrainment and Fine-Scale Mixing in Cumulus Clouds
Krueger, S.K.; Su, C. and McMurtry, P.A.
J. Atmos. Sci, (in press), 1996. Funded by National Science Foundation and Office of Naval Research.
The model used by Krueger (1993) to study entrainment and mixing of thermodynamic properties in the stratus-topped boundary layer has been extended to study these processes in cumulus clouds. The new model, called the "explicit mixing parcel model" (EMPM), represents the fine-scale internal structure of a rising thermal in a cumulus cloud using 1D domain. The internal structure evolves in the EMPM as a consequence of a sequence of discrete entrainment events and an explicit representation of turbulent mixing based on Kerstein's (1988) linear eddy model. In this version of the EMPM, a simple parameterization is used to determine the local condensation or evaporation rates. However, the EMPM can incorporate a droplet growth model to allow prediction of droplet spectra evolution.
The EMPM was used to predict the characteristics of Hawaiian cumulus clouds observed by RAGA, et. Al. (1990). All of these quantities required by the EMPM, except for the entrained blob size were obtained form the observations. Profiles of in-cloud mean and variances of thermodynamic properties calculated by the EMPM for entrained blob sized of 50 m, 100 m, and 200 m and by a parcel model with instantaneous mixing were compared to those both mixing representations, but the observed mean liquid water mixing ratio and buoyancy profiles and all of the observed variance profiles are better reproduced by the EMPM. The measurements were not accurate enough to allow further conclusions regarding the entrained blob size.
Additional results from the EMPM suggest that the characteristic entrained blob size may be more precisely determined from aircraft measurements of the clear-air segment size distribution. The model results also demonstrate that the fine-scale structure represented by the EMPM's 1D domain can be directly compared to high-frequency aircraft measurements.
Mixing Mechanisms in Turbulent Pipe Flow
Guilkey, J.E.; Kerstein, A.R.; McMurtry, P.A. and Klewicki, J.C.
Physics of Fluids, (in press), 1996. Funded by 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
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reacting Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
ASME Journal of Heat Transfer, 116:761-764, 1994. Funded by ACERC.
The understanding of turbulent reacting flows, which are characterized by the Navier-Stokes equations along with conservation equations of mass and energy, is one of the most challenging fields of engineering science. Various theoretical models based on simplifying assumptions have been developed to predict the behavior of such flows. In some of the models proposed, the problem of modeling the mean reaction rate is exchanged for the problem of describing a scalar dissipation function. Thus the scalar dissipation, which describes the destruction of the fluctuations of a passive scalar at the finest scales existing in a given flow, is an important parameter in modeling turbulent reacting flows.
The objective of this work is to present the statistics of dissipation of a conserved scalar from the DNS of a turbulent reacting shear layer. Since experimental data on the statistics of temperature dissipation in a reacting shear layer of jet flame is readily available, a comparison of this data with the DNS results will also be made.
The Structure of Premixed Flames in Isotropic and Shear Driven Turbulent Flows
Smith, T.M.; Menon, S. and McMurtry, P.A.
Proceedings of the 32nd Aerospace Sciences Meeting, Reno, NV, January 1994. Funded by ACERC and NASA.
The characteristic properties of constant density premixed flames in turbulent flows are analyzed using the results of direct simulations. A thin flame model is used to simulate the propagation of the flame sheet in both decaying isotropic turbulent flow and temporal mixing layers with three-dimensional instability. The study so far has focused on characterizing the geometry of the flame surface that evolves in different types of turbulent fields. The curvature of the flame surface and the strain field in the plane of the flame has been determined and the results show that the most probable shape of the scalar structure in three-dimensional flow fields is cylindrical (i.e. two-dimensional), in both isotropic turbulence and turbulent mixing layers. This agrees with the results of Ashurst, who showed that in constant energy systems, the flame sheet tends to align itself in the direction of the most compressive strain and attain a cylindrical shape. The preferential two-dimensional nature of the flame structure seen in different types of turbulent flows suggests that realistic premixed combustion studies could be carried out using two-dimensional simulations. However, conventional simulation of the propagating thin flames is still subject to some uncertainty since the flame is much thinner than the grid resolution, and thus, cannot be resolved properly. This problem has been addressed in a new 'subgrid' flame propagation model that simulates the flame evolution within each of the grid cells. This new model has shown potential for reproducing many characteristics of the premixed flame structure. However, before such a model can be used for simulating realistic reacting flows it must be demonstrated that the small-scale statistics of the flame structure are reproduced correctly as seen in the direct simulations. Therefore, the statistical data obtained from the subgrid approach will be compared to momentum transport. Based on the preliminary results obtained so far, it is expected that the new subgrid approach will not only reproduce geometrical properties such as the flame curvature and the effect of strain, as seen in the direct simulations, but also will give additional higher order statistical information such as, the time evolution of the flame brush thickness and flame crossing frequency that is difficult to obtain using conventional direct simulations.
1993
Turbulent Reacting Flows
McMurtry, P.A. and Queiroz, M.
Chapter 7, Fundamentals of Coal Combustion: For Clean and Efficient Use, (L.D. Smoot, ed.), Elsevier Science Publishers, The Netherlands, 1993. Funded by ACERC.
This chapter summarizes current technologies and developments for treating reacting turbulent flows. Accurately predicting the effects of turbulence on combustion processes ranks among the most challenging problems in the engineering sciences. Since most combustion occurs in a turbulent environment, effects of turbulence must be treated in a realistic manner in any predictive method. In addition to the effects of turbulence on the chemical species transport, density changes resulting from exothermic chemical reactions can alter the structure and development of the flow field. As such, the fluid mechanics, thermodynamics, and chemistry are strongly coupled, making the description of the turbulent combustion process extremely difficult. Moreover, other complications often arise. Among these are the effects of multiple phases, an inherent aspect of entrained solids and liquids. This chapter illustrates some of the characteristics of turbulent flows and outlines some of the methods used to treat turbulence in reacting flows, while pointing out the need for improved capabilities in this field of study. First, general background on turbulent flows is provided. The most popular approaches used to model turbulence in reactive systems for engineering applications are discussed, along with a few newly introduced techniques. Some of the complications that arise in multi-phase turbulent flow are also discussed. More computationally intensive numerical approaches, used primarily in fundamental research applications, are presented. These methods include Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). Direct simulation results for simplified flow configurations are discussed in light of the information they have provided concerning the physics of turbulent reacting flows.
Thrust Area 4 Research Program: Turbulent, Reacting Fluid Mechanics and Heat Transfer
McMurtry, P.A. and Queiroz, M.
Energy & Fuels, 7 (6):814-816, 1993. Funded by ACERC.
Two of the main reasons for poor turbulence model performance are the lack of understanding of the basic physical mechanisms acting in turbulent reaction flows and a lack of reliable data needed to "tune" model parameters. In addition, the physical complexity of the turbulent mixing process does not lend itself easily to packaged models. There is a need for true innovations and new approaches to treat the turbulence in reacting flows. The work in this thrust area consists of a combination of experiments and numerical studies aimed at (1) directly improving the performance and extending the generality of comprehensive combustion computer codes; (2) developing new approaches to modeling turbulent flows; and (3) conducting fundamental research to improve our understanding of the physical processes acting in turbulent reacting flows and heat transfer. The key products anticipated from the research in this thrust area include (1) new turbulent mixing models that can be incorporated in comprehensive predictive codes for turbulent combustion processes; (2) documented experimental data on planar sprays and particle dynamics in turbulent flows; (3) documented experimental data on radiation properties in multiphase combustion applications; (4) model improvements in the ACERC computer codes to handle spray flames and pulverized particles; (5) three-dimensional radiation submodels for incorporation into the comprehensive code; and (6) fundamental data on the mechanisms of turbulent mixing and reaction.
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.
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reacting Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
ASME Journal of Heat Transfer, 1993 (in press). Funded by ACERC.
The understanding of turbulent reacting flows, which are characterized by the Navier-Stokes equations along with conservation equations of mass and energy, is one of the most challenging fields of engineering science. Various theoretical models based on simplifying assumptions have been developed to predict the behavior of such flows. In some of the models proposed, the problem of modeling the mean reaction rate is exchanged for the problem of describing a scalar dissipation function. Thus the scalar dissipation, which describes the destruction of the fluctuations of a passive scalar at the finest scales existing in a given flow, is an important parameter in modeling turbulent reacting flows.
The objective of this work is to present the statistics of dissipation of a conserved scalar from the DNS of a turbulent reacting shear layer. Since experimental data on the statistics of temperature dissipation in a reacting shear layer of jet flame is readily available, a comparison of this data with the DNS results will also be made.
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.
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.
Statistical Properties of Scalar and Temperature Dissipation in a Turbulent Reaction Shear Layer
Shirolkar, J.S.; Queiroz, M. and McMurtry, P.A.
Heat Transfer in Fire and Combustion Systems, 223:97-103, 1992. (Also presented at the ASME National Heat Transfer Conference, San Diego, CA, August 1992). Funded by ACERC.
Data from a three-dimensional numerical simulations for a binary single step chemical reaction in a temporally developing turbulent shear layer were used to study the dissipation statistics of a conserved scalar as well as of temperature. Two specific chemical reaction cases were considered: isothermal reaction and chemical reaction with moderate heat release. The average and rms profiles of the mixture fraction dissipation are presented. The study indicated that in both cases the mixture fraction dissipation is related to the reaction rate. The temperature dissipation was found to be lognormally distributed in a region where there was significant chemical reaction. Also features of the temperature dissipation compare qualitatively well with experimental results reported in the literature.
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.
A Study of Favre Averaging Turbulent Flows with Chemical Reaction
Chen, C; Riley, J.J. and McMurtry, P.A.
Combustion and Flame, 87:257-277, 1992. Funded by Office of Naval Research and ACERC.
This article presents an investigation of the Favre averaging method for turbulent flows with chemical reaction. A set of data from direct numerical simulations of a chemically reacting turbulent mixing layer is employed. Favre-averaged quantities are compared directly with their corresponding Reynolds-averaged values. The gradient transport assumptions in the kappa-epsilon model in Favre-averaged form are also tested. Finally the transport equations for the Reynolds stress and scalar flux of the chemical product are studied term by term. Some Favre-averaged quantities such as u, ˜c, and ˜k are very similar numerically to their Reynolds-averaged values. Other Favre-averaged quantities, however, like ˜e, ˜p, ˜u, and ˜v, are significantly different from their Reynolds-averaged values. The gradient transport models generally work rather well when the mixing layer is in a naturally developing turbulent state, although some important weaknesses are noted. Some significant effects of pressure on they Reynolds stress and scalar flux are exhibited.
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.
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.
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
The Effect of Heat Release on Various Statistical Properties of a Reacting Shear Layer
Son, S.F.; McMurtry, P.A; and Queiroz, M.
Combustion and Flame, 85:51-67, 1991. Funded by ACERC.
Three-dimensional direct numerical simulations were used to study the effect of heat release from a binary, single-step chemical reaction on the statistical properties of a temporally developing turbulent mixing layer. Various statistical moments, probability density functions, power spectral densities, and autocorrelations of a conserved scalar, and the velocity field are presented. Scalar-velocity and pressure-velocity correlations, and joint probability density functions, which are extremely difficult to measure experimentally, were also calculated from the simulations. Many features of the calculated statistics compare qualitatively well with results reported from related experimental studies. Significant changes in the vortex structure occur with moderate heat release, resulting in more diffuse vortices than in the isothermal simulation. Consequently, slower rotation rates of the coherent structures occur with moderate heat release. This effect has previously been shown to be caused by the baroclinic torques and thermal expansion in the mixing layer. The statistics in this study reflect these changes in the vortex structure due to moderate heat release.
A Study of Favre Averaging Turbulent Flows with Chemical Reaction
Chen, C; Riley, J.J.; and McMurtry, P.A.
Combustion and Flame, 1991 (in press). Funded by ACERC.
This article presents an investigation of the Favre averaging method for turbulent flows with chemical reaction. A set of data from direct numerical simulations of a chemically reacting turbulent mixing layer is employed. Favre-averaged quantities are compared directly with their corresponding Reynolds-averaged values. The gradient transport assumptions in the k - model in Favre-averaged form are also tested. Finally the transport equations for the Reynolds stress and scalar flux of the chemical product are studied term by term. Some Favre-averaged quantities such as are very similar numerically to their Reynolds-averaged values. Other Favre-averaged quantities, however, like and , are significantly different from their Reynolds-averaged values. The gradient transport models generally work rather well when the mixing layer is in a naturally developing turbulent state, although some important weaknesses are noted. Some significant effects of pressure on they Reynolds stress and scalar flux are exhibited.
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
The Effect of Heat Release on Various Statistical Properties of a Reacting Shear Layer
Son, S.F.; McMurtry, P.A. and Queiroz, M.
Combustion and Flame, 1990 (In press). Funded by ACERC.
Three-dimensional direct numerical simulations were used to study the effect of heat release from a binary, single-step chemical reaction on the statistical properties of a temporally developing turbulent mixing layer. Various statistical moments, probability density functions, power spectral densities, and autocorrelations of a conserved scalar, and the velocity field are presented. Scalar-velocity and pressure-velocity correlations, and joint probability density functions, which are extremely difficult to measure experimentally, were also calculated from the simulations. Many features of the calculated statistics compare qualitatively well with results reported from related experimental studies. Significant changes in the vortex structure occur with moderate heat release, resulting in more diffuse vortices than in the isothermal simulation. Consequently, slower rotation rates of the coherent structures occur with moderate heat release. This effect has previously been shown to be caused by the baroclinic torques and thermal expansion in the mixing layer. The statistics in this study reflect these changes in the vortex structure due to moderate heat release.
Direct Numerical Simulation of a Planar Shear Layer Using the Spectral-Compact Finite Difference Technique
Clarksean, R. and McMurtry, P.A.
AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, Paper 90-1495, Seattle, Washington, 1990. Funded by ACERC and Environmental Protection Agency.
A numerical algorithm is presented for studying mixing processes in turbulent flows. The approach is a combination of the spectral method and the compact finite difference technique. The compact method is fourth order accurate in space and has good phase error characteristics. In addition, the compact finite difference technique is easily implemented on variable grids. The fourth order accuracy is only degraded to order 2.4 accuracy on large aspect ratio grids (6:1) for the two-dimensional advection equation. The application of this method is illustrated by performing direct numerical simulations of a spatially developing mixing layer. The evolving flow field is visualized by contour plots of vorticity magnitude and the scalar field. These figures show the shedding and pairing of vortices similar to previously conducted experimental work. The three-dimensional results show secondary structures developing, which enhance the mixing process. The structure of the three-dimensional flow field is similar to that observed experimentally, illustrating the ability of this hybrid scheme to accurately simulate the unsteady development of incompressible flows.
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.
1989
Flame Generation of Vorticity; Vortex Dipoles from Monopoles
Ashurst, W.T. and McMurtry, P.A.
Comb. Sci, and Tech., 66, 17-37, 1989. Funded by US Department of Energy.
Numerical simulation of premixed flame propagation through a two-dimensional vorticity distribution exhibits the coupling between combustion heat release and fluid dynamics. Effects of both thermal expansion and vorticity generation via baroclinic torques are considered. The rotational part of the velocity field is described by discrete vorticity. The irrotational velocity, given by a velocity potential, is determined by a Poisson equation where the chemical reaction determines the spatial distribution of volume expansion. The transport of a single reacting scalar is computed on an Eulerian mesh with a small-Mach number flow assumption so that the density gradient is nonzero only within the reaction zone. The vector cross product of density gradient and pressure gradient defines the baroclinic generation of vorticity. With a single initial vortical region - the monopole interacting with a premixed flame - the baroclinic effects produce opposite circulation, and, thus, creates a dipole configuration. We use the dipole description in a loose sense, because in some solutions the two signs of vorticity are spatially intermingled. However, in comparison to the monopole, the "dipole" solution has stronger local velocity fluctuations but weaker long-range velocities. Thus, the turbulence in the burnt gas is more intense with smaller length scales than the configuration before the flame-vortex interaction.
Mixing and Reaction in Turbulent Shear Flows: Direct Numerical Simulation
McMurtry, P.A.
1st International Congress. on Tox. Comb., Los Angeles, California, 1989. Funded by ACERC (National Science Foundation and Associates and Affiliates).
Results from numerical simulations of chemically reacting, turbulent mixing layers are presented. Effects of turbulent mixing, chemical heat release, and chemical nonequilibrium are discussed. Effects of chemical heat release in turbulent mixing layers are shown to result in lower chemical formation rates than similar isothermal reactions. A study of the flow in terms of vorticity dynamics and linear stability indicates that the large-scale characteristic vortex structures of mixing layers are inhibited by heat release. Phenomena resulting from chemical nonequilibrium are also presented. In agreement with previous analytic studies, incomplete combustion and flame quenching is shown to result when local diffusion time scales are lowered to those of characteristic chemical time scales. The statistical description of the scalar dissipation is the most important parameter describing the turbulence-chemical nonequilibrium interactions. An understanding of these phenomena is crucial for efficient and complete combustion in turbulent shear flows. On going research activities and suggestions for future work are presented.
1988-1986
Effects of Heat Release on the Large-Scale Structure in Turbulent Mixing Layers
McMurtry, P.A.; Riley, J.J. and Metcalfe, R.W.
To appear in Journal of Fluid Mechanics, 1988. Funded by NASA Lewis Research Center and Office of Naval Research.
The effects of chemical heat release on the large-scale structure in a chemically reacting, turbulent mixing layer are investigated using direct numerical simulations. Three-dimensional, time-dependent simulations are performed for a binary, single-step chemical reaction occurring across a temporally developing turbulent mixing layer. It is found that moderate heat release slows the development of the large-scale structures and shifts their wavelengths to larger scales. The resulting entrainment of reactants is reduced, decreasing the overall chemical product formation rate. The simulation results are interpreted in terms of turbulence energetics, vorticity dynamics, and stability theory. The baroclinic torque and thermal expansion in the mixing layer produce changes in the flame vortex structure that result in more diffuse vortices than in the large-scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques.
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.
The Use of Direct Numerical Simulation in the Study of Turbulent Chemically-Reacting Flows
Riley, J.J. and McMurtry, P.A.
To appear in Analysis of Reacting Flows, Springer-Verlag, 1988. Funded by NASA Lewis Research Center, Office of Naval Research, University of Washington, and US Office of Basic Energy Sciences.
At the present time the role of direct numerical simulation as applied to turbulent, chemically reacting flows is twofold; to understand the physical processes involved, and to develop and test theories. In this paper we present and example of the former. We employ full turbulence simulations to study the effects of chemical heat release on the large-scale structures in turbulent mixing layers. This work not only aids in understanding this phenomenon, but also gives insight into strengths and limitations of the methodology.
We find, in agreement with previous laboratory experiments, the heat release is observed to lower the rate at which the mixing layer grows and to reduce the rate at which chemical products are formed. The baroclinic torque and thermal expansion in the mixing layer are shown to produce changes in the flame vortex structure the act to produce more diffuse vortices than in the constant density case, resulting in lower rotation rates of the large scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques. The density reductions also lower the generation rates of turbulent kinetic energy and the turbulent shear stresses, resulting in less turbulent mixing of fluid elements.
Calculations of the energy in the various wave numbers shows that the heat release has a stabilizing effect on the growth rates of individual modes. A linear stability analysis of a simplified model problem confirms this, showing that low-density fluid in the mixing region will result in a shift in the frequency of the unstable modes to lower wave numbers (longer wavelengths). The growth rates of the unstable modes decrease, contributing to the slower growth of the mixing layer.
Finally, we find that this methodology can be confidently applied for Reynolds numbers less than several hundred and for Damkohler numbers less than about ten. With some modification it is possible to treat the infinite Damkohler number case using a conserved scalar.
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.
Direct Numerical Simulations of a Reacting Mixing Layer with Chemical Heat Release
McMurtry, P.A.; Metcalfe, R.W.; Jou, W.H. and Riley, J.J.
AIAA Journal, 24, (6), 962, 1986. Funded by NASA Lewis Research Center.
To study the coupling between chemical heat release and fluid dynamics, we have performed direct numerical simulations of a two-dimensional mixing layer undergoing a simple single-step chemical reaction with heat release. The reaction is function only of the species concentrations and does not depend on temperature. We have treated the fully compressible equations, as well as an approximate set of equations that is asymptotically valid for low Mach number flows. These latter equations have the computational advantage that high-frequency acoustic waves have been filtered out, allowing much larger time steps to be taken in the numerical solution procedure. A derivation of these equations along with an outline of the numerical solution technique is given. Simulation results indicate that the rate of chemical product formed, the thickness of the mixing layer, and the dynamics are studied to analyze and interpret some effects of heat release on the fluid motion.