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NASA NTRS1988

Numerical computation of space shuttle orbiter flow field

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

Tannehill, John C.↗

NASA NTRS1988

A generalized chemistry version of SPARK

An extension of the reacting H2-air computer code SPARK is presented, which enables the code to be used on any reacting flow problem. Routines are developed calculating in a general fashion, the reaction rates, and chemical Jacobians of any reacting system. In addition, an equilibrium routine is added so that the code will have frozen, finite rate, and equilibrium capabilities. The reaction rate for the species is determined from the law of mass action using Arrhenius expressions for the rate constants. The Jacobian routines are determined by numerically or analytically differentiating the law of mass action for each species. The equilibrium routine is based on a Gibbs free energy minimization routine. The routines are written in FORTRAN 77, with special consideration given to vectorization. Run times for the generalized routines are generally 20 percent slower than reaction specific routines. The numerical efficiency of the generalized analytical Jacobian, however, is nearly 300 percent better than the reaction specific numerical Jacobian used in SPARK.

Carpenter, Mark H.↗

NASA NTRS1990

CARS Temperature Measurements in a Hypersonic Propulsion Test Facility

Nonintrusive diagnostic measurements were performed in the supersonic reacting flow of the Hypersonic Propulsion Test Cell 2 at NASA-Langley. A Coherent Anti-stokes Raman Spectroscopy (CARS) system was assembled specifically for the test cell environment. System design considerations were: (1) test cell noise and vibration; (2) contamination from flow field or atmospheric borne dust; (3) unwanted laser or electrically induced combustion (inside or outside the duct); (4) efficient signal collection; (5) signal splitting to span the wide dynamic range present throughout the flow field; (6) movement of the sampling volume in the flow; and (7) modification of the scramjet model duct to permit optical access to the reacting flow with the CARS system. The flow in the duct was a nominal Mach 2 flow with static pressure near one atmosphere. A single perpendicular injector introduced hydrogen into the flow behind a rearward facing step. CARS data was obtained in three planes downstream of the injection region. At least 20 CARS data points were collected at each of the regularly spaced sampling locations in each data plane. Contour plots of scramjet combustor static temperature in a reacting flow region are presented.

Jarrett, Olin, Jr.↗

NASA NTRS1992

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Madnia, C. K.↗

NASA NTRS1992

Combustion instability analysis for liquid propellant rocket engines

The multi-dimensional numerical model has been developed to analyze the nonlinear combustion instabilities in liquid-fueled engines. The present pressure-based approach can handle the implicit pressure-velocity coupling in a non-iterative way. The additional scalar conservation equations for the chemical species, the energy, and the turbulent transport quantities can be handled by the same predictor-corrector sequences. This method is time-accurate and it can be applicable to the all-speed, transient, multi-phase, and reacting flows. Special emphasis is given to the acoustic/vaporization interaction which may act as the crucial rate-controlling mechanism in the liquid-fueled rocket engines. The subcritical vaporization is modeled to account for the effects of variable thermophysical properties, non-unitary Lewis number in the gas-film, the Stefan flow effect, and the effect of transient liquid heating. The test cases include the one-dimenisonal fast transient non-reacting and reacting flows, and the multi-dimensional combustion instabilities encountered in the liquid-fueled rocket thrust chamber. The present numerical model successfully demonstrated the capability to simulate the fast transient spray-combusting flows in terms of the limiting-cycle amplitude phenomena, correspondence between combustion and acoustics, and the steep-fronted wave and flame propagation. The investigated parameters include the spray initial conditions, air-fuel mixture ratios, and the engine geometry. Stable and unstable operating conditions are found for the liquid-fueled combustors. Under certain conditions, the limiting cycle behavior of the combusting flowfields is obtained. The numerical results indicate that the spray vaporization processes play an important role in releasing thermal energy and driving the combustion instability.

Kim, Y. M.↗

NASA NTRS1993

Sensitive, Selective Test For Hydrazines

Derivatives of hydrazines formed, then subjected to gas chromatography and detected via chemiluminescence. In method of detecting and quantifying hydrazine vapors, vapors reacted with dinitro compound to enhance sensitivity and selectivity. Hydrazine (HZ), monomethyl hydrazine, (MMH), and unsymmetrical dimethylhydrazine (UDMH) analyzed quantitatively and qualitatively, either alone or in mixtures. Vapors collected and reacted with 2,4-dinitrobenzaldehyde, (DNB), making it possible to concentrate hydrazine in derivative form, thereby increasing sensitivity to low initial concentrations. Increases selectivity because only those constituents of sample reacting with DNB concentrated for analysis.

Roundbehler, David↗

NASA NTRS1993

Development of dispersion-strengthened XD (trademark) Cu alloys for high heat-flux applications

In a previous effort sponsored by NASA LeRC, the XD(trademark) process was used to produce ZrB2 particulate reinforcements in Cu and the resulting extruded material was microstructurally characterized and evaluated in tension over a range of temperatures. A problem that was encountered in that study was microstructural inhomogeneity resulting from the frequent presence of 'ZrB2 agglomerates' that were several microns in size. The presence of these agglomerates was attributed to improper mixing of powders in the green compact used in the XD process for elemental boron powder segregation. In this program, several milling parameters were examined in an effort to optimize this processing step; two levels of ZrB2 reinforcements were considered (7 vol. percent and 15 vol. percent). Microstructures of the reacted powder mass were examined to verify the absence of these agglomerates. Larger bathes of powder were then mixed, reacted, machined to size, canned, and extruded. The microstructure and tensile properties of these extrusions were examined, and the measured properties were correlated with the observed microstructure. Large unreacted or partially reacted Zr particles were present. These particles affected the mechanical properties deleteriously, and their presence is attributed to insufficient heat of reaction during XD synthesis. Alternate processing routes are recommended.

Kumar, K. Sharvan↗

NASA NTRS1991

Investigations of turbulent scalar fields using probability density function approach

Scalar fields undergoing random advection have attracted much attention from researchers in both the theoretical and practical sectors. Research interest spans from the study of the small scale structures of turbulent scalar fields to the modeling and simulations of turbulent reacting flows. The probability density function (PDF) method is an effective tool in the study of turbulent scalar fields, especially for those which involve chemical reactions. It has been argued that a one-point, joint PDF approach is the one to choose from among many simulation and closure methods for turbulent combustion and chemically reacting flows based on its practical feasibility in the foreseeable future for multiple reactants. Instead of the multi-point PDF, the joint PDF of a scalar and its gradient which represents the roles of both scalar and scalar diffusion is introduced. A proper closure model for the molecular diffusion term in the PDF equation is investigated. Another direction in this research is to study the mapping closure method that has been recently proposed to deal with the PDF's in turbulent fields. This method seems to have captured the physics correctly when applied to diffusion problems. However, if the turbulent stretching is included, the amplitude mapping has to be supplemented by either adjusting the parameters representing turbulent stretching at each time step or by introducing the coordinate mapping. This technique is still under development and seems to be quite promising. The final objective of this project is to understand some fundamental properties of the turbulent scalar fields and to develop practical numerical schemes that are capable of handling turbulent reacting flows.

Gao, Feng↗

NASA NTRS1993

A coupled implicit solution method for turbulent spray combustion in propulsion systems

Many reacting flows in propulsion devices cannot be efficiently calculated by modern compressible flow CFD algorithms. Most low-speed reacting flow codes based on TEACH-type technologies are inefficient and lack robustness for complex flows. Tremendous progress has been made in high-speed compressible flow CFD in the past two decades; extending its application range to low-speed regimes is highly desirable. The objectives of this document is to present an efficient and robust algorithm for multi-phase chemically reacting flows at all speeds, with emphasis on low Mach number flows, and to calculate turbulent spray combustion flow in a gas turbine combustor.

Chen, K.-H.↗

NASA NTRS1993

Brain wave correlates of attentional states: Event related potentials and quantitative EEG analysis during performance of cognitive and perceptual tasks

The increased use of automation in the cockpits of commercial planes has dramatically decreased the workload requirements of pilots, enabling them to function more efficiently and with a higher degree of safety. Unfortunately, advances in technology have led to an unexpected problem: the decreased demands on pilots have increased the probability of inducing 'hazardous states of awareness.' A hazardous state of awareness is defined as a decreased level of alertness or arousal which makes an individual less capable of reacting to unique or emergency types of situations. These states tend to be induced when an individual is not actively processing information. Under such conditions a person is likely to let his/her mind wander, either to internal states or to irrelevant external conditions. As a result, they are less capable of reacting quickly to emergency situations. Since emergencies are relatively rare, and since the high automated cockpit requires progressively decreasing levels of engagement, the probability of being seduced into a lowered state of awareness is increasing. This further decreases the readiness of the pilot to react to unique circumstances such as system failures. The HEM Lab at NASA-Langley Research Center has been studying how these states of awareness are induced and what the physiological correlates of these different states are. Specifically, they have been interested in studying electroencephalographic (EEG) measures of different states of alertness to determine if such states can be identified and, hopefully, avoided. The project worked on this summer involved analyzing the EEG and the event related potentials (ERP) data collected while subjects performed under two conditions. Each condition required subjects to perform a relatively boring vigilance task. The purpose of using these tasks was to induce a decreased state of awareness while still requiring the subject to process information. Each task involved identifying an infrequently presented target stimulus. In addition to the task requirements, irrelevant tones were presented in the background. Research has shown that even though these stimuli are not attended, ERP's to them can still be elicited. The amplitude of the ERP waves has been shown to change as a function of a person's level of alertness. ERP's were also collected and analyzed for the target stimuli for each task. Brain maps were produced based on the ERP voltages for the different stimuli. In addition to the ERP's, a quantitative EEG (QEEG) was performed on the data using a fast Fourier technique to produce a power spectral analysis of the EEG. This analysis was conducted on the continuous EEG while the subjects were performing the tasks. Finally, a QEEG was performed on periods during the task when subjects indicated that they were in an altered state of awareness. During the tasks, subjects were asked to indicate by pressing a button when they realized their level of task awareness had changed. EEG epochs were collected for times just before and just after subjects made this reponse. The purpose of this final analysis was to determine whether or not subjective indices of level of awareness could be correlated with different patterns of EEG.

Freeman, Frederick G.↗

NASA NTRS1994

Phenylethynyl endcapping reagents and reactive diluents

A phenylethynyl composition which can be used to endcap nucleophilic species is employed in the production of phenylethynyl terminated reactive oligomers exclusively. These phenylethynyl terminated reactive oligomers display unique thermal characteristics, as exemplified by the model compound, 4-phenoxy 4'-phenylethynylbenzophenone, which is relatively stable at 200 C, but reacts at 350 C. In addition, a reactive diluent was prepared which decreases the melt viscosity of the phenylethynyl terminated oligomers and subsequently reacts therewith to increase density of the resulting thermoset. The novelty of this invention resides in the phenylethynyl composition used to terminate a nucleophilic reagent, resulting in the exclusive production of phenylethynyl terminated reactive oligomers which display unique thermal characteristics. A reactive diluent was also employed to decrease the melt viscosity of a phenylethynyl terminated reactive oligomer and to subsequently react therewith to increase the crosslink density of the resulting thermoset. These materials have features which make them attractive candidates for use as composite matrices and adhesives.

Jensen, Brian J.↗

NASA NTRS1993

Toward an embedded training tool for Deep Space Network operations

There are three issues to consider when building an embedded training system for a task domain involving the operation of complex equipment: (1) how skill is acquired in the task domain; (2) how the training system should be designed to assist in the acquisition of the skill, and more specifically, how an intelligent tutor could aid in learning; and (3) whether it is feasible to incorporate the resulting training system into the operational environment. This paper describes how these issues have been addressed in a prototype training system that was developed for operations in NASA's Deep Space Network (DSN). The first two issues were addressed by building an executable cognitive model of problem solving and skill acquisition of the task domain and then using the model to design an intelligent tutor. The cognitive model was developed in Soar for the DSN's Link Monitor and Control (LMC) system; it led to several insights about learning in the task domain that were used to design an intelligent tutor called REACT that implements a method called 'impasse-driven tutoring'. REACT is one component of the LMC training system, which also includes a communications link simulator and a graphical user interface. A pilot study of the LMC training system indicates that REACT shows promise as an effective way for helping operators to quickly acquire expert skills.

Hill, Randall W., Jr.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1997

Parallel ALLSPD-3D: Speeding Up Combustor Analysis Via Parallel Processing

The ALLSPD-3D Computational Fluid Dynamics code for reacting flow simulation was run on a set of benchmark test cases to determine its parallel efficiency. These test cases included non-reacting and reacting flow simulations with varying numbers of processors. Also, the tests explored the effects of scaling the simulation with the number of processors in addition to distributing a constant size problem over an increasing number of processors. The test cases were run on a cluster of IBM RS/6000 Model 590 workstations with ethernet and ATM networking plus a shared memory SGI Power Challenge L workstation. The results indicate that the network capabilities significantly influence the parallel efficiency, i.e., a shared memory machine is fastest and ATM networking provides acceptable performance. The limitations of ethernet greatly hamper the rapid calculation of flows using ALLSPD-3D.

Fricker, David M.↗

NASA NTRS1995

The Relative Reactivity of Deoxyribose and Ribose: Did DNA Come Before RNA?

If it is assumed that there was a precursor to the ribose-phosphate backbone of RNA in the preRNA world (such as peptide nucleic acid), then the entry of various sugars into the genetic material may be related to the stability and non-enzymatic reactivity of the aldose. The rate of decomposition of 2-deoxyribose has been determined to be 1/3 that of ribose. In addition we have measured the amount of free aldehyde by H-1 and C-13 NMR and find that it has approximately 0.15% free aldehyde compared to 0.05% for ribose at 25 C. This suggests that deoxyribose would be significantly more reactive with early bases in the absence of enzymes. This is confirmed by urazole and deoxyribose reacting to form the deoxynucleoside 45 times faster as 25 C than urazole reacts with ribose to form the Ribonucleoside. Urazole is a potential precursor of uracil and is a plausible prebiotic compound which reacts with aldoses to form nucleosides. Thus the non-enzymatic reactivity of deoxyribose would favor its early use over ribose until enzymes could change the relative reactivities. Most of the reasons that RNA is presumed to have come before DNA are extrapolations back from contemporary metabolism (e.g. the abundance of ribose based coenzymes, the biosynthesis of histidine, deoxyribonucleotides are synthesized from ribonucleotides, etc.). It is very difficult to reconstruct biochemical pathways much before the last common ancestor, and it is even more difficult to do more than guess at the biochemistry of very early self-replicating systems. Thus we believe that these reasons are not compelling and that the non-enzymatic chemistry may be more important than enzymatic pathways for constructing the earliest of biochemical pathways. While the RNA world has been discussed at great length, there has not been an exploration of the transition out of the RNA world. We have constructed many possible schemes of genetic takeover events from preRNA to modern DNA, RNA, protein system which could generate the RNA metabolic fossils we see today.

Dworkin, Jason P.↗

NASA NTRS1982

Frequency and Time Domain Modeling of Acoustic Liner Boundary Conditions

As part of a research program directed at the acoustics of advanced subsonic propulsion systems undertaken at NASA Langley, Duke University was funded to develop a boundary condition model for bulk-reacting nacelle liners. The overall objective of the Langley program was to understand and predict noise from advanced subsonic transport engines and to develop related noise control technology. The overall technical areas included: fan and propeller source noise, acoustics of ducts and duct liners, interior noise, subjective acoustics, and systems noise prediction. The Duke effort was directed toward duct liner acoustics for the development of analytical methods to characterize liner behavior in both frequency domain and time domain. A review of duct acoustics and liner technology can be found in Reference [1]. At that time, NASA Langley was investigating the propulsion concept of an advanced ducted fan, with a large diameter housed inside a relatively short duct. Fan diameters in excess of ten feet were proposed. The lengths of both the inlet and exhaust portions of the duct were to be short, probably less than half the fan diameter. The nacelle itself would be relatively thin-walled for reasons of aerodynamic efficiency. The blade-passage frequency was expected to be less than I kHz, and very likely in the 200 to 300 Hz range. Because of the design constraints of a short duct, a thin nacelle, and long acoustic wavelengths, the application of effective liner technology would be especially challenging. One of the needs of the NASA Langley program was the capability to accurately and efficiently predict the behavior of the acoustic liner. The traditional point impedance method was not an adequate model for proposed liner designs. The method was too restrictive to represent bulk reacting liners and to allow for the characterization of many possible innovative liner concepts. In the research effort at Duke, an alternative method, initially developed to handle bulk reacting layers as described in Reference [2], was extended to apply to a broad range of liner types. This method included the effect of local gradients along the liner surface, and was particularly appropriate for situations with flow over the liner and grazing incidence acoustic fields. In order to utilize time domain computational methods to solve for the propfan acoustic field, corresponding liner boundary conditions were developed for time domain solutions rather than frequency domain solutions.

Bliss, Donald B.↗

NASA NTRS1998

Prebiotic Amino Acid Thioester Synthesis: Thiol-Dependent Amino Acid Synthesis from Formose substrates (Formaldehyde and Glycolaldehyde) and Ammonia

Formaldehyde and glycolaldehyde (substrates of the formose autocatalytic cycle) were shown to react with ammonia yielding alanine and homoserine under mild aqueous conditions in the presence of thiol catalysts. Since similar reactions carried out without ammonia yielded alpha-hydroxy acid thioesters, the thiol-dependent synthesis of alanine and homoserine is presumed to occur via amino acid thioesters-intermediates capable of forming peptides. A pH 5.2 solution of 20 mM formaldehyde, 20 mM glycolaldehyde, 20 mM ammonium chloride, 23 mM 3-mercaptopropionic acid, and 23 mM acetic acid that reacted for 35 days at 40 C yielded (based on initial formaldehyde) 1.8% alanine and 0.08% homoserine. In the absence of thiol catalyst, the synthesis of alanine and homoserine was negligible. Alanine synthesis required both formaldehyde and glycolaldehyde, but homoserine synthesis required only glycolaldehyde. At 25 days the efficiency of alanine synthesis calculated from the ratio of alanine synthesized to formaldehyde reacted was 2.1%, and the yield (based on initial formaldehyde) of triose and tetrose intermediates involved in alanine and homoserine synthesis was 0.3 and 2.1%, respectively. Alanine synthesis was also seen in similar reactions containing only 10 mM each of aldehyde substrates, ammonia, and thiol. The prebiotic significance of these reactions that use the formose reaction to generate sugar intermediates that are converted to reactive amino acid thioesters is discussed.

Weber, Arthur L.↗

NASA NTRS2000

A Validation Summary of the NCC Turbulent Reacting/non-reacting Spray Computations

This pper provides a validation summary of the spray computations performed as a part of the NCC (National Combustion Code) development activity. NCC is being developed with the aim of advancing the current prediction tools used in the design of advanced technology combustors based on the multidimensional computational methods. The solution procedure combines the novelty of the application of the scalar Monte Carlo PDF (Probability Density Function) method to the modeling of turbulent spray flames with the ability to perform the computations on unstructured grids with parallel computing. The calculation procedure was applied to predict the flow properties of three different spray cases. One is a nonswirling unconfined reacting spray, the second is a nonswirling unconfined nonreacting spray, and the third is a confined swirl-stabilized spray flame. The comparisons involving both gas-phase and droplet velocities, droplet size distributions, and gas-phase temperatures show reasonable agreement with the available experimental data. The comparisons involve both the results obtained from the use of the Monte Carlo PDF method as well as those obtained from the conventional computational fluid dynamics (CFD) solution. Detailed comparisons in the case of a reacting nonswirling spray clearly highlight the importance of chemistry/turbulence interactions in the modeling of reacting sprays. The results from the PDF and non-PDF methods were found to be markedly different and the PDF solution is closer to the reported experimental data. The PDF computations predict that most of the combustion occurs in a predominantly diffusion-flame environment. However, the non-PDF solution predicts incorrectly that the combustion occurs in a predominantly vaporization-controlled regime. The Monte Carlo temperature distribution shows that the functional form of the PDF for the temperature fluctuations varies substantially from point to point. The results also bring to the fore some of the deficiencies associated with the use of assumed-shape PDF methods in spray computations.

Raju, M. S.↗