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NASA NTRS1995

Modeling complex chemical effects in turbulent nonpremixed combustion

Virtually all of the energy derived from the consumption of combustibles occurs in systems which utilize turbulent fluid motion. Since combustion is largely related to the mixing of fluids and mixing processes are orders of magnitude more rapid when enhanced by turbulent motion, efficiency criteria dictate that chemically powered devices necessarily involve fluid turbulence. Where combustion occurs concurrently with mixing at an interface between two reactive fluid bodies, this mode of combustion is called nonpremixed combustion. This is distinct from premixed combustion where flame-fronts propagate into a homogeneous mixture of reactants. These two modes are limiting cases in the range of temporal lag between mixing of reactants and the onset of reaction. Nonpremixed combustion occurs where this lag tends to zero, while premixed combustion occurs where this lag tends to infinity. Many combustion processes are hybrids of these two extremes with finite non-zero lag times. Turbulent nonpremixed combustion is important from a practical standpoint because it occurs in gas fired boilers, furnaces, waste incinerators, diesel engines, gas turbine combustors, and afterburners etc. To a large extent, past development of these practical systems involved an empirical methodology. Presently, efficiency standards and emission regulations are being further tightened (Correa 1993), and empiricism has had to give way to more fundamental research in order to understand and effectively model practical combustion processes (Pope 1991). A key element in effective modeling of turbulent combustion is making use of a sufficiently detailed chemical kinetic mechanism. The prediction of pollutant emission such as oxides of nitrogen (NO(x)) and sulphur (SO(x)) unburned hydrocarbons, and particulates demands the use of detailed chemical mechanisms. It is essential that practical models for turbulent nonpremixed combustion are capable of handling large numbers of 'stiff' chemical species equations.

Smith, Nigel S. A.↗

NASA NTRS2005

Simplified Two-Time Step Method for Calculating Combustion and Emission Rates of Jet-A and Methane Fuel With and Without Water Injection

A simplified kinetic scheme for Jet-A, and methane fuels with water injection was developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) or even simple FORTRAN codes. The two time step method is either an initial time averaged value (step one) or an instantaneous value (step two). The switch is based on the water concentration in moles/cc of 1x10(exp -20). The results presented here results in a correlation that gives the chemical kinetic time as two separate functions. This two time step method is used as opposed to a one step time averaged method previously developed to determine the chemical kinetic time with increased accuracy. The first time averaged step is used at the initial times for smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, initial water to fuel mass ratio, temperature, and pressure. The second instantaneous step, to be used with higher water concentrations, gives the chemical kinetic time as a function of instantaneous fuel and water mole concentration, pressure and temperature (T4). The simple correlations would then be compared to the turbulent mixing times to determine the limiting rates of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide and NOx are obtained for Jet-A fuel and methane with and without water injection to water mass loadings of 2/1 water to fuel. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentrations of carbon monoxide and nitrogen oxide as functions of overall equivalence ratio, water to fuel mass ratio, pressure and temperature (T3). The temperature of the gas entering the turbine (T4) was also correlated as a function of the initial combustor temperature (T3), equivalence ratio, water to fuel mass ratio, and pressure.

Molnar, Melissa↗

NASA NTRS2004

New Reduced Two-Time Step Method for Calculating Combustion and Emission Rates of Jet-A and Methane Fuel With and Without Water Injection

A simplified kinetic scheme for Jet-A, and methane fuels with water injection was developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) or even simple FORTRAN codes that are being developed at Glenn. The two time step method is either an initial time averaged value (step one) or an instantaneous value (step two). The switch is based on the water concentration in moles/cc of 1x10(exp -20). The results presented here results in a correlation that gives the chemical kinetic time as two separate functions. This two step method is used as opposed to a one step time averaged method previously developed to determine the chemical kinetic time with increased accuracy. The first time averaged step is used at the initial times for smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, initial water to fuel mass ratio, temperature, and pressure. The second instantaneous step, to be used with higher water concentrations, gives the chemical kinetic time as a function of instantaneous fuel and water mole concentration, pressure and temperature (T4). The simple correlations would then be compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates were then used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide and NOx were obtained for Jet-A fuel and methane with and without water injection to water mass loadings of 2/1 water to fuel. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentrations of carbon monoxide and nitrogen oxide as functions of overall equivalence ratio, water to fuel mass ratio, pressure and temperature (T3). The temperature of the gas entering the turbine (T4) was also correlated as a function of the initial combustor temperature (T3), equivalence ratio, water to fuel mass ratio, and pressure.

Molnar, Melissa↗

NASA NTRS1993

Mathematical description of complex chemical kinetics and application to CFD modeling codes

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Bittker, D. A.↗

NASA NTRS1993

Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes

Bittker, D. A.↗

NASA NTRS1995

Computational study of inlet injection for a Pre-Mixed, Shock-Induced Combustion (PM/SIC) engine

A computational simulation of reacting 2-D and 3-D flowfields in a model inlet section of a Pre-Mixed, Shock-Induced Combustion (PM/SIC) engine concept was performed. LARCK, a multi-dimensional Navier-Stokes code with finite-rate kinetics chemistry developed at NASA LaRC by J.A. White, was adapted for this simulation. The flow conditions in the simulation match those envisioned for the PM/SIC engine experiments currently planned at LaRC. The reacting flowfields were Mach 6.3 freestream air and Mach 2 hydrogen at various pressure and temperature conditions injected through a slot injector at the base of the inlet section. In the PM/SIC engine, fuel is injected at the inlet section upstream of the combustor, and reaction is initiated by the shock wave at the inlet which increases the gas temperature and pressure beyond the kinetic limits for reaction. Many challenges exist prior to establishing shock-controlled combustion as a practical engine concept. These challenges include fuel injection schemes that can provide proper fuel-air mixing without creating large losses in the inlet section, and control of the combustion process so that early ignition or combustion propagation through the inlet boundary layer does not occur. For this project, a parametrics study was carried out to model the fuel injection of hydrogen at different flow conditions. It was found that, as the fuel temperature and pressure were increased, the potential for pre-ignition was high at a short distance downstream of the slot injector. The next stage of this work will investigate injection techniques for enhancing mixing of fuel and air in a manner that prevents or reduces the potential for premature ignition observed numerically.

Gonzalez, D. E.↗

NASA NTRS2006

Fuel-Air Mixing and Combustion in Scramjets

At flight speeds, the residence time for atmospheric air ingested into a scramjet inlet and exiting from the engine nozzle is on the order of a millisecond. Therefore, fuel injected into the air must efficiently mix within tens of microseconds and react to release its energy in the combustor. The overall combustion process should be mixing controlled to provide a stable operating environment; in reality, however, combustion in the upstream portion of the combustor, particularly at higher Mach numbers, is kinetically controlled where ignition delay times are on the same order as the fluid scale. Both mixing and combustion time scales must be considered in a detailed study of mixing and reaction in a scramjet to understand the flow processes and to ultimately achieve a successful design. Although the geometric configuration of a scramjet is relatively simple compared to a turbomachinery design, the flow physics associated with the simultaneous injection of fuel from multiple injector configurations, and the mixing and combustion of that fuel downstream of the injectors is still quite complex. For this reason, many researchers have considered the more tractable problem of a spatially developing, primarily supersonic, chemically reacting mixing layer or jet that relaxes only the complexities introduced by engine geometry. All of the difficulties introduced by the fluid mechanics, combustion chemistry, and interactions between these phenomena can be retained in the reacting mixing layer, making it an ideal problem for the detailed study of supersonic reacting flow in a scramjet. With a good understanding of the physics of the scramjet internal flowfield, the designer can then return to the actual scramjet geometry with this knowledge and apply engineering design tools that more properly account for the complex physics. This approach will guide the discussion in the remainder of this section.

Drummond, J. Philip↗

NASA NTRS1982

Mechanisms of droplet combustion

The fundamental physico-chemical mechanisms governing droplet vaporization and combustion are discussed. Specific topics include governing equations and simplifications, the classical d(2)-Law solution and its subsequent modification, finite-rate kinetics and the flame structure, droplet dynamics, near- and super-critical combustion, combustion of multicomponent fuel blends/emulsions/suspensions, and droplet interaction. Potential research topics are suggested.

Law, C. K.↗

NASA NTRSDate not supplied

Effects of Ambient Inert Gas Properties on Cool-Flame Combustion of Normal-Alkane Droplets in Microgravity

Cool-flame-supported quasi-steady droplet combustion was first observed during droplet combustion experiments conducted onboard the International Space Station (ISS) in the Combustion Integrated Rack (CIR) with n-alkane fuels. These cool flames, not visible to the naked eye, result from the existence of the negative-temperature-coefficient (NTC) region during the combustion n-alkane fuels when the chemical-kinetic pathways experience a transition from the low-temperature chemistry to the normal, high-temperature-controlled chemistry. In this study, we present results for the cool-flame-supported droplet burning rates and extinction diameters for n-alkane fuels (n-heptane, n-octane, n-decane, and n-dodecane) in inert-diluent-substituted ambient environments. In these ISS experiments, some of the nitrogen in the ambient gas mixture is replaced by an inert gas, namely, carbon dioxide, helium, or xenon. Different diluents were observed to exert remarkably different influences on the cool-flame combustion of fuel droplets. The results show that the cool-flame extinction diameter is drastically increased with helium dilution compared to N2, CO2 or Xe, and Xe dilution leads to longer burning with a smaller extinction diameter. Unlike hot flames, the cool-flame burning rates are controlled by the cool-flame temperature established in the NTC region by the chemical kinetics, rather than by equilibrium thermodynamics, and the thermo-physical properties of the ambient gases, which control the heat feed back to the liquid droplet. The cool-flame extinction is triggered by the instability that occurs at the low-temperature end of the NTC region, below which cool diffusion flames become statically unstable. A quasi-steady theoretical model, presented earlier, which involves a six-step reduced-chemistry mechanism, valid around the lower end of the NTC region, is shown to explain the observed experimental trends qualitatively.

microgravity↗

NASA NTRS1994

Theoretical Basis for Estimated Test Times and Conditions for Drop Tower and Space-Based Droplet Burning Experiments With Methanol and N-Heptane

In order to develop an extensive envelope of test conditions for NASA's space-based Droplet Combustion Experiment (DCE) as well those droplet experiments which can be performed using a drop tower, the transient vaporization and combustion of methanol and n-heptane droplets were simulated using a recently developed fully time-dependent, spherically symmetric droplet combustion model. The transient vaporization of methanol and n-heptane was modeled to characterize the instantaneous gas phase composition surrounding the droplet prior to the introduction of an ignition source. The results for methanol/air showed that the entire gas phase surrounding a 2 mm methanol droplet deployed in zero-g .quickly falls outside the lean flammability limit. The gas phase surrounding an identically-sized n-heptane droplet, on the other hand, remains flammable. The combustion of methanol was then modeled considering a detailed gas phase chemical kinetic mechanism (168 steps, 26 species) and the effect of the dissolution of flame-generated water into the liquid droplet. These results were used to determine the critical ignition diameter required to achieve quasi-steady droplet combustion in a given oxidizing environment. For droplet diameters greater than the critical ignition diameter, the model predicted a finite diameter at which the flame would extinguish. These extinction diameters were found to vary significantly with initial droplet diameter. This phenomenon appears to be unique to the transient heat transfer, mass transfer and chemical kinetics of the system and thus has not been reported elsewhere to date. The extinction diameter was also shown to vary significantly with the liquid phase Lewis number since the amount of water present in the droplet at extinction is largely governed by the rate at which water is transported into the droplet via mass diffusion. Finally, the numerical results for n-heptane combustion were obtained using both 2 step and 96 step semi-emperical chemical kinetic mechanisms. Neither mechanism exhibited the variation of extinction diameter with initial diameter.

Marchese, Anthony J.↗

NASA NTRS1996

Shock Tunnel Studies of Scramjet Phenomena

Work focussed on a large number of preliminary studies of supersonic combustion in a simple combustion duct - thrust nozzle combination, investigating effects of Mach number, equivalence ratio, combustor divergence, fuel injecting angle and other parameters with an influence on the combustion process. This phase lasted for some three or four years, during which strongest emphasis was placed on responding to the request for preliminary experimental information on high enthalpy effects, to support the technology maturation activities of the NASP program. As the need for preliminary data became less urgent, it was possible to conduct more systematic studies of high enthalpy combustion phenomena, and to initiate other projects aimed at improving the facilities and instrumentation used for studying scramjet phenomena at high enthalpies. The combustion studies were particularly directed towards hypersonic combustion, and to the effects of injecting fuel along the combustion chamber wall. A substantial effort was directed towards a study of the effect of scale on the supersonic combustion process. The influence of wave phenomena (both compression waves and expansion waves) on the realization of thrust from a supersonic combustion process was also investigated. The effect of chemical kinetics was looked into, particularly as it affected the composition of the test flow provided by a ground facility. The effect of injection of the fuel through wall orifices was compared with injection from a strut spanning the stream, and the effect of heating the fuel prior to injection was investigated. Studies of fuel-air mixing by shock impingement were also done, as well as mass spectrometer surveys of a combustion wake. The use of hypersonic nozzles with an expansion tube was investigated. A new method was developed for measuring the forces acting of a model in less than one millisecond. Also included in this report are listings of published journal papers and conference presentations.

Stalker, R. J.↗

NASA NTRS1978

Droplet burning at zero G

Questions of the importance and feasibility of performing experiments on droplet burning at zero gravity in Spacelab were studied. Information on the physics and chemistry of droplet combustion, with attention directed specifically to the chemical kinetics, heat and mass transfer, and fluid mechanics of the phenomena involved, are presented. The work was divided into three phases, the justification, the feasibility, and the conceptual development of a preliminary design. Results from the experiments performed revealed a few new facts concerning droplet burning, notably burning rates in excess of theoretical prediction and a phenomenon of flash extinction, both likely traceable to accumulation of carbon produced by gas-phase pyrolysis in the fuel-rich zone enclosed by the reaction surface. These experiments also showed that they were primarily due to timing difficulties.

Williams, F. A.↗

NASA NTRS2000

Scale-Invariant Forms of Conservation Equations in Reactive Fields and a Modified Hydro-Thermo-Diffusive Theory of Laminar Flames

A scale-invariant model of statistical mechanics is applied to present invariant forms of mass, energy, linear, and angular momentum conservation equations in reactive fields. The resulting conservation equations at molecular-dynamic scale are solved by the method of large activation energy asymptotics to describe the hydro-thermo-diffusive structure of laminar premixed flames. The predicted temperature and velocity profiles are in agreement with the observations. Also, with realistic physico-chemical properties and chemical-kinetic parameters for a single-step overall combustion of stoichiometric methane-air premixed flame, the laminar flame propagation velocity of 42.1 cm/s is calculated in agreement with the experimental value.

Sohrab, Siavash H.↗

NASA NTRS2005

Summary of Simplified Two Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydrogen/Oxygen

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (greater than l x 10(exp -20)) moles per cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T(sub 4)). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/Air fuel and for H2/O2. A similar correlation is also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T(sub 4)) as a function of overall fuel/air ratio, pressure and initial temperature (T(sub 3)). High values of the regression coefficient R squared are obtained.

Marek, C. John↗

NASA NTRS2005

Simplified Two-Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydorgen/Oxygen

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two-time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (> 1 x 10(exp -20) moles/cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T4). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/air fuel and for the H2/O2. A similar correlation is also developed using data from NASA s Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T4) as a function of overall fuel/air ratio, pressure and initial temperature (T3). High values of the regression coefficient R2 are obtained.

Molnar, Melissa↗

NASA NTRS1995

An innovative approach to the development of a portable unit for analytical flame characterization in a microgravity environment

The availability of manned laboratory facilities in space offers wonderful opportunities and challenges in microgravity combustion science and technology. In turn, the fundamentals of microgravity combustion science can be studied via spectroscopic characterization of free radicals generated in flames. The laser-induced fluorescence (LIF) technique is a noninvasive method of considerable utility in combustion physics and chemistry suitable for monitoring not only specific species and their kinetics, but it is also important for imaging of flames. This makes LIF one of the most important tools for microgravity combustion science. Flame characterization under microgravity conditions using LIF is expected to be more informative than other methods aimed at searching for effects like pumping phenomenon that can be modeled via ground level experiments. A primary goal of our work consisted in working out an innovative approach to devising an LIF-based analytical unit suitable for in-space flame characterization. It was decided to follow two approaches in tandem: (1) use the existing laboratory (non-portable) equipment and determine the optimal set of parameters for flames that can be used as analytical criteria for flame characterization under microgravity conditions; and (2) use state-of-the-art developments in laser technology and concentrate some effort in devising a layout for the portable analytical equipment. This paper presents an up-to-date summary of the results of our experiments aimed at the creation of the portable device for combustion studies in a microgravity environment, which is based on a portable UV tunable solid-state laser for excitation of free radicals normally present in flames in detectable amounts. A systematic approach has allowed us to make a convenient choice of species under investigation, as well as the proper tunable laser system, and also enabled us to carry out LIF experiments on free radicals using a solid-state laser tunable in the UV.

Dubinskiy, Mark A.↗

NASA NTRS2015

Development of a Premixed Combustion Capability for Scramjet Combustion Experiments

Hypersonic air-breathing engines rely on scramjet combustion processes, which involve high speed, compressible, and highly turbulent flows. The combustion environment and the turbulent flames at the heart of these engines are difficult to simulate and study in the laboratory under well controlled conditions. Typically, wind-tunnel testing is performed that more closely approximates engine testing rather than a careful investigation of the underlying physics that drives the combustion process. The experiments described in this paper, along with companion data sets being developed separately, aim to isolate the chemical kinetic effects from the fuel-air mixing process in a dual-mode scramjet combustion environment. A unique fuel injection approach is taken that produces a nearly uniform fuel-air mixture at the entrance to the combustor. This approach relies on the precombustion shock train upstream of the dual-mode scramjet combustor. A stable ethylene flame anchored on a cavity flameholder with a uniformly mixed combustor inflow has been achieved in these experiments allowing numerous companion studies involving coherent anti-Stokes Raman scattering (CARS), particle image velocimetry (PIV), and planar laser induced fluorescence (PLIF) to be performed.

Rockwell, Robert D.↗

NASA NTRS2011

A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane

The reduction of elementary or skeletal oxidation kinetics to a subgroup of tractable reactions for inclusion in turbulent combustion codes has been the subject of numerous studies. The skeletal mechanism is obtained from the elementary mechanism by removing from it reactions that are considered negligible for the intent of the specific study considered. As of now, there are many chemical reduction methodologies. A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL (Lawrence Livermore National Laboratory) skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation (LES) in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; in LES, these small scales are unimportant as far as the overwhelming part of dynamic energy is concerned. Here, the scales thought unimportant for recovering the thermodynamic energy are removed. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is over-predicted, a fact traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into this conceptual reduction in addition to the modeling the evolution of the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasisteady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure, and initial temperature.

Harstad, Kenneth G.↗