F.C. Gouldin

An application of fractals to modeling premixed turbulent flames

A fractal description of the geometry of rough surfaces is applied to flamelets in premixed turbulent combustion, and a model to predict the turbulent flame speed, ut, is developed and tested against experimental data. At low to moderate turbulence levels reaction is known to occur in thin flamelets which are rough with multiple scales of wrinkling. It is hypothesized that flamelets may be represented by fractal surfaces, and the results of Mandelbrot [11] are used to find an expression for flamelet surface area valid in the limit of large velocity fluctuations relative to the laminar flame speed. The expression is then corrected for conditions away from this limit, and a prediction for ut is obtained under the assumption that flamelets propagate at the unstrained laminar flame speed, u0: utu0={[1−(1−At−14R1−34) exp(−(AtR1)14u′u0)]At14R134}D−2. D is the fractal dimension and has a value of 2.32 to 2.4 as inferred from experiment [12, 28] and by analysis [13, 14]. At = 0.37, based on turbulent pipe flow data. Comparison of predictions with the data of Abdel-Gayed, Bradley, and coworkers obtained for several different mixtures and for a broad range of turbulence conditions shows good results. While predictions are generally low, absolute values are in most cases within 30% of experimental results. A correction for flame stretch effects is proposed and model predictions are improved thereby.

Chemical closure model for fractal flamelets

Abstract A chemical closure model for premixed turbulent flames is proposed and tested by analysis and numerical computation for flames with vanishingly small density change. The model is based on the assumption that reaction zones can be modeled as thin sheets—flamelets—and that the geometry of these sheets can be represented by fractal surfaces. The model expression for mean fuel consumption rate is 〈ω〉=C R ρ〈δY f u L 〉 f (lƒ/η) D−2l F −1 〈C〉(1−〈c〉) with ƒ given by ƒ=[1−(1−A t −1 4 R 1 −3 4 ) exp (−A t 1 4 R 1 −1 4 u′/〈ul〉 f )] and l η =A t 1 4 R 1 3 4 where D is the fractal dimension of the flamelet surface and is the new parameter introduced by the fractal geometry assumption. This model is tested in simplified analyses of normal and oblique flames with good results. The oblique flame analysis provides new insight into the definition of the turbulent burning velocity. Numerical computations are performed with a conditioned second-order closure scheme, and the chemical closure model performance is found to be good. Computed results with a gradient transport model for species diffusion show that turbulent fluxes are significantly under predicted in comparison with the second-order closure results.

Inhibition of nonpremixed flames by phosphorus-containing compounds

Phosphorus-containing compounds (PCCs) are proposed as viable alternatives to current, ozone-destroying, flame-inhibiting agents. An opposed-jet burner apparatus was used to study the effectiveness of two low-vapor-pressure PCCs, dimethyl methylphosphonate (DMMP) and trimethyl phosphate (TMP), in extinguishing a nonpremixed methane-air flame. The global extinction strain rate was determined as a function of dopant loadings. Tests were also conducted using nitrogen as an inert additive for reference. Results demonstrate that these phosphorus-containing compounds are significant inhibitors of nonpremixed methane-air flames when introduced into the oxidizer stream, 40 times more effective than nitrogen on a molar basis. A novel technique for measuring the extinction strain rate while maintaining a constant dopant level in one gas stream was developed.

TEMPERATURE DEPENDENCE OF PHOSPHORUS-BASED FLAME INHIBITION

Abstract An investigation of the inhibition properties of Phosphorus-Containing Compounds (PCCs) in moderately strained (global strain rate of 300 s −1 ) non-premixed methane-N 2 /O 2 /Ar flames is presented. The effect of DMMP [dimethyl methylphosphonate, O=P(OCH 3 ) 2 (CH 3 )] on relative OH concentration profiles was measured by using quenching-corrected Laser-Induced Fluorescence (LIF) for the first time. LIF measurements indicate a reduction in the total OH present of 23% for a non-premixed methane-air flame doped with 572 ppm of DMMP. As the stoichiometric adiabatic flame temperature is increased via substitution of Ar for N 2 in the oxidizer stream, the measurements show a strong decrease in the magnitude of the OH reduction. Experimental results show reasonable agreement with computational predictions made using a kinetic model that has been proposed for DMMP decomposition and phosphorus-radical chemistry. Analysis of the computational results shows that the reactions involving phosphorus remove H and O atoms from the radical pool, thus weakening the flame. These reactions produce OH directly, but the rest of the mechanism responds to O and H reductions by reducing OH levels. The key reactions involved in this inhibition process are identified.

Variation of chemically active and inert flame-suppression effectiveness with stoichiometric mixture fraction

The need to find alternative fire suppressants has motivated experiments to determine the mode of action of possible candidates. An opposed-jet burner was used to characterize the effectiveness of one possible alternative, dimethyl methylphosphonate (DMMP). Similar tests were done with an inert compound, argon, for comparison. Flame strength was characterized by the extinction strain rate. Experiments included both oxidizer-side and fuel-side doping of methane-nitrogen versus oxygen-nitrogen flames of various compositions. The stoichiometric mixture fraction (Zst) is varied systematically while holding the undoped extinction strain-rate constant, by changing the amount of diluent in the reactant flows. This moves the flame location with respect to the stagnation plane, affecting the fraction of a particular reactant stream that reaches the flame. Measured effectiveness, of fuel-side and oxidant-side doping versus Zst reflects this change in quantity of dopant reaching the flame. To account for this dependence on quantity, effectiveness was normalized by the amount of dopant calculated to reach the maximum temperature contour of the flame. Argons normalized effectiveness was found to be independent of Zst, of adiabatic flame temperature, and of whether the oxidizer stream or the fuel stream is doped. DMMPs normalized effectiveness, however, was observed to be significantly greater when introduced in the oxidizer, rather than fuel, stream. It also exhibits a marked dependence on adiabatic flame temperature, with lower values at higher temperatures.

Tomographic Analysis of Unsteady, Reacting Flows: Numerical Investigation

The implementation of a new tomographic inversion method as a combustion diagnostic tool for the study of unsteady, reacting flows is evaluated using numerical experiments to reconstruct two-dimensional fuel concentration distributions obtained from a numerical simulation of a turbulent reacting square jet Reconstructions of nonaxisymmetric fuel concentration distributions are performed at various downstream locations from the jet exit using only a few line integrals made along multiple offsets and viewing angles. The new inversion method expresses the concentration distributions to be reconstructed as a weighted sum of Karhunen-Loeve eigenfunctions, produced by the Karhunen-Loeve procedure. These Karhunen-Loeve eigenfunctions and their associated time coefficients are mathematically constructed to form an optimal representation of the concentration distributions in the square jet and systematically quantify their spatial and temporal downstream evolution. Near the exit of the jet, only one eigenfunction is needed, and farther downstream more eigenfunctions (up to 24) are needed to capture the significant features in the concentration distributions. Ultimately, accurate reconstructions of the fuel concentration distributions at downstream locations away from the jet exit are obtained using only 28 line integrals. The effect of the number of eigenfunctions used in the reconstruction and the measurement configuration on the reconstruction accuracy is examined.

Tomographic analysis of unsteady, reacting flows

The implementation of a new tomographic inversion method as a combustion diagnostic tool for the study of unsteady, reacting flows is evaluated using numerical experiments to reconstruct 2D fuel concentration distributions obtained from a numerical simulation of a turbulent reacting square jet. Reconstructions of nonaxisymmetric fuel concentration distributions are performed at various downstream locations from the jet exit using a few well-configured line integrals made along multiple offsets and viewing angles. The new inversion method expresses the concentration distributions to be reconstructed as a weighted sum of Karhunen-Loeve eigenfunctions, produced by the Karhunen-Loeve procedure. These eigenfunctions and their associated time coefficients are mathematically constructed to form an optimal representation of the concentration distributions in the square jet and systematically quantify their spatial and temporal downstream evolution. Ultimately, accurate reconstructions of the fuel concentration distributions at downstream locations away from the jet exit are obtained using only 28 line integrals. The effect of the number of eigenfunctions used in the reconstruction and the measurement configuration on the reconstruction accuracy is examined. (Author)

Extinction of Opposed Jet Diffusion Flames of Scramjet Fuel Components at Subatmospheric Pressures

The effect of atmospheric and subatmospheric pressure on the global extinction strain rate of opposed-jet diffusion flames of gaseous and vaporized liquid fuels in air is quantified. After ignition of a flame between the burner tubes in a vacuum chamber, extinction was approached by gradually reducing the chamber pressure, while the momentum flux balanced flowrates of the fuel and air jets were held constant. Results for methane, ethylene, and n-heptane/methane and n-heptane/nitrogen mixtures are presented and compared to predictions based on new pressure dependent chemical-kinetic mechanisms concurrently being developed for scramjet engine simulations. The extinction strain rates for all fuels are seen to monotonically increase with pressure in the subatmospheric range explored, and to depend on other factors such as reactant temperature and composition, and burner tube geometry. The numerical simulations are in qualitative agreement with the experimental results, but over predict the extinction strain rates by up to 30%.

Experimental and numerical study of an incinerator- and furnace-related flow

Abstract The results of an experimental and computational study of the flow over a separation-inducing corner formed by a surface-mounted, triangular obstacle located close to a 90° turn are presented. The study was undertaken as part of a process to develop and validate numerical simulation methods for predicting incinerator and furnace flows, and the flow configuration studied is characteristic of such devices. The predictions from FEM simulations based on the standard k -ϵ turbulence model are compared with results from two-component LDV measurements from a water tunnel experiment. In the numerical simulations, two different outflow boundary conditions are used, one being the stress-free outflow condition and the other making use of special outflow elements. The results from the numerical simulation with the special outflow elements are in better agreement with the experimental results than those from the simulation with the stress-free outflow boundary condition. With the special outflow elements, the mean velocities and the gradients of the mean vertical velocity are well predicted. In the region separating the recirculation zone from the freestream where turbulent transport is most important, good agreement between the experiment and the special outflow elements simulation is achieved for the turbulent kinetic energy.

Reduced-Order Structure of Reacting Rectangular Jets

The results of proper orthogonal decomposition analyses on CO 2 number density and vorticity magnitude data from reacting rectangular jet simulations are presented. The resulting proper orthogonal decomposition eigenfunctions are used to develop physical insight of the vortex formations and dynamics of these jets and their related mixing and spreading characteristics. It is seen that different vortex structures are captured in the eigenfunctions and that CO 2 and vorticity eigenfunctions are very similar indicating that vortex-driven mixing dominates in these jets. The eigenvalue spectra associated with these eigenfunctions are used to evaluate the information content of the eigenfunctions and the potential for reduced-order models. Using subsets of eigenfunctions with high information content, CO 2 and vorticity magnitude distributions can be represented with relatively few eigenfunctions. However, as the flows develop downstream, more eigenfunctions are needed to represent them to the same level of accuracy. The potential for reduced-order modeling of each field is approximately the same for the jets of aspect ratios 1, 2, and 3; however, there is stronger potential for reduced-order modeling of the CO 2 field than of the vorticity field