Introduction

Many practical combustion devices premix fuel and air to lean conditions prior to combustion. Such devices include spark ignited piston engines and dry-low-NOx (DLN) premixed gas turbine combustors. By using excess air (or EGR) the flame temperature is reduced. The lower temperatures greatly reduce the rate of chemical reactions that produce the toxic pollutant nitric oxide. For example from the gas turbine industry, steam injected nonpremixed combustors have achieved 25ppm while the DLN lean premixed combustors have been able to achieve NOx levels from 15 to 10 ppm at 15% O2 [1,2]. In order for a lean premixed combustor to effectively reduce NOx levels, the air and fuel should be well mixed prior to the combustion event. A well mixed system is characterized by a mean fuel concentration, that is lean, with a small RMS about the mean. Inadequate fuel-air mixing can have the same mean, but has a larger RMS such that, occasionally, combustion may take place at near-stoichiometric air-fuel ratios at some time, while at other times the mixture is too lean to burn. The sporadic combustion at near-stoichiometric air-fuel ratios has higher than average temperatures. These high temperatures lead to very high NOx levels due to the well known exponential temperature dependence of the production rates of oxides of nitrogen (NOx) [3]. In addition, the incomplete combustion at temporally lean air-fuel ratios leads to high levels of hydrocarbon (HC) and carbon monoxide (CO) emissions. Additionally, lean premixed combustors are prone to high pressure oscillations, and the extent of mixing of the fuel and air has been shown to correlate with these oscillations in combustor pressure [4,5]. Thus, in the design of a lean premixed gas turbine, it is essential that the mixing of fuel and air is well characterized; minimally one needs a mean and RMS of fuel concentration.

The goals of the current research are two-fold. First, to study the performance of a Large Eddy Simulation (LES) for a simplified geometry as a step toward application of LES modeling to an actual lean premixed combustor. Simply stated, does the LES predict the mean and RMS fuel concentration that is measured. The second goal is to study the ability of generating both the mean and RMS of fuel concentration, at the exit of a premixer, from measurements obtained using a robust easy-to-use line of sight (LOS) laser absorption technique.

For the current research, this allows us to use experimental measurements of mean and RMS to characterize the performance of the LES model. As a future goal, we imagine this simple, but powerful diagnostic can be easily used for studies of gas turbine premixers. Reconstruction of a 2-dimensional field from a single (assuming axis-symmetry) or multiple 1-dimensional measurements (i.e. tomography) is very common. Some applications other than concentration measurements include reconstruction of density of human head tissue from x-ray absorption measurements [6], and reconstruction of particle speed distributions from imaging measurements in the reaction product imaging technique [7]. What is important about the current research is that the method has the potential to reconstruct an asymmetric concentration field with reasonable accuracy from a limited number of experimental measurements, and that we apply the technique to the RMS of the concentration profile. The research described in this paper consists of developing a genetic algorithm (GA) for tomography, applying it to some numerical "test cases" for validation, then using it on data from a turbulent coannular pipe flow to assess the ability of an LES model to resolve the fuel-air mixing spatially and temporally. EXPERIMENTAL SETUP/PROCEDURE

In most combustion models, such as Reynolds Averaged Navier-Stokes (RANS), time resolved details are not predicted. At the other end of the spectrum, direct numerical simulation (DNS) is a model that provides many details of the flow, resolved both temporally and spatially. However, due to the vast computational effort involved with DNS, it is usually only applied to simple flows. LES models are truncated DNS models that use subgrid models for small-scale turbulence to reduce the computational costs (see, for example Branley and Jones, [8]). LES gives time resolution in a 3-dimensional simulation, unlike most combustion models, but requires much more computer resources. Table 1 gives the input and grid parameters of current LES and details can be found [9].

In order to evaluate the performance of the LES mixing model, a coannular pipe flow setup was constructed, consisting of a center pipe flow of fuel, surrounded by a pipe flow of air. The diameter of the outer pipe was D = 7.6 cm, while that of the inner pipe was d = 6.4 mm. Thus the diameter ratio of the pipe flow setup was d/D = 0.084. The center fuel pipe was 3.3 meters in length, while the air pipe length varied from 3.3 to 3.5 meters. The long fuel pipe meant that there was a nearly fully developed coannular pipe flow. Figure 1 gives a schematic of the setup.

Laser absorption measurements were made at the exit of the outer (air) pipe. In this way measurements at different axial distances from the center (fuel) pipe exit were accomplished by changing the length of the outer pipe. Axial distance from the center pipe exit will be referred to as small x, and x/d will refer to this axial distance normalized by the diameter of the center pipe. Measurements of the fuel concentration were obtained by the use of a Helium-Neon laser at a wavelength of 3.392 mm. Hydrocarbons absorb radiation at this wavelength, and Beer's law can be used to relate the amount of absorption to the concentration of fuel (see, e.g. Lee et al. [10], Yoshiyama et al.[11], Perrin and Hartmann, [12], Mongia [13], or Ebert et al. [14]). At standard temperature and pressure, the absorption of laser light by a concentration of molecules follows Beer's Law:

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