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Show EFFECTS O F T U R B U L E N CE Turbulence causes species concentrations and gas temperature, T, to fluctuate over time. Ideally, the time-mean source of N O in a turbulent environment should be integrated over the joint probability density function (pdf) of all the associated species concentrations, cpj's, and temperature T. For simplicity, statistical independence between species concentrations and temperature is assumed. Therefore, Eq. (3) can be transformed to ^ = / /J~ S*o PV) ?(*) dT dip (3) J 9 *'7min and the integrations over T and species concentrations can be performed separately. The flamelet model automatically accounts for the integration over the species concentration space; whereas the integration of rate coefficient k over T is done within the N O model itself. In Eq. (3) T,^ is the lowest furnace inlet temperature T^ and T ^ is taken to be the adiabatic flame temperature T^. In the case of the species and temperature distributions, the pdfs are assumed to have a 0- functional form. P((pi) is generated by the mean and variance of mixture fraction while P(T) is defined by the mean and variance of temperature. Using the same approach as in Eq. (3), the time-mean sources for N-atoms (SN) and H C N (SHCN) in the turbulent environment are determined. This presumed pdf method combined with the k-e turbulence closure model provides a robust and computationally inexpensive way to account for the effects of turbulence. Since the burners being studied do not produce swirling flow, a higher order turbulence closure like Reynolds stress model (Launder, 1989) is not needed. The transported pdf method (see Pope, 1985 and Dopazo, 1994) offers a more rigorous pdf treatment than the one described above but it is still too computationally demanding to be implemented in industrial flame applications. VALIDATION EXPERIMENTS Two different commercial natural gas burners were used in the validation experiments. The first burner is a conventional design without any N O x reduction feature and is referred to here as the High N O x Burner (HNB). The second burner is equipped with some N O x reduction technology and is referred to here as the Ultra L o w N O x Burner (ULNB). Both burners consist of a burner tile about 18 c m in diameter and 18 c m deep, which provides separate entries for natural gas and combustion air. For the H N B case, over 9 9 % of combustion air was evenly introduced through the 8 combustion air ports (see Figure 1). In contrast, only 5 5 % of the combustion air in the U L N B was injected through the burner tile secondary air entry ports with the other 4 4 % provided through two side-arm tertiary air ports (see Figure 2). In both cases, there was a small air lance (1% of combustion air) applied through the centre of the burner tile. These burners were centrally mounted on a 0.7 M W front-firing cylindrical furnace (5.24 m long and 1 m in diameter, see Figure 3). The initial 1.0 m and the last 1.83 m of the furnace were lined with refractory to approximate adiabatic sections and the rest was divided into many separately cooled segments to provide a thermal load. The operating conditions for the two test cases were purposely set to be identical (27 kg/hr natural gas, 1 0 % excess air and 777 K preheat) so that any observed difference 5 |