Di1 Pas X 4ii

where I denotes intensity of laser radiation, a the absorption coefficient for given fuel (atm 1cm'1), 1 the coordinate along laser beam path (cm), Pabs the absolute pressure (atm), and Xch4 the fuel mole fraction.

Integration of Eqn. 1 yields

ln( I / Ia ) =-« • Pabs -J Xch 4(1 ) • dl , (3)

where I, is the initial (un-attenuated) laser radiation intensity. If the concentration is assumed constant across the measurement length, one obtains

where L is the pathlength of absorption (cm). The absorption coefficient a is dependent on temperature, pressure, and the type of fuel being characterized. The absorption coefficient for methane was measured by Perrin and Hartman [12] to be approximately a = 10 atm-1cm-1 at standard temperature and pressure. The absorption coefficient for ethane is aken from the results of Tsuboi et al. [15] to be approximately 5 atm-1cm-1. As can be seen from Eqn. 3, laser absorption measurements can only give an integrated fuel concentration over the path of the laser beam. In our application, the laser beam was passed across the pipe exit, at the same orientation, at various cords. This is shown in Fig. 1. In order to generate a radial profile of concentration from the laser beam absorption data, a computer aided tomography (CAT) program using a genetic algorithm was employed. The reconstruction program will be described in detail in the following section.

After demonstrating that the experimental measurement system was reasonably accurate, radial concentration profiles were generated at various downstream locations for comparison with the LES model. Table 2 describes the operating conditions at each of the sampling points. The flow rates shown in Table 2 were set with the goal of making the Reynolds number as high as possible, and of matching the average velocities of the inner and outer pipe flows. For the experiments described in the table, the nominal velocities for the inner and outer pipe flows were 26 to 27 m/s (making the friction velocities for the inner and outer pipe flows around 1.6 and 1.2 m/s, respectively).

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