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III3-4 viscosity roughly equal to that in A2330 at the point where the solution switches from A2330 to JETMIX is used in JETMIX, CHARNAL computes turbulent kinetic energy and its dissipation ratę from differential equations, but the initial distributions of these quantities are obtained from the Prandtl mixing-length model. In the following pages flow properties calculated with the tools described are compared with data from some of the experiments mentioned earlier.

Pitot Pressures in a Coaxial Bumer

In Figurę 1, pitot pressure measurements from Beach’s coaxia! mixing experiments¹⁶ are compared with those calculated using A2330 - a single-jet, diffusion-controlled, mixing program using the Eggers’ viscosity model. The nozzle, injector, and combustion duet are shown in Figurę 2. Agreement between theory and experiment is good. Not only do the data clearly show the radial positions of the mixing regions and the large variations in pitot pressure there, but they also show the evolution of profile shapes and the variation of center-line values with distance from the injection point. The fidelity with which the theory predicts these fairly complex curves is remarkable. Also, it was found that the same empirical constant in the viscosity model matched data in air, N₂, and vitiated air. Since pitot pressure is a good indicator for showing where mixing and reaction are taking place, these results lend confidence to the use of A2330 and Eggers’ model for predicting mixing of circular jets with a parallel airstream.

Composition Profiles in Multijet Mixing

The comparison of theory and experiment for multiple-jet injection from a strut in a rectangular duet¹⁷ is especially interesting. Figurę 3 shows a schematic of the experimental apparatus used. Both the jets and the surrounding vitiated airstream were at Mach 2.2; hydrogen and air stagnation temperatures were 300 K and 2000 K, respectively. The flow from any one of the five injectors was treated (using A2330) as a single jet mixing with an unbounded coaxial airstream until the edge of the mixing region approached the piane midway between two neighboring jets. Conditions along a radius at this station were used as input to JETMIX and the solution was continued. As fuel and air mixed they were considered to react instantaneously.

The flow region in which JETMIX calculates is illustrated in Figurę 4. Symmetry of the flow permits the bottom and sides of the rectangle shown to be treated as frictionless, impermeable walls. For convenience, the duet wali at the top is treated in the same way. The dimension s is the distance between injector holes. The dimension h is determined by the mass flow of hydrogen, the mass flow of air, and the constraint that the equivalence ratio would be 0.6 if mixing were complete. The wake flow behind the strut was ignored. Step profiles of all properties were used as input to A2330, and two ways of defining initial conditions at the injection point were tried. (The strut blocked 27% of the duet cross section.) In the first approach, both H₂ and air flows were expanded isen-tropically from an area defined as duet cross section minus strut cross section to the fuli duet area. Conditions in this expanded flow were used as initial conditions for A2330. In the second approach, H₂ jet exit conditions and air free-stream conditions were used for A2330 and duet height was reduced by the strut thickness to maintain the overall equivalence ratio at 0 = 0.6 . Comments on the results from the two approaches are given later.

The calculated amount of mixing achieved at a given station, x , is plotted in Figurę 5, where results are shown for both A2330 and for JETMIX. A reduced ratę of mixing is evident after JETMIX picks up the solution from A2330. The overal amount of mixing achieved at a givcn x does not differ greatly between calculations using the two different approaches to account for strut blockage.

Both reacting and nonreacting runs were madę during the tests. To avoid reaction for the hydrogen while nearly duplicating the conditions of mixing in a hot flow, oxygen replenishment was omitted in the production of the vitiated air for nonreacting runs. From the plots of measured wali pressure shown in Figurę 6, the rise in pressure due to burning of the fuel is easily visible, and the calculated variation of pressure (one-dimensional theory) is seen to agree well with the data.

Profiles-of total hydrogen concentration measured at a point 0.77 m downstream from the strut by nine probes equally spaced across the center linę of the duet exit are shown in Figurę 7 and are compared with calculated profiles. All samples collected were essentially completely reacted, and total hydrogen concentration is used so that the spread of injected fluid for both reacting and nonreacting cases can be compared directly. As noted earlier, reaction seems to have little effect on mixing, sińce the measured profiles differ little between the reacting and nonreacting flows. The data are plotted against distance from the nearest jet center linę with corrections applied as indicated to account for shifts in streamline positions caused by the duet exit shock. Notę that the corrections are large only for probes 2 and 8 and that they are larger for the nonreacting case than for the reacting case, because the duet flow is morę overexpanded for nonreacting flow.

Prediction of profile shape is good, but the distance downstream of the injector at which best agreement is found does not match well between theory and experiment. This is attributed to unsatisfactory modeling of the turbulent transport in JETMIX, sińce by varying the level of viscosity the calculated distance from the injector can be madę to agree with experiment. Assuming local Chemical equilibrium, the calculated fuel distribution profiles in Figurę 7 correspond to reacting between 68% and 79% of the injected fuel. This compares well with the amount of reaction (66%) required at the probe location to match the measured duet wali pressures with the one-dimensional calculation shown in Figurę 6.