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I. Introduction A TYPICAL empirical gas turbine cornbustor design and jTlLdevelopment approach is based on extensive use of an experience data base and empirical (semianalytical) correlations along with extensive component and subcomponent testing. Such an approach has historically been fairly successful in developing combustors based on proved design concepts. Empirical methods exhibit limitations in a number of critical areas, some of which are: 1) Empirically based design methods have shown severe limitations in scaling combustors. 2) If significantly big jumps are required in the technology levels (e.g., combustor temperature rise, cycle pressure ratio, cornbustor performance, and durability levels), combustion engineers are hesitant to use empirical correlations based on an available experimental data base. 3) The applicability of experience correlations (developed for a certain design concept) is quite limited for some other novel or revolutionary combustion concepts. 4) With ever exacting design requirements of advanced technology combustors (combustor operating conditions, wide operability, low smoke, and significantly improved durability characteristics), better tools are needed to achieve an optimum solution to satisfy conflicting combustor design requirements. The first extensive effort to develop and demonstrate an empirical/analytical combustor design methodology was initiated by the U.S. Army Research and Technology Laboratories in 1975. This technique was successfully applied in the design and development testing of two full-scale small reverse-flow annular combustors.1 Simultaneously, this new methodology was being used and refined under the NASA Pollution Reduction Technology Program. How this method was used for the design and development testing of a premix/prevaporized combustor is described in Ref. 2. In parallel with these two efforts, the empirical/analytical design procedure was being used for developing a ceramic combustor, which needed to have significantly lower wall temperature gradients for structural durability.3'4 Subsequent to successful applications of the empirical/analytical combustor design methodology, a number of advanced technology combustors have been developed with the aid of analytical models, as described in Sec. III. Section II describes the methodology. Although the method has been useful in providing design guidance, the model limitations are evident in regard to accuracy of the state-ofthe-art numerics and physical submodels of turbulence, turbulence/chemistry interaction, spray evaporation/mixing, soot formation/oxidation, and radiation. Some of these deficiencies are discussed in Sees. IV and V.