Reply by Authors to G. Y. Anderson

A comments and conclusions about the contents of Ref. 1 appear to be based on a misinterpretation or misunderstanding of its content and intent and a displeasure with the integral analysis technique" used as the standard. The intent of Ref. 1 was and is to show the limitations of assuming a constant-area/constant Mach combustion process for closure of the integral equations of motion in predicting scramjet engine performance compared to the "most widely accepted one...developed by Billig." The content of the Note does just that, using a representative case. Anderson's attempt to discredit the results presented (using Table 1 in his comment from Fig. 55 of Ref. 8) is a misrepresentation of the facts. First, there are no scramjet performance data given in Ref. 8 for a freestream Mach number of 3.5 at any altitude. Second, the performance numbers at Mach 6 are for a different engine configuration with different values assumed for a number of component efficiencies. Specifically, the performance given in Ref. 8 at Mach 6 is for an aft-mounted engine rather than a nose-mounted configuration with a combustor area ratio of 2.5 rather than 3 and a nozzle exit-to-diffuser inlet area ratio of 2 rather than 1.7. Furthermore, at Mach 6, Ref. 8 assumes an inlet air capture of 0.97 rather than 1.0, an inlet kinetic energy efficiency of 0.975 without including forebody bow shock losses, combustion skin-friction losses that are a factor of 2 to 3 lower than those measured, an exit nozzle efficiency of 0.985 rather than 0.975, and equilibrium thermo-chemistry is the exit nozzle rather than two-thirds frozen. In addition, the integral analysis used in Ref. 8 does not incorporate an oblique precombustion shock model; it permits only no shock or a normal shock. Table 1 of the comment is, therefore, a comparison of "apples-to-oranges," and is, at best, misleading in the context presented. Finally, if the same assumptions, geometries, and efficiencies used in Ref. 8 are used in our integral technique, one obtains identical performance predictions. These issues aside, the intent of any integral analysis technique is to provide an accurate engineering tool for predicting overall engine performance and parametric or sensitivity studies at minimum cost. No claim is made that it can predict the details of the flow between the initial and final stations assumed. Multidimensional models (see, e.g., Refs. 9 and 10) are required for that. However, even though a number of increasing complex multidimensional models have been developed and solutions obtained using advanced computational fluid dynamic (CFD) techniques, none have been validated, even for inlet diffusors, because of a lack of experimental data. More importantly, no current CFD technique using the full Navier-Stokes equations can solve for the flow in the region of the precombustion shock because it requires an estimated 10-10 grid points for resolution and 10 time steps for convergence, the combination of which is well beyond the capabilities of the most advanced class VI computer. Alternative methods, such as using an integral solution for the initial and boundary conditions downstream of the precombustion shock and then using CFD codes to iteratively solve for