Analysis of experimental results of the inlet for the NASA hypersonic research engine aerothermodynamic integration model

An aerodynamic engine inlet analysis was performed on the experimental results obtained at nominal Mach numbers of 5, 6, and 7 from the NASA Hypersonic Research Engine (HRE) Aerothermodynamic Integration Model (AIM). Incorporation on the AIM of the mixed-compression inlet design represented the final phase of an inlet development program of the HRE Project. The purpose of this analysis was to compare the AIM inlet experimental results with theoretical results. Experimental performance was based on measured surface pressures used in a one-dimensional force-momentum theorem. Results of the analysis indicate that surface static-pressure measurements agree reasonably well with theoretical predictions except in the regions where the theory predicts large pressure discontinuities. Experimental and theoretical results both based on the one-dimensional force-momentum theorem yielded inlet performance parameters as functions of Mach number that exhibited reasonable agreement. Previous predictions of inlet unstart that resulted from pressure disturbances created by fuel injection and combustion appeared to be pessimistic

qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

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Experimental and analytical study of an inlet forebody for an airframe-integrated scramjet concept

Preliminary analytical and experimental inlet forebody investigations have been conducted at Mach numbers of 6.0 and 8.5. The forebody design concept consisted of a sharp-nosed right circular cone followed by elliptical cross sections. This concept resulted in swept isentropic compression which would allow swept cowl leading edges. Measurements were made to define the condition of the inviscid flow field developed by the forebody, including flow profiles in the vicinity of cowl leading-edge stations, and the three-dimensional boundary-layer effects. The investigation verified some of the expected differences between the predicted and the experimental results

An inlet analysis for the NASA hypersonic research engine aerothermodynamic integration model

A theoretical analysis for the inlet of the NASA Hypersonic Research Engine (HRE) Aerothermodynamic Integration Model (AIM) has been undertaken by use of a method-of-characteristics computer program. The purpose of the analysis was to obtain pretest information on the full-scale HRE inlet in support of the experimental AIM program (completed May 1974). Mass-flow-ratio and additive-drag-coefficient schedules were obtained that well defined the range effected in the AIM tests. Mass-weighted average inlet total-pressure recovery, kinetic energy efficiency, and throat Mach numbers were obtained

Polynomial solutions of nonlinear integral equations

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.Comment: 10 page

Identifying the development in phase and amplitude of dipole and multipole radiation

The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity in such cases where, in consequence of retardation, the character and features significantly and progressively change as radiation propagates onwards, from the near-field and out towards the wave-zone. Readily developed analytical representations of the electric field, cast as a function of distance from the source, provide illuminating insights into the most prominent and distinctive properties of radiant electromagnetic emission. Graphical implementations and animations of the results prove particularly instructive in revealing the spatial form and temporal evolution of the emergent electromagnetic fields