The concept that the turbulent kinetic energy equation can be used to determine the shear in a turbulent flowfield through the use of a suitable relation between turbulent shear and turbulent kinetic energy has proved successful in the analysis of turbulent boundary-layer flows. In this paper, the application of a similar approach to the problem of turbulent free mixing of constant-density streams is described. By correlating measurements of turbulent shear and turbulent kinetic energy in a number of constant density free mixing flows, a linear relation between turbulent shear and turbulent kinetic energy is shown to exist. The combination of this relationship and a new rapid technique for the simultaneous solution of an arbitrary number of parabolic partial differential equations allows detailed calculation to be carried out for two-steam mixing systems of interest, one a plane mixing region and the other axisymmetric. Both mixing regions are constant density. Generally satisfactory agreement is achieved for both velocity and turbulent shear distribution. More important than the level of agreement reached, however, is the fact that the method used is more perceptive than previous phenomenological approaches and, thus, offers the promise of eventually leading to greater understanding of turbulent shear flow. Nomenclature a = coefficient of the general parabolic equation ai = constant in relation between turbulent shear and turbulent kinetic energy a2 = constant in turbulent kinetic energy dissipation relation b,c } d = coefficients of the general parabolic equation Dk = turbulent kinetic energy dissipation J k = turbulent kinetic energy flux k = kinetic energy of turbulence I = Prandtl mixing length Ik = mixing length for turbulent kinetic energy M = entrainment flow rate p = pressure U = mean stream velocity u,v = time-aver aged velocity components u',v' } w f = fluctuating turbulent velocity components x,y = independent coordinates a. = parameter; a = 0 for plane flow, a = 1 for axisymmetric flow e = eddy viscosity p = density ffk = turbulent kinetic energy quantity analogous to Prandtl number for total mean-flow energy T = turbulent shear stress
In two separate flights in 2004, the X-43A became the fastest aircraft ever to fly with an airbreathing propulsion system, reaching nearly Mach 7 in its first flight and approaching Mach 10 in its second flight. The X-43A was designed and manufactured by a contractor team of ATK GASL and Boeing. This paper recounts some of the design and manufacturing key features and challenges faced by the contractor team. That these challenges were successfully met is demonstrated by the success of the two flights, in both of which the aircraft and engine, its subsystems, and its separation system had to work the first time in flight. The research instrumentation system and all the integrated sensors performed as desired. Therefore, these two flights produced a wealth of aerodynamic and propulsion data, but moreover demonstrated that hypersonic aircraft can be designed and built using engineering tools and technologies available today.
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