The wavelength of steady Taylor vortices established through a sudden start of the inner cylinder has been studied experimentally. The sudden start procedure gives the fluid a choice in the selection of the wavelength. It was found that the preferred wavelength of singly periodic vortices in the steady state after a sudden start is smaller than the critical wavelength, with a minimum at around T / Tc = 15. When the Taylor number to which the sudden start was made was increased to around 60 Tc, then the preferred wavelength approached the critical wavelength. A wavelength once established through a sudden start did not change its value if afterwards the Taylor number was maintained for a very long time or if the Taylor number was varied over larger intervals, provided the flow was singly periodic. However, this rule does not hold when the critical Taylor number is approached from above with a flow created through a sudden start to a higher Taylor number. In this case the wavelength increases to approach the critical wavelength. Sudden starts to very high Taylor numbers created doubly periodic or turbulent flow with wavelengths larger than the critical wavelength.

Experiments studying steady supercritical Taylor vortex flow have been made using pairs of long cylinders with two different radius ratios, three fluids of different viscosities and three different end boundaries for the fluid column. The emphasis in these experiments is on the determination of the wavelength of the Taylor vortices and the size of the end rings. The wavelength which one measures in a finite cylinder differs from the wavelengths found theoretically for infinitely long cylinders. Provided that the end effects were properly taken into account, the wavelength of singly periodic Taylor vortices in an infinitely long cylinder was found to remain constant between TIE = 1 and TIT, w 80 in experiments with radius ratios 7 = 0.505 and 7 = 0.727. Further studies of Taylor vortex flow a t very high Taylor numbers, where the vortices are either doubly periodic or truly turbulent, showed that the wavelength increases under these conditions. However, the observed wavelengths were no longer unique but distributed statistically around a wavelength larger than the critical wavelength.

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This paper describes an effort to optimize the design of an entire space launch vehicle to low Earth (circular) orbit, consisting of multiple stages using a genetic algorithm with the goal of minimizing vehicle weight and ultimately vehicle cost. The entire launch vehicle system is analyzed using various multistage configurations to reach low Earth orbit. Specifically, three-and four-stage solid propellant vehicles have been analyzed. The vehicle performance modeling requires that analysis from four separate disciplines be integrated into the design optimization process. The disciplines of propulsion characteristics, aerodynamics, mass properties, and flight dynamics have been integrated to produce a high-fidelity system model of the entire vehicle. In addition, the system model has been validated using the existing launch vehicle data. The cost model is mass based and uses extensive historical data to produce a cost estimating relationship for a solid propellant vehicle. For the design optimization, the goal is for the genetic algorithm to minimize the differences between the desired and actual orbital parameters. This ensures that the payload achieves the desired orbit. One final goal is to minimize the overall vehicle mass, thus minimizing the system cost per launch. This paper will represent the first effort of its kind to minimize the solid propellant launch vehicle cost at the preliminary design level using a genetic algorithm.

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This paper describes an effort to optimize the design of an entire space launch vehicle to low-Earth (circular) orbit, consisting of multiple stages using a genetic algorithm (GA) with the goal of minimizing vehicle weight and ultimately vehicle cost. The entire launch vehicle system is analyzed using various multistage configurations to reach low-Earth orbit. Specifically, three and four-stage solid propellant vehicles have been analyzed. The vehicle performance modeling requires that analysis from four separate disciplines be integrated into the design optimization process. The disciplines of propulsion characteristics, aerodynamics, mass properties and flight dynamics have been integrated to produce a high fidelity system model of the entire vehicle. In addition, the system model has been validated using existing launch vehicle data. The cost model is mass-based and uses extensive historical data to produce a cost estimating relationship for a solid propellant vehicle. For the design optimization, the goals of the problem are for the GA to minimize the differences between the desired and actual orbital parameters. This ensures the payload achieves the desired orbit. One final goal is to minimize the overall vehicle mass thus minimizing the system cost per launch. The paper will represent the first effort of its kind to minimize solid propellant launch vehicle cost at the preliminary design level using a GA.

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Analytical methods for solid rocket motor grain design are proving to be tremendously beneficial to some recent efforts to optimize solid-rocket propelled missiles. The analytical approach has fallen out of favor in recent decades; however, for some classes of grains, the analytical methods are much more efficient than grid-based techniques. This paper provides a review of analytical methods for calculating burn area and port area for a variety of cylindrically perforated solid rocket motor grains. The equations for the star, long spoke wagon wheel, and dendrite grains are summarized and the development of the burn-back equations for the short spoke wagon wheel and the truncated star configurations are included. This set of geometries and combinations of these geometries represent a very wide range of possibilities for two-dimensional grain design.