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For any set X denote by m(X) the Banach space of all bounded real-valued functions on X, equipped with the supremum norm, and denote by (X) the semigroup (under functional composition) of all transformations of X, i.e. mappings with domain X and range contained in X. A pair (X, S), where S is a subsernigroup of (X), will be called a transformation semigroup. Important examples are obtained by letting X be the underlying set in an abstract semigroup and considering the pairs (X, S1) and (X, S2), where S1 [Sn] denotes the set of left [right] multiplication mappings of X. We shall call transformation semigroups in these classes of examples l-[r-] semigroups.

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Single stage to orbit propulsion devices are being developed as part of low cost access to space endeavors. Sea level operation of high area ratio rocket nozzle used in rocket engines leads to an overexpanded flow condition resulting in high side loads. Secondary injection of propellants in high area ratio nozzle is an attractive option to overcome the inefficiency of operation of such nozzles in sea level conditions in addition to the augmentation of thrust. A numerical study on thrust augmentation in high area ratio nozzle by secondary injection of propellants is presented here. The turbulent compressible reacting flow in rocket nozzle with auxiliary injection is simulated using conservation equations for chemical species based on finite rate chemistry model and compressible Navier-Stokes equations with AUSM+-up upwind scheme based unstuctured finite volume solver. An optimized eight step, six species reduced H2-O2finite chemistry reaction model is used to model the supersonic combustion. The indigenously developed solver has an efficient rescaling algorithm to alleviate the effect of stiffness in conventional explicit algorithm for simultaneous solution of reacting flow. The code is validated using the wall pressure and hydrogen concentration values reported for the similar high area ratio rocket nozzle. Accurate prediction of nozzle performance is possible with present turbulent reacting flow simulation as it take care of all losses in nozzle flow. Extensive computations have been performed for the performance estimation of high area ratio rocket nozzle for various prospective auxiliary injection options.

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Abstract. The main purpose of the present work is to investigate the influence of normal and lateral conduction on the temperature distribution and heat transfer coefficient on the surface of a typical sounding rocket.A two-dimensional heat conduction equation with a time dependent aerodynamic heating condition at one surface and a radiation boundary condition at the other end is solved using finite element method.

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