The Rayleigh Criterion is a common measure used to quantify the stability of thermal systems. Typically the Rayleigh Criterion is expressed as the correlation between unsteady pressure and unsteady heat release where an in-phase combustion response leads to driving of instabilities. This expression however, is defined under the guise of an isentropic flow where entropy generation due to irreversibilities in combustion processes or viscous and thermal dissipation are neglected. This is largely untrue in reacting flows. The impact of entropy generation due to unsteady combustion is shown to be significant. The implications of a non-negligible unsteady entropy field leads to a generalization of the Rayleigh Criterion as well as the emergence of several combustion related driving mechanisms commonly omitted from stability analysis. Nomenclature p c = specific heat = heat release m = tangential wave number p = pressure Q = heat release per unit temperature, / HT s = entropy T = temperature t = time u = velocity Symbols = density = tangential coordinate = phase = frequency of oscillation Superscripts and Subscripts i = (superscript) denotes the imaginary part of a complex number r = (superscript) denotes the real part of a complex number 0 = (subscript) denotes a steady field variable 1 = (subscript) denotes an unsteady field variable 1 Stability Engineer, AIAA Member 2 Stability Engineer, AIAA Member Downloaded by CORNELL UNIVERSITY on July 19, 2015 | http://arc.aiaa.org |
The past decade has seen efforts to lower costs by "doing more with less," instead of making innovative changes in the way missions are designed and implemented. Now, the industry is turning towards more intelligent approaches to mission design. AeroAstro has developed the Small Payload ORbit Transfer ( S P O R F ) system to provide a flexible low-cost orbit transfer capability, enabling small payloads to use low-cost secondary launch opportunities and still reach their desired final orbits. This allows small payloads to effectively use a wider variety of launch opportunities, including numerous under-utilized geosynchronous transfer orbit (GTO) slots. Its use, in conjunction with growing opportunities for secondary launches, enables "better, cheaper, faster" missions through innovative mission design and lower cost access to space, not increased risk.SPORT uses a suite of innovative technologies that are packaged in a simple, reliable, modular system. SPORT achieves its orbit transfer capability through a combination of chemical propulsion and aerobraking technology. This paper will discuss the SPORT design and its application to overall small satellite mission development.
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