This GOALI project aims at advancing the fundamental understanding of vortico-acoustic wave coupling with hydrodynamic instability and thermal waves, along with the nonlinear processes leading to wave steepening and limit cycle oscillations in solid and hybrid rocket motors. The analysis involves physical modeling, perturbation methods, and concepts derived from the biglobal instability theory and Liao?s homotopy approach for the treatment of nonlinearities. The work will lead to multidimensional solutions of compressible core flow models in simulated combustors that take into account flow directionality. An immediate example includes the multidirectional sweeping motion of the gases and the non-uniformity of the flow above and across the propellant surface. As organized, this program builds on the existing strengths of the PI and an industrial sponsor who is presently focused on the development of state-of-the-art hybrid motors. Given that no universally accepted acoustic stability model exists for hybrids, the basic research activities proposed under this grant will enhance the efforts taken by the industrial investigator to promote the commercialization potential of clean hybrid technology. Advancing a rigorous acoustic stability theory for propulsive systems will aid in promoting the deep scientific insight needed to improve existing diagnostic and design capabilities. The projected enhancements can have a substantial bearing on the future development of rocket and turbine based systems. The direct impact of a unifying stability framework on the mobility industry can thus be significant in both aerospace and power generation categories. For example, understanding and suppressing instability can critically aid in demonstrating the viability of hybrid technology and its use as a safe and clean propulsion alternative in both space and land applications. On the educational side, the principal investigators will combine their unique strengths in solid and hybrid flow field modeling to coordinate the training and mentoring of various researchers and participants. Their efforts will have a direct impact on society by exposing high school, college, and graduate students to vital research prospects in rocketry, acoustic noise control, and hybrid propulsion through strategically planned courses, colloquia, workshops, and capstone design activities.
This GOALI project represents a natural continuation to Dr. Majdalani’s CAREER program. Ongoing work has thus produced 4 MS theses, 1 MS project, 3 PhDs, and 1 upcoming PhD. To this date, the GOALI topic of "Acoustic Wave Dynamics in Solid and Hybrid Rocket Motors" has generated 69 publications, mostly in the field of wave dynamics and internal acoustics. These include 16 journal articles, 51 conference papers, and 2 book chapters. Of the conference articles, seven consist of graduate student papers that have won, four years in a row, one Third Place, three Second Place, and three First Place awards within the 2010-2013 Masters Division of the 61st–64th AIAA Southeastern Conferences. Moreover, a paper with Charles Haddad further advanced to win the national Abe M. Zarem Award for Distinguished Achievement in Astronautics. In fact, quite a few awards and recognitions have been captured by Dr. Majdalani and his group. The most noteworthy include: Dr. Majdalani is named the Quest Scholar of the week, on June 28, 2013. Dr. Majdalani receives the 2013 Special Service Award from AIAA for "remarkable scientific and academic productivity in the aeronautical and applied mathematical sciences" and for "outstanding graduate student mentorship." His seven-out-seven best paper awards record remains unprecedented in the Tennessee Section in general, and the UT Space Institute in particular. Dr. Majdalani receives the 2013 Abe M. Zarem Educator Award in Astronautics. Dr. Majdalani is featured in Aerospace America for "Ten Years of Excellence" in Tennessee and the Southeast Region. Michel H. Akiki, a PhD Candidate working on this GOALI grant receives the 2013 AIAA Special Service Award. Michel Akiki is similarly nominated for and receives the Chancellor’s Citation for Extraordinary Professional Promise. Brian A. Maicke is nominated by Dr. Majdalani and in consequence receives the 2010 AIAA Special Service Award. Dr. Majdalani and his students achieve a new record of most AIAA conference papers presented at a single conference in 2010. Brian A. Maicke presents 8 scientific papers in summer 2010. Dr. Maicke also receives a Senate Commendation for his exceptional research work. This GOALI and its CAREER prequel have cumulatively attracted 5 GRAs who have won, five years in succession, the Outstanding GRA Award of the Year. Other notable achievements associated with this GOALI project include (a) an award-nominated paper that later appeared in revised form as a review article in the Proceedings of the Royal Society; (b) a full length article in which several mathematical models for traveling acoustic waves in simulated combustors are presented; (c) a homotopy-based solution for the injection-driven porous chamber made possible through a new technique known as Homotopy Analysis Method (HAM). This technique specializes in the treatment of nonlinear problems; (d) viscous modeling of a simple cyclonic flowfield; (e) modeling the acoustic streaming mechanism and transverse wave motion in simulated liquid rocket engines; (f) providing two new theorems that establish the pressure integrability requirements of the continuity and momentum equations; (g) AIAA Paper ? 2010-4287 where an extended version of Kelvin’s Minimum Energy Theorem is provided for fluid domains with open regions; (h) an award winning framework for modeling helical motions in swirl-driven vortex chambers with arbitrary headwall velocities; (i) a coordinate-independent formulation leading to engineering approximations for compressible potential flow motions in a variety of physical settings; (k) a crisp connection between direct numerical simulation and the combination of vorticoacoustic and hydrodynamic modes; (l) a three-dimensional formulation and application of the biglobal stability approach to a cyclonic chamber with both complex-lamellar and Beltramian flows; (m) a generalized framework for producing mathematical solutions to high speed compressible flow problems with known axisymmetries; (n) a compressible stability framework that enables us to capture both hydrodynamic and vorticoacoustic modes simultaneously, thus eliminating the need to decompose the flow; (o) an improved mean flow formulation of the flowfield in a rocket with a non-circular cross section; and (p) a characterization of the particle-mean flow interactions in a rocket motor. Clearly, Dr. Majdalani’s group has been very active. Of particular interest to this program, Dr. Majdalani and his students have tackled the problem of hydrodynamic instability in simulated solid and hybrid motors as well as swirl-driven liquid thrust engines. In collaboration with Dr. Casalis at ONERA, this group has investigated the hydrodynamic instability of full-length, cylindrical models of solid and hybrid motors with headwall injection. In the process, both the one-dimensional, Local Non-Parallel (LNP) and biglobal stability approaches were implemented. These confirmed the instability behavior observed in most hybrid engines at large injection speeds. Then based on the biglobal approach, it was demonstrated that the addition of swirl will mitigate the known instabilities that ordinarily plague hybrid engines. The use of a fully compressible framework was also shown to be very effective in capturing the complete wave spectrum in large combustors by reproducing both hydrodynamic and vorticoacoustic modes simultaneously.
