University of Tennessee Space Institute (UTSI) doctoral candidate Tony Saad and Prof. Joe Majdalani are a team from Tennessee that will publish a Review article in the Proceedings of the Royal Society A (RSPA), considered by most to be the oldest scientific academy still in existence. Their manuscript is entitled “On the Lagrangian optimization of wall-injected flows: from the Hart-McClure potential to the Taylor-Culick rotational motion.” This scientific study introduces several new concepts for modeling gaseous motions in solid and hybrid rocket motors.

The study focuses on the Taylor-Culick model, a rotational motion that arises in several captivating applications, such as isotope separation and rocket internal ballistics. In this context, the Lagrangian optimization principle is used to unravel two complementary families of solutions showcasing energy signatures. These extend from the irrotational Hart-McClure potential with minimum kinetic energy to a highly rotational flow motion with peak energy. The Taylor-Culick motion is found to be at the confluence of both families.

To better understand the inclination of fluid particles to toggle between energy states, the entropy maximization principle is used. This principle helps to identify the Taylor-Culick configuration as the most probable pattern among those starting from rest. The Taylor-Culick solution is found to correspond to a local equilibrium point at the convergence of both Type I and Type II families.

Finally, the study culminates in a unique reconstruction of Kelvin’s 1849 energy theorem, mostly known for its applicability limitation to a specific class of fluid motions and surface boundaries. In their review article, Saad and Majdalani extend the theorem to a wider range of applications such as those involving open boundaries and arbitrary inlet and outlet conditions. In applying the generalized Kelvin theorem to the two families of injection driven motions, these researchers show that the Hart-McClure potential indeed carries the least amount of power among all possible solutions.

The Royal Society currently publishes seven peer reviewed journals covering many facets of mathematical, natural, and engineering disciplines.

From left to right, Dr. Joseph Majdalani and Tony Saad