Wednesday, November 25, 2009
Contributor: Joseph Majdalani
news@utsi.edu
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
