Main menu >> Theoretical and Applied Mechanics >> Applied Mathematics
Theoretical and Applied Mechanics
Applied Mathematics
- Ultrasonic Inspection of Thin Coatings Using Surface Waves
- Control of Turbulence as a Chaotic System
- Weakly Nonlinear Evolution Equations for Galloping and Cellular Detonations
- Theory of Detonation Instability
^ Ultrasonic Inspection of Thin Coatings Using Surface Waves
J. G. Harris*
National Science Foundation, CMS 98-12820
Thin films and coatings are used as thermal barriers and to increase the hardness of surfaces, especially engine parts. The goal of this work is to develop analytical expressions that describe the time delay and transmission loss or attenuation of ultrasonic surface waves, propagating in the coatings, caused by their thinning, flaking, or cracking. The coatings used as thermal barriers are such that their wavespeed steadily increases with depth until it matches that of the substrate. The coatings used for wear resistance are very thin and very fast. The defects found in both types of coating are slivers of defective material at many length scales oriented parallel to the surface.
^ Control of Turbulence as a Chaotic System
R. D. Moser,* P. L. Boyland (Univ. of Florida), M. Heath, V. Lopez
National Science Foundation, CTS 97-29189
r-moser@uiuc.edu
One of the difficulties with attempting active control of turbulent flows is that the required control inputs are often large, so large that the cost of the control can exceed the gains. A new strategy for controlling turbulence using very small control inputs is being pursued. It is based on the observation that as a chaotic system, turbulence is very sensitive to perturbations; thus carefully chosen very small control inputs can produce order-one effects. The strategy being pursued is to determine unstable periodic solutions to the turbulent flow problem that have desirable features (in this case low drag) and apply control to stabilize these solutions.
^ Weakly Nonlinear Evolution Equations for Galloping and Cellular Detonations
M. Short,* D. S. Stewart
U.S. Air Force Office of Scientific Research, F49620-96-1-0260
short1@uiuc.edu, dss@uiuc.edu
Gaseous detonation waves propagating in a tube are highly unstable because of nonlinear coupling between exothermic heat release from the reaction and the hydrodynamic motion of the gas. Such detonations either pulsate in a periodic fashion or form a sequence of fish-scale-like patterns on the walls of the tube. Using a multiscale asymptotic approach, we are deriving weakly nonlinear evolution equations for the one-dimensional pulsating and two-dimensional cellular forms of detonation instability. The aim of this project is to understand the physical dynamics of the chemical–hydrodynamic interactions that cause the instability.
^ Theory of Detonation Instability
D. S. Stewart,* M. Short
U.S. Air Force Office of Scientific Research
dss@uiuc.edu
Continuation of the project exploits relevant asymptotic limits for the standard detonation model to construct a wholly analytic theory of detonation stability. New theories for weak heat-release detonation are being considered. Recently, new results have been obtained for spinning detonation.
