# Current Research of Dr. Hafiz Atassi

Dr. Atassi conducts his research at various laboratories in the Hessert Laboratory for Aerospace Research and Fitzpatrick Hall of Engineering.

### Aerodynamics and Aeroacoustics of Nonuniform Flows

Aerodynamic structures such as airplane wings, turbomachine bladings, propeller and helicopter blades often operate in nonuniform flows. As a result, unsteady vorticity waves are generated and produces periodic aerodynamic excitations as they interact with structural components. This induces destructive vibrations of the structural components and radiates unwanted noise in the far field. The objective of our research, funded by the NASA Lewis Research Center, is to model the unsteady nonuniform flows around airfoils and cascades at subsonic and transonic speeds so as to determine the parameters affecting the unsteady aerodynamic forces and acoustic radiation. Both mathematical and computational methods are used to solve the unsteady subsonic and transonic flow equations. Asymptotic analytical solutions provide a basis for numerical computations carried out on IBM RISC stations and the Cray YMP. This research program closely interacts with investigations at NASA Lewis Research Center, the Office of Naval Research, General Electric, Pratt & Whitney and the University of Lyon, France.

### Direct Computation of Aerodynamically Generated Sound

A by-product of aircraft, helicopter, and ship propulsion systems is the intense noise they produce. How this noise can be suppressed depends largely upon our understanding of the various noise generating physical mechanisms. The objective of this research, funded by NASA Langley Research Center, is to model the noise resulting from the interaction of structural components with unsteady nonuniform flows. Both tonal and broadband noise are investigated. The model calculates directly the generated sound using high-order accurate numerical schemes. The current approach is applied to ducted turbofans of subsonic and transonic speeds. The computations are carried out on dedicated workstations and the Cray-YMP. This research program closely interacts with investigations at NASA Lewis Research Center and Cambridge Acoustical Inc.

### Direct and Inverse Problems in Hydrodynamics and Hydroacoustics

Can we hear the sound of a drum? About a hundred years ago, Lord Rayleigh answered "No" to this question. He, in fact, derived a theorem stating that the inverse acoustic problem is not unique. However, signal processing information and holography show the feasibility of performing inverse calculations for certain problems. Under a grant from the Office of Naval Research, the Notre Dame researchers are working to provide qualified answers to these inverse acoustic problems. First, the inverse calculation entails prediction of the unsteady pressure acting on the structural components from knowledge of the radiated sound. Secondly, it attempts to define the unsteady flow from the unsteady pressure of the components. Mathematical and numerical analyses and methods are currently being developed for the inverse problem and its application to marine acoustic signals. The approach is based on the mathematics formulation of the direct and inverse problems in unsteady flows. Solutions for the direct problems provide data for pattern recognition to be used in identifying the sources in the inverse. Computer schemes are developed for solving the analytical model using dedicated workstations.

### Turbulent Structure Modification by Streamlined Devices

Turbulent structure is modified as it interacts with high speed moving bodies. The turbulence energy spectra are analyzed and calculated in the wake of streamlined bodies such as airfoils on blades. The effect of this change on the transport properties of the fluid are then estimated. The approach uses the rapid distortion theory of turbulence. This research program interacts with experimental investigations at NASA Lewis Research Center and the Laboratorie de Mecanique des Fluides et d'Acoustique de Centre National de la Recherche Scientifique in Lyon, France.

### High Speed Swirling Flows

The flow through a high speed fan has a significant swirling motion. How does the swirl affect the stability and propagation of acoustic and vorticity waves is an open question. Experiments suggest the swirl has a significant effect on the blade forces and the noise radiated from the fan. The fundamental effect of the swirl is investigated by modeling the mean flow as a combination of a solid-body rotation and a potential axial vortex. Analysis of the acoustic modes indicates the swirl changes the propagating and evanescent modes. The swirl, however, significantly affects the blade upwash and, as a result, the unsteady response of the fan. This study is also applied to the determination of inflow/outflow conditions. The Investigation is supported by grants from NASA and the Office of Naval Research. This research program closely interacts with investigations at the U.S. Navy David Taylor Research and Development Center, Pratt & Whitney and NASA.

### Algorithms for Large Number of Equations

Physical systems are often modeled using partial differential equations. For problems with dominant frequencies, it is convenient to use a frequency-domain approach. For three-dimensional geometries, discretization leads to a large number (more than 106) of linear algebraic equations. Computer memory limitations require the development of iterative methods based on Krylov subspace and domain decomposition. These methods considerably reduce the computational time and memory requirement and are particularly suitable for parallel computers. The parallel algorithms are implemented for external acoustic problems. This research is supported by a grant from the National Science Foundation. This interdisciplinary research closely interacts with investigations at the Courant Institute, Old Dominion University, The University of Colorado, The Boeing Company, and General Motors.