My research consists of Analytical / Numerical Investigation and Modeling of various Fluid Mechanics phenomena. Several tools of Applied Mathematics such as Harmonics Analysis, Perturbation Analysis, Linear Algebra, Orthogonal Transformations, Fast Fourier Transforms, Advanced Root Finding Techniques, Implicit and ADI methods of solving Partial Differential Equations, e.t.c. have been used. In addition, some of my research required the use of Computational Fluid Dynamics. The package FLUENT by Fluent Inc. has been used by myself and my graduate students.

The body of my research can be summarized in five groups:

d) Wave Phenomena in Inviscid Fluid Flow

## Labyrinth Seals in Turbomachinery

Labyrinth seals, which prevent high pressure gas from flowing into low pressure regions, present several challenging fluid flow problems. The goal of research in this area is the accurate prediction of the leakage flow rate and the determination of the secondary flows due to a perturbed shaft rotation. The knowledge of these secondary flows, and of the stresses associated with them, can then be used to predict the effect of the labyrinth seals on the rotor stability.

• Mr. John L. Dillon
• Mr. Omar Sahor
• Dr. Dursun Eser
• Dr. Ugur Yucel

have been instrumental in developing this research area.

## Non-Newtonian and Viscoelastic Fluid Flows

Many common fluids ranging from toothpaste and paint to coal-water slurs exhibit Non-Newtonian behavior. In such fluids the shear stress is not directly proportional to deformation rate. The steady state flow of shear thinning polymer solutions, or of dilatant ( or shear thickening) suspensions of sand present several interesting phenomena which require challenging modeling for their interpretation and prediction.

When the deformation of the material is time dependent, certain fluids exhibit a "springy" viscoelastic character which may give rise to additional phenomena such as rod climbing, elastic recoil, creep and stress relaxation.

Some of my earlier work in this area deals with the steady state flow of Non-Newtonian fluids in a geometrically complex region formed by two eccentrically located rotating cylinders which may also move in the longitudinal direction.

This work was motivated by the need to determine the effect of a Non-Newtonian lubricant on the bearing stresses. It is seen that due to the nonlinear character of the fluid force components proportional to the product of speeds appear in addition to the additive components present in the case of a Newtonian lubricant.

This early work was followed by a sequence of papers dealing with the influence of vibration on the Poiseuille flow of Non-Newtonian fluids in various geometries such as circular and noncircular pipes, gaps between plates e.t.c. One of the predicted results is the enhancement of the average rate of discharge due to the vibration of the walls.

Another sequence of papers dealt with the mechanism of momentum transport from the boundaries of the fluid to the interior. These are the unsteady phenomena of run-up and spin-up. The wave reflections which accomplish this transfer were derived and explained for the case of a linear viscoelastic fluid of the Maxwell type.

Currently, I am working on the interfacial stability of two viscoelastic fluids undergoing a simple shearing motion. This work is motivated by manufacturing difficulties associated with multilayered products. These products are generally superior to their single-component counterparts because of the synergy resulting from the combination of materials with different properties into a single structure.

My graduate students that contributed to this research are:

• Mr. Martin

## Viscous Fluid Flow

My work in this area ranges from creeping motion of highly viscous fluids, to linearized corrections for inertial effects, to the modeling of Supersonic Turbulent Boundary Layers.

In a recent work ( which includes experimental work performed by my colleagues and co-authors) we predict the motion of highly viscous fluids in narrow tubes. This work, which has applications in manometry, can also be used to predict , in some instances, the spread of polymeric liquids in narrow gaps.

At the other limit of Reynolds' numbers, a sequence of papers dealing with the Turbulence Modeling of Supersonic Boundary Layers has produced a prediction algorithm which agrees very well with a great number of experimental results reported over the years. An expression for the adiabatic wall temperature has been derived on the basis of asymptotic analysis. This work was essentially the Ph.D. dissertation of

• Dr. Jun He

## Wave Phenomena in Inviscid Fluid Flow

My research in this area is twofold. One sequence of papers deals with the interaction of large amplitude shallow water waves with an ambient shear flow. The solutions obtained are generalizations of the classical simple wave solutions for unsheared flows.

The second sequence of papers deals with sound waves. Specifically, the issues of active attenuation of noise, the plane waves and the cross modes generated by rectangular or circular loudspeakers mounted on duct walls, and the propagation of sound waves in inhomogeneous liquids have been investigated.

Part of the work on acoustics was done by my graduate students:

• Mrs. Jeane Elbich
• Dr. Murat Ozturk