Fluid dynamics

This study pertaining to the settling of fine particles is developed using various models and formulas. The model considers two layers, i.e, the suspension zone dominated by perikinetic flocculation and the settling zone governed by gravitational force. In the suspension zone, floc formation of fine particles is simulated by the maximum chain model in which floc parameters and fractal dimension are compared with existing data. In addition, fractal dimension is compared with that of the hierarchical model. The main assumption of the model is that any floc having sixteen particles outweighs Brownian force, and thus the floc starts falling down into the settling zone. The flocs moving from the suspension zone are considered as nonspherical particles in the settling zone. The study uses a dimensionless settling velocity, omega*, for estimation of the sedimentation of flocs. Settling causes aggregation of the depositing flocs. The form of these aggregates is analyzed by the fractal relationship P ~ L delta.

An experimental study has been conducted to examine the flow field about and the wake behind truncated cylindrical obstacles of varying height, which are towed through a fluid with a free surface in a rotating system. The results show the development of a vortex street-type wake downstream of the obstacle for retrograde (westward) flows, even for very small ratios of obstacle height to water layer depth. For short obstacles, a pronounced backward flowing jet is observed, which impinges on the Taylor column from downstream. Prograde (eastward) flows are found to have a meandering wake that extends farther than eight obstacle diameters downstream and do not exhibit backjetting or vortex street formation. Upwelling is believed to occur within the side boundary layers of the Taylor column, which could play a significant role in deep water production in the ocean.

A swirling flow combustion system has been designed and constructed. An integral laser Doppler velocimeter is constructed for the investigations of fluid mechanics aspects of a swirling flow combustor. The combustor consists of one fuel flow and two swirled air flows. The inner air flow has a fixed swirling strength and the outer air flow has an adjustable swirler. Both counterswirl and coswirl flows with variable swirl strength can be generated. Premixed or non-premixed combustion can be investigated on this system. Evaluation of the swirling combustion system and performance check of the velocity measurement system are conducted. Detailed time mean and fluctuating flow measurements are obtained for coswirl and counterswirl conditions with the LDV system. A central recirculation zone is observed in both swirl conditions, but the size in counterswirl is much smaller. The reasons for the difference are discussed.

The discrete vortex method was applied to the calculation of separation flow past NACA 4412 airfoil: Vortex panel was used to represent the body surface and discrete vortices were used to model the wake. Generally the uniform upstream condition is used in the calculation of separation flow. But actually an airfoil could move in wake of other airfoils or disturbed fluid. In this thesis, discrete vortices were used to model the upstream disturbance to investigate the effect of upstream disturbance to the pressure, lift and drag coefficients around the airfoil. Also the animation of separation flow was made on HP workstation using "Starbase" computer graphic package to study the separation process.

A numerical technique is given to capture multiple shocks in steady, quasi one-dimensional flows by solving the Euler equations from a sequence of implicit/explicit solutions for the Riemann variables. A supersonic wind tunnel with a variable area diffuser is analyzed with the results compared to exact solutions. Examples are given with both one and two standing shocks. The technique given is an extension of Moretti's scheme for a single discontinuity in a De Laval nozzle. It is shown that this efficient technique is easily adaptable and is equally accurate for multiple discontinuities as it is for a single discontinuity.

This thesis addresses the issue of flow development near the boundary of a work table within a clean room. The flow is subjected to periodic external disturbance, either through the pulsation of a source of mass at fixed location, or a moving vortex. The global system consists of a flat table in a parallel oncoming laminar flow. The source of the disturbance is located in the vicinity of the boundary layer. The strength of disturbance is limited in order to apply the quasi-steady boundary layer theory. Based on a quasi-steady assumption, a Thwaytes type integration was performed in order to evaluate the displacement thickness and the shear stress on the wall. A parametric study based upon the change of the pulsation, the location and the strength of the disturbance was included in the study. Thwaytes's deviation applied to unsteady cases proved to be successful, and worth being used in further developments.

The phenomenon of flow-induced vibration is found in many
engineering systems. The fluid flow generates forces on the
structure that cause motion of the structure. In turn, the
structural motion changes the angle of attack between the flow and
the structure, hence the forces on the structure. Furthermore,
turbulence generally exists in a natural fluid flow; namely, the fluid
velocity contains a random part. Thus, the problem is formulated as
a nonlinear system under random excitations.
This thesis is focused on one type of motion known as
galloping. A mathematical model for the motion of an elastically
supported square cylinder in turbulent flow is developed. The
physical nonlinear equation is converted to ideal stochastic
differential equations of the Ito type using the stochastic averaging
method. The probability density for the motion amplitude and the
values for the most probable amplitudes are obtained for various
mean flow velocities and turbulence levels.

Turbulent pressure fluctuations and acoustical shock
waves formed at pipe discontinuities are the primary source
of flow noise. fhe pipe response is excited by the
fluctuating forces associated with the turbulent pressure
fluctuations. The forcing functions can be determined from
the frequency-wavenumber spectrum of the pressure
fluctuations. A procedure is developed here to obtain the
frequency-wavenumber spectrum due to fully developed
turbulent flow. The data analysis procedures developed in
this study to analyze the pressure fluctuations provide a
good means to determine the frequency-wavenumber spectrum
and represent this data in a clear form. Frequency-wavenumber
spectra have been obtained for simulated pressure
data. In the experimental system designed to collect
turbulent pressure data, it was determined that a recessed
transducer configuration cannot be used in water pipe flow
turbulent pressure fluctuation studies because of the
enhanced turbulence created by the upstream holes.
Therefore, flush mounted transducers are required.

The transition of two dimensional flow within a crack
with oscillating wall is studied experimentally to establish
the role of the parameters involved. Multiple instabilities
in the fluid are produced by the motion of the oscillating
wall. For a better understanding of the flow structure and
displaying in the whole flow field at a time, flow
visualization was used. Frequency, amplitude, and crack
width were systematically varied. The present study shows
that, in general, the frequency and crack width play a role
in the transition process at low frequencies of
oscillations. However, amplitude becomes progressively
important at its higher range. Results also show that the
flow changes its character approximately after a Reynolds
number 11420. After that the transition process continues
until the Reynolds number 34322 which is the upper limit of
variation of frequency (Reynolds number) in the present
study.

The dynamic behavior of straight cantilever pipes conveying fluid is studied, establishing the conditions of stability for systems, which are only limited to move in a 2D-plane. Internal friction of pipe and the effect of the surrounding fluid are neglected. A universal stability curve showing boundary between the stable and unstable behaviors is constructed by finding solution to equation of motion by exact and high-dimensional approximate methods. Based on the Boobnov-Galerkin method, the critical velocities for the fluid are obtained by using both the eigenfunctions of a cantilever beam (beam functions), as well as the utilization of Duncan's functions. Stability of cantilever pipes with uniform and non-uniform elastic foundations of two types are considered and discussed. Special emphasis is placed on the investigation of the paradoxical behavior previously reported in the literature.