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The turbulent flow through a 90o pipe bend is complex with secondary flow that can affect pressure drop and heat/mass transfer. The mean and unsteady flow is studied using refractive index matched two-dimensional two-component (2D2C) Particle Image Velocimetry in a single 90o bend with Rc/D = 1.5 and at Re = 34800. The measurements were performed in a closed loop using a 1-inch diameter test section that was machined out of acrylic. The flow is imaged in the symmetric plane parallel to the axial flow and at different cross sectional planes including 0.25D and 1D upstream, 10o, 20o, 70o, 80o from the bend inlet and 0.25D and 1D downstream of the bend. The axial flow accelerates on the inner wall at the inlet and then moves towards the outer wall at 40o-50o. A shear layer is formed between high velocity fluid near the outer wall and the slower moving fluid at the inner wall side in the second half of the bend. The axial turbulent kinetic energy ((u^2 ) ̅+(v^2 ) ̅) is found to be high in regions corresponding to high velocity gradient regions: (i) at the outer wall near the inlet that extends up to the outlet, (ii) near the inner wall at 40o-50o, and (iii) at the shear layer formed near the inner wall. In the cross sectional planes, two vortices are formed and have a maximum strength at 80o from the bend inlet. The cross sectional turbulent kinetic energy ((v^2 ) ̅+(w^2 ) ̅) is found to be highest on the inner wall at the 80o plane. The snapshot Proper Orthogonal Decomposition (POD) technique is used to study the unsteady flow structures within the flow. There are long and short flow structures in the upstream pipe which can be related to Very Large Scale and Large Scale Motions. The secondary flow at 20o and further downstream cross sectional planes show evidence of unsteadiness as two vortices oscillate about the symmetry axis with low frequencies of St ~ 0.07, 0.13 and higher frequency at St ~ 0.3-0.6. The low frequency oscillations can be related to Very Large Scale Motions while high frequency oscillations are related to separation of the flow on the inner wall side. Evidence of swirl switching in the high frequency range (St ~ 0.3-0.5) is found at cross sectional plane 1D downstream. / Thesis / Master of Applied Science (MASc)

Yes / New orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raisedcosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets.

Yes / The Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced.

A novel control method called orthogonal eigenstructure control is developed for active vibration cancellation in structures. Orthogonal eigenstructure control is a feedback control method applicable to multi-input multi-output linear systems. While the available control design methodologies offer a large and complex design space of options that can often overwhelm a designer, this control method offers a significant simplification of the design task while still allowing some experience-based design freedom. For example, eigenstructure assignment methods need definition of a desired eigenvector for the closed-loop system. The controller designer may also be required to do pole placement. Considering the fact that there are no one-to-one relationships between the elements of the closed-loop eigenvectors of a model and the states of the system, this effort could be inefficient for many practical systems. Moreover, for large-scale systems, defining or shaping the eigenstructures become a relatively difficult task. Orthogonal eigenstructure control is a state feedback-like control law that is relatively easy to design and implement to multiple-input multiple-output systems. It allows control engineers to achieve good performing designs even with little design experience, while the existing methods are highly dependent on designer experience. Orthogonal eigenstructure control is introduced and extended to be applicable to linear systems regardless of the number and location of the actuators and sensors. Also, the concept of progressive application of the proposed control method for increasing robustness is described. Finally, the result of application of the control method for vibration cancellation of a test plate is investigated through experiments for tonal and wideband disturbances. The results show a significant reduction of vibrations using the orthogonal eigenstructure control with relative ease in finding the control gain matrix. / Ph. D.

Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed. / Ph. D.

Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, reduced order control design is vital for practical controllers. The main contribution of this research is a method of control order reduction that uses a newly developed low order basis. The low order basis is obtained by applying Proper Orthogonal Decomposition (POD) to a set of functional gains, and is referred to as the functional gain POD basis. Low order controllers resulting from the functional gain POD basis are compared with low order controllers resulting from more commonly used time snapshot POD bases, with the two dimensional heat equation as a test problem. The functional gain POD basis avoids subjective criteria associated with the time snapshot POD basis and provides an equally effective low order controller with larger stability radii. An efficient and effective methodology is introduced for using a low order basis in reduced order compensator design. This method combines "design-then-reduce" and "reduce-then-design" philosophies. The desirable qualities of the resulting reduced order compensator are verified by application to Burgers' equation in numerical experiments. / Ph. D.

A new N-dimensional digital modulation technique is proposed as a bandwidth efficient method for the transmission of digital data. The technique uses an antipodal scheme in which parallel binary data signs baseband orthogonal waveforms derived from Hermite polynomials. Orthogonality guarantees recoverability of the data from N simultaneously transmitted Hermite waveforms. The signed Hermite waveform is transmitted over a radio link using either amplitude or frequency modulation. The bandwidth efficiency of the amplitude Hermite method is found to be as good as filtered BPSK in practice, while the bit error rates for both modulations are identical. Hermite Keying (HK), the FM modulation version of the N-dimensional Hermite transmission, outperforms constant envelope FSK in terms of spectrum efficiency. With a simple FM detector, the bit error rate of HK is as good as that of non-coherent FSK. In a frequency selective fading channel, the simulation results suggest that specific data bits of HK are relatively secure from errors, which is beneficial in some applications. Symbol synchronization is critical to the system. An optimal synchronization method for the N-dimensional antipodal scheme in additive white Gaussian noise channel is derived. Simulation results confirm that the synchronizer can operate successfully at E/No of 3 dB. / Ph. D.

Cavitation can be defined as the breakdown of a liquid (either static or in motion) medium under very low pressure. The hydrodynamic happened in high-speed flow, where local pressure in liquid falls under the saturating pressure thus the liquid vaporizes to form the cavity. During the evolution and collapsing of cavitation bubbles, extreme physical conditions like high-temperature, high-pressure, shock-wave, and high-speed micro-jets can be generated. Such a phenomenon shall be prevented in hydraulic or astronautical machinery due to the induced erosion and noise, while it can be utilized to intensify some treatment processes of chemical, food, and pharmaceutical industries, to shorten sterilization times and lower energy consumption. Advances in the understanding of the physical processes of cavitating flows are challenging, mainly due to the lack of quantitative experimental data on the two-phase structures and dynamics inside the opaque cavitation areas. This dissertation is aimed at finding out the physical mechanisms governing the cavitation instabilities and making contributions in controlling hydraulic cavitation for engineering applications. In this thesis, cavitation developed in various convergent-divergent (Venturi) channels was studied experimentally using the ultra-fast synchrotron X-ray imaging, LIF Particle Image Velocimetry, and high-speed photography techniques, to (1) investigate the internal structures and evolution of bubble dynamics in cavitating flows, with velocity information obtained for two phases; (2) measure the slip velocity between the liquid and the vapor to provide the validation data for the numerical cavitation models; (3) consider the thermodynamic effects of cavitation to establish the relation between the cavitation extent and the fluid temperature, then and optimize the cavitation working condition in water; (4) seek the coherent structures of the complicated high-turbulent cavitating flow to reduce its randomness using data-driven methods. / Doctor of Philosophy / When the pressure of a liquid is below its saturation pressure, the liquid will be vaporized into vapor bubbles which can be called cavitation. In many hydraulic machines like pumps, propulsion systems, internal combustion engines, and rocket engines, this phenomenon is quite common and could induce damages to the mechanical systems. To understand the mechanisms and further control cavitation, investigation of the bubble inception, deformation, collapse, and flow regime change is mandatory. Here, we performed the fluid mechanics experiment to study the unsteady cavitating flow underlying physics as it occurs past the throat of a Venturi nozzle. Due to the opaqueness of this two-phase flow, an X-ray imaging technique is applied to visualize the internal flow structures in micrometer scales with minor beam scattering. Finally, we provided the latest physical model to explain the different regimes that appear in cavitation. The relationship between the cavitation length and its shedding regimes, and the dominant mechanism governing the transition of regimes are described. A combined suppression parameter is developed and can be used to enhance or suppress the cavitation intensity considering the influence of temperature.

Communicating wirelessly underwater has been an area of interest for researchers, engineers, and practitioners alike. One of the main reasons for the slow rate of progress in this area is that the underwater acoustic channel is in general much more hostile — in terms of multipath, frequency selectivity, noise, and the Doppler effect — than the over-the-air radio frequency channel. In this work a time warp based technique which can be used to model time-varying wideband Doppler shifts (as seen in an UWA channel) in MATLAB is proposed. A corresponding procedure to estimate the parameters from observed data, required for inverting the effect of the time warp, is also proposed. Two different Doppler correction methods are compared; both can be used to undo the Doppler effect in measured data from an experiment subject to the wideband Doppler effect. The techniques presented correct for the wideband Doppler effect as if it changed the time scale of the received signal. The first resampling based technique corrects for the average expansion/contraction over a packet, inherently assuming the relative velocity to be constant over the duration of the packet. The second time warp based technique models time-varying Doppler shift. Sinusoids, added to the beginning and end of each packet, are used to estimate the parameters required to invert the effect of the warp. The time warp based methods are demonstrated using Orthogonal Frequency Division Multiplexing (OFDM) signals, but will in principle work for other kinds of wideband signals also. The presented results — using MATLAB based simulations, and over-the-air experiments performed in such a way as to introduce the Doppler effect in the received signals — emphasize the improvements that can be attained by using the time warp based Doppler modeling and correction method. The thesis concludes with suggestions for future work. / Master of Science