We investigate global pattern-switching effects in 2D cellular solids in which the voids are arranged in a square lattice. Uniaxial compression of these structures triggers an elastic instability which brings about a period-doubling transformation of the void shapes at a critical strain. Specifically, a square array of circular voids forms a pattern of mutually orthogonal ellipses and a similar effect is observed for diamond-shaped voids. The onset of instability is governed by the void fraction and size-effects are found for the experimental samples. We establish empirical laws which characterise the stiffness, strength and stability of cellular structures comprising square arrays of circular voids. A comparison of these with predictions from a discrete model implies underestimation of the resistance of the lattice to buckling, although the size effects are replicated. We find similar pattern-switching effects in the cubic lattice, which is a three-dimensional porous cube. The effect of buckling in this system is to produce a 2D pattern in one plane of voids. In two-phase granular crystals, rearrangement of a square lattice of particles results in a new, period-doubled, structural pattern. This switch can occur via an intermediate phase depending on the size ratio of the particles as shown in experiments and numerical simulations.

In the study, vibrations of small elastic cylinders mounted in the shear flow of an air jet are investigated experimentally. In such cases, the amplitude of the cylinder oscillation changed along with the variation of the jet velocity gradient is due to the influence of fluid elastic instability. The experiment is based on the method of the magnetic field induction to measure the motion of the small cylinder, and it involves measurements of the varying velocity in a jet through the hot- wire anemometer. We focus on the fluid-elastic instability of a circular cylinder in shear flow. The vibration behaviors of the cylinder above the critical condition are be examined with different velocity gradients, mass ratios and damping factors. The vibration amplitude of the cylinder is also larger as velocity gradient is larger. With lower mass ratios and damping factor, moreover, the orbit of cylinder is larger. When the velocity gradient is increasing, the frequency of cylinder vibration becomes higher.

The onset of fluid-elastic instability in cylinder arrays is usually thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequency of the cylinders. Currently, there is considerable evidence from experimental measurements and computational fluid dynamic (CFD) simulations that the Reynolds number is also an important parameter. However, the available data are not sufficient to understand or quantify this effect. In this study we use a high resolution pseudo-spectral scheme to solve 2-D penalized Navier-Stokes equations in order to accurately model turbulent flow past cylinder array. To uncover the Reynolds number effect we perform simulations that vary Reynolds number independent of flow velocity at a fixed Scruton number, and then analyze the cylinder responses. The computational complexity of our algorithm is a function of Reynolds number. Therefore, we developed a high performance parallel code which allows us to simulate high Reynolds numbers at a reasonable computational cost. The simulations reveal that increasing Reynolds number has a strong de-stabilizing effect for staggered arrays. On the other hand, for the in-line array case Reynolds number still affects the instability threshold, but the effect is not monotonic with increasing Reynolds number. In addition, our findings suggest that geometry is also an important factor since at low Reynolds numbers critical flow velocity in the staggered array is considerably higher than the in-line case. This study helps to better predict how the onset of fluid-elastic instability depends on Reynolds number and reduces uncertainties in the experimental data which usually do not consider the effect of Reynolds number. / Thesis / Master of Science (MSc)

No / Hot spots are high temperature thermal gradients and localisations that are circumferentially distributed on a disc surface which can occur during heavy duty braking. Vibrations and noise can be triggered by hot spotting as well as damage to the disc surface. The experimental investigations suggest that the trigger condition and distribution of hot spots are related to the disc geometry, especially for ventilated discs. To investigate the effects of geometry and structure of a ventilated disc on hot spotting, a 3D finite element model was established. A fast simulation method of hot spotting in 3D was implemented in the model to enable a parametric analysis to be performed more efficiently. The results were validated using experimental data from a laboratory dynamometer.

no / Hot spots are high thermal gradients on the disc surface during brake events which can cause the undesired phenomena of thermal judder and drone. The origin of hot spotting has been presented by various theories such as Thermo elastic instability (TEI) and progressive waviness distortions (PWD). However, majority of the numerical models based on these theories mainly concentrated on solid disc rather than ventilated disc which is the most commonly used nowadays. According to the experimental work done by the authors, disc geometry factors such as vents and pins also have correlations with hot spot distribution; these phenomena are difficult to be predicted analytically. Thus a convenient 2D asymmetric finite element simulation has been performed in order to obtain the correlations observed in experiments. Further parameter studies investigated factors such as uneven initial temperature, vents, pins and pad length. The results have been correlated with the experimental data and demonstrate the contribution of geometric factors in the generation of hot spots and hot judder.

no / The migration of hot banding is the phenomenon whereby hot bands or hot spots on the brake disc surface periodically migrate radially inward and outward. These migrations can cause the undesired brake torque variation (BTV) and further induce vibration problems such as brake judder. To investigate the forming and migration of hot banding problem, transient thermal mechanical finite element models of repetitive braking considering the effects of wear have been performed. The displacement, temperature, stress, and contact pressure distribution against time were obtained in this model. The thermal buckling, thermo-elastic instability (TEI) and hot band migration phenomena have been captured and investigated. The results suggest a cause-effect chain of radial hot band migration. Its determinants include mechanical loading, disc thermal buckling, and most importantly the transient interactions between TEI and wear.

It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. The main objective of this thesis is to introduce a new field of viscoelastic fluid-structure interactions by showing that the elastic instabilities that occur in the flow of viscoelastic fluids can drive the motion of a flexible structure placed in its path. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to the onset of a purely elastic flow instability. This instability occurs in the absence of nonlinear effects of fluid inertia and the Reynolds number of the flows studied here are in the order of 10-4. When such an elastic flow instability occurs in the vicinity of a flexible structure, the fluctuating fluid forces exerted on the structure grow large enough to cause a structural instability which in turn feeds back into the fluid resulting in a flow instability. Nonlinear periodic oscillations of the flexible structure are observed which have been found to be coupled to the time-dependent growth and decay of viscoelastic stresses in the wake of the structure. Presented in this thesis are the results of an investigation of the interaction occurring in the flow of a viscoelastic wormlike micelle solution past a flexible rectangular sheet. The structural geometries studied include: flexible sheet inclinations at 20°, 45° and 90° and flexible sheet widths of 5mm and 2.5mm. By varying the flow velocity, the response of the flexible sheet has been characterized in terms of amplitude and frequency of oscillations. Steady and dynamic shear rheology and filament stretching extensional rheology measurements are conducted in order to characterize the viscoelastic wormlike micelle solution. Bright field images show the deformation of the flexible sheet during an unstable oscillation while flow-induced birefringence images highlight the viscoleastic fluid stresses produced in the wake of the flexible sheet.

Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellar dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. Presented in this thesis are the results of an investigation into the flow fields generated by both a controllable and idealized porous media, effected as a periodic array of cylinders as well as a single circular cylinder. In order to fully characterize the kinematics, two rheologically documented test fluids were used. The first test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow, while the second consists of a single circular cylinder. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. A combination of particle image velocimetry in conjunction with flush mount pressure transducers were used to characterize the flow, while flow induced birefringence measurements were used to determine micelle deformation and alignment. In the periodic geometry, the pressure drop was found to decrease initially due to the shear thinning of the test fluid, and then exhibit a dramatic upturn as other elastic effects begin to dominate in one of the test fluids. In the case of the single cylinder, no such upturn was observed. Presented is evidence of the onset of an elastic instability in one of the test fluids above a critical Deborah number, manifest in fluctuating transient pressure drop measurements and asymmetric streamlines. This instability was observed in both test geometries. It is argued that this instability can be attributed to the measurable differences in the extensional rheology of the two fluids.

Os resultados de uma simulação numérica são apresentados para amplitudes de vibração induzidas por um escoamento transversal num feixe tubular no regime de instabilidade fluidelástica.O feixe tubular considerado tem geometria e características iguais às de uma instalação equivalente descrita na literatura, para a qual estão disponíveis as medições experimentais das amplitudes de vibração no regime de instabilidade elástica.O arranjo tipo triângulo rodado tem uma relação passo/diâmetro de 1,375 e consiste de um tubo móvel cercado por 134 tubos rígidos.A simulação numérica foi efetuada através de um software comercial de CFD (Computational Fluid dynamics).Para a região em torno de cada tubo foi considerada uma malha com dimensões do elemento crescendo geometricamente na direção normal ao tubo com fator de crescimento 1,13 , sendo a dimensão do elemento adjacente ao tubo igual a 0,1% do diâmetro externo do tubo.Na simulação numérica o escoamento foi considerado incompressível, monofásico, turbulento e bidimensional. Os dados do escoamento foram considerados idênticos aos das experiências da instalação descrita na literatura.Os resultados obtidos para as amplitudes pela simulação numérica são comparados com os resultados obtidos experimentalmente na instalação acima citada.Os desvios da maioria dos valores calculados em relação aos valores experimentais estão numa faixa aceitável. Isto mostra que existe a possibilidade de utilização, num futuro próximo, de CFD para análise deste tipo de problemas. / Results from a numerical simulation are reported for amplitudes of cross-flow induced vibrations at the fluid elastic instability regime in a tube bank. The tube bank has identical geometry and characteristics as for an experimental facility described in the literature, for which there are experimental measurements of the amplitudes of vibrations at the fluid elastic instability regime.The rotated triangular array has a pitch ratio of 1.375 and consists of 1 movable tube surrounded by 134 rigid tubes. The numerical simulations were accomplished with a commercial CFD (Computational Fluid Dynamics) software. For the region around each tube, a mesh with elements dimensions growing geometrically normal to the tube was considered, with growing factor 1.13, and the dimension for the element adjacent to the tube wall was set to 0.1% of the tube external diameter. The flow was considered incompressible, monophasic, turbulent and two-dimensional for the numerical simulation. The flow data considered were the same as for the experiments at the facility. The results presented in this paper for the amplitudes obtained by numerical simulation are compared with the experimental results obtained in the above mentioned experimental facility.The differences between the calculated values and the experimental values are acceptable. This show that in the near future there is the possibility to use CFD for these kind of problems.

Os resultados de uma simulação numérica são apresentados para amplitudes de vibração induzidas por um escoamento transversal num feixe tubular no regime de instabilidade fluidelástica.O feixe tubular considerado tem geometria e características iguais às de uma instalação equivalente descrita na literatura, para a qual estão disponíveis as medições experimentais das amplitudes de vibração no regime de instabilidade elástica.O arranjo tipo triângulo rodado tem uma relação passo/diâmetro de 1,375 e consiste de um tubo móvel cercado por 134 tubos rígidos.A simulação numérica foi efetuada através de um software comercial de CFD (Computational Fluid dynamics).Para a região em torno de cada tubo foi considerada uma malha com dimensões do elemento crescendo geometricamente na direção normal ao tubo com fator de crescimento 1,13 , sendo a dimensão do elemento adjacente ao tubo igual a 0,1% do diâmetro externo do tubo.Na simulação numérica o escoamento foi considerado incompressível, monofásico, turbulento e bidimensional. Os dados do escoamento foram considerados idênticos aos das experiências da instalação descrita na literatura.Os resultados obtidos para as amplitudes pela simulação numérica são comparados com os resultados obtidos experimentalmente na instalação acima citada.Os desvios da maioria dos valores calculados em relação aos valores experimentais estão numa faixa aceitável. Isto mostra que existe a possibilidade de utilização, num futuro próximo, de CFD para análise deste tipo de problemas. / Results from a numerical simulation are reported for amplitudes of cross-flow induced vibrations at the fluid elastic instability regime in a tube bank. The tube bank has identical geometry and characteristics as for an experimental facility described in the literature, for which there are experimental measurements of the amplitudes of vibrations at the fluid elastic instability regime.The rotated triangular array has a pitch ratio of 1.375 and consists of 1 movable tube surrounded by 134 rigid tubes. The numerical simulations were accomplished with a commercial CFD (Computational Fluid Dynamics) software. For the region around each tube, a mesh with elements dimensions growing geometrically normal to the tube was considered, with growing factor 1.13, and the dimension for the element adjacent to the tube wall was set to 0.1% of the tube external diameter. The flow was considered incompressible, monophasic, turbulent and two-dimensional for the numerical simulation. The flow data considered were the same as for the experiments at the facility. The results presented in this paper for the amplitudes obtained by numerical simulation are compared with the experimental results obtained in the above mentioned experimental facility.The differences between the calculated values and the experimental values are acceptable. This show that in the near future there is the possibility to use CFD for these kind of problems.