Experimental investigations on complex vortex flows using advanced flow diagnostic techniques

Using advanced diagnostic techniques, two complex vortex flow topics were addressed in the present thesis. First, the characteristics of flow structures around building models in a tornado-like vortex were studied by using a high-resolution Particle Image Velocimetry (PIV) system. Second, the 3D vortical structures of the film cooling flows in the trailing edge of a turbine blade were studied by using a stereoscopic PIV system. The flow measurement results were correlated to the film cooling effectiveness measured by the application of a relatively new technique, pressure sensitive paint (PSP). In the study of tornado-like vortex, by using the world-largest tornado simulator of Iowa State University, a comprehensive PIV study on the flow structures around a high-rise building model and a gable-roofed building model, as well as the surface pressure measurements and force measurements, was conducted to elucidate the underlying physics. The ultimate objective of the present study is to quantify the surface winds generated by tornadoes and flow-structure interactions between tornadoes and built environments to assess wind-induced damage with the purpose of mitigating damage and improving public safety. The characteristics of tornado like flow will be demonstrated and discussed in Chapter 2. The flow features around a building model and flow-structure interactions will be discussed in Chapter 3. In the study of vortex flow in the trailing edge of a turbine blade, detailed distributions of film cooling effectiveness measurements were obtained in the cutback region of trailing edge by using the PSP technique. Before the application of PSP, a self-designed calibration facility was developed to study the characteristics and to complete the calibration of the PSP. Corresponding to the film cooling effectiveness measurements, an experimental study was conducted to quantify the characteristics of coolant flows in the cutback region at the trailing edge of a turbine blade. A high-resolution stereoscopic PIV system were used to conduct detailed flow measurements to quantitatively visualize the evolution of the unsteady vortex and turbulent flow structures in coolant jet streams, and to quantify the mixing process between the wall jet cooling streams and main streams. The film cooling effectiveness and flow characteristics in the cutback region at the trailing edge of a turbine blade will be discussed in Chapter 4

On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup \G whose space of weight 3 cusp forms S_3(\G) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.Comment: 25 page

A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials

A three-dimensional nonlocal multiscale discrete-continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information-passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete-continuum coupling method retains the simplicity and efficiency of a continuum-based finite element model, while circumventing mesh pathology in the post-bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single-scale benchmark discrete element method simulations

Predicting possible leakage due to dynamics strain localization in granular materials with a coupled continuum-discrete coupling model

A three-dimensional multiscale model has been developed and used to analyze the evolutions of microstructural attributes and hydraulic properties inside dilatant shear bands. In the proposed multiscale coupled scheme, we establish links between the discrete element method, which explicitly replicates granular motion of individual -particles, and a finite element continuum model, which captures the homogenized responses of the granular assemblies. A spatial homogenization is performed to obtain the stress measure from representative elementary volume of discrete element simulations for macroscopic explicit dynamics finite element simulations. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands and replicate the induced anisotropy of the elasto-plastic responses, without employing any phenomenological plasticity model at macroscopic level. To improve cost-efficiency and prevent shear locking, a one-point quadrature rule is used along with an hour-glass control algorithm. Because discrete element simulations in each representatively elementary volume (Gauss point) requires no direct communication with its neighbors, the multiscale code can be programmed as a perfectly parallel problem, which is well suited to large scale distributed platforms and does not suffer parallel slowdown. The resultant multiscale continuum-discrete coupling method retains the simplicity and efficiency of a continuum-based finite element model while naturally introducing length-scale to cure mesh pathology. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now obtained directly from granular physics, without introducing unnecessary empirical relations and phenomenology. Microstructural information, such as force chain length, coordination numbers, and pore size distribution are compared with permeability inferred from lattice Boltzmann flow simulations to explain the mechanism that leads to the formation of flow conduit during strain localization

STUDY ON MECHANICAL BEHAVIOR OF CABLE - STAYED BRIDGE SUPPORT SYSTEM IN MULTI - FULCRUM UNBALANCED ROTATION

With the maturity and wide application of the bridge rotation construction technology, the single-fulcrum spherical hinge balance rotation can not meet the need of crossing over the high-speed railway catenary and other obstacles, so the unbalanced rotation construction is often needed. In order to ensure the stability and safety of the unbalanced rotation process, a multi-pivot rotation method is proposed. In this paper, the railway cable-stayed bridge over Harbin West Avenue is taken as the research object, and the multi-fulcrum rotating construction method over the metal contact network is adopted. The Abaqus finite element model is established, the influence of different rotation angular velocity, friction coefficient of slideway and position of support foot on the force of support system in the course of rotation is studied. The results show that, compared with the traditional single-pivot rotation, the force on the multi-pivot rotation support foot becomes the main force component, and the force on the spherical hinge decreases. The rotation angular velocity is positively correlated with Mises stress of the support foot and the spherical hinge. The friction coefficient of the slideway has a great influence on the force of the support foot. When the friction coefficient of the slideway changes in order of 0.02,0.04,0.06,0.08 and 0.1, the friction stress of the outer edge of the support foot increases linearly. Considering the force of spherical hinge and support foot, the best position of supporting foot is 7.3 m from the center of spherical hinge. The research in this paper can be used for reference in the future multi-pivot unbalanced rotation construction

Ergodic Theory Over {\F}_2[[T]]

In cryptography and coding theory, it is important to study the pseudo-random sequences and the ergodic transformations. We already have the $1$-Lipshitz ergodic theory over ${\Z}_2$ established by V. Anashin and others. In this paper we present an ergodic theory over {\F}_2[[T]] and some ideas which might be very useful in applications