Browsing by Subject "boundary conditions"
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Item An Inverse Finite Element Analysis and A Parametric Study of Small Punch Tests(2012-02-14) Xu, ZhenzhenSmall punch test (SPT) has been widely used to evaluate in-service materials in nuclear fusion facilities. Early use of SPTs is largely based on empirical relations or curve fitting from experimental data, while recent applications of SPTs take advantage of finite element methods. In this study, an improved inverse finite element analysis procedure is proposed to obtain constitutive relations from load-displacement curves recorded in SPTs. In addition, a parametric study is performed to evaluate the effects of SPT parameters including friction coefficient, punch head diameter, sample thickness, specimen scale and boundary conditions. The proposed inverse finite element (FE) method improves the accuracy of existing inverse FE methods, and the current parametric study provides a basis for the standardization of SPT procedures in the future.Item Euler-Bernoulli Implementation of Spherical Anemometers for High Wind Speed Calculations via Strain Gauges(2011-08-08) Castillo, DavisNew measuring methods continue to be developed in the field of wind anemometry for various environments subject to low-speed and high-speed flows, turbulent-present flows, and ideal and non-ideal flows. As a result, anemometry has taken different avenues for these environments from the traditional cup model to sonar, hot-wire, and recent developments with sphere anemometers. Several measurement methods have modeled the air drag force as a quadratic function of the corresponding wind speed. Furthermore, by incorporating non-drag fluid forces in addition to the main drag force, a dynamic set of equations of motion for the deflection and strain of a spherical anemometer's beam can be derived. By utilizing the equations of motion to develop a direct relationship to a measurable parameter, such as strain, an approximation for wind speed based on a measurement is available. These ODE's for the strain model can then be used to relate directly the fluid speed (wind) to the strain along the beam?s length. The spherical anemometer introduced by the German researcher Holling presents the opportunity to incorporate the theoretical cantilevered Euler-Bernoulli beam with a spherical mass tip to develop a deflection and wind relationship driven by cross-area of the spherical mass and constriction of the shaft or the beam's bending properties. The application of Hamilton's principle and separation of variables to the Lagrangian Mechanics of an Euler-Bernoulli beam results in the equations of motion for the deflection of the beam as a second order partial differential equation (PDE). The boundary conditions of our beam's motion are influenced by the applied fluid forces of a relative drag force and the added mass and buoyancy of the sphere. Strain gauges will provide measurements in a practical but non-intrusive method and thus the concept of a measuring strain gauge is simulated. Young's Modulus creates a relationship between deflection and strain of an Euler-Bernoulli system and thus a strain and wind relation can be modeled as an ODE. This theoretical sphere anemometer's second order ODE allows for analysis of the linear and non-linear accuracies of the motion of this dynamic system at conventional high speed conditions.Item Extension of the Entropy Viscosity Method to the Multi-D Euler Equations and the Seven-Equation Two-Phase Model(2014-10-13) Delchini, MarcThe work presented in this dissertation focuses on the application of the entropy viscosity method to low-Mach single- and two-phase flow equations discretized using a continuous Galerkin finite element method with implicit time integration. The technique has been implemented and tested using the multiphysics simulation environment MOOSE (D Gaston, C Newsman, G Hansen and D Lebrun-Grandie. A parallel computational framework for coupled systems of nonlinear equations. Journal of Nucl. Eng. Design, 239, 1768-1778, 2009). First, the entropy viscosity method, developed by Guermond et al. (J-L Guermond, R Pasquetti and B Popov. Entropy viscosity method for nonlinear conservation laws. Journal of Comput. Phys., 230, 4248-4267, 2011), is extended to the multi-dimensional Euler equations for both subsonic (very low Mach numbers) and supersonic flows. We show that the current definition of the viscosity coefficients is not adapted to low-Mach flows and we provide a robust alternate definition valid for any Mach number value. The new definitions are derived from a low-Mach asymptotic study, is valid for a wide range of Mach numbers and no longer requires an analytical expression of the entropy function. In addition, the entropy minimum principle is used to derive the viscous regularization terms for Euler equations with variable area for nozzle flow problems and was proved valid for any equation of state with a concave entropy. The new definition of the entropy viscosity method is tested on various 1-D and 2-D numerical benchmarks employing the ideal and the stiffened gas equation of states: flow in a converging-diverging nozzle, Leblanc shock tube, slow moving shock, strong shock for liquid phase, subsonic flows around a 2-D cylinder and over a circular hump, and supersonic flow in a compression corner. Convergence studies are performed using analytical solutions in 1-D and proved the entropy viscosity method to be second-order accurate for smooth solutions. In a second part, the entropy viscosity method is applied to the seven-equation two-phase flow model. After deriving the dissipative terms using the same procedure as for the multi-D Euler equations, a low-Mach asymptotic study is performed in order to obtain a definition for the viscosity coefficients. Because the seven-equation model is derived by assuming that each phase obeys the Euler equations, the dissipative terms and the definition of the viscosity coefficients are analogous to the ones obtained for the single-phase system of equations. Then, 1-D numerical tests were performed to demonstrate that the entropy viscosity method properly stabilizes the flow simulations based on the seven-equation model. Another focus of this work was to investigate the impact of source terms (gravity, friction, etc) onto the entropy viscosity method. The theoretical approach adopted here consists of deriving the entropy residual when accounting for the source terms and investigate the sign of the new terms in order to adapt the definition of the viscosity coefficients. Numerical 1-D tests are performed to validate this approach for both single- and two-phase flow models. In the last part of this dissertation, the entropy viscosity method is applied to the 1-D grey radiation-hydrodynamic equations where the 1-D Euler equations are coupled to a radiation diffusion equation through relaxation terms. The method of manufactured solutions was used to prove second-order accuracy of the numerical stabilization method and also show that the entropy viscosity method yields the correct asymptotic diffusion limit. 1-D tests for inlet Mach number ranging from 1.2 to 50 are presented and show good agreement with semi-analytical solutions.