Las tendencias del mercado de agua embotellada

The friction extrusion process has been studied successfully through numerical simulations in this dissertation. This work includes a flow visualization study by a physical model with transparent fluid and tools, a pure thermal model that focuses on heat transfer phenomenon, and a three-dimensional model which takes both heat transfer and material flow into consideration to provide a comprehensive understanding of the friction extrusion process.

First, a physical model with a Newtonian fluid was studied to mimic the friction extrusion process. The flow visualization study is to capture the material feature during friction extrusion process. It is a simplified model that only has tool rotation and there is no extrusion part. The model consists of a viscous Newtonian fluid, a chamber wall, and a back plate. The fluid and the tools are transparent so that experimental observations and measurements can be achieved easily. The Reynold number is equal to that approximated in friction extrusion process and it indicates a laminar flow. Due to the regular shapes of the fluid domain geometry and boundary conditions, an analytical solution about the flow field can be developed. Some assumptions, such as axisymmetric problem and zero velocity in radial and vertical directions, were made to enable the analytical solution attained. A three-dimensional CFD simulation of the simplified model was also performed. No assumption was made for the numerical modeling. Differences between the analytical

also compared with experimental measurements implemented by a DIC system on tiny particles in the fluid. A good agreement can be observed, serving as an evidence for experimental validation of the analytical solution and CFD simulation predictions.

Next, a pure thermal model was developed to investigate the heat transfer phenomenon during friction extrusion process. The heat generation approximation is the crucial when modeling the temperature field. A volume heating model has been proposed based on the characteristics of the friction extrusion process. The heat generation produced by friction between the die and aluminum alloy sample and the plastic deformation under the interface between the die and the sample is represented by a layer under the die-sample interface. The heat generation rate is assumed linearly distributed along vertical and radial directions. No frictional heat generation that is in the form of surface flux was included in the model since it is compensated in the volume heating model. The total power input into the system is related to the mechanical power during the friction extrusion experiment and it is assumed all mechanical power is transferred to heat.

The numerical model includes all parts involved in the friction extrusion experiment, such as the die, the chamber wall, the back plate, the support table, and the aluminum alloy sample. Only parts of the die, the back plate, and the table are included and their sizes are chosen to represent these bodies. The material flow is not modeled in the pure thermal model so all the bodied are treated as solids. As a result, only conduction equation is needed to solve for the temperature field. The boundary conditions have been carefully handled. The gap between the die and the aluminum sample is modeled by changing the conductivity and how it is filled was estimated.

The temperature predictions have a good agreement with the experimental measurements at several points, indicating that the volume heating model can be used to reasonably represent the heat generation during the friction extrusion process. The numerical results show the heat transfer phenomenon is a transient process and the temperature field is changing all the time. However, the temperature under the extrusion hole doesn’t change much after the start of extrusion. Since the material under the extrusion hole forms the wire, the thermal history of the extruded wire can be estimated. It’s seen although it is transient heat transfer, the highest temperature that the wire experiences changes small. The numerical results also show there is thermal resistance between the aluminum sample and the back plate.

A three-dimensional thermo-fluid model also has been presented to provide a comprehensive understanding of the friction extrusion process. Both heat transfer and material phenomena are modeled and more information can be obtained from the model. The volume heating model is used for the heat generation source and the assumption made in the pure thermal model, which is the material flow has small influence to the heat transfer during friction extrusion process, can be tested in the thermo-fluid model. The thermal initial and boundary conditions are the same as the pure thermal mode except the contact between the aluminum alloy sample and the back plate. The thermal resistance is simulated by changing the conductivity of the back plate. The predicted temperature results show that the material flow has unnoticeable effect on temperature field and the uncoupled heat transfer and material flow model works for friction extrusion process.

The Eulerian description of motion is used to simulate the material flow due to extreme deformation and distortion of the material. The aluminum alloy sample is treated

as a non-Newtonian fluid given that the flow stress is strain rate and temperature dependent. The Zener-Holloman parameter is adopted to describe the constitutive equation. Thus the fluid viscosity is a function of strain rat and temperature. The tools are seemed as rigid solids. The geometry sizes of the bodies are same as those in the pure thermal model. For the contact condition between the rotating die and the aluminum alloy sample which is treated as a fluid, different values, i.e. 0.3, 0.6, and 1.0, have been tried for the sticking factor. Massless solid particles are released in the fluid in the simulation as tracers to track the material flow paths. Since the particles don’t affect the temperature and fluid fields, they can represent the material flow. The distribution of the particles on the extruded wire cross sections was compared with experimental measurements. The qualitative comparisons show that the distribution trends and features can be captured by the thermo- fluid model. The numerical model provides information that is not available in experiment, such as the velocity, viscosity, and strain rate fields. The predicted flow fields almost keep the same after the start of extrusion although the temperature field changes. The path lines of the particles show that the material in the central zone of the process chamber is pushed spirally towards to extrusion hole to form the wire; then the material near the central zone moves to fill the space in the central region; and there is a dead zone in the upper corner where the material stays in the chamber.