Physics to PDE. Tutorial

Transcription

1 Physics to PDE Tutorial 1

2 1. Exercise Heat Transfer: Heat conduction in the steady state 2. Exercise Structural Mechanics: Bending test 3. Exercise Electrodynamics: Plate capacitor 4. Exercise Fluid Dynamics: Laminar incompressible flow If no further information on settings is given: use default values! 2

3 1. Exercise Heat Transfer: Heat conduction in the steady state Consider the strongly simplified two-dimensional model of the steady temperature distribution in a room: window 5m door 4m The room is filled only with air Initial temperature of the air: 18 C Very good insulation of the walls results in thermal insulation The door leads to the cellar and has constant temperature of 15 C The window temperature is assumed to be constant (25 C) Choose a two-dimensional approach Compute the distribution of temperature that adjusts after a while. 3

4 1. Exercise Heat Transfer: Heat conduction in the steady state Further questions: Install a point heater in the center of the room.the solvability of PDE is dependent on suitable boundary conditions. Assume exclusively no-flux boundary conditions which result in thermal insulation of the whole geometry. What happens in Comsol and what is the physical explanation? Which changes do you have to make to build a executable model? Is it possible to simulate the problem above with the Equation-Based Module of Comsol? Which Module(s) could you choose and which parameters do you need? 4

5 2.Exercise Structural Mechanics: Bending test Consider the 2d-reduced model of the bending of a solid plate made of structural steel in the Structural Mechanics Module (Solid Mechanics): 1m 5cm plate plunger with a punctual force of 1 N operating in the middle of the plate 60cm Plate fixed at point-shaped support 5

6 2.Exercise Structural Mechanics: Bending test Hints: No need to realize the support and plunger in the study, exchange it with equivalent boundary conditions Keep in mind that boundary conditions also have an effect on the required geometry! Choose a reduced two-dimensional model with plane-strain assumption Choose a stationary approach Further Questions: Evaluate the y-displacement in the point (0,0.5). Change the point load to 10N, 100N, 1000N and evaluate the y-displacements. Which material model do you use in the simulation? Compare the displacements for different materials (Aluminum, Copper,.) Instead of the point load install a prescribed displacement. 6

7 3. Exercise Electrodynamics: Plate Capacitor The electrical field between the two plates of a ideal plate capacitor is homogeneous and the streamlines run parallel. The potential behaves linearly between the plates. 0.4m 5cm 0.5m The capacitor plates are made of copper The whole geometry is located in the middle of a 1m x 1m box which is filled with air Use an electrostatic approach e.g. the electrostatics-module (es) found under the AC/DC branch in the physics tree. The two inner boundaries of the plates are loaded with 5V (left plate) and -5V (right plate), respectively. 7

8 3. Exercise Electrodynamics: Plate Capacitor Hints: Display streamlines of the electrical field with the help of a streamline plot: add a 2d Plotgroup. Right-click on the Plotgroup and add Streamline. In the settings window you can change the streamline positioning. Show the linear behaviour of the potential by plotting the potential along a cut line between the plates: Define a Cut Line in the Data Sets. Add a 1d Plot Group and choose the Cut Line as Data Set. Right-Click on the Plot an add a Line Graph. 8

9 4. Exercise Fluid Dynamics: Laminar incompressible Flow Laminar incompressible flow in a pipe. Display velocity field and pressure. d=0.2m l=1 m Use a rotational symmetric approach (2d Axissymmetric) Physics: Fluid Flow -> Single Phase Flow -> Laminar Flow with incompressible Flow- setting Inflow defined by Pressure of 1 Pa on the left side of the pipe. Outflow defined by pressure of 0 Pa at the right side. Define a Material with density=1 [kg/m^3] and dynamic viscosity= 1e-3[Pa*s] 9

10 4. Exercise Fluid Dynamics: Laminar incompressible flow Further Questions: Display the flow profile (velocity field, z-component) as a function of the radius of the pipe (define a Cut Line 2d in the middle of the pipe and add a 1D Plot Group with a Line Gaph) Compare the maximal velocity in the middle of the pipe (radius=0) with the theoretical result of the Hagen-Poiseuille-Law: Change the radius of the pipe from 0.1 to 0.2. What does it mean for the maximal velocity, what do you expect? 10