METU Mechanical Engineering Department ME 582 Finite Element Analysis in Thermofluids Spring 2018 (Dr. C. Sert) Handout 12 COMSOL 1 Tutorial 3

Transcription

1 METU Mechanical Engineering Department ME 582 Finite Element Analysis in Thermofluids Spring 2018 (Dr. C. Sert) Handout 12 COMSOL 1 Tutorial 3 In this third COMSOL tutorial we ll solve Example 6 of Handout 9 with a time dependent force function. The problem is defined as follows T t 2 T = f(x, t), 1 x 1, 0 t 15 x2 Initial condition T(0, x) = 0 Boundary conditions : T(t, x = 1) = 0, T x = 0 t,x=1 f(x, t) = { 4 pulse(t) 0 if 0.1 x 0.1 else where pulse(t) function is given below pulse t Force function is localized at the center of the domain. It also changes with time as seen above. pulse function defines the time dependent nature of the force function. Forcing is turned on and off at 2 s intervals up to t = 10, after which it is kept off. Step 1. Start COMSOL. Press Model Wizard. Select 1D. Select Mathematics PDE Interfaces Coefficient Form PDE (c). Press the Add button. Press the Study button. Select Time Dependent. Press the Done button. 1 COMSOL 5.3a is used to prepare this tutorial 12-1

2 Step 2. Right click Geometry 1 and select Interval. Define an interval between -1 and 1. Click Build Selected. Step 3. Let s define the space dependent part of the force function. Right click Global Definitions and select Functions -> Rectangle. A new item called Rectangle 1 (rect 1) will be created. Our force function is non-zero only in the interval 0.1 < x < 0.1. Set the lower and upper limits of the function as -0.1 and 0.1. Turn off smoothing. Press Plot to see the generated function This function, called rect1, is 1 in the interval 0.1 < x < 0.1 and it is zero elsewhere. This is how the force function f depends on x. 12-2

3 Step 4. Let s define the time dependency of the force function, i.e. the pulse function given in the first page of this tutorial. We ll define it as three separate functions; one Rectangle function for each nonzero part of it. Right click Global Definitions and select Functions -> Rectangle. A new item called Rectangle 2 (rect 2) will be created. The first nonzero part of the pulse function is between 0< t < 2. Set the lower and upper limits of the function as 0 and 2. Turn off smoothing. Press Plot to see the generated function. We created a function called rect2. We ll use it to define the force function. Step 5. Repeat the previous step to create a third Rectangle function called rect3. This is for the second nonzero part of the pulse function. Therefore, set its limits as 4 and 6. Do not forget to turn off smoothing. Step 6. Repeat the previous step to create a fourth Rectangle function called rect4. This is for the third nonzero part of the pulse function. Therefore, set its limits as 8 and 10. Do not forget to turn off smoothing. Now we have 4 functions. We ll combine these to generate f(x, t). Is this COMSOL lovely or what? I can only wish that other CAE software (ANSYS Fluent?) are as user friendly as this one. 12-3

4 Step 7. Select Coefficient Form PDE 1 under Coefficient Form PDE (c). For this unsteady diffusion problem set the functions as follows. Only c, f and d a are nonzero. Here the following force function is the critical one. 4 * rect1(x [1/m]) * (rect2(t [1/s]) + rect3(t [1/s]) + rect4(t [1/s])) It uses the previously defined four Rectangle functions. The coefficient 4 at the beginning of it comes from the definition of f(x, t) (see the first page). rect1 function is for space dependency and its argument is x. The other 3 Rectangle functions are for time dependency and their arguments are t. Total time dependency is obtained by adding rect2, rect3 and rect4 functions. By definition, Rectangle functions require uniless arguments, and that is why we use the units seen in green color. 12-4

5 Step 8. Right click Coefficient Form PDE (c) and select Dirichlet Boundary Condition. Select the left boundary node with the mouse. Do not change the default value of r = 0. By default, the right BC is already zero flux. No need to do anything extra for that. Step 9. Select Mesh 1. Change Element size to Extra fine. Click Build All. A mesh of 50 elements will be generated. Step 10. Select Step 1: Time Dependent under Study 1. Change Times as range(0,0.1,15), where 0 is the initial time, 0.1 is the time step and 15 is the final time. Click Compute. 12-5

6 Solution will finish in a couple of seconds and the following result will be plotted. This shows the time dependent solution at every time step, and it is very crowded. 12-6

7 Step 11. Select 1D Plot Group 1 under Results. Change Time indices to range(1,15,151). Click Plot. This will result in the following. Note: To see the legend, select Line Graph 1 under 1D Plot Group 1 and activate Legends. 12-7

8 Step 12. To see the animation of the time dependent solution right click Export and select Animation -> Player. Change Frame selection to All. Press the Play button on the Graphics tab. You ll see the animated solution. If you want to pause between the time steps increase Display each frame for value. To see the solution at a specific time level and go back and forth between the frames use the following slider. Press up and down arrows of your keyboards to go back and forth in the animation. 12-8

9 Step 13. To save the animation, right click Export and select Animation -> File. Select the Format and Filename. Set Frame selection to All. Click Export. Note: Before crating an animation it is better to solve the problem with a smaller time step such as 0.01 and create the animation using frames of every say 5 time levels. This way you can see more detailed transitions. Such an animated GIF created for this problem can be downloaded from the course web site. 12-9

10 Step 14. What time discretization scheme did COMSOL use for this solution? To find out, Select Time-Dependent Solver 1 under Study 1-> Solver Configurations -> Solution 1. For the Method, the default selection is BDF, which stands for backward differentiation formula. It is an implicit time discretization, but exactly which one and which order? Minimum and maximum orders are shown as 1 and 5. Is the order adjusted automatically? Also there are initial step and maximum step settings. Is it possible to adjust the time step automatically as the solution progresses? We need to read the documentation of COMSOL to understand all these advanced settings. Alternatives of BDF are Runge Kutta and Generalized Alpha (something like our θ scheme?) and under each of these there are various settings

11 Exercise. For an unsteady problem most probably we want to monitor the progress of the solution at various points, such as the variation of the value at the mid-point of the domain or at the right boundary. Find out how this is done in COMSOL and generate a graph that shows the time variation of the mid-point value. Exercise. Of course the question that comes to mind is whether our unsteady1d.m code can solve this problem or not? You ll find that out in your next homework. That s all for this tutorial. Work hard, love coding, have fun and do not use cracked software. Night night 12-11