Baixe Modelo de Conjugado de Transferência de Calor em COMSOL Multiphysics e outras Exercícios em PDF para Engenharia Mecânica, somente na Docsity!
Exercise 1: Intro to COMSOL
Transport in Biological Systems
Fall 2015
Overview
In this course, we will consider transport phenomena in biological systems. Generally speaking, biological
systems of interest have interesting geometries and we are interested in things happening in time and space.
This means that analytical solutions can be challenging to find. Therefore, a modeling and simulation
approach is often useful. Towards this, we will employ COMSOL in this course. It takes a little bit to get
up to speed but it’s a very powerful tool.
You will work on this in class (AC318) on September 3rd, the first day of class. Alisha will not be present,
but you should all work as a group on this. Please try to complete the first 3 training items before
class.
Training
1. Install COMSOL on your computer if you haven’t (http://wikis.olin.edu/it/doku.php?id=comsol).
2. Read: http://cdn.comsol.com/documentation/5.1.0.180/IntroductionToCOMSOLMultiphysics.pdf
3. Watch: https://www.comsol.com/blogs/how-to-use-comsol-multiphysics-a-tutorial-video/
4. Attend the COMSOL training from 9:30-12:30 on September 17th. (Note: I know a few of you have
class before this one. Please come as soon as you can. If it is acceptable for your other class to leave
early on that day, it would be great, but I also understand if you can’t.)
Exercises
1. Make a smiley face (Figure 1). Hint: think about using ellipses and intersections, not lines for the
smile.
2. Make a hollow sphere with holes in it (Figure 2). Don’t worry about dimensions, just the general
concept.
Figure 2: A hollow sphere with holes.
3. Do the 3 exercises attached at the end of this document. (credit: COMSOL)
Objectives and Deliverables
The objective of this course is for you to apply concepts and skills in modeling and simulation to problems
in biological transport. The objectives of this particular exercise are to gain practice using COMSOL.
Complete the exercises and provide figures showing the final results for the exercises you have completed.
It doesn’t have to be anything pretty. Your results are due by September 21st.
Model Definition
The modeled system consists of an aluminum heat sink for cooling of components in electronic circuits mounted inside a channel of rectangular cross section (see Figure 1).
Such a set-up is used to measure the cooling capacity of heat sinks. Air enters the channel at the inlet and exits the channel at the outlet. The base surface of the heat sink receives a 1 W heat flux from an external heat source. All other external faces are thermally insulated.
The cooling capacity of the heat sink can be determined by monitoring the temperature of the base surface of the heat sink.
The model solves a thermal balance for the heat sink and the air flowing in the rectangular channel. Thermal energy is transported through conduction in the aluminum heat sink and through conduction and convection in the cooling air. The temperature field is continuous across the internal surfaces between the heat sink and the air in the channel. The temperature is set at the inlet of the channel. The base of the heat sink receives a 1 W heat flux. The transport of thermal energy at the outlet is dominated by convection.
The flow field is obtained by solving one momentum balance for each space coordinate ( x , y , and z ) and a mass balance. The inlet velocity is defined by a parabolic velocity profile for fully developed laminar flow. At the outlet, the normal stress is equal the outlet pressure and the tangential stress is canceled. At all solid surfaces, the velocity is set to zero in all three spatial directions.
The thermal conductivity of air, the heat capacity of air, and the air density are all temperature-dependent material properties.
You can find all of the settings mentioned above in the predefined multiphysics coupling for Conjugate Heat Transfer in COMSOL Multiphysics. You also find the material properties, including their temperature dependence, in the Material Browser.
Results
In Figure 2, the hot wake behind the heat sink visible in the plot is a sign of the convective cooling effects. The maximum temperature, reached at the heat sink base, is about 380 K.
Figure 2: The surface plot shows the temperature field on the channel walls and the heat sink surface, while the arrow plot shows the flow velocity field around the heat sink.
Application Library path: Heat_Transfer_Module/
Tutorials,_Forced_and_Natural_Convection/heat_sink
Modeling Instructions
From the File menu, choose New.
N E W 1 In the New window, click Model Wizard.
3 Click the Wireframe Rendering button on the Graphics toolbar.
L A M I N A R F L O W ( S P F ) Since the density variation is not small, the flow can not be regarded as incompressible. Therefore set the flow to be compressible.
1 In the Model Builder window, under Component 1 (comp1) click Laminar Flow (spf).
2 In the Settings window for Laminar Flow, locate the Physical Model section.
3 From the Compressibility list, choose Compressible flow (Ma<0.3).
Create a selection for the air domain used the physics interfaces to define the fluid.
4 Locate the Domain Selection section. In the Selection list, choose 2 and 3.
5 Click Create Selection.
6 In the Create Selection dialog box, type Air in the Selection name text field.
7 Click OK.
H E A T T R A N S F E R ( H T ) On the Physics toolbar, click Laminar Flow (spf) and choose Heat Transfer (ht).
Heat Transfer in Fluids 1
1 In the Model Builder window, under Component 1 (comp1)>Heat Transfer (ht) click Heat Transfer in Fluids 1.
2 In the Settings window for Heat Transfer in Fluids, locate the Domain Selection section.
3 From the Selection list, choose Air.
M A T E R I A L S Next, add materials.
A D D M A T E R I A L 1 On the Home toolbar, click Add Material to open the Add Material window.
2 Go to the Add Material window.
3 In the tree, select Built-In>Air.
4 Click Add to Component in the window toolbar.
M A T E R I A L S
Air (mat1)
1 In the Model Builder window, under Component 1 (comp1)>Materials click Air (mat1).
2 In the Settings window for Material, locate the Geometric Entity Selection section.
3 From the Selection list, choose Air.
A D D M A T E R I A L 1 Go to the Add Material window.
2 In the tree, select Built-In>Aluminum 3003-H.
3 Click Add to Component in the window toolbar.
M A T E R I A L S
Aluminum 3003-H18 (mat2)
1 In the Model Builder window, under Component 1 (comp1)>Materials click Aluminum 3003-H18 (mat2).
2 Select Domain 2 only.
A D D M A T E R I A L 1 Go to the Add Material window.
Now define the physical properties of the model. Start with the fluid domain.
L A M I N A R F L O W ( S P F ) On the Physics toolbar, click Heat Transfer (ht) and choose Laminar Flow (spf).
The no-slip condition is the default boundary condition for the fluid. Define the inlet and outlet conditions as described below.
Inlet 1
1 On the Physics toolbar, click Boundaries and choose Inlet.
2 Select Boundary 121 only.
3 In the Settings window for Inlet, locate the Boundary Condition section.
4 From the list, choose Laminar inflow.
5 Locate the Laminar Inflow section. In the U av text field, type U0.
Outlet 1
1 On the Physics toolbar, click Boundaries and choose Outlet.
2 Click the Zoom Extents button on the Graphics toolbar.
3 Select Boundary 1 only.
H E A T T R A N S F E R ( H T ) Thermal insulation is the default boundary condition for the temperature. Define the inlet temperature and the outlet condition as described below.
Temperature 1
1 On the Physics toolbar, click Boundaries and choose Temperature.
2 Select Boundary 121 only.
3 In the Settings window for Temperature, locate the Temperature section.
4 In the T 0 text field, type T0.
Outflow 1
1 On the Physics toolbar, click Boundaries and choose Outflow.
2 Select Boundary 1 only.
T0 20[degC] (^) 293.2 K Inlet temperature P0 1[W] (^) 1 W Total power dissipated by the electronics package
Name Expression Value Description
Next, use the P0 parameter to define the total heat source in the electronics package.
Heat Source 1
1 On the Physics toolbar, click Domains and choose Heat Source.
2 Select Domain 3 only.
3 In the Settings window for Heat Source, locate the Heat Source section.
4 Click the Overall heat transfer rate button.
5 In the P 0 text field, type P0.
Finally, add the thin thermal grease layer.
Thin Layer 1
1 On the Physics toolbar, click Boundaries and choose Thin Layer.
2 Select Boundary 34 only.
3 In the Settings window for Thin Layer, locate the Thin Layer section.
4 In the d s text field, type 50[um].
M E S H 1 1 In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2 In the Settings window for Mesh, locate the Mesh Settings section.
3 From the Element size list, choose Extra coarse.
4 Click the Build All button.
To get a better view of the mesh, hide some of the boundaries.
5 Click the Click and Hide button on the Graphics toolbar.
6 Click the Select Boundaries button on the Graphics toolbar.
2 In the Settings window for Arrow Volume, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Laminar Flow>u,v,w - Velocity field.
3 Locate the Arrow Positioning section. Find the x grid points subsection. In the Points text field, type 40.
4 Find the y grid points subsection. In the Points text field, type 20.
5 Find the z grid points subsection. From the Entry method list, choose Coordinates.
6 In the Coordinates text field, type 5[mm].
7 Right-click Results>Temperature (ht)>Arrow Volume 1 and choose Color Expression.
8 In the Settings window for Color Expression, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Laminar Flow>spf.U - Velocity magnitude.
9 On the Temperature (ht) toolbar, click Plot.
Derived Values
1 On the Results toolbar, click Global Evaluation.
2 In the Settings window for Global Evaluation, type Net Energy Rate in the Label text field.
3 Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Heat Transfer>Global>Net powers>ht.ntefluxInt - Total net energy rate.
4 Click the Evaluate button.
T A B L E Go to the Table window.
R E S U L T S
Derived Values
1 On the Results toolbar, click Global Evaluation.
2 In the Settings window for Global Evaluation, type Heat Source in the Label text field.
3 Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Heat Transfer>Global>Heat source powers>ht.QInt - Total heat source.
4 Click the Evaluate button.
T A B L E 1 Go to the Table window.
The total rate of net energy and heat generation should be close to 1 W.
Appendix: Geometry Modeling Instructions
R O O T On the Home toolbar, click Add Component and choose 3D.
G L O B A L D E F I N I T I O N S First define the geometry parameters.
Parameters
1 On the Home toolbar, click Parameters.
2 In the Settings window for Parameters, locate the Parameters section.
3 In the table, enter the following settings:
G E O M E T R Y 1 Build the geometry in three steps. First, import the heat sink geometry from a file.
Import 1 (imp1)
1 On the Home toolbar, click Import.
2 In the Settings window for Import, locate the Import section.
3 Click Browse.
4 Browse to the application’s Application Library folder and double-click the file heat_sink.mphbin.
5 Click Import.
Name Expression Value Description L_channel 7[cm] (^) 0.07 m Channel length W_channel 3[cm] (^) 0.03 m Channel width H_channel 1.5[cm] (^) 0.015 m Channel height L_chip 1.5[cm] (^) 0.015 m Chip size H_chip 2[mm] (^) 0.002 m Chip height
5 Right-click Component 1 (comp1)>Geometry 1>Work Plane 1 (wp1)>Plane Geometry>Square 1 (sq1) and choose Build Selected.
6 Click the Zoom Extents button on the Graphics toolbar.
Rectangle 1 (r1)
1 On the Work Plane toolbar, click Primitives and choose Rectangle.
2 In the Settings window for Rectangle, locate the Size section.
3 In the Width text field, type L_channel.
4 In the Height text field, type W_channel.
5 Locate the Position section. In the xw text field, type -45[mm].
6 In the yw text field, type -W_channel/2.
7 Right-click Component 1 (comp1)>Geometry 1>Work Plane 1 (wp1)>Plane Geometry>Rectangle 1 (r1) and choose Build Selected.
Now extrude the chip imprint to define the chip volume.
Extrude 1 (ext1)
1 On the Geometry toolbar, click Extrude.
2 Select the object wp1.sq1 only.
3 In the Settings window for Extrude, locate the Distances from Plane section.
4 In the table, enter the following settings:
5 Right-click Component 1 (comp1)>Geometry 1>Extrude 1 (ext1) and choose Build Selected.
6 Click the Zoom Extents button on the Graphics toolbar.
To finish the geometry, extrude the channel imprint in the opposite direction to define the air volume.
Extrude 2 (ext2)
1 On the Geometry toolbar, click Extrude.
2 Select the object wp1.r1 only.
3 In the Settings window for Extrude, locate the Distances from Plane section.
Distances (m) H_chip
4 In the table, enter the following settings:
5 Select the Reverse direction check box.
6 Click the Build All Objects button.
7 Click the Zoom Extents button on the Graphics toolbar.
The model geometry is now complete.
Distances (m) H_channel
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Cooling and Solidification of Metal
Introduction
This example is a model of a continuous casting process. Liquid metal is poured into a mold of uniform cross section. The outside of the mold is cooled and the metal solidifies as it flows through the mold. When the metal leaves the mold, it is completely solidified on the outside but still liquid inside. The metal then continues to cool and eventually solidify completely, at which point it can be cut into sections. This tutorial simplifies the problem somewhat by not computing the flow field of the liquid metal and assuming there is no volume change at solidification. It is also assumed that the velocity of the metal is constant and uniform throughout the modeling domain. The phase transition from molten to solid state is modeled via the apparent heat capacity formulation. Issues of convergence and mesh refinement are addressed for this highly nonlinear model. The Continuous Casting application is similar to this one, except that the velocity is computed from the Laminar Flow interface instead of being considered constant and uniform. For a detailed description of the application, see Continuous Casting.
Figure 1: A continuous casting process. The section where the metal is solidifying is being modeled.
Modeling region
Solid metal billet
Spray cooling
Tundish
Nozzle
Cooled mold
Molten metal
Saw
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Model Overview
The model simplifies the 3D geometry of the continuous casting to a 2D axisymmetric model composed of two rectangular regions: one representing the strand within the mold, and one the spray cooled region outside of the mold, prior to the saw cutoff. In the second section, there is also significant cooling via radiation to the ambient. In this region it is assumed that the molten metal is in a hydrostatic state, that the only motion in the fluid is due to the bulk downward motion of the strand. This simplification allows the assumption of bulk motion throughout the domain. Since this is a continuous process, the system can be modeled at steady state. The heat transport is described by the equation:
where k and Cp denote thermal conductivity and specific heat, respectively. The velocity, u , is the fixed casting speed of the metal in both liquid and solid states. As the metal cools down in the mold, it solidifies. During the phase transition, a significant amount of latent heat is released. The total amount of heat released per unit mass of alloy during the transition is given by the change in enthalpy, Δ H. In addition, the specific heat capacity, Cp , also changes considerably during the transition. The difference in specific heat before and after transition can be approximated by
As opposed to pure metals, an alloy generally undergoes a broad temperature transition zone, over several Kelvin, in which a mixture of both solid and molten material co-exist in a “mushy” zone. To account for the latent heat related to the phase transition, the Apparent Heat capacity method is used through the Heat Transfer with Phase Change domain condition. The objective of the analysis is to make Δ T , the half-width of the transition interval small, such that the solidification front location is well defined. Table 1 reviews the material properties in this tutorial.
TABLE 1: MATERIAL PROPERTIES
PROPERTY SYMBOL MELT SOLID Density ρ (kg/m 3 ) 8500 8500
∇ ⋅ ( – k ∇ T ) =–ρ C (^) p u ⋅∇ T
Δ C (^) p =^ Δ^ -------- TH -
