comsol_v4.4_heat.pdf

COMSO

L MU

LTIPHYSICS V4

kimte 1. Introduction2. Heat Sink3. Droplet Breakup in a T-Junction4. Cooling of an Injection Mold5. Electroosmotic Micromixer6. Fluid-Structure Interaction

COMSOL MULTIPHYSICS

kimte Introduction

Heat Transfer and Fluid Flow

COMSOL V4.4 Product Suite

Heat Transfer Module

Conduction, convection and radiation

Radiation - Surface to surface, Surface to ambient,- External Radiation Source- Sun Radiation- Multi-Wavelength Heat Radiation

Easy to use for modeling a phase changeof materials

Add Moist air fluid type Bio heat Thermal contact Easy to evaluate for heat and energybalance

CFD Module

Model laminar and turbulent flows in single or multi phases

Simulation in the free and porous media flow

Ready coupling of heat and mass transport to fluid flow - heat exchangers, turbines, separations units, and ventilation systems

Thin Screen

Interior Wall

Wall Roughness(k-, k-w model)

Mixer Module

Impeller and a vessel in containing machinery-based mixers

Used in many industrial processes, such as the production of consumer products, pharmaceuticals, food, and fine chemicals.

Free surface

Add-on to the CFD Module

Microfluidics Module

Easy-to-use tools for the study microfluidic devices and rarefied gas flows.

Set up to coupled electrokinetic and magnetodynamic simulations easily including electrophoresis, magnetophoresis, dielectrophoresis, electroosmosis, and electrowetting.

Slip flow Analysis

Subsurface Flow Module

Model single and coupled processes related to subsurface flow

Oil and gas flow in porous media, the modeling of groundwater flow, and the spread of pollution through soil

Pipe Flow Module Flow, heat, and mass transport in

pipe networks.

Two-Phase Flow(gas-liquid

mixtures) in Pipes

Velocity, pressure variation,

temperature

1D lines or curves embedded in 2D

or 3D model.

Piping components such as Bend,

Valves, Pumps, T-junctions.

Molecular Module

Applies to the transitional flow and free molecular flow regimes.

Fast computations of steady-state free molecular flow with Angular Coefficient Method

Design and simulation of vacuum systems

Adsorption, desorption, and deposition

Particle Tracing Module Lets you compute trajectories of

particles in a fluid or an electromagnetic field.- Including particle-field interactions, particle-particle interaction force.

Applications include: flow visualization mixing spraying particle separation mass spectrometry ion optics beam physics ion energy distribution functions acoustic streaming ray tracing

Mixing in a static mixer

COMSOL MULTIPHYSICS

kimte Heat Sink

Heat Sink

Preview

LaminarNavier-Stokes

TurbulentRANSSmall pores

Large poresBrinkman

Fluid Flow

FreePorous

Newtonian Non-NewtonianSaturatedDarcyUnsaturatedRichards

Inlet / Outlet Condition Inflow, Outflow

Preview

Incompressible flow / Compressible flow

Newtonian fluid / Non-Newtonian fluid

Preview

Interior wall

no thickness

Preview

Preview

Domain / Boundary / Line / Point Heat Source

Temperature

Heat transfer in solid / fluid- Conduction / Convection Domain

Outflow Convection outlet Initial values

Preview Heat Flux

Convective Heat Flux

Highly Conductive Layer / Thin Thermally Resistive Layer

Preview Surface to ambient / surface radiation

Radiation Group

Preview Heat Balance(Global variables)

Energy Balance(Global variables)

ntfluxIntdEiInt QInt WnsInt

dEi0Int ntefluxInt QInt WInt

Model

Outlet

Inlet

Heat

Convection -> Cooling

Aluminum 3003-H18

Physics

Navier-stokes equation(Steady-State, Compressible flow)Heat Transfer equation

Heat Transfer in Solid + Laminar flow = Conjugate Heat Transfer

Modeling - condition

1 [W]

Inlet 5 [cm/s], 293.15 [K]Outlet Pressure, no viscous stress

Initial temperature 293.15[K]Wall condition No slip, Thermal insulation

Layer

Result

Solved with COMSOL Multiphysics 4.4Hea t S i n k

Introduction

This model is intended as a first introduction to simulations of fluid flow and conjugate heat transfer. It shows the following important points:

How to draw an air box around a device in order to model convective cooling in this box.

How to set a total heat flux on a boundary using automatic area computation.

How to display results in an efficient way using selections in data sets.

The model is also described in detail in the book Introduction to the Heat Transfer Module. An extension of the model that takes surface-to-surface radiation into account is also available; see Heat Sink with Surface-to-Surface Radiation.

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 1 | H E A T S I N K

Solved with COMSOL Multiphysics 4.4

2 | H E Asink receives a 1 W heat flux from an external heat source. All other external faces are thermally insulated.

inlet

outlet base surface

Figure 1: The model set-up including channel and heat sink.

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, a constant pressure is combined with the assumption that there are no viscous stresses in the direction perpendicular to the outlet. At all solid surfaces, the velocity is set to zero in all three spatial directions.T S I N K

Solved with COMSOL Multiphysics 4.4The 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 physics interface 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 slightly less than 376 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.

Model Library path: Heat_Transfer_Module/Tutorial_Models,_Forced_and_Natural_Convection/heat_sink 3 | H E A T S I N K


4 | H E AModeling Instructions

From the File menu, choose New.

N E W

1 In the New window, click the Model Wizard button.

M O D E L W I Z A R D

1 In the Model Wizard window, click the 3D button.

2 In the Select physics tree, select Heat Transfer>Conjugate Heat Transfer>Laminar Flow (nitf).

3 Click the Add button.

4 Click the Study button.

5 In the tree, select Preset Studies>Stationary.

6 Click the Done button.

G E O M E T R Y 1

1 On the Geometry toolbar, click Insert Sequence.

2 Browse to the models Model Library folder and double-click the file heat_sink_geom_sequence.mph.

Import 1The geometry sequence contains an imported binary file. Follow the steps below to make sure that the import path is correct.

1 In the Model Builder window, under Component 1>Geometry 1 click Import 1.

2 In the Import settings window, locate the Import section.

3 Click the Browse button.

4 Browse to the models Model Library folder and double-click the file heat_sink.mphbin.

5 Click the Import button.

6 Click the Build All Objects button.

7 Click the Go to Default 3D View button on the Graphics toolbar.

To facilitate face selection in the next steps, use the wireframe rendering option T S I N K

Solved with COMSOL Multiphysics 4.48 Click the Wireframe Rendering button on the Graphics toolbar.

M A T E R I A L S

On the Home toolbar, click Add Material.

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>Air.

3 In the Add material window, click Add to Component.



2 In the tree, select Built-In>Aluminum 3003-H18.

3 In the Add material window, click Add to Component. 5 | H E A T S I N K


6 | H E A

M A T E R I A L SAluminum 3003-H181 In the Model Builder window, under Component 1>Materials click Aluminum

3003-H18.

2 Select Domain 2 only.



2 In the tree, select Built-In>Silica glass.

3 In the Add material window, click Add to Component.

M A T E R I A L S

Silica glass1 In the Model Builder window, under Component 1>Materials click Silica glass.


Material 41 In the Model Builder window, right-click Materials and choose New Material.

2 Right-click Material 4 and choose Rename.

3 Go to the Rename Material dialog box and type Thermal Grease in the New name edit field.

4 Click OK.

5 In the Material settings window, locate the Geometric Entity Selection section.

6 From the Geometric entity level list, choose Boundary.

7 Select Boundary 34 only.

8 Click to expand the Material properties section. Locate the Material Properties section. In the Material properties tree, select Basic Properties>Thermal Conductivity.

9 Click Add to Material.

10 Locate the Material Contents section. In the table, enter the following settings:

Property Name Value Unit Property group

Thermal conductivity k 2[W/m/K] W/(mK) BasicT S I N K


G L O B A L D E F I N I T I O N SParameters1 In the Model Builder window, expand the Global Definitions node, then click

Parameters.

2 In the Parameters settings window, locate the Parameters section.

3 In the table, enter the following settings:

Now define the physical properties of the model. Start with the fluid domain.

C O N J U G A T E H E A T TR A N S F E R

Fluid 11 In the Model Builder window, under Component 1>Conjugate Heat Transfer click Fluid

1.


Next use the Ptot parameter to define the total heat source in the electronic package.

Heat Source 11 On the Physics toolbar, click Domains and choose Heat Source.


3 In the Heat Source settings window, locate the Heat Source section.

4 Click the Total power button.

5 In the Ptot edit field, type P_tot.

Wall, no slip, is the default boundary condition for the fluid. Define the inlet and outlet conditions as described below.

Inlet 11 On the Physics toolbar, click Boundaries and choose Inlet.


3 In the Inlet settings window, locate the Boundary Condition section.

Name Expression Value Description

U0 5[cm/s] 0.05000 m/s Mean inlet velocity

T0 20[degC] 293.2 K Inlet temperature

P_tot 1[W] 1.000 W Total power dissipated by the electronic package 7 | H E A T S I N K


8 | H E A4 From the Boundary condition list, choose Laminar inflow.

5 Locate the Laminar Inflow section. In the Uav edit field, type U0.

Thermal insulation is the default boundary condition for the temperature. Define the inlet temperature and the outlet condition as described below.

Outlet 11 On the Physics toolbar, click Boundaries and choose Outlet.

2 Click the Zoom Extents button on the Graphics toolbar.


Temperature 11 On the Physics toolbar, click Boundaries and choose Temperature.


3 In the Temperature settings window, locate the Temperature section.

4 In the T0 edit field, type T0.

Outflow 11 On the Physics toolbar, click Boundaries and choose Outflow.


Thin Thermally Resistive Layer 11 On the Physics toolbar, click Boundaries and choose Thin Thermally Resistive Layer.


3 In the Thin Thermally Resistive Layer settings window, locate the Thin Thermally Resistive Layer section.

4 In the ds edit field, type 50[um].

M E S H 1

1 In the Model Builder window, under Component 1 click Mesh 1.

2 In the Mesh settings window, 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, suppress some of the boundaries.

5 Click the Select and Hide button on the Graphics toolbar.

6 Click the Select Boundaries button on the Graphics toolbar.T S I N K

Solved with COMSOL Multiphysics 4.47 Select Boundaries 1, 2, and 4 only.

The finished mesh should look like that in the figure below.

To improve the accuracy in the numerical results, this mesh can be refined by choosing another predefined element size. However, doing so requires more computational time and memory.

S T U D Y 1

On the Home toolbar, click Compute.

R E S U L T S

Velocity (nitf)Two default plots are generated automatically. The first one shows the velocity magnitude on five parallel slices. The second one shows the temperature on the wall boundaries. Add an arrow plot to visualize the velocity field.

Temperature (nitf)1 In the Model Builder window, under Results right-click Temperature (nitf) and choose

Arrow Volume.

You notice that the velocity field is represented by default. 9 | H E A T S I N K


10 | H E2 In the Arrow Volume settings window, locate the Data section.

3 From the Data set list, choose Solution 1.

4 Locate the Arrow Positioning section. In the x grid points subsection, in the Points edit field, type 40.

5 In the y grid points subsection, in the Points edit field, type 20.

6 From the Entry method list, choose Coordinates.

7 In the Coordinates edit field, type 5[mm].

8 Right-click Results>Temperature (nitf)>Arrow Volume 1 and choose Color Expression.

9 In the Color Expression settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Conjugate Heat Transfer (Laminar Flow)>Velocity magnitude (nitf.U).

10 On the 3D plot group toolbar, click Plot.

Derived Values1 On the Results toolbar, click Global Evaluation.

2 In the Global Evaluation settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Conjugate Heat Transfer (Heat Transfer in Solids)>Global>Net powers>Total net energy power (nitf.ntefluxInt).

3 Right-click Results>Derived Values>Global Evaluation 1 and choose Rename.

4 In the Rename Global Evaluation dialog box, type Net Energy Power in the New name edit field.

5 Click OK.

6 Click the Evaluate button.

R E S U L T S


2 In the Global Evaluation settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Conjugate Heat Transfer (Heat Transfer in Solids)>Global>Heat source powers>Total heat source (nitf.QInt).

3 Right-click Results>Derived Values>Global Evaluation 2 and choose Rename.

4 In the Rename Global Evaluation dialog box, type Heat Source in the New name edit field.

5 Click OK.A T S I N K

Solved with COMSOL Multiphysics 4.46 Click the Evaluate button.

The net power from the total energy flux and the total heat source should be close to 1 W. 11 | H E A T S I N K

COMSOL MULTIPHYSICS

kimte Droplet Breakup in a T-Junction

Droplet Breakup in a T-Junction

Level Set and Phase Field- Base fluid : fluid1, Setting fluid : fluid2

Wetted wall- Level set : Dynamic contact angle(static contact angle + slip length)- Phase field : Static contact angle- Moving wetted wall : Only phase field.

Preview

Fluid 1 Fluid 2 Initial Values, Initial interfacePreview

Model

Inlet 1Fluid 2

Outlet

Inlet 2

Fluid 1

Physics

Momentum transport equation

Level set equation

Density and viscosity

Effective droplet diameter

Laminar Two-Phase Flow, Level Set


Inlet1Inlet2

0.4e-6/3600*step1(t[1/s])[m^3/s]0.2e-6/3600*step1(t[1/s])[m^3/s]

Outlet Pressure, no viscous stressWall condition Wetted wall

Surface tension coefficient 5e-3 [N/m]

Fluid 2

Fluid 1

Symmetry

Result

Solved with COMSOL Multiphysics 4.4Drop l e t B r e a kup i n a T - J u n c t i o n

Introduction

Emulsions consist of small liquid droplets immersed in another liquid, typically oil in water or water in oil. Emulsions find wide application in the production of food, cosmetics, and pharmaceutical products. The properties and quality of an emulsion typically depend on the size and the distribution of the droplets. This model studies in detail how to create uniform droplets in a microchannel T-junction.

Setting up the model you can make use of the Laminar Two-Phase Flow, Level Set interface. The model uses the predefined wetted wall boundary condition at the solid walls, with a contact angle of 135. From the results, you can determine the size of the created droplets and the rate with which they are produced.

Model Definition

Figure 1 shows the geometry of the T-shaped microchannel with a rectangular cross section. For the separated fluid elements to correspond to droplets, the geometry is modeled in 3D. Due to symmetry, it is sufficient to model only half of the junction geometry. The modeling domain is shown in Figure 1. The fluid to be dispersed into 1 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


2 | D R Osmall droplets, Fluid 2, enters through the vertical channel. The other fluid, Fluid 1, flows from the right to left through the horizontal channel.

Inlet,fluid 1

Inlet, fluid 2

Outlet

Initial fluid interface

Figure 1: The modeling domain of the T-junction.

The problem described is straight forward to set up with the Laminar Two-Phase Flow, Level Set interface. The interface sets up a momentum transport equation, a continuity equation, and a level set equation for the level set variable. The fluid interface is defined by the 0.5 contour of the level set function.

The interface uses the following equations:

In the equations above, denotes density (kg/m3), u velocity (m/s), t time (s), dynamic viscosity (Pas), p pressure (Pa), and Fst the surface tension force (N/m

3). Furthermore, is the level set function, and and are numerical stabilization parameters. The density and viscosity are calculated from

t

u u ( )u+ p I u u( )T+( )+[ ] Fst+=

u 0=

t------ u + 1 ( )

---------- +

=P L E T B R E A K U P I N A T- J U N C T I O N

Solved with COMSOL Multiphysics 4.4where 1, 2, 1, and 2 are the densities and viscosities of Fluid 1 and Fluid 2.

P H Y S I C A L P A R A M E T E R S

The two liquids have the following physical properties:

QUANTITY VALUE, FLUID 1 VALUE, FLUID 2

Density (kg/m3) 1000 1000

Dynamic viscosity (Pas) 0.00195 0.00671

The surface tension coefficient is 5103 N/m.

B O U N D A R Y C O N D I T I O N S

At both inlets, Laminar inflow conditions with prescribed volume flows are used. At the outflow boundary, the Pressure, no viscous stress condition is set. The Wetted wall boundary condition applies to all solid boundaries with the contact angle specified as 135 and a slip length equal to the mesh size parameter, h. The contact angle is the angle between the fluid interface and the solid wall at points where the fluid interface attaches to the wall. The slip length is the distance to the position outside the wall where the extrapolated tangential velocity component is zero (see Figure 2).

Fluid 1

Fluid 2

Wall

u Wall

Figure 2: The contact angle, , and the slip length, .

1 2 1( )+= 1 2 1( )+= 3 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


4 | D R OResults and Discussion

Figure 3 shows the fluid interface (the level set function 0.5= ) and velocity streamlines at various times. The first droplet is formed after approximately 0.03 s.

Figure 3: Velocity streamlines, velocity on the symmetry plane, and the phase boundary at t = 0.02 s, 0.04 s, 0.06 s, and 0.08 s.

You can calculate the effective diameter, deffthat is, the diameter of a spherical droplet with the same volume as the formed dropletusing the following expression:

(1)

Here, represents the leftmost part of the horizontal channel, where x < 0.2 mm. In this case, the results show that deff is about 0.12 mm. The results are in fair agreement with those presented in Ref. 1.

Reference

1. S. van der Graaf, et al., Lattice Boltzmann Simulations of Droplet Formation in a T-Shaped Microchannel, Langmuir, vol. 22, pp. 41444152, 2006.

deff 23

4------ 0.5>( ) d

3=P L E T B R E A K U P I N A T- J U N C T I O N

Solved with COMSOL Multiphysics 4.4Model Library path: CFD_Module/Multiphase_Benchmarks/droplet_breakup

Modeling Instructions

From the File menu, choose New.

N E W



1 In the Model Wizard window, click the 3D button.

2 In the Select physics tree, select Fluid Flow>Multiphase Flow>Two-Phase Flow, Level Set>Laminar Two-Phase Flow, Level Set (tpf).



5 In the tree, select Preset Studies>Transient with Initialization.


G E O M E T R Y 1

1 In the Model Builder window, under Component 1 click Geometry 1.

2 In the Geometry settings window, locate the Units section.

3 From the Length unit list, choose mm.

Work Plane 11 On the Geometry toolbar, click Work Plane.

2 In the Work Plane settings window, locate the Plane Definition section.

3 From the Plane list, choose xz-plane.

Rectangle 11 In the Model Builder window, under Component 1>Geometry 1>Work Plane 1

right-click Plane Geometry and choose Rectangle.

2 In the Rectangle settings window, locate the Size section.

3 In the Width edit field, type 0.1.

4 In the Height edit field, type 0.4. 5 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


6 | D R O5 Locate the Position section. In the yw edit field, type 0.1.

Rectangle 21 Right-click Plane Geometry and choose Rectangle.


3 In the Width edit field, type 1.

4 In the Height edit field, type 0.1.

5 Locate the Position section. In the xw edit field, type -0.7.

Plane Geometry1 On the Home toolbar, click Build All.


Polygon 11 Right-click Plane Geometry and choose Polygon.

2 In the Polygon settings window, locate the Object Type section.

3 From the Type list, choose Open curve.

4 Locate the Coordinates section. In the xw edit field, type 0 0.1.

5 In the yw edit field, type 0.2 0.2.

6 Click the Build Selected button.

Polygon 21 Right-click Plane Geometry and choose Polygon.

2 In the Polygon settings window, locate the Coordinates section.

3 In the xw edit field, type 0.1 0.1.

4 In the yw edit field, type 0 0.1.


Extrude 11 On the Geometry toolbar, click Extrude.

2 In the Extrude settings window, locate the Distances from Plane section.



Distances (mm)

0.05P L E T B R E A K U P I N A T- J U N C T I O N

Solved with COMSOL Multiphysics 4.45 Click the Zoom Extents button on the Graphics toolbar.

Form Union1 In the Model Builder window, under Component 1 >Geometry 1 right-click Form Union

and choose Build Selected. The model should look like in Figure 1.

M A T E R I A L S

Material 11 In the Model Builder window, under Component 1 right-click Materials and choose

New Material.


3 In the Rename Material dialog box, type Fluid 1 in the New name edit field.

4 Click OK.

5 In the Material settings window, locate the Material Contents section.


Material 21 In the Model Builder window, right-click Materials and choose New Material.


3 In the Rename Material dialog box, type Fluid 2 in the New name edit field.

4 Click OK.

5 In the Material settings window, click to expand the Material properties section.

6 Locate the Material Properties section. In the Material properties tree, select Basic Properties>Density.


8 In the Material properties tree, select Basic Properties>Dynamic Viscosity.



Density rho 1e3[kg/m^3] kg/m Basic

Dynamic viscosity mu 1.95e-3[Pa*s] Pas Basic 7 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


8 | D R O10 Locate the Material Contents section. In the table, enter the following settings:

D E F I N I T I O N S

Step 11 On the Home toolbar, click Functions and choose Global>Step.

2 In the Step settings window, locate the Parameters section.

3 In the Location edit field, type 1e-3.

4 Click to expand the Smoothing section. In the Size of transition zone edit field, type 2e-3.

Add an integration operator that you will use to calculate the effective droplet diameter according to Equation 1 in the Model Definition section.

Integration 11 On the Definitions toolbar, click Component Couplings and choose Integration.

2 In the Integration settings window, locate the Source Selection section.

3 From the Selection list, choose All domains.

Variables 11 In the Model Builder window, right-click Definitions and choose Variables.

2 In the Variables settings window, locate the Variables section.



Density rho 1e3[kg/m^3] kg/m Basic

Dynamic viscosity mu 6.71e-3[Pa*s] Pas Basic

Name Expression Unit Description

V1 0.4e-6/3600*step1(t[1/s])[m^3/s]

m/s Volume flow, inlet 1

V2 0.2e-6/3600*step1(t[1/s])[m^3/s]

m/s Volume flow, inlet 2

d_eff 2*(intop1((phils>0.5)*(x


L A M I N A R TW O - P H A S E F L O W, L E V E L S E TThe mesh can be controlled very well in this model, which makes it possible to use a lower element order without reducing the accuracy.

1 In the Model Builder windows toolbar, click the Show button and select Discretization in the menu.

2 In the Model Builder window, expand the Component 1>Laminar Two-Phase Flow, Level Set node, then click Laminar Two-Phase Flow, Level Set.

3 In the Laminar Two-Phase Flow, Level Set settings window, click to expand the Discretization section.

4 Find the Value types when using splitting of complex variables subsection. From the Discretization of fluids list, choose P1 + P1.

Fluid Properties 11 In the Model Builder window, under Component 1>Laminar Two-Phase Flow, Level Set

click Fluid Properties 1.

2 In the Fluid Properties settings window, locate the Fluid 1 Properties section.

3 From the Fluid 1 list, choose Fluid 1.

4 Locate the Fluid 2 Properties section. From the Fluid 2 list, choose Fluid 2.

5 Locate the Surface Tension section. From the Surface tension coefficient list, choose User defined. In the edit field, type 5e-3[N/m].

6 Locate the Level Set Parameters section. In the edit field, type 0.05[m/s].7 In the ls edit field, type 5e-6[m].

Wall 1Because this is the default boundary condition node, you cannot modify the selection explicitly. Instead, you override the default condition where it is not applicable by adding other boundary conditions.

1 In the Model Builder window, under Component 1>Laminar Two-Phase Flow, Level Set click Wall 1.

2 In the Wall settings window, locate the Boundary Condition section.

3 From the Boundary condition list, choose Wetted wall.

4 In the w edit field, type 3*pi/4[rad].

5 In the edit field, type 5e-6[m]. 9 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


10 | D RInitial Interface 11 In the Model Builder window, under Component 1>Laminar Two-Phase Flow, Level Set

click Initial Interface 1.


Initial Values 21 On the Physics toolbar, click Domains and choose Initial Values.


3 In the Initial Values settings window, locate the Initial Values section.

4 Click the Fluid 2 button.

For Domains 1 and 2, the default initial value settings apply.




4 From the Boundary condition list, choose Laminar inflow.

5 Locate the Laminar Inflow section. Click the Flow rate button.

6 In the V0 edit field, type V1.

7 In the Lentr edit field, type 0.01[m].




4 In the Vf edit field, type 1.

5 From the Boundary condition list, choose Laminar inflow.

6 Locate the Laminar Inflow section. Click the Flow rate button.

7 In the V0 edit field, type V2.

8 In the Lentr edit field, type 0.01[m].

Outlet 11 On the Physics toolbar, click Boundaries and choose Outlet.

2 Select Boundary 1 only.O P L E T B R E A K U P I N A T- J U N C T I O N

Solved with COMSOL Multiphysics 4.4Symmetry 11 On the Physics toolbar, click Boundaries and choose Symmetry.

2 Select Boundaries 5, 13, 14, and 21 only.

M E S H 1 { M E S H 1 }

Mapped 11 In the Model Builder window, under Component 1 right-click Mesh 1 and choose More

Operations>Mapped.

2 Select Boundaries 2, 7, 10, and 16 only.

Distribution 11 Right-click Component 1>Mesh 1>Mapped 1 and choose Distribution.

2 Select Edge 3 only.

3 In the Distribution settings window, locate the Distribution section.

4 In the Number of elements edit field, type 160.

Distribution 21 Right-click Mapped 1 and choose Distribution.

2 Select Edges 1 and 9 only.






4 From the Distribution properties list, choose Predefined distribution type.


6 In the Element ratio edit field, type 4.




4 From the Distribution properties list, choose Predefined distribution type.

5 In the Number of elements edit field, type 20. 11 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


12 | D R6 In the Element ratio edit field, type 3.

7 Select the Reverse direction check box.

Mapped 1Right-click Mapped 1 and choose Build Selected.

Swept 11 Right-click Mesh 1 and choose Swept.

2 In the Swept settings window, click to expand the Source faces section.

3 Locate the Source Faces section. Select the Active toggle button.

4 Select Boundaries 2, 7, and 10 only.

Distribution 11 Right-click Component 1>Mesh 1>Swept 1 and choose Distribution.



4 Click the Build All button.O P L E T B R E A K U P I N A T- J U N C T I O N


S T U D Y 1Step 2: Time Dependent1 In the Model Builder window, expand the Study 1 node, then click Step 2: Time

Dependent.

2 In the Time Dependent settings window, locate the Study Settings section.

3 In the Times edit field, type range(0,5e-3,0.08).

4 Click to expand the Results while solving section. Locate the Results While Solving section. Select the Plot check box.

5 From the Plot group list, choose Default.

This choice means that the Graphics window will show a surface plot of the volume fraction of Fluid 1 while solving, and this plot will be updated at each 5 ms output time step.

Manually tune the solver sequence for optimal performance and accuracy.

Solver 11 On the Study toolbar, click Show Default Solver.

2 In the Model Builder window, expand the Solver 1 node, then click Time-Dependent Solver 1.

3 In the Time-Dependent Solver settings window, click to expand the Time stepping section.

4 Locate the Time Stepping section. From the Method list, choose Generalized alpha.

5 Select the Time step increase delay check box.

6 In the associated edit field, type 3.

7 In the Amplification for high frequency edit field, type 0.3.

8 From the Predictor list, choose Constant.

9 In the Model Builder window, expand the Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1 node.

10 Right-click Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1 and choose Iterative.

11 In the Iterative settings window, locate the Error section.

12 In the Factor in error estimate edit field, type 20.

13 In the Maximum number of iterations edit field, type 200.

14 Right-click Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1>Iterative 1 and choose Multigrid. 13 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


14 | D R15 In the Model Builder window, expand the Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1>Iterative 1>Multigrid 1 node.

16 Right-click Presmoother and choose SCGS.

17 In the SCGS settings window, locate the Main section.

18 Select the Vanka check box.

19 Under Variables, click Add.

20 Go to the Add dialog box.

21 In the Variables list, choose comp1.tpf.Pinlinl1 and comp1.tpf.Pinlinl2.

22 Click the OK button.

23 In the Model Builder window, expand the Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1>Iterative 1>Multigrid 1>Postsmoother node.

24 Right-click Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1>Iterative 1>Multigrid 1>Postsmoother and choose SCGS.

25 In the SCGS settings window, locate the Main section.

26 Select the Vanka check box.

27 Under Variables, click Add.

28 Go to the Add dialog box.

29 In the Variables list, choose comp1.tpf.Pinlinl1 and comp1.tpf.Pinlinl2.


31 In the Model Builder window, expand the Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1>Iterative 1>Multigrid 1>Coarse Solver node, then click Direct.

32 In the Direct settings window, locate the General section.

33 From the Solver list, choose PARDISO.

34 In the Model Builder window, collapse the Study 1>Solver Configurations>Solver 1>Time-Dependent Solver 1 node.

S T U D Y 1

Solver 11 In the Model Builder window, collapse the Study 1>Solver Configurations>Solver

1>Time-Dependent Solver 1 node.

2 In the Model Builder window, collapse the Solver 1 node.

3 On the Home toolbar, click Compute.O P L E T B R E A K U P I N A T- J U N C T I O N


R E S U L T SThe first default plot group shows the volume fraction of fluid 1 as slice plot, and the second plot group shows a slice plot of the velocity combined with a contour plot of the volume fraction of fluid 1. Follow these steps to reproduce the series of velocity field plots shown in Figure 3.

3D Plot Group 31 On the Home toolbar, click Add Plot Group and choose 3D Plot Group.

2 In the Model Builder window, under Results right-click 3D Plot Group 3 and choose Slice.

3 In the Slice settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Laminar Two-Phase Flow, Level Set>Velocity magnitude (tpf.U).

4 Locate the Plane Data section. From the Plane list, choose zx-planes.

5 From the Entry method list, choose Coordinates.

6 On the 3D plot group toolbar, click Plot.

7 In the Model Builder window, right-click 3D Plot Group 3 and choose Isosurface.

8 In the Isosurface settings window, locate the Levels section.

9 From the Entry method list, choose Levels.

10 In the Levels edit field, type 0.5.

11 Locate the Coloring and Style section. From the Coloring list, choose Uniform.

12 From the Color list, choose Green.

13 Right-click 3D Plot Group 3 and choose Streamline.

14 In the Streamline settings window, locate the Streamline Positioning section.

15 From the Positioning list, choose Uniform density.

16 In the Separating distance edit field, type 0.05.

17 Locate the Coloring and Style section. From the Line type list, choose Tube.

18 Select the Radius scale factor check box.

19 In the associated edit field, type 2e-3.

20 From the Color list, choose Yellow.

21 In the Model Builder window, click 3D Plot Group 3.

22 In the 3D Plot Group settings window, locate the Data section.

23 From the Time (s) list, choose 0.02. 15 | D R O P L E T B R E A K U P I N A T- J U N C T I O N


16 | D R24 On the 3D plot group toolbar, click Plot.

25 Click the Go to Default 3D View button on the Graphics toolbar.

Compare the resulting plot with the upper-left plot in Figure 3.

26 To reproduce the remaining three plots, plot the solution for the time values 0.04, 0.06, and 0.08 s.

Next, evaluate the effective droplet diameter computed according to Equation 1.


2 In the Global Evaluation settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Definitions>Effective droplet diameter (d_eff).


TA B L E

The result, roughly 0.12 mm, is displayed in the table in the Table window.

Finally, generate a movie of the moving fluid interface and the velocity streamlines.

R E S U L T S

3D Plot Group 31 In the Model Builder window, under Results right-click 3D Plot Group 3 and choose

Player. COMSOL Multiphysics generates the movie and then plays it.

2 To replay the movie, click the Play button on the Graphics toolbar.

If you want to export a movie in GIF, Flash, or AVI format, right-click Export and create an Animation feature.O P L E T B R E A K U P I N A T- J U N C T I O N

COMSOL MULTIPHYSICS

kimte Cooling of an Injection Mold

Cooling of an Injection Mold

Simulations of fluid flow, heat and mass transfer, hydraulic transients, and acoustics in the 1D geometry. Fluid Model Newtonian, Power law, Bingham Pipe shape Round, Square, Rectangle, User defined(hydraulic diameter) Inlet / Outlet Mass flow rate, Velocity, Volumetric flow rate, SCCM

Preview

Friction model- Newtonian fluidsChurchill : Full range of Re (laminar, transition and turbulent) and e/dStokes : Laminar regime (Re < 2000)Wood : 4*103 < Re < 1*107 and 1*10-5 < e/d < 4*10-2Haaland : Commonly used for oil pipelines and wells, Re (4*103 < Re < 1*108)Colebrook : Very low relative roughness e/d, Simple Haaland modelVon Karman : Very large relative roughness e/d, Simple Haaland modelSwamee-Jain : Alternative method of Haaland model

10-6 < e/d < 10-2 and for Re (5*103 < Re < 108)

- Non-Newtonian fluidsIrvine(Power law) : Full range of Re (laminar, transition and turbulent) and e/dStokes(Power law) : Laminar regime (Re < 2000)Darby(Bingham) : Full range of Re (laminar, transition and turbulent) and e/d

Preview

Loss Coefficients

Preview

Wall Heat Transfer

Preview

Model

Steel AISI 4340 PolyurethaneThermal conductivity 44.5 [W/(m*K)] 0.32 [W/(m*K)]Density 7850 [kg/] 1250 [kg/]Heat capacity 475 [J/(kg*K)] 1540 [J/(kg*K)]

Physics

Continuity and Momentum Equations

Churchill Model

Energy Equation

+Pipe Flow + Heat Transfer in Pipes = Non-Isothermal Pipe Flow

Heat Transfer in Solid


Inlet 10 [Liter/min]Outlet 1[atm]

Initial temperature of mold 473.15KSurface roughness Commercial steel(0.046 mm)

Pipe diameter : 1cm

Result

Mold Material Water flow rate (l/min)

Surface roughness (mm)

average T after 10 min (K)

Line color

Steel 10 0.046 333 BlueSteel 20 0.046 325 GreenSteel 10 0.46 328 RedAluminium 10 0.046 301 Magenta

Solved with COMSOL Multiphysics 4.4Coo l i n g o f an I n j e c t i o n Mo l d

Introduction

Cooling is an important process in the production of injection molded plastics. First of all, the cooling time may well represent more than half of the production cycle time. Second, a homogeneous cooling process is desired to avoid defects in the manufactured parts. If plastic materials in the injection molding die are cooled down uniformly and slowly, residual stresses can be avoided, and thereby the risk of warps and cracks in the end product can be minimized.

As a consequence, the positioning and properties of the cooling channels become important aspects when designing the mold.

The simulation of heat transfer in molds of relatively complex geometries requires a 3D representation. Simulation of 3D flow and heat transfer inside the cooling channels are computationally expensive. An efficient short-cut alternative is to model the flow and heat transfer in the cooling channels with 1D pipe flow equations, and still model the surrounding mold and product in 3D.

This example shows how you can use the Non-Isothermal Pipe Flow interface together with the Heat Transfer in Solids interface to model a mold cooling process. The equations describing the cooling channels are fully coupled to the heat transfer equations of the mold and the polyurethane part.

Figure 1: The steering wheel of a car, made from polyurethane. 1 | C O O L I N G O F A N I N J E C T I O N M O L D


2 | C O OModel Definition

M O D E L G E O M E T R Y A N D P R O C E S S C O N D I T I O N S

The polyurethane material used for a steering wheel is produced by several different molds. The part considered in this model is the top half of the wheel grip, shown in gray in Figure 2.

Figure 2: Polyurethane parts for a steering wheel. The top half of the grip is modeled in this example.L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4The mold consists of a 50-by-50-by-15 cm steel block. Two cooling channels, 1 cm in diameter, are machined into the block as illustrated in Figure 3.

Water inlets

Figure 3: Mold block and cooling channels.

The after injection of the polyurethane, the average temperature of the mold a the plastic material is 473 K. Water at room temperature is used as cooling fluid and flows through the channels at a rate of 10 liters/min. The model simulates a 10 min cooling process.

For numerical stability reasons, the model is set up with an initial water temperature of 473 K, which is ramped down to 288 K during the first few seconds.

P I P E F L OW E Q U A T I O N S

The momentum and mass conservation equations below describe the flow in the cooling channels:

(1)

(2)

ut------- p fD

2dh----------u u=

At----------- Au( )+ 0= 3 | C O O L I N G O F A N I N J E C T I O N M O L D


4 | C O OAbove, u is the cross section averaged fluid velocity (m/s) along the tangent of the center line of a pipe. A (m2) is the cross section area of the pipe, (kg/m3) is the density, and p (N/m2) is the pressure. For more information, refer to the section Theory for the Pipe Flow Interface in the Pipe Flow Module Users Guide.

Expressions for the Darcy Friction FactorThe second term on the right hand side of Equation 2 accounts for pressure drop due to viscous shear. The Pipe Flow physics uses the Churchill friction model (Ref. 1) to calculate fD. It is valid for laminar flow, turbulent flow, and the transitional region in between. The Churchill friction model is predefined in the Non-Isothermal Pipe Flow interface and is given by:

(3)

where

(4)

(5)

fD 88

Re------

12A B+( )-1.5+

1 12=

A -2.457ln 7Re------

0.90.27 e d( )+

16=

B 37530Re

---------------- 16

=L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4As seen from the equations above, the friction factor depends on the surface roughness divided by diameter of the pipe, e/d. Surface roughness values can be selected from a list in the Pipe Properties feature or be entered as user-defined values.

Figure 4: The Friction model and Surface roughness settings are found in the Pipe Properties feature.

In the Churchill equation, fD is also a function of the fluid properties, flow velocity and geometry, through the Reynolds number:

(6)

The physical properties of water as function of temperature are directly available from the softwares built-in material library.

H E A T TR A N S F E R E Q U A T I O N S

Cooling ChannelsThe energy equation for the cooling water inside the pipe is:

(7)

where Cp (J/(kgK)) is the heat capacity at constant pressure, T is the cooling water temperature (K), and k (W/(mK)) is the thermal conductivity. The second term on the right hand side corresponds to heat dissipated due to internal friction in the fluid. It is negligible for the short channels considered here. Qwall (W/m) is a source term that accounts for the heat exchange with the surrounding mold block.

Re ud-----------=

ACpTt------- ACpu T+ Ak T fD+

A2dh---------- u 3 Qwall+= 5 | C O O L I N G O F A N I N J E C T I O N M O L D


6 | C O OMold Block and Polyurethane PartHeat transfer in the solid steel mold block as well as the molded polyurethane part is governed by conduction:

(8)

Above, T2 is the temperature in the solids. The source term Qwall comes into play for the heat balance in Equation 8 through a line heat source where the pipe is situated. This coupling is automatically done by the Wall Heat Transfer feature in the Non-Isothermal Pipe Flow interface.

Heat ExchangeThe heat exchange term Qwall (W/m) couple the two energy balances given by Equation 7 and Equation 8:

The heat transfer through the pipe wall is given by

(9)

In Equation 9 Z (m) is the perimeter of the pipe, h (W/(m2K)) a heat transfer coefficient and Text (K) the external temperature outside of the pipe. Qwall appears as a source term in the pipe heat transfer equation.

The Wall heat transfer feature requires the external temperature and at least an internal film resistance.

Text can be a constant, parameter, expression, or given by a temperature field computed by another physics interface, typically a 3D Heat Transfer interface. h is automatically calculated through film resistances and wall layers that are added as subnodes. For details, refer to the section Theory for the Heat Transfer in Pipes Interface in the Pipe Flow Module Users Guide.

In this model example, Text is given as the temperature field computed by a 3D heat transfer interface, and automatic heat transfer coupling is done to the 3D physics side as a line source. The temperature coupling between the pipe and the surrounding domain is implemented as a line heat source in the 3D domain. The source strength is proportional to the temperature difference between the pipe fluid and the surrounding domain.

CpT2t---------- k T2=

Qwall hZ Text T( )=L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4The Wall Heat Transfer feature is added to the Non-Isothermal Pipe Flow interface, and the External temperature is set to the temperature of the Heat Transfer in solids interface.

Figure 5: In the Wall Heat Transfer feature, set the External temperature to the temperature field calculated by the Heat Transfer in Solids interface.

The heat transfer coefficient, h, depends on the physical properties of water and the nature of the flow and is calculated from the Nusselt number:

(9-6)

where k is the thermal conductivity of the material, and Nu is the Nusselt number. dh is the hydraulic diameter of the pipe.

COMSOL detects if the flow is laminar or turbulent. For the laminar flow regime, an analytic solution is available that gives Nu = 3.66 for circular tubes (Ref. 2). For turbulent flow inside channels of circular cross sections the following Nusselt correlation is used (Ref. 3):

(10)

where Pr is the Prandtl number:

(11)

Note that Equation 10 is a function of the friction factor, fD, and therefore that the radial heat transfer will increase with the surface roughness of the channels.

Note: All the correlations discussed above are automatically used by the Wall Heat Transfer feature in the Pipe Flow Module, and it detects if the flow is laminar or turbulent for automatic selection of the correct correlation.

h Nu kdh------=

NuintfD 8( ) Re 1000( )Pr

1 12.7 fD 8( )1 2 Pr2 3 1( )+

------------------------------------------------------------------------------=

PrCp

k-----------= 7 | C O O L I N G O F A N I N J E C T I O N M O L D


8 | C O OResults and Discussion

The steel mold and polyurethane part, initially at 473 K, are cooled for 10 minutes by water at room temperature. Figures below show sample results when flow rate of the cooling water is 10 liters/minute and the surface roughness of the channels is 46 m. After two minutes of cooling, the hottest and coldest parts of the polyurethane part differ by approximately 40 K (Figure 7).

Figure 7: Temperature distribution in the polyurethane part and the cooling channels after 2 minutes of cooling.L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4Figure 8 shows the temperature distribution in the steel mold after 2 minutes. The temperature footprint of the cooling channels is clearly visible.

Figure 8: Temperature distribution in the steel mold block after 2 minutes of cooling. 9 | C O O L I N G O F A N I N J E C T I O N M O L D


10 | C OAfter 10 minutes of cooling, the temperature in the mold block is more uniform, with a temperature at the center of approximately 333 K (Figure 9). Still, the faces with cooling channel inlets and outlets are more than 20 K hotter.

Figure 9: Temperature distribution in the steel mold block after 10 minutes of cooling.

The blue line in Figure 10 shows the average temperature of the polyurethane part as function of the cooling time. The temperature is 333 K after 10 minutes of cooling. To evaluate the influence of factors affecting the cooling time, additional simulations were run varying the flow rate of the cooling water, the surface roughness of the cooling channels, and the mold material. The conditions are summarized in the table below.

MOLD MATERIAL

WATER FLOW RATE (L/MIN)

SURFACE ROUGHNESS (MM)

AVERAGE T AFTER 10 MIN (K)

LINE COLOR

Steel 10 0.046 333 Blue

Steel 20 0.046 325 Green

Steel 10 0.46 328 Red

Aluminium 10 0.046 301 Magenta

TABLE 1: COOLING CONDITIONSO L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4Figure 10: Average temperature of the polyurethane part as function of time and cooling conditions.

Clearly, the thermal conductivity of the mold material is the most important factor in this comparison, followed by flow rate and surface roughness of the cooling channels. Assuming that 340 K is an acceptable temperature at the end of the production cycle, it can be found that changing the mold material reduces the cooling time by 67%, increasing the flow rate reduces the cooling time by 17%, and increasing surface roughness reduces the cooling time by 11%.

References

1. S.W. Churchill, Friction factor equations span all fluid-flow regimes, Chem. Eng., vol. 84, no. 24, p.91, 1997.

2. F.P. Incropera, D.P. DeWitt. Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley & Sons, pp. 486487, 2002.

3. V. Gnielinski, New Equation for Heat and Mass Transfer in Turbulent Pipe and Channel Flow, Int. Chem. Eng. vol. 16, p. 359, 1976. 11 | C O O L I N G O F A N I N J E C T I O N M O L D


12 | C OModel Library path: Pipe_Flow_Module/Heat_Transfer/mold_cooling



1 Go to the Model Wizard window.

2 Click Next.

3 In the Add physics tree, select Fluid Flow>Non-Isothermal Flow>Non-Isothermal Pipe Flow (nipfl).

4 Click Add Selected.

5 In the Add physics tree, select Heat Transfer>Heat Transfer in Solids (ht).

6 Click Add Selected.

7 Click Next.

8 Find the Studies subsection. In the tree, select Preset Studies for Selected Physics>Time Dependent.

9 Click Finish.

G L O B A L D E F I N I T I O N S

Parameters1 In the Model Builder window, right-click Global Definitions and choose Parameters.

2 In the Parameters settings window, locate the Parameters section.


Step 1Create a smooth step function to decrease the coolant temperature at the beginning of the process.

1 Right-click Global Definitions and choose Functions>Step.

2 In the Step settings window, locate the Parameters section.

Name Expression Description

T_init_mold 473.15[K] Initial temperature, mold

T_coolant 288.15[K] Steady-state inlet temperature, coolantO L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.43 In the Location edit field, type 2.5.

4 In the From edit field, type 1.

5 In the To edit field, type 0.

6 Click to expand the Smoothing section. In the Size of transition zone edit field, type 5.

Optionally, you can inspect the shape of the step function:

7 Click the Plot button.

Variables 11 Right-click Global Definitions and choose Variables.

2 In the Variables settings window, locate the Variables section.


G E O M E T R Y 1

First, import the steering wheel part from a CAD design file.

Import 11 In the Model Builder window, under Model 1 right-click Geometry 1 and choose

Import.

Name Expression Description

T_inlet T_coolant+(T_init_mold- T_coolant)*step1(t[1/s])

Ramped inlet temperature, coolant 13 | C O O L I N G O F A N I N J E C T I O N M O L D


14 | C O2 In the Import settings window, locate the Import section.

3 Click the Browse button.

4 Browse to the models Model Library folder and double-click the file mold_cooling_top.mphbin.

5 Click the Import button.

Second, draw the mold and cooling channels. To simplify this step, insert a prepared geometry sequence from file. After insertion you can study each geometry step in the sequence.

6 In the Model Builder window, right-click Geometry 1 and choose Insert Sequence from File.

7 Browse to the models Model Library folder and double-click the file mold_cooling_geom_sequence.mph.

8 Click the Build All button.


10 Click the Transparency button on the Graphics toolbar.

D E F I N I T I O N S

Create the selections to simplify the model specification.

Explicit 11 In the Model Builder window, under Model 1 right-click Definitions and choose

Selections>Explicit.

2 In the Explicit settings window, locate the Input Entities section.

3 From the Geometric entity level list, choose Edge.

Select one segment of the upper channel and one segment of the lower.

4 Select Edges 6 and 7 only.O L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.45 Select the Group by continuous tangent check box to select entire channels.

6 Right-click Model 1>Definitions>Explicit 1 and choose Rename.

7 Go to the Rename Explicit dialog box and type Cooling channels in the New name edit field.

8 Click OK.

M A T E R I A L S

The next step is to specify material properties for the model. Select water and steel from the built-in materials database.

Material Browser1 In the Model Builder window, under Model 1 right-click Materials and choose Open

Material Browser.

2 In the Material Browser settings window, In the tree, select Built-In>Water, liquid.

3 Click Add to Current Geometry.

Water, liquid1 In the Model Builder window, under Model 1>Materials click Water, liquid.

2 In the Material settings window, locate the Geometric Entity Selection section.

3 From the Geometric entity level list, choose Edge.

4 From the Selection list, choose Cooling channels.

Material Browser1 In the Model Builder window, right-click Materials and choose Open Material Browser.

2 In the Material Browser settings window, In the tree, select Built-In>Steel AISI 4340.

3 Click Add to Current Geometry. 15 | C O O L I N G O F A N I N J E C T I O N M O L D


16 | C OSteel AISI 43401 In the Model Builder window, under Model 1>Materials click Steel AISI 4340.


Next, create a material with the properties of polyurethane.

Material 31 In the Model Builder window, right-click Materials and choose Material.


3 In the Material settings window, locate the Material Contents section.


5 Right-click Model 1>Materials>Material 3 and choose Rename.

6 Go to the Rename Material dialog box and type Polyurethane in the New name edit field.

7 Click OK.

N O N - I S O T H E R M A L P I P E F L OW

1 In the Non-Isothermal Pipe Flow settings window, locate the Edge Selection section.


Pipe Properties 11 In the Model Builder window, under Model 1>Non-Isothermal Pipe Flow click Pipe

Properties 1.

2 In the Pipe Properties settings window, locate the Pipe Shape section.

3 From the list, choose Round.

4 In the di edit field, type 1[cm].

5 Locate the Flow Resistance section. From the Surface roughness list, choose Commercial steel (0.046 mm).

Temperature 11 In the Model Builder window, under Model 1>Non-Isothermal Pipe Flow click

Temperature 1.

Property Name Value

Thermal conductivity k 0.32

Density rho 1250

Heat capacity at constant pressure Cp 1540O L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.42 In the Temperature settings window, locate the Temperature section.

3 In the Tin edit field, type T_inlet.

Inlet 11 In the Model Builder window, right-click Non-Isothermal Pipe Flow and choose the

point condition Pipe Flow>Inlet.

2 Select Points 3 and 4 only.

3 In the Inlet settings window, locate the Inlet Specification section.

4 From the Specification list, choose Volumetric flow rate.

5 In the qv,0 edit field, type 10[dm^3/min].

Heat Outflow 11 Right-click Non-Isothermal Pipe Flow and choose the point condition Heat Transfer

in Pipes>Heat Outflow.

2 Select Points 269 and 270 only.

Wall Heat Transfer 11 Right-click Non-Isothermal Pipe Flow and choose the edge condition Heat Transfer in

Pipes>Wall Heat Transfer.

2 In the Wall Heat Transfer settings window, locate the Edge Selection section.


4 Locate the Heat Transfer Model section. From the Text list, choose Temperature (ht).

5 Right-click Model 1>Non-Isothermal Pipe Flow>Wall Heat Transfer 1 and choose Internal Film Resistance.

Initial Values 11 In the Model Builder window, under Model 1>Non-Isothermal Pipe Flow click Initial

Values 1.


3 In the u edit field, type 0.1.

4 In the T edit field, type T_init_mold.

H E A T TR A N S F E R I N S O L I D S

1 In the Model Builder window, expand the Model 1>Heat Transfer in Solids node, then click Initial Values 1.


3 In the T2 edit field, type T_init_mold. 17 | C O O L I N G O F A N I N J E C T I O N M O L D


18 | C OHeat Flux 11 In the Model Builder window, right-click Heat Transfer in Solids and choose Heat Flux.

2 In the Heat Flux settings window, locate the Boundary Selection section.

3 From the Selection list, choose All boundaries.

4 Locate the Heat Flux section. Click the Inward heat flux button.

5 In the h edit field, type 2.

M E S H 1

Edge 11 In the Model Builder window, under Model 1 right-click Mesh 1 and choose More

Operations>Edge.

2 In the Edge settings window, locate the Edge Selection section.


Size 11 Right-click Model 1>Mesh 1>Edge 1 and choose Size.

2 In the Size settings window, locate the Element Size section.

3 From the Predefined list, choose Extra fine.

Free Tetrahedral 1In the Model Builder window, right-click Mesh 1 and choose Free Tetrahedral.

Size 11 In the Model Builder window, under Model 1>Mesh 1 right-click Free Tetrahedral 1

and choose Size.

2 In the Size settings window, locate the Geometric Entity Selection section.

3 From the Geometric entity level list, choose Domain.


5 Locate the Element Size section. From the Predefined list, choose Fine.


S T U D Y 1

Step 1: Time Dependent1 In the Model Builder window, under Study 1 click Step 1: Time Dependent.

2 In the Time Dependent settings window, locate the Study Settings section.O L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.43 In the Times edit field, type range(0,30,600).

4 In the Model Builder window, right-click Study 1 and choose Compute.

R E S U L T S

Data Sets1 In the Model Builder window, under Results right-click Data Sets and choose Solution.

2 Right-click Results>Data Sets>Solution 2 and choose Add Selection.

3 In the Selection settings window, locate the Geometric Entity Selection section.

4 From the Geometric entity level list, choose Domain.


6 In the Model Builder window, right-click Data Sets and choose Solution.

7 Right-click Results>Data Sets>Solution 3 and choose Add Selection.

8 In the Selection settings window, locate the Geometric Entity Selection section.

9 From the Geometric entity level list, choose Boundary.

10 Select Boundaries 3 and 5 only.

Temperature (nipfl)1 In the Model Builder window, expand the Results>Temperature (nipfl) node, then

click Line 1.1.

2 In the Line settings window, locate the Coloring and Style section.


4 In the associated edit field, type 1.

5 Clear the Color legend check box.

6 Locate the Data section. From the Data set list, choose Solution 1.

7 From the Time list, choose 120.

8 In the Model Builder window, right-click Temperature (nipfl) and choose Surface.

9 In the Surface settings window, locate the Data section.


11 From the Time list, choose 120.


Temperature (ht)1 In the Model Builder window, under Results click Temperature (ht).

2 In the 3D Plot Group settings window, locate the Data section. 19 | C O O L I N G O F A N I N J E C T I O N M O L D


20 | C O3 From the Time list, choose 120.


5 Click the Transparency button on the Graphics toolbar.

6 In the Model Builder window, expand the Temperature (ht) node, then click Surface.

7 In the Surface settings window, locate the Coloring and Style section.

8 From the Color table list, choose Rainbow.


3D Plot Group 61 In the Model Builder window, right-click Results and choose 3D Plot Group.

2 Right-click 3D Plot Group 6 and choose Surface.



5 In the Model Builder window, right-click 3D Plot Group 6 and choose Slice.

6 In the Slice settings window, locate the Plane Data section.

7 In the Planes edit field, type 4.

8 Click to expand the Inherit Style section. From the Plot list, choose Surface 1.

9 Right-click 3D Plot Group 6 and choose Surface.



12 Locate the Coloring and Style section. From the Coloring list, choose Uniform.

13 From the Color list, choose Gray.

14 Right-click 3D Plot Group 6 and choose Line.

15 In the Line settings window, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Non-Isothermal Pipe Flow (Heat Transfer in Pipes)>Temperature (T).

16 Locate the Coloring and Style section. From the Line type list, choose Tube.

17 In the Tube radius expression edit field, type 0.5*nipfl.dh.


19 From the Coloring list, choose Uniform.

20 From the Color list, choose Blue.

21 Click the Plot button.O L I N G O F A N I N J E C T I O N M O L D

Solved with COMSOL Multiphysics 4.4Derived Values1 In the Model Builder window, under Results right-click Derived Values and choose

Average>Volume Average.

2 In the Volume Average settings window, locate the Selection section.

3 Click Paste Selection.

4 Go to the Paste Selection dialog box.

5 In the Selection edit field, type 2.



8 In the Table window, click Table Graph. 21 | C O O L I N G O F A N I N J E C T I O N M O L D

COMSOL MULTIPHYSICS

kimte Electroosmotic Micromixer

Electroosmotic Micromixer

Particle release(Inlet, Release) Mesh based (refine^dimension)

Refinement factor = 1 Refinement factor = 3

Preview

Particle release(Inlet, Release) Density

Expression = 1 Expression = x+y2The resulting distribution will look a bit random, and it will depend on the order in which the mesh elements are numbered.

Preview

Particle release Grid(Release of grid), uniform density(inlet)

Release uniformly from 0.3 to 0.7 Uniform release on a boundary

Preview

Bounce - This option specularly reflects from the wall such that the particle momentum is conserved.- This option is not available for Massless particle tracing- This option is typically used when tracing microscopic particles in a fluid.

Freeze - This option (default) fixes the particle position and velocity at the instant a wall is struck.- This is useful to recover the velocity and energy distribution function of particles when

they strike the wall- Used to compute the ion energy distribution function in plasma models

Stick - This option fixes the particle position at the instant the wall is struck. - This can be used if the velocity or energy of the particles striking a wall is not of interest.

Preview

Disappear - This option means that the particle is not displayed once it has made contact with the wall. - This option should be used if display of the particle location after contact with the wall is

not of interest. Diffuse reflection

- Particles bounce off surfaces according to Knudsens cosine law General reflection

- Specify an arbitrary expression for the post collision particle velocity - In the example to the right particles will be specularly reflected off a wall with half of their

incident velocity - This option gives complete freedom over

Preview

ModelInlet

Electroosmotic velocity

MixingOutlet

Property Name ValueDensity rho 1e3[kg/m^3]Dynamic viscosity mu 1e-3[Pa*s]Electric conductivity

sigma 0.11845[S/m]Relative permittivity

epsilonr 80.2

Physics

Navier-stokes equation(Compressible flow)

Ohms law

Convection-diffusion equation

Electric Currents + Laminar Flow + Transport of Diluted Species


Inlet 0.1 [mm/s]Outlet Normal stress is zero

Wall condition Electroosmotic velcity

1 [mol/]0 [mol/]

Result

Solved with COMSOL Multiphysics 4.4E l e c t r o o smo t i c M i c r om i x e r 1

Introduction

Microlaboratories for biochemical applications often require rapid mixing of different fluid streams. At the microscale, flow is usually highly ordered laminar flow, and the lack of turbulence makes diffusion the primary mechanism for mixing. While diffusional mixing of small molecules (and therefore of rapidly diffusing species) can occur in a matter of seconds over distances of tens of micrometers, mixing of larger molecules such as peptides, proteins, and high molecular-weight nucleic acids can require equilibration times from minutes to hours over comparable distances. Such delays are impractically long for many chemical analyses. These problems have led to an intense search for more efficient mixers for microfluidic systems.

Most microscale mixing devices are either passive mixers that use geometrical stirring, or active mixers that use moving parts or external forces, such as pressure or electric field.

In a passive mixer, one way of increasing the mixing is by shredding two or several fluids into very thin alternating layers, which decreases the average diffusion length for the molecules between the different fluids. However, these mixers often require very long mixing channels because the different fluids often run in parallel. Another way of improving mixing efficiency is to use active mixers with moving parts that stir the fluids. At the microscale level moving parts in an active mixer are very fragile. One alternative is to use electroosmotic effects to achieve a mixing effect that is perpendicular to the main direction of the flow.

This model takes advantage of electroosmosis to mix fluids. The system applies a time-dependent electric field, and the resulting electroosmosis perturbs the parallel streamlines in the otherwise highly ordered laminar flow.

Model Definition

This example of a rather simple micromixer geometry (Figure 1) combines two fluids entering from different inlets into a single 10 m wide channel. The fluids then enter a ring-shaped mixing chamber that has four microelectrodes placed on the outer wall at angular positions of 45, 135, 45, and 135 degrees, respectively. Assume that the

1. This model is courtesy of H. Chen, Y. T. Zhang, I. Mezic, C. D. Meinhart, and L. Petzold of the University of California, Santa Barbara (Ref. 1 and Ref. 2). 1 | E L E C T R O O S M O T I C M I C R O M I X E R


2 | E L E Caspect ratio (channel depth to width) is large enough that you can model the mixer using a 2D cross-sectional geometry. The material parameters relevant for the model are given in Table 1.

1 2

34

10m

V0sin(t) V0sin(t)

V0sin(t)V0sin(t)

Figure 1: Geometry of the micromixer with four symmetric electrodes on the wall of the mixing chamber. This example does not model the two inlet channels. Here you assume a parabolic inflow at the beginning of the computational domain (the gray area).

The Navier-Stokes equations for incompressible flow describe the flow in the channels:

Here denotes the dynamic viscosity (kg/(ms)), u is the velocity (m/s), equals the fluid density (kg/m3), and p refers to the pressure (Pa).

Because you do not model the two inlet channels, assume that the entrance channel starts at a position where the flow has a fully developed laminar profile. The mixed fluid flows freely out of the right end boundary, where you specify vanishing total stress components normal to the boundary:

When brought into contact with an electrolyte, most solid surfaces acquire a surface charge. In response to the spontaneously formed surface charge, a charged solution forms close to the liquid-solid interface. Known as an electric double layer, it forms because of the charged groups located on the surface that faces the solution. When the operator applies an electric field, the electric field generating the electroosmotic flow displaces the charged liquid in the electric double layer. This scheme imposes a force on the positively charged solution close to the wall surface, and the fluid starts to flow

t

u u u( )T+( ) u u p+ + 0= u 0=

n pI u u( )T+( )+[ ] 0=T R O O S M O T I C M I C R O M I X E R

Solved with COMSOL Multiphysics 4.4in the direction of the electric field. The velocity gradients perpendicular to the wall give rise to viscous transport in this direction. In the absence of other forces, the velocity profile eventually becomes almost uniform in the cross section perpendicular to the wall.

This model replaces the thin electric double layer with the Helmholtz-Smoluchowski relation between the electroosmotic velocity and the tangential component of the applied electric field:

In this equation, w = 0r denotes the fluids electric permittivity (F/m), 0 represents the zeta potential at the channel wall (V), and V equals the potential (V). This equation applies on all boundaries except for the entrance and the outlet.

Assuming that there are no concentration gradients in the ions that carry the current, you can express the current balance in the channel with Ohms law and the balance equation for current density

where denotes conductivity (S/m) and the expression within parentheses represents the current density (A/m2).

The electric potentials on the four electrodes are sinusoidal in time with the same maximum value (V0 = 0.1 V) and the same frequency (8 Hz), but they alternate in polarity. The potentials on electrodes 1 and 3 are V0sin(2ft), whereas those on electrodes 2 and 4 are V0sin(2ft) (see Figure 1).Assume all other boundaries are insulated. The insulation boundary condition

sets the normal component of the electric field to zero.

At the upper half of the inlet (see Figure 1) the solute has a given concentration, c0; at the lower half the concentration is zero. Thus, assume that the concentration changes abruptly from zero to c0 at the middle of the inlet boundary. The mixed solution flows out from the right outlet by convection, and all other boundaries are assumed insulated.

Inside the mixer, the following convection-diffusion equation describes the concentration of the dissolved substances in the fluid:

uw0

------------ VT=

V( ) 0=

V n 0= 3 | E L E C T R O O S M O T I C M I C R O M I X E R


4 | E L E C (1)

Here c is the concentration, D represents the diffusion coefficient, R denotes the reaction rate, and u equals the flow velocity. In this model R = 0 because the concentration is not affected by any reactions.

PARAMETER VALUE DESCRIPTION

1000 kg/m3 Density of the fluid 10-3 Pas Dynamic viscosity of the fluid U0 0.1 mm/s Average velocity through the inlet

r 80.2 Relative electric permittivity of the fluid

-0.1 V Zeta potential on the wall-fluid boundary 0.11845 S/m Conductivity of the ionic solution

D 10-11 m2/s Diffusion coefficient

c0 1 mol/m3 Initial concentration

Results and Discussion

Figure 2 shows a typical instantaneous streamline pattern. It reveals that electroosmotic recirculation of the fluid vigorously stirs the flow, typically in the form of two rotating vortices near the electrodes.

The fundamental processes of effective mixing involve a combination of repeated stretching and folding of fluid elements in combination with diffusion at small scales. As the system applies the AC field (Figure 3), the resulting electroosmotic flow perturbs the laminar pressure-driven flow such that it pushes the combined stream pattern up and down at the beginning of the mixing chamber, causing extensive folding and stretching of material lines.

TABLE 1: MODEL INPUT DATA

ct----- Dc( )+ R u c=T R O O S M O T I C M I C R O M I X E R

Solved with COMSOL Multiphysics 4.4Figure 2: Fluid streamlines in an electroosmotic micromixer at t = 0.0375 s.

Figure 3: Electric potential lines for an electroosmotic micromixer. The contour lines show the shape when the device uses maximal potentials (V0). 5 | E L E C T R O O S M O T I C M I C R O M I X E R


6 | E L E CThe following plots further exemplify how the mixer operates. Figure 4 shows the concentration at steady state when the electric field is not applied. The flow is laminar and the diffusion coefficient is very small, so the two fluids are well separated also at the outlet. When the alternating electric field is applied, the mixing increases considerably owing to the alternating swirls in the flow. Figure 5 depicts the system at the instant when the electric field and the electroosmotic velocity have their largest magnitudes during the cycle (that is, when |sin t| = 1). From the plot you can estimate that the concentration at the output fluctuates with the same frequency as the electric field. Thus, this mixer should be further improved to get a steadier output.

Figure 4: Steady-state solution in the absence of an electric field.T R O O S M O T I C M I C R O M I X E R

Solved with COMSOL Multiphysics 4.4Figure 5: Time-dependent solution at the time when the alternating electric field has its largest magnitude.

This example demonstrates a rather simple and effective use of electrokinetic forces for mixing. The scheme is easy to implement, and you can easily control both the amplitude and the frequency. At low Reynold numbers the inertial forces are small, which makes it possible to calculate stationary streamlines patterns using the parametric solver to control amplitude.

Notes About the COMSOL Implementation

Cummings and others (Ref. 3) have shown that in order to use the Helmholtz-Smoluchowski equation at the fluid-solid boundaries, the electric field must be at least quasi-static to neglect transient effects. In other words, the time scale of the unsteady electric field must be much larger than that of the transient flow. Y. T. Zhang and others (Ref. 1) estimated that the time scale of the transient effect in the modeled micromixer (with a channel width of 10 microns) is roughly 0.0127 s. In this simulation the frequency of the applied electric potential is 8 Hz, which corresponds to a time scale of the electric field 10 times larger than that of the flow. 7 | E L E C T R O O S M O T I C M I C R O M I X E R


8 | E L E CBecause you can model the time-dependent electric field as a product of a stationary electric field and a time-dependent phase factor (sint), it is possible to reduce the simulation time and memory requirements by dividing the solution into two stages. In the first, calculate the amplitude of the electric potential field and the initial state for the time-dependent flow model using a stationary solver. In the second stage, you deactivate the Electric Currents interface and calculate the transient solution for the Laminar Flow and the Transport of Diluted Species interfaces. You obtain the tangential electric field components used in the electroosmotic velocity boundary condition by multiplying the stationary DC solution by sin(t). This approach is permissible because there is only a one-way coupling between the electric field and the fluid fields.

References

1. H. Chen, Y.T. Zhang, I. Mezic, C.D. Meinhart, and L. Petzold, Numerical Simulation of an Electroosmotic Micromixer, Proc Microfluidics 2003 (ASME IMECE), 2003.

2. Y.T. Zhang, H. Chen, I. Mezic, C.D. Meinhart, L. Petzold, and N.C. MacDonald, SOI Processing of a Ring Electrokinetic Chaotic Micromixer, Proc NSTI Nanotechnology Conference and Trade Show (Nanotech 2004), vol. 1, pp. 292295, 2004.

3. E. Cummings, S. Griffiths, R. Nilson, and P. Paul, Conditions for Similitude Between the Fluid Velocity and the Electric Field in Electroosmotic Flow, Anal. Chem., vol. 72, pp. 25262532, 2000.

Model Library path: Microfluidics_Module/Micromixers/electroosmotic_mixer


N E W



1 In the Model Wizard window, click the 2D button.T R O O S M O T I C M I C R O M I X E R

Solved with COMSOL Multiphysics 4.42 In the Select physics tree, select Fluid Flow>Single-Phase Flow>Laminar Flow (spf).


4 In the Select physics tree, select AC/DC>Electric Currents (ec).


6 In the Select physics tree, select Chemical Species Transport>Transport of Diluted Species (chds).



9 In the tree, select Preset Studies for Selected Physics>Stationary.


G L O B A L D E F I N I T I O N S

Parameters1 On the Home toolbar, click Parameters.

2 In the Parameters settings window, locate the Parameters section. 9 | E L E C T R O O S M O T I C M I C R O M I X E R


10 | E L E3 In the table, enter the following settings:

You need the constant t (used in the scalar expressions below) when first solving the model using a stationary solver. In the time-dependent simulation, the internal time variable, t, overwrites this constant.

Now define a smoothed step function that you will later use to impose a step in the concentration in the middle of the channel entrance.

Step 11 On the Home toolbar, click Functions and choose Global>Step.

2 In the Step settings window, click to expand the Smoothing section.

3 In the Size of transition zone edit field, type 0.1e-6.

G E O M E T R Y 1

1 In the Model Builder window, under Component 1 click Geometry 1.

2 In the Geometry settings window, locate the Units section.

3 From the Length unit list, choose m.

Rectangle 11 Right-click Component 1>Geometry 1 and choose Rectangle.


3 In the Width edit field, type 80.

Name Expression Value Description

U0 0.1[mm/s] 1.000E-4 m/s Mean inflow velocity

sigma_w 0.11845[S/m] 0.1185 S/m Conductivity of the ionic solution

eps_r 80.2 80.20 Relative permittivity of the fluid

zeta -0.1[V] -0.1000 V Zeta potential

V0 0.1[V] 0.1000 V Maximum value of the AC potential

omega 2*pi[rad]*8[Hz] 50.27 Hz Angular frequency of the AC potential

t 0[s] 0 s Start time

D 1e-11[m^2/s] 1.000E-11 m/s Diffusion coefficient of the solution

c0 1[mol/m^3] 1.000 mol/m Initial concentrationC T R O O S M O T I C M I C R O M I X E R

Solved with COMSOL Multiphysics 4.44 In the Height edit field, type 10.

5 Locate the Position section. From the Base list, choose Center.


Circle 11 In the Model Builder window, right-click Geometry 1 and choose Circle.

2 In the Circle settings window, locate the Size and Shape section.

3 In the Radius edit field, type 15.


Circle 21 Right-click Geometry 1 and choose Circle.

2 In the Circle settings window, locate the Size and Shape section.

3 In the Radius edit field, type 5.


Compose 11 On the Geometry toolbar, click Compose.

2 Click the Select All butt

comsol_v4.4_heat.pdf

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