introduction - mr-cfddl.mr-cfd.com/tutorials/ansys-fluent/01-inkjet.pdf · introduction the purpose...

Tutorial: Drop Ejection from a Printhead Nozzle

Introduction

The purpose of this tutorial is to provide guidelines for the transient simulation of dropejection from the nozzle of the printhead in an inkjet printer. The volume of fluid (VOF)model is used to predict the droplet shape. The time-dependent boundary condition requiresa user-defined function (UDF).

This tutorial demonstrates how to do the following:

• Use the VOF multiphase model.

• Use an UDF to define a time dependent boundary condition.

• Set up and solve the case using appropriate solver settings.

• Postprocess the resulting data.

Prerequisites

This tutorial is written with the assumption that you have completed Tutorial 1 fromANSYS FLUENT 13.0 Tutorial Guide, and that you are familiar with the ANSYS FLUENTnavigation pane and menu structure. Some steps in the setup and solution procedure willnot be shown explicitly.

In this tutorial, you will use VOF multiphase model. For details on VOF model, see Section26.3, Setting Up the VOF Model in ANSYS FLUENT 13.0 User’s Guide. This tutorial willnot cover the mechanics of using this model. Instead, it will focus on the application of thismodel to the drop ejection from a printhead nozzle. For more details on UDFs, see ANSYSFLUENT 13.0 UDF Manual.

Problem Description

The problem to be solved in this tutorial is shown in Figure 1.

To capture the capillary effect on the ejected ink, the surface tension and prescription ofthe wetting angle will be specified. The surface inside the nozzle is neutrally wettable, whilethe surface surrounding the nozzle orifice is non-wettable.

At time zero, ink fills the nozzle, while the rest of the domain is filled with air. Both fluidsare assumed to be at rest. To initiate the ejection, the ink velocity at the inlet boundarysuddenly rises from 0 to 3.58 m/s and drops according to a cosine law.

c© ANSYS, Inc. February 9, 2011 1


Figure 1: Schematic of the Problem

A user-defined subroutine is shown in the Appendix for reference. After 10 microseconds,the velocity returns to zero. The calculation is run for 30 microseconds overall, i.e., threetimes the duration of the initial impulse. Gravity is not included in the simulation. Due tothe axial symmetry of the problem a 2D geometry is used. The computation mesh consistsof 24,600 cells. The domain consists of two regions: an ink chamber and an air chamber.The ink chamber dimensions are summarized in the following table.

Ink chamber Cylindrical region: radius (mm) 0.015Ink chamber Cylindrical region: length (mm) 0.050Ink chamber Tapered region: final radius (mm) 0.009Ink chamber Tapered region: length (mm) 0.050Air chamber: radius (mm) 0.030Air chamber: length (mm) 0.280

Strategy

As the dimensions are small, ANSYS FLUENT is used with double precision. The primaryphase is air and the secondary phase is water-liquid. Patching is required to fill the inkchamber with the secondary phase.

2 c© ANSYS, Inc. February 9, 2011


Setup and Solution

Preparation

1. Copy the files (inkjet.msh, inlet1.c, and udfconfig.h) to your working folder.

2. Use FLUENT Launcher to start the 2D version of ANSYS FLUENT.

For more information about FLUENT Launcher see Section 1.1.2, StartingANSYS FLUENT Using FLUENT Launcher in ANSYS FLUENT 13.0 User’s Guide.

3. Enable Double-Precision in the Options list.

4. Click the UDF Compiler tab and ensure that the Setup Compilation Environment forUDF is enabled.

The path to the .bat file which is required to compile the UDF will be displayed as soonas you enable Setup Compilation Environment for UDF.

If the UDF Compiler tab does not appear in the FLUENT Launcher dialog box by default,click the Show More >> button to view the additional settings.

The Display Options are enabled by default. Therefore, after you read in the mesh, itwill be displayed in the embedded graphics window.

Step 1: Mesh

1. Read the mesh file (inkjet.msh).

File −→ Read −→Mesh...

As the mesh file is read, ANSYS FLUENT will report the progress in the console.

Step 2: General Settings

1. Define the solver settings.

General

(a) Select Transient from the Time list.

(b) Select Axisymmetric from the 2D Space list.

2. Check the mesh.

General −→ Check

ANSYS FLUENT will perform various checks on the mesh and will report the progressin the console. Make sure the minimum volume reported is a positive number.



3. Scale the mesh.

General −→ Scale...

(a) Select Specify Scaling Factors from the Scaling group box.

(b) Scale the mesh using 1e-6 as the Scaling Factors for X and Y.

(c) Select mm from View Length Unit In drop-down list.

(d) Click Scale.

(e) Close the Scale Mesh dialog box.

4. Define the units for the mesh.

Define −→Units...

(a) Select mm as the unit for length.

(b) Select dyn/cm as the unit for surface-tension.

(c) Close the Set Units dialog box.

5. Mirror the view across the axis.

Display −→Views...

(a) Select axis from the Mirror Planes list.

(b) Click Apply.

This updates the mesh display with both sides of the chamber.

(c) Click Camera... to open the Camera Parameters dialog box.

i. Drag the indicator of the dial with the left mouse button in the counter-clockwise direction until the upright view is displayed (see Figure 2).

ii. Click Apply and close the Camera Parameters dialog box.

(d) Click Apply and close the Views dialog box.



Figure 2: Mesh Display

Step 3: Models

1. Define the multiphase model.

(a) Select Volume of Fluid from the Model list.

(b) Click OK to close the Multiphase Model dialog box.



Step 4: Materials

The default properties of water and air are suitable for this problem. You can verify themin the Create/Edit Materials dialog box.

Materials −→ Create/Edit...

1. Retain the default settings for air.

2. Copy water-liquid (h2o<l>) from the database.

3. Click Change/Create and close the Create/Edit Materials dialog box.

Step 5: Phases

1. Select air for primary phase and enter air for the Name.

Phases −→ phase-1-Primary Phase −→ Edit...

2. Select water-liquid for secondary phase and enter water-liquid for the Name.

Phases −→ phase-2-Secondary Phase −→ Edit...

3. Define the Phase Interaction.

Phases −→ Interaction...



(a) Enable Wall Adhesion so that contact angles can be prescribed.

(b) Click the Surface Tension tab.

i. Select constant from the Surface Tension Coefficients drop-down list.

ii. Enter 73.5 dyn/cm for the value.

(c) Click OK to close the Phase Interaction dialog box.

Step 6: User-Defined Functions

Define −→ User-Defined −→ Functions −→Interpreted...

1. Enter inlet1.c for Source File Name.

Ensure that the C source code (udfconfig.h) for the UDF and the mesh file are inthe working folder. If the source code is not in the working folder, you must enter thecomplete folder path for the file in the Interpreted UDFs dialog box, instead of just thefile name. You can also use the Browse... button to select the file.

2. Click Interpret to compile the UDF.

3. Close the Interpreted UDFs dialog box.

Step 7: Boundary Conditions

1. Set the boundary conditions for inlet.

Boundary Conditions −→ inlet



(a) Select mixture from the Phase drop-down list and click the Edit....

i. Select udf membrane speed from the Velocity Magnitude drop-down list.

ii. Click OK to close the Velocity Inlet dialog box.

(b) Select water-liquid from the Phase drop-down list and click the Edit....

i. Click the Multiphase tab and enter 1 for Volume Fraction.

ii. Click OK to close the Velocity Inlet dialog box.

2. Set the boundary conditions for outlet.

Boundary Conditions −→ outlet −→ Edit...

(a) Select water-liquid from the Phase drop-down list and click the Edit....

i. Click the Multiphase tab and retain the default value of zero for BackflowVolume Fraction.

ii. Click OK to close the Pressure Outlet dialog box.

3. Set the conditions for wall no wet.

Boundary Conditions −→ wall no wet

(a) Select mixture from the Phase drop-down list and click Edit....

i. Enter 175 degrees in the Contact Angles group box.

ii. Click OK to close the Wall dialog box.

4. Set the conditions for wall wet.

Boundary Conditions −→ wall wet −→ Edit...

(a) Retain the default value of 90 degrees in the Contact Angles group box.

(b) Click OK to close the Wall dialog box.

Step 8: Operating Conditions

Boundary Conditions −→ Operating Conditions...



1. Enter 0.10 mm for X and 0.03 mm for Y in the Reference Pressure Location groupbox.

Set the Reference Pressure Location at a point where the fluid will always be 100% air.

2. Click OK to close the Operating Conditions dialog box.

Step 9: Solution

1. Set the solution method parameters.

Solution Methods

(a) Select PISO from the Scheme drop-down list.

(b) Select PRESTO! and Second Order Upwind from the Pressure and Momentumdrop-down lists respectively.

2. Retain the default solution control parameters.

Solution Controls



3. Enable the plotting of residuals during the calculation.

Monitors −→ Residuals −→ Edit...

(a) Enter 0.0001 for the Absolute Criteria for all equations.

(b) Click OK to close the Residual Monitors dialog box.

4. Initialize the solution.

Solution Initialization

(a) Retain 0 for Gauge Pressure, Axial Velocity, Radial Velocity, and water-liquid Vol-ume Fraction.

(b) Click Initialize.

5. Define a register for the ink chamber region.

Adapt −→Region...

(a) Enter 0 for X Min and 0.10 mm for X Max.

(b) Enter 0 for Y Min and 0.03 mm for Y Max.

(c) Click Mark.

(d) Close the Region Adaption dialog box.

You can display and manipulate the generated adaption registers using theManage... button in the Region Adaption dialog box.



6. Patch the initial distribution of water-liquid.

Solution Initialization −→ Patch...

(a) Select water-liquid from the Phase drop-down list.

(b) Select Volume Fraction from the Variable list.

(c) Select hexahedron-r0 from the Registers to Patch list.

(d) Enter 1 for the Value.

(e) Click Patch.

(f) Close the Patch dialog box.

7. Autosave the data files every 100 steps.

Calculation Activities

(a) Enter 100 for Autosave Every (Time Steps).

(b) Click Edit... to open Autosave dialog box.

i. Retain the default settings.

ii. Click OK to close the Autosave dialog box.

8. Save the initial case and data files (inkjet.cas/dat.gz).

9. Set the time-stepping parameters.

Run Calculation

(a) Enter 2.0e-8 s for Time Step Size.

(b) Enter 1500 for Number of Time Steps.

(c) Retain the default selection of Fixed in the Time Stepping Method list.

(d) Click Calculate.



Step 10: Postprocessing

1. Read the data file, inkjet0300.dat.

(a) Display filled contours of water volume fraction after 6 microseconds.

Graphics and Animations −→ Contours −→ Set Up...

i. Enable Filled in the Options group box.

ii. Select Phases... and Volume fraction from the Contours of drop-down lists.

iii. Select water-liquid from the Phase drop-down list.

iv. Click Display (see Figure 3).

Figure 3: Contours of water Volume Fraction After 6 µs

2. Similarly, display the contours of water-liquid volume fraction after 12, 18, 24, and 30microseconds (see Figures 4-7) using the corresponding data files: inkjet0600.dat,inkjet0900.dat, inkjet1200.dat, and inkjet1500.dat, respectively.



Figure 4: Contours of water-liquid Volume Fraction After 12 µs




Appendix

The contents of the UDF input file (inlet1.c) are as follows:

#include "udf.h"

#include "sg.h"

#include "sg_mphase.h"

#include "flow.h"

#define PI 3.141592654

DEFINE_PROFILE(membrane_speed, /* function name */

th , /* thread */

nv) /* variable number */

{

face_t f;

real x[ND_ND];

real f_time = RP_Get_Real("flow-time");

begin_f_loop (f,th)

{

F_CENTROID(x,f,th);

if (f_time<=10e-6)

{F_PROFILE(f,th,nv) = 3.58*cos(PI*f_time/30e-6);

}

else F_PROFILE(f,th,nv) = 0;

}

end_f_loop (f,th)

}

Results

The VOF model in ANSYS FLUENT was adequately able to predict the formation anddevelopment of an ink droplet ejected from the printhead of an inkjet printer.

Summary

This tutorial demonstrated the application of the VOF model with surface tension effects.The ANSYS FLUENT calculation agreed well with the prediction published in the literatureusing the same injection scenario. Good agreement was achieved in predicting the numberand volume of the ink droplets. As these parameters are crucial to the print quality, ANSYSFLUENT VOF model can be used in the design of inkjet printheads.

References

[1] W. J. Rider, D.B. Kothe, E.G. Pucket, I. D. Aleinov “Accurate and robust methodsfor variable density incompressible flow with discontinuities”, 1996, Proc. of ICASE/LaRCworkshop on barriers and challenges in CFD, NASA Langley Research Center, Hampton,Virginia, August 5-7, M. Salas (Ed.), Kluwer Academic Publishers (in press).


introduction - mr-cfddl.mr-cfd.com/tutorials/ansys-fluent/01-inkjet.pdf · introduction the purpose...

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