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Falling Box

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Tutorial: Solving a 2D Box Falling into Water Introduction The purpose of this tutorial is to provide guidelines and recommendations for setting up and solving a dynamic mesh (DM) case along with the six degree of freedom (6DOF) solver and the volume of fluid (VOF) multiphase model. The 6DOF UDF is used to calculate the motion of the moving body which also experiences a buoyancy force as it hits the water (modeled using the VOF model). Gravity and the bouyancy forces drive the motion of the body and the dynamic mesh. This tutorial demonstrates how to do the following: Use the 6DOF solver to calculate motion of the moving body. Use the VOF multiphase model to model the buoyancy force experienced by the moving body. Set up and solve the dynamic mesh case. Create TIFF files for graphic visualization of the solution. Postprocess the resulting data. Prerequisites This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have a good understanding of the basic setup and solution procedures. Some basic steps in the setup and solution procedure will not be shown explicitly. Problem Description The schematic of the problem is shown in Figure 1. The tank is partially filled with water. A box is dropped into the water at time t = 0. The box is subjected to a viscous drag force and a gravitational force. When the box is immersed in water, it is also subjected to a buoyancy force. The walls of the box undergo a rigid body motion and will displace according to the cal- culation performed by the 6DOF solver. Whenever the box and its surrounding boundary layer mesh are displaced, the mesh outside of the boundary layer will be smoothed and/or remeshed. c Fluent Inc. October 12, 2006 1
Transcript

Tutorial: Solving a 2D Box Falling into Water

IntroductionThe purpose of this tutorial is to provide guidelines and recommendations for setting up and solving a dynamic mesh (DM) case along with the six degree of freedom (6DOF) solver and the volume of uid (VOF) multiphase model. The 6DOF UDF is used to calculate the motion of the moving body which also experiences a buoyancy force as it hits the water (modeled using the VOF model). Gravity and the bouyancy forces drive the motion of the body and the dynamic mesh. This tutorial demonstrates how to do the following: Use the 6DOF solver to calculate motion of the moving body. Use the VOF multiphase model to model the buoyancy force experienced by the moving body. Set up and solve the dynamic mesh case. Create TIFF les for graphic visualization of the solution. Postprocess the resulting data.

PrerequisitesThis tutorial assumes that you are familiar with the menu structure in FLUENT and that you have a good understanding of the basic setup and solution procedures. Some basic steps in the setup and solution procedure will not be shown explicitly.

Problem DescriptionThe schematic of the problem is shown in Figure 1. The tank is partially lled with water. A box is dropped into the water at time t = 0. The box is subjected to a viscous drag force and a gravitational force. When the box is immersed in water, it is also subjected to a buoyancy force. The walls of the box undergo a rigid body motion and will displace according to the calculation performed by the 6DOF solver. Whenever the box and its surrounding boundary layer mesh are displaced, the mesh outside of the boundary layer will be smoothed and/or remeshed.

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Tutorial: Solving a 2D Box Falling into Water

Figure 1: Schematic of the Problem

Preparation1. Copy the les, 6dof-mesh.msh.gz and 6dof 2d.c to your working folder. 2. Create a subfolder named tiff-files to store the tiff les created for postprocessing purposes. 3. Start the 2D version of FLUENT.

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Setup and SolutionStep 1: Grid 1. Read the mesh le 6dof-mesh.msh.gz. File Read Case... 2. Check the grid. Grid Check 3. Display the grid (Figure 2). Display Grid...

Grid

FLUENT 6.3 (2d, pbns, lam)

Figure 2: Grid Display

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Step 2: Models 1. Dene the solver settings. Dene Models Solver... (a) Select Unsteady from the Time list. (b) Retain the default selection of 1st-Order Implicit for Unsteady Formulation. (c) Select the Green-Gauss Node Based option from the Gradient Option list. (d) Click OK to close the Solver panel. 2. Dene the multiphase model. Dene Models Multiphase... (a) Select Volume of Fluid from the Model list. (b) Set Number of Phases to 2. (c) Retain the default settings for VOF Scheme and Courant Number. (d) Enable Implicit Body Force formulation. (e) Click OK to close the Multiphase Model panel. 3. Enable the standard k- turbulence model. Dene Models Viscous... Step 3: Compile the UDF Dene User-Dened Functions Compiled... 1. Click the Add... button in the Source Files section to open the Select File panel. 2. Select the source le, 6dof 2d.c and click OK. 3. Click Build to build the library. A Warning dialog box will open asking you to make sure that the UDF source les are in the same folder that contains the case and data les. (a) Click OK. FLUENTwill compile the code and show the progress in the console. Monitor the progress for compilation and linking errors. 4. Click Load to load the newly created UDF library.

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Step 4: Materials Dene Materials... 1. Retain the properties of air. 2. Copy water-liquid (h2o) from the FLUENTdatabase. 3. Modify the properties of water-liquid(h2o). (a) Select user-dened from the Density drop-down list and water density from the User-Dened Functions panel. (b) Select user-dened from the Speed of Sound drop-down list and water speed of sound from the User-Dened Functions panel. (c) Click Change/Create and close the Materials panel. Step 5: Phases Dene Phases... 1. Dene the primary phase (water). Dene Phases... (a) Select phase-1 and click Set... to open the Primary Phase panel. (b) Enter water for Name, . (c) Select water-liquid from the Phase Material drop-down list. (d) Click OK. 2. Similarly, dene the secondary phase (air), specifying air for Name and air for Phase Material.

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Step 6: Operating Conditions Dene Operating Conditions... 1. Enter 101325 pascal for Operating Pressure. 2. Enable Gravity. The panel expands to show additional inputs. 3. Enter -9.81 m/s2 for Gravitational Acceleration in the Y direction. 4. Enable Specied Operating Density and retain the default setting of 1.225 kg/m3 for Operating Density. Step 7: Boundary Conditions Dene Boundary Conditions... 1. Dene the boundary conditions for tank outlet. (a) Set the boundary conditions for the mixture phase. i. Select mixture from the Phase drop-down list and click Set.... ii. Select Intensity and Viscosity Ratio from the Turbulence Specication method drop-down list. iii. Enter 1 % for Backow Turbulence Intensity and 10 for Backow Turbulent Viscosity Ratio. iv. Click OK to close the Pressure Outlet panel. (b) Set the boundary conditions for the air phase. i. Select air from the Phase drop-down list and click Set.... ii. Click the Multiphase tab and enter 1 for Backow Volume Fraction. iii. Click OK to close the Pressure outlet panel. (c) Close the Boundary Conditions panel.

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Tutorial: Solving a 2D Box Falling into Water

Step 8: Dynamic Mesh Setup 1. Set the dynamic mesh parameters. Dene Dynamic Mesh Parameters... (a) Enable Dynamic Mesh from the Models list. The panel expands to show additional inputs.

(b) Enable Six DOF Solver from the Models list. (c) Enable Smoothing and Remeshing from the Mesh Methods list. (d) Enter 0.5 for Spring Constant Factor. (e) Click the Remeshing tab and set the remeshing parameters.

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Tutorial: Solving a 2D Box Falling into Water

i. Enter 0.056 m for Minimum Length Scale and 0.13 m for Maximum Length Scale. The Minimum Length Scale and Maximum Length Scale can be obtained from the Mesh Scale Info panel. Click the Mesh Scale Info... button to open the Mesh Scale Info panel. ii. Enter 0.5 for Maximum Cell Skewness. Gravitational acceleration must be specied in the Six DOF Solver tab. The necessary parameters have already been specied in the Operating Conditions panel. Hence, you need not do so again. (f) Click OK to close the Dynamic Mesh Parameters panel. 2. Set up the moving zones. Dene Dynamic Mesh Zones...

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(a) Create the dynamic zone, moving box. i. Select moving box from the Zone Names drop-down list. ii. Select Rigid Body from the Type list. iii. Select test box::libudf from the Six DOF UDF drop-down list. iv. Enable On from the Six DOF Solver Options group box. v. Click Create. FLUENTwill create the dynamic zone moving box which will be available in the Dynamic Zones list. (b) Create the dynamic zone, moving uid. i. Select moving uid from the Zone Names drop-down list. ii. Select Rigid Body from the Type list. iii. Select test box::libudf from the Six DOF UDF drop-down list. iv. Enable On and Passive from the Six DOF Solver Options group box. v. Click Create. FLUENTwill create the dynamic zone moving uid which will be available in the Dynamic Zones list. 9

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Tutorial: Solving a 2D Box Falling into Water

(c) Close the Dynamic Mesh Zones panel. Step 9: Mesh Preview The purpose of the preview is to verify the quality of the mesh yielded by the mesh motion parameters. Since the ow is not initialized, the motion of the box will be vertical due to gravity. 1. Save the case le, 6dof-init.cas.gz. 2. Display the grid. 3. Preview the motion. Solve Mesh Motion...

(a) Enter 0.0005 for Time Step Size. (b) Enter 1000 for Number of Time Steps. (c) Click Preview (Figures 3 and 4). The motion is acceptable. (d) Close the Mesh Motion panel. 4. Exit FLUENTwithout saving.

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Tutorial: Solving a 2D Box Falling into Water

Grid (Time=2.5000e-01)

FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 3: Motion at t = 0.25 s

Grid (Time=5.0000e-01)

FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 4: Mesh Motion at t = 0.5 s

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Step 10: Solution Parameters 1. Start the 2D version of FLUENTand read the le 6dof-init.cas.gz. 2. Set the solution parameters. Solve Controls Solution... (a) Select PRESTO! from the Pressure drop-down list in the Discretization group box. (b) Select Second Order Upwind for all other equations except Volume Fraction. (c) Retain the default discretization method of Geo-Reconstruct for Volume Fraction. (d) Select Coupled from the Pressure-Velocity Coupling drop-down list. (e) Enter 1000000 for Courant Number. (f) Enter 1.0 for Momentum and Pressure in the Explicit Relaxation Factors group box. (g) Enter 0.5 for Body Forces in the Under Relaxation Factor group box. (h) Click OK to close the Solution Controls panel. 3. Initialize the solution. Solve Initialize Initialize... (a) Enter 0.001 m2 /s2 for Turbulence Kinetic Energy and 0.001 m2 /s3 for Turbulence Dissipation Rate. (b) Enter 1 for air Volume Fraction. (c) Click Init and close the Solution Initialization panel. 4. Create an adaption register for patching. Adapt Region... (a) Set the Input Coordinates as follows: Input Co-ordinates Xmin(m),Xmax(m) Ymin(m),Ymax(m) (b) Click Mark. (c) Close the Region Adaption panel. 5. Patch the air volume fraction. Solve Initialize Patch... (a) Select air from the Phase drop-down list. (b) Select Volume Fraction from the Variable selection list. (c) Select hexahedron-r0 from the Registers to Patch selection list. (d) Retain the default Value of zero. (e) Click Patch. Values (-5,5) (-5,-1.5)

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(f) Close the Patch panel. 6. Enable the plotting of residuals. Solve Monitors Residual... (a) Enable Plot in the Options list. (b) Enter 400 for number of iterations in the Plotting group box. 7. Dene a surface monitor for Y Velocity. Solve Monitors Surface... (a) Increase the number of Surface Monitors to 1. (b) Enable Plot, Print, and Write for monitor-1. (c) Select Time Step from the When drop-down list. (d) Click the Dene... button to open the Dene Surface Monitor panel. i. Select Area-Weighted Average from the Report Type drop-down list. ii. Select Flow Time from the X Axis drop-down list. iii. Retain the default setting of 1 for Plot Window. iv. Select Velocity... and Y Velocity from the Report of drop-down lists. v. Select moving box from the Surfaces selection list. vi. Enter 6dof yvel.out for File Name. vii. Click OK. (e) Click OK to close the Surface Monitors panel. 8. Activate Autosave option. File Write Autosave... (a) Enter 100 for Autosave Case File Frequency. (b) Enter 100 for Autosave Data File Frequency. (c) Enable Overwrite Existing Files option. (d) Set the Maximum Number of Each File Type to 2. (e) Enter falling-box.gz for File Name. FLUENTwill append the timestep number so that each le created has a unique lename. (f) Click OK to close the Autosave Case/Data panel. Step 11: Set Hardcopy Options File Hardcopy... 1. Select TIFF from the Format list. 2. Select Color from the Coloring list. 13

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Tutorial: Solving a 2D Box Falling into Water

3. Select Raster from the File Type list. 4. Enter 800 (pixels) for Width and 600 (pixels) for Height in the Resolution group box. 5. Click Apply and close the Graphics Hardcopy panel. Step 12: Dene commands to create TIFF les for animation purposes Solve Execute Commands... 1. Set Dened Commands to 4. 2. Dene the commands as follows:

Command-1 Command-2 Command-3 Command-4

Every 100 100 100 100

When Time Step Time Step Time Step Time Step

Command display set-window 2 display contour water vof 0 1 display hard-copy "tiff-files/box-%t.tiff" display set-window 3

Be sure to create the subfolder ti-les before clicking the OK button. 1. Enable On for the four commands. 2. Click OK to close the Execute Commands panel. Step 13: Solution 1. Set the iteration parameters. (a) Enter 0.0005 for Time Step Size. (b) Enter 10000 for Number of Time Steps. (c) Set Max Iterations per Time Step to 50. (d) Click Iterate. Step 14: Postprocessing 1. Convert the TIFF les in the subfolder ti-les to form an animation sequence for postprocessing purposes, using a third party software package like QuickTime or Fast Movie Player. Figures 524 show the contours of volume fraction of water at dierent time steps.

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Tutorial: Solving a 2D Box Falling into Water

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=2.5000e-01) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=5.0000e-01) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 5: Contours at t = 0.25 s

Figure 6: Contours at t = 0.5 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=7.5001e-01) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=1.0000e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 7: Contours at t = 0.75 s

Figure 8: Contours at t = 1.0 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=1.2500e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=1.5000e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 9: Contours t = 1.25 s

Figure 10: Contours t = 1.5 s

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Tutorial: Solving a 2D Box Falling into Water

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=1.7500e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=1.9999e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 11: Contours at t = 1.75 s

Figure 12: Contours at t = 2.0 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=2.2499e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=2.4999e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 13: Contours of at t = 2.25 s

Figure 14: Contours at t = 2.5 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=2.7499e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=2.9999e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 15: Contours at t = 2.75 s

Figure 16: Contours at t = 3.0 s

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1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=3.2499e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=3.4998e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 17: Contours at t = 3.25 s

Figure 18: Contours at t = 3.5 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=3.7498e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=3.9998e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 19: Contours at t = 3.75 s

Figure 20: Contours at t = 4.0 s

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=4.2499e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=4.5000e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 21: Contours at t = 4.25 s

Figure 22: Contours at t = 4.5 s

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1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

1.00e+00 9.50e-01 9.00e-01 8.50e-01 8.00e-01 7.50e-01 7.00e-01 6.50e-01 6.00e-01 5.50e-01 5.00e-01 4.50e-01 4.00e-01 3.50e-01 3.00e-01 2.50e-01 2.00e-01 1.50e-01 1.00e-01 5.00e-02 0.00e+00

Contours of Volume fraction (water) (Time=4.7501e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Contours of Volume fraction (water) (Time=5.0002e+00) FLUENT 6.3 (2d, pbns, dynamesh, vof, ske, unsteady)

Figure 23: Contours at t = 4.75 s

Figure 24: Contours at t = 5.0 s

SummaryThis tutorial demonstrated the setup and solution of a dynamic mesh case along with the 6DOF solver and the VOF multiphase model. The 6DOF UDF was used to calculate the motion of the box dropped into the water. The TIFF les created in the tutorial can be used to provide a graphic visualization of the solution.

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