problem description - adina · problem description in this problem, we perform a fully-coupled...

Problem 66: FSI analysis of a piston with suction reed valve

ADINA R & D, Inc. 66-1

Problem description In this problem, we perform a fully-coupled fluid-structure interaction analysis of a piston with a suction reed valve.

Inlet channel

Reed valve

Piston motion

Piston cylinder

In this model we consider the expansion process in a reciprocating compressor. The analysis starts with the piston at top dead center (fully compressed fluid), and ends with the piston at bottom dead center (fully expanded fluid). The inlet of the inlet channel is at atmospheric pressure. As the piston moves upwards, the pressure in the piston cylinder decreases and, when the pressure in the piston cylinder is low enough, the reed valve opens and fluid enters the piston cylinder. Overview of fluid model A diagram of the fluid model is shown schematically on the next page. This diagram gives the fluid properties. The k turbulence model is employed with an ideal gas law.


66-2 ADINA Primer

Fluid properties:

μ = 2.18 10 g�-8

/(mm∙ms)

k = 4.00 10 (g�-5

∙mm)/(ms∙K)2 2

cp = 1011 mm /(ms K)∙= 825 mm /(ms K)cv

2 2∙

Valve (shell thickness = 0.2 mm)

Gap 0.2 mm (Layer 1)

Initial height0.5 mm (Layer 2)

15.0 mm

Not drawn to scale 8.0 mm

Piston cylinder

Piston (moving wall)

Inletchannel

32.6 mm

The units chosen for this problem are length: mm time: ms mass: grams temperature: degrees K

The corresponding force unit is 2

g - mm

ms, and 1 N = 1

2

g - mm

ms. The corresponding pressure

unit is 2

g

mm - ms, and 1 MPa = 1

2

g

mm - ms.

Also shown is a gap boundary condition. This gap condition separates the fluid in the inlet channel from the fluid in the piston cylinder. As will be seen, the gap condition is controlled by the motion of the valve; as the valve opens, the gap opens and as the valve closes, the gap closes.

Also notice that there is a small layer of fluid directly below the valve. The geometry of this layer changes as the valve moves, however the layer is always present, even when the valve is closed.



Initial conditions The next figure shows the initial conditions:

Initial conditions in inlet channel:Pressure: 0.113 g/(mm ms∙

2)

Temperature: 338 K

Initial conditions in piston cylinder:Pressure: 1.4 g/(mm ms∙

2)

Temperature: 383 K

Inlet conditions:

Normal traction: 0.113 g/(mm ms∙2)

Temperature: 338 KTurbulence intensity = 0.025Turbulence mean time-averaged velocity = 150 mm/msTurbulence dissipation length scale = 8 mm It is seen that there is an unbalanced pressure acting on the valve. If we begin the expansion process with the valve undeformed and at rest, the unbalanced pressure dynamically deforms the valve at the same time that the expansion process begins. This causes convergence difficulties at the start of the solution. Therefore we solve this problem in two parts. During the first part of the solution, we apply the initial fluid pressures to the valve using a steady-state analysis, and solve for the static deformed shape of the valve. Then we restart with a transient analysis. This modeling decision is discussed in more detail in the Modeling Comments at the end of this primer problem.


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Thus the initial conditions for the transient analysis are as shown in the following figure:

Initial conditions in inlet channel:Pressure: 0.113 g/(mm ms∙

2)

Temperature: 338 K

Initial conditions in piston cylinder:Pressure: 1.4 g/(mm ms∙

2)

Temperature: 383 K

Contact forces

At the beginning of the transient analysis, the valve is in static equilibrium under the initial fluid pressures and contact forces. Piston motion The piston is assumed to be connected to a crankshaft rotating at 3600 rpm. The next figure shows the piston motion as a function of time:

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

0.

2.

4.

6.

8.

10.

12.

14.

16.

18.

Pis

ton m

otion (

mm

)

Time (ms)

Transient

Steady-state



During the first millisecond, the piston is motionless. (It is during this first millisecond that the steady-state analysis is performed.) Then the piston moves upwards with a sinusoidal motion until the piston reaches bottom dead center. Overview of fluid boundary conditions The next figure shows the geometry used to build the fluid model, along with the boundary conditions applied to the fluid model. The blue geometry corresponds to the piston cylinder and the green geometry corresponds to the inlet channel.

Gap boundarycondition

Fluid-structureboundary condition

Moving wallboundary condition

The FCBI-C element is used in the fluid part of the model.


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Overview of solid model The following figure shows the solid element model.

Reed valve, modeledwith shell elements

Valve seat, modeled withrigid contact segments

Chamfer

E=207000 g/mm-ms2

�=0.29

�=0.00792 g/mm3

Thickness = 0.2 mm

Clamped

Contact between the reed valve and valve seat prevents the valve from moving through the bottom wall of the piston cylinder. The valve is the contactor and the valve seat is the target. The chamfer is used so that a contactor node that is in contact on the boundary of the hole in the target does not abruptly change contact state as the contactor node moves slightly.



The contact offsets used are shown in more detail in the next figure.

Offset applied tocontactor surface

Valve seat

Offset surfaces separated in this figure for clarity. Offset applied totarget surface

0.2 mm

0.1

0.1

Valve

Fluid layer 1

The contactor and target offsets are used so that the fluid layer between the valve and valve seat does not collapse when the valve is in contact with the valve seat. Topics demonstrated In this primer problem, we will demonstrate the following topics that have not been presented in previous problems.

Using low-speed compressible flow assumptions with the total energy formulation. Using the boundary layer tables to create boundary layers on a mesh of 2D elements. Using the body sweep feature to generate a 3D fluid mesh from 2D elements. Using the zone group feature to organize the Model Tree Using the mesh split feature on 3D fluid elements. Defining coincident FSI boundaries for use with shell elements. Defining a moving wall special boundary condition. Defining a wall special boundary condition applied to all external boundaries. Defining a gap special boundary condition. Adjusting the primary relaxation factors for the FCBI-C element. Using a contact surface extension factor in the structural model. Plotting the fluid densities. Calculating the mass flux and integrated mass flux through a gap boundary condition.

Before you begin Please refer to the Icon Locator Tables chapter of the Primer for the locations of all of the AUI icons. Please refer to the Hints chapter of the Primer for useful hints. This problem cannot be solved with the 900 nodes version of the ADINA System because this model contains more than 900 nodes.


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This problem might take several hours to run on your computer. Much of the input for this problem is stored in files prob66_1.in, prob66_1.x_t, prob66_2.in, and prob66_2.x_t. You need to copy these files from the folder samples\primer into a working directory or folder before beginning this analysis. Invoking the AUI and choosing the finite element program Invoke the AUI and set the Program Module drop-down list to ADINA Structures. Model definition for the structural model Batch file prob66_1.in contains commands for defining the model control data, generating the structural geometry and mesh, applying fixities, and setting the material properties. Choose FileOpen Batch, select file prob66_1.in and click Open. The graphics window should look something like this:

TIME 1.000

X Y

Z

The geometry defined in this batch file is shown in the figure on the next page. We will refer to this geometry in the following instructions.



B2

F1

S20

S21

S22

S23S24 S25

S26S19

S15

S16

S17S18

F2

Defining the FSI boundary conditions All free surfaces of the reed valve are exposed to fluid and must be defined as an FSI boundary. We need to define two coincident FSI boundaries, one for the top surface of the shell element group, and a second for the bottom surface of the shell element group. Choose Model→Boundary Conditions→FSI Boundary, add Boundary Number 1 and set the Apply to field to Faces. Fill in the table as follows and click Save. Do not close the dialog box.

Face 1 2

Click the Copy... button and copy the boundary condition to boundary condition 2, and click OK.

When you click the Redraw icon , the graphics window should look something like the figure on the next page.


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TIME 1.000

X Y

Z

If you click the Query icon and click repeately on one of the yellow lines, you will see text similar to Fsboundary 1, cell 63 Fsboundary 1, cell 64 Fsboundary 2, cell 63 Fsboundary 2, cell 64 ... This text shows that there are two coincident fluid-structure boundaries. (Note, if you are using the OpenGL graphics system, you will likely only see text for Fsboundary 2. Choose Edit→Graphics System and select either X Window or Windows GDI in order to see text for both fsboundaries.)

Click the Show Fluid Structure Boundary icon to hide the fluid-structure boundaries. Defining the contact conditions

Click the Contact Groups icon and add contact group 1. Set the type to 3-D Contact. Set the Compliance Factor to 1E-4, set the “Offset Distance from Defined Surface” to 0.1 and click OK.



Click the Define Contact Surfaces icon , add contact surface 1, and set the Description to "Reed valve". Set “Defined on” to “Faces on Body #” and set the Body # to 2. Check the “Specify Orientation” field. Fill in the table as follows and click Save. (Do not close the dialog box yet.)

Face Body # Orientation 1 Opposite to Geometry 2 Opposite to Geometry

Add contact surface 2 and set the Description to "Valve seat". Set “Defined on” to “Surfaces”, fill in the table as follows and click OK.

Surface 15 16 17 18 19 20 21 22 23 24 25 26

Click the Define Contact Pairs icon , add contact pair 1, set the Target Surface to 2 and the Contactor Surface to 1, then click OK.

Click the Mesh Rigid Contact Surface icon , set the Contact Surface to 2 and click OK.

After you click the Color Element Groups icon , the graphics window should look something like the top figure on the next page.


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TIME 1.000

X Y

Z

To verify that the contact surface orientations are correct, display zone CG1 using the Model

Tree, then click the Show Segment Normals icon . The graphics window should look something like this:

TIME 1.000

X Y

Z



All of the magenta arrows should point upwards and all of the cyan arrows should point downwards. Generating the ADINA Structures data file and saving the AUI database

Click the Data File/Solution icon , set the file name to prob66_aa, uncheck the “Run

Solution” button, and click Save. Now click the Save icon and save the database to file prob66_a. ADINA-CFD model

Click the New icon to create a new database (you can discard all changes), and set the Program Module drop-down list to ADINA CFD. Importing the geometry We will start from an initial 2D geometry that has already been defined. Click the Import

Parasolid Model icon , choose prob66_2.x_t, and click Open. The graphics window should look something like this:

TIME 1.000

X

Y

Z


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Building the fluid mesh geometry, overview The following figures show the steps that we will follow in building the fluid mesh geometry. Predefined geometry This figure shows the faces and edges of geometry body 1 (which is the body that we just imported). This geometry body is at the base of the piston cylinder.

F1

F2

F3

E1

E2E3

E4

E5

E6

E7

E8

E9

E10

E11

E12

E13E14

E15

E16

E17

E18

E19

E20

E21

E22

E23

E24F4

Inlet channel, below base of piston cylinder Faces 1 and 4 of body 1 are swept downwards to form the inlet channel. The resulting bodies are shown in the top figure on the next page (shown in exploded view).



B2

B1 F1F4

F5F5

B3

Face 5 of body 2 and face 5 of body 3 are at the inlet. Inlet channel, above base of piston cylinder Faces 1 and 4 of body 1 are swept upwards to form the fluid region in the inlet channel that is just below the valve, as shown in the next figure.

B1

B2

B3

B4

F5

F1

F2

F3

F4

F3

F4

F5

B5

F1F4

Faces 1, 3, 4 of body 4 and faces 2, 3, 4 of body 5 are used for the gap boundary condition.


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Face 5 of body 4 and face 5 of body 5 will be used in a subsequent sweep operation. Piston cylinder, below valve Faces 2 and 3 of body 1 are swept upwards to form the rest of the piston cylinder below the valve, as shown in the next figure.

B1

B6

F18

F16F17

F15

B7

B2B3

F2

F3

Piston cylinder, above valve Face 5 of body 4, face 5 of body 5, face 17 of body 6 and face 15 of body 7 are swept upwards to form the piston cylinder above the valve, as shown in the figure on the next page.



B1

B6

B7

F17

F15

B10

F17

F15

B11

B2B3

F5F5

B4B5

B8F5

F5B9

The shaded faces are the faces at the top of the piston cylinder. A moving wall boundary condition will be prescribed at these faces.


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Building the fluid mesh Meshing geometry body 1 Before performing the body sweep operations described above, we will mesh geometry body 1. In order to create thin elements near the walls, we will use boundary layer tables. Choose Meshing→Mesh Density→Complete Model, set the Subdivision Mode to Use Length, set the Element Edge Length to 1.25 and click OK.

Click the Subdivide Edges icon , set the Edge Number to 1, set the Element Edge Length to 1.8, enter 12, 13, 14, 22, 23 in the first five rows of the table and click Save. Now set the Edge Number to 24, set the Method to Use Number of Divisions, set the Number of Subdivisions to 5 and click OK.

Click the Mesh Faces icon and click the + to the right of the Element Group text. The Element Group number should be 1. Then click the ... button to the right of the Boundary Layer Table field. In the Define Boundary Layer Table dialog box, add table 1, set the Number of Layers to 3, the Default Settings to “Generate on All Edges Except Those Specified in Table”, the Thickness of First Layer to 0.5, the Total Thickness to 2, enter the following information into the table and click OK. Edge Body # 1st Layer Thickness

24 1 0 In the Mesh Faces dialog box, make sure that the Boundary Layer Table is set to 1, enter the following information into the table and click OK.

Face Body # 1 1 4 1

The graphics window should look something like the figure on the next page.



TIME 1.000

X

Y

Z

Click the Mesh Faces icon , then click the ... button to the right of the Boundary Layer Table field. In the Define Boundary Layer Table dialog box, add table 2, set the Number of Layers to 3, the Default Settings to “Generate on All Edges Except Those Specified in Table”, the Thickness of First Layer to 0.15, the Total Thickness to 1.25, enter the following information into the table and click OK. Edge Body # 1st Layer Thickness

1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 9 1 0

10 1 0 11 1 0 12 1 0 13 1 0 14 1 0 22 1 0 23 1 0


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In the Mesh Faces dialog box, make sure that the Boundary Layer Table is set to 2, enter the following information into the table and click OK.

Face Body # 2 1 3 1

The graphics window should look something like this:

TIME 1.000

X

Y

Z

Meshing the inlet channel below the piston cylinder (geometry bodies 2 and 3)

Click the Body Sweep icon , set the Vector Direction to (0, 0, -15), check the “Generate 3-D Mesh from 2-D mesh on Face” button and click the + button to the right of the 3-D Element Group field. The 3-D Element Group number should be 2. Then make sure that the “Action on 2-D Mesh” is set to “Delete elements + group”, set the “# of Elements in Swept Direction” to 15 and the Last/First Element Size Ratio to 5. Fill in the table as follows and click Apply (we do not want to close the dialog box yet).

Face Body # 1 1 4 1



Move the dialog box out of the way of the graphics window. When you click the Iso View 1

icon , the graphics window should look something like this:

TIME 1.000

X Y

Z

Use the Model Tree to plot just zone EG1. The graphics window should look something like this:

TIME 1.000

X Y

Z


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Notice that the elements in element group 1 that were used for the sweep operation have been deleted. To return to the previous view, use the Model Tree to plot the WHOLE_MODEL zone. Meshing the inlet channel above the piston cylinder (geometry bodies 4 and 5) In the Body Sweep dialog box, set the Vector Direction to (0, 0, 0.2), make sure that the “Generate 3-D Mesh from 2-D mesh on Face” button is checked and make sure that the 3-D Element Group is set to 2. Set the “# of Elements in Swept Direction” to 5 and the Last/First Element Size Ratio to 1. Fill in the table as follows and click Apply (we do not want to close the dialog box yet).

Face Body # 6 2 6 3

Use the Zoom icon to enlarge the region near the inlet channel. The graphics window should look something like this:

Inlet channel abovebottom of cylinder

Use the Unzoom All icon to return to the previous view.



Meshing the piston cylinder below the valve (geometry bodies 6 and 7) In the Body Sweep dialog box, make sure that the Vector Direction is set to (0, 0, 0.2), make sure that the “Generate 3-D Mesh from 2-D mesh on Face” button is checked and click the + button to the right of the 3-D Element Group field. The 3-D Element Group number should be 3. Then make sure that “# of Elements in Swept Direction” is set to 5, fill in the table as follows and click Apply (we do not want to close the dialog box yet).

Face Body # 2 1 3 1

After you click the Color Element Groups icon , the graphics window should look something like this:

TIME 1.000

X Y

Z

Notice that element group 1 and zone EG1 have been removed from the Model Tree. This is because the last body sweep operation used all of the remaining elements in element group 1, and the body sweep operation by default removes the element group when all of the elements are swept.


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Meshing the piston cylinder above the valve (geometry bodies 8 to 11) In the Body Sweep dialog box,, set the Vector Direction to (0, 0, 0.5), make sure that the “Generate 3-D Mesh from 2-D mesh on Face” button is checked and make sure that the 3-D Element Group is set to 3. Then set the “# of Elements in Swept Direction” to 10, fill in the table as follows and click OK.

Face Body # 5 4 5 5

17 6 15 7

The graphics window should look something like this:

TIME 1.000

X Y

Z

Zone groups We will use zone groups to organize the Model Tree. We will create one zone group containing the geometry and elements in the inlet channel and another zone group containing the geometry and elements in the piston cylinder. In the Model Tree, right-click on EG2, choose Move to→New, enter name INLET_CHANNEL and click OK. Notice that the Model Tree now contains INLET_CHANNEL. Click the + to the left of INLET_CHANNEL to expand it, and notice that INLET_CHANNEL is defined by EG2. Now right-click on GB2 and choose Move to→



INLET_CHANNEL, then right click on GB3 and choose Move to→INLET_CHANNEL. When you click the + to the left of INLET_CHANNEL, notice that INLET_CHANNEL is defined by zones EG2, GB2 and GB3. Proceed similarly to define zone group PISTON_CYLINDER using EG3 and GB4 through GB11. Notice that you can move the entire range of zones from GB4 through GB11 by selecting these zones, before moving them all to zone group PISTON_CYLINDER. When you right-click zone group INLET_CHANNEL and choose Display, the graphics window should look something like this:

TIME 1.000

X Y

Z

When you right-click zone group PISTON_CYLINDER and choose Display, the graphics window should look something like the figure on the next page.


66-26 ADINA Primer

TIME 1.000

X Y

Z

Splitting the mesh We need to split the fluid mesh in the region corresponding to the valve. Use the Model Tree to display zones GB8, GB9, GB11, then rotate the model so that the underside of these bodies are visible. You should be able to verify that the faces that correspond to the valve are face 6 of body 8, face 6 of body 9 and face 18 of body 11. Choose Meshing→Nodes→Split Mesh. Set “Split Interface Defined By” to Surfaces/Faces and make sure that “At Boundary of Interface” is set to “Split Only Nodes on External Boundary”. Fill in the table as follows, and click OK to close the dialog box. Face/Surf Body #

6 8 6 9

18 11

Display element group 3 using the Model Tree, then click the Shading icon , the Cull

Front Faces icon and the Model Outline icon . The graphics window should look something like the figure on the next page.



TIME 1.000

X Y

Z

As you rotate the mesh using the mouse, you can see the outline of the valve. Face-links It is necessary to face-link the body faces due to the gap condition that we will specify later on. Choose Geometry→Faces→Face Link, add Face Link Number 1, set the “Create” field to “Links for All Faces/Surfaces”, then click OK to close the dialog box. Leader-followers As the valve moves, we would like the corresponding points on the cylinder wall to move.

Use the Model Tree to display zone GB7 (body 7), then click the Point Labels icon . The graphics window should look something like the figure on the next page.


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P8

P11

P12

P18

P19

P20

P21

P35

P38

P39

P40

P41

P42

P43

P44

P45

P46 P47

P48

P49

P50

TIME 1.000

X Y

Z

Geometry points 39 to 44 are on the boundary of the valve, and geometry points 45 to 50 are corresponding points on the cylinder wall. Choose Meshing→ALE Mesh Constraints→Leader-Follower, enter the following information into the table and click OK. Label # Leader Point # Follower Point #

1 39 45 2 40 46 3 41 47 4 42 48 5 43 49 6 44 50

Defining the model control parameters, loads and initial conditions Flow assumptions: Choose Model→Flow Assumptions, set the Flow Model to Turbulent K-Epsilon, set the Flow Type to Low Speed Compressible, set the Temperature Equation to Total Energy, and click OK. FSI analysis: Set the Multiphysics Coupling field to “with Structures”



Outer-iteration primary relaxation factors: Choose Control→Solution Process and set Flow-Condition-Based Interpolation Elements to FCBI-C. Then click the Outer Iteration button and set the Primary Relaxation Factors as follows: Velocity to 0.65, Temperaure to 0.95, Turbulence-K to 0.92 and Turbulence-Epsilon to 0.92. Click OK to close both dialog boxes. Remaining model control parameters, material properties, loads, initial conditions: We have put the commands for the remaining model control parameters, material properties, loads and initial conditions into file prob66_2.in. Choose FileOpen Batch, select file prob66_2.in and click Open. Defining the special boundary conditions The fluid model uses four special boundary condition types: moving wall, wall, FSI and gap boundaries. Moving wall boundaries: We begin by specifying the moving wall boundary conditions on the top surface of the piston cylinder. These faces displace in the z-direction according to a time

function. Click the Special Boundary Conditions icon , and add Condition Number 1. Set the type to Moving Wall, and make sure the Apply to field is set to Faces/Surfaces. In the “Time Functions for Displacement” box, set Z to 2. Fill in the table as follows and click Save (do not close the dialog box yet). Face/Surf Body #

5 8 5 9

15 10 17 11

FSI boundaries: Add Condition Number 2 and set the Type to Fluid-Structure Interface. Make sure that the Fluid-Structure Boundary # is set to 1. Fill in the table as follows, and click Save (do not close the dialog box yet). Face/Surf Body #

6 8 6 9

18 11 The faces in this table correspond to fluid above the valve.


66-30 ADINA Primer

Now add Condition Number 3 and make sure that the Type is set to Fluid-Structure Interface. Set the Fluid-Structure Boundary # to 2. Fill in the table as follows, and click Save (do not close the dialog box yet). Face/Surf Body #

5 4 5 5

17 6 The faces in this table correspond to fluid below the valve. Wall boundaries: Add Condition Number 4 and set the Type to Wall. Set the field immediately below the “Apply to” field to “Apply to All Free External Boundaries”, then click Save (do not close the dialog box yet). Gap boundaries: The following diagram shows the bodies used to define the gap boundary conditions.

B4

F1

F2

0.2

4

F3

F4

F3

F4

B5

The total surface area of the gap is 2 (4)(0.2) 5.026544 , so the surface area of the gap for

each of the bodies is 5.026544 / 2 2.51327 . Based on this surface area, we will set the gap closed value to 2.5 and the gap open value to 2.75 (about 10% higher than the gap closed value). Add Condition Number 5 and set the Type to Gap. Make sure the Apply to field is set to Faces, set the Body # to 4 and set “Gap Open-Close Condition Controlled by” to “Gap Size”. Set the Gap-Open Value to 2.75, and set the Gap-Closed Value to 2.5. Fill in the table as follows, then click Save (do not close the dialog box yet). Face Orientation

1 Follow Geometry 3 Follow Geometry 4 Follow Geometry



Click Copy… to copy the condition to condition 6. Set the Body # to 5, fill in the table as follows, then click OK to close the dialog box. Face Orientation

2 Follow Geometry 3 Follow Geometry 4 Follow Geometry

Generating the ADINA CFD data file, saving the AUI database

Click the Data File/Solution icon , set the file name to prob66_fa, uncheck “Run

Solution”, and click Save. Now click the Save icon and save the database to file prob66_f. Running ADINA-FSI - Steady-state analysis Choose Solution→Run ADINA-FSI, click the Start button, select file prob66_aa.dat, then hold down the Ctrl key and select file prob66_fa.dat. The File name field should display both filenames in quotes. Set Max. Memory for Solution to at least 50 MB, then click Start. The analysis takes one solution step. When the analysis is finished, close all open dialog boxes, set the Program Module drop-

down list to Post-Processing (you can discard all changes), click the Open icon and open porthole file prob66_aa.por.


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Post-processing - Steady-state analysis ADINA Structures model

When you click the Color Element Groups icon and the Scale Displacements icon , the graphics window should look something like this:

TIME 1.000 DISP MAG 28.23

X Y

Z

The unbalanced pressure causes the valve to deform into the inlet channel. ADINA CFD model

Click the New icon (you can discard all changes and continue), then click the Open icon

and open porthole file prob66_fa.por. Click the Cut Surface icon , set the Type to Cutting Plane, uncheck the Display the Plane(s) button and click OK. After you click the

Color Element Groups icon , the Group Outline icon and the Quick Band Plot icon

, the graphics window shold look something like the top figure on the next page.



TIME 1.000

X Y

Z

NODAL_PRESSURE

TIME 1.000

1.260

1.080

0.900

0.720

0.540

0.360

0.180

MAXIMUM1.400

NODE 14673

MINIMUM0.1130

NODE 8

This plot shows that the fluid pressures are the same as the initial fluid pressures. Now click

the Modify Band Plot icon , set the Band Plot Variable to (Temperature: TEMPERATURE) and click OK. The graphics window should look something like this:

TIME 1.000

X Y

Z

TEMPERATURE

TIME 1.000

380.0

373.3

366.7

360.0

353.3

346.7

340.0

MAXIMUM383.0

NODE 6295

MINIMUM338.0

NODE 8


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This plot shows that the fluid temperatures are the same as the initial fluid temperatures. Model definition for the transient analysis ADINA Structures model Set the Program Module to ADINA Structures (you can discard all changes and continue), and choose database file prob66_a.idb from the recent file list near the bottom of the File menu. Restart analysis, switching to dynamics Choose Control→Solution Process, set the Analysis Mode to Restart Run, set the Solution Start Time to 1.0 and click OK. Set the Analysis Type to Dynamics-Implicit. Selecting the time steps for which results are saved

Because the model uses a large number of time steps, we will specify that element and nodal

results are saved every 5 time steps. Choose Control→Porthole (.por)→Time Steps (Element

Results). Set the “Copy Time Step Blocks to Nodal Results” field to “Copy Over if it is

Empty”. Fill in the table as follows, and click OK.

Block Initial Time Step Final Time Step Increment 1 5 10000 5

Creating the data file

Click the Data File/Solution icon , set the file name to prob66_ab, uncheck “Run

Solution”, and click Save. Click the Save icon to save the updated database. ADINA CFD model

Click the New icon (you can discard all changes and continue), set the Program Module to ADINA CFD and choose database file prob66_f.idb from the recent file list near the bottom of the File menu.



Restart analysis, switching to a transient solution Choose Control→Solution Process, set the Solution Start Time to 1.0, check the Restart Analysis button and click OK.

Set the Analysis Type to Transient. Then click the Analysis Options icon , set the Integration Method to Composite and click OK. Time stepping Choose ControlTime Step, edit the table as follows and click OK.

Number of Steps

Magnitude

4166 0.002 Selecting the time steps for which results are saved

Choose Control→Porthole (.por)→Time Steps (Element Results). Set the “Copy Time Step

Blocks to Nodal Results” field to “Copy Over if it is Empty”. Fill in the table as follows, and

click OK.

Block Initial Time Step Final Time Step Increment 1 5 10000 5

Creating the data file

Click the Data File/Solution icon , set the file name to prob66_fb, uncheck “Run

Solution”, and click Save. Click the Save icon to save the updated database. Running ADINA-FSI - Transient analysis Choose Solution→Run ADINA-FSI, click the Start button, select file prob66_ab.dat, then hold down the Ctrl key and select file prob66_fb.dat. The File name field should display both filenames in quotes. Set Max. Memory for Solution to at least 50 MB, then click Start. The AUI displays two “Specify the Restart File” dialog boxes sequentially, one dialog box for the fluid model and one dialog box for the structural model. The order in which the dialog boxes are displayed depends on the order in which the file names appear in the preceding “Start an ADINA FSI job” dialog box.


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(Hint, if you forget which restart file to enter, the title of the dialog box displays the filename. So if the structural model filename is displayed, enter the structural model restart file, and if the fluid model filename is displayed, enter the fluid model restart file.)

Linux: We selected file prob66_ab.dat before selecting file prob66_fb.dat, and the File name field reads “prob66_ab.dat” “prob66_fb.dat”, therefore the first dialog box displayed is for the structural model. In the first Specify the Restart File dialog box, verify that the filename in the dialog box title is ...prob66_ab.dat , enter restart file prob66_aa.res, then click Copy.

In the second Specify the Restart File dialog box, , verify that the filename in the dialog box title is ...prob66_fb.dat , enter restart file prob66_fa.res, then click Copy. Windows: We selected file prob66_ab.dat before selecting file prob66_fb.dat, and the File name field reads “prob66_fb.dat” “prob66_ab.dat”, therefore the first dialog box displayed is for the fluid model. In the first Specify the Restart File dialog box, verify that the filename in the dialog box title is ...prob66_fb.dat , enter restart file prob66_fa.res, then click Copy.

In the second Specify the Restart File dialog box, , verify that the filename in the dialog box title is ...prob66_ab.dat , enter restart file prob66_aa.res, then click Copy.

The analysis takes 4166 solution steps. It takes four hours for this model to run on our computer, so it might take a similar amount of time for this model to run on your computer. When the analysis is finished, close all open dialog boxes, set the Program Module drop-

down list to Post-Processing (you can discard all changes), click the Open icon and open porthole file prob66_fb.por. Post-Processing Overall motion of fluid mesh

Click the Model Outline icon and the Wire Frame icon . The graphics window should look something like the top figure on the next page.

Now click the Movie Load Step icon to create an animation, then the Animate icon to play back the animation. You can see the valve opening, then closing and reopening.

Click the Refresh icon to clear the animation.



TIME 9.3300

X Y

Z

Fluid velocity vectors

Click the Quick Vector Plot icon . The graphics window should look something like this:

TIME 9.3300

X Y

Z

VELOCITY

TIME 9.3300

21.41

19.50

16.50

13.50

10.50

7.50

4.50

1.50


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Now click the Movie Load Step icon to create an animation. The valve opens about solution time 4 and the velocity vectors immediately become very large. In order to reduce

the length of the velocity vectors, use the Solution Time icons ( ... ) to set the solution

time to 4.3, then click the Clear Vector Plot icon and the Quick Vector Plot icon .

Click the Movie Load Step icon to create an animation. Particle traces We will now visualize the motion using the particle trace feature. We will inject particles into the flow field at the inlet, starting at a solution time just before the valve opens.

Click the Clear Vector Plot icon and use the Solution Time icons ( ... ) to set the solution time to 4.0. Now choose Display→Particle Trace Plot→Create and click the ... button to the right of the Trace Plot Style field. Click the ... button to the right of the Trace Rake field, and, in the Define Trace Rake dialog box, set the Type to Grids. Enter the following information into the first row of the table and click OK three times to close all three dialog boxes. X Y Z Plane Shape Side 1

Length NSIDE1 Side 2

Length NSIDE2

0 8.7 66 Z-Plane Rectangular 12 10 12 10 The graphics window should look something like the top figure on the next page. Now choose Display→Particle Trace Plot→Modify. Click the ... button to the right of the Trace Type field, set the Particle Size to 1 and click OK. Now click the ... button to the right of the Trace Calculation field, set the “Time Interval between Particle Emission” to 0.1 and click OK. Click the ... button to the right of the Trace Rendering field, uncheck the “Display Symbols at Injector Locations” button and click OK twice to close both dialog boxes. Click

the Next Solution icon . The graphics window should look something like the bottom figure on the next page.



TIME 4.0000

X Y

Z

PARTICLE TRACEUNSTEADY FLOW, TIME = 4.0000MULTIPLE PARTICLES/EMITTEREMIT INTERVAL = 0.000START TIME = 4.0000

TIME 4.0100

X Y

Z


Notice that the particle injectors that are outside of the fluid domain are ignored.


66-40 ADINA Primer

Let’s draw the mesh outline in a less obtrusive color. Click the Modify Mesh Plot icon and click the Element Depiction... button. Set the Appearence of Deformed Mesh to GRAY_50, then click OK twice to close both dialog boxes. The graphics window should look something like this:

TIME 4.0100

X Y

Z


Click the Movie Load Step icon to create an animation. The particles move through the inlet channel and enter the piston cylinder. The graphics window should look something like the figure on the next page. You can observe the particle traces from different views. For example, click the YZ view

icon and create another animation. It is easier to visualize the motion of the particles through the valve in this view.



TIME 9.3300

X Y

Z


Velocities in the X plane

Click the Clear Trace Plot icon , click the Cut Surface icon , set the Type to Cutting Plane, set Defined by to X-Plane, uncheck the Display the Plane(s) button and click OK.

Now use the Solution Time icons ( ... ) to set the solution time to 4.3 and click the

Quick Vector Plot icon . The graphics window should look something like the figure on the next page.

Click the Movie Load Step icon to create an animation.


66-42 ADINA Primer

TIME 4.3000

X Y

Z

VELOCITY

TIME 4.3000

129.3

117.0

99.0

81.0

63.0

45.0

27.0

9.0

Pressure distribution in the X plane

Click the Clear Vector Plot icon and use the Solution Time icons ( ... ) to set the

solution time to the first solution time (1.01). Now click the Quick Band Plot icon . The graphics window should look something like the figure on the next page.

Click the Movie Load Step icon to create an animation. The pressure in the cylinder drops to slightly below the inlet pressure when the gap opens. Because the scaling does not change in the animation, we cannot see more detail in the pressure distribution.



TIME 1.010

X Y

Z

NODAL_PRESSURE

TIME 1.010

1.260

1.080

0.900

0.720

0.540

0.360

0.180

MAXIMUM1.400

NODE 14656

MINIMUM0.1130

NODE 2111

Click the Modify Band Plot icon , click the Band Table... button, uncheck the Freeze

Range button and click OK to close both dialog boxes. Click the Movie Load Step icon to create an animation. Ths time the band scaling is reset based on the maximum and minimum pressures in each time step. For example, at time 5.6, the graphics window looks something like this:

TIME 5.6000

X Y

Z

NODAL_PRESSURE

TIME 5.6000

0.1213

0.1200

0.1187

0.1173

0.1160

0.1147

0.1133

MAXIMUM0.1217

NODE 2144

MINIMUM0.1130

NODE 1114


66-44 ADINA Primer

It is easier to see the pressure drop in the inlet channel and the increased pressure just below the valve.

Click the Last Solution icon to show the pressure at the end of the solution. By eye, we can estimate that the average pressure in the cylinder at the end of the solution is about 0.115 MPa. Temperature distribution in the X plane

Click the Clear Band Plot icon and use the Solution Time icons ( ... ) to set the

solution time to the first solution time (1.01). Now click the Create Band Plot icon , set the Band Plot Variable to (Temperature: TEMPERATURE) and click OK. Click the Modify

Band Plot icon , click the Band Table... button, uncheck the Freeze Range button and click OK to close both dialog boxes. The graphics window should look something like this:

TIME 1.010

X Y

Z

TEMPERATURE

TIME 1.010

380.0

373.3

366.7

360.0

353.3

346.7

340.0

MAXIMUM383.0

NODE 14685

MINIMUM338.0

NODE 2144

Click the Movie Load Step icon to create an animation. The temperature in the cylinder drops to about 230 K by the time the gap opens. Then the warmer fluid in the inlet channel circulates within the piston cylinder. For example, at the end of the solution, the graphics window should look something like the figure on the next page.



TIME 9.3300

X Y

Z

TEMPERATURE

TIME 9.3300

340.0

332.0

324.0

316.0

308.0

300.0

292.0

MAXIMUM344.8

NODE 82

MINIMUM288.7

NODE 6323

By eye, we can estimate that the average temperature in the cylinder at the end of the solution is about 300 K. Density distribution in the X plane

Click the Clear Band Plot icon and use the Solution Time icons ( ... ) to set the

solution time to the first solution time (1.01). Now click the Create Band Plot icon , set the Band Plot Variable to (Fluid Variable: NODAL_DENSITY) and click OK. Click the

Modify Band Plot icon , click the Band Table... button, uncheck the Freeze Range button and click OK to close both dialog boxes. The graphics window should look something like the top figure on the next page. From this plot, we see that the initial density of the fluid in the cylinder is 1.965E-5 (g/mm3) and the initial density of the fluid in the inlet channel is 1.797E-6 (g/mm3).

Click the Movie Load Step icon to create an animation. The density in the cylinder drops to about 2.3E-6 by the time the gap opens, which is still denser than the fluid in the inlet channel. Then the less dense fluid in the inlet channel circulates within the piston cylinder. For example, at the end of the solution, the graphics window should look something like the bottom figure on the next page.


66-46 ADINA Primer

TIME 1.010

X Y

Z

NODAL_DENSITY

TIME 1.010

1.867E-05

1.600E-05

1.333E-05

1.067E-05

8.000E-06

5.333E-06

2.667E-06

MAXIMUM1.965E-05

NODE 14656

MINIMUM1.797E-06

NODE 2113

TIME 9.3300

X Y

Z

NODAL_DENSITY

TIME 9.3300

2.125E-06

2.075E-06

2.025E-06

1.975E-06

1.925E-06

1.875E-06

1.825E-06

MAXIMUM2.144E-06

NODE 6323

MINIMUM1.793E-06

NODE 256 (1.794E-06)

By eye, we can estimate that the average density in the cylinder at the end of the solution is about is 2E-6 (g/mm3).



Mass flux through the gap

Click the Clear icon , then display zone EG3 using the Model Tree. Click the Last

Solution icon , the Model Outline icon and the Wire Frame icon . The graphics window should look something like this:.

TIME 9.3300

X Y

Z

We now need to determine the element face-sets corresponding to the gap. Since there are two gap boundary conditions, there are four element face-sets for the gap, two element face-sets for the upstream side of the gap and two element face-sets for the downstream side of the gap. We will use the downstream face-sets because we want the mass flux to be positive when there is flow into the cylinder.

Click the Element Face Set icon , choose Element Face Set 34 and move the dialog box out of the way of the mesh plot. You will notice that the Description is “GAP (DOWNSTREAM) CONDITION OF LABEL 5” and the elements corresponding to this gap are highlighted. Now choose Element Face Set 35. You will notice that the Description is “GAP (DOWNSTREAM) CONDITION OF LABEL 6” and the elements corresponding to this gap are highlighted. We would like to determine the mass flux through both of these gaps. Add Element Face Set 40, set the Method to Merge Sets, enter 34, 35 in the first two rows of the table and click Save. The entire gap is highlighted. Click OK to close the dialog box. Then choose Definitions→Model Point→Element Face Set, add Model Point Name GAP, set the Element


66-48 ADINA Primer

Face Set # to 40 and click OK.

Click the Clear icon , then choose Graph→Response Curve (Model Point), set the Y Coordinate Variable to (Flux: MASS_FLUX_ELFACE) and click OK. The graphics window should look something like this:

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.-2.

0.

2.

4.

6.

8.

10.

*10

-3

RESPONSE GRAPH

MASS_FLUX_ELFACE,GAP

TIME

MA

SS

_F

LU

X_E

LF

AC

E, G

AP

Evidently the gap opens just after solution time 4, then briefly closes near time 7.5. Near the end of the solution, the gap is open, however the net flow is reversed so that fluid is flowing from the cylinder into the inlet chamber. We would like to determine the total mass of fluid that flows into the cylinder during the entire solution process. We can do this by integrating (in time) the mass flux time history. Choose Definitions→Response, add Response Name TIME_INTEGRAL, set the Type to Envelope and the Type of Envelope Values to Time Integral, then click OK. Now choose List→Value List→Model Point, set the Response Option to Single Response, the Response to TIME_INTEGRAL, Variable 1 to (Flux: MASS_FLUX_ELFACE) and click Apply. The result is 1.98276E-02 (g). At the end of this primer problem, we have performed a hand check of the results, and it is seen that this time-integrated mass flux is very reasonable. Exiting the AUI: Choose FileExit to exit the AUI. You can discard all changes.



Modeling comments 1) In the model solution, we first solve for the static deformed shape of the valve using a steady-state analysis, then restart to a transient analysis. Here we give an explanation for using for the static deformed shape of the valve as the structural initial condition in the transient analysis. Consider the exhaust process of the preceding compression - expansion cycle. During the exhaust process, the piston cylinder is at high pressure and the discharge valve is open, so that the cylinder pressure is (approximately) constant in time during the exhaust process. During that time the suction reed valve is subjected to an unbalanced pressure. Therefore at the beginning of the expansion cycle, it is reasonable to assume that the deformed shape of the suction reed valve is approximately equal to the static deformed shape obtained using the unbalanced pressure during the exhaust phase of the preceding compression cycle. 2) Since there is no actual flow during the steady-state solution, there is no reason to specify initial conditions for the turbulence variables. 3) Even though the valve is closed initially, the initial fluid pressure for fluid in the cylinder underneath the valve is specified to be the same as the initial fluid pressure in the rest of the cylinder (at high presssure). 4) The inlet turbulence quantities are calculated based on a velocity of 150 mm/ms. In the solution, we observe that the fluid velocities are of this order of magnitude. 5) If we perform the transient analysis without the steady-state analysis first, the valve is immediately subjected to an unbalanced pressure and begins to respond dynamically to this pressure. Convergence is more difficult and a smaller time step needs to be used. 6) If the heat transfer temperature equation for low-speed compressible flow is used instead of the total energy temperature equation, the computed temperatures are inaccurate in this problem. Hand check of results Let’s see if the results obtained are reasonable. We will focus on the fluid in the cylinder. Confirmation of the mass balance At the start of the solution, we know that the pressure is 1.4 MPap and the temperature is

383 KT . Using the relation p RT , in which 2 2186 mm / ms -Kp vR c c , the


66-50 ADINA Primer

density at the start of the solution is 31.97E-5 g/mm . This density agrees well with the

value that we observed in the ADINA CFD results at the start of the solution. We also know that the cylinder diameter is 32.6 mm and the initial cylinder height is

0.7 mmh , therefore the cylinder volume at the beginning of the solution is

2 332.6 / 2 0.7 584 mmV . The total mass of fluid in the cylinder, at the start of the

solution is therefore (1.97E-5)(584)=1.15E-2 gM .

According to the ADINA-FSI results obtained above, at the end of the solution, the presssure in the cylinder is approximately 0.115 MPap and the temperature is approximately

300 KT . Again using p RT , or from examining the density of the fluid in the cylinder

at the end of the solution, the density at the end of the solution is approximately 32E-6 g/mm . The final cylinder height is 18.7 mm , so the final cylinder volume is

232.6 / 2 18.7V 315600 mm , and the total mass of fluid in the cylinder, at the end of

the solution is (2E-6)(15600)=3.12E-2 gM .

Therefore the change in the fluid mass is 3.12E-2 1.15E-2 = 1.97E-2 gM , which

agrees very well with the time-integrated mass flux 1.98276E-02 given above. Confirmation that the expansion process is isentropic We also can confirm that the expansion process is isentropic (adiabatic), up to the point when

the valve opens. The relevant equation is 2 1 1

1 2 2

p V h

p V h

, where 1.23p

v

c

c . The

valve opens at solution time 4.06, corresponding to a piston motion of 5.35 mm, and at

solution time 4.06, the average pressure in the cylinder is about 0.099 MPa. Therefore 0.099

1.4

should be close to 1.23

0.7

0.7 5.35

, and in fact both quantities are close to 0.07 .

problem description - adina · problem description in this problem, we perform a fully-coupled...

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