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

Transcription

1 Problem description This tutorial illustrates the use of ADINA for analyzing the fluid-structure interaction (FSI) behavior of a flexible splitter behind a 2D cylinder and the surrounding fluid in a channel. The 2D model under consideration is shown schematically in the following figure. Flexible splitter Inlet 0.05 Outlet Fluid 3 = 1000 kg/m = 1.0 Pa-s Not drawn to scale 0.02 Splitter E = 5.6E06 Pa = 0.4 = 1000 kg/m 3 The FCBI-C element is used in the fluid part of the model. In this tutorial, we will demonstrate the following topics that have not been presented in previous problems. Performing a steady-state solution for only the fluid model of an FSI problem. Using the mesh split command in the fluid model. Using plane strain iso-beam elements to model the 2D flexible splitter. Mapping the steady-state solution as the initial condition for the transient analysis of the same FSI problem. Performing a Fourier analysis of the FSI results to obtain the resonant frequency of the splitter. ADINA R & D, Inc. 64-1

2 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. The total solution time for this FSI problem is around a couple of hours. Much of the input for this problem is stored in files prob64_1.in, prob64_2.in, and prob64_1a.in. 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. Set the Analysis Type to "Dynamics-Implicit" and set the Multiphysics Coupling drop-down list to "with CFD". Model definition for the structural model Defining model control data Problem heading: Choose Control Heading, set the Problem Heading to "2D channel flow around a cylinder with a flexible splitter" and click OK. Analysis assumptions: We anticipate that the structural displacements will be large, but that the strains will be small. Choose Control Analysis Assumptions Kinematics, set the Displacements/Rotations field to "Large" and click OK. Solution tolerances and maximum number of iterations: Choose Control Solution Process, click the Tolerances... button, set Convergence Criteria to Energy and Force, set Force (Moment) Tolerances to 1.0E-06, the Reference Force to 1.0, the Reference Moment to 1.0 and click OK to close the Iteration Tolerances dialog box. Now click the Method... button, set the Maximum Number of Iterations to 999 and click OK twice to close both dialog boxes ADINA Primer

3 Geometry definitions The included batch file prob64_1a.in contains commands for generating the structural model's geometry. To run this batch file, choose File Open Batch, select file prob64_1a.in and click Open. Click the Mesh Plot icon like this:. The graphics window should look something TIME Z X Y Defining the splitter's material properties Click the Manage Material icon and click the Elastic Isotropic button. In the Define Isotropic Linear Elastic Material dialog box, add material 1, set the Young s Modulus to 5.6E6, the Poisson s Ratio to 0.4, and the Density to 1.0E3. Click OK, then click Close to close the Manage Material Definitions dialog box. Defining the cross-section Click the Cross Sections icon and add Section Number 1. Make sure that the Type is set to Rectangular, set the Width W field to 0.02 and the Height H field to 1.0. Click OK to close the Define Cross Section dialog box. Meshing the splitter Element group: Click the Element Groups icon, add element group 1, set the Type to Isobeam, set the Element Sub-Type to Plane Strain and click OK. Subdivision data: Click the Subdivide Lines icon, set the Number of Subdivisions to 12, then click OK. ADINA R & D, Inc. 64-3

4 Meshing: Click the Mesh Lines icon, make sure that the Type is set to Isobeam and that Nodes per Element is set to 2. In the first row of the table, enter 1, and click OK to close the Mesh Lines dialog box. The graphics window should look something like this: TIME Z X Y Defining boundary conditions Fixities: The left end of the splitter is fixed against the cylinder wall. Click the Apply Fixity icon, make sure that the Fixity is set to ALL, and that the Apply to option is set to Point. Enter 1 in the first row of the table and click OK to close the Apply Fixity dialog box. Fluid-structure boundaries: Except the point at which the fixity is defined, the remainder of the splitter is exposed to the fluid and must be defined as a fluid-structure interface. Although the iso-beam elements lie on a single line, we need to define two FSI boundaries, one for the top surface of the beam, and a second for the bottom surface. Choose Model Boundary Conditions FSI Boundary, add Boundary Number 1, make sure that the Apply to field is set to Lines, enter 1 in the first row of the table and click Save. Copy boundary 1 to boundary 2, then click OK to close the Define Fluid-Structure-Interaction Boundary dialog box. When you click the Redraw icon figure on the next page., the graphics window should look something like the 64-4 ADINA Primer

5 TIME Z X Y The FSI boundaries are drawn in yellow. Click the Show Fluid Structure Boundary icon to hide the FSI boundaries. Generating the ADINA Structures data file and saving the AUI database Click the Data File/Solution icon Solution button, and click Save. Now click the Save icon prob64_a. ADINA-CFD model, set the file name to prob64_a, uncheck the Run and save the database to file For this FSI problem, we will build two fluid models. The first is a steady-state model, and the second is a transient model. The solution to the steady-state problem will be mapped as the initial condition for the transient fluid model. Steady-state fluid model Click the New icon to ADINA CFD. to create a new database, and set the Program Module drop-down list Defining model control data FSI analysis: Set the Multiphysics Coupling drop-down list to "with Structures". Problem heading: Choose Control Heading, set the Problem Heading to 2D channel flow around a cylinder with a flexible splitter and click OK. ADINA R & D, Inc. 64-5

6 Flow assumptions: Choose Model Flow Assumptions, set Flow Dimension to 2D (in YZ plane), make sure that the Flow Type is set to Incompressible, uncheck the Includes Heat Transfer button and click OK. FSI solution coupling: Click the Coupling Options icon, make sure that the FSI Solution Coupling is set to Iterative, Convergence Criteria is set to Force and Displacement, and that the Relative Force Tolerance and Relative Displacement Tolerance are both set to Set the Force Relaxation Factor to 0.1 and click OK. Importing the geometry The included batch file prob64_1.in contains the commands for generating the fluid model s geometry, element groups and associated mesh, and definitions and settings for the material. A 2D element group is defined and a mapped, rule-based mesh is generated. Choose File Open Batch, select file prob64_1.in and click Open. When you click the Mesh Plot icon, the graphics window should look something like this: TIME Z X Y Splitting the mesh Click the Model Outline icon. Click the Line/Edge Labels icon and use the mouse to zoom in on the area of the splitter. You will notice that there are two sets of coincident lines that outline the splitter, as shown in the following diagram ADINA Primer

7 Because the lines are coincident, the current mesh in this area consists of one set of nodes along the lines. To create separate top and bottom surfaces of the flexible splitter, we need to split the mesh along these lines using the MESH-SPLIT command, which will result in an additional set of nodes along these lines. Choose Meshing Nodes Split Mesh, make sure that At Boundary of Interface is set to Split Only Nodes on External Boundary, enter lines 29 and 26 in the first two rows of the table, and then click OK. To confirm that the mesh has been split, click the Show Geometry icon geometry). The graphics window should look something like this: (to hide the ADINA R & D, Inc. 64-7

8 Defining the boundary conditions The fluid model uses two special boundary condition types: Wall (no-slip), and FSI boundaries. Wall boundaries: We begin by specifying the no-slip boundary conditions along the channel walls and cylinder. Click the Special Boundary Conditions icon, and add Condition Number 1. Make sure that the Type is set to Wall and that the Apply to option is set to Lines. Fill in the table as follows and click Save (do not close the dialog box yet). Line {p} Fluid-structure boundaries: Four lines of the splitter, two on the top surface and two on the bottom surface, are exposed to the fluid and must be defined as FSI boundaries. In the Define Special Boundary Condition dialog box, add Condition Number 2 and set the Type to Fluid- Structure Interface. Fill in the table as follows, then click Save. Line {p} ADINA Primer

9 Add Condition Number 3, set the Fluid Structure Boundary # to 2, fill in the table as follows, then click OK. Line {p} Defining loadings Velocity loading at the channel inlet: A fully developed 2-D channel flow velocity profile is used in this model. The parabolic velocity profile is defined through two spatial functions, which are stored in the batch file prob64_2.in. Choose File Open Batch, select file prob64_2.in and click Open. When you click the Load Plot icon, the graphics window should look something like this. The maximum velocity at the inlet is 3.0 m/s. TIME Z PRESCRIBED VELOCITY TIME X Y Defining the solution process Choose Control Solution Process and set Flow-Condition-Based Interpolation Elements to FCBI-C. Now click the Outer Iteration button, click the Advanced Settings button, then, in the Equation Residual box, set Use to All, and set the Tolerance to 1E-06. In the Variable Residual box, set the Tolerance to 1E-06. Click OK three times to close all dialog boxes. Setting the mapping control The steady-state fluid solution will be mapped as the initial condition for the transient simulation. Choose Control Mapping(.map), check "Create Mapping File and click OK. ADINA R & D, Inc. 64-9

10 Generating the ADINA CFD data file, saving the AUI database Click the Data File/Solution icon Solution, and click Save. Now click the Save icon prob64_initial. Running ADINA-FSI, set the file name to prob64_initial, uncheck Run and save the database to file The steady-state fluid model contains FSI boundaries, requiring us to run this model as an FSI problem. However, because we need only the steady-state fluid solution, we do not want to include the coupled fluid-structure interaction behavior. Choose Solution Run ADINA-FSI, click the Start button, select file prob64_initial.dat, then hold down the Ctrl key and select file prob64_a.dat. The File name field should display both filenames in quotes. Set Run to Fluid Only. Set Max. Memory for Solution to at least 40 MB, then click Start. The analysis will take a few minutes to run. When the analysis is finished, close all open dialog boxes, set the Program Module dropdown list to Post-Processing (you can discard all changes), click the Open icon porthole file prob64_initial. and open Post-processing Click the Model Outline icon and click the Quick Vector Plot icon. The graphics window should look something like this: This solution will be used as the initial condition for the transient model ADINA Primer

11 Building the transient fluid model Problem 64: 2D flow around a cylinder with a flexible splitter Set the Program Module drop-down list to ADINA CFD (you can discard all changes). We can build the transient model using the steady-state database file as the starting point. Choose file prob64_initial.idb from the recent file list near the bottom of the File menu. Set the Analysis Type drop-down list to Transient. Click the Analysis Options icon, set the Integration Method to Composite, and click OK. We would also like to save the fluid vorticities, for post-processing. Choose Control Porthole Select Element Results, add Result Selection Number 1, check the Vorticity button and click OK. Setting the initial mapping Choose File Initial Mapping and choose file prob64_initial.res (do not click Open yet). Set Time to 1.0. In the Initial Variables table, set the first three rows of the table to Y-Velocity, Z-Velocity and Pressure. Click Open. The steady-state solution is mapped onto the transient model as the initial condition. Setting the solution process parameters Choose Control Solution Process, click the Outer Iteration button, and click the Advanced Settings button. In the Outer Iterations Advanced Settings dialog box, set Space Discretization Accuracy Order to Second, and set Maximum Iterations in Fluid Variable Loop to 10. Click OK to close all three dialog boxes. Specifying the time steps Choose Control Time Step, fill in the table as follows and click OK. # of Steps Magnitude Setting the leader-followers As the splitter deforms due to the forces from the fluid, the fluid mesh deforms accordingly. To maintain good mesh quality, we will use leader-follower constraints and slipping boundaries in ADINA CFD. ADINA R & D, Inc

12 Choose Meshing ALE Mesh Constraints Leader-Follower, fill the table as follows, then click OK. Label # Leader Point # Follower Point # Choose Meshing ALE Mesh Constraints Slipping Boundary, add Boundary # 1, fill in the table as follows, then click OK. Line {p} Generating the ADINA CFD data file, saving the AUI database Click the Data File/Solution icon, set the file name to prob64_f, uncheck Run Solution, and click Save. Now choose File Save As, and save the database to file prob64_f.idb. Running ADINA-FSI Choose Solution Run ADINA-FSI, click the Start button, select file prob64_f.dat, then hold down the Ctrl key and select file prob64_a.dat. The File name field should display both filenames in quotes. Set the Number of Processors to the maximum number of processors available on your computer. Make sure that Run is set to Normal FSI, and that Max. Memory for Solution is set to at least 40 MB. Click Start. It may take up to 10 hours to complete the simulation. Using more processors will speed up the simulation. When the analysis is finished, close all open dialog boxes, set the Program Module dropdown list to Post-Processing (you can discard all changes), click the Open icon porthole file prob64_f.por. In the same way, open prob64_a.por. and open ADINA Primer

13 Post-processing Displacement of the splitter In the Model Tree, expand the Zone list, right click on ADINA, and choose Display. The graphics window should look something like this: TIME Z X Y Click the Node Labels icon splitter. The node label is 13. and find the node label on the right trailing edge of the Choose Definitions Model Point Node, add Model Point Name N13, set the Node # to 13, then click OK. Click the Clear icon, then choose Graph Response Curve (Model Point). In the X Coordinate box, make sure that the Variable is set to Time. In the Y Coordinate box, set the Variable to (Displacement: Z-DISPLACEMENT), set the Model Point to N13, and click OK. The plot should like something like the top figure on the next page. ADINA R & D, Inc

14 6. RESPONSE GRAPH 5. Z-DISPLACEMENT, N Z-DISPLACEMENT, N13 * TIME The plot shows the trailing edge of the splitter as having a periodic behavior after 1.7 seconds. Fourier analysis Click the Clear icon. Choose Graph Fourier Analysis, set the Variable to (Displacement: Z-DISPLACEMENT) and the Model Point to N13. Click the "..." button on the right side of the Response Range field, set Start Time to 1.7 and click OK twice to close both dialog boxes. The resulting plot should look like the figure below: 35. Fourier analysis Z-DISPLACEMENT, point N Amplitude * Frequency (cycles/unit time) From this plot, we can determine the resonance frequency. Choose Graph List. From the list dialog box, the maximum amplitude occurs at a frequency of (Hz), the maximum amplitude is E-02 (m) ADINA Primer

15 Vortex shedding We will create an animation displaying the formation of vortices in the channel. Click the Clear icon and the Model Outline icon. Click the Create Band Plot icon, set the Band Plot Variable to (Fluid Variable: OMEGA-X) and click OK. We will modify the band table to emphasize the vortices. Click the Modify Band Plot icon, and click the Band Table button. In the Value Range field, set the Maximum to 100 and the Minimum to Click OK twice to close both dialog boxes. Click the Smooth Plots icon window should look something like this:. The graphics To animate the vorticity plot, click the Movie Load Step icon icon., then click the Animate Exiting the AUI: Choose File Exit to exit the AUI. You can discard all changes. Modeling comments 1. For this FSI problem, iterative FSI coupling is selected and the FCBI-C element is used in the fluid model. The nature of the solution process associated with the FCBI-C element is also an iterative process: fluid equations are solved iteratively in a certain order. Due to these iterative features, it requires that both fluid and solid solutions be fully converged for every time step. In this problem, we demonstrate the settings for this requirement. 2. In the plane strain iso-beam, the cross-section s direction always lies in the y-z plane. Therefore the Width of 0.02 entered into the Define Cross-Section dialog box corresponds to the thickness of the splitter in the y-z plane. ADINA R & D, Inc

16 3. Mapping an initial solution is a useful function to obtain a proper initial condition from a model with similar geometry and boundary conditions/loadings. It saves computational time and also improves convergence at initial solution stages. For this first fluid model, no initial condition is explicitly given, so the default initial conditions used by ADINA CFD are zero velocity and zero pressure. This initial condition is far different from the final fluid solution. If this initial condition is directly used for the transient analysis, it may take a relatively long time to develop the vortex shedding flow pattern. To save computational time, we first perform a steady-state run to obtain a solution that will be mapped as the initial condition for the second, transient fluid model. 4. If the FCBI-C element is used in the fluid model of a transient FSI analysis, it is necessary to force both the fluid and solid models to convergence, by using tighter tolerances for both models. For solid models, the Energy and Force tolerance is generally used, and the tolerance values should be small enough to let the structural solver run at least 3-4 iterations per FSI iteration. For fluid models, the Equation and Variable Residual tolerances should also be small, typically 1.0E-06, as used here. To allow the fluid solution to converge within every FSI iteration, the maximum iteration number in the Fluid Variable Loop field should be much larger than unity, especially when the structural model has relatively soft materials. This helps in obtaining convergence, and in this model 10 was used for the Fluid Variable Loop. 5. In the steady-state fluid model, first order schemes were used for both spatial discretization and time integration, which carry large numerical dissipations and dispersions. These schemes can dampen both numerical and physical oscillations in the fluid solutions. Second order composite time integration, as used in the second fluid model, is highly recommended for transient analysis. For spatial discretization, a first order scheme is generally used for fluid models with a free-formed mesh, or with extremely large displacements due to moving mesh/boundaries. If mapped, rule-based meshing is used, and the mesh quality does not change significantly, as demonstrated here, a second order spatial scheme can be used. 6. In this model, some followers are defined on physical boundaries (no-slip walls), while others are not. Follower points defined on physical boundaries can only move along those physical boundaries. Followers not defined on physical boundaries can move in any direction as to follow their leaders. For example, the followers defined on the channel outlet lines can leave these lines because these are not physical boundary lines. To keep the followers along the outlet lines as the mesh deforms, we can define the outlet lines as "slipping boundaries." When a slipping boundary is defined, the follower is constrained to move only along that boundary ADINA Primer