Solved with COMSOL Multiphysics 4.2
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1 Backstep Introduction This tutorial model solves the incompressible Navier-Stokes equations in a backstep geometry. A characteristic feature of fluid flow in geometries of this kind is the recirculation region that forms where the flow exits the narrow inlet region. The model clearly demonstrates the formation of such a region, which is best displayed by visualizing the flow streamlines. Model Definition MODEL GEOMETRY The model consists of a pipe connected to a block-shaped tank; see Figure 1. Due to symmetry, it is sufficient to model one eighth of the full geometry. The pipe has an inlet at one end, and the tank has an outlet at the opposite end. All other boundaries are solid walls. Figure 1: Model geometry COMSOL 1 BACKSTEP
2 DOMAIN EQUATION AND BOUNDARY CONDITIONS The flow in the system is laminar, so the model uses the Laminar Flow interface. The inlet flow is fully developed laminar flow, described by the corresponding inlet boundary condition. The boundary condition at the outlet sets a constant relative pressure. Furthermore, the vertical and inclined boundaries along the length of the geometry are symmetry boundaries. All other boundaries are solid walls described by a non-slip boundary condition. Results Figure 2 shows a combined surface and arrow plot of the flow velocity. This plot does not reveal the recirculation region in the tank immediately beyond the inlet pipe s end. For this purpose, a streamline plot is more useful, as demonstrated in Figure 3. Figure 2: The velocity field in the backstep geometry. 2 BACKSTEP 2011 COMSOL
3 Figure 3: The recirculation region visualized using a velocity streamline plot. Model Library path: CFD_Module/Single-Phase_Tutorials/backstep Modeling Instructions MODEL WIZARD 1 Go to the Model Wizard window. 2 Click Next. 3 In the Add physics tree, select Fluid Flow>Single-Phase Flow>Laminar Flow (spf). 4 Click Next. 5 In the Studies tree, select Preset Studies>Stationary. 6 Click Finish COMSOL 3 BACKSTEP
4 GLOBAL DEFINITIONS Parameters 1 In the Model Builder window, right-click Global Definitions and choose Parameters. 2 Go to the Settings window for Parameters. 3 Locate the Parameters section. In the Parameters table, enter the following settings: NAME EXPRESSION DESCRIPTION v0 1[cm/s] Inlet velocity GEOMETRY 1 Cylinder 1 1 In the Model Builder window, right-click Model 1>Geometry 1 and choose Cylinder. 2 Go to the Settings window for Cylinder. 3 Locate the Size and Shape section. In the Radius edit field, type 2.5e-3. 4 In the Height edit field, type 1.5e-2. 5 Locate the Position section. In the x edit field, type 0. 6 Locate the Axis section. In the z edit field, type 0. 7 In the x edit field, type 1. 8 Click the Build Selected button. Block 1 1 In the Model Builder window, right-click Geometry 1 and choose Block. 2 Go to the Settings window for Block. 3 Locate the Size and Shape section. In the Width edit field, type 3e-2. 4 In the Depth edit field, type 1e-2. 5 In the Height edit field, type 1e-2. 6 Locate the Position section. In the x edit field, type 1.5e-2. 7 In the y edit field, type -5e-3. 8 In the z edit field, type -5e-3. 9 Click the Build Selected button. 10 Click the Zoom Extents button on the Graphics toolbar. 4 BACKSTEP 2011 COMSOL
5 Union 1 1 In the Model Builder window, right-click Geometry 1 and choose Boolean Operations>Union. 2 Select the objects cyl1 and blk1 only. 3 Go to the Settings window for Union. 4 Locate the Union section. Clear the Keep interior boundaries check box. 5 Click the Build Selected button. Work Plane 1 1 In the Model Builder window, right-click Geometry 1 and choose Work Plane. 2 Go to the Settings window for Work Plane. 3 Locate the Work Plane section. From the Plane list, select yz-plane. 4 From the 3D projection list, select Entire 3D geometry. 5 Click the Build Selected button. Bézier Polygon 1 1 In the Model Builder window, right-click Geometry and choose Bézier Polygon. 2 Go to the Settings window for Bézier Polygon. 3 Locate the Polygon Segments section. Click the Add Linear button. 4 Find the Control points subsection. In row 2, set y to 5e-3. 5 Click the Add Linear button. 6 In row 2, set x to 5e-3. 7 Click the Add Linear button. 8 Click the Close Curve button. 9 Click the Build Selected button. Extrude 1 1 In the Model Builder window, right-click Work Plane 1 and choose Extrude. 2 Go to the Settings window for Extrude. 3 Locate the Distances from Work Plane section. In the associated table, enter the following settings: DISTANCES (M) 4.5e-2 4 Click the Build Selected button COMSOL 5 BACKSTEP
6 5 Click the Zoom Extents button on the Graphics toolbar. Intersection 1 1 In the Model Builder window, right-click Geometry 1 and choose Boolean Operations>Intersection. 2 Select the objects uni1 and ext1 only. 3 Click the Build Selected button. 4 Click the Zoom Extents button on the Graphics toolbar. Form Union 1 In the Model Builder window, right-click Form Union and choose Build Selected. The model geometry is now complete. MATERIALS 1 In the Model Builder window, right-click Model 1>Materials and choose Open Material Browser. 2 Go to the Material Browser window. 3 Locate the Materials section. In the Materials tree, select Built-In>Water, liquid. 4 Right-click and choose Add Material to Model from the menu. LAMINAR FLOW Inlet 1 1 In the Model Builder window, right-click Model 1>Laminar Flow and choose Inlet. 2 Select Boundary 1 only. 3 Go to the Settings window for Inlet. 4 Locate the Boundary Condition section. From the Boundary condition list, select Laminar inflow. 5 Locate the Laminar Inflow section. In the U av edit field, type v0. Symmetry 1 1 In the Model Builder window, right-click Laminar Flow and choose Symmetry. 2 Select Boundaries 2 and 3 only. Outlet 1 1 In the Model Builder window, right-click Laminar Flow and choose Outlet. 2 Select Boundary 7 only. 6 BACKSTEP 2011 COMSOL
7 MESH 1 1 In the Model Builder window, click Model 1>Mesh 1. 2 Go to the Settings window for Mesh. 3 Locate the Mesh Settings section. From the Element size list, select Coarse. 4 Click the Build All button. STUDY 1 In the Model Builder window, right-click Study 1 and choose Compute. RESULTS Velocity (spf) 1 In the Model Builder window, expand the Velocity (spf) node. 2 Right-click Slice 1 and choose Delete. Click Yes to confirm. 3 Right-click Velocity (spf) and choose Arrow Surface. 4 Go to the Settings window for Arrow Surface. 5 Locate the Coloring and Style section. From the Arrow length list, select Logarithmic. 6 From the Color list, select Yellow. 7 Click the Zoom Extents button on the Graphics toolbar. To see the recirculation effects, create a streamline plot of the velocity field. RESULTS 3D Plot Group 3 1 In the Model Builder window, right-click Results and choose 3D Plot Group. 2 Right-click Results>3D Plot Group 3 and choose Streamline. 3 Select Boundary 1 only. 4 Go to the Settings window for Streamline. 5 Locate the Coloring and Style section. From the Line type list, select Tube. 6 Right-click Streamline 1 and choose Color Expression. Compare the resulting plot to that in Figure COMSOL 7 BACKSTEP
8 8 BACKSTEP 2011 COMSOL
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