微機(jī)電糸統(tǒng)分析ppt課件

1、微機(jī)電糸統(tǒng)分析微機(jī)電糸統(tǒng)分析期末報(bào)告期末報(bào)告( (二二) ) Inkjet Inkjet 授課教師授課教師: :李旺龍李旺龍 學(xué)學(xué) 生生: :李聰瑞李聰瑞 Q28961038Q28961038Inkjet Model Inkjet printers are attractive tools for printing text and images because of their low cost, high resolution, and acceptable speed. The working principle behind inkjet technology is to eject

2、small droplets of liquid from a nozzle onto a sheet of paper. Important properties of a printer are its speed and the resolution of the final images. Designers can vary several parameters to modify a printers performance. For instance, they can vary the inkjet geometry and the type of ink to create

3、droplets of different sizes. The size and speed of the ejected droplets are also strongly dependent on the speed at which ink is injected into the nozzle. Simulations can be very useful to improve the understanding of the fluid flow and to predict the optimal design of an inkjet for a specific appli

4、cation.Although initially invented to produce images on paper, the inkjet technique has since been adopted for other application areas. Instruments for the precise deposition of microdroplets often employ inkjets. These instruments are used within the life sciences for diagnosis, analysis, and drug

5、discovery. Inkjets have also been used as 3D printers to synthesize tissue from cells and to manufacture microelectronics. For all of these applications it is important to be able to accurately control the inkjets performance.This example demonstrates how to use COMSOL Multiphysics to model the flui

6、d flow within an inkjet. The model uses the Navier Stokes equations to describe the momentum transport and conservation of mass. Surface tension is included in the momentum equations. A reinitialized, conservative level set method represents and moves the interface between the air and ink.Figure 4-6

7、1 shows the geometry of the inkjet studied in this example. Because of its symmetry you can use an axisymmetric 2D model. Initially, the space between the inlet and the nozzle is filled with ink. Additional ink is injected through the inlet during a period of 10 s, and it consequently forces ink to

8、flow out of the nozzle. When the injection stops, a droplet of ink snaps off and continues to travel until it hits the target. Model Definition Figure 4-61: Geometry of the inkjetTransport of Mass and Momentum The Navier-Stokes equations describe the transport of mass and momentum for fluids of cons

9、tant density. It is possible to model both ink and air as being incompressible as long as the fluid velocity is small compared to the speed of sound. In this model, you must add a term to account for surface tension. The Navier-Stokes equations with surface tension areHere, denotes density (kg/m3),

10、equals the dynamic viscosity (Ns/m2), u represents the velocity (m/s), and p denotes pressure (Pa). Fst is the surface tension force, which iswhere I is the identity matrix, n is the interface normal, equals the surface tension coefficient (N/m), and equals a Dirac delta function being nonzero only

11、at the fluid interface. In COMSOL Multiphysics, the Navier-Stokes equations are already formulated in the Incompressible Navier-Stokes application mode, which is available in the MEMS Module. You must add only the surface-tension force expressed in cylindrical coordinates.The following table gives t

12、he physical parameters of ink and air:REPRESENTATION AND CONVECTION OF THE FLUID INTERFACEIn this model you use a reinitialized, conservative level set method to describe and convect the interface. The 0.5 contour of the level set function defines the interface, where equals 0 in air and 1 in ink. I

13、n a transition layer close to the interface, goes smoothly from 0 to 1. The normal to the interface is The interface moves with the fluid velocity, u, at the interface. The following equation describes the reinitialized convection of the level set function: The thickness of the transition layer is p

14、roportional to . For this model you can use = 2h, where h is the mesh size. You then obtain a sharper interface in the regions where the mesh is finer. In this example you use a structured mesh. For unstructured meshes, avoid letting depend on h. The parameter determines the amount of reinitializati

15、on. If the velocity gradients are small at the fluid interface you can choose = 1. In this example the velocity gradients at the interface are significant, and you must therefore choose a larger value for to keep the thickness of the transition layer constant. You can use the level set function to s

16、mooth the density and viscosity jump across the interface by letting To simplify the calculation of the surface tension force, set Initial Conditions Figure 4-62 shows at t = 0, that is, the initial distribution of ink and air. The velocity is initially 0. Figure 4-62: Initial distribution of ink. B

17、lack corresponds to ink and white corresponds to air.Boundary Conditions InletThe inlet velocity in the z-direction increases from 0 to the parabolic profile during the first 2 s. The velocity is then v(r) for 10 s and finally decreases to 0 for another 2 s. You can obtain this effect by using the s

18、mooth step function H(t 1,2), which is 0 for t 1 + 2 as shown in Figure 4-63. Figure 4-63: Smooth step function f(t) = H(t 1,2).The time-dependent velocity profile in the z-direction can then be defined as For the level set equation, use = 1 as the boundary condition.OutletSet a constant pressure at

19、 the outlet. The value of the pressure given here is not important because the velocity depends only on the pressure gradient. You thus obtain the same velocity field regardless of whether the pressure is set to 1 atm or to 0. Use convective flux as the boundary condition for the level set equation.

20、WallsOn all other boundaries except the target, set no slip conditions. If you use them at the target, the interface cannot move along this boundary. You can resolve this problem by replacing the no slip condition with a Navier slip condition. In this case, the Navier slip condition for the velocity

21、 component in the r-direction, u, is given bywhere is a small parameter called the slip length. Note that should be of the same order as the size of the mesh.Use insulation/symmetry as the boundary condition for the level set equation on all walls including the target. This prevents any outflow of w

22、ater or ink through the walls.Results and DiscussionFigure 4-64 and Figure 4-65 show the ink surface and the velocity field at different times. The droplet hits the target after approximately 160 s.Figure 4-64: Position of air/ink interface and velocity field at various times.Figure 4-65: Position o

23、f air/ink interface and velocity field at various times.Figure 4-66 illustrates the mass of ink that is further than m from the inlet. The figure shows that the mass of the ejected droplet is approximately kg.Figure 4-66: Amount of ink just above the nozzle.This example studies only one inkjet model

24、, but it is easy to modify the model in several ways. You can, for example, change properties such as the geometry or the inlet velocity and study the influence on the size and the speed of the ejected droplets. You can also investigate how the inkjet would perform if the ink were replaced by a diff

25、erent fluid. It is also easy to add forces such as gravitation to the model.Modeling in COMSOL Multiphysics To set up the model in COMSOL Multiphysics you use two 2D axisymmetric application modes: Incompressible Navier-Stokes, and Convection and Diffusion. In the Navier-Stokes equations you must ad

26、d the surface-tension force. You must also modify the Convection/Diffusion equation to obtain the level set equation.You use a structured mesh and refine it in the regions where the fluid interface passes. Before starting the calculations, you must reinitialize the level set function. Do so by solvi

27、ng only for the level set function with zero velocity. Then use the resulting solution as initial data.To calculate the droplets mass use an integration coupling variable. To visualize the droplet in 3D, revolve the 2D axisymmetric solution to a 3D geometry.ReferencesJyi-Tyan Yeh, “A VOF-FEM Coupled

28、 Inkjet Simulation, Proc. ASME FEDSM01, New Orleans, Louisiana, 2019.2. E. Olsson and G. Kreiss, “A Conservative Level Set Method for Two Phase Flow, J. Comput. Phys., vol. 210, pp. 225-246, 2019.Modeling Using the Graphical User Interface Model Navigator Geometry Modeling 1 From the Draw menu selec

29、t Specify ObjectsLine2 Select Closed polyline (solid) from the Style list.3 In the r edit field, enter 0 1e-4 1e-4 2.5e-5 2.5e-5 1e-4 1e-4 2e-4 2e-4 0, and in the z edit field 0 0 2e-4 5.75e-4 6e-4 6e-4 1.5e-3 1.5e-3 1.6e-3 1.6e-3.4 Click OK.5 Click the Zoom Extents button on the Main toolbar.6 Shif

30、t-click the Rectangle/Square button on the Draw toolbar. Enter 1e-4 in the Width edit field, 2e-4 in the Height edit field, and 0 in both the r field and the z fields. Make sure Corner is selected in the Base list. Click OK.7 Repeat the previous step three times to specify three more rectangles acco

31、rding to the following table: OPTIONS AND SETTINGS1 From the Options menu select Constants.2 Enter the following constant settings:3 Click OK.4 From the Options menu select ExpressionsScalar Expressions.5 Insert the following expressions:6 Click OK.Physics Settings Subdomain SettingsIncompressible N

32、avier Stokes 1 In the Model Tree, right-click Incompressible Navier-Stokes (mmglf) and select Subdomain Settings.2 Select Subdomain 1 and press Ctrl+A to select all the subdomains. Enter rho in the Density edit field, then enter eta in the Dynamic viscosity edit field.3 Click the Element tab. Select

33、 P2P-1 from the Predefined Elements list.4 Click OK.Next add the surface-tension force, expressed in cylindrical coordinates and in the weak form:1 Select PhysicsEquation SystemSubdomain Settings. Click the Weak tab.2 In the first row of the Weak edit field enter -r*sigma*(test(ur)*(1-normr*normr)-t

34、est(uz)*normr*normz+test(u)/r)*gphi and in the second row enter -r*sigma*(-test(vr)*normr*normz+test(vz)*(1-normz*normz)*gphi3 Click OK.Boundary ConditionsIncompressible Navier-Stokes 1 In the Model Tree, right-click Incompressible Navier-Stokes (mmglf) and select Boundary Settings.2 Press Ctrl and

35、select all the boundaries at the symmetry line, that is, Boundaries 1, 3, 5, 7, and 9. Select Axial Symmetry from the Boundary condition list.3 Select the inlet (Boundary 2) and select the boundary condition Inflow/Outflow velocity. Type inletvel in the z-velocity edit field.4 Select Boundary 24 (th

36、e outlet) and specify the boundary condition Outflow/Pressure.5 Select Boundaries 11, 18, and 23 (the target). Select the boundary condition Inflow/Outflow velocity and type lambdaslip*uz in the r-velocity edit field.6 Verify that the boundary condition for the remaining boundaries (12, 13, 15, 19,

37、20, and 22) is No slip.7 Click OK.Subdomain SettingsConvection and Diffusion 1 In the Model Tree window, right-click Convection and Diffusion (cd) and select Subdomain Settings.2 Make sure that all the subdomains are selected.3 Enter 0 in the Diffusion coefficient edit field, u in the r-velocity edi

38、t field, and v in the z-velocity edit field.4 Click the Init tab and enter phi0 in the edit field.5 Click the Element tab and select Lagrange Linear in the Predefined elements list.6 Click OK.Adjust the convection/diffusion equation to obtain the conservative level set equation:1 Select PhysicsEquat

39、ion SystemSubdomain Settings. Click the f tab.2 Replace the expression in the fourth row with 0.3 Click the tab.4 Replace the expression in the first column, fourth row with r*u_phi_cd*phi+gamma*(r*phi*(1-phi)*normr-2*h*r*phir). Replace the expression in the second column, fourth row with r*v_phi_cd

40、*phi+gamma*(r*phi*(1-phi)*normz-2*h*r*phiz).5 Click OK.Boundary ConditionsConvection and Diffusion 1 In the Model Browser, right-click Convection and Diffusion and select Boundary Settings.2 Select Boundaries 1, 3, 5, 7, and 9, then select Axial symmetry in the Boundary condition list.3 Select the i

41、nlet (Boundary 2) and set Concentration as the boundary condition. Enter 1 in the Concentration edit field.4 Select the outlet (Boundary 24) and set Convective flux as the boundary condition.5 The default boundary condition Insulation/Symmetry holds for all other boundaries.6 Click OK.Mesh Generatio

42、n 1 From the Mesh menu select Mapped Mesh Parameters.2 Click the Boundary tab.3 Select Boundaries 1, 2, 3, 5, 7, 9, 15, and 22, then select the Constrained edge element distribution check box. Next select each boundary separately and specify the Number of edge elements according to this table:4 Clic

43、k Remesh and then click OK.Computing the Solution First reinitialize to obtain the correct shape of in the transition layer.1 From the Solve menu select Solver Parameters.2 Click the General tab and enter 0 2e-6 in the Times edit field. Click OK.3 Select SolveSolver Manager.4 Click the Solve For tab

44、. Select Convection and Diffusion (cd). Click OK.5 Select SolveSolve Problem. This creates a good initial solution to the level set function.6 To visualize the initial level set function, click the Plot Parameters button on the Main toolbar. Click the Surface tab, then select Convection and Diffusio

45、nConcentration, phi from the Predefined quantities list. Click OK.Use the obtained solution as an initial condition to the simulation of the droplet motion.1 Click the Solver Manager button on the Main toolbar. Click the Initial Value tab.2 Click the Store Solution button. Select the time 2e-6. Clic

46、k OK.3 In the Initial value area select Stored solution.4 Select 2e-6 from the Solution at time list.5 Click the Solve For tab. Click Geom1 (2D) to select all the variables. Click OK.6 From the Solve menu select Solver Parameters.7 Click the General tab, then enter 0:1e-5:2e-4 in the Times edit fiel

47、d. Click OK.8 Click the Solve button on the Main toolbar.Postprocessing and Visualization To visualize the inkjet surface in 3D, perform these steps:1 From the Draw menu select Revolve.2 In the Objects to revolve list select all the elements (select any one and then press Ctrl+A). Click OK.3 In the

48、Model Tree click Geom1 to return to the 2D model.4 Select OptionsExtrusion Coupling VariablesSubdomain Variables.5 Select any subdomain and then press Ctrl+A to select all the subdomains.6 Enter phi3d in the Name field and phi in the Expression field.7 Click the General transformation option button.

49、8 Locate the second row, then enter vel3d in the Name field and sqrt(u2+v2) in the Expression field.9 Select General transformation for this variable.10 Click the Destination tab. In the Geometry list select Geom2. In the Level list select Subdomain.11 Select any subdomain and press Ctrl+A to select

50、 all the subdomains.12 Select the Use selected subdomains as destination check box.13 Enter sqrt(x2+z2) in the x edit field, then click OK.14 Select phi3d from the Variable list. 15 Select the Use selected subdomains as destination check box and enter sqrt(x2+z2) in the x edit field. Click OK.16 From the Solve menu select Update