Determining the drag force with CFD method ANSYS Workbench Ott Pabut

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1 Determining the drag force with CFD method ANSYS Workbench Ott Pabut Tallinn 2010

2 Task 1 Determine analytically and with CFD method the moment which is generated on the foundation of the water tower. The mass of the tower can be ignored. D 1 U Data b+d 1 /2 b/2 D 2 b D 1 = 15 m D 2 = 5 m b = 20 m U = 30 m/s C sphere = 0,42 C cylinder = 1,15 Ρ air = 1,2401 kg/m 3 M Fig 1 The water tower 1.1 Analytical solution The drag force for each element can be determined separately with Reyleigh equation., 1 where F D drag force generated by the body, ρ density of the fluid, U speed of the body or the fluid, C d experimentally determined drag force coefficient, A surface area of the body perpendicular to the flow. For the sphere: , ,42 3, For the cylinder: 41397,17 N 41,4 kn , , ,18 N 64,2 kn 2

3 Force applied to the water tower 41,4 64,2 105,6 kn In order to find the moment at the foundation the forces must be applied to their centers of area: , ,2 1780,5 kn m 2 2 Answer: Foundation must resist bending moment M=1780,5 kn m. 1.2 CFD solution In this case the model for Ansys Workbench would have been with dimensions 45x15x15 m. With these figures the flow analysis would have taken up much time and computer resource. To decrease the calculation time element count could have been made smaller, but that would have also taken down accuracy of the results. For a better solution the hydrodynamic similarity laws are used. This enables to conduct experiments on smaller models but ensures that the results are transferable to reality. As we are dealing with incompressible flow, Reynlods similarity criteria is used. Two systems are similar, when their Reynolds numbers are equal., 2 where D system dimension, μ dynamical viscosity of the fluid, ν kinematical viscosity of the fluid. From the equation 2 it can be seen that in order to reduce the dimensions of the system, speed of the fluid U must be increased or kinematic viscosity μ must be decreased. In our task dimensions must be reduced at least 10 times, which means that the speed of the flow would go up to 300 m/s. This is unfavorable since it is close to the speed of sound 343 m/s. Systems with sonic flows are not stable and our results might be inadequate. To solve the problem we will change the viscosity by choosing a different fluid water instead of air. Table 1 Physical parameters of air and water air water density ρ 1,2041 kg/m 3 998,19 kg/m 3 dynamical viscosity μ 1, Pa/s 1, Pa/s kinematical viscosity ν 1, m 2 /s 1, m 2 /s 3

4 Proportional coefficient: 1, ,15 1,01 10 Therefore the dimensions of the new model must be 15,15 smaller. Table 2 New dimensions of the system D 1 = 0,990 m D 2 = 0,330 m b = 1,320 m U = 30 m/s Creating a new project Open program ANSYS Workbench 1. Click Empty project 2. Inside the wizard choose File, Save As Save the project as Veetorn 4. From the left menu choose Advanced CFD, New Simulation Workbench offers possibilities for different flow analysis General, Turbomachinery, Quick Setup, Library Template 5. Choose General as the simulation type Workbench opens the preprocessing unit CFX-pre 6. Inside the wizard choose File, Save Simulation As... Save the project as Veetorn.cfx Importing the mesh 1. Choose File, Import mesh... and upload the file Veetornmesh.cfx 2. Save the simulation 4

5 1.2.3 Creating the computational domain Fig 1 Imported mesh It is assumed that the flow inside the computational domain is turbulent and isothermal. These are the most similar conditions to those in the real environment. For these simulations the Shear Stress Transport (SST) turbulence model with automatic wall condition analysis is used. This enables for very precise separation of flow particles when there are at least 10 mesh nods in the boundary layer. Currently the mesh is more robust to save calculation time. 1. From the upper taskbar click Create a Domain and name it Veetorn. 2. Apply the following settings General Basic Settings > Fluids List Water options Domain Models > Pressure > Reference Pressure 1 [atm] Fluid Models Heat Transfer > Option Isothermal Heat Transfer > Fluid Temperature 288 [K] Turbulence > Option Shear Stress Transport In order to get realistic results the boundary conditions must be similar to those in the reality. For that reason atmospheric pressure and possible temperatures of the fluid are determined. 3. Click OK 5

6 1.2.4 Determining the boundary conditions The imported mesh contains predefined 2D regions, which make it easier to apply boundary conditions. For the simulation following conditions are needed: inlet, outlet and walls (no slip and slip condition). Inlet 1. From the upper taskbar click Create a Boundary Condition 2. Name it Inlet 3. Apply following settings Basic Settings Boundary Type Inlet Location Inlet Boundary Flow Regime > Option Subsonic Details Mass and Momentum > Option Normal Speed Mass and Momentum > Normal speed 30 [m s ^-1] Turbulence > Option Low (Intensity = 1%) Turbulence intensity is similar to the average wind tunnel where it is approximately 1-2 %. Outlet 4. Click OK 1. Create a new boundary condition Outlet Basic Settings Boundary Type Outlet Location Outlet Boundary Flow Regime > Option Subsonic Details Mass and Momentum > Option Static pressure Mass and Momentum > Relative Pressure 0 [Pa] Relative pressure defines the difference between the outlet and inlet pressure, currently the same pressure applies for both and therefore the relative is 0 Pa. 3. Click OK 6

7 Fig 2 Inlet and Outlet For sides and the upper plane of the rectangle slip wall condition is suitable. For those walls the shear stress value is 0 and the flow of the fluid is not interrupted. If wind tunnel is used, the dimensions of the rectangle should be equal to the tunnel. Computational domain for atmospheric simulations must be big enough to ensure that streamlines exiting the area are straight. FreeWalls 1. Create new boundary condition FreeWalls Basic Settings Boundary Type Wall Location Free1 Boundary Details Wall Influence On Flow > Option Free Slip 3. Click Ok 7

8 Noslip wall 1. Create a new boundary condition Body Basic Settings Boundary Type Wall Location Body Boundary Details Wall Influence On Flow > Option No Slip 3. Click OK Properties for the remaining 2D regions (in this case the lower XZ plane) are determined by default. Currently the adiabatic no slip wall condition is suitable. Name of the default conditions is Default Boundary. Even though Body and Default Boundary conditions are identical, the Body condition was applied separately to allow easier post processing of the results Determining the initial conditions 1. Click Define the Global Initial Conditions Global Initial Conditions > Cartesian Velocity Automatic With Value Settings Components > Options Initial Conditions > Cartesian Velocity 0 [m s ^-1] Components > U Initial Conditions > Cartesian Velocity 0 [m s ^-1] Components > V Initial Conditions > Cartesian Velocity 30 [m s ^-1] Components > W Initial Conditions > Turbulence Eddy Dissipation (Selected) 3. Click OK 8

9 1.2.6 Setting the output data As Workbench does not automatically calculate forces and moments, the parameters in question must be set manually. 1. Click Create Output Files and Monitor Points Results Output Boundary Flows (Selected) Output Boundary Flows > Boundary Flows All 3. Click OK Calculating the drag force To find the drag force on a surface, module Expressions must be used. It will apply CFX expression language ((CEL) to find suitable parameters. 1. Click Create Expression 2. Name it FFlow and click OK 3. Under Definition write the following code: 4. Click OK Modifying the solver control 1. Click Solver Control Basic settings Convergence Control > Max. Iterations 15 Convergence Criteria > Residual Target 1e Vajuta OK In normal condition the number of iterations must be at least 100, but in order to reduce the calculation time it has been reduced. 9

10 1.2.9 Getting the solution 1. Click Write Solver File 2. Name it Veetorn.def 3. Click Save Workbench opens the Run Definition window 4. Click Start Run Progress of the calculations can be observed form the Momentum and Mass charts. If the results appear to go into the wrong direction, we can stop the calculations and enforce necessary changes. On the right, info about the progress of the calculation and iterations is displayed. Fig 3 Progress of the calculations When the number of iterations has been reached or results have converged Workbench will issue a message. To display and process results, question Post-process results now? must be answered Yes. To study the simulation progress, the answer should be No. The results can also be viewed by selecting CFX-Post form the lower taskbar. 10

11 1.3 Visualization and processing of results To display results a base plane with sampling points must be created. This will determine the starting points of the velocity vectors. 1. From the upper taskbar click Insert, Location, Plane 2. Name it Baseplane 1 3. Apply following settings Geometry Definition > Method Point and Normal Definition > Point 0, 2.5, 0 Definition > Normal 1, 0, 0 Plane Bounds > Type Rectangular Plane Bounds > X size 5 [m] Plane Bounds > Y size 10 [m] Plane Type Plane Type > X Samples 50 Plane Type > Y Samples 50 Sample Render Draw Faces (Selected) Draw Lines (Selected) 4. Click Apply Display the pressure distribution on the base plane 1. Double-click Baseplane Color Mode Variable Variable Pressure 3. Click Apply Next the velocity vectors on the base plane are visualized. This helps to determine the directions of flow particles and helps to display the recirculation zones. 1. Click Insert, Vector 2. Name it velocityvectors 3. Apply following settings 11

12 Geometry Definition > Locations Baseplane Definition > Sampling Vertex Symbol Symbol Size Click Apply Next streamlines are displayed to observe the flow. 1. Click Insert, Streamline 2. Name it Streamlines 3. Apply following settings Geometry Type 3D Streamline Definition > Start From Inlet Definition > # of Points Click Apply Fig 4 Streamlines To find the drag force, click Quantitative on the Outline toolbar and then click Fflow Result is = [N], computational time 0:8:42 12

13 Drag force determined analytically was F sum =105,6 kn and with CFD method Z = 211, 4 kn. Analytical and CFD results differ about 2 times. The reason for big difference can be found in the size of the generated mesh and in the small number of iterations. 13

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