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Flow Over a Cylinder

- Flow over a cylinder Finite Element Tutorial
- By Dr. Essam A. Ibrahim, Tuskegee University, Mechanical Engineering Dept., [email protected] Copyright 2006
- Expected completion time for this tutorial: 45 minutes to 1 hour
- Companion tutorial for Fluid Mechanics Course
- Reference Text: Fluid Mechanics, 5th Edition, by Frank M. White

Table of Contents

- Educational Objectives
- Problem Description
- Introduction to COSMOSFloWorks
- Step by Step Process
- Viewing the Results of the FE Analysis
- Comparison of Analytical to Finite Element Analysis
- Conclusion
- Acknowledgment

Educational Objectives

1. Be familiar with the basis of FE theory for two-dimensional flow analysis.

2. Understand the fundamentals of external flow over cambered bodies through the use of the COSMOSFloWorks finite element software.

3. Be able to construct a correct solid model using the SolidWorks CAD and perform an accurate finite element analysis using COSMOSFloWorks.

4. Know how to interpret and evaluate finite element solution quality including verifying analytically the drag coefficient of a cylinder immersed in a uniform fluid stream.

5. Learn to apply the appropriate ambient and boundary conditions and decide on the suitable size for the computational domain.

Problem Description

- In this tutorial we use COSMOSFloWorks to determine the aerodynamic drag coefficient of a circular cylinder immersed in a uniform fluid stream. The cylinder axis is oriented perpendicular to the stream.
- The computations are performed for Reynolds number = 10 and 1,000 where Re = UD/ = UD/, D is the cylinder diameter, U is the velocity of the fluid stream, and , and are the fluid density, dynamic viscosity and kinematic viscosity, respectively.

Problem Description

- The aerodynamic drag coefficient for the cylinder is defined as:

where FD is the total force in the flow direction (i.e. drag) acting on a cylinder of diameter D and length L.

- The Goal of the simulation is to obtain the drag coefficient for a circular cylinder of D = L = 0.1m, placed in air stream at 20 C using COSMOS FloWorks and compare it with experimental data.

Introduction to COSMOSFloWorks Overview

- COSMOSFloWorks 2007 Capabilities
- Governing Equations of Fluid Motion
- COSMOSFloWorks Theoretical Background
- Fluid Flow Terminology
- Steps to Analysis
- COSMOSFloWorks Project
- Ambient and Boundary Conditions

Introduction to COSMOSFloWorks Overview

- Run, Solve
- Solve Command
- Monitoring the Solution
- FloWorks Results

COSMOSFloWorks 2007 Capabilities

- COSMOSFloWorks is based on advanced Computational Fluid Dynamics (CFD) techniques and allows you to analyze a wide range of complex flows with the following characteristics:

COSMOSFloWorks 2007 Capabilities

- Two- and Three-Dimensional analyses
- External and Internal Flows
- Steady-state and Transient flows
- Incompressible liquid and Compressible gas flows including subsonic, transonic and supersonic regimes

COSMOSFloWorks 2007 Capabilities

- Non-Newtonian liquids*(laminar only)
- Compressible liquids* (liquid density is dependent on pressure)
- Laminar, turbulent, and transonic flows
- Swirling flows and Fans
- Multi-species flows
- Flows with Heat Transfer within and between fluids and solids (Conjugate Heat Transfer)
- *Professional Version only

COSMOSFloWorks 2007 Capabilities

- Surface-to-surface radiation* (including solar heating)
- Flows with Gravitational effects (also known as buoyancy effects)
- Porous media
- Fluid flows with liquid droplets or solid particles
- Walls with roughness
- Tangential motion on walls* (translation and rotation)

Governing Equations of Fluid Motion

- COSMOSFloWorks solves the full Navier-Stokes Equations- The equations are supplemented by fluid state equations defining the nature of the fluid, and by empirical laws for dependency of viscosity and thermal conductivity on other flow parameters
- Conservation equations are conserved
- Conservation of mass (Continuity equation)
- Newton’s second law of motion( Momentum Equation)
- The First Law of Thermodynamics (Conservation of Energy Equation)
- Transport equations are used for turbulent kinetic energy and dissipation rate (k-e model)

COSMOSFloWorks Theoretical Background

- COSMOSFloWorks solves the governing equations using the finite volume (FV) method rather than the finite element method
- On spatially rectangular computational mesh designed in the Cartesian coordinate system
- With the planes orthogonal to its axes and refined locally a the solid/fluid interface.
- And, if necessary, additionally in specified fluid regions, at the solid/solid interfaces, and in the fluid region during calculation.

COSMOSFloWorks Theoretical Background

- Values of all physical variables are stored at the mesh centers..
- The governing equations are discretized in a conservation form.
- The spatial derivatives are approximated with implicit difference operators of second order accuracy.

COSMOSFloWorks Theoretical Background

- A laminar/turbulent boundary layer model is used to describe flows in near-wall regions. The model is based on the so-called Modified Wall Functions approach.
- This model is employed to characterize laminar and turbulent flows near walls, and to describe transitions from laminar to turbulent flow and vice versa.

COSMOSFloWorks Theoretical Background

- Iterative Methods for Nonsymmetrical Problems
- To solve the asymmetric systems of linear equations that arise from approximations of momentum, temperature and species equations, preconditioned generalized conjugate gradient method is used. Incomplete LU factorization is used for preconditioning.
- Iterative Methods for Symmetric Problems
- To solve symmetric algebraic problem for pressure-correction an original double-preconditioned iterative procedure is used. It is based on a specifically developed multigrid method.

Fluid Flow Terminology

- COMOSFloWorks always uses absolute pressure
- Absolute Pressure- when pressure is given relative to zero pressure (i.e. psia)
- Gage Pressure-when pressure is given relative to the atmospheric pressure of the surroundings (i.e. psig)
- For example at sea level the absolute pressure would be 14.6959 psia (pounds per square inch absolute, or 0.00 psig (pounds per square inch gage) if the gage were set to sea level pressure.

Fluid Flow Terminology

- There are two ways to measure pressure in fluid flow: Static Pressure, P, and Total (Stagnation) Pressure,
- Static pressure is the pressure indicated by a measuring device moving with the flow or by a device that introduces no change to the flow.
- Total pressure is the pressure measured by bringing the flow to rest isentropically (without loss)

Fluid Flow Terminology

- Dynamic pressure
- Dynamic pressure can also be defined as the difference between Total pressure and Static pressure
- For compressible flow
- Using state adiabatic equations and the gas state equation ( ) the relation between static and total pressure can be written.

Steps to Analysis

- Create design in SolidWorks
- FloWorks can analyze Parts, Assemblies, Subassemblies, Multibodies
- Create COSMOSFloWorks Project file
- Use FloWorks Wizard to create project file

COSMOSFloWorks Project

- A COSMOSFloWorks project contains all the settings and results of a problem.
- Each COSMOSFloWorks project is associated with a SolidWorks configuration
- By modifying a COSMOSFloWorks project you can analyze flows under various conditions and for modified SolidWorks models
- When a basic project has been created, a new COSMOSFloWorks Design Tree tab appears on the right of the right side of the SolidWorks Configuration Manager tab.
- You can use the COSMOSFloWorks Design Tree to specify the remaining project data such as boundary conditions, initial conditions, heat sources, material conditions, and goals.

COSMOSFloWorks Project

- To create a project, you must define the following:
- A project name
- A system of units
- An analysis type (external or internal)
- The type of fluid (gas, incompressible liquid, Non-Newtonian laminar liquid, or compressible liquid)

Overview of SolidWorks Window

- Menu bar
- Sketch toolbar/Sketch Relations toolbar
- Confirmation Corner with sketch indicator
- Graphics area
- Sketch origin
- Reference Triad

COSMOSFloWorks Project

- To create a project, you must also define the following (if applicable):
- The substances (fluids and solids)
- Initial or ambient conditions
- The geometry resolution and the results resolution
- A wall roughness value
- Physical features include heat transfer in solids, high Mach number gas flow effects, gravitational effects, time dependent effects, surface-to-surface radiation and laminar only flow.

COSMOSFloWorks Project

- To create a project, you define the following (if applicable):
- Default wall conditions, e.g. adiabatic wall, if heat transfer in solids is not considered.
- Default outer wall thermal conditions in case of internal analysis with heat transfer,
- Default radiation wall conditions in case of surface-to-surface radiation

Wall Boundary Conditions

- The default velocity boundary conditions at solid walls corresponds to the no-slip condition (velocity goes to zero at the wall).
- The ”Ideal Wall” condition is also available. For example Ideal Walls can be used to model planes of flow symmetry.

COSMOSFloWorks Project

- You can create a new COSMOSFloWorks project in three ways:
- 1. The Wizard is the most straightforward way to create a COSMOSFloWorks project. It guides you step-by-step through the analysis set-up process.
- 2. You can create a COSMOSFloWorks project by using a Template created from a previous COSMOSFloWorks project. Then click Project, NEW and enter the required information.
- 3. To analyze different flow or model variations, the most efficient method is to clone (copy) your current project. The new project will have all the settings of the cloned project, including the results settings.

Run , Solve

- COSMOSFloWorks discretizes the time –de-pendent Navier-Stokes equations and solves them on the computational mesh.
- Under certain conditions, to resolve the solution’s features better, COSMOSFloWorks will automatically refine the computational mesh during the flow calculation.
- Since COSMOSFloWorks solves steady-state problems by solving time-dependent equations, COSMOSFloWorks has to decide when a steady-state solution is obtained ( i.e. the solution converges), so that the calculation can be stopped. COSMOSFloWorks offers for you a choice of different conditions to finishing the calculation.

Monitoring the Solution

- Goals Tab
- Monitor each goal for convergence; it should flatten out
- Its good practice to monitor mass balance (SG’s)
- You can stop the calculation and view the results to determine if additional iterations are necessary
- Preview Tab
- Check flow behavior to ensure proper set up
- Info Tab
- Cell count, CPU time, & No. of Iterations

FloWorks Results

- Results Plots (Qualitative)
- Vectors, Contours, Isolines
- Cut Plots, Surface Plots, Flow Trajectories, Isosurfaces
- Processed Results (Quantitative)
- X-Y plots (Excel)
- Goals (Excel)
- Surface Parameters
- Point Parameters
- Report
- Reference Fluid Temperature

Solve Command

- To solve your project ,go to the FloWorks command line and click Solve.
- You will have one of two methods to solve your project
- RUN
- BATCH RUN

Using the SolidWorks Interface

- Toolbar area
- Feature Manager window
- Graphical Interface window

Overview of SolidWorks Window

- Menu bar
- Sketch toolbar/Sketch Relations toolbar
- Confirmation Corner with sketch indicator
- Graphics area
- Sketch origin
- Reference Triad

Left Side of SolidWorks Window

- Feature Manager icon
- Feature Manager design tree
- COSMOSWorks icon
- COSMOSWorks Manager tree

Toolbars

- You can select which toolbars to display under View in the menu heading
- Toolbars are moveable to top, and sides of the window
- Icon Buttons for frequently used commands

Create a New Part

- In SolidWorks main tool bar click File, New.The New Solid Document window appears
- The part icon is highlighted
- Click OK. The SoliWorks graphical interface window appears.

Sketch Part

- In SolidWorks menu tool bar click the Sketch icon
- A menu of shapes appears. Select circle

Create a Plane

- The Front, Top, and Right planes appear in the graphical interface window
- Select the Front plane to start the sketch. The display changes so that the front plane is facing you. A sketch opens on the front plane.

Draw a Circle

- Move the pointer in the graphical interface window to the sketch origin and drag the mouse to draw a circle
- In the circle command window adjust the circle radius to 50 mm or 5cm.
- Accept the new dimensions by clicking the check mark .

Create a Cylinder

- In the SolidWorks menu bar click the Feature icon and select Extruded/Boss Base
- The circle is extruded into a cylinder. In the Extrude window set the cylinder length to 100 mm or 10 cm
- Accept the part by clicking the check mark.

Save Part

- The part is displayed as Trimetric view. To change the view to Isometric click the view tab located at the lower left corner of the graphical interface window area and choose Isometric
- To save the part, click File, Save as in the SolidWorks menu bar. Save the part in my documents folder under the name cylinder

Importing the Solid Part

- Click File, Open, my documents folder opens
- Select the file named “cylinder” which contains the part previously created using SolidWorks
- The part is imported

Create New Configuration

- Click FlowWorks on the main toolbar then click Project, Wizard (The Wizard guides you through the definition of a new project)
- Select Create new. In the configuration name type Cylinder_Re_ 10
- Click Next

Select Unit System

- In the Unit System dialog box you can select the desired system of units for both input and output (results)
- Specify the International System SI by default
- Click Next

Specify Analysis Type

- In the Analysis Type dialog box select an External type of flow analysis. This dialog box allows you to specify advanced physical features you want to include in the analysis. In this project we will not use any of the advanced physical features
- Click Next

Choose Default Fluid

- In the Default Fluid dialog box open the Gases folder (by clicking the square to its left)
- Double-click the Air item
- Click Next

Set Wall Conditions

- Since we don’t intend to calculate heat conduction in solids, we keep the default Adiabatic wall setting denoting that all the model walls are heat insulated
- We also keep the default 0 micrometer wall roughness
- Click Next

Initial and Ambient Conditions

- In the Initial and Ambient Conditions dialog box we specify the incoming flow velocity by clicking the Velocity in X direction box
- The Dependency button is enabled
- Click Dependency. The Dependency dialog box appears

Velocity Calculation Formula

- In the Dependency type list select Formula definition
- In the Formula box type the formula defining the flow velocity using Reynolds number = 10. Here the kinematic viscosity of air is

n=1.51E-5 m2 /sec at a temperature of 293.2 K and the cylinder diameter is 0.1 m.

- Click OK you will return to the Initial and Ambient Conditions dialog box.

Results and Geometry resolution

- In the Results and Geometry Resolution specify a result resolution level of 7
- Accept the automatically defined minimum gap size

and wall thickness

- Click Finish. The project is created and the 3D Computational Domain is automatically generated

Computational Domain

- In this tutorial we are only interested in determining the drag coefficient of the cylinder without the 3D effects. Thus, to reduce the required CPU time and computer memory, we will perform 2 – dimensional (2D) calculations.
- In the COSMOSFloWorks analysis tree (located to the left of the graphical interface window) expand the Input Data icon.
- Right click the Computational Domain icon and select Edit Definition. The Computational Domain dialog box appears.

Boundary Conditions

- In the Computational Domain dialog box click Boundary Conditions tab
- In the 2D Plane flow list select XY-Plane Flow (since the z axis is the cylinder axis). Automatically the symmetry condition is specified at Z min = 0.04 m and Z max = 0.06 m boundaries of the Computational Domain

Computational Domain Size

- In the Computational Domain dialog box click the Size tab
- Specify the coordinates of the Computational Domain as shown in the picture (the default Computational Domain is manually set farther away from the cylinder to eliminate any disturbances of the incoming flow due to the presence of the cylinder)
- Click OK

Global Goals

- Since the incoming flow is aligned with the X – axis direction, the cylinder drag is calculated through the X-component of the force acting on the cylinder. The X – Component of Force can be easily determined by specifying it as a COSMOSFloWorks global goal.
- Click FloWorks, Insert, Global Goals
- In the Parameter table select the first check box in the X – Component of Force row

Global Goals

- Click OK. The new GG X – Compnent of Force 1 item appears in the COSMOSFloWorks analysis tree

Obtaining Solution

- Click FloWorks, Solve. The Run window appears
- Accept the default settings for New calculation, Solver, and Load results
- Click Run

Monitor Solver

- The Solver window appears. Monitor convergence status, number of iterations, and any warnings

Load Results

- Click FloWorks, Results, Load/Unload Results. The Load Results dialog box appears
- In the Load Results dialog box, keep the default project’s results file 1.fld and click Open

Displaying Cut Plots

- In the COSMOSFloWorks analysis tree, under Results, right click the Cut Plots icon.
- An Insert option window appears

View Settings

- In the Cut Plot settings window, choose the Front Plane in the Selection.
- Push the Contours radio button in.
- Click open the View Settings window

View Settings

- Push the Contours radio button in.
- Choose Velocity in the Parameter Menu
- Click Reset Min/Max button.
- Slide Number of colors bar to about 100.
- Click OK.

Velocity Profile

- A 2-Dimensional Velocity Profile is shown in the Cut Plot window.
- Use Left and Right Mouse buttons to rotate the Cylinder for Pan and Zoom functions.

Flow Trajectory 1

- Click open the Flow Trajectory window and choose Use fixed color option to overlap flow tajectories on the Velocity Profile.
- The Use from contours option is chosen when only the Flow Trajectories to be shown
- Click OK

Flow Trajectory 2

- The Flow Trajectory is shown on top of the Velocity Profiles.

Calculation of the Drag Coefficient

- In the COSMOSFloWorks analysis tree, under Results, right click the Goals icon.
- An Insert option window will open

Add Goals

- The Goals dialog box appears
- Click Add All
- Click OK

Display Results

- The goals 1 Excel workbook is created. Use the average value of the X-Component of Force to calculate the drag coefficient from the formula:
- Compare the drag coefficient computed by COSMOSFloWorks with the experimental value found in your Fluid Mechanics Textbook at Re = 10.

Drag Coefficient

- Substitute Average Value of X-direction Force ( 8.72127E-09 N) in to Fx.
- Substitute Flow Properties and Cylinder Geometry in the denominator:

r=1.204 kg/m3, m=1.82E-5 Ns/m2,D=0.1m, U=(Re*m)/(r*D),

and L=0.02m, the width of the computational domain

Calculated Drag Coefficient (Cd) =3.17687

Validation

- Compare the drag coefficient computed by COSMOSFloWorks with the experimental value at Re = 10.
- Red squares represent the computational results obtained using FloWorks at Re= 1, 1x103, and 1x105, respectively.

Reference: Roland L. Panton, “Incompressible Flow” 2nd ed. John Wiley & sons Inc., 1995

Error Calculation

- Calculate the error by comparing the values of drag coefficients from experimental and computational results.

Advanced Studies

- We can further study the flow properties of the flow around the cylinder by changing the flow velocity
- Student use the same model to run the case with Reynolds Number of 1,000.

- One may use ‘Clone’ function to run the same model with many different flow conditions.
- When Cloning, folders with new flow properties will be created automatically

Cloning of the Project 1

- Create a new project with different name
- This uses the same cylinder geometry data used for the Re=10 case; reduced the amount of time to run cases with new sets of flow parameters.
- All cloned projects’ data are stored in the same folder where the original Cylinder geometry is.

Cloning of the Project 2

- New sets of Flow parameters are entered using General Settings menu.

- Since over Re=60 the flow is unsteady,choose time dependent feature in the Analysis Type
- Unless the working fluid and roughness of the cylinder surface are to be changed, use the input used for Re=10 case.

Cloning of the Project 3

- Open the Initial and ambient condition window; change the flow velocity by changing the Dependency parameters.

- Modify the velocity dependency for the new Renolds number of 1,000.
- The kinematic viscosity and the diameter of the cylinder are constant values

Obtaining Results for Re=1,000

- After the project is cloned and saved, the procedure to solve the flow is identical to the case of Re=10. By using this option, one can reduce time required to run different flow case studies.
- Once students acquired basic skills of using SolidWorks and FloWorks functions, students are encouraged to parametric research of the external flow by changing velocity, temperature, and pressure. When doing this research, this Cloning Project option is useful.

Pressure Distribution Re=1,000

- As Reynolds number increases i.e., velocity increases, the flow becomes unsteady and develops wakes behind the cylinder .

Velocity Distribution Re=1,000

- The results show the separations of the flow from the cylinder surface. The wake tail propagates through the flow medium

Flow Trajectory Re=1,000

- As flow separates from the main stream, circulating vortex is generated behind the cylinder. These unsteady vortices shed and propagate downstream.

Drag CoefficientRe=1,000

- We use the same method to calculate the Drag Coefficient of the cylinder with Re=1,000

Calculated Drag Coefficient (Cd) =0.924023

ValidationRe=1,000

- Compare the drag coefficient computed by COSMOSFloWorks with the experimental value at Re = 1,000.
- Red squares represent the computational results obtained using FloWorks at Re = 1 and 1x105, respectively.

Reference: Roland L. Panton, “Incompressible Flow” 2nd ed. John Wiley & sons Inc., 1995

Error CalculationRe=1,000

- Calculate the error by comparing the values of drag coefficients from experimental and computational results.

As Reynolds number increases, turbulent nature of the flow becomes stronger. This also affects to the accuracy of the computation.

Conclusion

- The accuracy of the simulation is diminished as the Reynolds number is increased due to transition from laminar to turbulent flow. The flow characteristics of turbulent flow are far more complex than laminar flow.
- Parametric studies can be performed with relative ease using numerical methods compare to experimentation.
- The computational results can be visualized and examined via graphical representations.

Acknowledgment

This tutorial was developed under the NSF Grant DUE Number 0536197

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