CFD Training Manual - University of Connecticut …barbertj/CFD Training/UConn Modules... · Web viewCFD Training Manual CFD Training Manual CFD Training Manual Momtchil Petkov Mario

CFD Training Manual

1 | P a g e

Momtchil Petkov

Mario Roman University of Connecticut

Mechanical Engineering Department

Advisor: Professor Barber

Table of Contents

Abstract………………………………………………………. 3

Nomenclature…………………………………….…………… 3

I. Introduction………………………………..……….…… 4

II. CFD Analysis Roadmap…………………..…….……… 4

III. Theory……………………………….….…..……. 7

IV. Module Example—Laminar Flow Past a Cylindrical Pipe……… 18

V. Summary of Tutorials……………………………….…….. 27

VI. Conclusion ………………………………………..……. 43

VII. References………………………………………………. 44

VIII. Appendices - ModulesA--Laminar Pipe Flow……………………….……………

B--Turbulent Pipe Flow…………………….………..……

C--Laminar Flow Over Flat Plate (Geometry and Mesh)…

D--Laminar Flow Over Flat Plate…………………………

E--Nozzle Tutorial ………………………………………..

F--Jets: Turbulent Flow……………………………..…….

G—External Turbulent Compressible and Incompressible Flow across an airfoil…. `

H—Turbulent Incompressible Flow across a Periodic Airfoil …………

I—Discrete Phase Modeling: Particle Injection into a Pipe………………

2 | P a g e

Abstract

ANSYS FLUENT, computational fluid dynamics (CFD) software is very difficult to use especially for new users. To help with this, tutorials have been created to be able to guide users in the use of ANSYS FLUENT. They were created to mimic a classroom-like structure, where the fundamentals are learned first. The creation of fundamental tutorials will allow users to have projects where they will utilize the learning modules as references to guide them in more complicated projects. Through the use of FLUENT and several validation efforts, which are referenced from scholarly sources, the user will be able to validate the accuracy of their results. In addition, with the help of the provided learning modules, the user will be able to create a roadmap to achieve competence to solve more complicated problems.

Nomenclature

A Area C f Coefficient of friction along wall CL Coefficient of LiftCD Coefficient of DragC p Coefficient of PressureD Diameter g Gravity K−Epsilon-Turbulence model to simulate and read turbulent flow M Mach number P Pressure Re Reynolds number ℜx Reynolds number along a position x U cl Centerline Velocity u∞ Fluid velocity u Friction velocity Umax Max. Velocity V Velocity V inlet Inlet Velocity Yp Distance to the wall from center of pipe y+¿¿ Non-dimensionalized distance of first grid point from wall

ρ – Density τ – Shear Stress μ – Dynamic viscosity

3 | P a g e

I. Introduction

One of the biggest challenges in the engineering industry is being able to come up with efficient and optimal designs for new products. One of the strongest tools offered is FLUENT. FLUENT is a very useful program recently acquired by ANSYS. It has the capability to model fluid flow past objects with the ability to design, test, and analyze results all under one program. Although it is a strong tool for engineering, it is also very difficult to use. For this reason, tutorials have been created to teach FLUENT with the hope that these tutorials will serve as a fundamental tool in teaching and as references for future senior design projects. The way the tutorials are set up are by creating and analyzing basic flow fields and then to ensure the accuracy of each test case it is then validated against a scholarly reference.

The structure of the tutorials is to first reproduce the fundamentals learned in a Fluid Mechanics and Thermo Dynamics courses. One of the first scenarios learned in fluid mechanics is the flow through a cylindrical pipe. The tutorials created follow very closely to how a fluid mechanics course would be taught. For this reason, the first tutorial is the laminar flow of fluid through a cylindrical pipe. The next tutorial is turbulent flow of fluid through a cylindrical pipe. By doing the turbulent case, it will allow the user to see the difference between laminar and turbulent flows and to gain some insight as to why different methods of analyzing structures in FLUENT are necessary.

The next created learning module is to analyze flow over a flat plate. Analyzing the flow over a flat plate is very important because it will give the user a more in-depth look as to what happens when flow passes over an object. In addition, other tutorials such as a turbulent flow past a nozzle, turbulent jet flow, turbulent compressible and incompressible flow past an airfoil, turbulent incompressible flow past a periodic airfoil, and a discrete phase modeling tutorials are created to be able to serve as fundamental tutorials so that the user may then use them as precursors to analyzing more complicated problems.

In addition, one of the most important parts in creating the tutorials is the need for validation. Validation is extremely important when analyzing solutions, because it is the only way to ensure the accuracy of the results obtained in FLUENT. Validation is made by comparing results from FLUENT to theoretical and experimental data from scholarly sources.

II. CFD Analysis Roadmap

The importance of the created learning tutorials is to guide users into ANSYS FLUENT and provide them with a friendly introduction to the CFD software. For this reason fundamental learning modules have been created which are: laminar and turbulent fluid flow through a cylindrical pipe, laminar fluid flow over a flat plate, turbulent flow through a nozzle, turbulent jet flow, turbulent compressible and incompressible flow past an airfoil, turbulent incompressible flow past a periodic airfoil and discrete phase modeling. So why were these specific modules chosen and created?

The purpose for these tutorials is to lead a new user through options of increasing difficulty. The laminar pipe flow tutorial helped to introduce the icons and tools that ANSYS has to

4 | P a g e

offer. By having the user work with this very simple tutorial, they could familiarize themselves with where certain icons are and where certain tools are located. Once the user has completed this tutorial then the next tutorial added increased in complexity. The reason for this method is to be able to instill confidence in the user to make them feel confident in doing simple cases and build up to more complicated ones.

After each of the simple cases is run, the user has to validate each result. By validating one’s results the user is ensured they have created an accurate simulation. For instance, if a first time user has to analyze an airfoil, they should not start by designing an airfoil. Although they might obtain results, how would they know if the results are accurate? For this reason, the user would first figure out how flow develops through a pipe.

The user would take the laminar tutorial and figure out how to model fluid flow and then be able to validate it. Next, since the airfoil is close to flow over an isolated surface, they would then want to analyze the flat plate flow tutorial. Again the user should then have to validate these results.

Next, since the airfoil is going to have a specific set of coordinates, the user could then want to use the Nozzle tutorial, which explains how to import coordinates in order to create an object. Now the user is ready to create an airfoil and analyze it. The user now knows how to model flow and initialize a solution (laminar tutorial), they also know how to model flow over an isolated surface (flat plate tutorial) and they know how to import coordinates into FLUENT (nozzle tutorial). Since they have all the information needed to create an accurate airfoil, they user can now apply the previous knowledge to analyze a complicated geometry. From here the user is a step closer to creating an accurate airfoil and of course like all the other tutorials the user needs to validate the results. Refer to Fig.1 for a visual representation of the mentioned roadmap.

Fig.1—Example of a Roadmap

Another example of a roadmap is for analyzing the flow through a guide vane. First the novice user will want to be able to model fluid flow so they would begin with a laminar tutorial. Once they have learned the icons and what each tool does, then they would want to analyze turbulent flow. They would then refer to the turbulent flow through a pipe and figure out how to apply biasing and what models to use to analyze turbulence (See appendix B). The user will then want to again create a 2D airfoil which would give them the knowledge to analyze how to fluid passes an isolated surface. Once they have validated this they can then

5 | P a g e

move to a 3D airfoil and again validate it. Then they would want create a 2d cascade, validate it, and lastly create a 3D cascade and validate it. Now the user has the necessary information and knowledge to create a guide vane and have the confidence to know that it is accurate. Refer to Fig.2 for a visual representation of the described roadmap.

Fig.2—Example of a Guide Vane Roadmap

The creation of a roadmap is of crucial importance in order to be able to build the knowledge on how to create and analyze complicated geometry. Before wanting to analyze any complicated geometry, the user should make a roadmap of their own so that they can build confidence in how they will figure out the problem and make sure it will be accurate. Like mentioned before the user can create any geometry they want and can get results but how will they know if it is accurate? The only way of knowing this is by simplifying the complicated object into several steps (the roadmap) and work part by part in order to have accurate analytical data for their object. Sometimes validation for complex problems is not readily available. If however a roadmap is correctly followed then the need for validation for the specific complex problem in question while needed is not as crucial.

III. Theory

ANSYS FLUENT is Computational Fluid Dynamics (CFD) software that allows users to simulate flow problems of ranging complexity. It contains broad physical modeling capabilities needed to model flow, turbulence, heat transfer, and reactions over objects designed by the user. Thousands of companies around the world benefit from the use of CFD software as a main part of their design phases in their product development. It uses the finite-volume method to solve the

6 | P a g e

governing Navier-Stokes equations for a fluid which are derived from the conservation mass equation (1), the conservation of momentum (2) and the conservation of energy (3) equations [6].

∂ ρ∂t

+∇ ∙ ( ρV )=0 (1)

ρ ∂V∂ t

+ρ (V ∙∇) V=−∇ ρ+ρ g+∇ ∙ τ ij (2)

∂∂ t∫ e∗ρ d ∀+∫(u¿+ p

ρ+ V 2

2+gz) ρ V ∙ n dA= ˙Qnet∈¿+ ˙W net∈¿¿¿¿ (3)

The difficulty arises from the fact that the conservation of mass, momentum and energy are coupled and non-linear set of differential equations making them practically impossible to solve analytically for practical engineering problems. Hence CFD software such as FLUENT is utilized to provide very reasonable approximation upon solving the specified governing equations [2].

Additionally, FLUENT also allows the users to model a range of flows such as incompressible or compressible, inviscid or viscous, laminar or turbulent flow. The advanced solver technology that FLUENT has, provides fast and accurate results through flexible moving and deforming meshes to be able to create optimal designs. Ultimately, FLUENT allows engineers to design, create and analyze a configuration all under one program.

In order to model the object that a user wants to work with, its geometry and mesh must be first created in ANSYS Workbench. Another option is to import the geometry and mesh from Computer Aided Design (CAD) software packages such as Unigraphics, ProE or others. In Workbench, the user creates the object he or she wishes to analyze and Workbench guides the user through very complex metaphysics for fluid flow with drag and drop simplicity. Once the geometry has been created, the user can take advantage of several meshing options that Workbench provides. The user can implement the meshing in the specimen to analyze the structure as they try to analyze fluid flow past/through their object. As seen in Fig.3 below that is a mesh for a jet.

Fig.3 Mesh for flow through a jet

A few different ways of modeling and analyzing fluid flow are through turbulence modeling, k-, and Y+. Turbulence modeling is used to model turbulent flow. Turbulent flows are characterized by large, nearly random fluctuations in velocity and pressure in both space and time. These fluctuations arise from instabilities that eventually are dissipated (into heat) by the action of

7 | P a g e

viscosity. Turbulent flows occur in the opposite limit of high Reynolds numbers. The two approaches to solving the flow equations for turbulent flow flied can be roughly divided into two classes, direct numerical simulations and k- [2]. Direct numerical simulation numerically integrates the Navier-Stokes equations, resolving all of the spatial and temporal fluctuations without resorting to modeling. k-, models Reynolds stress in two turbulent parameters, the turbulent kinetic energy (k) and the turbulent energy dissipation rate ∈ defined below by Equations 4 and 5 respectively.

κ ≡ 12

(u'2+v '2+w'2 ) (4)

ϵ ≡υ ¿ (5)The next type of modeling is known as y+. Y+ is a mesh-dependent dimensionless

distance that quantifies to what degree the wall layer is resolved. Y+ plus is a non-dimensional parameter defined by Eq. [6] [10]. y

+¿=ρu yp

μ¿ (6)

where u= √ τw

ρw which is the friction velocity and Yp is the distance to the wall.

Workbench offers several meshing options, one being structured meshing. In structured meshing the user decides how many user defined shapes they want placed over the object they are analyzing. An example is seen in Fig.4. Structured meshing consists of tetrahedrons and exhibits a clearly pronounced pattern.

Fig.4 Structured mesh for a pipeThe mesh interior to a pipe shown is 100 by 5, meaning 100 elements in the horizontal directions and 5 elements in the vertical direction. Which is an example of structured mesh, however as the geometries increase in complexity it is necessary to adjust the meshing accordingly. However, when dealing with other cases such as flow across an airfoil, it is important to use a different mesh structure. One such structure is a structured “O- grid” around the airfoil. Because of the

8 | P a g e

existence of the layers around the airfoil, it can be ensured the flow gradients are properly captured.

Fig.5 “O grid” around an airfoil

Referring to the airfoil grid in Fig. 5 it should be noted that FLUENT obtains a solution such that the mass, momentum, energy and other quantities are conserved for each cell. The code of the CFD software solves directly the values of the flow variables at the cell centers and the values at other locations are appropriately interpolated [2]. In other cases, where there is no complicated geometry, but rather there is more flow gradients occurring around a certain area, the user can apply a bias. Applying a bias means concentrating the mesh around a certain area. For example, in the turbulent flow past a cylindrical pipe tutorial a bias is applied because as previously learned when dealing with turbulent cases, there are large gradients near the wall requiring the mesh generated as seen in Fig 6.

Fig.6 Bias Mesh for a turbulent flow In this bias mesh the farther away from the wall, the meshes seem to go back into the same structured mesh seen before. It is important to mention that at the bottom of this mesh it represents the centerline because since cylinders are radially symmetric we’re only showing the top part of the radius. It is expected for the flow to be less turbulent near the centerline and for that reason the mesh is less biased.

9 | P a g e

Finally, once the test object has been drawn and meshed in Workbench, FLUENT then allows the user to analyze it in different flow parameters. Another modeling capability FLUENT is capable of using is enhanced wall treatment. When the user chooses to use enhanced wall treatment, they can use this especially for turbulent cases using the k-epsilon model because it analyzes the object closer near the wall region. The initial and boundary conditions can be specified in FLUENT and upon initializing the problem; it can be checked for convergence. If the convergence is not achieved accurate results will not be obtained. Finally, FLUENT provides a wide variety of parameters that can be plotted and analyzed.

The topic of convergence requires further explanation in order for a better understanding to be achieved of the underlying steps, undertaken by FLUENT and other CFD packages, necessary to derive a solution. It has already been mentioned that the FLUENT code utilizes the finite-volume method to solve the governing differential equations to obtain a solution for a particulate problem. For simplicity purposes let us consider the finite-difference method which is in 1D. If the grid has equally-spaced points with ∆ x being the spacing between successive points, the truncation error is O (∆ x). As a result as the number of grid points is increased, and the spacing between successive points is reduced, the error in the numerical solution would decrease. Therefore the obtained numerical solution will closely agree to the exact solution [2]. In FLUENT during the obtainment of convergence the governing equations are solved for a predetermined by the user number of times (iterations). Specifically the magnitude of the average of particulate variable is computed as illustrated in Eq. [7] [2].

R=√∑i=1

N

(ui−ugi)2

N(7)

where R is the residual, N is the number of iterations to be performed, u indicates a particulate variable to be computed, and the subscript g indicates a guessed value.

Laminar and Turbulent Flow into a Pipe:While FLUENT is a very powerful tool in obtaining solutions to a wide range of fluid flow problems, the results obtained should be carefully validated with known theory or empirical data to make sure they are accurate. For example, in the case of a laminar flow through a pipe, the obtained results for the velocity profile can be compared with the theoretical data. For a steady state (fluid properties are not changing with respect to time) laminar flow in circular tubes the Navier-Stokes upon making the necessary assumptions can be solved to obtain a theoretical solution to the velocity profile. The incompressible Navier-Stokes equations in Cartesian coordinates are shown in Eqs. [8-10] [6].

x-direction: ρ( ∂ u∂t

+u ∂u∂ x

+v ∂ u∂ y

+w ∂u∂ z )=−∂ p

∂ x+ ρ gx+μ ( ∂2 u

∂ x2 +∂2 u∂ y2 +

∂2 u∂ z2 ) (8)

y-direction: ρ( ∂ v∂t

+u ∂ v∂ x

+v ∂ v∂ y

+w ∂ v∂ z )=−∂ p

∂ y+ρ g y+μ(∂2 v

∂ x2 +∂2v∂ y2 + ∂2 v

∂ z2 ) (9)

z-direction: ρ( ∂ w∂ t

+u ∂ w∂ x

+v ∂ w∂ y

+w ∂ w∂ z )=−∂ p

∂ z+ρ gz+μ( ∂2 w

∂ x2 + ∂2w∂ y2 + ∂2 w

∂ z2 ) (10)

10 | P a g e

The parabolic velocity profile for steady laminar flow in a cylindrical pipe is provided in Eq. [ 11]. It should be noted the obtained equation is a result of solving the Navier-Stokes equations in cylindrical coordinates.

Uumax

=1−¿ (11)

umax=2∗V inlet (12)

In the case of turbulent flow past a cylinder a comparison can be established by using Nikuradse’s empirical correlation. In the case of turbulence one can rely only on empirical correlations because of the randomness associated with turbulent flow. Depending on how accurate the experimental results correlate to the theoretical or empirical ones, one can decide whether or not the mesh used needs improvement or whether or not the initial conditions or the boundary ones specified in FLUENT need enhancement.

The reason why there is such a high dependency on empirical data is due to the randomness associated with turbulence. In turbulence there is no exact equation, all solutions are empirical data points. An example of this is the equation for skin friction for turbulence which is

λ=.3164( u dv

)−14 =

.3164ℜ.25 (13)

The main reason that it is an empirical equation, it has a few limiting conditions. Some of those limiting conditions are that it has to be only for smooth pipes and it is only useful for Reynolds number less than 100,000.

Also, another very important one is Nikuradse’s empirical correlation for turbulent flow which is given by Eq. [14] [6].

uU

=( yR

)1n (14)

where n, the power-law exponent varies with respect to the Reynolds number. Turbulent cases are very difficult to analyze because there is no exact answer, however the Moody diagram [6; Pg 412-413 Fundamentals of fluid Mechanics 6th ed.] in which the coefficient of friction with respect to the Reynolds number is displayed, serves as a reference as to what the solutions should appear to be. The Moody diagram is based off of

f =ϕ(ℜ , εD

) (15)

where the results are obtained from numerous set of experiments plotted on the Moody diagram

11 | P a g e

Fig.7 Moody diagram

Flow over a Flat PlateAnother case which is very important is the flow over a flat plate. This tutorial is very important because it will help simulate how flow develops over a flat plate. For this tutorial, a Re of

ℜ=ρu∞ xc

μ=5 x105 (16)

is critical because above this value the flow is turbulent and flow under this value is laminar. Provided a sufficiently long flat plate eventually turbulent flow will be encountered since the value of the Reynolds number is related to the length of the plate. The length of the flat plate in the created learning module (Appendix C and D) is of length 1 meter and the viscosity, density and inlet velocity are chosen such that the maximum Reynolds number reached is 10,000 which is well within the laminar flow range.

Fig.8 Flow Distribution past a flat plate [13]

In the laminar layer, the fluid flow is highly ordered and is possible to identify streamlines along which fluid particles move. This fluid continues until it hits a transition zone, which is where a conversion from laminar to turbulent conditions occurs. After it passes this region, it reaches turbulent flow which is where random motion is relatively high. Solution for the velocity profile for a laminar flow over a flat plate has been done by solving the Navier-Stokes equations. The Navier-Stokes equation can be simplified for boundary layer flow analysis. It can be assumed that the boundary layer is thin and the fluid flow is primarily parallel to the plate. Hence:

12 | P a g e

∂ u∂ x

+ ∂ v∂ y

=0 (17)

u ∂ u∂ x

+v ∂ v∂ y

=v ∂2u∂ y2 (18)

H. Blasius, one of Prandtl’s students was able to solve those equations for flat plate parallel to the flow [8]. By introducing the dimensionless parameter η (the similarity variable) the partial differential equations are reduced to an ordinary differential equation.

η= y∗√ Uν∗x

(19)

where U is the inlet velocity, and ν is the kinematic viscosity, ν=μρ .

The convenience of validating the boundary layer velocity profile in terms of the similarity variable is that the boundary layer velocity profiles (which depends both on x and y) at any point along the plate will overlap one another and can be analyzed versus the empirical Blasius correlation.

Flow Through a Convergent-Divergent NozzleAnother tutorial created is for flow through a convergent-divergent nozzle. The channel is supplied with a flow at high pressure and exhausts into lower pressure at the outlet. An example is seen in Fig. 9.

Fig. 9 Convergent Divergent nozzles

In addition, from the figure, A[x] is the local cross-sectional area, u[x] the local axial velocity and p[x] the local static pressure. To analyze how the flow passes through a nozzle, the user can do it by imposing restrictions on the geometry or on the character of the flow. It can then be compared to quasi-1D theory which assumes that the nozzle is slender. FLUENT can be used to analyze flow, which is what the nozzle learning module demonstrates.

Quasi -1D flow is one where the properties across each cross section are assumed uniform. Changes in flow properties in the x-direction are brought about by area change of the duct. In order to assume this, another assumption that has to be made, the assumption is that the nozzle geometry is long and thin. Additionally, it neglects viscous effects on the flow field, and maximum velocity occurs at the minimum area which is called “the throat”. The dependence of the axial velocity and static pressure is due to the area variation, and it’s a function of whether the flow is subsonic or supersonic which is given by Eq. [10].

13 | P a g e

dAA

= [M 2−1 ] duu

=[1−M2] dpρu2 (20)

For isentropic flows, the following relations Eqs. [11-13] govern the variation of Mach number, static pressure and static temperature with nozzle area.

TT0

=[1+( γ−12 )M 2]

−1

(21)

PP0

=[1+( γ−12 )M 2]

− γ(γ−1) (22)

AA0

= AAT

= 1M

[( 2γ−1 )(1+{γ−1

2 }M 2)]γ+1

2(γ−1) (23)

Fig. 10 Back pressure effects on Mach & Pressure for a nozzle

The static pressure distributions in the Fig 8 illustrate the dependence of the distribution on the exit or back pressure for a given A[x] nozzle contour.

Flow Over an Isolated AirfoilAirfoils operate upon theories of lift and drag. Consider a typical symmetric airfoil as illustrated in Fig.11.

14 | P a g e

α

M ∞

c=1m

Fig.11

M ∞ represents the free stream Mach number, ∝ is the angle of attack and c represents the chord length of the airfoil. The airfoil experiences a net force due to the fluid acting on the object. The Drag Force, D, acts in the direction of the free stream while the Lift Force, L, is normal to the free stream. Airfoils are designed to generate lift. However for objects such as cars it is desired to reduce the lift since the lift on a car reduces the contact force between the wheels and the ground. Typically the lift and drag are given in terms of the Coefficient of Lift and the Coefficient of Drag which are dimensionless forms of the Lift and Drag forces.

CL=L

0.5∗ρ∗U 2∗A(24)

CD= D0.5∗ρ∗U 2∗A

(25)

Most of the airfoil lift is a result of the surface pressure distribution which is consistent with Bernoulli’s equation analysis [6].

p1−p2=12∗ρ∗(V 2

2−V 12) (26)

∴V 2>V 1∧p2< p1

The effect of stall in airfoils must be avoided because loss of control and stability issues arise from it. The stall can visually be inspected on the upper surface in Fig.12 where a transition from high velocity to low velocity can be observed.

Fig.12--Turbulent Compressible Flow Across an Airfoil, M=0.8, Re=19.04∗106, ∝=10 ° ;Velocity Contours

The theoretical value for the coefficient of lift depends on the angle of attack and is provided by Eq. [27]:

(CL)th .=2∗π∗α (27)

15 | P a g e

where α is in radians.1 °=1°∗π /180°=¿0.01745 rad

The coefficient of pressure is an important dimensionless parameter used for data validation specifically for the velocity profile [6]. Since due to no-slip condition meaning the velocity on the solid boundary on the airfoil relative to the boundary is zero, pressure data obtained in FLUENT is meaningful to analyze and validate in Excel. In Theory of Wing Sections by Abbott and Doenhoff [11] data is provided for various airfoil models assuming the flow is turbulent incompressible with zero degree angle of attack.

CP=ps− p∞

.5∗ρ∞∗U∞2 =1−¿ (28)

∴¿

where C p is the coefficient of pressure; p∞is the free-stream pressure equaling 0; ρ∞ is the density being 1.225 kg /m3 and U∞is the free-stream velocity.

Discrete Phase Modeling [DPM] of Particle in Pipe FlowANSYS FLUENT can output the trajectory of a discrete phase particle and that case is showcased in Appendix I. Specifically, the force balance on the particle is integrated under Lagrangian reference frame considerations. Recall flow can be analyzed either by Eulerian or Lagrangian considerations. In the Eulerian representation fluid motion is given by completely describing the necessary properties such as pressure, density, velocity and others. Flow information is obtained at fixed points in space as fluid flows through those points. The Lagrangian method is characterized by following individual fluid particles as they move [6].

The force balance of the particle for the x-direction is provided in Eq. [29].d u p

dt=F D (u−u p )+

gx (ρp−ρ)ρp

+Fx (29)

where F x is an additional acceleration in force/unit particle mass, FD (u−up ) is the drag force per unit particle mass, u is the fluid phase velocity and up is the particle velocity. Additionally, FD is given by Eq. [30].

FD=

18 μρp d p

2∗CD∗ℜ

24(30)

where μ is the fluid’s molecular viscosity, ρ is the fluid density, ρp is the density of the particle, Re is the relative Reynolds number provided by Eq. [31] and d p is the diameter of the particle.

ℜ=ρ dp|up−u|

μ(31)

The additional acceleration term F x in Equation X can be of particulate importance during special circumstances. When a force is required to accelerate the fluid surrounding the particle,

16 | P a g e

or the virtual mass force as it is referred, is taken under consideration, the acceleration term takes the form of Eq. [32].

F x=12

ρρp

ddt

(u−up) (32)

Equation X is of particulate importance when the fluid density is greater than the density of the particle. Due to the pressure gradient an additional force must be considered and the acceleration term takes the form of Eq. [33] [12].

F x=( ρρp )u pi

∂u∂ xi

(33)

IV. Module Example—Laminar Flow Past a Cylindrical Pipe

The major steps taken into the creation of the learning module are outlined and explained. While the focus is on the laminar pipe flow module it needs to be noted the exact same approach is undertaken for the other learning modules. The goal of the section is for the user to become more acquainted with the flow of the tutorial and if more details are desired, the user can consult with the provided Appendixes—Appendix A for the particular laminar pipe flow module. Hence the actual step-by-step procedures are explained in much more detail in the Appendices.

The Laminar Pipe Flow Learning Module has seven distinct components.

1. Problem Statement 2. Geometry Creation and Mesh Creation

a. Actual geometry creation of the pipe and the corresponding mesh creation for it are done here

3. Problem Setupa. The specific values and important selections that need to be made in ANSYS

FLUENT prior to obtaining convergence and getting results4. Solution

a. The user learns the important steps that need to be taken in order to obtain convergence for the problem.

5. Results sectiona. Contains the obtainment of various plots such as the velocity and pressure profile,

skin friction coefficient and their manipulations b. Visual representation of the velocity profile along the pipe in the form of velocity

vectors is also included in the section6. Validation section

a. This section provides the necessary information of how meaningful validation can be performed in order for the user to make sure the obtained data is meaningful.

b.

17 | P a g e

Center Line

V inlet

L=8m

D=0.2m

Fig. 13 Geometry of Pipe Laminar Pipe flow modeling

(1) Problem Statement: The user learns the basics of the problem at hand as well as important given information

in the Problem Statement section. The given parameters are-- ρ=1.0 kgm3 ; V inlet=1.0 m

s ; μ=

2.0∗10−3 kgm∗s , where ρ is the density and µ is the dynamic viscosity.

Based on the given information, the Reynolds number can be computed to determine whether or not the problem as stated is laminar, transitional or turbulent. Recall that for flow in a round pipe, the flow is laminar if the Reynolds number is less than approximately 2100; the flow is transitional if the Reynolds number is between 2100 and 4000 and it is fully turbulent if Re is greater than 4000. Based on the given parameters the flow that is to be analyzed is laminar.

ℜ=ρ∗V inlet∗D

μ = 100

(34)

(2) Geometry Creation: The user is introduced to the basics of ANSYS Workbench--specifically how to create a sketch of the problem and then how to obtain a surface from the made sketch. Since a 2d model is created it can be assumed the shape of the pipe is rectangular. Furthermore the problem is assumed as axisymmetric hence only the upper portion of the pipe’s diameter is to be taken under consideration. The learnt basics then can be applied in the geometry creation for more complicated problems such as when turbulent pipe flow, flow past a flat plate and others are analyzed.

Fig.14—2d pipe sketched and made into a surface in ANSYS Workbench.

(3) Mesh Creation: The mesh is created in ANSYS Workbench as well. In the Mesh Creation section it is

explained to how to create a structured mesh—the grid exhibits clearly pronounced shape with tetrahedral shaped elements. Structured mesh is recommended for problems of such basic geometry. It is specifically explained to how size individual edges of the geometry as well as how to ensure elements on opposite ends correspond to each other—mapped face meshing. In Meshing specific zones of the geometry are named. Those zones will later be further specified in ANSYS FLUENT. The learned techniques are a very important starting point in ensuring the user will be able to handle more complicated problems.

18 | P a g e

(4) Problem Setup: Careful consideration must be exercised upon entering specific information in ANSYS

FLUENT as it relates an axis symmetric pipe flow. It is recommended a top-bottom approach is utilized in order not to miss anything. First the mesh must be checked for errors and the dimensions must be verified. The problem must be set as axisymmetric. Then the model must be specified as laminar. The given initial information as it relates to the density and viscosity must be entered in the material properties. Next, the Boundary Conditions must be specified. The user must first make sure the zones named in Workbench are of the proper type. The inlet zone must be of velocity-inlet type, outlet—pressure-outlet type, wall—wall type and finally axis—axis type. The next step is to input the relevant given information in the specific boundaries—the inlet velocity given as 1 m/s should be entered in the velocity-inlet boundary. The reference value must be specified at the inlet (ref. Fig.3) in order to be able to obtain certain data such as the skin friction coefficient.

(5) Solution: The importance of obtaining convergence is stressed in the solution section. If

convergence is not obtained, it will be impossible to obtain any results. However first the problem must be initialized to take into an account initially specified parameters—usually the given parameters specified at the inlet. Upon obtaining convergence the governing equations are solved by FLUENT. They are the conservation of mass, momentum and energy—Eqs.[2-4]. However since temperature effects are of no concern and neither is the fluid flow taken as compressible in the particular analysis of laminar pipe flow, the energy equation is not solved. The convergence residuals are a measure of how well the solution obtained satisfies the discrete form of the governing equations. As can be seen in Fig. 16, convergence is obtained as those residuals after certain number of iterations.

Fig. 16--Laminar Pipe Flow Convergence History

19 | P a g e

Fig.15—Structured

Inlet OutletWall

Axis

(6) Results: In Results section, the user becomes familiar with various ways of creating XY Plots of

the obtained data as well as methods of manipulating plots to make them more useful. The color and shape of the curves can be changed and scaling of the axis can be changed. Plots of skin friction, static pressure and velocity profile are created and the user also learns how to save them so they can be later opened in Excel to perform data validation. Figs. 17-18 show how by manipulating a plot, it can be more visually appealing or easier to interpret.

Fig. 17 —Velocity Profile XY Plot before Manipulation

Fig. 18-- Velocity Profile XY Plot after Manipulation

These graphs are the graphs that ANSYS has the ability to show however, for closer analyzing to upload the values to excel it is very simple.

Uploading to Excel

20 | P a g e

1. Select plot, here you figure out what you would like to plot whether velocity pressure etc. 2. In the Plot box on the left side, there is a radio button which says write to file, select that

button 3. Save it as choosename.xls 4. Open this file in Excel and when prompted if Excel should up load the file select yes and

then finish.

In the Results section it is also explained how to obtain the velocity vectors to observe the parabolic velocity profile along the pipe. Techniques of adjusting the scale, significant figures and location of the color map are introduced. It is introduced how to mirror the plane to get a complete grasp of the velocity profile (recall the problem is analyzed as axisymmetric)—Fig. 19. The user learns how to scale the rectangular shape, representing the pipe in 2d in order for the whole shape to visible on the screen making the velocity vectors easier to distinguish—Fig. 20. Having learned the mentioned techniques the user can then proceed to obtain different visual representations.

Fig.19—Plane is mirror for the full parabolic profile to be seen.

21 | P a g e

Fig.20—Through Scaling the Whole Shape is Visible

Validation:The data validation is explained in significant detail in order to ensure the user can apply the learnt knowledge to other fluid flow problems. However validation does not stop there. As engineers one should always ask himself whether the obtained data is correct. Computational Fluid Dynamics (CFD) software like ANSYS FLUENT is not a “magic box”. One cannot rely that the data being outputted is correct. The data will be only as meaningful as the parameters specified and models and options selected. Hence the user must not only be knowledgeable of how to use the CFD client properly, but depending on the actual flow problem a significant knowledge of fluid mechanics is required as well.

First in the validation process it is explained how the written to file XY Plots can be opened in Excel for further manipulation. As part of the post-processing process the initial mesh is enhanced in Workbench in order to investigate how increasing the number of elements will impact the accuracy of the solution. Validation in Excel is performed using dimensional analysis, meaning both the experimental data and the theoretical validation will be manipulated so that one will not need to rely on dimension to perform the analysis. It must be noted that while for the laminar pipe flow it can be relied on theoretical validation as it relates to entry-length (5), velocity profile (6), skin friction (7, 8) and static pressure drop (9) in other cases empirical correlation (extensive experiments performed by others such as Nikuradse or Blasius empirical correlations) may be the only means of obtaining validation. Empirical validation is illustrated in the turbulent pipe flow and laminar flow past a flat plate learning modules.

Fig. 21--Skin Friction vs. Pipe length along the wall, dimensionless

Dimensional analysis is convenient and preferred because one need not depend on unit limitations and validation can be performed for pipes of various dimensions if need be. Figure 21 represents validation performed for the skin friction coefficient. Correlation for the entry length

22 | P a g e

is displayed in Figs. 22-24, which illustrate the velocity profile validation along the radius of the pipe. Figure 25 provides validation for the static pressure drop from the inlet to the outlet of the pipe. Finally, Fig. 26 investigates the case where two different materials are chosen—air and oil. If the Reynolds number is kept the same but the inlet velocity is manipulated to obtain equal Reynolds number for the two materials, then the data in dimensional form should exactly match. The statement is proven for the velocity profile in Fig. 26.

Fig. 22 --Centerline Velocity in Axial Direction, Dimensionless

Fig. 23 --Dimensionless F.D Velocity Profile in Radial Direction

23 | P a g e

Fig. 24 -Dimensionless F.D Velocity profile in Radial Direction

Fig. 25 --Static Pressure Drop vs. Axial length, Dimensionless

24 | P a g e

Fig. 26 --Fully Developed Pipe Velocity Profile for Air and Oil, Re=1369

While basic in nature the laminar pipe flow module is crucial in illustrating the basics that first must be learned in order to be able to create, mesh, setup, solve and most importantly validate data obtained for more complicated problems. Other learning modules of increasing difficulty, included in the Appendices, are turbulent pipe flow, laminar flow past a flat plate, turbulent flow past a nozzle, analysis of turbulent jets, turbulent compressible and incompressible flow past an airfoil, turbulent incompressible flow across a periodic airfoil and discrete phase modeling—particle injection into a pipe. Each of those learning modules teaches the user something new and by incorporating and applying the learned knowledge from all tutorials, the user should be able to solve complex problems more efficiently.

V. Summary of Available Learning Modules

C. Turbulent Pipe Flow Case

The turbulent case, similar to the laminar case, is started the same way all the way up to the meshing. All the previous steps such as centering and building the sketch are done in the same way. However, when it comes to the mesh it is very different. From Fluid Mechanics, it is known that turbulence will be most significant near the wall. For that reason biased meshing is then applied. The reason for this biased meshing is so that there is more mesh (smaller ∆x) where the flow gradients are large. In addition, k−ϵ turbulence model is turned on because this is another feature that FLUENT has to evaluate.

25 | P a g e

Fig.27 Biased Mesh for Turbulent Pipe Flow

After creating the sketch and specifying the bias, both done in Workbench, the mesh size is then specified; the first one that is tried is 100X30 Grid (100 element divisions in the axial direction and 30 element divisions in the radial direction). The second grid choice is 100X54 Grid. Similarly to the laminar pipe flow tutorial, the relevant initial and boundary conditions are specified in FLUENT. Then the problem is initialized and checked for convergence. One of the graphs that are analyzed is for the Y+ values with respect to the pipe’s length, where the graph represents the Y+ values comparison for the k- model for the two created meshes—Fig.28. Since Y+ is a dimensionless quantity there is no need to manipulate the column any further. However the x-axis values are computed by dividing each value in the column for the axial pipe distance by the total length of the pipe—in this specific case, 8 meters. It can be seen that as the mesh is refined the Y+ values are getting closer to one signaling the 100X54 is the better mesh choice. Results however in fig.29 show little difference. Recall that the dimensionless parameter Y+ has been defined in the theory section.

Fig. 28—Y+ values for Turbulent Pipe Flow with Re=10,000

26 | P a g e

Lastly, like the laminar tutorial, validation is very important. One of the validation methods used to analyze the obtained experimental results is the Nikuradse fully develop velocity profile for smooth pipes. In dimensionless form, the Nikuradse equation is plotted and then analyzed—Fig. 29. It is very important to mention however that this is empirical correlation due to the flow being turbulent thus exhibiting unique and random behavior. The relevant Nikuradse empirical correlation theory has been explained in the theory section. One reason for the mismatch may be the simulation pipe length is not long enough to get a fully developed profile.

Fig. 29--Normalized Axial Velocity Profile

D. Laminar Flow over a Flat Plate CaseThe tutorial modeling laminar flow over a flat plate will express results as a is function of the Reynolds number which varies with the distance along the plate, ℜx. The flow remains laminar until the Reynolds number reaches 500,000. The geometry of the problem is created in the same manner as with the laminar pipe flow. Like the turbulent pipe flow case, bias is needed in order to obtain more accurate results in the areas of biggest flow gradients, even though the flow is laminar. For the flat plate that is near the wall—the bottom horizontal edge (recall in the turbulent pipe flow case the bias is used to obtain more meshing towards the upper horizontal edge).

Fig.19

27 | P a g e

Symmetry

Wall

OutletInletWidth,w

Length,L

Air

The key thing is to define the various surfaces properly in FLUENT. The inlet is Velocity inlet; the outlet is a Pressure Outlet; the named wall zone in Workbench should be by default specified as a type Wall in FLUENT. Finally the Symmetry zone should be specified as type symmetry. After the boundary conditions are specified and convergence is obtained after initialization of the problem (see Appendix D) the obtained data is validated in order to make sure it makes sense. The validation comparisons are for the skin friction coefficient and the velocity profile.

The steady incompressible Navier-Stokes equations which are solved to yield the obtained data can be simplified for boundary layer flow analysis. It can be assumed that the boundary layer is thin and the fluid flow is primarily parallel to the plate. Hence for 2D incompressible flow

∂ u∂ x

+ ∂ v∂ y

=0 (35)

u ∂ u∂ x

+v ∂ v∂ y

=v ∂2u∂ y2 (36)

H. Blasius, one of Prandtl’s students, was able to solve those equations for flat plate parallel to the flow. By introducing the dimensionless similarity parameter η, the partial differential equations can be reduced to a single ordinary differential equation in terms of the independent variable .

η= y∗√ Uν∗x

(37)

where U is the inlet velocity and ν is the kinematic viscosity, ν=μρ

The convenience of validating the boundary layer velocity profile in terms of the similarity variable is that the boundary layer velocity profile (which depends both on x and y) at any point along the plate will overlap one another and can be analyzed versus the Blasius solution.

28 | P a g e

Fig. 31 --Boundary Layer profile for Flow over Flat PlateThe validation performed for the skin friction coefficient (Fanning friction) can be seen to correlate accurately against the Blasius numerical solution data. The Blasius prediction is specified by Eq. [38].

C f =0.664√ℜx

(38)

Fig. 32 Centerline skin friction coefficient

It needs to be emphasized bias towards the wall surface is to be used otherwise the results will not be accurate. As it can be seen the most accurate results are yielded upon using structured biased towards the wall tetrahedral mesh—see Fig. 33.

29 | P a g e

Fig. 33 --Velocity profile comparison for different Mesh Types E. Turbulent Flow Past a Nozzle Case

The nozzle case is another fundamental case for learning FLUENT. Unlike the previous tutorials. Specifically an already created mesh (done in FlowLab) is imported into FLUENT. An additional part of this specific learning module is in-depth description of how a similar nozzle would be created and meshed in Workbench. Specifically the user learns how to import coordinates, specified in Excel, to form curves. By importing an already created mesh file into FLUENT, time is saved and more focus can be placed on the problem setup and its validation. This is shown in more detail in Appendix E.

30 | P a g e

Fig.34--Nozzle sketch The user must possess knowledge in Turbo Machinery and Fluid Mechanics, not only to properly setup the boundary conditions, but also to correctly validate the problem. Specifically the turbulent flow past a nozzle module is validated against the 1D Quasi model already described in the theory section.

Fig.35--Mesh for Nozzle In order to validate the FLUENT results, they are validated against data provided by Professor Barber, a professor of Turbo Machinery at the University of Connecticut. They can be seen in the tutorial in Appendix and they correlate very well.

31 | P a g e

Fig. 36--Mach number vs. Position

Fig. 37--Mach number vs. Position from other tests (cited at the reference page)

F. Turbulent Jet Flow

For the turbulent jet flow, this problem is set up like the laminar and turbulent pipe flow cases. However when the design of this is done, first a pipe is created. The flow exits (jets) from the pipe into a large domain. It is expected that the flow gradients will be the greatest and spreads out into the area and the flow gradients decrease. When conducting this tutorial, it was very important to take into account the turbulent pipe flow tutorial because it allowed the user to know where to make the mesh more biased.

32 | P a g e

Inviscid Results Pe/Pi=0.75

X

0 2 4 6 8 10

Mac

h N

umbe

r

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Maxis Mwall Maxis-visc

Fig. 38--Mesh for jet

Fig. 39 Boundaries

In addition, it allows the user to be able to implement the pressure outlet boundaries. See Fig. 39 for the boundary conditions. However, unlike the turbulent case using simply the k- model to analyze this flow will not be enough to achieve correct results. The k- model is used more for flow analyzing what happens near a wall however, it is needed to analyze what happens near the centerline and for this reason the amount of reversed flow allowed must be reduced. For that reason, specified intensity and viscosity ratio is used. By applying this, the flow is then able to reach the other side and can then be analyzed completely across the centerline as opposed to analyzing data closer to the wall.

33 | P a g e

Fig. 40 Axial Velocity for jetWhen validating this, the velocity across the centerline has to increase in the orifice and

then decrease in a linear manner. (To see the validation refer to Appendix F)

G. External Turbulent Compressible and Incompressible Flow across an Airfoil

This learning module, discussed in detail in Appendix G, showcases the flexibility of ANSYS FLUENT by importing into the CFD software an already created geometry and mesh—Fig. 41. By doing so, the time saved can be spent in ensuring the problem is setup properly in FLUENT and that correct results are obtained by validating the obtained data against theoretical correlation. The used mesh, Fig. 41, defines the area around the airfoil as pressure far field. To be able to use a boundary condition of pressure far field, the flow must be considered compressible. The density of the material chosen must be that for ideal gas conditions and the energy equation (the governing conservation of energy will be solved during the convergence process in FLUENT) must be turned on as well. The pressure far field boundary condition is fine for the first case considered in this module—external turbulent compressible flow over a NACA0012 airfoil. The Mach number for that case is 0.8. However while the second case considered, external turbulent incompressible flow over the same airfoil, can be setup exactly like the compressible case only lowering the Mach number to 0.2. More accurate results can be obtained if instead of using pressure far field boundary condition with the energy equation on, velocity inlet and pressure outlet conditions with the energy equation off are utilized. One can recall that in general compressibility effects cannot be ignored for Mach numbers greater than 0.3. This module explains how to separate the pressure far field into two zones to be defined as velocity inlet and pressure outlet.—Fig. 42. The module also describes how to obtain convergence for both the compressible and incompressible cases.

34 | P a g e

Fig. 41 Boundary condition definitions – compressible airfoil case

Fig. 42 Boundary condition definitions – compressible airfoil case

It is also explained how the user can determine the specific designation of the airfoil model. In the case considered, a NACA 0012 is analyzed. The velocity magnitude along the airfoil is zero because of the no-slip condition. Specific focus is placed on the validation aspect of the case. The coefficient of lift is validated against theoretical data as given by theory of lift—Eq. [39].

CL=2∗π∗α (39)

35 | P a g e

where CL is the lift coefficient, α is the angle of attack in radians. The lift coefficient is validated for various angles of attack for both the turbulent compressible and the turbulent incompressible cases. Fig.43 shows a comparison of results for the compressible and incompressible cases. The incompressible simulation strongly agrees with the theoretical model, which makes sense since the theory of lift correlation is valid for incompressible inviscid flows. For the compressible case, the agreement is only good for angles of attack less than 4 degrees.

Fig. 43 Coefficient of Lift Validation for Turb. Compr. And Incompr. Cases

Fig. 44 Determination of Most Optimum Angle of Attack

36 | P a g e

The module also explains how to determine the optimum angle of attack which corresponds to the largest Lift to Drag Coefficient ratio—Fig. 44. In Fig. 45, one can see the velocity contours on the upper surface, a supersonic region [red] is formed and ends in a shock. The shock induces a region of separation or stall [blue]. The region of separation is less visible in the contours of static pressure, Fig.G30, where static pressure is approximately constant through a region of separation. For an incompressible flow, the region of separation / stall does not occur until angles of attack near 18 degrees.

Fig.45 Velocity Magnitude Contours [m/s], =10 degs., Turbulent Compr. Case

Furthermore, validation is obtained for the velocity profile utilizing the equation for the Coefficient of Pressure and data for the static pressure from FLUENT. If the specific NACA model of an airfoil is known, validation of the solution can be performed by considering the velocity at different locations along the surface. The theoretical surface velocity can be obtained from Abbott and Von Doenhoff’s “Theory of Wing Sections” [11]. The computational surface velocity has to be zero from the imposed no-slip condition. However, one can apply Eq. [40] to extract a surface velocity from the surface static pressure. The infinity subscript indicates ref. value and the s subscript—static value.

CP=ps− p∞

.5∗ρ∞∗U∞2 =1−¿ (40)

∴¿

37 | P a g e

Fig. 46

H. Turbulent Incompressible Flow across a Planar [2D] Cascade of Airfoils

This (Appendix H) demonstrates how turbulent incompressible flow past a cascade of laterally periodic NACA 0012 airfoils can be modeled in FLUENT. It is shown in detail how the geometry and mesh for a periodic case can be created in Workbench. In the periodic case, the focus is placed only on one of the blades in a rotor or turbine and the boundary surrounding the airfoil reflects that. New tools in geometry creation in Workbench are introduced such as [1] Boolean subtraction to subtract the airfoil walls from the surrounding boundary, [2] vertex blending to make sure the trailing edge of the airfoil is smooth in order to obtain better mesh for the case and [3] others—Fig. 47. This module explains how to properly mesh the wake region after the airfoil. Also it is demonstrated how to obtain an O-type grid around the airfoil by utilizing inflation. Better results are obtained by employing an O-type grid because the flow gradients will be analyzed better during the solution process in FLUENT.

38 | P a g e

Fig. 47

Fig. 48

Fig. 49

The procedure of obtaining convergence for the turbulent incompressible case of Appendix G is used to obtain results for the periodic case. The difference is that the user must manually define the periodic boundary condition in FLUENT by typing specific commands in the command prompt and the module specifically explains the appropriate steps. The velocity contours for an angle of attack of 4 degrees can be seen in Fig. 50.

39 | P a g e

Fig. 50

I. Discrete Phase Modeling—Particle Injection into 3-D Turbulent Pipe Flow

Senior Design Group 18 working for Alstom has provided the needed Workbench project for the learning module in question. The Workbench project includes not only the geometry and mesh creation for the case but the FLUENT problem setup, solution and results. The learning module (Appendix I) demonstrates in depth how the user can create the geometry for the pipe by utilizing the Sweep Feature in Workbench. Two sketches are created one in the XY plane outlining the line shape of the pipe. The second sketch is in the YZ Plane and includes the diameter of the pipe. The circle is then swept along the line to create a 3D pipe.

Fig. 51

40 | P a g e

Fig. 52

Fig. 53

To obtain the mesh for the problem inflation is utilized in Workbench. As the geometry the whole body is selected and as the boundary the three faces making the pipe—the horizontal, the bend and the vertical portions. When inflation is specified in 3D, the body of the geometry and the faces of the boundaries are selected. For a 2D inflation, as done for the turbulent incompressible flow across a periodic airfoil (Appendix H), the face of the geometry and the edges of the boundaries are specified.

Fig. 54

The real focus of the learning module is to demonstrate how to specify material to be injected into the pipe. Specifically the Discrete Phase Model interface is manipulated in which injections can be created starting from a specified zone, inlet in the particulate case. Additionally the velocity, temperature, diameter, and other parameters of the injection can be entered. Once

41 | P a g e

proper convergence is obtain in similar manner as outlined in other learning modules the particles’ residence time can be tracked—Fig. 55.

Fig. 55a

Fig. 55b

VI. Conclusion

Conclusively, what is seen constantly over and over regardless of what type of problem or design the user is working with is a consistency in working with geometry, meshing, and validation. In geometry phase, it is important to recall that the user can design the geometry in ANSYS Workbench. However the software is flexible enough that the geometry can be created in Unigraphics, ProE or other Computer-Aided (CAD) software packages and the exported into Workbench. Again a rough sketch can first be generated and then the user can go in the editing

42 | P a g e

window and put the dimensions he or she chooses. Additionally, the user is not only limited to that, the user may also create already primitive designs. This means the user can select basic shapes in Workbench that have already been done like boxes, pipes, etc. These shapes can save the user a lot of time if they are just analyzing certain flow over feasible objects. However, if the user needs a different design that was possibly done on another CAD package, the user has the option of importing the design and then being able to work with it.

The next very important part once the geometry is determined, is meshing. Again recall that the user can have structured, unstructured, and bias types of meshing. The structured meshing works for very simple designs and simple flows. An example was the laminar flow past a cylindrical pipe (Appendix A) because since the flow is laminar no extra meshing is required near the wall due to its simplicity. However, when dealing with different types of flow or sketches such as nozzle, or turbulent cases, the meshing needed to be adjusted accordingly. The unstructured meshing is extremely useful especially for shapes that are not symmetrical such as bends or curves.

When dealing with complicated flow or complicated geometry; biased meshing changes how a mesh is refined near a wall. For instance, in the turbulent flow through a pipe case biased meshing was implemented since at turbulent cases the most flow gradients occur near the wall. Therefore, to obtain better results the mesh was refined near the wall to be able to get better data. However this still leaves one questions, how does one choose what mesh to start at?

The answer is that there is no actual starting point, based on experience the user will begin to determine what meshing sizes he or she should start at. In the laminar pipe flow tutorial the meshing chosen is based on other tutorials, however, meshing does not have a starting point but rather serves as a reference value. Therefore, when choosing a meshing size it is always recommended to start with simple small mesh and increase gradually based on how the accuracy increases or decreases, which is why validation is very important

Validation is the utmost important part in the design process. When validating results it allows the user to see the accuracy of their experiment. By doing hand calculations or referencing to other scholarly sources it allows the user to see what needs to be improved to get better answers. In addition, validation allows the user to go back and adjust parameters such as the meshing, like it was done in the laminar pipe flow tutorial.

Lastly, the importance for all these tutorials is to be able to create a roadmap for future complex problems. It is strongly suggested that before designing and analyzing complicated geometry, the user break it down into parts and create a roadmap with each step increasing in complexity to be able to not only build confidence in the values they get but also build knowledge on the uses of FLUENT into more complex parts.

References

1. Cornell University .FLUENT Learning Modules. 4/10/11 https://confluence.cornell.edu/display/SIMULATION/FLUENT+Learning+Modules

43 | P a g e

2. Cornell University . Introduction to CFD Basics. 5/7/11, https://confluence.cornell.edu/download/attachments/90736159/intro.pdf?version=1&modificationDate=1222889778000

3. Lee, Huei-Huang. Finite Element Simulations with ANSYS Workbench 12. Schroff development corporation, 2010.

http://www.sdcpublications.com/pdfsample/978-1-58503-604-2-2.pdf

4. Lawrence, Kent. ANSYS Workbench tutorial. Schroff development corporation, 2007.

5. Moran, Howard Shapiro. Fundamental of Eng. Thermodynamics. USA: NJ, 2008.

6. Munson, Young, Okiishi, Huebsch. Fundamentals of fluid mechanics 6 th ed . USA: West Virginia , 2009.

7. N.Rajaratnam. Turbulent Jets. New York: Elsevier scientific, 1976.

8. Schlichting, Hermann. Boundary Layer Theory. New York: McGraw, 1976.

9. Senior Design Project Website. University of Connecticut. 5/7/11 http://www.engr.uconn.edu/~barbertj/

10. Y+ definition, 5/7/11, http://my.fit.edu/itresources/manuals/fluent6.3/

11. Abbott, Doenhoff. Theory of Wing Sections. Dover Publications, New York, 1959.

12. ANSYS FLUENT 12.1 Theory Guide, Discrete Phase Modeling, 5/7/11 http://www3.hi.is/~halldorp/fluent_theory.pdf

13. Flow Velocity Profile, 12/10/10http://www.tpub.com/content/doe/h1012v3/css/h1012v3_40.htm

44 | P a g e