Water Flow Over an Ogee Profile Report

8/13/2019 Water Flow Over an Ogee Profile Report

1/18

FINITE ELEMENT METHOD TECHNICAL REPORT

Computational Fluid Dynamics modeling of a

Water Flow Over an Ogee Profile

ANSYS CFX 12

ENME 547 Finite Element Method

Dr. Sudak

Matias Sessarego

Written Report Due Date:

Friday December 10th2010

Date of Presentation:

Friday November 26th2010


2/18

Final Project Report Finite Element Method

Page 2

Abstract

A consulting company named Canadian Projects Limited is sponsoring a team in the

Mechanical Engineering Design Methodology and Application course (ENME 538) to

investigate the flow pattern overtop of an Ogee profile, which will subsequently encounter

the Very Low Head (VLH) Water Turbine. The team will be conducting experimental testsusing the flume located at the Civil Engineering building with an Ogee profile fabricated

from the Rapid Prototyping machine. A computational model of the flume and the rapid

prototyped Ogee part has been made using ANSYS CFX to provide results that could be

used to compare with or reinforce the results obtained from the experiment.

Two approaches for meshing the model have been performed, and their results are

compared. One approach involves using mesh refinement techniques, and the other does

not, only a general volume mesh. The results obtained from using the mesh refinement

techniques are much more rewarding. Flow circulation occurs on the back side of the Ogee,

and the boundary layer on top of the Ogee surface is very well defined. The flow circulation

is non-existent in the general volume mesh, and the boundary layer is thick and imprecise.

For the moment, the most useful model for the VLH project is the one which the mesh

refinement techniques were implemented, as it is more consistent with computational

models of a very similar problem made from researchers[7]who have not used ANSYS CFX.

Future improvements should be made to the CFX model, especially with the boundary

conditions used. For example, the Free Slip Wall boundary condition set for the side walls

of the CFX model should be changed such that they replicate the plexiglass walls on the

flume, and the top of the CFX model should act as a free surface.


3/18


Page 3

Introduction

Canadian Projects Limited (CPL) is a consulting company who specialize in renewable

energy development. Some examples of their projects include hydro, wind, bioenergy and

solar. They are currently the sponsor for the Optimization of Very Low Head Water Turbine

for Cold-Climate Conditions project in the Mechanical Engineering Design Methodology andApplication course (ENME 538). Wes Dick, an employee of CPL, has asked the student team

working on this project to answer a series of questions regarding a water turbine

prototype that is currently being used in Millau, France. Companies such as Coastal

Hydropower Corporation are currently interested in incorporating this new water turbine

into potential sites in Canada.

The designers of the water turbine, MJ2 Technologies, have named this turbine the VLH.

VLH stands for Very Low Head. The VLH has a Kaplan runner, with a diameter between

3.55 m to 5.6 m and 8 adjustable blades. The magnet generator is located at the center of

the turbine and runs directly from the shaft. The advantage of the VLH is its ability to be

installed wherever civil infrastructures are already in place. For example, dams, weirs andcanals. This reduces the cost considerably in comparison with other small hydro concepts,

which require expensive civil work.

Fig. 1VLH Turbine installed in Millau, France.

However, civil infrastructures such as weirs and dams have water flowing overtop of

essential geometries integrated into them. Examples include the Carseland, Lock 25, and

the Step profiles. The names of the Carseland and the Lock 25 profiles were derived from

the locations where these geometries are situated. The Lock 25 profile is defined by the

third order Bzier curve and is related to the gravitational constant. This particular profile

is also known as the Ogee profile. One of the questions that the CPL sponsor has asked the

student team to study was the effect of these different upstream geometries on approach

flow leading up to the VLH.


4/18


Page 4

Fig. 2Side view schematic of the VLH and the different upstream geometries

The focus of this report is to determine an approximation of the flow pattern across the

Ogee profile using the computational fluid analysis capabilities of ANSYS CFX. Using this

model, the team will have some insight as to how the flow pattern across the Ogee can

affect the efficiency and performance of the VLH. The differences between two approachesof meshing the domain and their results will be analyzed.

The geometric model made in ANSYS CFX will be based on the dimensions of the water

flume located at the Civil Engineering building at the University of Calgary. The reason is

because the team will be conducting experimental tests using this flume and an Ogee

profile manufactured from a Rapid Prototyping machine. The team is interested in

supporting the experimental results with results acquired from Computational Fluid

Dynamics software.

Fig. 3Water flume located at the Civil Engineering Building

Computational Method of ANSYS CFX

ANSYS CFX is a computational tool commonly known as Computational Fluid Dynamics

(CFD). CFD can be used to solve or model fluid flow and heat transfer problems. ANSYS

CFX solves fluid flow problems by using the unsteady Navier-Stokes equations in their

conservation form (or divergence form). These partial differential equations are shown


5/18


Page 5

below in Cartesian coordinates for a compressible Newtonian fluid. Note that SMis the

momentum source and is the dissipation function.

Table 1Governing Equations of Fluid Flow for a compressible Newtonian fluid[8]

Although these equations are difficult to solve analytically, they can be discretized and

solve numerically. This is the basis for the common solution methods that CFD codes use

today, including ANSYS CFX. The solution method that ANSYS CFX uses is called the finite

volume technique. This technique involves the process of dividing the entire domain into

smaller control volumes, where for each control volume the governing equations are

solved numerically. As a result, by combining the solutions for each and all of the control

volumes, an approximation for variable values at numerous points throughout the entire

domain is achieved.

Domain and Boundary Physics

The first step was to construct the Ogee profile using the Computer Aided Design software,

SolidWorks. The model was then imported into ANSYS CFX, and the channel where the

water would be flowing was included.

Fig. 4SolidWorks model of the Ogee (left) imported into ANSYS CFX with a channel (right)


6/18


Page 6

After designing the domain and before solving the governing equations describing the

water flow over the Ogee profile, many physics and boundary conditions must be inputted

into ANSYS CFX. Tables 2 and 3 summarize the domain physics and boundary conditions

that were entered in.

Table 2 Domain Physics for OgeeDomain

Type Fluid

Location B31

Materials

Water

Fluid Definition Material Library

Morphology Continuous Fluid

Settings

Buoyancy Model Buoyant

Buoyancy Reference

Temperature

25 [C]

Gravity X Component 0 [m s^-2]

Gravity Y Component -g

Gravity Z Component 0 [m s^-2]

Buoyancy Reference

Location

Automatic

Domain Motion Stationary

Reference Pressure 1 [atm]

Heat Transfer Model Isothermal

Fluid Temperature 25 [C]

Turbulence Model SST

Turbulent Wall Functions Automatic

A fluid domain type was specified withinthe region of B31, which is the geometric

model of the channel with the Ogee

profile in place (as shown on the right

figure of fig. 4).

For the materials, water was selected

from the material library already installed

into ANSYS CFX, and for the morphology,

a continuous fluid was selected. Water

was selected due to the nature of the

problem, and the fluid is treated ascontinuous rather than a dispersed or

particle fluid.

The effect of employing a buoyancy model

is to exclude the hydrostatic pressure in

the pressure field for the given problem.

When it is activated, the hydrostatic

gradient is excluded in the pressure term

of the momentum equation. This would

result in being able to observe the

pressure field solely due to the dynamiccomponent of pressure.

The Reference pressure is the datum for

all other pressures that will be calculated.

Specified Relative pressures are relative

to the Reference pressure.

The k based Shear-Stress-Transport (SST) model was selected due to its accurate

prediction of flow separation. It will later be shown what is meant by flow separation in the

Resultssection of this report. ANSYS CFX has also recommended SST turbulence modelling

for high accuracy boundary layer simulations, which will be needed to study the boundarylayer that will form on top of the surface of the Ogee profile.


7/18


Page 7

Table 3 Boundary Physics for Ogee

Boundaries

Boundary Inflow (Fig. 5)

Type INLET

Location inletSettings

Flow Regime Subsonic

Mass And Momentum Normal Speed

Normal Speed 0.35215 [m s^-1]

Turbulence Intensity & Length Scale

Eddy Length Scale 0.1 [m]

Fractional Intensity 0.05

Boundary Outflow (Fig. 6)

Type OUTLET

Location outlet

Settings

Flow Regime Subsonic

Mass And Momentum Static Pressure

Relative Pressure 0 [Pa]

Boundary Body (Fig. 7)

Type WALL

Location body, floor

Settings

Mass And Momentum No Slip Wall

Wall Roughness Smooth Wall

Boundary FreeWalls (Fig. 8)

Type WALL

Location top, wall1, wall2

Settings

Mass And Momentum Free Slip Wall

The flow through the channel is known to be subsonic, and have a normal speed of 0.35215

m/s. This value was calculated based on the width of the flume, and the flow rate and

approach height of the water flow from an Excel file given to us from the project sponsor.

The normal speed means that there is one velocity component of the flow, which is strictly

normal to the surface from which the inlet boundary condition was selected. This simplifies

Fig. 5

Fig. 6

Fig. 7

Fig. 8


8/18


Page 8

the complexity of the problem. The turbulence parameters such as the Eddy Length Scale

and the Fractional Intensity were unknown, and thus the values recommended from ANSYS

CFX for a similar problem were selected.

For the outlet, the boundary condition was set to a subsonic flow, and a static Relative

pressure of 0 Pa. Because of the necessity of specifying a static Relative pressure at theoutlet, the geometric model in CFX had to be designed such that the downstream side of the

Ogee must be very long. The reason is because of the coupled pressure and velocity terms

in the governing equations of fluid flow. If the downstream side of the geometric model was

made much shorter, and a static Relative pressure boundary condition was set at the end,

then the flow behaviour past the Ogee would be restricted in too short of a distance in

order to satisfy that boundary condition. By designing the downstream part of the

geometric model to be very long, it will allow the water to flow until it stabilizes at the end,

and thus the velocity field just after passing the Ogee will be much more accurate.

For the Ogee surface and the floor, a No Slip Wall boundary condition and a Smooth surface

were selected. What No Slip Wall means is that the velocity located right next to the wall isequal to the velocity of the wall, which in this case is zero because the Ogee surface and

floor are not moving. A smooth surface was selected instead of a rough surface because if a

rough surface were selected, then a surface roughness must be specified which was an

unknown for the flume.

For the top and the side walls, a Free Slip Wall boundary condition was chosen. What Free

Slip Wall means is that the shear stress at the wall is zero. In other words, the fluid velocity

located right next to the wall does not experience any kind of friction which slows it down.

The reason why this was selected was to simplify the computation of the problem.

Meshing the Domain

This section outlines two different approaches of meshing the domain. One involves a high

level of mesh refinement and requires some knowledge of where the boundary layers are

likely to occur, and whether a turbulent flow exists. The other approach is by using a

simpler mesh with no refinement. The purpose of using two different approaches of

meshing is to demonstrate the importance of using mesh refinement to properly model

fluid problems. The differences between the results from each approach will be shown in

the Resultssection of this report.

Meshing using Mesh Refinement Techniques

To accurately model the water flow over the Ogee profile, it is important that the user

knows the areas which require a higher level of mesh refinement. Before refining the mesh

in these particular areas, the general mesh encompassing the geometric model should

begin with a small amount of element spacing. The following figure displays the side view

of the geometric model with a mesh grid of maximum element spacing equal to 0.05 m. It

includes the mesh refinement made along the boundary of the floor and the Ogee surface.


9/18


Page 9

Fig. 9Side view of geometric model with mesh grid (refined volume mesh)

The following figure illustrates in detail the mesh on top of the surface of the Ogee profile.

Fig 10Inflated Boundary mesh on top of the Ogee profile surface

As shown in fig. 10, the mesh on top of the Ogee profile surface has been refined using a

feature in ANSYS CFX called the Inflated Boundary. The Inflated Boundary refines the

mesh on top of a surface to a specified number of element levels using wedge shaped

elements. For the CFX model of the water flow over the Ogee profile, a number of 8 element

levels were specified, with a maximum thickness of 0.05 m. By refining the mesh on top of

the Ogee profile surface, the boundary layer that will occur in this region will be accurately

captured. Fig. 11 displays the shape of the wedge finite volume element.

Fig. 11Wedge finite volume element

The remainder of the mesh grid is composed of the default tetrahedral finite volume

element, shown in fig. 12.

Fig. 12Tetrahedral finite volume element


10/18


Page 1

The next step was to refine the mesh within the areas where turbulent flow would take

place and where velocities would be rapidly changing. This was accomplished using a

feature in ANSYS CFX called Mesh Adaption. Mesh Adaption works simultaneously with

the CFX Solver. The CFX Solver is used once the entire preliminary meshing and the domain

and boundary physics have been inputted, and is the last step before being able to analyze

the results of the CFX model using CFX Post. While the CFX Solver is calculating thesolutions for each finite volume, for a variable that user chooses, it automatically refines

the areas of the mesh where the numerical solutions for this variable are rapidly changing,

to a maximum specified amount of Adaption Levels. Fig. 13 illustrates an example of Mesh

Adaption Level 1.

(Adaption Level 1)

Fig. 13Example of Mesh Adaption Level 1

The wedge and the tetrahedral finite volumes would be refined as follows for Mesh

Adaption Level 1.

Fig. 14Mesh refinement for wedge and tetrahedral finite volumes

Adaption Level 2 would be one further mesh refinement within the refined mesh area

made from Adaption Level 1. The CFX Solver knows whether it should proceed to mesh

Adaption Level 1, or Adaption Level 1 and 2 by a Target Residual value inputted by the

user. For the CFX model of the water flow over the Ogee profile, a maximum Mesh AdaptionLevel of 2 and a Target Residual value of 0.001 were set. The variable selected which the

CFX Solver used to determine the high variation in numerical solutions was velocity. The

following figure illustrates the result of the Mesh Adaption feature.

Numerical Solutions are changing

rapidly between elements in this

area of the mesh


11/18


Page 11

Fig. 15Resulting mesh after the implementation of the Mesh Adaption feature.

From looking at fig. 15, it is known that velocity will rapidly change where the darkest

regions of the mesh are located, because this is where the mesh is heavily refined.

The following figures illustrate nicely the resultant finite volumes from the preliminary

meshing and the Mesh Adaption feature at the mid-plane of the geometric model of the

channel and the Ogee profile.

Fig. 16Finite volumes at mid-plane (top), tetrahedral (bottom-left), and wedge (bottom-right)

The following table presents the total number of nodes and elements used to construct the

final mesh.

Table 4Mesh nodes and elements(Refined Volume Mesh)

Domain Nodes Elements

Default Domain 80218 329087


12/18


Page 12

Meshing using General Volume Mesh

The second approach of meshing the domain involves starting CFX Mesh, and simply

clicking on Generate Volume Mesh button and saving it. There are no mesh refinements,

and it is strictly a tetrahedral mesh. The element spacing has been enlarged from the

default spacing in CFX Mesh to observe its effect on the results, which will be discussed inthe Resultssection of this report. Fig. 17 displays the side view of the geometric model with

a mesh grid of maximum element spacing equal to 0.25 m.

Fig. 17Side view of geometric model with mesh grid (general volume mesh)

The mesh shown on fig. 17 is much coarser than the mesh shown on fig. 9, and the InflatedBoundary feature on top of the Ogee profile surface has not been implemented (fig. 18).

Fig. 18Unrefined mesh on top of the Ogee profile surface

The following table presents the total number of nodes and elements used to construct the

general volume mesh. Note that the number of nodes and elements are much smaller in

comparison with the refined volume mesh (Table 4).

Table 5Mesh nodes and elements

(General Volume Mesh)

Domain Nodes Elements

Default Domain 653 1786


13/18


Page 13

Results

This section outlines the results obtained from both approaches of meshing the domain.

Results from using proper mesh refinement will be discussed first, and subsequently the

results from using the general volume mesh.

Results from using Mesh Refinement Techniques

Fig. 19 is a side view vector plot placed at the mid-plane of the geometric model. The

different magnitudes of velocity are shown as varied colors, yellow being the highest and

dark blue being the lowest.

Fig. 19Side view of geometric model with velocity vector plot (refined volume mesh)

From fig. 19, it can be seen that the flow from the inlet separates into two distinct regions

when it encounters the Ogee profile. The velocity of the water flow on the upper region is

horizontal and is high in magnitude, and on the lower region, the flow is circulating at a

much lower speed. The phenomenon occurring at the lower region is known as flow

circulation, and is shown more closely in fig. 20 below.

Fig. 20Flow circulation occurring on the back side of the Ogee profile

The flow separation occurring on the above figure is the flow separation that was

mentioned in the Domain and Boundary Physicssection of this report, where the k - basedShear-Stress-Transport (SST) was selected for the turbulence modeling.


14/18


Page 14

There is a paper published from the International Journal of Heat and Fluid Flow called

Computational analysis of locally forced flow over a wall-mounted hump at high-Re number

by S. Saric, S. Jakirlic, A. Djugum, and C. Tropea, in which they have modeled a very similar

problem using different computational methods. The time-averaged streamlines they

obtained using the LES method (Large Eddy Simulation) over the hump is shown in the

figure below, where cis the chord length andxis the position on the horizontal axis.

Fig. 21Time-averaged streamlines obtained by LES method

It is reassuring that what has been modeled in ANSYS CFX with the Ogee profile is fairly

consistent with the results obtained from researchers using other computational methods

for a nearly identical problem.

Fig. 22 is a contour velocity plot displaying in great detail the boundary layer that forms on

top of the surface of the Ogee profile. The Inflated Boundary meshing technique has

modeled the rapidly increasing velocity profile very well as shown from the numerous thin

layers of varying colors.

Fig. 22Boundary layer formation on top of the Ogee surface due to the No Slip Wall boundary condition


15/18


Page 15

Results from using General Volume Mesh

The results gained from using the general volume mesh in comparison with those from

using the mesh refinement techniques are poor. There is a significant loss of flow behavior.

Fig. 23Side view of geometric model with velocity vector plot (general volume mesh)

The flow circulation happening on the back side of the Ogee profile shown on fig. 20 is non-

existent in fig. 24. The boundary layer in fig. 25 is also not as well defined as in fig. 22. The

layers of varying colors on top of the Ogee surface are much thicker and imprecise.

Fig. 24Absent flow circulation on the back side of the Ogee profile

Fig. 25Boundary layer formation on top of the Ogee surface is not well defined


16/18


Page 16

Further Useful Results and Future Improvements

Some further useful results that can be gained from the CFX model with the refined mesh,

or of an improved version of this model, that could be used for the VLH Water Turbine

project are properties of the flow incident on the plane where the turbine would be

installed. Some examples would include the pressure and the velocity distribution on theface of the plane as shown in figures 26, 27 and 28. However, it is very important to note

that this CFX model does not include the turbine geometry, which would affect the flow

conditions in the domain. In other words, all of the results from the CFX model of the Ogee

alone will not be the same as the results from a CFX model with an Ogee and a turbine.

Even though, the following figures do provide some idea as to what the turbine will

experience in terms of the pressure and velocity of the water flow.

Fig. 26 Example of a plane where the water turbine would be installed

Fig. 27 Total pressure distribution (dynamic only) on the water turbine face


17/18


Page 17

Fig. 28 Velocity distribution on the water turbine face

Some improvements to this CFX model can be made in the future. The boundary conditions

were over simplified. For example, for the top and the side walls, a Free Slip Wall boundary

condition was set. This greatly simplifies the computing time, but does not accurately

represent the walls in the actual experiment. The flume shown in fig. 3 has plexiglass walls,

and the top of the water flow will act as a free surface. In the future, the boundary

conditions will be improved such that they represent more closely with the walls in the

actual experiment. Modeling the water flow over the Ogee profile with a free surface is

currently underway.

Fig. 29Free surface water flow over a varying version of the Ogee profile


18/18


Conclusion

In conclusion, a general approximation of the flow pattern overtop of the Ogee profile has

been achieved. Before the simulation of this problem, it was unexpected to observe a

circulating flow on the back side of the Ogee profile. A lot has been learned from meshing,

setting the domain and boundary physics, and solving and analyzing the results of thisproblem. The results obtained from the approach using the mesh refinement techniques

are much more useful for the VLH project, and more interesting that those obtained using

the general volume mesh. They are also consistent with computational models made by

researchers for a very similar problem. However, there are still some improvements that

can be made with the CFX model. Especially with respect to the boundary conditions that

were used.

References

[1] ANSYS CFX Release 12.0 - 2009 ANSYS Help

[2] ANSYS CFX Release 11.0 - 2006 ANSYS Help (Source of fig. 13)

http://www.kxcad.net/ansys/ANSYS/ansyshelp/Hlp_G_MOD8_2.html

[3] Aquaveo, GMS: Editing a 3D Mesh, 2009. (Source of fig. 11, 12 & 14)

http://www.xmswiki.com/xms/GMS:Editing_a_3D_Mesh

[4] Coastal Hydropower Corporation, Very Low Head Turbine Description. (n.d.)

[5] DMCS, Fluids Mechanics and Fluids Properties. (n.d.)

http://www.slideshare.net/maztinaz/definition-of-fluid

[6] Fraser, F., Deschnes, C., ONeil, C., and Leclerc, M.,VLH: Development of a new turbine

for Very Low Head sites. (n.d.)

[7] Saric, S., Jakirlic, S., Djugum, A., and Tropea, C., Computational analysis of locally forced

flow over a wall-mounted hump at high-Re number. International Journal of Heat and Fluid

Flow, 2006.

[8] Versteeg, H.K., and Malalasekera, W.,An Introduction to Computational Fluid Dynamics.Edinburgh Gate: Pearson Education, 1995.

Documents

Water Flow Over an Ogee Profile Report