Department Of Material Science And Department Of Material Science And EngineeringEngineering

FINITE ELEMENT FINITE ELEMENT METHODMETHOD

UNIVERSITY OF CHEMICAL UNIVERSITY OF CHEMICAL TECHNOLOGY AND METALLURGYTECHNOLOGY AND METALLURGY

SofiaSofia

Nina Velikova, June 2010Nina Velikova, June 2010

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Table Of ContentsTable Of Contents

Review of the problem.

Creation of geometry.

Procedure of solution.

Results.

Answering on some questions.

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Review Of The ProblemReview Of The ProblemAssignment:Assignment:   Incompressible Newtonian fluid (water) goes trough the inlet of the pipe system with Incompressible Newtonian fluid (water) goes trough the inlet of the pipe system with

velocity 5 m/s and is separated into the three branches А, В and С. The flow into the branch A is velocity 5 m/s and is separated into the three branches А, В and С. The flow into the branch A is controlled by constriction, varied from 100 mm (full opening) to 0 mm (full closing).controlled by constriction, varied from 100 mm (full opening) to 0 mm (full closing).

Determine the general dependence between the maximum of the fluid Determine the general dependence between the maximum of the fluid velocities VA, VB and VC at the outlets and the constriction rate.velocities VA, VB and VC at the outlets and the constriction rate.

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Submit:Submit: Geometrical model, including the mesh and the boundary conditions.Geometrical model, including the mesh and the boundary conditions. The stream lines during the full open constriction. The stream lines during the full open constriction. The pressure field during 50% closed constriction.The pressure field during 50% closed constriction. The velocity field during 100% closed constriction. The velocity field during 100% closed constriction. Drawing of the dependence between the maximum of the fluid velocities at the Drawing of the dependence between the maximum of the fluid velocities at the

outlets, the constriction rate. outlets, the constriction rate.

Answer the next questions:Answer the next questions: What does the term “incompressible fluid” mean and where it is treated in the What does the term “incompressible fluid” mean and where it is treated in the

solution? solution? What does the term “Newtonian fluid” mean and where it is treated in the What does the term “Newtonian fluid” mean and where it is treated in the

solution?solution? What element type was used ? What element type was used ? What element options were used ? What element options were used ?

What real constants were used ?What real constants were used ? How many nodes and elements were created ? How many nodes and elements were created ? What is the % error (SEPC) for your solution ? What is the % error (SEPC) for your solution ?

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Creation Of GeometryConstriction with D=0.10m (full opening)Constriction with D=0.10m (full opening)

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Creation Of GeometryConstriction with D=0.05mConstriction with D=0.05m

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Constriction with D=0.00m (full closing)Constriction with D=0.00m (full closing)

Creation Of Geometry

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MeshingConstriction with D=0.10m (full opening)Constriction with D=0.10m (full opening)

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MeshingConstriction with D=0.05m Constriction with D=0.05m

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MeshingConstriction with D=0.00m (full closing)Constriction with D=0.00m (full closing)

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Defining The Material Properties

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Defining The Material Properties

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Boundary ConditionsDefining the inletDefining the inlet

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Boundary ConditionsDefining the inletDefining the inlet

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Boundary ConditionsDefining the outletsDefining the outlets

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Boundary ConditionsDefining the outletsDefining the outlets

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Boundary ConditionsDefining the wallsDefining the walls

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Solution

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Solution

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SolutionSolution for Constriction with D=0.10m (full opening)Solution for Constriction with D=0.10m (full opening)

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SolutionSolution for Constriction with D=0.05m Solution for Constriction with D=0.05m

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SolutionSolution for Constriction with D=0.00m (full closing)Solution for Constriction with D=0.00m (full closing)

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The stream lines during the full open construction

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The pressure field during 50%closed construction

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The velocity field during 100% closed construction

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Dependence between the maximum of the fluid velocities VA, VB Dependence between the maximum of the fluid velocities VA, VB and VC at the outlets and constriction rateand VC at the outlets and constriction rate

3,99

1,310

7,26

9,098,65

8,29

10,439,79

0

2

4

6

8

10

12

0.00 0.05 0.10Narrowing Diameter, [meter]

Vel

oci

ty, [m

/s]

VAVBVC

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Dependence between the maximum of the fluid velocities at the outlets, Dependence between the maximum of the fluid velocities at the outlets, the constriction rate and the values of the viscositythe constriction rate and the values of the viscosity

3,85 3,82 3,79

0,991,1

1

0 0 00

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 1,1 1,2 1,3 1,4 1,5 1,6Kinematic viscosity [mm^2/s]

Vel

oci

ty [

m/s

]

VA D=0,10m

VA D=0,05m

VA D=0,00m

6,9877,01

8,68 8,638,66

8,62 8,68,61

6

6,5

7

7,5

8

8,5

9

1 1,1 1,2 1,3 1,4 1,5 1,6

Kinematic viscosity [mm^2/s]

Vel

oci

ty [

m/s

]

VB D=0,10m VB D=0,05m

VB D=0,00m

8,128,138,14

10,1110,1410,16

9,88 9,889,88

8

8,5

9

9,5

10

10,5

1 1,1 1,2 1,3 1,4 1,5 1,6Kinematic viscosity [mm^2/s]

Velo

cit

y [

m/s

]

VC D=0,10m

VC D=0,05m

VC D=0,00m

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Answers of the questions

ΤΤ – – is the shear stress exerted by the fluid is the shear stress exerted by the fluid [Pa][Pa]μ μ --is the fluid viscosity – a constant of proportionality is the fluid viscosity – a constant of proportionality [Pa*s].[Pa*s].dv/dx –dv/dx –is the velocity gradient perpendicular to the direction of is the velocity gradient perpendicular to the direction of shear shear [1/s[1/s ].].

ΤΤ = = μμ dvdv

dxdx

A fluid in which theA fluid in which the density density remains constant for remains constant for isothermal isothermal pressure changes, pressure changes, that is, for which thethat is, for which the coefficient coefficient of compressibility of compressibility is zero. is zero.

What does the term “incompressible fluid” mean and where it What does the term “incompressible fluid” mean and where it is treated in the solution?is treated in the solution?

A Newtonian fluid is defined to be aA Newtonian fluid is defined to be a fluid fluid whose whose shear stress shear stress is linearly is linearly proportional to theproportional to the velocity gradient velocity gradient in the direction in the direction perpendicular perpendicular to the plane to the plane

of shear. of shear.

What does the term “Newtonian fluid” mean and where it is What does the term “Newtonian fluid” mean and where it is treated in the solution?treated in the solution?

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Answers of the questionsWhat element options were used?What element options were used?

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Answers of the questions

Constriction with ;Constriction with ;

D=0.00m (full closing) D=0.05m D=0.10m (full opening)D=0.00m (full closing) D=0.05m D=0.10m (full opening)

How many nodes and elements were created ?How many nodes and elements were created ? What element type was used?What element type was used?

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Answers of the questions

D=0.00m (full closing)D=0.00m (full closing)

D=0.05m D=0.05m

D=0.10m (full D=0.10m (full opening)opening)

What is the % error ( SEPC) for your solution?What is the % error ( SEPC) for your solution?

Constriction with ;Constriction with ;

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