Department Of Material Science And Engineering FINITE ELEMENT METHOD UNIVERSITY OF CHEMICAL TECHNOLOGY AND METALLURGY Sofia Nina Velikova, June 2010

2 Table Of Contents Review of the problem. Creation of geometry. Procedure of solution. Results. Answering on some questions.

3 Review Of The Problem Assignment: 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 controlled by constriction, varied from 100 mm (full opening) to 0 mm (full closing). 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 controlled by constriction, varied from 100 mm (full opening) to 0 mm (full closing). Determine the general dependence between the maximum of the fluid velocities VA, VB and VC at the outlets and the constriction rate. Determine the general dependence between the maximum of the fluid velocities VA, VB and VC at the outlets and the constriction rate.

4Submit:  Geometrical model, including the mesh and the boundary conditions.  The stream lines during the full open constriction.  The pressure field during 50% closed constriction.  The velocity field during 100% closed constriction.  Drawing of the dependence between the maximum of the fluid velocities at the outlets, the constriction rate. Answer the next questions:  What does the term “incompressible fluid” mean and where it is treated in the solution?  What does the term “Newtonian fluid” mean and where it is treated in the solution?  What element type was used ?  What element options were used ?  What real constants were used ?  How many nodes and elements were created ?  What is the % error (SEPC) for your solution ?

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

6 Creation Of Geometry Constriction with D=0.05m

7 Constriction with D=0.00m (full closing) Creation Of Geometry

8 Meshing Constriction with D=0.10m (full opening)

9 Meshing Constriction with D=0.05m

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

11 Defining The Material Properties

12 Defining The Material Properties

13 Boundary Conditions Defining the inlet

14 Boundary Conditions Defining the inlet

15 Boundary Conditions Defining the outlets

16 Boundary Conditions Defining the outlets

17 Boundary Conditions Defining the walls

18 Solution

19 Solution

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

21 Solution Solution for Constriction with D=0.05m

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

23 The stream lines during the full open construction

24 The pressure field during 50%closed construction

25 The velocity field during 100% closed construction

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

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

28 Answers of the questions Τ – is the shear stress exerted by the fluid [Pa] μ -is the fluid viscosity – a constant of proportionality [Pa*s]. dv/dx –is the velocity gradient perpendicular to the direction of shear [1/s ]. Τ = μ dvdx A fluid in which the density remains constant for isothermal pressure changes, that is, for which the coefficient of compressibility is zero. What does the term “incompressible fluid” mean and where it is treated in the solution? A Newtonian fluid is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. What does the term “Newtonian fluid” mean and where it is treated in the solution?

29 Answers of the questions What element options were used?

30 Answers of the questions 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 ? What element type was used? What element type was used?

31 Answers of the questions D=0.00m (full closing) D=0.05m D=0.05m D=0.10m (full opening) D=0.10m (full opening) What is the % error ( SEPC) for your solution? Constriction with ;

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