1. 1 Department: Material science and engineering Discipline: Finite element method By: Anelia Ivanova To: Prof. V. Iliev Subject : Hydrodynamics Simulation

2. 2 Table of contents Review of the problem Creation of geometry Meshing Defining the material property Boundary conditions Results Answers on some questions

3. 3 Incompressible Newtonian fluid flows through the valve is controlled by distance h of the flap A. The fluid velocity at the inlet is 2 m/s. Submit: The stream lines when h = 15 mm. The pressure field when h = 30 mm. The velocity field when h = 45 mm. The dependence between the mean velocity V 2, the values of the h and the viscosity. Assignment: Review of the problem

4. 4 Creation of geometry

5. 5 h = 15 mm h = 30 mm h = 45 mm

6. 6 Meshing

7. 7

8. 8

9. 9 Defining the material properties

10. 10 Defining the material properties

11. 11 Defining the material properties

12. 12 Defining the material properties

13. 13 Boundary Conditions

14. 14 Boundary Conditions

15. 15 Boundary Conditions

16. 16 Solution

17. 17 Results The stream lines when h =15 mm

18. 18 Results The pressure field when h = 30 mm

19. 19 Results The velocity field when h = 45 mm

20. 20 Dependence between the mean velocities at the outlet and the distance h of the flap

21. 21 Answers of the questions 1.What does the term “incompressible fluid” mean and where it is treated in the solution? Incompressible fluid Incompressible fluid is a fluid which is not reduced in volume by an increase in pressure. 2. What does the term “Newtonian fluid” mean and where it is treated in the ? 2. What does the term “Newtonian fluid” mean and where it is treated in the solution? A Newtonian fluid is a fluid whose stress at each point is linearly proportional to its strain rate at that point. All gases are Newtonian and most common liquids such as water, hydrocarbons, and oils. A simple equation to describe Newtonian fluid behaviour is where  is the shear stress exerted by the fluid, [Pa] μ is the fluid viscosity, [Pa.s] (du/dy) is the velocity gradient perpendicular to the direction of shear,[s -1 ]

22. 22 Answers of the questions 3. What element type was used? The type of the elements which was used is tetrahedra. 4. What element options were used?

23. 23 5. How many nodes and elements were created? Answers of the questions h = 15 mm h = 30 mm h = 45 mm

24. 24 6. What is the % error for your solution? Answers of the questions h = 15mm h = 30mm h = 45mm

25. 25