1. Your Success is Our Goal www.siemens.com/itps1 www.chemtech.com.br SHEAR STRESS ANALYSIS IN A ROTATOR-STATOR SYSTEM IX International PHOENICS Users Conference Moscow, 24 th September 2002

2. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 2 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference Chemtech - A Siemens Company, Rio de Janeiro / RJ – Brazil Petrobras / CENPES, Rio de Janeiro / RJ – Brazil AUTHORS Flávio Martins de Queiroz Guimarães Bruno de Almeida Barbabela Luiz Eduardo Ganem Rubião Ricardo Serfaty

3. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 3 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference Vertical axis rotating device with eight test plates attached submerged into a viscous medium. Vertical axis rotating device with eight test plates attached submerged into a viscous medium. Axial symmetric – just one eighth of it has been simulated. Axial symmetric – just one eighth of it has been simulated. INTRODUCTION – THE SYSTEM

4. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 4 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference COMPUTATIONAL GRID The domain definition was one of the majors steps of the system setting-up. It was created as: Body-fitted coordinates; Body-fitted coordinates; Multi-block approach; Multi-block approach; Sliding interface between the blocks. Sliding interface between the blocks.

5. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 5 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference COMPUTATIONAL GRID

6. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 6 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference GENERAL SETTINGS All simulations were run on PHOENICS v3.4. The follow configuration was setting: Grid: Multi-block sliding-grid Grid: Multi-block sliding-grid Energy Equation: no Energy Equation: no Turbulence Model: Low-Reynolds k- model Turbulence Model: Low-Reynolds k- model Transient: no Transient: no Relaxation: By GROUND implementation Relaxation: By GROUND implementation Equation Formulation: GCV Equation Formulation: GCV

7. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 7 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL SHEAR STRESS EVALUATION SHEAR STRESS

8. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 8 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT PROBLEM: How to evaluate the near wall velocity gradients? SOLUTION: Finite – elements approach with a 6 (six) nodes quadrilateral element.

9. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 9 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT For the solution of the gradient profile, the partial derivatives are solved as a sum of the variable node values pondered by the shape functions derived in respect to the spatial coordinates.

10. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 10 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT A bidimensional local coordinate system (R and S spatial directions) was defined based on the heterogeneous derivatives. As shown below:

11. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 11 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT First Case: NO WALL CONTACT

12. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 12 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT First Case: NO WALL CONTACT

13. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 13 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT Second Case: LOWER WALL

14. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 14 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT Second Case: LOWER WALL

15. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 15 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT Third Case: UPPER WALL

16. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 16 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference NEAR WALL VELOCITY GRADIENT Third Case: UPPER WALL

17. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 17 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION The Couette Flow This simulation consisted of the flow in the gap region between two concentric cylinders with the inner cylinder rotating with constant angular velocity, as shown in the figure below:

18. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 18 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Navier – Stokes Equations

19. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 19 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Assumptions & Constrains For an ideal flow, the two assumptions below are taken as true: In steady-state laminar flow, fluid moves following a fully circular profile with null radial and axial velocity components. In steady-state laminar flow, fluid moves following a fully circular profile with null radial and axial velocity components. Since the system is axially symmetric, the pressure gradient in the angular direction is considered null. Since the system is axially symmetric, the pressure gradient in the angular direction is considered null.

20. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 20 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Navier – Stokes Equations The solution of the Navier – Stokes Equations for a Couette like flow were described following:

21. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 21 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Boundary Conditions For the case of inner cylinder rotating with angular velocity and the outer cylinder stationary: At r = kR (inner rotating cylinder) v = kR At r = kR (inner rotating cylinder) v = kR At r = R (outer cylinder) v = 0 At r = R (outer cylinder) v = 0 Integrating the angular component between the boundary conditions limits:

22. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 22 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Shear Stress Components The shear stress components in cylindrical-polar coordinates are given by:

23. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 23 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Shear Stress Evaluation For a Couette flow in the gap region:

24. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 24 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference ANALYTICAL VALIDATION Performed for an specific set of physical- chemical properties at a constant rotating speed. Performed for an specific set of physical- chemical properties at a constant rotating speed. Since the analytical solution is laminar, no turbulence model was considered in the simulation. Since the analytical solution is laminar, no turbulence model was considered in the simulation.

25. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 25 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference FIELD TEST VALIDATION The velocity profile and the rotating wall shear stress were compared for both cases in order to verify the precision of the system.

26. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 26 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference FINAL RESULTS To provide more detailed and easy to get information about the resulting shear stress profile, additional code was programmed into GROUND file to print treated data to the end of the RESULT file. The following information is provided: Average shear stress on the south surface (SAVG_in) and on north surface of the plate (SAVG_out); Average shear stress on the south surface (SAVG_in) and on north surface of the plate (SAVG_out); Shear stress at the center of the plate on the south surface (SHST_in) and on the north surface (SHST_out); Shear stress at the center of the plate on the south surface (SHST_in) and on the north surface (SHST_out); Shear stress at each cell of the south surface (slab by slab); Shear stress at each cell of the south surface (slab by slab); Shear stress at each cell of the north surface (slab by slab); Shear stress at each cell of the north surface (slab by slab);

27. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 27 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference CONCLUSIONS The results showed good quantitative agreement with analytical data though several sweeps are need to guarantee the convergence. The results showed good quantitative agreement with analytical data though several sweeps are need to guarantee the convergence. Although the resulting shear stress profile for de k- turbulence model seems to fit better near the walls, it was more unstable and harder to converge than the standard k- one. Although the resulting shear stress profile for de k- turbulence model seems to fit better near the walls, it was more unstable and harder to converge than the standard k- one. Also, it was verified that near the open borders of the plate the shear stress is usually higher because of an increase in the turbulence effects at these elements. It was important to point out that in some cases the shear stress near the borders seems to be over-predicted and unfortunately it was impossible to check experimentally this data Also, it was verified that near the open borders of the plate the shear stress is usually higher because of an increase in the turbulence effects at these elements. It was important to point out that in some cases the shear stress near the borders seems to be over-predicted and unfortunately it was impossible to check experimentally this data

28. Your Success is Our Goal INERTARGON_IX_IPUC_MOSKOW2002.ppt Slide 28 © IT PS 2002 Shear Stress IX International PHOENICS Users Conference CONCLUSIONS Finally this case was used as a base for a general q1 template and implemented in a Human-Machine Interface (HMI) in order to turn typical sensibility analysis into an easy task, allowing series of tests to be performed with very few clicks of the mouse. This enables even new users or equipment designers who may wish not to invest in training in PHOENICS to perform similar studies. Finally this case was used as a base for a general q1 template and implemented in a Human-Machine Interface (HMI) in order to turn typical sensibility analysis into an easy task, allowing series of tests to be performed with very few clicks of the mouse. This enables even new users or equipment designers who may wish not to invest in training in PHOENICS to perform similar studies.