Your Success is Our Goal SHEAR STRESS ANALYSIS IN A ROTATOR-STATOR SYSTEM IX International...

Your Success is Our Goalwww.siemens.com/itps1 www.chemtech.com.br

SHEAR STRESS ANALYSIS IN A ROTATOR-STATORSYSTEM

IX International PHOENICS Users ConferenceIX International PHOENICS Users Conference

Moscow, 24Moscow, 24thth September 2002 September 2002

Your Success is Our Goal

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IX International PHOENICS Users Conference

Chemtech - A Siemens Company, Rio de Janeiro / RJ – BrazilChemtech - A Siemens Company, Rio de Janeiro / RJ – Brazil

Petrobras / CENPES, Rio de Janeiro / RJ – BrazilPetrobras / CENPES, Rio de Janeiro / RJ – Brazil

AUTHORS

Flávio Martins de Queiroz GuimarãesFlávio Martins de Queiroz Guimarães

Bruno de Almeida BarbabelaBruno de Almeida Barbabela

Luiz Eduardo Ganem Rubião Luiz Eduardo Ganem Rubião

Ricardo SerfatyRicardo Serfaty


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Vertical axis rotating device with eight test plates Vertical axis rotating device with eight test plates attached submerged into a viscous medium.attached submerged into a viscous medium.

Axial symmetric – just one eighth of it has been Axial symmetric – just one eighth of it has been simulated.simulated.

INTRODUCTION – THE SYSTEM


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COMPUTATIONAL GRID

The domain definition was one of the majors steps The domain definition was one of the majors steps of the system setting-up. It was created asof the system setting-up. It was created as::

BodyBody-fitted -fitted coordinates;coordinates;

Multi-block approach;Multi-block approach;

SSliding interface between the blocks.liding interface between the blocks.


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COMPUTATIONAL GRID


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GENERAL SETTINGS

All simulations were run on PHOENICS v3.4. The All simulations were run on PHOENICS v3.4. The follow configuration was setting:follow configuration was setting:

Grid: Grid: Multi-block sliding-gridMulti-block sliding-grid Energy Equation: Energy Equation: nono Turbulence Model: Turbulence Model: Low-Reynolds k-Low-Reynolds k- model model Transient: Transient: nono Relaxation: Relaxation: By GROUND implementationBy GROUND implementation Equation Formulation: Equation Formulation: GCVGCV


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NEAR WALL SHEAR STRESS EVALUATION

SHEAR STRESSSHEAR STRESS


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NEAR WALL VELOCITY GRADIENT

PROBLEMPROBLEM::

How to evaluate the near wall velocity gradients? How to evaluate the near wall velocity gradients?

SOLUTIONSOLUTION::

Finite – elements approach with a 6 (six) nodes Finite – elements approach with a 6 (six) nodes quadrilateral element.quadrilateral element.


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For the solution of the gradient profile, the partial For the solution of the gradient profile, the partial derivatives are solved as a sum of the variable derivatives are solved as a sum of the variable node values pondered by the shape functions node values pondered by the shape functions derived in respect to the spatial coordinates.derived in respect to the spatial coordinates.


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A bidimensional local coordinate system (R and S A bidimensional local coordinate system (R and S spatial directions) was defined based on the spatial directions) was defined based on the heterogeneous derivatives.heterogeneous derivatives. As shown below:As shown below:


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First Case: First Case: NO WALL CONTACTNO WALL CONTACT


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First Case: First Case: NO WALL CONTACTNO WALL CONTACT


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Second Case: Second Case: LOWER WALLLOWER WALL


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Second Case: Second Case: LOWER WALLLOWER WALL


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Third Case: Third Case: UPPER WALLUPPER WALL


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Third Case: Third Case: UPPER WALLUPPER WALL


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ANALYTICAL VALIDATION The Couette Flow

This simulation consisted of the flow in the gap This simulation consisted of the flow in the gap region between two concentric cylinders with the region between two concentric cylinders with the inner cylinder rotating with constant angular inner cylinder rotating with constant angular velocity velocity , as shown in the figure below:, as shown in the figure below:


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ANALYTICAL VALIDATION Navier – Stokes Equations


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ANALYTICAL VALIDATION Assumptions & Constrains

For an ideal flow, the two assumptions below are For an ideal flow, the two assumptions below are taken as true:taken as true:

In steady-state laminar flow, fluid moves In steady-state laminar flow, fluid moves following a fully circular profile with null radial following a fully circular profile with null radial and axial velocity components.and axial velocity components.

Since the system is axially symmetric, the Since the system is axially symmetric, the pressure gradient in the angular direction is pressure gradient in the angular direction is considered null.considered null.


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ANALYTICAL VALIDATION Navier – Stokes Equations

The solution of the Navier – Stokes Equations for The solution of the Navier – Stokes Equations for a Couette like flow were described following:a Couette like flow were described following:


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ANALYTICAL VALIDATION Boundary Conditions

For the case of inner cylinder rotating with angular For the case of inner cylinder rotating with angular velocity velocity and the outer cylinder stationary: and the outer cylinder stationary:

At r = kR (inner rotating cylinder) At r = kR (inner rotating cylinder) v v = = kRkR

At r = R (outer cylinder) At r = R (outer cylinder) v v = 0 = 0

Integrating the angular component between the Integrating the angular component between the

boundary conditions limits:boundary conditions limits:


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ANALYTICAL VALIDATION Shear Stress Components

The shear stress components in cylindrical-polar The shear stress components in cylindrical-polar coordinates are given by:coordinates are given by:


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ANALYTICAL VALIDATION Shear Stress Evaluation

For a Couette flow in the gap region: For a Couette flow in the gap region:


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ANALYTICAL VALIDATION

Performed for an specific set of physical-Performed for an specific set of physical-chemical properties at a constant rotating speed.chemical properties at a constant rotating speed.

Since the analytical solution is laminar, no Since the analytical solution is laminar, no turbulence model was considered in the turbulence model was considered in the simulation. simulation.


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Case Shear Stress (Pa) Deviation (%)

Analytical 0.047 -

Simulation (dU/dY derivative) 0.042 -10.6

Simulation (all derivatives) 0.058 23.4

FIELD TEST VALIDATION

The velocity profile and the rotating wall shear The velocity profile and the rotating wall shear stress were compared for both cases in order to stress were compared for both cases in order to verify the precision of the system.verify the precision of the system.


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FINAL RESULTS

To provide more detailed and easy to get information about To provide more detailed and easy to get information about the resulting shear stress profile, additional code was the resulting shear stress profile, additional code was programmed into GROUND file to print treated data to the end programmed into GROUND file to print treated data to the end of the RESULT file. The following information is provided:of the RESULT file. The following information is provided:

Average shear stress on the south surface (Average shear stress on the south surface (SAVG_inSAVG_in) ) and on north surface of the plate (and on north surface of the plate (SAVG_outSAVG_out););

Shear stress at the center of the plate on the south Shear stress at the center of the plate on the south surface (surface (SHST_inSHST_in) and on the north surface () and on the north surface (SHST_outSHST_out););

Shear stress at each cell of the south surface (slab by Shear stress at each cell of the south surface (slab by slab);slab);

Shear stress at each cell of the north surface (slab by Shear stress at each cell of the north surface (slab by slab);slab);


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CONCLUSIONS

The results showed good quantitative agreement with The results showed good quantitative agreement with analytical data though several sweeps are need to analytical data though several sweeps are need to guarantee the convergence. guarantee the convergence.

Although the resulting shear stress profile for de k-Although the resulting shear stress profile for de k- turbulence model seems to fit better near the walls, it was turbulence model seems to fit better near the walls, it was more unstable and harder to converge than the standard more unstable and harder to converge than the standard k-k- one. one.

Also, it was verified that near the open borders of the Also, it was verified that near the open borders of the plate the shear stress is usually higher because of an plate the shear stress is usually higher because of an increase in the turbulence effects at these elements. It increase in the turbulence effects at these elements. It was important to point out that in some cases the shear was important to point out that in some cases the shear stress near the borders seems to be over-predicted and stress near the borders seems to be over-predicted and unfortunately it was impossible to check experimentally unfortunately it was impossible to check experimentally this datathis data


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CONCLUSIONS

Finally this case was used as a base for a general q1 Finally this case was used as a base for a general q1 template and implemented in a Human-Machine Interface template and implemented in a Human-Machine Interface (HMI) in order to turn typical sensibility analysis into an (HMI) in order to turn typical sensibility analysis into an easy task, allowing series of tests to be performed with easy task, allowing series of tests to be performed with very few clicks of the mouse. This enables even new very few clicks of the mouse. This enables even new users or equipment designers who may wish not to invest users or equipment designers who may wish not to invest in training in PHOENICS to perform similar studies.in training in PHOENICS to perform similar studies.

Your Success is Our Goal SHEAR STRESS ANALYSIS IN A ROTATOR-STATOR SYSTEM IX International...

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