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Maximal tipping angles of nonempty bottles

Maximal tipping angles of nonempty bottles. ESSIM 2012, Dresden Group 12 NAMES. Outline. Problem Restrictions Creating bottle Calculations Calculating th e liquid mass centre Monte Carlo method Mesh method Results Conclusion. Problem.

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Maximal tipping angles of nonempty bottles

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  1. Maximal tipping angles of nonempty bottles ESSIM 2012, Dresden Group 12 NAMES

  2. Outline • Problem • Restrictions • Creating bottle • Calculations • Calculating the liquid mass centre • Monte Carlo method • Mesh method • Results • Conclusion

  3. Problem • Determine the maximal inclination angle and the corresponding fill quantity for various existing bottles. • Figure sources: • http://www.4thringroad.com/wp-content/uploads/2009/08/coca-cola-main-design.jpg • http://s3.amazonaws.com/static.fab.com/inspiration/154695-612x612-1.png

  4. Modelling ideas • The bottle will fall when the system’s mass centre passes the tipping point. • First, the problem was solved for totally full or totally empty cylindrical bottle, because it is easy to solve analytically. • Only 2-dimensional case was considered because of the radial symmetry.

  5. Problem restrictions • Assumptions made: • Bottle density is homogeneous • Liquid density is homogeneous • Bottle has to be radial symmetric • Tilting point is fixed during inclination

  6. Creating bottle • For creating the bottle, coordinates of one edge are given • Bottle mass is measured • Next You will see the bottles we used! 

  7. Water bottle

  8. Coke bottle

  9. Cylinder

  10. Fat wine bottle

  11. Calculating the bottle mass centre • Take the mass centre of each line between given coordinates • Length of the line • Mass centre of system of lines is

  12. Calculating the mass centre of liquidMonte Carlo

  13. Calculating the mass centre of liquidMesh • Calculate a triangular mesh • Find the water level by minimizing the V-V(h) • Use coarse grid, but refine in the water level • Calculate the mass centre of every triangle

  14. Will the bottle fall? • Add mass centres of the whole system • Has the mass centre passed the tipping point? • Picture of a bottle on the edge of falling

  15. Results Monte Carlo method

  16. ResultsMesh model

  17. Conclusion • Monte Carlo method is quite slow to use • 3D would have been more accurate • For cylindrical bottles, the maximum tipping angle is easily calculated

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