1 / 17

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.

tamal
Download Presentation

Maximal tipping angles of nonempty bottles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related