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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. - PowerPoint PPT Presentation
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Maximal tipping angles of nonempty bottles
ESSIM 2012, DresdenGroup 12NAMES
Outline
• Problem– Restrictions
• Creating bottle– Calculations
• Calculating the liquid mass centre– Monte Carlo method– Mesh method
• Results• Conclusion
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
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.
Problem restrictions
• Assumptions made:– Bottle density is homogeneous– Liquid density is homogeneous– Bottle has to be radial symmetric– Tilting point is fixed during inclination
Creating bottle
• For creating the bottle, coordinates of one edge are given
• Bottle mass is measured• Next You will see the bottles we used!
Water bottle
Coke bottle
Cylinder
Fat wine bottle
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
€
R = 1M
mirii∑
Calculating the mass centre of liquidMonte Carlo
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
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
Results Monte Carlo method
ResultsMesh model
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