Combination of cartesian and cylindrical coordinate system

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SUMMARY

The discussion focuses on solving a numerical problem involving airflow through a porous medium and a narrow channel, utilizing the Laplace equation for the porous media and the Reynolds equation for the gap flow. It is confirmed that a Cartesian coordinate system can be employed for the Reynolds equation while a cylindrical coordinate system is suitable for the Laplace equation, provided that the boundary nodes for pressure calculations are aligned. The geometry and dimensions of the system, as well as the specific type of bearing (journal porous air bearing), are crucial for accurate modeling.

PREREQUISITES
  • Understanding of Laplace equation and its application in fluid dynamics.
  • Familiarity with Reynolds equation and its role in flow analysis.
  • Knowledge of coordinate systems, specifically Cartesian and cylindrical coordinates.
  • Basic principles of porous media flow and boundary conditions.
NEXT STEPS
  • Research the application of Laplace equation in porous media flow modeling.
  • Study Reynolds equation in the context of fluid flow in narrow channels.
  • Explore numerical methods for solving coupled equations iteratively.
  • Investigate the design and characteristics of journal porous air bearings.
USEFUL FOR

Engineers, fluid dynamics researchers, and anyone involved in the design and analysis of airflow systems in porous media and narrow channels.

hermano
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Hi,

I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing).

This problem can be described with the use of two equations namely the Laplace equation describing the flow in the porous media, and the Reynolds equation describing the flow in the gap.

These equations must be solved both separately on an iterative manner until the pressure at the boundary between the porous media and the gap is equal to each other (continuity).

My question is: Can I use a cartesian coordinate system for solving the Reynolds equation (flow in the gap) and a cylindrical coordinate system for solving the Laplace equation (flow in the porous media) if I take care that the nodes where I calculate the pressure at the boundary between the gap and the porous media lie at the same place?
 
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What is the exact geometry with the exact dimensions? What kind of bearing is this?
 

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