scholarly journals Local orthogonal rectification: Deriving natural coordinates to study flows relative to manifolds

2020 ◽  
Vol 25 (9) ◽  
pp. 3725-3747
Author(s):  
Benjamin Letson ◽  
◽  
Jonathan E. Rubin
Keyword(s):  
Natural Coordinates

Velocity Field Computation in Plastic Flow in Non-Circular Tubes Using Natural Coordinates

2012 ◽  
Author(s):  
Mario F. Letelier ◽  
Juan S. Stockle
Keyword(s):  
Velocity Field ◽  
Plastic Flow ◽  
Momentum Equation ◽  
Senior Author ◽  
Radius Of Curvature ◽  
Natural Coordinates ◽  
Cross Sectional ◽  
Relevant Variable ◽  
Bingham Plastic ◽  
Circular Tubes

A numerical method to determine the velocity field, and related variables, in plastic flow in non-circular straight ducts is presented. The method is an extension of previous work of the senior author related to modeling laminar flow in pipes of arbitrary cross-sectional contours using natural coordinates. In this case the concept of “natural coordinates” is applied to the system of orthogonal curves determined by the plane isovels and their normal counterparts. The momentum equation for the axial velocity is expressed in natural coordinates in which one relevant variable is the radius of curvature of isovels. The method is applied to a selected set of shapes when the fluid is a Bingham plastic. Isovels and plug zones are determined drawing on the properties of the isolvels and normal curves. Computations start at the pipe perimeter and advance toward the center.

Self-Adaptation of Natural-Coordinate System

2013 ◽  
Vol 367 ◽  
pp. 286-291
Author(s):  
Ke Wei Zhang ◽  
Yun Qing Zhang
Keyword(s):  
Coordinate System ◽  
Equal Weight ◽  
Natural Coordinates ◽  
Model Quality ◽  
Step Method ◽  
Natural Coordinate System ◽  
Self Adaptation ◽  
Natural Coordinate ◽  
Analysis Platform ◽  
Adaptation Method

A self-adaptation method for natural-coordinate systems is proposed, in order to automate the selection of natural coordinates for each rigid element of a multibody system. The four-step method includes: First, find out all empty positions, which come from the feature points or vectors of the joints attached to the element, and give equal weight to them; second, delete redundant empty positions and add their weight to the unique one; third, select at most four empty positions which have a maximum total weight and can be occupied by a natural-coordinate system at the same time; fourth, the standard natural-coordinate system on the element can adapt itself to the selected empty positions, leading to an actual natural-coordinate system, which contains twelve rational natural coordinates for the element. The implementation of the method has been achieved on a multibody dynamics and motion analysis platform, InteDyna, with the result that modeling efficiency is enhanced and model quality improved.

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