Curvilinear coordinate and momentum operators in configuration representation

1980 ◽  
Vol 10 (7-8) ◽  
pp. 581-599 ◽  
Author(s):  
Boris Leaf
Keyword(s):  
Curvilinear Coordinate ◽  
Configuration Representation

Bending Stiffener Design Through Structural Optimization

2009 ◽  
Author(s):  
Rafael Loureiro Tanaka ◽  
Lauro Massao Yamada da Silveira ◽  
Joa˜o Paulo Zi´lio Novaes ◽  
Eduardo Esterqui de Barros ◽  
Clo´vis de Arruda Martins
Keyword(s):  
Optimization Problem ◽  
Design Procedure ◽  
Complex Task ◽  
Load Case ◽  
Shear Forces ◽  
Design Variables ◽  
Curvilinear Coordinate ◽  
Regular Design ◽  
Curvature Deformation ◽  
Flexible Risers

Bending stiffeners are very important ancillary equipments of umbilicals or flexible risers, since they protect the lines from overbending. Their design however is a complex task, since many load cases must be taken into account; the structure itself has a section that is variable with curvilinear coordinate. To aid the designer in this task, optimization algorithms can be used to automate the search for the best design. In this work an optimization algorithm is applied to the design of the bending stiffener. First, a bending stiffener model is created, which is capable of simulating different load case conditions and provide, as output, results of interest such as maximum curvature, deformation along the stiffener, shear forces and so on. Then, a bending stiffener design procedure is written as an optimization problem and, for that, objective function, restrictions and design variables defined. Study cases were performed, comparing a regular design with its optimized counterpart, under varying conditions.

Curvilinear-Coordinate-Based Object and Situation Assessment for Highly Automated Vehicles

2015 ◽  
Vol 16 (3) ◽  
pp. 1559-1575 ◽  
Author(s):  
Junsoo Kim ◽  
Kichun Jo ◽  
Wontaek Lim ◽  
Minchul Lee ◽  
Myoungho Sunwoo
Keyword(s):  
Automated Vehicles ◽  
Situation Assessment ◽  
Curvilinear Coordinate

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals Numerical Computation and Investigation of the Characteristics of Microscale Synthetic Jets

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ann Lee ◽  
Guan H. Yeoh ◽  
Victoria Timchenko ◽  
John Reizes
Keyword(s):  
Velocity Fields ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Moving Mesh ◽  
Experimental Result ◽  
Computational Domain ◽  
Governing Equations ◽  
Curvilinear Coordinate ◽  
Pulsating Jet ◽  
Good Agreement

A synthetic jet results from periodic oscillations of a membrane in a cavity. Jet is formed when fluid is alternately sucked into and ejected from a small cavity by the motion of membrane bounding the cavity. A novel moving mesh algorithm to simulate the formation of jet is presented. The governing equations are transformed into the curvilinear coordinate system in which the grid velocities evaluated are then fed into the computation of the flow in the cavity domain thus allowing the conservation equations of mass and momentum to be solved within the stationary computational domain. Numerical solution generated using this moving mesh approach is compared with an experimental result measuring the instantaneous velocity fields obtained by μPIV measurements in the vicinity of synthetic jet orifice 241 μm in diameter issuing into confined geometry. Comparisons between experimental and numerical results on the streamwise component of velocity profiles at the orifice exit and along the centerline of the pulsating jet in microchannel as well as the location of vortex core indicate that there is good agreement, thereby demonstrating that the moving mesh algorithm developed is valid.

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