Effective specification of the surface shape of aspheric optics

SPIE Newsroom ◽  
2007 ◽  
Author(s):  
Greg Forbes
Keyword(s):  
Surface Shape ◽  
Aspheric Optics

Stability of thermocapillary flows in non-cylindrical liquid bridges

2002 ◽  
Vol 458 ◽  
pp. 35-73 ◽  
Author(s):  
CH. NIENHÜSER ◽  
H. C. KUHLMANN
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Critical Reynolds Number ◽  
Volume Fraction ◽  
Thermocapillary Flow ◽  
Surface Shape ◽  
Liquid Bridges ◽  
Gravity Level ◽  
Neutral Curves ◽  
Prandtl Numbers

The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

Electrostatic energy and screened charge interaction near the surface of metals with different Fermi surface shape

1980 ◽  
Vol 94 (1) ◽  
pp. 179-203 ◽  
Author(s):  
A.M. Gabovich ◽  
L.G. Il'chenko ◽  
E.A. Pashitskii ◽  
Yu.A. Romanov
Keyword(s):  
Fermi Surface ◽  
Surface Shape ◽  
Electrostatic Energy ◽  
Charge Interaction

Bidirectional Fractal Test of Dust Particle

2010 ◽  
Vol 108-111 ◽  
pp. 954-959
Author(s):  
Fan Jiang ◽  
Wei Ping Chen ◽  
Zhong Wei Liang
Keyword(s):  
Spherical Particle ◽  
Dust Particle ◽  
Identical Particle ◽  
Fractal Dimensions ◽  
Surface Shape ◽  
Flat Type ◽  
Type Particle

To describe surface shape of the dust particle comprehensively, uses the bidirectional CCD to shoot picture of dust particle, through recognizing the bidirectional particle picture, matching the particle, computing the fractal results of identical particle in two pictures, and integrating two fractal results, obtains the dust particle bidirectional fractal. The results indicated that three fractal dimensions of spherical particle are quite closed, but the three fractal dimensions of flat type particle are significantly different.

Laminar Natural Convection About Downward Facing Heated Blunt Bodies to Liquid Metals

1976 ◽  
Vol 98 (2) ◽  
pp. 208-212 ◽  
Author(s):  
G. M. Harpole ◽  
I. Catton
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Series Expansion ◽  
Surface Heat Flux ◽  
Liquid Metals ◽  
Surface Heat ◽  
Surface Shape ◽  
Boundary Layer Equations ◽  
Stagnation Points ◽  
Shape Dependence

The laminar boundary layer equations for free convection over bodies of arbitrary shape (i.e., a three-term series expansion) and with arbitrary surface heat flux or surface temperature are solved in local Cartesian coordinates. Both two-dimensional bodies (e.g., horizontal cylinders) and axisymmetric bodies (e.g., spheres) with finite radii of curvature at their stagnation points are considered. A Blasius series expansion is applied to convert from partial to ordinary differential equations. An additional transformation removes the surface shape dependence and the surface heat flux or surface temperature dependence of the equations. A second-order-correct, finite-difference method is used to solve the resulting equations. Tables of results for low Prandtl numbers are presented, from which local Nusselt numbers can be computed.

scholarly journals Quantitative Evaluation of the In Vivo Vocal Fold Medial Surface Shape

2017 ◽  
Vol 31 (4) ◽  
pp. 513.e15-513.e23 ◽  
Author(s):  
Andrew M. Vahabzadeh-Hagh ◽  
Zhaoyan Zhang ◽  
Dinesh K. Chhetri
Keyword(s):  
Quantitative Evaluation ◽  
Vocal Fold ◽  
Surface Shape ◽  
Medial Surface
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