scholarly journals Fluence Rate in UV Photoreactor for Disinfection of Water: Isotropically Radiating Cylinder

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Roman Ilinsky ◽  
Andrey Ulyanov
Keyword(s):  
Numerical Integration ◽  
Light Source ◽  
Uv Radiation ◽  
Infinite Length ◽  
Fluence Rate ◽  
Chebyshev Method ◽  
Limiting Case

The calculation of fluence rate in the photochemical reactor using ultraviolet (UV) radiation for disinfection of water for the case, when a cylinder of infinite length is used as a light source, has been considered. Such a cylinder is filled with an isotropically radiating medium. The dependence of the fluent rate on the diameter of the radiating cylinder has been analytically analyzed. The limiting case when the diameter of the radiating cylinder tends to zero has been considered and the notion of “effective interval” has been introduced. Based on this notion, the comparison of fluence rates for the cylinders of finite and infinite lengths has been performed. In the calculations of fluence rate, it is advisable to use the Chebyshev method for the operations of numerical integration.

A Mechanical Model of Helical Elements in Textured Yarns

1976 ◽  
Vol 46 (4) ◽  
pp. 278-283 ◽  
Author(s):  
M. Konopasek
Keyword(s):  
Differential Equations ◽  
Mechanical Model ◽  
Mechanical Characteristics ◽  
Functional Relationship ◽  
Three Dimensional ◽  
Infinite Length ◽  
Fiber Properties ◽  
Helical Angle ◽  
Limiting Case ◽  
Special Case

The helical model of the spontaneously collapsed filaments in twist-textured yarns is defined as reflecting the limiting case of a free-filament segment with infinite length (or number of coils) between two reversal points. The fundamental relationships linking fiber properties and parameters of the texturing process with geometrical and mechanical characteristics of the helices are derived directly from the differential equations of the three-dimensional elastica. Bicomponent and similar fibers are interpreted as a special case of twist-textured filaments with original (permanently set) helical angle equal to π/2; for this case an explicit functional relationship between contraction and stretching force is obtained.

Trajectories of charged tracer particles around a charged sphere in a simple shear flow

1994 ◽  
Vol 263 ◽  
pp. 185-206 ◽  
Author(s):  
A. S. Dukhin ◽  
T. G. M. Van De Ven
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Tracer Particle ◽  
Simple Shear Flow ◽  
Infinite Length ◽  
Charged Sphere ◽  
Neutral Particles ◽  
Tracer Particles ◽  
Two Parameters ◽  
Limiting Case

The trajectories of electrically charged tracer particles travelling around a charged sphere subjected to a simple shear flow have been calculated. This is a limiting case of the relative trajectories of two unequal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivity of hydrodynamic and electrostatic forces, while neglecting the electroviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 → 0, it is found that these trajectories depend on two parameters, α and β, which depend on the surface charge density of the tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles. There exist six intervals of α-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutral particles, which we refer to as uni- and bidirectional infinite length trajectories, uni- and bidirectional finite length trajectories, open returning trajectories, and prolate, oblate and circular closed trajectories. This richness of possible trajectories is the result of three electrokinetic phenomena, affecting particle motion: electro-osmotic slip, electrophoretic and diffusiophoretic motion.

The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities

1986 ◽  
Vol 170 ◽  
pp. 199-232 ◽  
Author(s):  
P. W. Carpenter ◽  
A. D. Garrad
Keyword(s):  
Viscous Fluid ◽  
Numerical Integration ◽  
Critical Velocity ◽  
Finite Length ◽  
Irreversible Processes ◽  
Infinite Length ◽  
Material Damping ◽  
Compliant Surfaces ◽  
Sommerfeld Equation ◽  
Good Agreement

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

scholarly journals On coefficient of mutual inductance between solenoid and coiled circuit with parallel axes

2021 ◽  
Vol 2 (396) ◽  
pp. 93-98
Author(s):  
G. Tsitsikyan ◽  
Keyword(s):  
Numerical Integration ◽  
Computational Methods ◽  
Mutual Inductance ◽  
Axial Displacement ◽  
Written Expression ◽  
Numerical Estimation ◽  
Limiting Case

Object and purpose of research. Current recommendations on calculation of mutual inductance between solenoids and coiled circuits with parallel axes are shown and compared. Advisability of such verification for a limiting case when the axes are aligned is revealed. Materials and methods. Verification of these recommendations for cases of zero axial displacement is performed on the basis of well-tested expressions. For this purpose alternative expressions for the mutual inductance of the coaxial circuit and solenoid and two circuits. Main results. A number of significant discrepancies are identified between numerical values including difference in signs for the case of a solenoid and a circuit with parallel axes. For circuits with parallel axes, attention is focused on the necessity to use auxiliary tables, which confirms the complexity of numerical estimation in this case either. Conclusion. In terms of the identified flaws, the conclusion was drawn about the advisability of using computational methods for configurations with parallel axes. For circuits with parallel axes, as follows from the written expression, it is sufficient to apply a single numerical integration.

The deformation of the ground around surface faults

1961 ◽  
Vol 51 (3) ◽  
pp. 355-372 ◽  
Author(s):  
M. A. Chinnery
Keyword(s):  
San Andreas Fault ◽  
Displacement Vector ◽  
Good Description ◽  
Analytical Form ◽  
Infinite Length ◽  
Dislocation Theory ◽  
Contour Maps ◽  
San Andreas ◽  
Limiting Case

Abstract A rectangular dislocation surface (i.e., a surface across which there is a discontinuity in the displacement vector) is used as a model of a vertical transcurrent fault. The results of Steketee (1958a) are employed to derive, in analytical form, the displacement field throughout a semi-infinite elastic medium due to such a dislocation. In particular, the displacements of the surface of the medium are calculated in some detail, and contour maps of the various components are given for two representative cases. The solution to the limiting case of a fault of infinite length is also included. Methods are then discussed for the determination of the depth of a surface fault from measurements of the deformation of the ground produced by it, and these are applied to the faults associated with the Tango and North Idu earthquakes, and to the San Andreas fault. In each of these cases, the general features of the crustal deformations agree well with the predictions of the theory, and it is concluded that dislocation theory provides a good description of the effects of fracture in the earth's crust.

scholarly journals Light propagation within N95 Filtered Face Respirators: A simulation study for UVC decontamination

2020 ◽  
Author(s):  
Lothar Lilge ◽  
Angelica Manalac ◽  
Madrigal Weersink ◽  
Fynn Schwiegelshohn ◽  
Tanner Young-Schultz ◽  
...  
Keyword(s):  
Optical Properties ◽  
Numerical Simulations ◽  
Light Source ◽  
Exposure Time ◽  
Simulation Study ◽  
Light Propagation ◽  
Fluence Rate ◽  
Doubling Method ◽  
Selection Of

This study presents numerical simulations of UVC light propagation through seven different filtered face respirators (FFR) to determine their suitability for UV germicidal inactivation (UVGI). UV propagation was modelled using the FullMonte program for two external light illuminations. The optical properties of the dominant three layers were determined using the inverse adding doubling method. The resulting fluence rate volume histograms and the lowest fluence rate recorded in the modelled volume, sometimes in the nW cm-2, provide feedback on a respirator’s suitability for UVGI and the required exposure time for a given light source. While UVGI can present an economical approach to extend an FFR’s useable lifetime, it requires careful optimization of the illumination setup and selection of appropriate respirators.Abstract Figure

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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