The Involution Correspondence in Plane Elastostatics for Regions Bounded by a Circle

1988 ◽  
Vol 55 (3) ◽  
pp. 566-573 ◽  
Author(s):  
T. Honein ◽  
G. Herrmann
Keyword(s):  
Outer Region ◽  
Elastic Field ◽  
Circular Disk ◽  
Infinite Plane ◽  
Infinite Domain ◽  
Circular Boundary ◽  
Inner Region ◽  
Plane Elastostatics

It is shown that the elastic field induced by prescribed displacements or surface tractions acting on a circular disk (inner region) can be expressed in terms of the elastic field induced by the same quantities acting on the circular boundary (hole) of an infinite plane (outer region), and vice versa. It is shown further that this correspondence is an involution. This novel representation permits one to express the elastic field in a disk with either vanishing displacements or tractions along the boundary in terms of the elastic field of an infinite domain, provided all singularities are in the inner region. Similarly, the elastic field in the outer region can be expressed in terms of the elastic field of the infinite domain, provided all singularities reside in the outer region. The expressions so-derived possess simple algebraic character and are universal in the sense of being independent of the applied loads (singularities) in the two problems.

Measurement and Analysis of Buoyancy-Induced Heat Transfer in Aero-Engine Compressor Rotors

2020 ◽  
Author(s):  
Richard W. Jackson ◽  
Dario Luberti ◽  
Hui Tang ◽  
Oliver J. Pountney ◽  
James A. Scobie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Outer Region ◽  
Conjugate Problem ◽  
Radial Temperature ◽  
Nusselt Numbers ◽  
Induced Flow ◽  
Aero Engines ◽  
Inner Region ◽  
Buoyancy Induced Flow

Abstract The flow inside cavities between co-rotating compressor discs of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the discs, and the disc temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anti-cyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady and unstable, and it is a challenge to compute and measure the heat transfer from the discs to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both discs in a rotating cavity of the Bath Compressor-Cavity Rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disc temperature were collected under carefully-controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disc temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disc increase as the buoyancy forces increase. At high rotational speeds the temperature rise in the core, created by compressibility effects in the air, attenuates the heat transfer and there is a critical rotational Reynolds number for which the Nusselt number is a maximum. In the cavity, there is an inner region dominated by forced convection and an outer region dominated by buoyancy-induced flow. The inner region is a mixing region, in which entrained cold throughflow encounters hot flow from the Ekman layers on the discs. Consequently, the Nusselt numbers on the downstream disc in the inner region tend to be higher than those on the upstream disc.

Small Péclet-number mass transport to a finite strip: An advection–diffusion–reaction model of surface-based biosensors

2019 ◽  
Vol 31 (5) ◽  
pp. 763-781
Author(s):  
EHUD YARIV
Keyword(s):  
Shear Flow ◽  
Mass Transport ◽  
Sherwood Number ◽  
Peclet Number ◽  
Outer Region ◽  
Diffusion Reaction ◽  
Background Concentration ◽  
Leading Order ◽  
Péclet Number ◽  
Inner Region

AbstractWe consider two-dimensional mass transport to a finite absorbing strip in a uniform shear flow as a model of surface-based biosensors. The quantity of interest is the Sherwood number Sh, namely the dimensionless net flux onto the strip. Considering early-time absorption, it is a function of the Péclet number Pe and the Damköhler number Da, which, respectively, represent the characteristic magnitude of advection and reaction relative to diffusion. With a view towards modelling nanoscale biosensors, we consider the limit Pe«1. This singular limit is handled using matched asymptotic expansions, with an inner region on the scale of the strip, where mass transport is diffusively dominated, and an outer region at distances that scale as Pe-1/2, where advection enters the dominant balance. At the inner region, the mass concentration possesses a point-sink behaviour at large distances, proportional to Sh. A rescaled concentration, normalised using that number, thus possesses a universal logarithmic divergence; its leading-order correction represents a uniform background concentration. At the outer region, where advection by the shear flow enters the leading-order balance, the strip appears as a point singularity. Asymptotic matching with the concentration field in that region provides the Sherwood number as $${\rm{Sh}} = {\pi \over {\ln (2/{\rm{P}}{{\rm{e}}^{1/2}}) + 1.0559 + \beta }},$$ wherein β is the background concentration. The latter is determined by the solution of the canonical problem governing the rescaled inner concentration, and is accordingly a function of Da alone. Using elliptic-cylinder coordinates, we have obtained an exact solution of the canonical problem, valid for arbitrary values of Da. It is supplemented by approximate solutions for both small and large Da values, representing the respective limits of reaction- and transport-limited conditions.

scholarly journals Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites

2019 ◽  
Vol 629 ◽  
pp. A106 ◽  
Author(s):  
Sota Arakawa ◽  
Yuhito Shibaike
Keyword(s):  
Density Distribution ◽  
Accretion Disks ◽  
Surface Density ◽  
Outer Region ◽  
Dust Particles ◽  
Magnetorotational Instability ◽  
Galilean Satellites ◽  
Ionization Fraction ◽  
Orbital Configuration ◽  
Inner Region

Jupiter has four large regular satellites called the Galilean satellites: Io, Europa, Ganymede, and Callisto. The inner three of the Galilean satellites orbit in a 4:2:1 mean motion resonance; therefore their orbital configuration may originate from the stopping of the migration of Io near the bump in the surface density distribution and following resonant trapping of Europa and Ganymede. The formation mechanism of the bump near the orbit of the innermost satellite, Io, is not yet understood, however. Here, we show that photophoresis in the circumjovian disk could be the cause of the bump using analytic calculations of steady-state accretion disks. We propose that photophoresis in the circumjovian disk could stop the inward migration of dust particles near the orbit of Io. The resulting dust-depleted inner region would have a higher ionization fraction, and thus admit increased magnetorotational-instability-driven accretion stress in comparison to the outer region. The increase of the accretion stress at the photophoretic dust barrier would form a bump in the surface density distribution, halting the migration of Io.

Investigation on the Radial Heat-Transfer of Pumping Secondary Flow in Semiclosed Rotating Disk Cavity

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Guohu Luo ◽  
Zhenqiang Yao
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Outer Region ◽  
Rotating Disk ◽  
Mean Flow ◽  
Coolant Pump ◽  
Radial Temperature ◽  
Type Flow ◽  
Radial Heat ◽  
Inner Region

Abstract This study investigates the mean flow and radial heat-transfer behaviors in semiclosed rotating disk cavity within the canned reactor coolant pump. The flow in the semiclosed cavity contains the Stewartson type flow at inner region and the Batchelor type flow at outer region. The heat is radially transported from the outer rim of the semiclosed disk cavity to discharge-hole through the nondirect discharge (ND) portion of the superimposed flow from inlet. The effects of rotating Reynolds numbers, cavity aspect ratio and radial location of discharge-hole on the discharge ratio, pumping mass flow rate, local wall shear stress and radial heat-transfer coefficient are examined in the semiclosed rotating cavity flow, respectively. Based on the radial heat transfer behaviors of pumping secondary flow, an equivalent thermal network is proposed and validated by experiments, which can effectively predict the radial temperature distribution from the discharge hole to periphery with the viscous-heating and nonisothermal effects.

scholarly journals 11.16. On the origin of density cusp in galactic nuclei by central black hole

1998 ◽  
Vol 184 ◽  
pp. 487-488
Author(s):  
T. Nakano ◽  
T. Fukushige ◽  
J. Makino
Keyword(s):  
Black Hole ◽  
Hubble Space Telescope ◽  
Outer Region ◽  
Elliptical Galaxies ◽  
Heating Process ◽  
Massive Black Hole ◽  
Weak Density ◽  
The Galaxy ◽  
Galaxy Model ◽  
Inner Region

We investigated the dynamical reaction of the central region of galaxies to a falling massive black hole by N-body simulations. As the initial galaxy model, we used an isothermal King model and placed a massive black hole at around the half-mass radius of the galaxy. We found that the central core of the galaxy is destroyed by the heating due to the black hole and a very weak density cusp (ρ ∝ r−α, with α ∼ 0.5) is formed around the center. This result is consistent with recent observations of large elliptical galaxies by Hubble Space Telescope (Lauer et al. 1995; Byun et al. 1996; Gebhardt et al. 1996; Faber et al. 1996; Kormendy et al. 1996). The radius of the weak cusp region is large for large black hole mass. The velocity of the stars become tangentially anisotropic in the inner region, while in the outer region the stars have radially anisotropic velocity dispersion. Our result naturally explains the mechanism of the formation of the weak cusp found in the previous simulations of galaxy merging, and implies that the weak cusp observed in large elliptical galaxies may be formed by the heating process by sinking black holes during merging events.

scholarly journals Changes in Morphological and Physicochemical Properties of Waxy and Non-waxy Proso Millets during Cooking Process

Foods ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 583 ◽  
Author(s):  
Qinghua Yang ◽  
Long Liu ◽  
Weili Zhang ◽  
Jing Li ◽  
Xiaoli Gao ◽  
...  
Keyword(s):  
Physicochemical Properties ◽  
Cross Sections ◽  
Nutritional Value ◽  
Outer Region ◽  
Pasting Properties ◽  
Cooking Time ◽  
Ordered Structures ◽  
Proso Millet ◽  
Cooking Process ◽  
Inner Region

Proso millet, a grain which is principally consumed in cooked form, is favored by consumers because of its rich nutritional value. However, the changes in morphological and physicochemical properties of proso millet grains occurring during the cooking process have rarely been reported. In this study, we investigated the changes in morphological and physicochemical properties of cooked waxy and non-waxy proso millets. During the cooking process, starch granules in the grains were gradually gelatinized starting from the outer region to the inner region and were gelatinized earlier in waxy proso millet than in non-waxy proso millet. Many filamentous network structures were observed in the cross sections of cooked waxy proso millet. As the cooking time increased, the long- and short-range, ordered structures of proso millets were gradually disrupted, and the ordered structures were fully disrupted by 20 min of cooking. In both waxy and non-waxy proso millets, thermal and pasting properties significantly changed with an increase in the cooking time. This study provides useful information for the processing of proso millet in the food industry.

scholarly journals A new model for dark matter fluid sphere

2020 ◽  
Vol 35 (34) ◽  
pp. 2050280
Author(s):  
Shyam Das ◽  
Nayan Sarkar ◽  
Monimala Mondal ◽  
Farook Rahaman
Keyword(s):  
Dark Matter ◽  
Compact Star ◽  
Outer Region ◽  
Fluid Sphere ◽  
Constant Density ◽  
Spherically Symmetric ◽  
Causality Condition ◽  
New Model ◽  
Inner Region ◽  
Tov Equation

We develop a new model for a spherically symmetric dark matter fluid sphere containing two regions: (i) Isotropic inner region with constant density and (ii) Anisotropic outer region. We solve the system of field equation by assuming a particular density profile along with a linear equation of state. The obtained solutions are well-behaved and physically acceptable which represent equilibrium and stable matter configuration by satisfying the Tolman–Oppenheimer–Volkoff (TOV) equation and causality condition, condition on adiabatic index, Harrison–Zeldovich–Novikov criterion, respectively. We consider the compact star EXO 1785-248 (Mass [Formula: see text] and radius R[Formula: see text]8.8 km) to analyze our solutions by graphical demonstrations.

Ultrastructure and cleavage of chlamydospore chains of Thielaviopsis basicola

1970 ◽  
Vol 48 (12) ◽  
pp. 2305-2308 ◽  
Author(s):  
Christos Christias ◽  
Kenneth F. Baker
Keyword(s):  
Thin Film ◽  
Electron Microscopy ◽  
Endoplasmic Reticulum ◽  
Germ Tube ◽  
Outer Region ◽  
Thielaviopsis Basicola ◽  
Thin Electron ◽  
Ultra Thin Section ◽  
Inner Region ◽  
Septal Pores

Electron microscopy revealed that numerous spherical or ellipsoidal globules of reserve nutrient material fill the chlamydospore cells, with cytoplasm as a thin film between these globules. The basal cell of the chain is not a chlamydospore; it is filled with cytoplasm and does not contain these globules. Its plasma membrane, nucleus, mitochondria, lomasomes, and endoplasmic reticulum are evident in ultra-thin section. The walls of chlamydospore cells are thick and without distinct layers, except for an electron-dense outer region and a more electron-transparent inner region. Chlamydospore cells in the chain are separated by a very thin electron-transparent binding layer. A thin two-layered envelope surrounds the entire chain. When chlamydospore chains are treated with chitinase, this envelope remains attached around single separated cells, rather than dissolving away. Cytoplasm of cells in the chain is continuous through septal pores. The end walls of the cells become the opercula after the cells are freed from the chain. The germ tube always emerges at the side where the operculum opens, never through the septal pore.

An ultrastructural comparison of soft and hardened spermatophores from the crayfish Pacifastacus leniusculus Dana

1983 ◽  
Vol 61 (1) ◽  
pp. 182-194 ◽  
Author(s):  
E. E. Dudenhausen ◽  
P. Talbot
Keyword(s):  
Structural Changes ◽  
Periodic Acid ◽  
Light And Electron Microscopy ◽  
Outer Region ◽  
Middle Layer ◽  
Pacifastacus Leniusculus ◽  
Periodic Acid Schiff ◽  
Structural Modifications ◽  
Inner Region ◽  
Region Ii

The spermatophore of the crayfish Pacifastacus leniusculus consists of two main parts: a sperm mass composed of sperm embedded in a dense fibrillar matrix and an acellular wall which surrounds the sperm mass and is formed from secretions produced in the vas deferens. Following extrusion from the male, the spermatophore wall, which is initially soft and sticky, undergoes a hardening process. In this study, the structure of the spermatophore walls of unextruded (soft) and hardened spermatophores were compared using light and electron microscopy. The wall of the unextruded spermatophore is composed of three concentric layers: a thin primary spermatophore layer which directly surrounds the sperm mass; a thick middle layer composed primarily of electron-dense, spherical granules; and a thick outer layer formed from a dense globular secretion. The primary spermatophore layer and outer globular layer are positive for carbohydrate with the periodic acid – Schiff method. Following extrusion and hardening, the walls of spermatophores showed several structural changes. These are (i) division of the middle granular layer into a compact inner region and a highly reticulated outer region; (ii) the loss of the outer globular layer; and (iii) the formation of a thickened ridge along one side of the spermatophore wall. The thickened ridge is fibrillar in structure and is believed to be derived from a structural modification of the outer globular layer. No structural modifications in the primary spermatophore layer were observed. We interpret these observations to indicate that the outer globular layer functions in attachment of the spermatophore to the female and the middle layer is involved in spermatophore hardening and sperm protection during storage.

scholarly journals Numerical simulation of dynamic contact-line problems

1997 ◽  
Vol 352 ◽  
pp. 113-133 ◽  
Author(s):  
IVAN B. BAZHLEKOV ◽  
PETER J. SHOPOV
Keyword(s):  
Contact Line ◽  
Contact Region ◽  
Outer Region ◽  
Dynamic Contact ◽  
Momentum Conservation ◽  
Phase Region ◽  
Contact Lines ◽  
Three Phase ◽  
Inner Region ◽  
Dynamic Contact Line

The presence of a three-phase region, where three immiscible phases are in mutual contact, causes additional difficulties in the investigation of many fluid mechanical problems. To surmount these difficulties some assumptions or specific hydrodynamic models have been used in the contact region (inner region). In the present paper an approach to the numerical solution of dynamic contact-line problems in the outer region is described. The influence of the inner region upon the outer one is taken into account by means of a solution of the integral mass and momentum conservation equations there. Both liquid–fluid–liquid and liquid–fluid–solid dynamic contact lines are considered. To support the consistency of this approach tests and comparisons with a number of experimental results are performed by means of finite-element numerical simulations.

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