Reexamination of Unsteady Fluid Dynamic Forces on a Two-Dimensional Finite Plate at Small Mach Numbers

1980 ◽  
Vol 47 (4) ◽  
pp. 720-724 ◽  
Author(s):  
Y. Matsuzaki ◽  
T. Ueda
Keyword(s):  
Incompressible Flows ◽  
Fluid Dynamic ◽  
Control Surface ◽  
Analytical Determination ◽  
Natural Mode ◽  
Two Dimensional ◽  
Mach Numbers ◽  
Unsteady Fluid ◽  
The Fourier Transform

The Fourier transform theory is applied to the analytical determination of the disturbance velocity potential and pressure acting on a two-dimensional plate, in order to reexamine those of previous analyses by other investigators. Simplified expressions of the generalized forces are presented for incompressible and nearly incompressible flows. As the Mach number tends to zero, the virtual mass induced by an oscillating fluid becomes infinitely large for a natural mode symmetric with respect to the midchord point. It is recommended to take into account a symmetric mode which changes no fluid volume contained in a control surface, when a coupled flutter oscillation at very low Mach numbers is analyzed. Incorrectness in the generalized forces of the previous analyses is pointed out by comparing with the present analysis.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Unsteady fluid-dynamic force solely in terms of control-surface integral

2005 ◽  
Vol 17 (9) ◽  
pp. 098102 ◽  
Author(s):  
Jie-Zhi Wu ◽  
Ze-Liang Pan ◽  
Xi-Yun Lu
Keyword(s):  
Fluid Dynamic ◽  
Control Surface ◽  
Dynamic Force ◽  
Surface Integral ◽  
Unsteady Fluid

Nonlinear Stability Analysis of a Two-Dimensional Model of an Elastic Tube Conveying a Compressible Flow

1979 ◽  
Vol 46 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. Matsuzaki ◽  
Y.-C. Fung
Keyword(s):  
Fluid Dynamic ◽  
Elastic Tube ◽  
Two Dimensional ◽  
Nonlinear Stability Analysis ◽  
Internal Wall ◽  
Equilibrium Configurations ◽  
Dynamic Forces ◽  
Unsteady Fluid ◽  
The Stability ◽  
Small Disturbances

This paper examines the dynamic behavior of a two-dimensional channel whose upper and lower walls deform symmetrically with respect to the center line of the channel. Unsteady fluid dynamic forces acting on the internal wall are analytically evaluated on the basis of a linearized compressible potential flow theory. The effects of distributed springs outside the channel and an internal pressure on the stability characteristics are studied by considering small disturbances about flat and buckled equilibrium configurations of the wall. The analytic methods indicate that no flutter of the flat or buckled wall is predicted when the Mach number is small and the viscous damping coefficient is positive. Numerical results by the Runge-Kutta-Gill method suggest that nonlinear effect of flow should be taken into account to fully examine the dynamic characteristics of the channel conveying a flow.

scholarly journals Exterior Shape Factors From Interior Shape Factors

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
John H. Lienhard
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Conformal Mapping ◽  
Analytical Determination ◽  
Two Dimensional ◽  
Shape Factors ◽  
Transfer Rates ◽  
Steady Heat Conduction ◽  
Steady Heat

Shape factors for steady heat conduction enable quick and highly simplified calculations of heat transfer rates within bodies having a combination of isothermal and adiabatic boundary conditions. Many shape factors have been tabulated, and most undergraduate heat transfer books cover their derivation and use. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. In this paper, we show that known shape factors for the interior of two-dimensional objects are identical to the corresponding shape factors for the exterior of those objects. The canonical case of the interior and exterior of a disk is examined first. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. Both a geometrical and a mathematical argument are introduced to show that shape factors are invariant under conformal mapping. Finally, the general case is demonstrated using Green's functions. In addition, the “Yin-Yang” phenomenon for conduction shape factors is explained as a rotation of the unit disk prior to conformal mapping.

Numerical Simulation on Circular-Arc Grid-Fin Configurations

2013 ◽  
Vol 444-445 ◽  
pp. 342-346
Author(s):  
Yong Hong Li ◽  
Ji Xiang Shan ◽  
Ji Chuan Su ◽  
Yong Huang
Keyword(s):  
Fluid Dynamic ◽  
Control Surface ◽  
Dynamic Simulations ◽  
Circular Arc ◽  
Planar Surfaces ◽  
Grid Fin ◽  
Flow Through ◽  
Mach Numbers ◽  
Single Baseline ◽  
And Control

A grid fin is an unconventional lifting and control surface which consists of an outer frame with an inner grid of intersecting planar surfaces of small chord. Normal shocks form at the back of the lattice cells at transonic Mach numbers thus choking the flow through the cells and causing a significant reduction in lift force and increase in drag force. An improved circular-arc grid-fin configuration is proposed in the present study to reduce transonic flow choking. Viscous computational fluid dynamic simulations were performed to investigate flows over single baseline and circular-arc grid fins and body-fin configurations under transonic and supersonic flow with Mach numbers in the range of 0.6-4.0. The present numerical results indicate the drag coefficient on single circular-arc grid fin and body-fin configuration is decreased by approximately 10%-24% and 8% respectively for all the Mach numbers investigated in the present study.

Small Angle Electron Scattering From Vacuum Condensed Metallic Films

1968 ◽  
Vol 26 ◽  
pp. 380-381
Author(s):  
J. Silcox ◽  
R. H. Wade
Keyword(s):  
Electron Scattering ◽  
Small Angle ◽  
Ring Structure ◽  
Two Dimensional ◽  
Metallic Films ◽  
Micro Structure ◽  
Angle Scattering ◽  
The Fourier Transform ◽  
Source Of Information ◽  
Kinematical Theory

Recent work has drawn attention to the possibilities that small angle electron scattering offers as a source of information about the micro-structure of vacuum condensed films. In particular, this serves as a good detector of discontinuities within the films. A review of a kinematical theory describing the small angle scattering from a thin film composed of discrete particles packed close together will be presented. Such a model could be represented by a set of cylinders packed side by side in a two dimensional fluid-like array, the axis of the cylinders being normal to the film and the length of the cylinders becoming the thickness of the film. The Fourier transform of such an array can be regarded as a ring structure around the central beam in the plane of the film with the usual thickness transform in a direction normal to the film. The intensity profile across the ring structure is related to the radial distribution function of the spacing between cylinders.

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

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