Aspect Ratio Effects on the Added-Mass of a Slender Pulsating Cylinder

1972 ◽  
Vol 39 (4) ◽  
pp. 1047-1049 ◽  
Author(s):  
A. M. Whitman
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Analysis ◽  
Finite Length ◽  
Unit Length ◽  
Added Mass ◽  
Simple Expression ◽  
Breathing Mode ◽  
Half Length

We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit length of a finite length, slender, cylinder vibrating in the breathing mode. We find, to dominant order in the expansion, that when the wavelength of the vibration is smaller than the half length, the added mass is independent of the aspect ratio while in the antithetical case it is solely dependent on that quantity.

scholarly journals Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling

2021 ◽  
pp. 1-1
Author(s):  
David G. M. Mitchell ◽  
Pablo M. Olmos ◽  
Michael Lentmaier ◽  
Daniel J. Costello
Keyword(s):  
Asymptotic Analysis ◽  
Finite Length ◽  
Ldpc Codes ◽  
Length Scaling

Natural Frequencies of a Railroad Track

1987 ◽  
Vol 54 (2) ◽  
pp. 299-304 ◽  
Author(s):  
S. P. Patil
Keyword(s):  
Natural Frequency ◽  
Elastic Layer ◽  
Natural Frequencies ◽  
Unit Length ◽  
Added Mass ◽  
Winkler Foundation ◽  
Railroad Track

The natural frequency of an infinite railroad track was first determined by Timoshenko as ωR = √k/m, where k is the constant for the massless Winkler foundation and m is the mass per unit length of the rail. The natural frequencies of the track are determined here by modeling the track as a beam resting on a 3-D inertial elastic layer. It is shown that the mass of the supporting foundation has a significant effect on the natural frequencies of a railroad track. Finally, the concept of “added mass” is introduced in order to determine the natural frequency in a desired mode of vibration, by modeling the track as a beam on the massless Winkler foundation and adding the mass of the foundation to the beam.

scholarly journals Three-dimensional scaling laws of cetacean propulsion characterize the hydrodynamic interplay of flukes' shape and kinematics

2020 ◽  
Vol 17 (163) ◽  
pp. 20190655 ◽  
Author(s):  
Fatma Ayancik ◽  
Frank E. Fish ◽  
Keith W. Moored
Keyword(s):  
Aspect Ratio ◽  
Scaling Laws ◽  
Three Dimensional ◽  
Force Production ◽  
Numerical Data ◽  
Added Mass ◽  
Cetacean Species ◽  
Propulsive Efficiency ◽  
Fluid Environment ◽  
Pitch Ratio

Cetaceans convert dorsoventral body oscillations into forward velocity with a complex interplay between their morphological and kinematic features and the fluid environment. However, it is unknown to what extent morpho-kinematic features of cetaceans are intertwined to maximize their efficiency. By interchanging the shape and kinematic variables of five cetacean species, the interplay of their flukes morpho-kinematic features is examined by characterizing their thrust, power and propulsive efficiency. It is determined that the shape and kinematics of the flukes have considerable influence on force production and power consumption. Three-dimensional heaving and pitching scaling laws are developed by considering both added mass and circulatory-based forces, which are shown to closely model the numerical data. Using the scaling relations as a guide, it is determined that the added mass forces are important in predicting the trend between the efficiency and aspect ratio, however, the thrust and power are driven predominately by the circulatory forces. The scaling laws also reveal that there is an optimal dimensionless heave-to-pitch ratio h * that maximizes the efficiency. Moreover, the optimal h * varies with the aspect ratio, the amplitude-to-chord ratio and the Lighthill number. This indicates that the shape and kinematics of propulsors are intertwined, that is, there are specific kinematics that are tailored to the shape of a propulsor in order to maximize its propulsive efficiency.

Falling Needle Rheometry for General Viscoelastic Fluids

1994 ◽  
Vol 116 (3) ◽  
pp. 619-624 ◽  
Author(s):  
R. Zheng ◽  
N. Phan-Thien ◽  
V. Ilic
Keyword(s):  
Aspect Ratio ◽  
Power Law ◽  
Unit Length ◽  
Cylindrical Tube ◽  
Terminal Velocity ◽  
Fluid Viscosity ◽  
General Technique ◽  
Drag Forces ◽  
Numerical Studies ◽  
Power Law Index

This paper reports theoretical and numerical studies on a flow of a general viscoelastic fluid past a needle placed at the centerline of a cylindrical tube, supplemented by a comparative experimental study. It is shown that the drag per unit length on the needle, which is assumed to be infinitely long, depends on the fluid viscosity only, whatever the first and second normal stress differences may be. This general theory is then specified to obtain solutions for the power-law and the Phan-Thien-Tanner fluids. The power-law fluid results provide a general technique for obtaining flow curves of non-Newtonian fluids from the measured drag forces on falling needles. This is achieved by using KU/R as the effective shear rate, where U is the terminal velocity of the needle, R is the radius of the tube, and K is a function of the power-law index n and the system geometry a/R (where a is the radius of the needle). The effect of the aspect ratio of the needle on the drag force is investigated numerically using a boundary element method for the flow of Phan-Thien-Tanner fluid. Experimentally, a flow curve was obtained for a kerosene solution of PIB (3.39 percent by weight), using falling needles of aspect ratio greater than 40 in a circular cylinder. The result compared well with Carri-Med 50 CS rheometer data.

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