Optimal Approximation of the Added Mass Matrix of Two Spheres of Unequal Radii by an Asymptotic Short Distance Expansion

1990 ◽  
Vol 70 (2) ◽  
pp. 83-90 ◽  
Author(s):  
H. Raszillier ◽  
I. Guiasu ◽  
F. Durst
Keyword(s):  
Short Distance ◽  
Mass Matrix ◽  
Added Mass ◽  
Optimal Approximation ◽  
Short Distance Expansion

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

scholarly journals QCD CORRECTIONS IN Γsl(B)

2002 ◽  
Vol 17 (35) ◽  
pp. 2317-2325 ◽  
Author(s):  
NIKOLAI URALTSEV
Keyword(s):  
Fourth Order ◽  
Short Distance ◽  
Quark Masses ◽  
The Third ◽  
Short Distance Expansion

Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. The effect of higher perturbative orders with running quark masses is found to be very small. Numerical consequences for |Vcb| are addressed.

Modeling of Fuel Assemblies in a Boiling Water Reactor for Seismic Analysis

2014 ◽  
Author(s):  
Yuichi Koide ◽  
Yoshihiro Goto ◽  
Yuki Sato ◽  
Shohei Onitsuka ◽  
Hirokuni Ishigaki
Keyword(s):  
Fuel Assembly ◽  
Seismic Analysis ◽  
Mass Matrix ◽  
Added Mass ◽  
Vibration Characteristics ◽  
Boiling Water ◽  
Boiling Water Reactor ◽  
Water Reactor ◽  
Excited Vibration ◽  
Fuel Assemblies

The purpose of this study is to develop a seismic analysis model of a group of fuel assemblies in a boiling water reactor and to confirm the validity of the developed model. Each fuel assembly was modeled as a beam on the basis of the finite element method. The mass matrix of the model includes an added mass matrix, which represents the coupled inertia effect caused by the coolant water, in order to simulate the coupled vibration of fuel assemblies. The added mass matrix was obtained by calculating the coefficient matrix of the acceleration vector and fluid force vector under the condition that each fuel assembly moves at unit acceleration. The validity of the model was confirmed by comparing the calculated results with experimental ones. The compared specimens for the experiments were full-scale mock-ups. The vibration characteristics of fuel assemblies in each case of 4 bodies and 368 bodies were compared. As a result of the comparison, the calculations of the frequency response were in agreement with the experimental results. Particularly, the calculation results on the resonance frequency were in good agreement, with an error of less than 2 percent, with the experimental ones. Furthermore, the calculated vibration characteristics of 368 fuel assemblies in the case of an earthquake, such as the excited vibration mode and phase characteristics, were in agreement with the experimental ones. We concluded that the developed model of fuel assemblies was applicable to seismic analysis of a boiling water core.

scholarly journals The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method

2011 ◽  
Vol 18 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Hassan Ghassemi ◽  
Ehsan Yari
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Boundary Element ◽  
Mass Matrix ◽  
Added Mass ◽  
Experimental Results ◽  
Marine Propellers ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Element Method

The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method Added mass is an important and effective dynamic coefficient in accelerating, non uniform motion as a result of fluid accelerating around a body. It plays an important role, especially in vessel roll motion, control parameters as well as in analyzing the local and global vibration of a vessel and its parts like propellers and rudders. In this article, calculating the Added Mass Coefficient has been examined for a sphere, ellipsoid, marine propeller and hydrofoil; using numerical Boundary Element Method. Since an Ellipsoid and a sphere have simple geometric shapes and the Analytical values of their added mass coefficients are available, so that the results of added mass matrix are obtained and evaluated, using the boundary element method. Then the added mass matrix is computed in a given geometrical and flow specifications for a specific propeller and its results are studied versus experimental results, which it's current numerical data In comparison with other numerical methods has a good conformity with experimental results. The most important advantage of the method in determining the added mass matrix coefficients for the surface and underwater vessels and the marine propellers is extracting all the added mass coefficients with very good Accuracy, while in other numerical methods it is impossible to extract all the coefficients with the Desired Accuracy.

Panel method predictions of added mass for flexible airship

2013 ◽  
Vol 117 (1191) ◽  
pp. 519-531 ◽  
Author(s):  
M. Zhang ◽  
X. Wang ◽  
D. Duan
Keyword(s):  
Membrane Structure ◽  
Dynamic Models ◽  
Mass Matrix ◽  
Added Mass ◽  
Panel Method ◽  
Arbitrary Geometry ◽  
State Equations ◽  
Ellipsoid Of Revolution ◽  
And Control ◽  
Manipulation And Control

Abstract Because of the huge volume and inflated membrane structure of stratosphere airship, the deformation of stratosphere airship is very sensitive to the change of environment conditions such as wind, temperature and so on. The influence of deformation on manipulation and control is very remarkable. So, during the course of building flight dynamic model of the flexible airship, the added-mass matrix of deformation is very important part in the state equations of dynamic models. For obtaining the accurate added-mass matrix of different flexible airship, we proposed an approach that can calculate the added-mass matrix of a flexible airship with arbitrary geometry shape by the panel method. Through the comparison of results of computation and theory for ellipsoid of revolution and the flexible Skyship-500 airship, the proposed method can calculate the added-mass matrix for arbitrary geometric shape very accurately.

Flight Performance Analysis of Hybrid Airship Considering Added Mass Effects

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Lanchuan Zhang ◽  
Mingyun Lv ◽  
Cong Sun ◽  
Junhui Meng
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Prolate Spheroid ◽  
Added Mass ◽  
Flight Performance ◽  
Mass Coefficient ◽  
Computational Fluid Dynamics Cfd ◽  
Added Mass Coefficient ◽  
Cfd Method

In this paper, an analysis is applied to a hybrid airship considering the added mass. First, based on the dynamic mesh technology, a computational fluid dynamics (CFD) method is employed to obtain the added mass coefficient matrix. Through a validation process using the 6:1 prolate spheroid, the 6 × 6 added mass matrix of hybrid airship is obtained. After a dynamic modeling, the equations of motion with added mass are developed. Through the linearization based on small perturbation, the linearized longitude model is used to simulate the dynamic response of a trim condition. The take-off and landing performance has been analyzed and affected by the added mass. The result shows an obvious vertical destabilizing trend on the hybrid airship dynamics due to the added mass and the inertial effect has little influence on the vehicle during the take-off and landing.

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