Dynamic Similarity Scaling Laws Applied to Cables

1972 ◽  
Vol 6 (2) ◽  
pp. 111-114 ◽  
Author(s):  
M. LOWELL COLLIER
Keyword(s):  
Scaling Laws ◽  
Dynamic Similarity ◽  
Similarity Scaling

Reconsideration of the Fan Scaling Laws: Part I — Theory

2003 ◽  
Author(s):  
Asad M. Sardar ◽  
William K. George
Keyword(s):  
Scaling Laws ◽  
Stokes Equations ◽  
Performance Testing ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Navier Stokes Equations ◽  
Fan Performance ◽  
Dynamic Similarity ◽  
Scaling Parameters ◽  
Fan Speed

Generalized Fan Scaling Laws (GSFL) are derived for the scaling of fan performance. These follow from first principles using the Navier-Stokes equations appropriate to rotating and swirling flows. Not surprisingly, both Strouhal and Reynolds number similarity must be maintained. Thus for a geometrically similar family of fans, dynamic similarity is only possible if ΩD/U = constandUD/ν = const. If the second relation is solved for U and substituted into the first, it follows that full dynamic similarity is possible only if ΩD2/ν = const. This can be contrasted with the classical fan laws (CFSL) which for the same flow rate coefficient would imply that Q/ΩD3 (or U/ΩD) = const, implying that both fan size ratio and fan speed ratio are independent fan scaling parameters. Clearly for dynamic similarity to be maintained, the velocity and fan speed can not be varied independently (i.e. fan size and fan speed are not independent scaling parameters), contrary to the implications of the classical fan scaling laws. Further implications of the differences between the classical and generalized scaling laws for fan performance testing and design will be explored. Also several examples will be given in Part II as to how the generalized scaling laws can be applied in design practice.

Dynamic similarity analysis for a piezo-electromechanical system

2020 ◽  
Vol 64 (1-4) ◽  
pp. 103-110
Author(s):  
Shuo Hou ◽  
Xing Tan ◽  
Jincheng He ◽  
Xi Deng ◽  
Chen Xi ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Scaling Laws ◽  
Proof Mass ◽  
Electromechanical System ◽  
Similarity Analysis ◽  
Dynamic Similarity ◽  
Prototype Structure ◽  
Similarity Problem ◽  
Piezoelectric Stacks ◽  
Similitude Theory

Most research about using piezoelectric stacks to suppress vibration of mechanical structures didn’t involve the similarity problem for the piezoelectric stacks. The goal of this paper is to investigate the dynamic similarity between a prototype piezo stack and a scaled up or down piezo stack, whilst discussing the feasibility of predicting the vibration of prototype structure which use the piezoelectric stacks for vibration control. To illustrate this problem concisely, a single-DOF system consists of a proof mass and a piezo stack shunted with a series RL circuit is considered. Firstly, the governing equation of such piezo-electromechanical system in frequency domain is derived. Next the dynamic similarity of prototype and model stack is analyzed by similitude theory. After that the scaling laws are derived. Finally, a numerical simulation and relative error analysis are given to demonstrate the scaling laws.

Design Method of Dynamic Similarity of the Rotor-Bearing System

2013 ◽  
Vol 300-301 ◽  
pp. 1148-1151 ◽  
Author(s):  
Zhong Luo ◽  
Jian Zhang Li ◽  
Yu Long Yan ◽  
Qing Kai Han
Keyword(s):  
Scaling Laws ◽  
Similarity Theory ◽  
Design Method ◽  
Similarity Criteria ◽  
Scale Model ◽  
The Finite Element Method ◽  
Dynamic Similarity ◽  
Equation Analysis ◽  
Rotor Bearing ◽  
Bearing System

To predict the vibration characteristics of the rotor-bearing system by using the scale model and the associated scaling laws may significantly reduce the time and money required by the experiments. To this end, the dynamic similarity criteria are investigated inferring from the model behavior of rotor-bearing system to the vibration response of the prototype. The similar relationship was established by combining method of dimensional analysis and equation analysis based on similarity theory, and the effectiveness was verified through the finite element method. The result provide the theoretical rational for further study of the similarity design of the rotor-bearing system.

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

Equilibrium scaling laws for layered spin glasses

1993 ◽  
Vol 3 (10) ◽  
pp. 2041-2062 ◽  
Author(s):  
M. J. Thill ◽  
H. J. Hilhorst
Keyword(s):  
Spin Glasses ◽  
Scaling Laws ◽  
Layered Spin

Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

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