Identification of Transition to Turbulence in a Highly Accelerated Start-Up Pipe Flow

2005 ◽  
Vol 128 (4) ◽  
pp. 680-686 ◽  
Author(s):  
T. Koppel ◽  
L. Ainola
Keyword(s):  
Pipe Flow ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Transition To Turbulence ◽  
Unsteady Boundary Layer ◽  
Physical Explanation ◽  
Pipe Flows ◽  
Flow Parameters ◽  
Start Up ◽  
Laplace Transformation Method

The transition from a laminar to a turbulent flow in highly accelerated start-up pipe flows is described. In these flows, turbulence springs up simultaneously over the entire length of the pipe near the wall. The unsteady boundary layer in the pipe was analyzed theoretically with the Laplace transformation method and the asymptotic method for small values of time. From the experimental results available, relationships between the flow parameters and the transition time were derived. These relationships are characterized by the analytical forms. A physical explanation for the regularities in the turbulence spring-up time is proposed.

Development of Accelerating Pipe Flow Starting From Rest

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Ivar Annus ◽  
Tiit Koppel ◽  
Laur Sarv ◽  
Leo Ainola
Keyword(s):  
Pipe Flow ◽  
Large Scale ◽  
Transformation Method ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Axial Velocity Component ◽  
Flow Equations ◽  
Continuity Equations ◽  
Start Up ◽  
Experimental Findings

A uniformly accelerated laminar flow in a pipe, initially at rest, is analyzed. One-dimensional unsteady flow equations for start-up flow were derived from the Navier–Stokes and continuity equations. The dynamical boundary layer in a pipe is described theoretically with the Laplace transformation method for small values of time. A mathematical model describing the development of the velocity profile for accelerating flow starting from rest up to the point of transition to turbulence is given. The theoretical results are compared with experimental findings gained in a large-scale pipeline. Particle image velocimetry (PIV) technique is used to deduce the development of accelerating pipe flow starting from rest. The measured values of the axial velocity component are found to be in a good agreement with the analytical values.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

scholarly journals A new Laplace transformation method for dynamic testing of solar collectors

2015 ◽  
Vol 75 ◽  
pp. 448-458 ◽  
Author(s):  
Weiqiang Kong ◽  
Bengt Perers ◽  
Jianhua Fan ◽  
Simon Furbo ◽  
Federico Bava
Keyword(s):  
Laplace Transformation ◽  
Dynamic Testing ◽  
Transformation Method ◽  
Solar Collectors ◽  
Laplace Transformation Method

Improvement of inverse heat conduction solution using Laplace transformation: Method of partial division of time

2003 ◽  
Vol 32 (7) ◽  
pp. 630-638 ◽  
Author(s):  
Masanori Monde ◽  
Wei Liu ◽  
Hirofumi Arima ◽  
Yuhichi Mitsutake ◽  
J.A. Hammad
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Inverse Heat Conduction ◽  
Laplace Transformation Method ◽  
Partial Division

scholarly journals Improvement of Inverse Heat Conduction Solution using Laplace Transformation. (Method of Partial Division of Time).

2002 ◽  
Vol 68 (671) ◽  
pp. 2093-2097 ◽  
Author(s):  
Masanori MONDE ◽  
Wei LIU ◽  
Hirofumi ARIMA ◽  
Yuhichi MITUTAKE ◽  
Jaffar A. HAMMAD
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Inverse Heat Conduction ◽  
Laplace Transformation Method ◽  
Partial Division

Higher-order schemes for the Laplace transformation method for parabolic problems

2011 ◽  
Vol 14 (1) ◽  
pp. 39-47 ◽  
Author(s):  
C. Douglas ◽  
I. Kim ◽  
H. Lee ◽  
D. Sheen
Keyword(s):  
Laplace Transformation ◽  
Transformation Method ◽  
Higher Order ◽  
Parabolic Problems ◽  
Laplace Transformation Method

Laplace-Weighted Residual Method For Problems with Semi-Infinite Domain

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Babatunde Sunday Ogundare
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Numerical Method ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Weighted Residual Method ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Residual Method ◽  
Laplace Transformation Method

This paper presents an efficient numerical method for the approximate solution of problems involving boundary condition at infinity. The whole idea of the method is based on the combination of Laplace transformation method and weighted residual method. Numerical examples are given to show the validity and applicability of the proposed method and the results obtained are compared with other methods in the literatures.

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