On the Velocity Distribution of Turbulent Flow in Pipes and Channels of Constant Cross Section

1946 ◽  
Vol 13 (2) ◽  
pp. A85-A90
Author(s):  
Chi-Teh Wang
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Length Distribution ◽  
Critical Examination ◽  
Large Reynolds Number ◽  
Good Picture ◽  
Von Karman ◽  
Von Kármán ◽  
New Formula ◽  
Good Agreement

Abstract This paper follows the Prandtl conception of momentum transport and gives a critical examination of the so-called Prandtl-Nikuradse formula and the von Kármán formula for the velocity distribution of the turbulent flow in tubes or channels at large Reynolds number. It shows that both formulas would not give a good picture of the turbulent flow near the center of the conduit, and indeed they actually do not. A new formula for the velocity distribution is developed from a study of the mixing-length distribution across the section. This new formula checks quite well with the experiments and yields the same skin-friction formula as derived by von Kármán and Prandtl, which itself is in very good agreement with experiments.

Symmetric Turbulent Mixing of Two Parallel Streams

1953 ◽  
Vol 20 (1) ◽  
pp. 63-71
Author(s):  
T. P. Torda ◽  
W. O. Ackermann ◽  
H. R. Burnett
Keyword(s):  
Experimental Data ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Turbulent Mixing ◽  
Energy Equation ◽  
Mixing Process ◽  
Analytical Results ◽  
Von Karman ◽  
Parallel Streams ◽  
Von Kármán

Abstract The analysis of turbulent, incompressible, symmetric mixing of two parallel streams is presented. The influence of the upstream boundary layers on the mixing process is taken into account. The von Kármán integral concept is applied to a momentum and energy equation. These equations are used to evaluate the thickness of the mixing region and the velocity distribution in it. The results are presented in nondimensional form. A numerical illustrative example is given. Comparison with Tollmien’s analytical results and with experimental data of Liepmann and Laufer is made.

Velocity Distribution in Turbulent Flow

1970 ◽  
Vol 12 (6) ◽  
pp. 391-399 ◽  
Author(s):  
W. K. Allan
Keyword(s):  
Surface Roughness ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Flat Plate ◽  
Reynolds Numbers ◽  
Pressure Gradients ◽  
Roughness Effects ◽  
High Reynolds ◽  
Independent Effects ◽  
Good Agreement

A general equation for the velocity distribution in steady, incompressible, two-dimensional, turbulent flow is constructed by correction of the logarithmic velocity profile for the independent effects of pressure gradients and of surface roughness. Predicted characteristics of pipe flows, flat plate flows, and diffusing flows over smooth surfaces are found to be in good agreement with empirical data at high Reynolds numbers. Pipe flow data are used to evaluate surface roughness effects, and hence to describe flat plate flows and diffusing flows over rough surfaces.

Approximation of the time-dependent induction equation with advection using Whitney elements

2016 ◽  
Vol 35 (1) ◽  
pp. 326-338 ◽  
Author(s):  
Caroline Nore ◽  
Houda Zaidi ◽  
Frederic Bouillault ◽  
Alain Bossavit ◽  
Jean-Luc Guermond
Keyword(s):  
Velocity Field ◽  
Dynamo Action ◽  
Content Type ◽  
Kinematic Dynamo ◽  
Von Karman ◽  
Whitney Forms ◽  
Dependent Variables ◽  
Induction Equation ◽  
Von Kármán ◽  
Good Agreement

Purpose – The purpose of this paper is to present a new formulation for taking into account the convective term due to an imposed velocity field in the induction equation in a code based on Whitney elements called DOLMEN. Different Whitney forms are used to approximate the dependent variables. The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. DOLMEN is developed to investigate the dynamo action in non-axisymmetric domains like the impeller driven flow of the von Kármán Sodium (VKS) experiment. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field. Design/methodology/approach – Different Whitney forms are used to approximate the dependent variables. The vector potential is discretized using first-order edge elements of the first family. The velocity is approximated by using the first-order Raviart-Thomas elements. The time stepping is done by using the Crank-Nicolson scheme. Findings – The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field. Originality/value – The findings offer a basis to a scenario for the VKS dynamo.

A Born–von Karman Force Constant Model for Aluminum

1974 ◽  
Vol 52 (17) ◽  
pp. 1714-1715 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Force Constant ◽  
Frequency Distribution ◽  
Brillouin Zone ◽  
Normal Modes ◽  
Frequency Distribution Function ◽  
Von Karman ◽  
Von Kármán ◽  
Good Agreement

A Born–von Karman force constant model of aluminum, fitted to the frequencies of normal modes with wave vectors distributed throughout the Brillouin zone, is described, and the frequency distribution function calculated. The result is in very good agreement with a distribution function calculated directly from the experimental data.

scholarly journals Stochastic Intermittency Fields in a von Kármán Experiment

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1752
Author(s):  
Jürgen Schmiegel ◽  
Flavio Pons
Keyword(s):  
Time Series ◽  
Energy Dissipation ◽  
Turbulent Flow ◽  
Turbulence Intensity ◽  
Statistical Properties ◽  
Close Resemblance ◽  
Von Karman ◽  
The One ◽  
Von Kármán

We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In particular, we show that the three-point correlations can be predicted from observed two-point statistics. Our analysis is motivated by observed stylised features of the energy dissipation in homogeneous and isotropic situations where these statistical properties are well represented within the framework of stochastic intermittency fields. We find a close resemblance and conclude that stochastic intermittency fields may be relevant in more general situations.

On von Karman modeling for turbulent flow near a wall

2019 ◽  
Vol 26 (3) ◽  
pp. 291-296
Author(s):  
Jacques Rappaz ◽  
Jonathan Rochat
Keyword(s):  
Turbulent Flow ◽  
Von Karman ◽  
Von Kármán
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