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.

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.

Prediction of Heat Transfer in Turbulent, Transpired Boundary Layers

1999 ◽  
Vol 121 (1) ◽  
pp. 186-190 ◽  
Author(s):  
J. Sucec
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Energy Equation ◽  
Integral Form ◽  
Turbulent Boundary Layers ◽  
Equation Solving ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

Considered here is turbulent boundary layer flow with injection or suction and pressure gradient along the surface. The velocity and thermal inner laws for transpired turbulent boundary layers are represented by simple power law forms which are then used to solve the integral form of the thermal energy equation. Solving this equation leads to the variation of Stanton number with position, x, along the surface. Predicted Stanton numbers are compared with experimental data for a number of different cases. These include both blowing and suction with constant blowing fractions, F, in zero and non-zero pressure gradient and more complicated situations in which the blowing fraction, F, varies with position or where F or the surface temperature have step changes in value.

Diffusion-flame dynamics in Von Kármán boundary layers

2001 ◽  
Vol 125 (1-2) ◽  
pp. 974-981 ◽  
Author(s):  
V Nayagam ◽  
F.A Williams
Keyword(s):  
Boundary Layers ◽  
Diffusion Flame ◽  
Flame Dynamics ◽  
Von Karman ◽  
Von Kármán

2D Numerical Study on Wake Scenarios for a Flapping Foil

2021 ◽  
Author(s):  
Hui-li Xu ◽  
Marilena Greco ◽  
Claudio Lugni
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Grid Method ◽  
Navier Stokes ◽  
Flapping Foil ◽  
Von Karman ◽  
Overset Grid Method ◽  
Von Kármán

Abstract Fishes are talented swimmers. Depending on the propulsion mechanisms many fishes can use flapping tails and/or fins to generate thrust, which seems to be connected to the formation of a reverse von Kármán wake. In the present work, the flow past a 2D flapping foil is simulated by solving the incompressible Navier-Stokes equations in the open-source OpenFOAM platform. A systematic study by varying the oscillating frequency, peak-to-peak amplitude and Reynolds number has been performed to analyze the transition of vorticity types in the wake as well as drag-thrust transition. The overset grid method is used herein to allow the pitching foil to move without restrictions. Spatial convergence tests have been carried out with respect to grid resolution and the size of overset mesh domain. Numerical results are compared with available experimental data and discussed. The results show that the adopted methodology can be well applied to simulate large amplitude motions of the flapping foil. The transitions in the types of wake are consistent with the benchmark experimental data, and the drag-thrust transition of the pitching foil does not coincide with von Kármán (vK)-reverse von Kármán (reverse-vK) wake transition and it is highly dependent on the Reynolds number.

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 On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness

2016 ◽  
Vol 28 (1) ◽  
pp. 014104 ◽  
Author(s):  
S. J. Garrett ◽  
A. J. Cooper ◽  
J. H. Harris ◽  
M. Özkan ◽  
A. Segalini ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Boundary Layers ◽  
Rotating Disk ◽  
Anisotropic Surface ◽  
Von Karman ◽  
The Stability ◽  
Von Kármán
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