An Experimental and Numerical Study of Turbulent Swirling Pipe Flows

1998 ◽  
Vol 120 (1) ◽  
pp. 54-61 ◽  
Author(s):  
R. R. Parchen ◽  
W. Steenbergen

Both experimental and numerical studies have been performed aimed at the description of the decay of swirl in turbulent pipe flows. Emphasis is put on the effect of the initial velocity distribution on the rate of decay. The experiments show that, even far downstream of the swirl generator, the decay of the integral amount of angular momentum depends on the initial velocity distribution. This suggests that the description of the decay in terms of the widely suggested single exponential, function, is not sufficient. The calculations are based on (i) a standard k – ε model and (ii) models based on an algebraic transport model for the turbulent stresses. It appears that in a weakly swirling pipe flow, second-order models reduce to simple modifications of the standard k – ε model. While the standard k – ε model predicts a decay largely insensitive to the initial velocity distribution, the modified versions of the k – ε model, the ASM and the RSM, predict a strong sensitivity to the initial velocity distribution. Nevertheless, the standard k – ε model seems to predict the rate of decay of the swirl better than the second-order models. It is concluded that the corrections for the streamline curvature introduced by the second-order closures, largely overestimate the effect of rotation on the radial exchange of angular momentum.

Chemosphere ◽  
2012 ◽  
Vol 87 (11) ◽  
pp. 1260-1264 ◽  
Author(s):  
Soon-Bark Kwon ◽  
Jaehyung Park ◽  
Jaeyoun Jang ◽  
Youngmin Cho ◽  
Duck-Shin Park ◽  
...  

1934 ◽  
Vol 11 (6) ◽  
pp. 770-779 ◽  
Author(s):  
G. N. Patterson

The motion of air through a channel of small exponential divergence has been investigated experimentally. A flow form derived by Blasius from theoretical considerations has been shown to exist in the range [Formula: see text] for the Reynolds number. The dependence of the general flow form on the initial velocity distribution where the divergence begins has been studied. It has been found that when this initial velocity distribution is parabolic, indicating a laminar motion in the throat of the channel, the flow form is symmetrical. Further investigations have shown that when the initial velocity distribution indicates that the motion near the walls in the throat of the channel lies in the transitional region between a laminar and a turbulent flow, then the flow form is unsymmetrical. Empirical equations have been obtained which give (1) the initial velocity distribution in the transitional region at R = 75.1, and (2) the motion near the walls where the divergence begins for Reynolds numbers lying in the range [Formula: see text].


1996 ◽  
Vol 119 (3) ◽  
pp. 469-481 ◽  
Author(s):  
W. L. Marar ◽  
F. Tari

In this paper we investigate the geometry of simple germs of co-rank 1 maps from ℝ3 to ℝ3. Those of co-dimension 1 have already been dealt with by several authors. In [2], V. I. Arnold considered the problem of evolution of galaxies. For a medium of non-interacting particles in ℝ3 with an initial velocity distribution v = v(x) (and a positive density distribution), the initial motion of particles defines a time-dependent map gt: ℝ3 → ℝ3 given by gt(x) = x + tv(x). At some time t singularities occur and the critical values of gi correspond to points of condensation of particles. Arnold assumed the vector field v is a gradient, that is v = ∇S, for some potential S. J. W. Bruce generalized these results in [4] by dropping the assumption on the velocity distribution and studied generic 1-parameter families of map germs F: ℝ3, 0 → ℝ3, 0.


Author(s):  
S. Goldstein

The boundary layer equations for a steady two-dimensional motion are solved for any given initial velocity distribution (distribution along a normal to the boundary wall, downstream of which the motion is to be calculated). This initial velocity distribution is assumed expressible as a polynomial in the distance from the wall. Three cases are considered: first, when in the initial distribution the velocity vanishes at the wall but its gradient along the normal does not; second, when the velocity in the initial distribution does not vanish at the wall; and third, when both the velocity and its normal gradient vanish at the wall (as at a point where the forward flow separates from the boundary). The solution is found as a power series in some fractional power of the distance along the wall, whose coefficients are functions of the distance from the wall to be found from ordinary differential equations. Some progress is made in the numerical calculation of these coefficients, especially in the first case. The main object was to find means for a step-by-step calculation of the velocity field in a boundary layer, and it is thought that such a procedure may possibly be successful even if laborious.The same mathematical method is used to calculate the flow behind a flat plate along a stream. The results are shown in Figures 1 and 2, drawn from Tables III and IV.


Sign in / Sign up

Export Citation Format

Share Document