Turbulence Modelling of Strongly Swirling Flows
A two-dimensional swirling flow is considerably more complicated than two- dimensional plane flows, for additional strains arise due to the azimuthal motion, requiring the solution for azimuthal momentum. Swirl introduces intense azimuthal streamline curv
- PDF / 419,028 Bytes
- 2 Pages / 439.37 x 666.14 pts Page_size
- 22 Downloads / 190 Views
1
Introduction
A two-dimensional swirling flow is considerably more complicated than twodimensional plane flows, for additional strains arise due to the azimuthal motion, requiring the solution for azimuthal momentum. Swirl introduces intense azimuthal streamline curvature and hence curvature-turbulence interaction affects all six independent stress components. Therefore, the natural route is to apply Second-Moment Closures in predicting the Swirling flows. However, this is expensive computationally. One alternative is to adopt a non-linear stress and strain relationship of the Reynolds stresses. This can be achieved by assuming that the Reynolds stresses are taken to be non-linear function of the mean velocity gradients. The present study aims at investigating the capability of variants of non-linear eddy viscosity models on strongly swirling flows. Within the framework of eddy-viscosity the Reynolds stress is approximated by linear and non-linear stress and strain relations. The stress and strain relationship can be expressed in a general form,
(1) where.
s aUi aUj {} au. ij = axj + ax. ' ij = axj
-
aUj ax,
The function F and the eddy viscosity can be made non-linear functions of the strain rates and k and f.". Three non-linear eddy viscosity models (Shih2[1], SSG[2], GL[2]) are adopted in the present study.
2
Results
Experimental data had been obtained by So et al. [3]. This consists of a pipe into which an annular swirling stream is introduced together with a non-swirling central jet. The latter is introduced to inhibit extensive reverse flow (vortex J,ro UWr 2 dr
breakdown) along the centre-line. The swirl number, S, S = ro°lro U2 d for this 0 r r case is 2.25, where ro is the radius of the pipe and U and W are the axial and tangential velocity, respectively. According to the rule of thumb, a sub-critical N. Satofuka (ed.), Computational Fluid Dynamics 2000 © Springer-Verlag Berlin Heidelberg 2001
780
L. K. Yeh and C. A. Lin X/d,=2.00
X/d,=IO.O
X/d,=5.00
1::0.5
05 /
r' -,
X/d,=20.0
05
05
- - - KE - - _. GL -SSG - - Shih2
'"
0.3
0.6
03
U/U 1
0.3
06
U/U j
06
0.3
U/U,
0.6
U/U,
Fig. 1. Axial velocity distributions
state is reached when the maximum swirl velocity to the averaged streamwise velocity exceeds unity. A suD-critical state appears to reflect a strong decay in turbulent mixing, and a corresponding dominance of convective features, making the governing equations nearly hyperbolic in nature. This is confirmed from the measured axial and tangential velocity, shown in Figures 1 and 2. Non-linear model predictions (G L,SSG) and experimental data show the shape of the mean flow profiles to remain similar over the whole length of domain, and this implies that the mixing is weak. The k - £ and Shih2 predictions show, on the contrary, an excessively radial diffusive transport, with a faster decay of the centreline axial velocity and early return of solid body rotation of the swirling motion.
References 1. T. H. Shih, J. Zhu and J. L. Lumely: Computer Methods in Applied Mechan
Data Loading...
