Experimental and Numerical Study of Swirling ... - Solid Mechanics

Experimental and Numerical Study of Swirling Flow in Scavenging Process for 2-Stroke
Marine Diesel Engines
Chapter 2
levels etc. (Sloan et al., 1986). The adoption of a relation that local stresses
being directly proportional to local strain rates rules out any special
sensitivity to the streamline curvature (Craft et al., 2008). The assumption of
turbulent/ eddy viscosity as isotropic cannot be valid in flows influenced by
body forces acting in a preferred direction, such as buoyancy, rotation and
streamline curvature (Sloan et al., 1986). Algifri et al. (1988) proposed, using
experimental data on confined swirling flow, that the eddy viscosity is
function of Reynolds and swirl numbers. Further, the k model is a
simplistic function of a single time scale (proportional to a turbulence energy
turnover time k ) which implies that the spectral energy transfer rates for
production of turbulent kinetic energy by mean shear, the intermediate
transferal regime and the viscous dissipation regime are equal without any
characteristic lag (Sloan et al., 1986).
The second order closure schemes having transport equations for individual
components of Reynolds Stress tensor account for the curvature of
streamlines however the effect is at least an order of magnitude large than
expected (Moene A.F., 2003) i.e. a 1% curvature strain produces for a
boundary layer a 10% or greater effect on the turbulent stresses (Bradshaw,
1973). The source terms in dissipation equation, to a significant degree
control the magnitude of turbulent kinetic energy, mean velocity decay and
the spreading rates (Sloan et al., 1986). However, the transport equations for
k and have no specific terms (source) to account for sensitiveness to
rotation and swirl (Jakirlic´ et al., 2002). Since both of these transport
equations are common in two-equation and second order closure schemes,
the performance of second order closure schemes are also affected to some
degree for modeling the swirling flows. Numerical issues also have
significant impact on predicting the behavior of swirling flows (Craft et al.,
2008).
Different modeling approaches so far have been adopted to improve the
performance of the aforementioned turbulence models and some of them are
discussed here in brief. In order to include a rapid response to streamline
curvature, the coefficient C in the turbulent viscosity equation (2.12) has
been altered to a functional form (see Leshcziner et al., 1981). Sloan et al.,
(1986) reports that more complex versions of C have been developed that
include non-equilibrium turbulence and wall damping.
2
k
t C. . (2.12)
Where t is turbulent viscosity, C is a constant and has empirically
determined value of 0.09 and is the fluid density.
Yakhot et al., (1992) developed the RNG k model which, unlike the
standard k model, is derived using a statistical technique called
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Swirling Flows