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
that have been used by the scientific community and this often makes it
difficult to compare the results of one case of swirling flow with the other. In
its simplest definition, the swirl parameter is defined as ‘the ratio of
maximum tangential velocity to the maximum axial velocity’ (Alekseenko et
al., 2007). Greitzer et al. (2004) has adopted the definition as the ratio of
tangential to axial velocity. The definition by Gupta et al (1984) defines swirl
number as ‘the ratio of axial flux of angular momentum to axial flux of axial
momentum times the size L (which in case of cylindrical vortex chamber is
the internal radius R of the chamber)’ (Alekseenko et al., 2007).
Where
S
F
mm
(2.5)
Fm
L
F v v vv r dA (2.6)
mm a z
A
is the angular momentum flux taking into account the component of the
Reynolds shear stress tensor and
2 2
F v vp p dA (2.7)
m a a
A
is the momentum flux in axial direction taking in to account the normal
component of Reynolds stress tensor in axial direction. The pressure
represents the axial thrust (Khanna V. K., 2001).
The calculation of swirl number based on above equations (2.5-2.7) is often
very difficult because the velocity fields are usually unknown a priori
(Alekseenko et al., 2007). The above equations are also simplified by
dropping the shear stress and pressure terms. In case of experimental results,
the use of above equations requires a complete knowledge of the velocity
field for both axial and tangential components for a given cross-sectional
plane. Consequently, for experiments where measurements are conducted
for a part of the cross-sectional plane, the aforementioned equations cannot
be used to estimate the degree of swirl.
Another estimate of the swirl parameter is based on the geometrical
parameters of the vortex chamber called as ‘design swirl parameter’
(Alekseenko et al., 2007):
Ddc
S
(2.8)
A
i
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Swirling Flows