Experimental and Numerical Study of Swirling ... - Solid Mechanics
Experimental and Numerical Study of Swirling ... - Solid Mechanics 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 20 Swirling Flows
Experi imental and Numerical N Stud dy of Swirling g Flow in Scaveenging Processs for 2-Stroke Marin ne Diesel Engin nes Fig gure 2.7: Illus stration of design n swir rl parameter. dc D tan Where D is the intern nal diameter between n cylinder rad dius and direct the con nditional circ cle (an imagi directio on makes a tan ngent) and i 2.6). A of the cylindrrical chamber, is the anggle tion of nozzlee/ inlet, d c is the diameter of inary circle tto which thee nozzle/ inllet i is the total aarea of nozzles/ inlets (Figuure Estimat tion of swirl in ntensity can aalso be based oon streamline angle equatioon (2.10) evaluated e at some s positionn in the cross-section. However, an axiial change in the swirl angle a can alsoo be due to axxial changes inn the axial floow field an nd near the wall w the swirl aangle is a funnction of rate of decay rathher than to swirl intensity y itself (Steenbbergen et al., 11998). 1 V tan n Va The sw wirl paramete er though immportant is nnot the onlyy parameter to characte erize the swi irling flows. There can bbe swirl flowws having samme Reynold ds number an nd the swirl intensity but having quitee different floow structur res due to dif fferent bounddary conditionns (Alekseenkko et al., 20077). Parame eters like swir rl distributionn, distributionn of stagnatioon pressure annd vorticity y are also imp portant to chaaracterize a givven swirling fllow yet none of the mentioned param meters can independently ccharacterize a given swirlinng flow (G Greitzer et al., 2004). 2 The dec cay of the swi irl is caused bby the transpoort of angular momentum to the vor rtex chamber wall (wall fr friction) and is a functionn of streamwiise position n z . Steenberg gen et al. (19998) reports thaat in most obseerved referencces with lo ow swirl inten nsities the deccay in the swiirl is exponential and can bbe Chapter 2 (2. 9) (2.10) 21 Swirling Flows
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Experi imental <strong>and</strong> <strong>Numerical</strong> N Stud dy <strong>of</strong> <strong>Swirling</strong> g Flow in Scaveenging<br />
Processs<br />
for 2-Stroke<br />
Marin ne Diesel Engin nes<br />
Fig gure 2.7:<br />
Illus stration <strong>of</strong> design n<br />
swir rl parameter.<br />
dc<br />
D tan <br />
Where D is the intern nal diameter<br />
between n cylinder rad dius <strong>and</strong> direct<br />
the con nditional circ cle (an imagi<br />
directio on makes a tan ngent) <strong>and</strong> i<br />
2.6).<br />
A<br />
<strong>of</strong> the cylindrrical<br />
chamber,<br />
is the anggle<br />
tion <strong>of</strong> nozzlee/<br />
inlet, d c is the diameter <strong>of</strong><br />
inary circle tto<br />
which thee<br />
nozzle/ inllet<br />
i is the total aarea<br />
<strong>of</strong> nozzles/<br />
inlets (Figuure<br />
Estimat tion <strong>of</strong> swirl in ntensity can aalso<br />
be based oon<br />
streamline angle equatioon<br />
(2.10) evaluated e at some s positionn<br />
in the cross-section.<br />
However,<br />
an axiial<br />
change in the swirl angle a can alsoo<br />
be due to axxial<br />
changes inn<br />
the axial floow<br />
field an nd near the wall w the swirl aangle<br />
is a funnction<br />
<strong>of</strong> rate <strong>of</strong> decay rathher<br />
than to swirl intensity y itself (Steenbbergen<br />
et al., 11998).<br />
1 V<br />
tan<br />
n Va<br />
The sw wirl paramete er though immportant<br />
is nnot<br />
the onlyy<br />
parameter to<br />
characte erize the swi irling flows. There can bbe<br />
swirl flowws<br />
having samme<br />
Reynold ds number an nd the swirl intensity but having quitee<br />
different floow<br />
structur res due to dif fferent bounddary<br />
conditionns<br />
(Alekseenkko<br />
et al., 20077).<br />
Parame eters like swir rl distributionn,<br />
distributionn<br />
<strong>of</strong> stagnatioon<br />
pressure annd<br />
vorticity y are also imp portant to chaaracterize<br />
a givven<br />
swirling fllow<br />
yet none <strong>of</strong><br />
the mentioned<br />
param meters can independently<br />
ccharacterize<br />
a given swirlinng<br />
flow (G Greitzer et al., 2004). 2<br />
The dec cay <strong>of</strong> the swi irl is caused bby<br />
the transpoort<br />
<strong>of</strong> angular momentum to<br />
the vor rtex chamber wall (wall fr friction) <strong>and</strong> is a functionn<br />
<strong>of</strong> streamwiise<br />
position n z . Steenberg gen et al. (19998)<br />
reports thaat<br />
in most obseerved<br />
referencces<br />
with lo ow swirl inten nsities the deccay<br />
in the swiirl<br />
is exponential<br />
<strong>and</strong> can bbe<br />
<br />
Chapter 2<br />
(2. 9)<br />
(2.10)<br />
21<br />
<strong>Swirling</strong> Flows