the tilting angle. These calculations are done as if none of the body
under the liquid. This point is intersection point liquid with lower body
and it is needed to be calculated. The moment of inertia is calculated
around this point (note the body is ende
nozzle is actuated. A water-resistant actuating cable is connected to the
hairpin junction of each support spar at the nozzle exit plane; the cable
extends radially to a perforated conical shell that acts as a fixed pulley.
The apex of the cone is truncat
formation time when the instantaneous or time-averaged exit diameter is
increasing. Consistent with the preceding result, the circulation is
properly normalized using the terms ( ) Ue De and 2 Ue as ( ) 2 * e e e U
U D = . (5.3.7) Despite the inclusion o
entrainment can proceed. This relationship can be visualized
quantitatively, by superimposing the measured vorticity field on
instantaneous streamlines of the flow in the vortex reference frame.
Figure 2.5 plots these data for the protocol LD2-CF0 at time
velocity components u and v and the corresponding scaling of each of
the terms therein: u t + u u x + v u y + w u z | cfw_z U2/L =
2u x2 + 2u y2 | cfw_z U/L2 + 2u z2 |cfw_z U/H2 1 p x, v
t + u v x + v v y + w v z | cfw_z U2/L = 2 v x2 + 2 v y2 |
cfw_z
selected as the focus of this proof-of-concept study because they have
been observed to form some of the simplest vortex wakes in the animal
kingdom, a train of nearly axisymmetric vortex rings (Dabiri et al.,
2005). This wake structure can be more easily
flux by the revised correction at early times is related to the dynamics of
flow initiation, during which nozzle exit overpressure has been observed
to play an important role (Krueger and Gharib 2003). Nonetheless the
current result demonstrates the signi
water density , instantaneous bell volume V, and aperture area A: 2 d d
= t V A T . (7.2.1) Similarly, the drag and acceleration
reactions can be computed from these parameters by utilizing the fact
that medusae are nearly neutrally buoyant so that body
in metric spaces,see Babin and Vishik [BV92]. We consider a
dynamical system whose state is described by an element u(t) of a metric
space H. The evolution of the system is described by the semigroup S(t).
We recall that a family of operators cfw_S(t)t0 t
phenomena. The equation,that we consider,is the basic one to be solved
in the (first step of) Chorin-Temam method (recall Section 1.4.3). We
observe that the advection-diffusion equations are themselves an
important numerical problem,because just in the o
is different because in the Navier-Stokes equations the pressure p is an
unknown and not a given datum. 2.4 Energy-type methods In this
section we present other results regarding the effect of the pressure. The
methods used are now very similar to that on
Lolliguncula brevis squid (Bartol, Patterson and Mann, 2001), and the
nozzle exit has been observed to close completely between fluid pulses
in the Loligo pealei squid (Anderson and DeMont, 2000). In many
instances, the temporal variation of the exit diam
vortex rings formed below and above the limiting stroke ratio and
showed that the force production is maximized as the limit is reached.
The discovery and characterization of a limiting process during vortex
ring formation has generated substantial intere
Conclusions These results elucidate important principles governing
vortex ring pinch-off in starting jets. Specifically, we have empirically
demonstrated the sufficient condition for complete avoidance of vortex
ring pinch-off that is suggested by the Kel
depart from the thin-ring limit typically studied in theory. Nevertheless
the literature contains notable examples of agreement between classical
theoretical predictions and empirical observations (e.g., Widnall and
Sullivan, 1973; Liess and Didden, 1976)
element functions using local regularization,Rev. Francaise Automat.
Informat. Recherche Operationnelle Ser. Rouge Anal. Numer. 9
(1975),no. R-2,7784. [CF88] P. Constantin and C. Foias, NavierStokes equations,University of Chicago Press, Chicago,IL,1988.
circulation. The impulse I is related to the ring circulation and the
characteristic dimension of the vortex bubble 1 3 B by 2 3 C1 B I =
, (2.4.1) where C1 is a dimensionless constant dependent on the
bubble shape. The vortex ring velocity Uv is related
Figure 6.9 Normalized circulation versus formation time for SMAX, SC,
and FC cases 102 Figure 6.10 Vorticity profile along radial section of
vortex ring core for SMAX, SC, and FC
cases .10
2 Figure 6.11 Normalized vortex generator energy versus formation
well. Measurement results are presented herein typically using single
representative data sets for each nozzle program (figure 6.6 is a notable
exception). Three or more iterations were conducted for each program of
nozzle exit diameter temporal variation
the vortex ring axis of symmetry. Thus, relative to the growing vortex
bubble, the location of peak vorticity is moving away from the ambient
fluid on the opposite side of the bounding streamsurface. 21 By contrast,
as the vortex rings generated by protoc
thickness. Shusser et al. (2002) introduced a correction to the slug model
that accounts for boundary layer growth within the cylinder. We show
that their implemented boundary layer solution contains an error, leading
to an underestimate of the calculated
increasing nozzle exit diameter cases might show even greater increase
in the delivered energy, and the temporally decreasing nozzle exit
diameter cases might suffer decreases in the delivered energy. These
scenarios can be neither conclusively affirmed n
boundary. Hence, the measured data trends at early formation time are
not necessarily indicative of the actual rate of vorticity generation by the
starting flow. This effect has been previously observed by Didden (1979)
using LDV measurements and Dabiri a
to the actual bubble shape. 30 Before concluding this section, it is useful
to explore the final important prediction of Maxworthy (1972), namely
the formation of a wake behind the vortex ring. Figure 2.9 plots the
vorticity patches and instantaneous stre
return to the ring in this entrainment process, while the remainder will
form a small wake behind the ring. Formation of the wake is facilitated
by free-stream fluid that still possesses sufficient total pressure after the
dissipation process to convect t
= P = O UL/H2 . An exactly analogous scaling argument applies to
the second equation above and thus we see that the final equations for
these two components are (with = ) p x = 2u z2 , p y =
2 v z2 . Third consider the NavierStokes equation for the veloc
different from the typical Gaussian profile. From figure 6.13 we can now
see that this effect is due to the shear layer vorticity that was fed close to
the axis of symmetry and subsequently passed from the rear of the ring
to the front stagnation point. T
across all of the test cases. An important goal of these experiments is to
implement the strategies for pinch-off delay suggested by Mohseni et al.
(2001) and examined by Allen (2003). The observed starting flow
dynamics are explained in terms of the shea
upstream hollow cylinder by fitting the elastic tube over the outer
diameter of the cylinder lip (Do = 3.1 cm). To facilitate a smooth
transition from the cylinder to the nozzle, the cylinder lip is sharpened to
form a 7 degree wedge from its outer diamet
in the previous sections. We define the tangential divergence of a vector
field . Definition 4.3.3. Given (H1/2(D)3 such that ( n)|D =
0, we define its tangential divergence div H3/2(D) as the
distribution such that ! div, "D := !,()|D"D
H3/2(D), where H