Environmental Engineering Reference
In-Depth Information
( f opt
24Hz) or maximum efficiency ( f opt
21Hz). This can be explained by the
fact that the consumed power, which enters the quotient defining efficiency Eq. ( 2 )in
the denominator, increases monotonically with increasing frequency. This will thus
shift the location of the peak in the efficiency that corresponds to the aerodynamic
power peak.
In order to focus on the effect of the forewing-hindwing phase lag, a fixed fre-
quency can be chosen. In Fig. 2 , for each of the two frequencies represented, the same
trends are observed in the cruising speed and the consumed power and, as shown
in the insets, the frequency dependence is well explained using the “elasto-inertial”
dimensionless variables u and p defined above. Now, with respect to the phase lag
˕
, two main points appear clearly: on the one hand, the fastest flying performance
is found around in-phase flapping (i.e.
˕ =
0), while around anti-phase flapping
(
) this cruising speed is the lowest. We may note that the curve is not sym-
metric with respect to
˕ = ˀ
˕ =
0, since it diminishes only slightly (one could consider a
plateau) between
˕ =
0 and
ˀ/
2, whereas it drops more rapidly when the hindwing
leads (i.e., when going from
˕ =
0
=
2
ˀ
towards
˕ =
3
ˀ/
2). The consumed power
curve on the contrary has two maxima (around
˕ =
0 and
ˀ
) and two minima around
(
2). In-phase and anti-phase flapping being the most expensive can
be explained by a simple inertial argument since during these configurations the mo-
tor has to accommodate the acceleration/deceleration of both pairs of wings at the
same time, contrary to the intermediate phase lags
˕ = ˀ/
2 and 3
ˀ/
2, where the
deceleration of one pair of wings occurs while the other pair is accelerating, hence
redistributing the load on the motor.
The shape of the cruising speed and consumed power curves determines the lo-
cation of the maximum observed in the efficiency contours in Fig. 3 being around
˕ = ˀ/
˕ = ˀ/
2 and 3
ˀ/
2 (a zone of
the parameter space that was not fully explored in the present experiments). We can
now compare the optimum phase-lags that lead to peaks of cruising speed and of
efficiency and comment on their physical origin: while the maximum cruising speed
is observed for phase-lags between zero and
2. A secondary maximum can be expected around
˕ =
3
ˀ/
ˀ/
4, the optimum phase-lags in terms of
efficiency are around
2. The former are ruled solely by the aerodynamics, where
the performance of different kinematic patterns will have to be analysed considering,
for instance, the interaction between hindwing and the vortex structures shed by the
forewing. A wake capture process of this sort has been proposed by Kolomenskiy
et al. ( 2013 ) as a possible explanation for the large propulsive force found at 0
ˀ/
ˀ
in their 2D numerical simulations. 1 Concerning the optimum phase lag in terms of
efficiency requires, on the other hand, considering the power consumption, which is
not only correlated to the aerodynamics, but has a large contribution determined by
solid inertia, as we have mentioned in reference to the power plot in Fig. 2 b.
The effect of the modulation of
.
75
in terms of aerodynamics, as mentioned previ-
ously, will be intrinsically related to the roles of the distance d between the two wing
pairs and the deformation kinematics. In this paper, we have fixed d and considered
˕
1 Note that in Kolomenskiy et al. ( 2013 ) the phase lag is defined with a negative sign with respect
to
˕
as used here so that 0
.
75
ˀ
here corresponds to their 1
.
25
ˀ
.
Search WWH ::




Custom Search