Abstract: This paper presents a nonlinear differential model,
for a three-bladed horizontal axis wind turbine (HAWT) suited
for control applications. It is based on a 8-dofs, lumped
parameters structural dynamics coupled with a quasi-steady sectional
aerodynamics. In particular, using the Euler-Lagrange Equation
(Energetic Variation approach), the authors derive, and successively
validate, such model. For the derivation of the aerodynamic model,
the Greenbergs theory, an extension of the theory proposed by
Theodorsen to the case of thin airfoils undergoing pulsating flows,
is used. Specifically, in this work, the authors restricted that theory
under the hypothesis of low perturbation reduced frequency k,
which causes the lift deficiency function C(k) to be real and equal
to 1. Furthermore, the expressions of the aerodynamic loads are
obtained using the quasi-steady strip theory (Hodges and Ormiston),
as a function of the chordwise and normal components of relative
velocity between flow and airfoil Ut, Up, their derivatives, and
section angular velocity ε˙. For the validation of the proposed model,
the authors carried out open and closed-loop simulations of a 5
MW HAWT, characterized by radius R =61.5 m and by mean chord
c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec.
The first analysis performed is the steady state solution, where
a uniform wind Vw = 11.4 m/s is considered and a collective
pitch angle θ = 0.88◦ is imposed. During this step, the authors
noticed that the proposed model is intrinsically periodic due to
the effect of the wind and of the gravitational force. In order
to reject this periodic trend in the model dynamics, the authors
propose a collective repetitive control algorithm coupled with a PD
controller. In particular, when the reference command to be tracked
and/or the disturbance to be rejected are periodic signals with a
fixed period, the repetitive control strategies can be applied due to
their high precision, simple implementation and little performance
dependency on system parameters. The functional scheme of a
repetitive controller is quite simple and, given a periodic reference
command, is composed of a control block Crc(s) usually added
to an existing feedback control system. The control block contains
and a free time-delay system eτs in a positive feedback loop, and a
low-pass filter q(s). It should be noticed that, while the time delay
term reduces the stability margin, on the other hand the low pass
filter is added to ensure stability. It is worth noting that, in this
work, the authors propose a phase shifting for the controller and
the delay system has been modified as e^(−(T−γk)), where T is the
period of the signal and γk is a phase shifting of k samples of the
same periodic signal. It should be noticed that, the phase shifting
technique is particularly useful in non-minimum phase systems, such
as flexible structures. In fact, using the phase shifting, the iterative
algorithm could reach the convergence also at high frequencies.
Notice that, in our case study, the shifting of k samples depends
both on the rotor angular velocity Ω and on the rotor azimuth
angle Ψ: we refer to this controller as a spatial repetitive controller.
The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades.
The performance of the spatial repetitive controller is compared
with an industrial PI controller. In particular, starting from wind
speed velocity Vw = 11.4 m/s the controller is asked to maintain the
nominal angular velocity Ωn = 1.266rad/s after an instantaneous
increase of wind speed (Vw = 15 m/s). Then, a purely periodic
external disturbance is introduced in order to stress the capabilities
of the repetitive controller. The results of the simulations show that,
contrary to a simple PI controller, the spatial repetitive-PD controller
has the capability to reject both external disturbances and periodic
trend in the model dynamics. Finally, the nominal value of the
angular velocity is reached, in accordance with results obtained with
commercial software for a turbine of the same type.
Abstract: The exploitation of flow pulsation in micro- and
mini-channels is a potentially useful technique for enhancing cooling
of high-end photonics and electronics systems. It is thought that
pulsation alters the thickness of the hydrodynamic and thermal
boundary layers, and hence affects the overall thermal resistance
of the heat sink. Although the fluid mechanics and heat transfer
are inextricably linked, it can be useful to decouple the parameters
to better understand the mechanisms underlying any heat transfer
enhancement. Using two-dimensional, two-component particle image
velocimetry, the current work intends to characterize the heat transfer
mechanisms in pulsating flow with a mean Reynolds number of
48 by experimentally quantifying the hydrodynamics of a generic
liquid-cooled channel geometry. Flows circulated through the test
section by a gear pump are modulated using a controller to achieve
sinusoidal flow pulsations with Womersley numbers of 7.45 and
2.36 and an amplitude ratio of 0.75. It is found that the transient
characteristics of the measured velocity profiles are dependent on the
speed of oscillation, in accordance with the analytical solution for
flow in a rectangular channel. A large velocity overshoot is observed
close to the wall at high frequencies, resulting from the interaction
of near-wall viscous stresses and inertial effects of the main fluid
body. The steep velocity gradients at the wall are indicative of
augmented heat transfer, although the local flow reversal may reduce
the upstream temperature difference in heat transfer applications.
While unsteady effects remain evident at the lower frequency, the
annular effect subsides and retreats from the wall. The shear rate at
the wall is increased during the accelerating half-cycle and decreased
during deceleration compared to steady flow, suggesting that the flow
may experience both enhanced and diminished heat transfer during
a single period. Hence, the thickness of the hydrodynamic boundary
layer is reduced for positively moving flow during one half of the
pulsation cycle at the investigated frequencies. It is expected that the
size of the thermal boundary layer is similarly reduced during the
cycle, leading to intervals of heat transfer enhancement.
Abstract: There have been widespread applications of fluidized beds in industries which are related to the combination of gas-solid particles during the last decade. For instance, in order to crack the catalyses in petrochemical industries or as a drier in food industries. High capacity of fluidized bed in heat and mass transfer has made this device very popular. In order to achieve a higher efficiency of fluidized beds, a particular attention has been paid to beds with pulsating air flow. In this paper, a fluidized bed device with pulsating flow has been designed and constructed. Size of particles have been used during the test are in the range of 40 to 100μm. The purpose of this experimental test is to investigate the air flow regime, observe the particles- movement and measure the pressure loss along the bed. The effects of pulsation can be evaluated by comparing the results for both continuous and pulsating flow. Results of both situations are compared for various gas speeds. Moreover the above experiment is numerically simulated by using Fluent software and its numerical results are compared with the experimental results.
Abstract: The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.
Abstract: Periodic vortex shedding in pulsating flow inside wavy
channel and the effect it has on heat transfer are studied using the
finite volume method. A sinusoidally-varying component is superimposed
on a uniform flow inside a sinusoidal wavy channel and
the effects on the Nusselt number is analyzed. It was found that a
unique optimum value of the pulsation frequency, represented by the
Strouhal number, exists for Reynolds numbers ranging from 125 to
1000. Results suggest that the gain in heat transfer is related to the
process of vortex formation, movement about the troughs of the wavy
channel, and subsequent ejection/destruction through the converging
section. Heat transfer is the highest when the frequencies of the
pulsation and vortex formation approach being in-phase. Analysis of
Strouhal number effect on Nu over a period of pulsation substantiates
the proposed physical mechanism for enhancement. The effect of
changing the amplitude of pulsation is also presented over a period
of pulsation, showing a monotonic increase in heat transfer with
increasing amplitude. The 60% increase in Nusselt number suggests
that sinusoidal fluid pulsation can an effective method for enhancing
heat transfer in laminar, wavy-channel flows.