oscillations can be found in [20–22]. The model-based control
takes effect on the basis of process model of combustion
dynamics. However, a model which can describe the combustion
process faithfully is not economical or practical. A control strat-
egy, which is independent of the physical model of combustion
chamber, is of great theoretical and practical value.
The Rijke tube is an open-ended, cylindrical tube which
contains an electrical heat source or a flame. In general, the tube
is vertical and the heat source is introduced from below to the
tube. For a certain range of position of the heat source, the
coupling between resonant acoustic waves and unsteady heat
release excites self-sustained oscillations in the Rijke tube. The
kind of experiment is known as Rijke tube, named after P.L. Rijke,
the first man who discovered such kind of phenomenon for the
first time in 1859 [23]. Rijke found that the highest intensity of
sound was excited when the heat source was placed at 1/4 length
of the tube, and the sound was stopped when the top end was
covered. He tried to give out the reason for this phenomenon with
a series of expansion and contraction of the convecting air as a
result of the heating and the cooling due to the side walls.
According to this theory, he was not able to illustrate the fact
that 1/4 length is the optimal driving position, but Rayleigh’s
criterion [1] is also effective for the Rijke tube. For detail
explanation of the thermo-acoustic instabilities in Rijke tube
one may refer to Ref. [24].
The Rijke tube provides an elementary example of thermo-
acoustic oscillations with a heater as the source of excitation.
Such oscillations also exist in many practical propulsion and
power generation systems with a combustion process as the
source of excitation. Since the need to control thermo-acoustic
instabilities in propulsion and power generation systems’ com-
bustion chambers, and Rijke tube is the simplest system for the
study of thermo-acoustic instabilities in laboratory, it is normal to
demonstrate any development in combustion theory firstly on a
Rijke tube apparatus.
So far, Rijke tube has also been widely studied and reviewed in
the literature. Yoon et al. developed mathematical models [25,26],
which focused on linear and nonlinear velocity sensitive thermo-
acoustic interactions respectively, for generalized Rijke tube.
The oscillations in Rijke tube can be stabilized by active control
[27–32], and for a complete review on experiments carried out on
the Rijke tubes and Rijke burners, one can find details in [33] . The
newest report on a modified Rijke tubes for waste thermal energy
harvesting can be found in [34].
The aim of the work in this paper is to stabilize the thermo-
acoustic oscillations in Rijke tube, which is a prototypical system
for the research of thermo-acoustic instabilities on a laboratory
scale, via an adaptive controller based on dynamic compensation.
The control technology employed is model free and its para-
meters can be tuned easily to suppress the oscillations. In what
follows, the experiment facility is provided in Section 2. Adaptive
control and its ability to suppress oscillations are given in Section
3. Section 4 shows the real-time control effects. In Section 5,we
make some discussion and conclude the paper.
2. Schematic of the experimental apparatus
2.1. The Rijke tube setup
The experimental Rijke tube is composed of a quartz glass
tube, a flame holder, a pressure transducer, a loudspeaker etc. The
structure of the experimental apparatus and the physical drawing
of Rijke tube and loudspeaker are shown in Figs. 1 and 2,
respectively.
Related parameters of the experimental apparatus are shown
in Table 1.
2.2. Sensors and actuators chosen in the closed-loop control
The choice of sensor and actuator is necessary to stabilize the
oscillations in the Rijke tube. Sensors provide dynamic informa-
tion of the combustion oscillations in Rijke tube. Microphones,
pressure transducers, optical filters, diode lasers etc. are used as
sensors to get useful information in combustors. A detailed
review of sensors could be found in Ref. [21]. In our experiments,
pressure transducers are chosen to obtain the pressure fluctua-
tions in Rijke tube, and it placed over the flame.
Actuators applied to combustion control, in general, can
be classified into two classes. One is loudspeaker, the other is
fuel valve. The fuel valve is an efficient actuator in practical
combustion systems. However, obtaining a satisfactory fuel valve
is one of the main challenges in reliable realization of closed-loop
control of combustion oscillations. Loudspeakers provide a
N2
CH4
H2
Control
Valve
Controller
Cabinet
Premixed
Pressure
Transducer
Flame Stabilised
on Grid
Loudspeaker
Fig. 1. Experimental apparatus of the Rijke tube.
W. Wei et al. / ISA Transactions 52 (2013) 450–460 451