Quenching and amplification of thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling

Fokker-Planck modeling of the stochastic dynamics of a Rijke tube

We derive and numerically validate a low-order oscillator model to capture the stochastic dynamics of a prototypical thermoacoustic system (a Rijke tube) undergoing a subcritical Hopf bifurcation in the presence of additive noise. We find that on the fixed-point branch before the bifurcation, the system is dominated by the first duct mode, and the Fokker-Planck solution for the first Galerkin mode can adequately predict the stochastic dynamics of the overall system. We also find that this analytical framework predicts well the dominant mode on the limit-cycle branch, but underperforms in the hysteretic bistable zone where the role of nonlinearities is more pronounced. Besides offering new insights into stochastic thermoacoustic behavior, this study shows that an analytical framework based on the Fokker-Planck equation can facilitate the early detection of thermoacoustic instabilities in a Rijke-tube model subjected to noise.

Robust design against frequency variation for amplitude death in delay-coupled oscillators

Amplitude death has the potential to suppress unwanted oscillations in various engineering applications. However, in some engineering applications, such as dc microgrids, airfoil systems, and thermoacoustic systems, oscillation frequency is highly susceptible to external influences, leading to considerable variations. To maintain amplitude death amidst these frequency variations, we propose a design procedure that is robust against frequency variation for inducing amplitude death in delay-coupled oscillators. We first analytically derive the oscillator frequency band in which amplitude death can occur. The frequency bandwidth is maximized when the coupling strength is inversely proportional to the connection delay. Furthermore, our analysis reveals that the oscillator frequency band is influenced by the minimum eigenvalue of the normalized adjacency matrix (i.e., network topology) and that bipartite networks exhibit limited robustness to frequency variations. Our design procedure maintains the stability of amplitude death even under substantial frequency variations and is applicable to various network topologies. Numerical simulations confirm the validity of the proposed design.

Delay-induced amplitude death in multiplex oscillator network with frequency-mismatched layers

The present paper analytically investigates the stability of amplitude death in a multiplex Stuart-Landau oscillator network with a delayed interlayer connection. The network consists of two frequency-mismatched layers, and all oscillators in each layer have identical frequencies. We show that, if the matrices describing the network topologies of each layer commute, then the characteristic equation governing the stability can be reduced to a simple form. This form reveals that the stability of amplitude death in the multiplex network is equally or more conservative than that in a pair of frequency-mismatched oscillators coupled by a delayed connection. In addition, we provide a procedure for designing the delayed interlayer connection such that amplitude death is stable for any commuting matrices and for any intralayer coupling strength. These analytical results are verified through numerical examples. Moreover, we numerically discuss the results for the case in which the commutative property does not hold.

Application of different Trombe wall solutions on the reduction of energy load and sustainable development in an eco-resort residential building in Binalood region with a cold and dry climate

Trombe wall is a passive strategy that reduces the energy consumption in buildings and helps for sustainable development of the residential sector. Applying these walls is very important in areas that need heating load in winter. This study evaluates a set of Trombe walls for the energy management of a residential building under real conditions in Binalood region with a cold and dry climate. In order to study the potentials of the Trombe wall, four different designs, including cubic Trombe wall with rectangular structure and three-sided glass, Trombe wall with trapezoidal structure and three-sided glass, Trombe wall with trapezoidal structure and four-sided glass, and Trombe wall with thicker storage wall, trapezoidal structure, and three-sided glass, for Trombe wall are considered. Trombe walls of all four suggested designs are exposed to outdoor conditions and installed at 17 places on the southern walls of the residential building. The results show that the most optimal design, i.e., Trombe wall with thicker storage wall, trapezoidal structure, and three-sided glass, leads to the greatest decrease (1637 kWh) in heating load in January. In addition, this design of the Trombe wall has the greatest effect in increasing the indoor air temperature among other Trombe walls investigated in this study. The Trombe wall with thicker storage wall, trapezoidal structure, and three-sided glass with a storage wall thickness of 40 cm is able to reduce the heating load of the building by 5.59 MWh in 5 months. This plan reduces the energy demand of the building by 8% more than the conventional structure of Trombe wall.

Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback

We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.