A Novel Theoretical Approach to Passive Control of Thermo-Acoustic Oscillations: Application to Ducted Heat Sources

2013 ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Heat Release ◽  
Passive Control ◽  
Adjoint Equations ◽  
Heat Sources ◽  
Acoustic System ◽  
Acoustic Oscillations ◽  
Hot Wire ◽  
Adjoint Sensitivity ◽  
Cross Sectional ◽  
Rijke Tube

In this paper, we develop a linear technique that predicts how the stability of a thermo-acoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically-heated hot wire and the second contains a diffusion flame. Both heat sources are assumed to be compact so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermo-acoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermo-acoustic system should be changed in order to make it stable.

A Theoretical Approach for Passive Control of Thermoacoustic Oscillations: Application to Ducted Flames

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Heat Release ◽  
Passive Control ◽  
Local Variation ◽  
Control Device ◽  
Adjoint Equations ◽  
Hot Wire ◽  
Adjoint Sensitivity ◽  
Cross Sectional ◽  
Rijke Tube ◽  
Thermoacoustic Oscillations

In this paper, we develop a linear technique that predicts how the stability of a thermoacoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically heated hot wire, and the second contains a diffusion flame. Both heat sources are assumed to be compact, so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermoacoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermoacoustic system should be changed in order to make it stable.

scholarly journals Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

2013 ◽  
Vol 719 ◽  
pp. 183-202 ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Growth Rate ◽  
Sensitivity Analysis ◽  
Heat Release ◽  
Passive Control ◽  
Feedback Mechanism ◽  
Control Element ◽  
Acoustic System ◽  
Hot Wire ◽  
Small Oscillations ◽  
Structural Sensitivity

AbstractWe apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates.

Sensitivity Analysis of Beam Cross-Section Stiffness Using Adjoint Method

2017 ◽  
Author(s):  
Alfonso Callejo ◽  
Olivier Bauchau ◽  
Boris Diskin ◽  
Li Wang
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Cross Section ◽  
Structural Parameters ◽  
Flexible Multibody Dynamics ◽  
Numerical Differentiation ◽  
Adjoint Equations ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Cross Sectional

The design optimization of rotorcraft through multidisciplinary aeroelastic models with hundreds of thousands of degrees of freedom requires a computationally efficient sensitivity analysis to obtain the objective function gradient. A fundamental part of rotorcraft analysis is the flexible multibody dynamics solver, which in the current work relies on an accurate three-dimensional representation of the beams. This paper presents the theoretical adjoint sensitivity analysis of the first structural analysis step, namely the computation of cross-sectional properties of the beams in the form of six-dimensional stiffness matrices. The adjoint equations are carefully derived, as are the derivatives of the objective function with respect to the design parameters. The method is then validated by comparing certain design sensitivities of a three-ply, composite cross-section with those obtained through real-step and complex-step numerical differentiation. The presented analysis allows the user to quantify the effect of basic structural parameters on fundamental sectional properties that can later be used in the full dynamic simulation.

scholarly journals Global modes, receptivity, and sensitivity analysis of diffusion flames coupled with duct acoustics

2014 ◽  
Vol 752 ◽  
pp. 237-265 ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Growth Rate ◽  
Sensitivity Analysis ◽  
Heat Release ◽  
Slot Width ◽  
Adjoint Equations ◽  
Flame Velocity ◽  
Acoustic System ◽  
Duct Acoustics ◽  
Structural Sensitivity ◽  
Global Modes

AbstractIn this theoretical and numerical paper, we derive the adjoint equations for a thermo-acoustic system consisting of an infinite-rate chemistry diffusion flame coupled with duct acoustics. We then calculate the thermo-acoustic system’s linear global modes (i.e. the frequency/growth rate of oscillations, together with their mode shapes), and the global modes’ receptivity to species injection, sensitivity to base-state perturbations and structural sensitivity to advective-velocity perturbations. Some of these could be found by finite difference calculations but the adjoint analysis is computationally much cheaper. We then compare these with the Rayleigh index. The receptivity analysis shows the regions of the flame where open-loop injection of fuel or oxidizer will have the greatest influence on the thermo-acoustic oscillation. We find that the flame is most receptive at its tip. The base-state sensitivity analysis shows the influence of each parameter on the frequency/growth rate. We find that perturbations to the stoichiometric mixture fraction, the fuel slot width and the heat-release parameter have most influence, while perturbations to the Péclet number have the least influence for most of the operating points considered. These sensitivities oscillate, e.g. positive perturbations to the fuel slot width either stabilizes or destabilizes the system, depending on the operating point. This analysis reveals that, as expected from a simple model, the phase delay between velocity and heat-release fluctuations is the key parameter in determining the sensitivities. It also reveals that this thermo-acoustic system is exceedingly sensitive to changes in the base state. The structural-sensitivity analysis shows the influence of perturbations to the advective flame velocity. The regions of highest sensitivity are around the stoichiometric line close to the inlet, showing where velocity models need to be most accurate. This analysis can be extended to more accurate models and is a promising new tool for the analysis and control of thermo-acoustic oscillations.

scholarly journals Thermoacoustic Instability in a Rijke Tube with a Distributed Heat Source

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaochuan Yang ◽  
Ali Turan ◽  
Shenghui Lei
Keyword(s):  
Heat Source ◽  
Heat Release ◽  
Method Of Lines ◽  
Nonlinear Behaviour ◽  
Heat Sources ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acoustic Perturbation ◽  
The Stability ◽  
The Galerkin Method

A Rijke tube with a distributed heat source is investigated. Driven by the widely existing thermoacoustic instability in lean premixed gas turbine combustors, this work aims to explore the physicochemical underpinning and assist in the elucidation and analysis of this problem. The heat release model consists of a row of distributed heat sources with individual heat release rates. The integrated heat release rate is then coupled with the acoustic perturbation for thermoacoustic analysis. A continuation approach is employed to conduct the bifurcation analysis and capture the nonlinear behaviour inherent in the system. Unlike the conventional approach by the Galerkin method, the acoustic equations are originally discretized using the Method of Lines (MOL) to build up a dynamic system. The model is first validated and shown to yield good predictions with available experimental data. Influences of multiple heat sources, time delay, and heat release distribution are then studied to reveal the extensive nonlinear characteristics involved in the case of a distributed heat source. It is found that distributed heat source plays an important role in determining the stability of a thermoacoustic system.

Transistors with a Profiled Active Layer Made by Hot-Wire Cvd

1998 ◽  
Vol 507 ◽  
Author(s):  
H. Meiling ◽  
A.M. Brockhoff ◽  
J.K. Rath ◽  
R.E.I. Schropp
Keyword(s):  
Thin Film ◽  
Active Layer ◽  
Hot Wire ◽  
Semiconductor Interface ◽  
Cross Sectional ◽  
Silicon Matrix ◽  
Bias Stress ◽  
Silicon Devices ◽  
Transmission Electron ◽  
Conducting Research

ABSTRACTIn order to obtain stable thin-film silicon devices we are conducting research on the implementation of hot-wire CVD amorphous and polycrystalline silicon in thin-film transistors, TFFs. We present results on TFTs with a profiled active layer (deposited at ≥9 Å/s), and correlate the electrical properties with the structure of the silicon matrix at the insulator/semiconductor interface, as determined with cross-sectional transmission electron microscopy. Devices prepared with an appropriate H2 dilution of SiH4 show cone-shaped crystalline inclusions. These crystals start at the interface in some cases, and in others exhibit an 80nm incubation layer prior to nucleation. The crystals in the TFTs with the incubation layer are not cone-shaped, but are rounded off. The hot-wire CVD deposited devices exhibit a high fieldeffect mobility up to 1.5 cm2V−1s−l. Also, these devices have superior stability upon continuous gate bias stress, as compared to conventional glow-discharge α-Si:H TFTs. We ascribe this to a combination of enhanced structural order of the silicon and a low hydrogen content.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH
Keyword(s):  
Mach Number ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Heat Release ◽  
Acoustic Field ◽  
Release Rate ◽  
Governing Equations ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acceleration Term

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.

Smart Passive Control of Thermoacoustic Instability in a Bluff-Body Stabilized Combustor: A Lagrangian Analysis of Critical Structures

2020 ◽  
Author(s):  
C. P. Premchand ◽  
Manikandan Raghunathan ◽  
Midhun Raghunath ◽  
K. V. Reeja ◽  
R. I. Sujith ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Flow Field ◽  
Heat Release ◽  
Shear Layer ◽  
Heat Release Rate ◽  
Release Rate ◽  
Sound Production ◽  
Bluff Body ◽  
Passive Control ◽  
Thermoacoustic Instability

Abstract The tonal sound production during thermoacoustic instability is detrimental to the components of gas turbine and rocket engines. Identifying the root cause and controlling this oscillatory instability would enable manufacturers to save in costs of power outages and maintenance. An optimal method is to identify the structures in the flow-field that are critical to tonal sound production and perform control measures to disrupt those “critical structures”. Passive control experiments were performed by injecting a secondary micro-jet of air onto the identified regions with critical structures in the flow-field of a bluff-body stabilized, dump, turbulent combustor. Simultaneous measurements such as unsteady pressure, velocity, local and global heat release rate fluctuations are acquired in the regime of thermoacoustic instability before and after control action. The tonal sound production in this combustor is accompanied by a periodic flapping of the shear layer present in the region between the dump plane (backward-facing step) and the leading edge of the bluff-body. We obtain the trajectory of Lagrangian saddle points that dictate the flow and flame dynamics in the shear layer during thermoacoustic instability accurately by computing Lagrangian Coherent Structures. Upon injecting a secondary micro-jet with a mass flow rate of only 4% of the primary flow, nearly 90% suppression in the amplitude of pressure fluctuations are observed. The suppression thus results in sound pressure levels comparable to those obtained during stable operation of the combustor. Using Morlet wavelet transform, we see that the coherence in the dominant frequency of pressure and heat release rate oscillations during thermoacoustic instability is affected by secondary injection. The disruption of saddle point trajectories breaks the positive feedback loop between pressure and heat release rate fluctuations resulting in the observed break of coherence. Wavelet transform of global heat release rate shows a redistribution of energy content from the dominant instability frequency (acoustic time scale) to other time scales.

Development of an Analog Controller for Tuning an Adaptive-Passive Control Device

2005 ◽  
Author(s):  
Marty Johnson ◽  
Edward C. Diggs
Keyword(s):  
Passive Control ◽  
Low Frequency ◽  
Helmholtz Resonator ◽  
Dc Motor ◽  
Control Device ◽  
Inner Product ◽  
Variable Cross ◽  
Error Signal ◽  
Cross Sectional ◽  
Drive Frequency

Adaptive-passive devices such as adaptive Helmholtz Resonators (HR) and tunable vibration absorbers have been shown to be suitable for controlling both narrowband disturbances and lightly damped structural/acoustic modes driven by broadband disturbances. In order to track changes in the disturbance or changes in the modes, the natural frequency of the absorber, ωn, is tuned to match the observed signals. This is achieved by altering some physical parameter of the control device such as the stiffness of a vibration absorber or the neck cross-sectional area of a Helmholtz resonator. In order to automatically adjust these devices, control systems and tuning algorithms have been developed, most of which involve a digital controller. However, this paper looks specifically at the development of a simple analog controller used to drive a DC motor in order to tune a mechanical device. A two sensor dot product method is employed where one sensor is placed inside of the control device, such as a Helmholtz Resonator, and the other on/in the system under control, such as in a room. The outputs from the two sensors are multiplied together and subsequently low passed in order to extract a low frequency “DC” voltage which acts as an error signal. The error signal is related to the relative phase of the two sensor signals and determines the direction in which the device should be tuned. When the two signals are 90° apart, the system is tuned (i.e. the inner product produces zero DC level). If the drive frequency ω is different than the tuned frequency, then the system is mis-tuned. The relationship between the mis-tuning, ωn-ω, and the error is not linear, but for small perturbations a linear approximation can be used to investigate the stability and performance of the system. The gradient of the function is shown to be largest when the mis-tuning error is zero and is inversely proportional to the damping level in the control device. Once stability of the system has been ensured the ability of the system to track changes in drive frequency is investigated experimentally. The control system is demonstrated using an adaptive Helmholtz resonator which has a variable cross-sectional neck via an iris diaphragm. The iris is controlled using a small DC motor; two microphones (one mounted internally and one externally) are used to supply the driving signal to the circuit.

scholarly journals Four-Poles Parameter of an Elliptical Cavity Having the Outlet on the Body

2020 ◽  
Vol 5 (7) ◽  
pp. 763-766
Author(s):  
Yuya Nishimura ◽  
Sohei Nishimura
Keyword(s):  
Wave Equations ◽  
Sound Pressure ◽  
Elliptic Cylinder ◽  
The Body ◽  
Noise Characteristic ◽  
Acoustic System ◽  
Cross Sectional ◽  
Elliptical Cavity ◽  
Input Side ◽  
In Series

This paper deals with the computation of the four-poles parameter of a thin elliptic cylinder in which the output is fitted to the side that is perpendicular to the input side. The four-poles parameter is based on the sound pressure calculated by solving the wave equations, with the assumption that the loss can be ignored. The four-poles parameter is widely used to estimate the noise characteristic for the acoustic system which are composed of several elements of various cross-sectional areas, various shape connected in series.

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