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.

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.

One-dimensional model for the Rijke tube

1989 ◽  
Vol 202 ◽  
pp. 83-96 ◽  
Author(s):  
C. Nicoli ◽  
P. Pelcé
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Dimensional Model ◽  
Unsteady Heat Transfer ◽  
Order Unity ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
One Dimensional ◽  
The Stability ◽  
Stability Limits

We develop a simple model in which longitudinal, compressible, unsteady heat transfer between heater and gas is computed in the small-Mach-number limit. This calculation is used to determine the transfer function of the heater, which plays an important role in the stability limits of the thermoacoustic instability of the Rijke tube. The transfer function is determined analytically in the limit of small expansion parameter γ, and numerically for γ of order unity. In the case ρμ/cp = constant, an analytical solution can be found.

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.

scholarly journals Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160182 ◽  
Author(s):  
Umut Zalluhoglu ◽  
Nejat Olgac
Keyword(s):  
Feedback Control ◽  
Helmholtz Resonator ◽  
Dynamic Mode ◽  
Multiple Time ◽  
Interference Phenomenon ◽  
Stabilizing Controller ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Characteristic Roots ◽  
The Stability

This paper brings a novel mathematical perspective in assessing the rise of the secondary dynamic modes to prominence during the suppression of thermoacoustic instability. This phenomenon is observed by many earlier investigators; however, without a complete analytical reasoning. We consider a Rijke tube with both a passive Helmholtz resonator and an active feedback control to suppress instabilities. The core dynamics is represented as a linear time-invariant multiple time-delay system of neutral type. Parametric stability of the resulting infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots paradigm. This tool reveals the stability outlook of such systems exhaustively and non-conservatively in the parameter space of the system. First, we examine the stability with and without the Helmholtz resonator. We then select an unstable operation for the resonator-mounted Rijke tube, impose a time-delayed integral feedback control over it and reveal the stabilizing controller parameters using the cluster treatment of characteristic roots methodology. When high control gains are inappropriately selected, the new analytical procedure declares how the secondary dynamic modes of the system exhibit instability although the initially unstable mode is now stabilized. All of these stability assessments are cross-validated using experimental results from a laboratory-scale Rijke tube set-up.

scholarly journals Influence of the heat source location on the stability of the solution to the Cauchy problem

2021 ◽  
Vol 323 ◽  
pp. 00016
Author(s):  
Magda Joachimiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Heat Source ◽  
Source Function ◽  
Regularization Parameter ◽  
Cauchy Type ◽  
Heat Sources ◽  
Calculation Domain ◽  
The Cauchy Problem ◽  
The Stability ◽  
Stability Of The Solution

In this paper the solution to the Cauchy-type inverse problem for the Laplace’s equation is presented. A modified Tikhonov regularization was applied here. The regularization parameter was chosen using the Morozov principle. The relation between the location of the heat source (function singularity) and the stability of the solution to the inverse problem was analyzed. Variable thermal loads in the area were simulated by changing the location of heat sources along two boundaries of the rectangle calculation domain.

Analysis of the Thermoacoustic Flame Instability With Proper Orthogonal Decomposition

2015 ◽  
Author(s):  
Jianan Zhang ◽  
Albert Ratner
Keyword(s):  
Heat Release ◽  
Proper Orthogonal Decomposition ◽  
Heat Release Rate ◽  
Release Rate ◽  
Local Heat ◽  
Orthogonal Decomposition ◽  
Thermoacoustic Instability ◽  
Acoustic Perturbation ◽  
Rate Oscillation ◽  
Proper Orthogonal

Lean premixed combustion technology is a method that can inhibit the NOx emission by decreasing the flame temperature. Nevertheless, lean combustion systems are more sensitive to acoustic oscillations than rich systems. As a result, thermoacoustic instability, which is caused by the coupling between pressure and heat release rate oscillations, could causes serious device failure in the lean operating systems. A common mechanism that can trigger thermoacoustic instability is the flame-vortex interaction. The vortices forming in the shear layer can directly affect the energy exchange between combustion and the pressure field. Flame structure can experience significantly spatial change with the effect of the vortex. Therefore, this is essential to obtain the local heat release rate information to understand the global flame behavior. To capture the local information of the flame, planar laser induced fluorescence of OH radicals (OH-PLIF) was used to obtain the flame surface density (FSD), which is directly related to the local mean heat release rate. However, interruptions from the turbulent flow makes the raw local FSD data are difficult to be analyzed, especially when the acoustic perturbation level is low. To overcome this problem, the proper orthogonal decomposition (POD) method was used in the current research to analyze the FSD data to capture the dominant trend of the flame oscillation. The POD method was applied to a 5 m/s premixed low swirl flame forced by different levels of acoustic perturbation. After the dominant POD modes that contain most of the oscillation energy were obtained, they were used to reconstruct FSD results. By comparing the FSD results gained with and without POD method, it can be concluded that the dominant modes of POD can reasonably capture the key features of the heat release rate oscillation. Analysis results demonstrate that the POD method is a good candidate that can be applied to unstable combustion study to capture the dominant global and local heat release rate oscillation information, which is essential in understanding the thermoacoustic instability.

PLANETARY SELF-ORGANIZATION

2020 ◽  
Vol 42 (3) ◽  
pp. 271-282
Author(s):  
OLEG IVANOV
Keyword(s):  
Dynamical System ◽  
Heat Source ◽  
Mantle Convection ◽  
Plate Tectonics ◽  
Rotation Speed ◽  
Self Organization ◽  
Heat Sources ◽  
Kinematic Parameters ◽  
The Earth ◽  
New Type

The general characteristics of planetary systems are described. Well-known heat sources of evolution are considered. A new type of heat source, variations of kinematic parameters in a dynamical system, is proposed. The inconsistency of the perovskite-post-perovskite heat model is proved. Calculations of inertia moments relative to the D boundary on the Earth are given. The 9 times difference allows us to claim that the sliding of the upper layers at the Earth's rotation speed variations emit heat by viscous friction.This heat is the basis of mantle convection and lithospheric plate tectonics.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals The Effect of RME-1-Butanol Blends on Combustion, Performance and Emission of a Direct Injection Diesel Engine

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2941
Author(s):  
Wojciech Tutak ◽  
Arkadiusz Jamrozik ◽  
Karol Grab-Rogaliński
Keyword(s):  
Diesel Engine ◽  
Heat Release ◽  
Direct Injection ◽  
Specific Energy Consumption ◽  
Combustion Process ◽  
Constant Load ◽  
Combustion Stability ◽  
Performance And Emission ◽  
Energy Share ◽  
The Stability

The main objective of this study was assessment of the performance, emissions and combustion characteristics of a diesel engine using RME–1-butanol blends. In assessing the combustion process, great importance was placed on evaluating the stability of this process. Not only were the typical COVIMEP indicators assessed, but also the non-burnability of the characteristic combustion stages: ignition delay, time of 50% heat release and the end of combustion. The evaluation of the combustion process based on the analysis of heat release. The tests carried out on a 1-cylinder diesel engine operating at a constant load. Research and evaluation of the combustion process of a mixture of RME and 1-butanol carried out for the entire range of shares of both fuels up to 90% of 1-butanol energetic fraction. The participation of butanol in combustion process with RME increased the in-cylinder peak pressure and the heat release rate. With the increase in the share of butanol there was noted a decrease in specific energy consumption and an increase in engine efficiency. The share of butanol improved the combustion stability. There was also an increase in NOx emissions and decrease in CO and soot emissions. The engine can be power by blend up to 80% energy share of butanol.

scholarly journals Analysis and Comparison of Some Low-Temperature Heat Sources for Heat Pumps

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1853 ◽  
Author(s):  
Pavel Neuberger ◽  
Radomír Adamovský
Keyword(s):  
Heat Transfer ◽  
Low Temperature ◽  
Heat Source ◽  
Heat Pump ◽  
Heat Exchangers ◽  
Ambient Air ◽  
Heat Transfer Fluid ◽  
Heat Sources ◽  
Ground Heat Exchangers ◽  
Temperature Heat

The efficiency of a heat pump energy system is significantly influenced by its low-temperature heat source. This paper presents the results of operational monitoring, analysis and comparison of heat transfer fluid temperatures, outputs and extracted energies at the most widely used low temperature heat sources within 218 days of a heating period. The monitoring involved horizontal ground heat exchangers (HGHEs) of linear and Slinky type, vertical ground heat exchangers (VGHEs) with single and double U-tube exchanger as well as the ambient air. The results of the verification indicated that it was not possible to specify clearly the most advantageous low-temperature heat source that meets the requirements of the efficiency of the heat pump operation. The highest average heat transfer fluid temperatures were achieved at linear HGHE (8.13 ± 4.50 °C) and double U-tube VGHE (8.13 ± 3.12 °C). The highest average specific heat output 59.97 ± 41.80 W/m2 and specific energy extracted from the ground mass 2723.40 ± 1785.58 kJ/m2·day were recorded at single U-tube VGHE. The lowest thermal resistance value of 0.07 K·m2/W, specifying the efficiency of the heat transfer process between the ground mass and the heat transfer fluid, was monitored at linear HGHE. The use of ambient air as a low-temperature heat pump source was considered to be the least advantageous in terms of its temperature parameters.

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