scholarly journals Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos

2014 ◽  
Vol 761 ◽  
pp. 399-430 ◽  
Author(s):  
Karthik Kashinath ◽  
Iain C. Waugh ◽  
Matthew P. Juniper
Keyword(s):  
Acoustic Waves ◽  
Stable State ◽  
Period Doubling ◽  
Premixed Flame ◽  
Mode Switching ◽  
Multiple Time ◽  
Flame Surface ◽  
Nonlinear Behaviour ◽  
Mean Flow ◽  
Routes To Chaos

AbstractThermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional premixed flame in a duct via numerical simulations of a $G$-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle–Takens–Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.

Resonance dynamics in compressible cavity flows using time-resolved velocity and surface pressure fields

2017 ◽  
Vol 830 ◽  
pp. 494-527 ◽  
Author(s):  
Justin L. Wagner ◽  
Steven J. Beresh ◽  
Katya M. Casper ◽  
Edward P. DeMauro ◽  
Srinivasan Arunajatesan
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Surface Pressure ◽  
Coherent Structures ◽  
Acoustic Waves ◽  
Mode Switching ◽  
Recirculation Region ◽  
Mean Flow ◽  
Time Resolved ◽  
Phase Velocities

The resonance modes in Mach 0.94 turbulent flow over a cavity having a length-to-depth ratio of five were explored using time-resolved particle image velocimetry (TR-PIV) and time-resolved pressure sensitive paint (TR-PSP). Mode switching was quantified in the velocity field simultaneous with the pressure field. As the mode number increased from one through three, the resonance activity moved from a region downstream within the recirculation region to areas further upstream in the shear layer, an observation consistent with linear stability analysis. The second and third modes contained organized structures associated with shear layer vortices. Coherent structures occurring in the velocity field during modes two and three exhibited a clear modulation in size with streamwise distance. The streamwise periodicity was attributable to the interference of downstream-propagating vortical disturbances with upstream-travelling acoustic waves. The coherent structure oscillations were approximately $180^{\circ }$ out of phase with the modal surface pressure fluctuations, analogous to a standing wave. Modal propagation (or phase) velocities, based on cross-correlations of bandpass-filtered velocity fields were found for each mode. The phase velocities also showed streamwise periodicity and were greatest at regions of maximum constructive interference where coherent structures were the largest. Overall, the phase velocities increased with modal frequency, which coincided with the modal activity residing at higher portions of the cavity where the local mean flow velocity was elevated. Together, the TR-PIV and TR-PSP provide unique details not only on the distribution of modal activity throughout the cavity, but also new understanding of the resonance mechanism as observed in the velocity field.

scholarly journals Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

1993 ◽  
Vol 256 ◽  
pp. 499-534 ◽  
Author(s):  
M. C. A. M. Peters ◽  
A. Hirschberg ◽  
A. J. Reijnen ◽  
A. P. J. Wijnands
Keyword(s):  
Experimental Data ◽  
Reflection Coefficient ◽  
Strouhal Number ◽  
Acoustic Waves ◽  
High Frequency ◽  
Nonlinear Behaviour ◽  
Mean Flow ◽  
Frequency Limit ◽  
Low Frequencies ◽  
Open Pipe

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared.In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies.Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5.The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/a = 0.6133, to a value of δ/a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/a = 0.26.The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982b) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly.The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number.The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

Numerical Simulation of Premixed Propane/Air Flame Propagation Using a Dynamically Thickened Flame Approach

2013 ◽  
Vol 444-445 ◽  
pp. 1574-1578 ◽  
Author(s):  
Hua Hua Xiao ◽  
Zhan Li Mao ◽  
Wei Guang An ◽  
Qing Song Wang ◽  
Jin Hua Sun
Keyword(s):  
Numerical Simulation ◽  
Flame Propagation ◽  
Numerical Study ◽  
Vortex Motion ◽  
Combustion Process ◽  
Single Step ◽  
Premixed Combustion ◽  
Premixed Flame ◽  
Flame Surface ◽  
Arrhenius Kinetics

A numerical study of premixed propane/air flame propagation in a closed duct is presented. A dynamically thickened flame (TF) method is applied to model the premixed combustion. The reaction of propane in air is taken into account using a single-step global Arrhenius kinetics. It is shown that the premixed flame undergoes four stages of dynamics in the propagation. The formation of tulip flame phenomenon is observed. The pressure during the combustion process grows exponentially at the finger-shape flame stage and then slows down until the formation of tulip shape. After tulip formation the pressure increases quickly again with the increase of the flame surface area. The vortex motion behind the flame front advects the flame into tulip shape. The study indicates that the TF model is quite reliable for the investigation of premixed propane/air flame propagation.

Routes to Chaos in the Peroxidase−Oxidase Reaction:  Period-Doubling and Period-Adding

1997 ◽  
Vol 101 (25) ◽  
pp. 5075-5083 ◽  
Author(s):  
Marcus J. B. Hauser ◽  
Lars F. Olsen ◽  
Tatiana V. Bronnikova ◽  
William M. Schaffer
Keyword(s):  
Period Doubling ◽  
Routes To Chaos ◽  
Oxidase Reaction

ACOUSTIC CHAOS

1991 ◽  
Vol 01 (01) ◽  
pp. 13-26 ◽  
Author(s):  
WERNER LAUTERBORN ◽  
JOACHIM HOLZFUSS
Keyword(s):  
Liquid Layer ◽  
Acoustic Waves ◽  
High Intensity ◽  
Period Doubling ◽  
Musical Instruments ◽  
History Of

The history of chaos pertaining to acoustics is briefly reviewed from the first period-doubling experiments reported by Faraday (vibrated liquid layer) and Melde (string oscillations) to today's investigations on chaos in thermoacoustics, musical instruments, the hearing process, and ultrasonics. A closer analysis is given of the sound produced in a liquid by standing acoustic waves of high intensity.

scholarly journals Streaming by leaky surface acoustic waves

2010 ◽  
Vol 467 (2130) ◽  
pp. 1779-1800 ◽  
Author(s):  
J. Vanneste ◽  
O. Bühler
Keyword(s):  
Surface Waves ◽  
Acoustic Waves ◽  
Surface Acoustic Waves ◽  
Acoustic Streaming ◽  
Stokes Drift ◽  
Mean Flow ◽  
Matched Asymptotics ◽  
Flow Generation ◽  
Solid Liquid Interface ◽  
Solid Liquid

Acoustic streaming, the generation of mean flow by dissipating acoustic waves, provides a promising method for flow pumping in microfluidic devices. In recent years, several groups have been experimenting with acoustic streaming induced by leaky surface waves: (Rayleigh) surface waves excited in a piezoelectric solid interact with a small volume of fluid where they generate acoustic waves and, as result of the viscous dissipation of these waves, a mean flow. We discuss the computation of the corresponding Lagrangian mean flow, which controls the trajectories of fluid particles and hence the mixing properties of the flows generated by this method. The problem is formulated using the averaged vorticity equation which extracts the dominant balance between wave dissipation and mean-flow dissipation. Particular attention is paid to the thin boundary layer that forms at the solid/liquid interface, where the flow is best computed using matched asymptotics. This leads to an explicit expression for a slip velocity, which includes the effect of the oscillations of the boundary. The Lagrangian mean flow is naturally separated into three contributions: an interior-driven Eulerian mean flow, a boundary-driven Eulerian mean flow and the Stokes drift. A scale analysis indicates that the latter two contributions can be neglected in devices much larger than the acoustic wavelength but need to be taken into account in smaller devices. A simple two-dimensional model of mean flow generation by surface acoustic waves is discussed as an illustration.

An Acoustic Time-of-Flight Approach for Unsteady Temperature Measurements: Characterization of Entropy Waves in a Model Gas Turbine Combustor

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Dominik Wassmer ◽  
Bruno Schuermans ◽  
Christian Oliver Paschereit ◽  
Jonas P. Moeck
Keyword(s):  
Gas Turbine ◽  
Acoustic Waves ◽  
Fuel Injection ◽  
Acoustic Pulse ◽  
Time Of Flight ◽  
Phase Lag ◽  
Mean Flow ◽  
Unsteady Temperature ◽  
Arrival Times ◽  
Flow Velocities

Lean premixed combustion promotes the occurrence of thermoacoustic phenomena in gas turbine combustors. One mechanism that contributes to the flame–acoustic interaction is entropy noise. Fluctuations of the equivalence ratio in the mixing section cause the generation of hot spots in the flame. These so-called entropy waves are convectively transported to the first stage of the turbine and generate acoustic waves that travel back to the flame; a thermoacoustic loop is closed. However, due to the lack of experimental tools, a detailed investigation of entropy waves in gas turbine combustion systems has not been possible up to now. This work presents an acoustic time-of-flight based temperature measurement method which allows the measurement of temperature fluctuations in the relevant frequency range. A narrow acoustic pulse is generated with an electric spark discharge close to the combustor wall. The acoustic response is measured at the same axial location with an array of microphones circumferentially distributed around the combustion chamber. The delay in the pulse arrival times corresponds to the line-integrated inverse speed of sound. For the measurement of entropy waves in an atmospheric combustion test rig, fuel is periodically injected into the mixing tube of a premixed combustor. The subsequently generated entropy waves are measured for different forcing frequencies of the fuel injection and for different mean flow velocities in the combustor. The amplitude decay and phase lag of the entropy waves adhere well to a Strouhal number scaling for different mean flow velocities.

Bistable Flow Patterns in a Free Surface Water Channel

1989 ◽  
Vol 111 (4) ◽  
pp. 408-413
Author(s):  
E. W. Adams ◽  
A. I. Stamou
Keyword(s):  
Free Surface ◽  
Surface Water ◽  
Stable State ◽  
Flow Patterns ◽  
Shear Layers ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Free Shear Layers ◽  
Side Flow ◽  
Bistable Flow

A series of experiments is reported on a free surface water tunnel with a slot inlet centered at mid-depth in which the flow exhibited equally probable bistable flow patterns. The two flow fields are strongly asymmetric even when the geometry is symmetric and consists of a long stall on one side of the inlet and a short stall on the opposite side. Flow visualization and laser-Doppler velocimetry were performed to examine the flow structure of both stable states in detail. Results showed that the mean flow and turbulence structure of the two bistable states are largely mirror images of each other within the separation zone. The effect of the wall on the flow is minor, only very close to the wall/free surface did the difference in wall constraints cause the two flow patterns to diverge. After reattachment both flows relax to free-surface channel flow. It is shown that the bistable flow pattern results from the interaction of the free shear layers and that only strong disturbances in the free shear layers can cause the flow in one stable state to switch to the other stable state. Bistable flow exists for geometries with asymmetry up to 10 percent for the expansion ratio studied.

Sign in / Sign up

Export Citation Format

Share Document