Thermoacoustic Stability of Quasi-One-Dimensional Flows—Part II: Application to Basic Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 645-653 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Acoustic Energy ◽  
System Stability ◽  
Combustion Stability ◽  
Mean Flow ◽  
One Dimensional ◽  
Numerical Formulation ◽  
The Mean ◽  
Flow Gradients ◽  
The Stability

In this paper, applications of a previously developed numerical formulation (Prasad, D., and Feng, J., 2004, “Thermoacoustic stability of Quasi-One-Dimensional Flows—Part I: Analytical and Numerical Formulation,” J. Turbomach., 126, pp. 636–643. for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.

Thermoacoustic Stability of Quasi-One-Dimensional Flows: Part II — Application to Basic Flows

2004 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Acoustic Energy ◽  
System Stability ◽  
Combustion Stability ◽  
Mean Flow ◽  
One Dimensional ◽  
Numerical Formulation ◽  
The Mean ◽  
Flow Gradients ◽  
The Stability

In this paper, applications of a previously developed numerical formulation (Prasad and Feng 2004) for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.

Thermoacoustic Stability of Quasi-One-Dimensional Flows–Part I: Analytical and Numerical Formulation

2004 ◽  
Vol 126 (4) ◽  
pp. 637-644 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Problem Formulation ◽  
Mean Flow ◽  
Sonic Point ◽  
Impedance Boundary ◽  
One Dimensional ◽  
Natural Modes ◽  
Local Wave ◽  
Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.

Effects of the Mean Flow Field on the Thermo-Acoustic Stability of Aero-Engine Combustion Chambers

2012 ◽  
Author(s):  
Jannis Gikadi ◽  
Thomas Sattelmayer ◽  
Antonio Peschiulli
Keyword(s):  
Flow Field ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Acoustic Energy ◽  
System Stability ◽  
Mean Flow ◽  
Combustion Chambers ◽  
Hydrodynamic Modes ◽  
Aero Engine ◽  
The Mean

This paper presents a finite element methodology to predict the thermoacoustic eigenmodes of combustion chambers using the linearized Navier-Stokes equations (LNSE) in frequency space. The effect of the mean flow on the acoustics is accounted for. Besides scattering and refraction of acoustic waves in shear layers, this set of equation describes two main damping mechanisms. One is related to the generation of entropy waves, so called hot-spots, in flame regions. The other is related to the transformation of acoustic energy into vorticity waves at sharp leading or trailing edges. Both fluctuation types, i.e. entropy and vorticity, are convected by the mean flow, leading to significant damping when the fluid discharges into an open outlet. In combustion chamber environments these waves are accelerated in the downstream high pressure distributor and are partially transformed back into acoustic waves constituting to the feedback loop of thermo-acoustic instabilities. Accurate prediction of the eigenmodes and eigenfrequencies of instability require therefore to take these interaction effects into account. First, the accuracy of the LNSE approach, to capture the damping generated by the first mechanism of entropy generation and convection, is investigated for a generic premixed flame configuration. Solutions of the LNSE are compared to the analytic solutions as well as eigenvalues determined by an Helmholtz ansatz. Later methodology assumes a quiescent medium and neglects all interactions of acoustics with the mean flow. It is shown that large errors are introduced with increasing Mach-number. To illustrate errors assuming a quiescent medium for realistic combustion chambers, the LNSE are used to assess the eigenmodes of a two-dimensional aero-engine combustor including strong shear regions, in the next step. The non-isothermal mean flow field is obtained performing an incompressible RANS simulation. It features an expanding jet with inner and outer recirculation zones. The acoustic computations using LNSE reveal a set of unstable and neutral hydrodynamic modes in addition to acoustic modes. Both damping mechanisms are present and contribute to the overall system stability. Again the obtained solution is compared to the solution of an Helmholtz code and differences are discussed.

Thermoacoustic Stability of Quasi-One-Dimensional Flows: Part I — Analytical and Numerical Formulation

2004 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Problem Formulation ◽  
Mean Flow ◽  
Sonic Point ◽  
Impedance Boundary ◽  
One Dimensional ◽  
Natural Modes ◽  
Local Wave ◽  
Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.

Sidewall finite-conductivity effects in confined turbulent thermal convection

2002 ◽  
Vol 473 ◽  
pp. 201-210 ◽  
Author(s):  
ROBERTO VERZICCO
Keyword(s):  
Boundary Conditions ◽  
Thermal Convection ◽  
Lateral Wall ◽  
Finite Conductivity ◽  
Mean Flow ◽  
Number Range ◽  
Additional Heat ◽  
Low Aspect Ratio ◽  
Temperature Boundary ◽  
The Mean

The effects of a sidewall with finite thermal conductivity on confined turbulent thermal convection has been investigated using direct numerical simulation. The study is motivated by the observation that the heat flowing through the lateral wall is not always negligible in the low-aspect-ratio cells of several recent experiments. The extra heat flux modifies the temperature boundary conditions of the flow and therefore the convective heat transfer. It has been found that, for usual sidewall thicknesses, the heat travelling from the hot to the cold plates directly through the sidewall is negligible owing to the additional heat exchanged at the lateral fluid/wall interface. In contrast, the modified temperature boundary conditions alter the mean flow yielding significant Nusselt number corrections which, in the low Rayleigh number range, can change the exponent of the Nu vs. Ra power law by 10%.

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

Experimental Investigation of the Acoustic Reflection Coefficient of a Modeled Gas Turbine Impingement Cooling Section

2012 ◽  
Author(s):  
Christoph Jörg ◽  
Michael Wagner ◽  
Thomas Sattelmayer
Keyword(s):  
Reflection Coefficient ◽  
Flow Velocity ◽  
Gas Turbines ◽  
Acoustic Energy ◽  
Quality Data ◽  
Mean Flow ◽  
Impingement Cooling ◽  
Acoustic Reflection ◽  
The Mean ◽  
Mean Flow Velocity

The thermoacoustic stability of gas turbines depends on a balance of acoustic energy inside the engine. While the flames produce acoustic energy, other areas like the impingement cooling system contribute to damping. In this paper, we investigate the damping potential of an annular impingement sleeve geometry embedded into a realistic environment. A cold flow test rig was designed to represent real engine conditions in terms of geometry, and flow situation. High quality data was delivered by six piezoelectric dynamic pressure sensors. Experiments were carried out for different mean flow velocities through the cooling holes. The acoustic reflection coefficient of the impingement sleeve was evaluated at a downstream reference location. Further parameters investigated were the number of cooling holes, and the geometry of the chamber surrounding the impingement sleeve. Experimental results show that the determining parameter for the reflection coefficient is the mean flow velocity through the impingement holes. An increase of the mean flow velocity leads to significantly increased damping, and to low values of the reflection coefficient.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

scholarly journals Estimation of peak discharges of historical floods

2014 ◽  
Vol 11 (5) ◽  
pp. 5463-5485 ◽  
Author(s):  
J. Herget ◽  
T. Roggenkamp ◽  
M. Krell
Keyword(s):  
Flood Frequency ◽  
River Channels ◽  
Sources Of Information ◽  
Mean Flow ◽  
General Outline ◽  
One Dimensional ◽  
Flood Level ◽  
Alternative Approaches ◽  
The Mean ◽  
Generalized Statement

Abstract. There is no doubt, that the hazard assessment of future floods especially under consideration of the recent environmental change can be significantly improved by the consideration of historic flood events. While flood frequency inventories on local, regional and even European scale are already developed and published, the estimation of their magnitudes indicated by discharges is still challenging. Such data are required due to significant human impact on river channels and floodplains though historic flood levels cannot be related to recent ones or recent discharges. Based on own experiences from single local key studies the general outline of an approach to estimate the discharge of the previous flood based on handed down flood level and topographic data is presented. The model for one-dimensional steady flow is based on the empirical Manning equation for the mean flow velocity. Background and potential sources of information, acceptable simplifications and data transformation for each element of the model-equation are explained and discussed. Preliminary experiences on the accuracy of ±10% are documented and potential approaches for the validation of individual estimations given. A brief discussion on benefits and limitations including a generalized statement on alternative approaches closes the review presentation of the approach.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

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