Ranking of Aircraft Fuel-Injectors Regarding Low Frequency Thermoacoustics Based on an Energy Balance Method

2021 ◽  
Author(s):  
André Fischer ◽  
Claus Lahiri
Keyword(s):  
Energy Balance ◽  
Low Frequency ◽  
Network Models ◽  
Operating Conditions ◽  
Balance Method ◽  
Energy Balance Method ◽  
Fuel Injectors ◽  
Thermoacoustic Instabilities ◽  
Aircraft Fuel ◽  
Flame Response

Abstract Many modern low emission combustion systems suffer from thermoacoustic instabilities, which may lead to customer irritation (noise) or engine damages. The prediction of the frequency response of the flame is oftentimes not straightforward, so that it is common practice to measure the flame response in an experiment. The outcome of the measurement is typically a flame transfer-function (FTF), which can be used in low order acoustic network models to represent the flame. This paper applies an alternative criterion to evaluate the potential of the flame to become instable, the flame-amplification factor (FAF). It is based on an energy balance method and can be directly derived from the measured flame-transfer-matrix (FTM). In order to demonstrate this approach two different kerosene-driven aircraft fuel injectors were measured in the Rolls-Royce SCARLET rig in a single-sector RQL-combustor under realistic operating conditions. Here the multi-microphone method has been applied with acoustic forcing from up- and downstream side to determine the FTM. In contrast to the FTF-approach the full FTM data has been post-processed to derive the FAF. The FAF is then successfully used to rank the fuel injectors regarding their low frequency thermo-acoustic behaviour, because it is proportional to amplitudes of self-excited frequencies in FANN-rig (full annular) configuration.

Acoustic Energy Balance During the Onset, Growth and Saturation of Thermoacoustic Instabilities

2020 ◽  
Author(s):  
R. Gaudron ◽  
D. Yang ◽  
A. S. Morgans
Keyword(s):  
Energy Balance ◽  
Network Models ◽  
Acoustic Energy ◽  
Dimensionless Numbers ◽  
Weakly Nonlinear ◽  
Acoustic Damping ◽  
Thermoacoustic Instabilities ◽  
Wide Range ◽  
Acoustic Absorption Coefficient ◽  
Flame Describing Function

Abstract Thermoacoustic instabilities can occur in a wide range of combustors and are prejudicial since they can lead to increased mechanical fatigue or even catastrophic failure. A well-established formalism to predict the onset, growth and saturation of such instabilities is based on acoustic network models. This approach has been successfully employed to predict the frequency and amplitude of limit cycle oscillations in a variety of combustors. However, it does not provide any physical insight in terms of the acoustic energy balance of the system. On the other hand, Rayleigh’s criterion may be used to quantify the losses, sources and transfers of acoustic energy within and at the boundaries of a combustor. However, this approach is cumbersome for most applications because it requires computing volume and surface integrals and averaging over an oscillation cycle. In this work, a new methodology for studying the acoustic energy balance of a combustor during the onset, growth and saturation of thermoacoustic instabilities is proposed. The two cornerstones of this new framework are the acoustic absorption coefficient Δ and the cycle-to-cycle acoustic energy ratio λ, both of which do not require computing integrals. Used along with a suitable acoustic network model, where the flame frequency response is described using the weakly nonlinear Flame Describing Function (FDF) formalism, these two dimensionless numbers are shown to characterize: 1) the variation of acoustic energy stored within the combustor between two consecutive cycles, 2) the acoustic energy transfers occurring at the combustor’s boundaries and 3) the sources and sinks of acoustic energy located within the combustor. The acoustic energy balance of the well-documented Palies burner is then analyzed during the onset, growth and saturation of thermoacoustic instabilities using this new methodology. It is demonstrated that this new approach allows a deeper understanding of the physical mechanisms at play. For instance, it is possible to determine when the flame acts as an acoustic energy source or sink, where acoustic damping is generated, and if acoustic energy is transmitted through the boundaries of the burner.

Dynamics research of Fangzhu’s nanoscale surface

2021 ◽  
pp. 146134842110527
Author(s):  
Pinxia Wu ◽  
Weiwei Ling ◽  
Xiumei Li ◽  
Xichun He ◽  
Liangjin Xie
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Numerical Experiments ◽  
Fractal Model ◽  
Balance Method ◽  
Transform Method ◽  
Energy Balance Method ◽  
Collection Rate ◽  
Fractal Derivative ◽  
Approximate Analytical Solutions

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

scholarly journals A distributed snowmelt prediction model in mountain areas based on an energy balance method

1994 ◽  
Vol 19 ◽  
pp. 107-113 ◽  
Author(s):  
Takeshi Ohta
Keyword(s):  
Energy Balance ◽  
Prediction Model ◽  
Deciduous Forest ◽  
Balance Method ◽  
Evergreen Forest ◽  
Snowmelt Runoff ◽  
Mountain Areas ◽  
Mountain Area ◽  
Energy Balance Method ◽  
Surface Cover

A distributed snowmelt prediction model was developed for a mountain area. Topography of the study area was represented by a digital map. Cells On the map were divided into three surface-cover types; deciduous forest, evergreen forest and deforested area. Snowmelt rates for each cell were calculated by an energy balance method. Meteorological elements were estimated separately in each cell according to topographical characteristics and surface-cover type. Distributions of water equivalent of snow cover were estimated by the model. Snowmelt runoff in the watershed was also simulated by snowmelt rates calculated by the model. The model showed thai the snowmelt period and snowmelt runoff after timber harvests would be about two weeks earlier than under the forest-covered condition.

Technology of Protection Against the Dynamic Effect of Nuclear Pipe Rupture

2017 ◽  
Author(s):  
Feng He ◽  
Feng Yuan ◽  
Honglei Ai ◽  
Xinjun Wang ◽  
Xifeng Lu ◽  
...  
Keyword(s):  
Finite Element ◽  
Energy Balance ◽  
Nuclear Power ◽  
Dynamic Method ◽  
Plastic Hinge ◽  
Dynamic Effect ◽  
Element Model ◽  
High Energy ◽  
Balance Method ◽  
Energy Balance Method

The special safety facilities and important equipment, etc. of the nuclear power plant will be damaged due to the whipping nuclear high-energy piping after the rupture, and more serious further damage will be caused. In this paper, the process and method of protection analysis of the nuclear high-energy piping rupture have been given from four aspects. The four aspects are location of high-energy piping break, the jet thrust, whipping behavior analysis, and protection analysis of whipping. On the basis of the traditional energy balance method, the method is improved by considering the energy absorbed by the plastic hinge of the piping and the change in the direction of the jet thrust. And then, the comparisons among the traditional energy balance method, the improved energy balance method, and the 3-D finite element dynamic method have been carried out. The deformation of the whip limiter analyzed by the traditional energy balance method is 20.31% larger than which analyzed by the improved energy balance method, and the deformation of the whip limiter analyzed by the 3-D finite element dynamic method is 30.59% smaller than which analyzed by the improved energy balance method. For the first time, a 3-D finite element model according to the true arrangement of the pipe and the whip limiter model are built to simulate the process of whipping not in the plane, considering the energy dissipation of the whip limiter. For the pipe whipping not in the plane and protecting against the pipe rupture by whip limiter, there is no good way to carry out the protection analysis of the piping rupture in the past. Now, the problem can be solved by the 3-D finite element dynamic method.

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