scholarly journals The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

2021 ◽  
Author(s):  
Meysam Sahafzadeh
Keyword(s):  
Time Scales ◽  
Equivalence Ratio ◽  
Transfer Functions ◽  
Premixed Flames ◽  
Scalar Fields ◽  
Individual Species ◽  
Response Analysis ◽  
Stretch Rate ◽  
Non Linear ◽  
Linear Behaviour

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

scholarly journals The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

2021 ◽  
Author(s):  
Meysam Sahafzadeh
Keyword(s):  
Time Scales ◽  
Equivalence Ratio ◽  
Transfer Functions ◽  
Premixed Flames ◽  
Scalar Fields ◽  
Individual Species ◽  
Response Analysis ◽  
Stretch Rate ◽  
Non Linear ◽  
Linear Behaviour

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

scholarly journals Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

2021 ◽  
Author(s):  
Nilanjan Chakraborty ◽  
Alexander Herbert ◽  
Umair Ahmed ◽  
Hong G. Im ◽  
Markus Klein
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Premixed Flames ◽  
Turbulent Premixed Flames ◽  
Reaction Progress ◽  
Progress Variable ◽  
Stretch Rate ◽  
Non Linear ◽  
Displacement Speed ◽  
Curvature Dependence

AbstractA three-dimensional Direct Numerical Simulation (DNS) database of statistically planar $$H_{2} -$$ H 2 - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed $$S_{d}^{*}$$ S d ∗ . It has been found that the correlation between $$S_{d}^{*}$$ S d ∗ and curvature remains negative and a significantly non-linear interrelation between $$S_{d}^{*}$$ S d ∗ and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of $$S_{d}^{*}$$ S d ∗ but allows for a non-linear stretch rate dependence of $$S_{d}^{*}$$ S d ∗ , has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express $$S_{d}^{*}$$ S d ∗ as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of $$S_{d}^{*}$$ S d ∗ more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of $$S_{d}^{*}$$ S d ∗ , has been shown to exhibit promising predictions of $$S_{d}^{*}$$ S d ∗ for all cases considered here.

scholarly journals Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

2021 ◽  
Author(s):  
Meysam Sahafzadeh ◽  
Seth B. Dworkin ◽  
Larry W. Kostiuk
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Time Scale ◽  
Transfer Functions ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Turbulent Flames ◽  
Response Analysis ◽  
Phase Lag

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

scholarly journals Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

2021 ◽  
Author(s):  
Meysam Sahafzadeh ◽  
Seth B. Dworkin ◽  
Larry W. Kostiuk
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Time Scale ◽  
Transfer Functions ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Turbulent Flames ◽  
Response Analysis ◽  
Phase Lag

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

scholarly journals Flame Transfer Functions and Dynamics of a Closely Confined Premixed Bluff Body Stabilised Flame With Swirl

2020 ◽  
Author(s):  
Håkon T. Nygård ◽  
Nicholas A. Worth
Keyword(s):  
Time Scales ◽  
Equivalence Ratio ◽  
Bluff Body ◽  
Transfer Functions ◽  
Time Lag ◽  
Operating Conditions ◽  
Flame Height ◽  
Time Lags ◽  
Temporal Shift ◽  
Wide Range

Abstract The Flame Transfer Function (FTF) and flame dynamics of a single, highly swirled, closely confined, premixed flame is studied over a wide range of operating conditions at a fixed perturbation level at the dump plane. The equivalence ratio and bulk velocity are varied in order to examine the important ratio of flame height to velocity in scaling the flame response function. The enclosure geometry is kept constant, and therefore due to the close confinement and varying flame height, strong flame-wall interactions are present for some operating conditions. The effect of these interactions on the FTF due to changes in the “relative” or “effective confinement” of the flame can therefore be studied. When the equivalence ratio is sufficiently high, and therefore the effective confinement sufficiently small, modulations, or dips, in the gain and phase of the FTF are observed, due to interference of the perturbations created at the swirler and at the dump plane. Due to the small length scales and relatively high velocities in the current configuration, the dip is at a high frequency and spans a wide range of frequencies compared to similar studies which have previously identified similar phenomena. It is also observed that when the equivalence ratio was decreased, increasing the effective confinement, a critical point is reached where the modulations are suppressed. This is linked to a temporal shift in the heat release rate at the downstream location where the flame impinges on the combustion chamber walls during the oscillation cycle. The shift causes a decrease in the expected level of interference, demonstrating that the effective confinement is an important parameter to consider for the nature of the FTF response. Additionally, a Distributed Time Lag (DTL) model with two distinct time lags, capturing the swirler perturbations and the perturbations at the inlet, is successfully applied to the FTFs. The model provides a simple way to accurately capture the two dominant time scales in the problem without the need of prior knowledge of the cause of the perturbations, and a simple expression to recreate the complex valued FTF. In addition the model also provides insight into the time scales of the problem, demonstrating in the current work that time scales recovered from the DTL analysis are offset from simple Strouhal number scaling, due to the effects of increasing effective confinement.

scholarly journals Self-consistent method to extract non-linearities from pulsating star light curves – I. Combination frequencies

2020 ◽  
Vol 498 (1) ◽  
pp. 1194-1204
Author(s):  
M Lares-Martiz ◽  
R Garrido ◽  
J Pascual-Granado
Keyword(s):  
Transfer Functions ◽  
Volterra Series ◽  
Power Spectra ◽  
Light Curves ◽  
Stellar Structure ◽  
Mode Identification ◽  
Driving Mechanisms ◽  
Non Linear ◽  
Linear Behaviour ◽  
Combination Frequencies

ABSTRACT Stellar pulsation is a common phenomenon and is sustained because of coherent driving mechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based.

Frequency Response Analysis for Dynamic Model Identification and Control of a Ducted Fan Aerial Vehicle in Hover

2013 ◽  
Vol 332 ◽  
pp. 56-61 ◽  
Author(s):  
Meysam Effati ◽  
Afshin Banazadeh
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Transfer Functions ◽  
Complex Dynamics ◽  
Model Identification ◽  
Response Analysis ◽  
Ducted Fan ◽  
Power Spectral ◽  
Modern Engineering ◽  
Non Linear

System Identification is a key technology for the development and integration of modern engineering systems including unconventional flying vehicles. These systems are highly parametric with complex dynamics and nonlinearities. Ducted fans are special class of these vehicles that can take off vertically, hover and cruise at very low speed. In this paper, an exact equivalent linear system is found from the non-linear dynamic model of a ducted fan by use of frequency response identification. Here, power spectral density analysis is performed, using CIFER software, to evaluate the input-output responses in hover and to derive the transfer functions based on the coherence criterion. Then, PID controllers are designed by utilizing the identified transfer functions and the performance characteristics of the controllers are evaluated in fully non-linear simulation of the system.

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