The relation between sampling-tube measurements and concentration fluctuations in a turbulent gas jet

Richardson, John M.; Howard, H. C.; Smith, Robert W.

doi:10.1016/s0082-0784(53)80106-2

Cited by 34 publications

(14 citation statements)

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“…Conventionally, two-parameter beta-distributions have been used for scalar mixing models as the natural limits are between zero and unity which is assumed to fit the scalar data. Therefore, information of the mean and variance only is required (Alvani and Fairweather 2002;Bakosi and Ristorcell 2010;Girimaji 1991;Pope 1979;Richardson et al 1953). This assumption at large downstream/radial positions, particularly the upper limit, is unsuitable.…”

Section: Suitability Of the Two-parameter Beta-distributionmentioning

confidence: 99%

Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

Ruggles

2015

Exp Fluids

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used to separate the turbulent and pure air data, and thusly estimate intermittency. Beta-distributions (four parameters) are used to accurately represent the turbulent distribution moments. This combination of measured intermittency and four-parameter beta-distributions constitutes a new, simple approach to model scalar mixing. Comparisons between global moments from the data and moments calculated using the proposed model show excellent agreement. This was attributed to the high quality of the measurements which reduced the width of the correctly identified, noiseaffected pure air distribution, with respect to the turbulent mixing distribution. The ignitability of the atmospheric jet is determined using the flammability factor calculated from both kernel density estimated (KDE) PDFs and PDFs generated using the newly proposed model. Agreement between contours from both approaches is excellent. Ignitability of the under-expanded jet is also calculated using KDE PDFs. Contours are compared with those calculated by applying the atmospheric model to the under-expanded jet. Once again, agreement is excellent. This work demonstrates that self-similar scalar mixing statistics and ignitability of atmospheric jets can be accurately described by the proposed model. This description can be applied with confidence to under-expanded jets, which are more realistic of leak and fuel injection scenarios.Abstract This paper presents improved statistical insight regarding the self-similar scalar mixing process of atmospheric hydrogen jets and the downstream region of underexpanded hydrogen jets. Quantitative planar laser Rayleigh scattering imaging is used to probe both jets. The self-similarity of statistical moments up to the sixth order (beyond the literature established second order) is documented in both cases. This is achieved using a novel self-similar normalization method that facilitated a degree of statistical convergence that is typically limited to continuous, pointbased measurements. This demonstrates that image-based measurements of a limited number of samples can be used for self-similar scalar mixing studies. Both jets exhibit the same radial trends of these moments demonstrating that advanced atmospheric self-similarity can be applied in the analysis of under-expanded jets. Self-similar histograms away from the centerline are shown to be the combination of two distributions. The first is attributed to turbulent mixing. The second, a symmetric Poisson-type distribution centered on zero mass fraction, progressively becomes the dominant and eventually sole distribution at the edge of the jet. This distribution is attributed to shot noise-affected pure air measurements, rather than a diffusive superlayer at the jet boundary. This conclusion is reached after a rigorous measurement uncertainty analysis and inspection of pure air data collected with each hydrogen data set. A threshold based upon the measurement noise analysis is

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Section: Suitability Of the Two-parameter Beta-distributionmentioning

confidence: 99%

Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

Ruggles

2015

Exp Fluids

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“…The instantaneous mass fraction of fuel, oxidizer and products is calculated from (1) the mean local value of f, solved for by the transport equation, (2) the local value of the variance of f, which accounts for fluctuation produced by turbulence, and (3) from the ''presumed'' probability density function (Eq. 16 in the Appendix) for f (see Richardson et al 1953, for details). The heat released by the progress of the chemical reaction is then calculated from the enthalpy balance.…”

Section: Combustion Modelmentioning

confidence: 99%

Computing flow, combustion, heat transfer and thrust in a micro-rocket via hierarchical problem decomposition

Campolo

Andreoli

Soldati

2008

Microfluid Nanofluid

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This work describes the methodology developed to optimize the design of the combustion chamber, the thrust generating nozzle and the cooling system of a micro-rocket using numerical simulations. The coupling between combustion, subsonic/sonic/supersonic flow transition and heat transfer inside the micro-rocket is analysed using a problem decomposition strategy and state-of-the-art numerical techniques. First, the design of the thrust-generating nozzle is optimized, then, the mixing performances and the combustion efficiency are evaluated, finally, the design of the cooling system is verified calculating the heat transfer from the hot gases to the solid shell and to the cooling fluid. Results show that sub-optimal micro-rocket design alternatives can be easily identified through self-validated numerical analyses. In this way, the number of time consuming and costly experiments required for prototypes qualification in the lab can be reduced, focusing the tests on the limited set of sub-optimal alternatives identified by numerical simulations, thus speeding up the development of new devices

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“…The idea of an assumed distribution to statistically describe one or several scalars for application to turbulent combustion has been studied by different authors, 51 although not in a LES context until more recently. Several choices have been made: a Gaussian profile, 52 a beta-PDF, 53 a density function composed of a uniform distribution with two delta functions at the limits 0 and 1, 54 or a clipped Gaussian. 55 All these density functions are based on the first two moments.…”

Section: Sensitivity Of the Fdf Approach To The Assumed Distributionmentioning

confidence: 99%

Reconstruction subgrid models for nonpremixed combustion

2003

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Large-eddy simulation of combustion problems involves highly nonlinear terms that, when filtered, result in a contribution from subgrid fluctuations of scalars, Z, to the dynamics of the filtered value. This subgrid contribution requires modeling. Reconstruction models try to recover as much information as possible from the resolved field Z , based on a deconvolution procedure to obtain an intermediate field Z M . The approximate reconstruction using moments ͑ARM͒ method combines approximate reconstruction, a purely mathematical procedure, with additional physics-based information required to match specific scalar moments, in the simplest case, the Reynolds-averaged value of the subgrid variance. Here, results from the analysis of the ARM model in the case of a spatially evolving turbulent plane jet are presented. A priori and a posteriori evaluations using data from direct numerical simulation are carried out. The nonlinearities considered are representative of reacting flows: power functions, the dependence of the density on the mixture fraction ͑relevant for conserved scalar approaches͒ and the Arrhenius nonlinearity ͑very localized in Z space͒. Comparisons are made against the more popular beta probability density function ͑PDF͒ approach in the a priori analysis, trying to define ranges of validity for each approach. The results show that the ARM model is able to capture the subgrid part of the variance accurately over a wide range of filter sizes and performs well for the different nonlinearities, giving uniformly better predictions than the beta PDF for the polynomial case. In the case of the density and Arrhenius nonlinearities, the relative performance of the ARM and traditional PDF approaches depends on the size of the subgrid variance with respect to a characteristic scale of each function. Furthermore, the sources of error associated with the ARM method are considered and analytical bounds on that error are obtained.

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The relation between sampling-tube measurements and concentration fluctuations in a turbulent gas jet

Cited by 34 publications

References 0 publications

Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

Computing flow, combustion, heat transfer and thrust in a micro-rocket via hierarchical problem decomposition

Reconstruction subgrid models for nonpremixed combustion

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