Linearized unsteady flame surface approximation result in complex notation

AIAA Journal ◽  
1983 ◽  
Vol 21 (12) ◽  
pp. 1770-1772 ◽  
Author(s):  
T. S. Sheshadri
Keyword(s):  
Flame Surface ◽  
Approximation Result ◽  
Surface Approximation ◽  
Unsteady Flame

scholarly journals Fitting Terrestrial Laser Scanner Point Clouds with T-Splines: Local Refinement Strategy for Rigid Body Motion

2021 ◽  
Vol 13 (13) ◽  
pp. 2494
Author(s):  
Gaël Kermarrec ◽  
Niklas Schild ◽  
Jan Hartmann
Keyword(s):  
Point Cloud ◽  
Goodness Of Fit ◽  
Laser Scanner ◽  
Point Clouds ◽  
Statistical Testing ◽  
Computational Time ◽  
Terrestrial Laser Scanner ◽  
Reference Surface ◽  
Local Refinement ◽  
Surface Approximation

T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.

scholarly journals Modelling of Conditional Scalar Dissipation Rate in Turbulent Premixed Combustion

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 26 ◽  
Author(s):  
Shokri Amzin ◽  
Mariusz Domagała
Keyword(s):  
Dissipation Rate ◽  
Premixed Flames ◽  
Moment Closure ◽  
Navier Stokes ◽  
Scalar Dissipation ◽  
Flame Surface ◽  
Scalar Dissipation Rate ◽  
Turbulent Premixed Flames ◽  
Conditional Moment ◽  
Turbulent Premixed

In turbulent premixed flames, for the mixing at a molecular level of reactants and products on the flame surface, it is crucial to sustain the combustion. This mixing phenomenon is featured by the scalar dissipation rate, which may be broadly defined as the rate of micro-mixing at small scales. This term, which appears in many turbulent combustion methods, includes the Conditional Moment Closure (CMC) and the Probability Density Function (PDF), requires an accurate model. In this study, a mathematical closure for the conditional mean scalar dissipation rate, <Nc|ζ>, in Reynolds, Averaged Navier–Stokes (RANS) context is proposed and tested against two different Direct Numerical Simulation (DNS) databases having different thermochemical and turbulence conditions. These databases consist of lean turbulent premixed V-flames of the CH4-air mixture and stoichiometric turbulent premixed flames of H2-air. The mathematical model has successfully predicted the peak and the typical profile of <Nc|ζ> with the sample space ζ and its prediction was consistent with an earlier study.

NORMAL FORMS FOR FUZZY LOGIC — AN APPLICATION OF KOLMOGOROV’S THEOREM

1996 ◽  
Vol 04 (04) ◽  
pp. 331-349 ◽  
Author(s):  
VLADIK KREINOVICH ◽  
HUNG T. NGUYEN ◽  
DAVID A. SPRECHER
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Normal Form ◽  
Normal Forms ◽  
Approximation Property ◽  
Universal Approximation ◽  
Approximation Result ◽  
Logical Operations ◽  
Kolmogorov's Theorem

This paper addresses mathematical aspects of fuzzy logic. The main results obtained in this paper are: 1. the introduction of a concept of normal form in fuzzy logic using hedges; 2. using Kolmogorov’s theorem, we prove that all logical operations in fuzzy logic have normal forms; 3. for min-max operators, we obtain an approximation result similar to the universal approximation property of neural networks.

A numerical study of the transition of jet diffusion flames

1990 ◽  
Vol 431 (1882) ◽  
pp. 301-314 ◽  
Keyword(s):  
Reynolds Number ◽  
Diffusion Coefficient ◽  
Large Scale ◽  
Numerical Study ◽  
Small Scale ◽  
Surface Model ◽  
Flame Surface ◽  
Transition Mechanism ◽  
Air Stream ◽  
Scale Fluctuation

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

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.

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