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Comment on 'Conformal invariance of the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence'

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2021年第43期54卷

作者： Frewer, Michael Khujadze, George Univ Siegen Chair Fluid Mech D-57068 Siegen Germany

The recent claim by Grebenev et al (2017 J. Phys. A: Math. Theor. 50 435502) that the inviscid 2D Lundgren-Monin-Novikov (LMN) equations on a zero-vorticity characteristic naturally would reveal local conformal invariance when only analyzing these by means of a classical Lie-group symmetry approach, is invalid. To note is that within this comment the (possible) existence of conformal invariance in 2D turbulence is not questioned, only the conclusion as given by Grebenev et al and their approach how this invariance was derived is criticized and refuted herein. In fact, the algebraic derivation of conformal invariance of the 2D LMN vorticity equations in Grebenev et al (2017 J. Phys. A: Math. Theor. 50 435502) is flawed. Its correction will reveal a globally constant scaling in the fields, instead of a local one as claimed.

关键词： Lie groups Lie symmetries conformal invariance symmetry breaking probability density functions integro differential equations turbulence

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A Computationally Efficient Approach for Stochastic Reachability Set Analysis

A Computationally Efficient Approach for Stochastic Reachabi...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Jain, Amit Gueho, Damien Singla, Puneet Penn State Univ Dept Aerosp Engn State Coll PA 16802 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

The reachability set is defined as the collection of all states which can be traversed from arbitrary initial conditions due to the application of admissible control. Three different probabilistic approaches to compute the reachability sets for a class of discrete time nonlinear systems is discussed. The main idea of the probabilistic approach is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. In the first approach, the computation of the state density function due to variation in control input at each time is made tractable by computing the M-fold convolution of state density function at each time. To overcome the significant challenge of taking multi-dimension convolution of state density function, the second approach computes the probability density function using the Principle of Maximum Entropy (PME). The third approach utilizes the Conjugate Unscented Transform (CUT) method to curtail the combinatorial growth of samples. Finally, three numerical example problems are considered to show the efficacy and utility of the proposed ideas.

关键词： probability density functions Computing Principle of Maximum Entropy Nonlinear Systems Aeroplane Unmanned Aerial Vehicle Autonomous Systems Lagrange Multipliers Optimal Control Broyden Fletcher Goldfarb Shanno

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Global Sensitivity Analysis of Shockwave Location during Transonic Flight

Global Sensitivity Analysis of Shockwave Location during Tra...

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AIAA Aviation Forum

作者： Robinson, Brandon Yuan, Weixing Poirel, Dominique Carleton Univ Dept Civil & Environm Engn Ottawa ON K1S 5B6 Canada Natl Res Council NRC Canada Aerosp Res Ctr Ottawa ON K1A 0R6 Canada Royal Mil Coll RMC Canada Dept Mech & Aerosp Engn Kingston ON K7K 7B4 Canada

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

This study was inspired by the significant variation that may be observed in the numerical analysis of the pressure distribution over airfoils in transonic flight conditions. Our ability to predict the location of the formation of localized shockwaves is directly dependent on the accuracy of the pressure distributions obtained from the computational fluid dynamics (CFD) simulations. In dynamic aeroelasticity, the location of these shockwaves has a significant influence on flutter predictions. This paper provides a qualitative study of the sensitivity of the pressure coefficient (C-p) to certain parameters of interest, before delving into a formal global sensitivity analysis (GSA). The GSA is performed by constructing a polynomial chaos expansion (PCE) surrogate model of the output, namely the shockwave location.

关键词： Sensitivity Analysis Transonic Flight Computational Fluid Dynamics Simulation Numerical Analysis Reynolds Averaged Navier Stokes Dynamic Aeroelasticity Angle of Attack Aerodynamic Configurations Wind Tunnel Walls probability density functions

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Expert Decision Support System for Aeroacoustic Classification from Deconvolved Beamforming Maps

Expert Decision Support System for Aeroacoustic Classificati...

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AIAA Aviation Forum

作者： Goudarzi, A. Spehr, C. Herbold, S. German Aerosp Ctr Gottingen Germany Karlsruhe Inst Technol (KIT Inst AIFB Karlsruhe Germany

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

We present an expert decision support system for time-invariant aeroacoustic source classification from deconvolved beamforming maps and results based on scaled airframe half-model wind tunnel measurements. The system consists of three steps: the identification of acoustic sources from the deconvolved maps, the calculation of their acoustic properties, and the clustering of the sources based on their properties. In this paper, we present and compare two methods to identify and extract source spectra from the beamforming maps. The first relies on the spatial normal distribution of CLEAN-SC results for aeroacoustic broadband sources. The second uses hierarchical clustering methods. We propose a variety of aeroacoustic features that capture the characteristics of the spectra while being independent of absolute parameters such as the Mach number. Based on these features the aeroacoustic sources are clustered using unsupervised machine learning methods to determine similar or atypical behavior. This expert support system helps aeroacoustic specialists in classifying the identified sources to support them in analyzing their typical behavior and identifying spurious sources.

关键词： Decision Support System Mach Numbers Airframes Wind Tunnel Models Acoustic Properties Gaussian Mixture Models Angle of Attack Power Spectral density Karman Vortex Street probability density functions

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Tomographic Time-Resolved Laser-Induced Incandescence

Tomographic Time-Resolved Laser-Induced Incandescence

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Hall, Elise M. Halls, Benjamin R. Richardson, Daniel R. Guildenbecher, Daniel R. Cenker, Emre Paciaroni, Megan E. Sandia Natl Labs Diagnost Sci & Engn Albuquerque NM 87125 USA Saudi Aramco Dhahran Saudi Arabia Benedictine Coll Elect Engn Atchison KS 66002 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

Three ultra-high-speed, 10 MHz, cameras imaged the time-resolved decay of laser-induced incandescence (LII) from soot in a turbulent non-premixed ethylene jet flame. Cameras were equipped with a stereoscope allowing each CMOS array to capture two separate views of the flame. The resulting six views were reconstructed into a volumetric soot decay series using commercially available DaVis tomographic software by LaVision. Primary soot particle sizes were estimated from the decay time history on a per voxel basis by comparing measured signals to an LII model. Experimentally quantified soot particle sizes agree with existing predictions and previous measurements.

关键词： Lasers Combustion Process Band Pass Filter Laser Energy Optical Properties probability density functions Image Processing 3D Imaging

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Centralized Autonomous Relative Navigation of Multiple Spacecraft Around Small Bodies

Centralized Autonomous Relative Navigation of Multiple Space...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Silvestrini, Stefano Capannolo, Andrea Piccinin, Margherita Lavagna, Michele Fernandez, Jesus Gil Politecn Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy European Space Agcy ESTEC ESA ESTEC Keplerlaan 1 NL-2201 AZ Noordwijk Netherlands

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

This paper presents an on-board, centralized autonomous navigation algorithm able to reconstruct the trajectories of a fleet of CubeSats relative to an asteroid binary system. The algorithm is executed on-board the main spacecraft, which takes relative measurements using a narrow optical camera and an additional relative measurement, being inter satellite ranging in this paper. The image processing algorithm detects and tracks the CubeSats, deriving line-of-sight measurements. A non-linear estimation filter is employed to reconstruct the trajectory. The algorithm is tested using high-fidelity trajectory simulator and synthetic images generation routines.

关键词： Spacecrafts Satellites Asteroids Autonomous Navigation Image Processing Unscented Kalman Filter Hyperbolic Trajectories probability density functions Vision Based Navigation Algorithm Performance

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Uncertainty Quantification of Ship Resistance via Multi-Index Stochastic Collocation and Radial Basis Function Surrogates: A Comparison

Uncertainty Quantification of Ship Resistance via Multi-Inde...

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AIAA Aviation Forum

作者： Piazzola, Chiara Tamellini, Lorenzo Pellegrini, Riccardo Brogli, Riccardo Serani, Andrea Diez, Matteo CNR Inst Appl Math & Informat Technol E Magenes CNR IMATI Pavia Italy CNR CNR INM Inst Marine Engn Rome Italy

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

This paper presents a comparison of two methods for the forward uncertainty quantification (UQ) of complex industrial problems. Specifically, the performance of Multi-Index Stochastic Collocation (MISC) and adaptive multi-fidelity Stochastic Radial Basis functions (SRBF) surrogates is assessed for the UQ of a roll-on/roll-off passengers ferry advancing in calm water and subject to two operational uncertainties, namely the ship speed and draught. The estimation of expected value, standard deviation, and probability density function of the (model-scale) resistance is presented and discussed obtained by multi-grid Reynolds averaged Navier-Stokes (RANS) computations. Both MISC and SRBF use as multi-fidelity levels the evaluations on different grid levels, intrinsically employed by the RANS solver for multi-grid acceleration;four grid levels are used here, obtained as isotropic coarsening of the initial finest mesh. The results suggest that MISC could be preferred when only limited data sets are available. For larger data sets both MISC and SRBF represent a valid option, with a slight preference for SRBF, due to its robustness to noise.

关键词： probability density functions Reynolds Averaged Navier Stokes Surrogate Model Numerical Simulation Particle Swarm Optimization Computer Aided Design Aero Military Vehicles Mesh Generation Froude Number Computing

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Analytic Sensitivities of Stochastic and Statistical Moments for Uncertainty Quantification

Analytic Sensitivities of Stochastic and Statistical Moments...

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AIAA Aviation Forum

作者： Forster, Edwin E. Aerosp Syst Directorate Wright Patterson AFB OH 45433 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Stochastic analysis of a function of distributed variables may provide essential information for Uncertainty Quantification (UQ) in the form of raw and central moments including, but not limited to: mean, variance, skewness, and kurtosis. The statistical analysis of a population that represents function evaluations of variates, such as the result of a Monte Carlo simulation, may be performed when the function is not easily defined, as in a "black box" operation. The distribution shape or stochastic quantities associated with the variable or variate are often defined inputs, and reliability analysis in the form of probability for failure and most probable point of failure are often the desired output. Analytic partial derivatives of stochastic moments of functions of distributed variables with respect to stochastic inputs (variable mean or variance) can be accomplished when the function is known and operations for Expectation can be performed analytically. Similarly, sensitivities of statistical moments of functions of variates, represented as populations, with respect to the variate statistical quantities (mean or variance) can also be determined analytically. The resulting errors in predicting analytic sensitivities of statistical parameters are dependent upon the representation of the population to accurately capture the distributed variable behavior. A foundational problem of a polynomial function shall be examined to compare analytic sensitivities of stochastic quantities and analytic sensitivities of statistical parameters. Errors in predictions performed on populations formulated through quadrature (Gauss-Legendre) shall be compared to predictions performed on populations composed of pseudo-random samples. Sensitivity analysis of stochastic parameters for UQ of Finite Element Analysis (FEA) of canonical structure problems shall also be performed to better illustrate the potential benefits in future design optimization.

关键词： probability density functions Finite Element Analysis Sensitivity Analysis Monte Carlo Simulation Black Box Factor of Safety Trusses Structural Optimization Aerospace Engineering Binomial Theorem

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Propagating and Combining Aleatory Uncertainties characterized by Continuous Random Variables and Sparse Discrete Realizations from Random functions

Propagating and Combining Aleatory Uncertainties characteriz...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Romero, Vicente J. Sandia Natl Labs V&V UQ Credibil Proc Dept POB 5800 Albuquerque NM 87185 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

This paper presents a practical methodology for propagating and combining the effects of random variations of several continuous scalar quantities and several random-function quantities affecting the failure pressure of a heated pressurized vessel. The random functions are associated with stress-strain curve test-to-test variability in replicate material strength tests (uniaxial tension tests) on nominally identical material specimens. It is demonstrated how to effectively propagate the curve-to-curve discrete variations and appropriately account for the small sample size of functional data realizations. This is coordinated with the propagation of aleatory variability described by uncertainty distributions for continuous scalar quantities of pressure-vessel wall thickness, weld depth, and thermal-contact factor. Motivated by the high expense of the pressure vessel simulations of heating, pressurization, and failure, a simple dimension- and order-adaptive polynomial response surface approach is used to propagate effects of the random variables and enable uncertainty estimates on the error contributed by using the surrogate model. Linear convolution is used to aggregate the resultant aleatory uncertainty from the parametrically propagated random variables with an appropriately conservative probability distribution of aleatory effects from propagating the multiple stress-strain curves for each material. The response surface constructions, Monte Carlo sampling of them for uncertainty propagation, and linear sensitivity analysis and convolution procedures, are demonstrated with standard EXCEL spreadsheet functions (no special software needed).

关键词： Stress Strain Curve probability density functions Sensitivity Analysis Surrogate Model Computational Heat Transfer Structural Simulation Structural Response Strength of Materials Thermal Modeling Materials Testing

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Large Eddy Simulation of Sooting Turbulent Non-Premixed Mixing Layers

Large Eddy Simulation of Sooting Turbulent Non-Premixed Mixi...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Karpe, S. Menon, S. Ranjan, R. Georgia Inst Technol Sch Aerosp Engn 270 Ferst Dr Atlanta GA 30332 USA Univ Tennessee Chattanooga Dept Mech Engn 615 McCallie Ave Chattanooga TN 37403 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

As soot is one of the major pollutants impacting environmental welfare, accurate estimation about its evolution from combustion processes is a necessity to design eco-friendly combustion engines. However, complex interactions between fluid dynamics, soot chemistry and heat transfer exacerbate the task of quantitative estimations of soot in a practical scenario. Therefore, efficient modeling approaches need to be developed that will account for essential physical processes such as nucleation, coagulation and agglomeration etc. observed during the soot formation and can be easily coupled with the CFD solver in a computationally tractable manner. In the present study, a higher order model for soot dynamics is presented that uses a 5 moment based method of moments approach with Lagrangian interpolative closure (MOMIC) so that no prior knowledge of the particles distribution is required. The present model accounts for nucleation, coagulation and surface growth of soot particles and is coupled with well established CFD solver. The developed LES-MOMIC framework is then used to study initial stages of soot formation in a temporally evolving turbulent mixing layers.

关键词： Lagrangian Particle Tracking Laminar Flame Speed Turbulent Diffusion Turbulence Intensity Heat Transfer Shear Layers Chemical Kinetics Compressible Flow Turbulent Reacting Flow probability density functions

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