scholarly journals On the Interpretation and Scope of the V&V 20 Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer

2020 ◽  
Author(s):  
L. Eça ◽  
K. Dowding ◽  
P. J. Roache
Keyword(s):  
Parameter Uncertainty ◽  
Solid Mechanics ◽  
Model Error ◽  
Parameter Uncertainties ◽  
Figures Of Merit ◽  
Validation Procedure ◽  
Degree Of Confidence ◽  
The Difference ◽  
Experimental Values ◽  
Quantities Of Interest

Abstract The goal of this paper is to summarize and clarify the scope and interpretation of the validation procedure presented in the V&V20-2009 ASME Standard. In V&V20-2009, validation is an assessment of the model error, without regard to the assessment satisfying validation requirements. Therefore, validation is not considered as a pass/fail exercise. The purpose of the validation procedure is the estimation of the accuracy of a mathematical model for specified validation variables (also known as quantities of interest, system responses or figures of merit) at a specified validation point for cases in which the conditions of the actual experiment are simulated. The proposed procedure can be applied to variables defined by a scalar. For the sake of clarity, the paper reiterates the development and assumptions behind the V&V20-2009 procedure that requires the knowledge of the experimental values D and simulation values S at the set point and an estimate of the experimental, numerical and parameter uncertainties. The difference E between S and D is the centre of the interval that should contain the model error (with a certain degree of confidence) and the width of the interval is obtained from the validation uncertainty that is a consequence of the combination of the experimental, numerical and parameter uncertainties. The paper presents the alternatives to address parameter uncertainty and expands upon the interpretation of the final result. The paper also includes two examples demonstrating the application of the V&V20-2009 validation procedure including one problem from V&V10.1-2012 on solid mechanics.

Robust Optimization With Mixed Interval and Probabilistic Parameter Uncertainties, Model Uncertainty, and Metamodeling Uncertainty

2019 ◽  
Author(s):  
Yanjun Zhang ◽  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Real World ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Optimization Problems ◽  
Probability Distributions ◽  
Parameter Uncertainties ◽  
True Value ◽  
Uncertainty Model ◽  
The Difference

Abstract Various types of uncertainties, such as parameter uncertainty, model uncertainty, metamodeling uncertainty may lead to low robustness. Parameter uncertainty can be either epistemic or aleatory in physical systems, which have been widely represented by intervals and probability distributions respectively. Model uncertainty is formally defined as the difference between the true value of the real-world process and the code output of the simulation model at the same value of inputs. Additionally, metamodeling uncertainty is introduced due to the usage of metamodels. To reduce the effects of uncertainties, robust optimization (RO) algorithms have been developed to obtain solutions being not only optimal but also less sensitive to uncertainties. Based on how parameter uncertainty is modeled, there are two categories of RO approaches: interval-based and probability-based. In real-world engineering problems, both interval and probabilistic parameter uncertainties are likely to exist simultaneously in a single problem. However, few works have considered mixed interval and probabilistic parameter uncertainties together with other types of uncertainties. In this work, a general RO framework is proposed to deal with mixed interval and probabilistic parameter uncertainties, model uncertainty, and metamodeling uncertainty simultaneously in design optimization problems using the intervals-of-statistics approaches. The consideration of multiple types of uncertainties will improve the robustness of optimal designs and reduce the risk of inappropriate decision-making, low robustness and low reliability in engineering design. Two test examples are utilized to demonstrate the applicability and effectiveness of the proposed RO approach.

The metachor as a characteristic of the association of electrolytes in aqueous solutions

1984 ◽  
Vol 49 (5) ◽  
pp. 1061-1078 ◽  
Author(s):  
Jiří Čeleda ◽  
Stanislav Škramovský
Keyword(s):  
Aqueous Solutions ◽  
Apparent Volume ◽  
Solutions Of Electrolytes ◽  
Molal Volumes ◽  
The Difference ◽  
High Concentrations ◽  
Experimental Values ◽  
Suitable Characteristic ◽  
Association Of Ions ◽  
Very High

Based on the earlier paper introducing a concept of the apparent parachor of a solute in the solution, we have eliminated in the present work algebraically the effect which is introduced into this quantity by the additivity of the apparent molal volumes. The difference remaining from the apparent parachor after substracting the contribution corresponding to the apparent volume ( for which the present authors suggest the name metachor) was evaluated from the experimental values of the surface tension of aqueous solutions for a set of 1,1-, 1,2- and 2,1-valent electrolytes. This difference showed to be independent of concentration up to the very high values of the order of units mol dm-3 but it was directly proportional to the number of the free charges (with a proportionality factor 5 ± 1 cm3 mol-1 identical for all studied electrolytes). The metachor can be, for this reason, a suitable characteristic for detection of the association of ions and formation of complexes in the solutions of electrolytes, up to high concentrations where other methods are failing.

scholarly journals Figures of merit for stellarators near the magnetic axis

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Matt Landreman
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Axis ◽  
Configuration Design ◽  
New Paradigm ◽  
First Order ◽  
Figures Of Merit ◽  
Minor Radius ◽  
Error Field ◽  
Quantities Of Interest

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

scholarly journals The Mechanical Properties and Damage Evolution of UHPC Reinforced with Glass Fibers and High-Performance Polypropylene Fibers

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2455
Author(s):  
Jiayuan He ◽  
Weizhen Chen ◽  
Boshan Zhang ◽  
Jiangjiang Yu ◽  
Hang Liu
Keyword(s):  
Mechanical Properties ◽  
Glass Fiber ◽  
Damage Evolution ◽  
High Performance ◽  
High Performance Concrete ◽  
Glass Fibers ◽  
Ultra High Performance Concrete ◽  
Concrete Damaged Plasticity ◽  
The Difference ◽  
Experimental Values

Due to the sharp and corrosion-prone features of steel fibers, there is a demand for ultra-high-performance concrete (UHPC) reinforced with nonmetallic fibers. In this paper, glass fiber (GF) and the high-performance polypropylene (HPP) fiber were selected to prepare UHPC, and the effects of different fibers on the compressive, tensile and bending properties of UHPC were investigated, experimentally and numerically. Then, the damage evolution of UHPC was further studied numerically, adopting the concrete damaged plasticity (CDP) model. The difference between the simulation values and experimental values was within 5.0%, verifying the reliability of the numerical model. The results indicate that 2.0% fiber content in UHPC provides better mechanical properties. In addition, the glass fiber was more significant in strengthening the effect. Compared with HPP-UHPC, the compressive, tensile and flexural strength of GF-UHPC increased by about 20%, 30% and 40%, respectively. However, the flexural toughness indexes I5, I10 and I20 of HPP-UHPC were about 1.2, 2.0 and 3.8 times those of GF-UHPC, respectively, showing that the toughening effect of the HPP fiber is better.

Gas pipeline leakage detection in the presence of parameter uncertainty using robust extended Kalman filter

2021 ◽  
pp. 014233122198911
Author(s):  
Mohadese Jahanian ◽  
Amin Ramezani ◽  
Ali Moarefianpour ◽  
Mahdi Aliari Shouredeli
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Parameter Uncertainty ◽  
Oil And Gas ◽  
Estimation Error ◽  
Real Data ◽  
Gas Pipeline ◽  
Pipeline System ◽  
Parameter Uncertainties ◽  
Simulation Results

One of the most significant systems that can be expressed by partial differential equations (PDEs) is the transmission pipeline system. To avoid the accidents that originated from oil and gas pipeline leakage, the exact location and quantity of leakage are required to be recognized. The designed goal is a leakage diagnosis based on the system model and the use of real data provided by transmission line systems. Nonlinear equations of the system have been extracted employing continuity and momentum equations. In this paper, the extended Kalman filter (EKF) is used to detect and locate the leakage and to attenuate the negative effects of measurement and process noises. Besides, a robust extended Kalman filter (REKF) is applied to compensate for the effect of parameter uncertainty. The quantity and the location of the occurred leakage are estimated along the pipeline. Simulation results show that REKF has better estimations of the leak and its location as compared with that of EKF. This filter is robust against process noise, measurement noise, parameter uncertainties, and guarantees a higher limit for the covariance of state estimation error as well. It is remarkable that simulation results are evaluated by OLGA software.

Transverse Young's Moduli and Cell Shapes in Coniferous Early Wood

Holzforschung ◽  
2002 ◽  
Vol 56 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ugai Watanabe ◽  
Minoru Fujita ◽  
Misato Norimoto
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Bending Moment ◽  
Cell Models ◽  
Young’S Moduli ◽  
Cell Shapes ◽  
The Difference ◽  
Square Cells ◽  
Experimental Values ◽  
The Relationship

Summary The relationship between transverse Young's moduli and cell shapes in coniferous early wood was investigated using cell models constructed by two dimensional power spectrum analysis. The calculated values of tangential Young's modulus qualitatively explained the relationship between experimental values and density as well as the difference in experimental values among species. The calculated values of radial Young's modulus for the species having hexagonal cells agreed well with the experimental values, whereas, for the species having square cells, the calculated values were much larger than the experimental values. This result was ascribed to the fact that the bending moment on the radial cell wall of square cell models was calculated to be small. It is suggested that the asymmetrical shape of real wood cells or the behavior of nodes during ell deformation is an important factor in the mechanism of linear elastic deformation of wood cells.

Thermoelectric Power of the Liquid Sn—Te Alloy

1982 ◽  
Vol 37 (10) ◽  
pp. 1127-1131 ◽  
Author(s):  
D. H. Kurlat ◽  
M. Rosen
Keyword(s):  
Thermoelectric Power ◽  
Hard Sphere ◽  
Stoichiometric Composition ◽  
Band Model ◽  
Liquid Alloys ◽  
Sphere Approximation ◽  
The Difference ◽  
Predicted Values ◽  
Experimental Values ◽  
Two Band Model

The Seebeck coefficient (S) of Sni1-x- Tex liquid alloys was measured as a function of concentration and temperature. For 0 ≦ x <0.45 the behaviour is metallic; S values are small and negative, rising linearly with temperature. The predicted values of Ziman's theory when using the hard sphere approximation disagree with the experimental ones. The change in sign occurs for 0.45. For x = 0.5 (stoichiometric composition) the thermoelectric power decreases linearly with temperature. This fact is explained assuming a two-band model. For x ≧ 0.6 the liquid alloy becomes more semiconducting and presents a maximum in the isotherms of S for x = 0.65. For the excess tellurium concentration range we have calculated the difference EF - EV and γ/kB, assuming a S(1/T) law. The experimental values are compared with those of Dancy and Glazov.

Experimental and computed dipole moments in donor–bridge–acceptor systems with p-phenylene and p-carboranediyl bridges

2009 ◽  
Vol 74 (1) ◽  
pp. 131-146 ◽  
Author(s):  
Ladislav Drož ◽  
Mark A. Fox ◽  
Drahomír Hnyk ◽  
Paul J. Low ◽  
J. A. Hugh MacBride ◽  
...  
Keyword(s):  
Dipole Moment ◽  
Dipole Moments ◽  
Electronic Effects ◽  
Electronic Interactions ◽  
Donor And Acceptor ◽  
Homo And Lumo ◽  
Pull Systems ◽  
The Difference ◽  
Experimental Values ◽  
2D And 3D

Dipole moments were measured for a series of substituted benzenes, biphenyls, terphenyls, C-monoaryl- and C,C′-diaryl-p-carboranes. For the donor–bridge–acceptor systems, Me2N–X–NO2, where X is 1,4-phenylene, biphenyl-4,4′-diyl, terphenyl and 1,4-C6H4-p-CB10H10C-1,4-C6H4, the measured interaction dipole moments are 1.36, 0.74, 0.51 and 0.00 D, respectively. The magnitude of the dipole moment reflects the ability of the bridge to transmit electronic effects between donor and acceptor groups. Thus, whilst the 1,4-phenylene bridges allow moderate electronic interactions between the remote groups, the p-carboranediyl unit is less efficient as a conduit for electronic effects. Averaged dipole moments computed at the DFT (B3LYP/6-31G*) level of theory from two distinct molecular conformers are in good agreement with the experimental values. Examination of the calculated electronic structures provides insight into the nature of the interactions between the donor and acceptor moieties through these 2D and 3D aromatic bridges. The most significant cooperative effect of the bridge on the dipole moment occurs in systems where there is some overlap between the HOMO and LUMO orbitals. This orbital overlap criterion may help to define the difference between “push-pull” systems in which electronic effects are mediated by the bridging moiety, and simpler systems in which the bridge acts as an electronically innocent spacer unit and through-space charge transfer/separation is dominant.

X-ray powder diffraction analysis of a nonlinear optical material o–chlorobenzol–benzoyl thiourea

1997 ◽  
Vol 12 (1) ◽  
pp. 47-48 ◽  
Author(s):  
Zong-ming Jin ◽  
Bo Zhao ◽  
Weiqun Zhou ◽  
Zheng Jin
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Nonlinear Optical ◽  
Optical Material ◽  
Nonlinear Optical Material ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters ◽  
Figures Of Merit ◽  
Experimental Values

A nonlinear optical material, o–chlorobenzol–benzoyl thiourea (C14H11ClN2OS), has been characterized by X-ray powder diffraction. Experimental values of 2θ corrected for systematic errors, relative peak intensities, values of d, and the Miller indices of 78 observed reflection with 2θ up to 72° are reported. The powder diffraction data have been evaluated, and the figures-of-merit are reported. The unit cell parameters least-squares refined from 28 nonoverlapping peaks of the monoclinic compound with a P2 space group are a=13.2797(4) Å, b=12.4058(8) Å, c=8.1561(2) Å, β=95.398(1)°, V=1337.7(4) Å3, Z=4, Dx=1.444 g/cm3. © 1997 International Centre for Diffraction Data.

Evaluation of Low-Temperature Properties and the Fragility of Asphalt Binders with Non-Arrhenius Viscosity–Temperature Dependence

2005 ◽  
Vol 1901 (1) ◽  
pp. 44-51 ◽  
Author(s):  
Huachun Zhai ◽  
Delmar Salomon
Keyword(s):  
Temperature Dependence ◽  
Asphalt Binders ◽  
Arrhenius Behavior ◽  
Direct Tension ◽  
Different Temperatures ◽  
Rotational Viscosity ◽  
Liquid Fragility ◽  
The Difference ◽  
Critical Cracking Temperature ◽  
Experimental Values

Rotational viscosities of different asphalt binders were determined at temperatures between 80°C and 185°C. Viscosity–temperature dependence of asphalt binders was described with the use of the Vogel–Tammann–Fulcher (VTF) and the William–Landel–Ferry (WLF) equations. The Vogel temperature ( Tv) and the glass transition temperature ( Tg) for different asphalt binders were determined by fitting experimental values of viscosity at different temperatures with these two equations. For asphalt binders, the difference between Tv and Tg was about 40K. Effects of asphaltenes, aging, chemical modification, and polymer content on these temperatures were evaluated. As asphaltene content increased, both temperatures, Tv and Tg, increased. Different polymers showed different effects on these temperatures. The values of Tv and Tg were correlated with the critical cracking temperature ( Tcr) determined through use of a bending beam rheometer and a direct tension tester. The results suggested that the correlations between Tv, Tg, and Tcr could be used to determine Tcr from the rotational viscosity results tested at high temperature. With simple rotational measurements, a quick estimation of Tcr of asphalt binders could be obtained. Liquid fragility theory was also used to study Tg of asphalt binders. Parameters determined with the VTF and WLF equations indicated that asphalt binders behaved as fragile liquids because of their non-Arrhenius behavior in the temperature range studied.

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