Experimental Measurement Uncertainty Research Articles

Measures of agreement between computation and experiment: Validation metrics

With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables to sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric, as well as features that we believe should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.

Viscosity of aqueous Ni(NO 3) 2 solutions at temperatures from (297 to 475) K and at pressures up to 30 MPa and concentration between (0.050 and 2.246) mol · kg −1

Viscosity of nine aqueous Ni(NO 3) 2 solutions (0.050, 0.153, 0.218, 0.288, 0.608, 0.951, 1.368, 1.824, and 2.246) mol · kg −1 was measured in the temperature range from (297 to 475) K and at pressures (0.1, 10, 20, and 30) MPa. The measurements were carried out with a capillary flow technique. The total experimental uncertainty of viscosity, pressure, temperature, and composition measurements were estimated to be less than 1.6%, 0.05%, 15 mK, and 0.02%, respectively. All experimental and derived results are compared with experimental and calculated values reported in the literature. Extrapolation of the solution viscosity measurements to zero concentration (pure water values) for the given temperature and pressure are in excellent agreement (average absolute deviation, AAD = 0.13%) with the values of pure water viscosity from IAPWS formulation [J. Kestin, J.V. Sengers, B. Kamgar-Parsi, J.M.H. Levelt Sengers, J. Phys. Chem. Ref. Data 13 (1984) 175–189]. The viscosity data for the solutions as a function of concentration have been interpreted in terms of the extended Jones–Dole equation for strong electrolytes. The values of viscosity A-, B-, and D-coefficients of the extended Jones–Dole equation for the relative viscosity ( η/ η 0) of aqueous Ni(NO 3) 2 solutions as a function of temperature are studied. The derived values of the viscosity A- and B-coefficients were compared with the results predicted by Falkenhagen–Dole theory (limiting law) of electrolyte solutions and the values calculated with the ionic B-coefficient data. The measured values of viscosity for the solutions were also used to calculate the effective rigid molar volumes in the extended Einstein relation for the relative viscosity ( η/ η 0).

Numerical modeling and experimental measurements of a high speed solid-cone water spray for use in fire suppression applications

Experimental measurements and numerical simulations of a high-speed water spray are presented. The numerical model is based on a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet collisions. Because the spray characteristics near the nozzle are difficult to ascertain, a new method for initialization of particle diameter size is developed that assumes a Rosin–Rammler distribution for droplet size, which correctly reproduces experimentally measured Sauter and arithmetic mean diameters. By relating the particle initialization to lower moments of the droplet statistics, it is possible to take advantage of measurements without substantial penalties associated with the greater experimental uncertainty of individual droplet measurements. Overall, very good agreement is observed in the comparisons of experimental measurements to computational predictions for the streamwise development of mean drop size and velocity. In addition, the importance of modeling droplet–droplet collisions is highlighted with comparison of selected droplet–droplet collision models.

B→sγin the littlest Higgs model

The inclusive process $b \to s \gamma$ is studied in the littlest Higgs model. The contributions arising from new particles are normally suppressed by a factor of $O(v^2/f^2)$. Due to the large uncertainties of experimental measurements and theoretical predictions, the model parameters can escape from the constraints of present experiments provided $f \ge 1$ TeV.

Z→bb¯bb¯in the light gluino and light sbottom scenario

The light gluino (12 - 16 GeV) and light sbottom (2 - 6 GeV) scenario has been used to explain the apparent overproduction of b-quarks at the Tevatron. This scenario also predicts the decay Z -> b b-bar ~g ~g where the gluinos subsequently decay into b-quarks and sbottoms. We show that this can contribute to the width Gamma_4b = Gamma(Z -> b b-bar b b-bar) since most of the sbottoms and b-quarks arising from gluino decay have a small angular separation. We find that while no excess in Gamma_4b is observable due to large uncertainties in experimental measurements, the ratio Gamma(Z -> b b-bar ~g ~g)/Gamma(Z -> b b-bar b b-bar) can be large due to sensitivity to b-quark mass, the sbottom mixing angle and the gluino mass. We calculate it to be in the range 0.05 - 0.41 inclusive of the entire parameter space.

Line assignments and global analysis of the tunneling–rotational microwave absorption spectrum of dimethyl methylphosphonate

Line assignments were carried out for about 600 Fourier-transform microwave transitions for dimethyl methylphosphonate involving levels of all six symmetry species in the G 18 molecular symmetry group appropriate for three large-amplitude motions and covering J and K values of 1 ⩽ J ⩽ 6 and 0 ⩽ | K | ⩽ 3 . The assignments are based on combination–difference loops, variations in line shape for different symmetry species caused by the small internal-rotor splitting patterns of the third, high-barrier methyl top, and agreement with theoretically expected positions. A global fit of 609 lines to a phenomenological tunneling–rotational Hamiltonian with 54 constants was performed, yielding a standard deviation of 8.0 kHz, which is close to the experimental measurement uncertainty. The A/ E tunneling splitting for the lowest barrier methyl group internal rotation motion was determined indirectly to be about 34 GHz. The much smaller tunneling splitting for the methoxy interchange motion was determined (with some assumptions) to be 3.3 MHz.

Vapor-Liquid Equilibria of HFC-32/n-Butane Mixtures

The vapor-liquid equilibria of HFC-32 and n-butane mixtures were measured in a temperature range of 283.15 to 313.15 K using a circulation method. The experimental standard uncertainties of temperature, pressure, and composition measurements were estimated to be within 10 mK, 2 kPa, and 0.2% in mole fraction, respectively. The measured data were correlated with the Peng–Robinson (PR) equation of state using Wong and Sandler mixing rules. The relative deviations of the measured bubble-point pressure from the calculated bubble-point pressure as a function of the measured bubble-point pressure were found to be less than 2.5%.

The uncertainty tree: Reducing the uncertainty of uncertainty analysis

Uncertainty analysis is an integral aspect of experimental measurements, though accurately assessing the flow of uncertainty in a measurement system—particularly for complicated systems with more than a few variables—can become a challenging, error-prone task, while being less enjoyable than it should be. This note proposes the uncertainty tree, a graphical, hierarchal structure to quickly and accurately assess the flow of uncertainty in experimental measurements. A few basic rules for tree construction are set forth that provide the essential building blocks to construct the tree. An example is provided that illustrates the use of the uncertainty tree concept in a real-world problem.

Measurements of Saturation Densities in the Critical Region of Pentafluoroethyl Methyl Ether (245cbEβγ)

We have measured 10 saturated-vapor densities and 13 saturated-liquid densities in the critical region of pentafluoroethyl methyl ether, CF3CF2OCH3 (245cbEβγ), based on the direct visual observation of the meniscus disappearance in an optical cell. The critical temperature and density have been determined by taking into consideration the meniscus disappearing level of the sample within the optical cell as well as the intensity of the critical opalescence. The experimental uncertainties of saturation temperature and density measurements were estimated to be within ±12 mK and ±(0.5 to 4.0) kg·m-3, while those of the critical temperature and density values determined are to be within ±17 mK and ±3 kg·m-3, respectively. We have also determined the critical exponent, β, and the critical amplitude, B, on the basis of the vapor−liquid coexistence curve correlation developed.

A new measurement of the 7Be(p, γ) 8B cross-section with an implanted 7Be target

The 7Be(p, γ) 8B capture reaction is of major importance to the physics of the sun and the issues of the “solar neutrino puzzle”. We report here on a new determination of the absolute cross section of this reaction, using a novel method which overcomes some of the major experimental uncertainties of previous measurements. We utilize a 7Be target implanted into a Cu substrate and a uniformly scanned particle beam larger than the target spot, eliminating issues of target homogeneity and backscattering loss of 8B reaction products. The target was produced using a beam of 1.8·10 10/s 7Be nuclei extracted at ISOLDE (CERN) from a graphite target bombarded by 1 GeV protons in a two-step resonant laser ionization source. The 7Be nuclei were directly implanted into a copper substrate to obtain a target of 2 mm diameter with a total of 3.10 15 atoms. The measurement of the 8B production cross section was carried out at the Van de Graaff laboratory of the Weizmann Institute of Science. We obtain for the S factor of the reaction: S 17( E cm = 1.09 MeV) = 22.7(1.2) eV. barn and S 17( E cm = 1.29 MeV) = 23.8(1.5) eV. barn, somewhat higher than other recent measurements. The present results can serve as a benchmark for further measurements of this cross section.

An Analog Light Scattering Experiment of Hexagonal Icelike Particles. Part II: Experimental and Theoretical Results

Abstract The scattering properties of hexagonal icelike crystals as measured in the analog manner by the experimental apparatus described in Part I are presented. The crystals are made out of sodium fluoride (NaF), which has an index of refraction similar to that of water ice. The experimentally determined light intensities scattered from fixed and integrated random orientations of a NaF hexagonal crystal, oriented to produce a two-dimensional scattering profile, compares favorably to the expectations derived from geometric ray tracing methods. Also, the three-dimensional scattering properties of a simulated NaF Parry column, a NaF crystal aggregate, and a NaF plate with a rough surface are compared to results computed from the geometric ray tracing approach. From these comparisons the authors conclude that within the experimental measurement uncertainties and to the degree in which the NaF crystal models approach the geometric and optical ideal, the geometric ray tracing approach is an excellent method t...

Vapor-liquid equilibria for the binary difluoromethane (R-32) + propane (R-290) mixture

The vapor–liquid equilibrium of the mixture composed of difluoromethane (R-32) and propane (R-290) was studied in the temperature range between 273.15 and 313.15 K. The experimental uncertainties of temperature, pressure, and composition measurements were estimated to be within ±10 mK, ±3 kPa, and ±0.4mol%, respectively. Comparisons between the present data and available experimental data were made using the Helmholtz free energy mixture model (HMM) adopted in the thermophysical properties program package, REFPROP 6.0, as a baseline. In addition, the existence of an azeotrope and the determination of new adjustable parameters for HMM for the R-32 + R-290 mixture are discussed.

Measurements of Gaseous PVTx Properties and Saturated Vapor Densities of Refrigerant Mixture R-125+R-143a

The experimental PVTx properties of a binary refrigerant mixture, R-125 (pentafluoroethane)+R-143a (1,1,1-trifluoroethane), have been measured for a composition of 50 mass% R-125 by a constant-mass method coupled with an expansion procedure in a range of temperatures from 305 to 400 K, pressures from 1.5 to 6.1 MPa, and densities from 92 to 300 kg·m−3. The experimental uncertainties of the present measurements are estimated to be within ±7.2 mK in temperature, ±3.0 kPa in pressure, ±0.12 kg·m−3 in density, and ±0.040 mass% in composition. The sample purities are 99.953 mass% for R-125 and 99.998% for R-143a. Seven saturated vapor densities and dew point pressures of the R-125+R-143a system were determined, on the basis of rather detailed PVTx properties measured in the vicinity of the saturation boundary as well as the thermodynamic behavior of isochores near saturation. The second and third virial coefficients for temperatures from 330 to 400 K were also determined.

A new measurement of the 7Li(d,p) 8Li cross section and consequences for 7Be(p,γ) 8B

A novel scheme for measuring the cross section of the 7Be(p,γ) 8B reaction, the major source of high energy neutrinos from the sun, is presented. The scheme involves a strictly uniform particle beam and overcomes some of the recognized experimental uncertainties of previous measurements. A new measurement of σ[ 7Li(d,p) 8Li] has been carried out using this setup, and the present value of σ [ 7Li(d,p) 8Li] = 155(8) mb at the top of the E d (lab.) = 776 keV resonance is compared with previous measurements. A new issue regarding both the (d,p) and (p,γ) reactions has been examined: reaction-product nuclei which are backscattered out of the target. Measurements and simulations carried out in the course of this investigation are presented and discussed in the context of possible effects on the measured cross sections of these reactions.

Measurements ofPVTx properties of refrigerant mixture HFC-32+HFC-125 in the gaseous phase

The experimental 156PVTx properties of an important binary refrigerant mixture, HFC-32 (difluoromethane)+HFC-125 (pentafluorethane), have been measured for three compositions, i.e., 50, 60, and 80 wt% HFC-32, by a constant-mass-method coupled with expansion procedure in an extensive range of temperaturesT from 320 to 440 K, of pressuresP from 1.8 to 5.3 M Pa, and of densities p from 50 to 124 kg · m−3. The experimental uncertainties of the present measurements are estimated to be within ±7 mK in temperature, ±2 kPa in pressure, ±0.2% in density and ±0.02 wt% of HFC-32. The sample purities are 99.998 wt% for HFC-32 and 99.99 wt% for HFC-125. Seventy-eight second and third virial coeflicients for temperatures from 320 to 440 K have been determined by the present measurements.

Gas-Phase PVT Properties and Vapor Pressures of Pentafluoroethane (HFC-125) Determined According to the Burnett Method

The gaseous compressibility factors of pentafluoroethane (HFC-125) have been measured by a Burnett apparatus in the range of temperatures from 290 to 390 K and pressures up to 3.6 MPa. The vapor pressures in the range of temperatures from 290 K to the critical temperature have also been measured, and a vapor-pressure correlation has been developed. The critical pressure was determined to be 3.6199±0.0018 MPa on the basis of the present measurements. The second virial coefficients have been determined along 11 isotherms, and a truncated virial equation of state has also been developed to represent the temperature dependence of the second virial coefficients and the present Burnett measurements. The experimental uncertainties of temperature, pressure, and density measurements throughout the present study were estimated to be better than ±10 mK, ±0.8 kPa, and ±0.12%, respectively. The purity of the HFC-125 sample used was better than 99.998 mass %

Vapor-Liquid Coexistence Curves in the Critical Region and the Critical Temperatures and Densities of Difluoromethane and Pentafluoroethane

The vapor-liquid coexistence curves in the critical region of difluoromethane (HFC-32) and pentafluoroethane (HFC-125) were measured by a visual observation of the meniscus in an optical cell. Seventeen saturated-liquid and 13 saturated-vapor densities have been measured in a temperature range from 330 K to the critical temperature, corresponding to a density range from 218 to 790 kg -3 for HFC-32. Sixteen saturated-liquid and 13 saturated-vapor densities have been measured in a temperature range from 331 K to the critical temperature, corresponding to a density range from 342 to 895 kg -3 for HFC-125. The experimental uncertainties of temperature and density measurements are estimated to be with ±10 mK and between ±0.10% and ±0.42%, respectively.

Use of a laser-induced fluorescence thermal imaging system for local jet impingement heat transfer measurement

In this paper the efficacy of a novel thermal imaging system designed for use in the study of local convective heat transfer is examined. The transient temperature measurements employed to calculate local heat transfer coefficients in this study rely on the temperature-sensitive fluorescence properties of a europium-doped lanthanum oxysulfide (La 2O 2S:Eu 3+) thermographic phosphor. A series of temperature-time data sets acquired during the heat-up of a test surface, oriented normal to an impinging heated jet, are used to calculate the local heat transfer coefficient about the stagnation point. These results are qualitatively compared to theoretical predictions and previous experimental observations to evaluate the ability to detect expected flow-field phenomena, such as the initial thinning of the boundary layer near the stagnation point and the eventual laminar to turbulent transition of boundary-layer flow away from the stagnation point. In addition, the measured stagnation point Nusselt number data are compared with theoretical and pertinent empirical data. The agreement of the stagnation point heat transfer in this comparison is excellent, with the variation between measured values based on the laser-induced fluorescence transient surface temperature measurements and existing data well within the bounds of the experimental measurement uncertainty of the present technique.

Prediction of the solubility of aromatic hydrocarbons in supercritical CO 2 with EoS GE models

Prediction of the solubility of liquid and solid aromatic hydrocarbons in supercritical CO 2 with the recently proposed LCVM model and the MHV2 model is presented. Satisfactory results are obtained in the case of LCVM, considering in particular the uncertainty of experimental measurements at such low mole fraction values and the pure component properties involved. Correlation of existing data is also considered in order to determine the limits of our expectations for the prediction results, including cases where the required solid vapor pressures are not available.

Journal of Heat Transfer Policy on Reporting Uncertainties in Experimental Measurements and Results

The JOURNAL OF HEAT TRANSFER (JHT) has, for some time, recognized the need to prepare a set of guidelines on estimating experimental uncertainty. This was warranted for two major reasons: to ensure uniformity of presenting experimental data, and to raise the authors' awareness regarding the importance of giving a more precise statement about their measurement uncertainties.