No abstract

Particle image velocimetry is a powerful and flexible fluid velocity measurement tool. In spite of its widespread use, the uncertainty of PIV measurements has not been sufficiently addressed to date. The calculation and propagation of local, instantaneous uncertainties on PIV results into the measured mean and Reynolds stresses are demonstrated for four PIV error sources that impact uncertainty through the vector computation: particle image density, diameter, displacement and velocity gradients. For the purpose of this demonstration, velocity data are acquired in a rectangular jet. Hot-wire measurements are compared to PIV measurements with velocity fields computed using two PIV algorithms. Local uncertainty on the velocity mean and Reynolds stress for these algorithms are automatically estimated using a previously published method. Previous work has shown that PIV measurements can become ‘noisy’ in regions of high shear as well as regions of small displacement. This paper also demonstrates the impact of these effects by comparing PIV data to data acquired using hot-wire anemometry, which does not suffer from the same issues. It is confirmed that flow gradients, large particle images and insufficient particle image displacements can result in elevated measurements of turbulence levels. The uncertainty surface method accurately estimates the difference between hot-wire and PIV measurements for most cases. The uncertainty based on each algorithm is found to be unique, motivating the use of algorithm-specific uncertainty estimates.

Uncertainties are typically assumed to be constant or a linear function of the measured value; however, this is generally not true. Particle image velocimetry (PIV) is one example of a measurement technique that has highly nonlinear, time varying local uncertainties. Traditional uncertainty methods are not adequate for the estimation of the uncertainty of measurement statistics (mean and variance) in the presence of nonlinear, time varying errors. Propagation of instantaneous uncertainty estimates into measured statistics is performed allowing accurate uncertainty quantification of time-mean and statistics of measurements such as PIV. It is shown that random errors will always elevate the measured variance, and thus turbulent statistics such as . Within this paper, nonlinear, time varying errors are propagated from instantaneous measurements into the measured mean and variance using the Taylor-series method. With these results and knowledge of the systematic and random uncertainty of each measurement, the uncertainty of the time-mean, the variance and covariance can be found. Applicability of the Taylor-series uncertainty equations to time varying systematic and random errors and asymmetric error distributions are demonstrated with Monte-Carlo simulations. The Taylor-series uncertainty estimates are always accurate for uncertainties on the mean quantity. The Taylor-series variance uncertainty is similar to the Monte-Carlo results for cases in which asymmetric random errors exist or the magnitude of the instantaneous variations in the random and systematic errors is near the ‘true’ variance. However, the Taylor-series method overpredicts the uncertainty in the variance as the instantaneous variations of systematic errors are large or are on the same order of magnitude as the ‘true’ variance.

Los Alamos National Laboratory is interested in developing high-energy-density physics validation capabilities for its multiphysics code xRAGE. xRAGE was recently updated with the laser package Mazinisin to improve predictability. We assess the current implementation and coupling of the laser package via validation of laser-driven, direct-drive spherical capsule experiments from the Omega laser facility. The ASME V&V 20-2009 standard is used to determine the model confidence of xRAGE, and considerations for high-energy-density physics are identified. With current modeling capabilities in xRAGE, the model confidence is overwhelmed by significant systematic errors from the experiment or model. Validation evidence suggests cross-beam energy transfer as a dominant source of the systematic error.

We prove the double bubble conjecture in ‫ޒ‬ 2 : that the standard double bubble in ‫ޒ‬ 2 is boundary length-minimizing among all figures that separately enclose the same areas. Our independent proof is given using the new method of metacalibration, a generalization of traditional calibration methods useful in minimization problems with fixed volume constraints.MSC2000: 49Q05, 49Q10, 53A10.