Brandon Wilson

Uncertainty on PIV mean and fluctuating velocity due to bias and random errors

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.

Taylor-series and Monte-Carlo-method uncertainty estimation of the width of a probability distribution based on varying bias and random error

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.

Single-Interface Richtmyer–Meshkov Turbulent Mixing at the Los Alamos Vertical Shock Tube

Mach number and initial conditions effects on Richtmyer–Meshkov (RM) mixing are studied by the vertical shock tube (VST) at Los Alamos National Laboratory (LANL). At the VST, a perturbed stable light-to-heavy (air–SF6, A = 0.64) interface is impulsively accelerated with a shock wave to induce RM mixing. We investigate changes to both large and small scales of mixing caused by changing the incident Mach number (Ma = 1.3 and 1.45) and the three-dimensional (3D) perturbations on the interface. Simultaneous density (quantitative planar laser-induced fluorescence (PLIF)) and velocity (particle image velocimetry (PIV)) measurements are used to characterize preshock initial conditions and the dynamic shocked interface. Initial conditions and fluid properties are characterized before shock. Using two types of dynamic measurements, time series (N = 5 realizations at ten locations) and statistics (N = 100 realizations at a single location) of the density and velocity fields, we calculate several mixing quantities. Mix width, density-specific volume correlations, density–vorticity correlations, vorticity, enstrophy, strain, and instantaneous dissipation rate are examined at one downstream location. Results indicate that large-scale mixing, such as the mix width, is strongly dependent on Mach number, whereas small scales are strongly influenced by initial conditions. The enstrophy and strain show focused mixing activity in the spike regions.

Simultaneous PIV and PLIF Measurements of Mach Number Effects on Single-Interface Richtmyer-Meshkov Mixing

Introduction of favorable (e.g. combustion within scram-jet engines) or adverse (e.g. inertial confinement fusion) mixing conditions in engineering applications are intensified by the Richtmyer-Meshkov instability (RMI). Despite numerous experimental and numerical research, the mechanisms behind RMI-induced small-scale mixing, particularly late-time turbulent mixing and turbulent statistics are not well understood.

Simultaneous PIV/PLIF Measurements of Multi-mode Perturbed Initial Conditions of Single-Interface Richtmyer-Meshkov Mixing

A Richtmyer-Meshkov Instability (RMI) might occur when a shock wave interacts with the interface between two fluids of different density. An initial perturbation in the interface is an optimal condition for the RMI. This is so because local misalignments between the density gradient across the interface and the pressure gradient of the shock wave induce non-zero baroclinic vorticity that amplifies the initial perturbation. RMI is known to occur in supernovas, collapsing gas bubbles in liquids, supersonic and hypersonic combustion, interacting flame fronts and pressure waves, laser-matter interactions, and inertial confinement fusion (ICF). The effects of RMIinduced mixing are detrimental to energy conversion efficiency in ICF, but can be advantageous in combustion processes.