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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

An observational signal of the void shape correlation and its link to the cosmic web

The shapes of cosmic voids are prone to distortions caused by external tidal forces since their low densities imply a lower internal resistance. This susceptibility of the void shapes to tidal distortions makes them useful as indicators of large-scale tidal and density fields, despite the practical difficulty in defining them. Using the void catalog constructed by Pan et al. from the Seventh Data Release of the Sloan Digital Sky Survey (SDSS DR7), we detect a clear 4σ signal of spatial correlations of the void shapes on a scale of 20 h{sup −1} Mpc and show that the signal is robust against the projection of the void shapes onto the plane of sky. By constructing a simple analytic model for the void shape correlation, within the framework of tidal torque theory, we demonstrate that the void shape correlation function scales linearly with the two-point correlation function of the linear density field. We also find direct observational evidence for the cross-correlation of the void shapes with the large-scale velocity shear field that was linearly reconstructed by Lee et al. from SDSS DR7. We discuss the possibility of using the void shape correlation function to break the degeneracy between the density parameter and the power spectrum amplitude and to independently constrain the neutrino mass as well.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Interpreting radial correlation Doppler reflectometry using gyrokinetic simulations

A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al 2007 Plasma Phys. Control. Fusion 49 1019) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wavenumber $k_{\perp}$ selected by the Doppler backscattering (DBS) signal. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a nonseparable power law spectrum in wavenumber space, leading to a power law dependence of the radial correlation length with binormal wavenumber $l_r \sim C k_{\perp}^{-\alpha} (\alpha \approx 1)$ which agrees with the inverse proportionality relationship between the measured $l_r$ and $k_{\perp} $ observed in experiments (Fernández-Marina et al 2014 Nucl. Fusion 54 072001). This new insight indicates that RCDR characterizes the eddy aspect ratio in the perpendicular plane to the magnetic field. It also motivates future use of a nonseparable turbulent spectrum to quantitatively interpret RCDR and potentially other turbulence diagnostics. The radial correlation length is only measurable when the radial resolution at the cutoff location $W_\text n$ satisfies $W_\text n \ll l_r$, while the measurement becomes dominated by $W_\text n$ for $W_\text n \gg l_r$. This suggests that $l_r$ is likely to be inaccessible for electron-scale DBS measurements (${k_{\perp}}{\rho_{\text s}} \gt 1$). The effect of $W_\text n$ on ion-scale radial correlation lengths could be nonnegligible.

radial correlation Doppler reflectometry↗
DOE OSTI2015

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

When can reliable inference be drawn in the ‘‘Big Data’’ context? This article presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large-scale inference. In large-scale data applications like genomics, connectomics, and eco-informatics, the data set is often variable rich but sample starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than the number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for ‘‘Big Data.’’ Sample complexity, however, has received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; and 3) the purely high-dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high-dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. We demonstrate various regimes of correlation mining based on the unifying perspective of high-dimensional learning rates and sample complexity for different structured covariance models and different inference tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Measurements of long-range two-particle correlation over a wide pseudorapidity range in p–Pb collisions at $ \sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

Correlations in azimuthal angle extending over a long range in pseudorapidity between particles, usually called the “ridge” phenomenon, were discovered in heavy-ion collisions, and later found in pp and p–Pb collisions. In large systems, they are thought to arise from the expansion (collective flow) of the produced particles. Extending these measurements over a wider range in pseudorapidity and final-state particle multiplicity is important to understand better the origin of these long-range correlations in small collision systems. In this Letter, measurements of the long-range correlations in p–Pb collisions at $\sqrt{^SNN}$ = 5.02 TeV are extended to a pseudorapidity gap of Δη ~ 8 between particles using the ALICE forward multiplicity detectors. After suppressing non-flow correlations, e.g., from jet and resonance decays, the ridge structure is observed to persist up to a very large gap of Δη ~ 8 for the first time in p–Pb collisions. This shows that the collective flow-like correlations extend over an extensive pseudorapidity range also in small collision systems such as p–Pb collisions. The pseudorapidity dependence of the second-order anisotropic flow coefficient, v 2 (η), is extracted from the long-range correlations. The v 2 (η) results are presented for a wide pseudorapidity range of –3.1 < η < 4.8 in various centrality classes in p–Pb collisions. To gain a comprehensive understanding of the source of anisotropic flow in small collision systems, the v 2 (η) measurements are compared with hydrodynamic and transport model calculations. The comparison suggests that the final-state interactions play a dominant role in developing the anisotropic flow in small collision systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Multiplicity-dependent jet modification from di-hadron correlations in pp collisions at $ \sqrt{s} $ = 13 TeV

Short-range correlations between charged particles are studied via two-particle angular correlations in pp collisions at $\sqrt{s}$ = 13 TeV. The correlation functions are measured as a function of the relative azimuthal angle ∆φ and the pseudorapidity separation ∆η for pairs of primary charged particles within the pseudorapidity interval |η| < 0.9 and the transverse-momentum range 1 < p T < 8 GeV/c. Near-side (|∆φ| < 1.3) peak widths are extracted from a generalised Gaussian fitted over the correlations in full pseudorapidity separation (|∆η| < 1.8), while the per-trigger associated near-side yields are extracted for the short-range correlations (|∆η| < 1.3). Both are evaluated as a function of charged-particle multiplicity obtained by two different event activity estimators. The width of the near-side peak decreases with increasing multiplicity, and this trend is reproduced qualitatively by the Monte Carlo event generators PYTHIA 8, AMPT, and EPOS. However, the models overestimate the width in the low transverse-momentum region (p T < 3 GeV/c). The per-trigger associated near-side yield increases with increasing multiplicity. Although this trend is also captured qualitatively by the considered event generators, the yield is mostly overestimated by the models in the considered kinematic range. The measurement of the shape and yield of the short-range correlation peak can help us understand the interplay between jet fragmentation and event activity, quantify the narrowing trend of the near-side peak as a function of transverse momentum and multiplicity selections in pp collisions, and search for final-state jet modification in small collision systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Improved natural convection heat transfer correlations for reactor cavity cooling systems of high-temperature gas-cooled reactors: From computational fluid dynamics to Pronghorn

The Reactor Cavity Cooling System (RCCS) is a common reactor safety system in High Temperature Gas Cooled Reactors (HTGR) that removes heat from the Reactor Pressure Vessel (RPV) by radiation ($\sim 80\%$) and natural convection ($\sim 20\%$). For simulation of accident scenarios of HTGRs, intermediate fidelity and system codes models must be employed for limiting the models' execution time. While accurate quantification of the radiative heat transfer is available in these models, quantification of natural convection must rely on correlations of questionable accuracy for the Nusselt number. Commonly used correlations are based in experiments performed at low Rayleigh numbers and/or using isothermal walls in simplified geometries. Here, this work improves on the accuracy of natural convection heat transfer correlations in support for HTGR designs. These correlations include both local and average Nusselt numbers as a function of the global Rayleigh number, the local Rayleigh number, and the temperature profile at the hot wall of the RCCS. In the absence of dedicated experiments and the difficulty of performing high-fidelity simulations at realistic Rayleigh numbers, the data to fit the correlations are generated with Computational Fluid Dynamics (CFD) using Reynolds Averaged Navier-Stokes (RANS) models. First, a careful selection of the RANS turbulence model is performed by comparing the results obtained with different RANS turbulence models against high fidelity simulations of natural convection at $Ra \ 1 \times 10^{11}$ in a rectangular cavity. Next, the selected model is used to perform simulations of an HTGR cavity at different high Rayleigh numbers $\in [6.1 \times 10^{11},2.9 \times 10^{13}]$ to encompass several HTGR designs, assuming an isothermal RPV wall. The results obtained are used to fit a correlation for the average and space-varying Nusselt number as a function of the global and local Rayleigh numbers via a sparsity-promoting least-squares method. The selected RANS model is then used to perform simulations of a PBMR 400 HTGR cavity with the temperature profiles at the RPV wall obtained during a PLOFC transient. We use the results obtained to fit a temperature-dependent correction to the space-varying Nusselt number with the sparsity-promoting least-squares method. The results obtained in this work, enable system-level codes, such as Pronghorn, to perform higher-fidelity simulations of the heat exchange process in the RCCS while still maintaining a low computational cost.

42 ENGINEERING↗
DOE OSTI2018

Characterization of the quantumness of unsteerable tripartite correlations

Quantumness for a bipartite unsteerable quantum correlation is operationally characterized by the notion of super-unsteerability. Super-unsteerability refers to the requirement of a larger dimension of the random variable that the steering party has to preshare with the party to be steered in the classical simulation protocol to generate an unsteerable correlation than the local Hilbert space dimension of the quantum states (reproducing the given unsteerable correlation) at the steering party’s side. In the present study, this concept of super-unsteerability is generalized by defining the notion of super-bi-unsteerability for tripartite correlations, which is unsteerable across a bipartite cut. Genuine super-bi-unsteerability is defined as the occurrence of super-bi-unsteerability across all possible bipartite cuts. Specific example of genuine super-bi-unsteerability for tripartite correlations has been presented. This study provides a tool to characterize the genuine quantumness of tripartite quantum correlations which are unsteerable across every bipartite cut.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Genuine k -partite correlations and entanglement in the ground state of the Dicke model for interacting qubits

Here, in this work, we calculate and study correlations of the Dicke model in the presence of qubit–qubit interaction. Whereas the analysis of correlations among its subsystems is essential for the understanding of corresponding critical phenomena and for performing quantum information tasks, the majority of correlation measures are restricted to bipartitions due to the inherent challenges associated with handling multiple partitions. To circunvent this we employ the calculation of Genuine Multipartite Correlations (GMC) based on the invariance of our model under particle permutation. We then quantify the correlations within each subpart of the system, as well as the percentage contribution of each GMC of order $k$, highlighting the many-body behaviors for different regimes of parameters. Additionally, we show that GMC signal both first- and second-order quantum phase transitions present in the model. Furthermore, as GMC encompasses both classical and quantum correlations, we employ Quantum Fisher Information (QFI) to detect genuine multipartite entanglement. Ultimately, we map the Dicke model with interacting qubits to spin in solids interacting with a quantum field of magnons, thus demonstrating a potential experimental realization of this model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Universal correlation for falling film evaporation heat transfer coefficients of water and seawater

Horizontal falling film evaporators are widely utilized in desalination industries to increase fresh water supply. However, universal correlations for seawater falling film evaporation under varied operational and geometrical conditions are simply unavailable in open literature. Thus, this study aims to develop such a universal correlation for both plain and enhanced tubes. The detailed heat transfer mechanisms are reviewed, and rational parameters are incorporated to develop the universal correlation. A dataset of 994 data points from 9 sources covering a wide range of conditions was compiled. These conditions include Reynolds numbers from 10 to 7235, heat fluxes from 7.7 to 208 kW/m -2 , saturation temperatures from 278 to 401 K, salinities from 0 to 60 gsalt kg -1 water, tube diameters from 15.8 to 50.8 mm, and liquid feeder height to diameter ratios from 1 to 2.25. Upon analysis, it was found that most of the recommended existing correlations exhibited poor predictive accuracy, as evidenced by larger MADs. The developed correlation in this study demonstrated the best predictive accuracy for the entire dataset, yielding a MAD of 16.8 % and an R 2 of 0.82. Furthermore, the performance of the new correlation was individually assessed across a broader spectrum of operational and design conditions, reflecting the individual conditions’ influences with an overall MAD of 20 %.

42 ENGINEERING↗
DOE OSTI2022

Real-space visualization of short-range antiferromagnetic correlations in a magnetically enhanced thermoelectric

Short-range magnetic correlations can significantly increase the thermopower of magnetic semiconductors, representing a noteworthy development in the decades-long effort to develop high-performance thermoelectric materials. Here, we reveal the nature of the thermopower-enhancing magnetic correlations in the antiferromagnetic semiconductor MnTe. Using magnetic pair distribution function analysis of neutron scattering data, we obtain a detailed, real-space view of robust, nanometer-scale, antiferromagnetic correlations that persist into the paramagnetic phase above the Neel temperature $T_N$ = 307 K. In this work, the magnetic correlation length in the paramagnetic state is significantly longer along the crystallographic c axis than within the ab plane, pointing to anisotropic magnetic interactions. Ab initio calculations of the spin-spin correlations using density functional theory in the disordered local moment approach reproduce this result with quantitative accuracy. These findings constitute the first real-space picture of short-range spin correlations in a magnetically enhanced thermoelectric and inform future efforts to optimize thermoelectric performance by magnetic means.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Experimental validation of scintillator detector response to correlated neutrons with MCNP and associated packages

Time, energy, and angle correlated neutrons are emitted in nuclear fission. New, physics-based fission event generators that capture these correlations have been incorporated into MCNP6.2 because correlations can impact nuclear non-proliferation and safeguards systems response. DRiFT is a detector response code that takes MCNP outputs and reproduces laboratory analogous detector quantities. Previous work has compared DRiFT to single detector experiment data and has discussed recent updates to DRiFT specific to correlated fission experiments. In this work, we demonstrate a validation of recent updates to DRiFT for organic scintillator response in correlated fission neutron experiments using a 252Cf source. Furthermore, outputs from MCNP with the FREYA fission event generator were post-processed with DRiFT and compared to experiment data. Simulation and experiment results are in reasonably good agreement for multiple correlated neutron quantities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Long-range correlation energy calculated from coupled atomic response functions

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Reference Correlation for the Viscosity of Ethane

A new representation of the viscosity for the fluid phase of ethane includes a zero-density correlation and a contribution for the critical enhancement, initially both developed separately, but based on experimental data. The higher-density contributions are correlated as a function of the reduced density δ = ρ/ρ{sub c} and of the reciprocal reduced temperature τ = T{sub c}/T (ρ{sub c}—critical density and T{sub c}—critical temperature). The final formulation contains 14 coefficients obtained using a state-of-the-art linear optimization algorithm. The evaluation and choice of the selected primary data sets is reviewed, in particular with respect to the assessment used in earlier viscosity correlations. The new viscosity surface correlation makes use of the reference equation of state for the thermodynamic properties of ethane by Bücker and Wagner [J. Phys. Chem. Ref. Data 35, 205 (2006)] and is valid in the fluid region from the melting line to temperatures of 675 K and pressures of 100 MPa. The viscosity in the limit of zero density is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temperatures 290 < T/K < 625, increasing to 1.0% at temperatures down to 212 K. The uncertainty of the correlated values is 1.5% in the range 290 < T/K < 430 at pressures up to 30 MPa on the basis of recent measurements judged to be very reliable as well as 4.0% and 6.0% in further regions. The uncertainty in the near-critical region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2) increases with decreasing temperature up to 3.0% considering the available reliable data. Tables of the viscosity calculated from the correlation are listed in an appendix for the single-phase region, for the vapor–liquid phase boundary, and for the near-critical region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Surface waves on quantum plasma half-space with electron exchange-correlation effects

The propagation of surface waves on a quantum plasma half-space is investigated, taking into account the electron exchange-correlation effect. Using the modified quantum hydrodynamic model in conjunction with the Poisson equation, the dispersion relation of surface waves is obtained. It is found that due to the presence of electron exchange-correlation effect the wave frequency is shifted to lower frequencies. For different ranges of Brueckner parameter r{sub s}, the effect of electron exchange-correlation is investigated. It is indicated that for weak coupling region with r{sub s} < 0.1, the wave frequency remains unchanged and in this region the effect of electron exchange-correlation is negligible. For moderate coupling region, i.e., (0.1 < r{sub s} < 1), the influence of electron exchange-correlation is important and as r{sub s} increases, the electron exchange-correlation effect also increases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Constant-time 2D and 3D through-bond correlation NMR spectroscopy of solids under 60 kHz MAS

Establishing connectivity and proximity of nuclei is an important step in elucidating the structure and dynamics of molecules in solids using magic angle spinning (MAS) NMR spectroscopy. Although recent studies have successfully demonstrated the feasibility of proton-detected multidimensional solid-state NMR experiments under ultrafast-MAS frequencies and obtaining high-resolution spectral lines of protons, assignment of proton resonances is a major challenge. In this study, we first re-visit and demonstrate the feasibility of 2D constant-time uniform-sign cross-peak correlation (CTUC-COSY) NMR experiment on rigid solids under ultrafast-MAS conditions, where the sensitivity of the experiment is enhanced by the reduced spin-spin relaxation rate and the use of low radio-frequency power for heteronuclear decoupling during the evolution intervals of the pulse sequence. In addition, we experimentally demonstrate the performance of a proton-detected pulse sequence to obtain a 3D {sup 1}H/{sup 13}C/{sup 1}H chemical shift correlation spectrum by incorporating an additional cross-polarization period in the CTUC-COSY pulse sequence to enable proton chemical shift evolution and proton detection in the incrementable t{sub 1} and t{sub 3} periods, respectively. In addition to through-space and through-bond {sup 13}C/{sup 1}H and {sup 13}C/{sup 13}C chemical shift correlations, the 3D {sup 1}H/{sup 13}C/{sup 1}H experiment also provides a COSY-type {sup 1}H/{sup 1}H chemical shift correlation spectrum, where only the chemical shifts of those protons, which are bonded to two neighboring carbons, are correlated. By extracting 2D F1/F3 slices ({sup 1}H/{sup 1}H chemical shift correlation spectrum) at different {sup 13}C chemical shift frequencies from the 3D {sup 1}H/{sup 13}C/{sup 1}H spectrum, resonances of proton atoms located close to a specific carbon atom can be identified. Overall, the through-bond and through-space homonuclear/heteronuclear proximities determined from the 3D {sup 1}H/{sup 13}C/{sup 1}H experiment would be useful to study the structure and dynamics of a variety of chemical and biological solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole–hole Tamm–Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole–hole counterpart to the more established particle–particle TDA (pp-TDA) method, both of which are derived from the particle–particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. Furthermore, the treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. Additionally, we show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states—particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

EPPUR SI MUOVE: POSITIONAL AND KINEMATIC CORRELATIONS OF SATELLITE PAIRS IN THE LOW Z UNIVERSE

We have recently shown that pairs of satellite galaxies located diametrically opposite to each other around their host possess predominantly anti-correlated velocities. This is consistent with a scenario in which ≳50% of satellite galaxies belong to kinematically coherent rotating planar structures. Here we extend this analysis, examining satellites of giant galaxies drawn from an SDSS photometric redshift catalog. We find that there is a ∼17% overabundance (>3σ significance) of candidate satellites at positions diametrically opposite to a spectroscopically confirmed satellite. We show that ΛCDM cosmological simulations do not possess this property when contamination is included. After subtracting contamination, we find ∼2 times more satellites diametrically opposed to a spectroscopically confirmed satellite than at 90° from it, at projected distances ranging from 100 to 150 kpc from the host. This independent analysis thus strongly supports our previous results on anti-correlated velocities. We also find that those satellite pairs with anti-correlated velocities have a strong preference (∼3:1) to align with the major axis of the host whereas those with correlated velocities display the opposite behavior. We finally show that repeating a similar analysis to Ibata et al. with same-side satellites is generally hard to interpret, but is not inconsistent with our previous results when strong quality cuts are applied on the sample. This addresses all of the concerns recently raised by Cautun et al., who did not uncover any flaw in our previous analysis, but may simply have hinted at the physical extent of planar satellite structures by pointing out that the anti-correlation signal weakens at radii >150 kpc. All these unexpected positional and kinematic correlations strongly suggest that a substantial fraction of satellite galaxies are causally linked in their formation and evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Particle image velocimetry (PIV) uncertainty quantification using moment of correlation (MC) plane

Here, we present a new uncertainty estimation method for particle image velocimetry (PIV), that uses the correlation plane as a model for the probability density function (PDF) of displacements and calculates the second order moment of the correlation (MC). The cross-correlation between particle image patterns is the summation of all particle matches convolved with the apparent particle image diameter. MC uses this property to estimate the PIV uncertainty from the shape of the cross-correlation plane. In this new approach, the generalized cross-correlation (GCC) plane corresponding to a PIV measurement is obtained by removing the particle image diameter contribution. The GCC primary peak represents a discretization of the displacement PDF, from which the standard uncertainty is obtained by convolving the GCC plane with a Gaussian function. Then a Gaussian least-squares-fit is applied to the peak region, accounting for the stretching and rotation of the peak, due to the local velocity gradients and the effect of the convolved Gaussian. The MC method was tested with simulated image sets and the predicted uncertainties show good sensitivity to the error sources and agreement with the expected RMS error. Subsequently, the method was demonstrated in three PIV challenge cases and two experimental datasets and was compared with the published image matching (IM) and correlation statistics (CS) techniques. Results show that the MC method has a better response to spatial variation in RMS error and the predicted uncertainty is in good agreement with the expected standard uncertainty. The uncertainty prediction was also explored as a function of PIV interrogation window size. Overall, the MC method performance establishes itself as a valid uncertainty estimation tool for planar PIV.

47 OTHER INSTRUMENTATION↗