One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now "fast-forwarded" to the "infinity" iteration, leading to a different matrix equation that can be solved in a single iteration, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of $\sim10^6$ when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of $\sim 10^9$ points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a new type of boundary condition, which treats the boundary points as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.Comment: 17 pages, 7 figure

Validation and uncertainty framework for variable-density mixing experiments

Variable-density mixing (e.g., mixing due to the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities) is observed in many engineering applications. For example, RT mixing is observed in geophysical flows, stratified oceanic or atmospheric layers, and contaminant mixing, such as oil spills or pollution. Although less common, RM mixing is present in hypersonic combustion, supernova, and inertial confinement fusion. Current computational fluid dynamics models inadequately predict variable-density mixing physics and developments need to be validated with experimental data. However, variable-density experiments are complicated due to the range of spatial mixing scales and inherent coupling of density and velocity. This requires simultaneous measurement of the density and velocity fields and is typically accomplished via simultaneous particle image velocimetry (PIV) and planar laser--induced fluorescence (PLIF) with two distinct measurement systems. This introduces additional error sources to traditional PIV. Correlated density-velocity quantities (e.g., Favre-averaged Reynolds stresses and mass fluxes) are contaminated by both PIV and PLIF uncertainties. Moreover, spatial registration and sheet alignment errors between PIV and PLIF measurements are introduced for all flow quantities and magnified for correlated quantities. The Extreme Fluids Team at Los Alamos National Laboratory (LANL) is conducting multiple variable density validation experiments. The vertical shock tube (VST) is designed to statistically characterize RM mixing, whereas the turbulent mixing tunnel (TMT) investigates RT and Kelvin–Helmholtz mixing. Simultaneous two-component PIV and PLIF diagnostics are used in both facilities. Although the TMT can acquire large ensemble averaged datasets, the ability of acquiring large numbers of dataset realizations from the VST is severely limited. A framework for variable-density uncertainty quantification and validation is presented for both experiments. This framework follows the validation experiment assessment criteria presented by Oberkampf and Smith [1] with a goal of achieving at least a Level 2 completeness level. Both facilities have been designed to accurately describe the experimental conditions. The most difficult issue is quantifying the measurement uncertainties. Instantaneous PIV uncertainties are estimated using the uncertainty surface method [2] the peak ratio method [3], then propagated into the velocity statistics [4]. The effects of spatial registration sheet alignment errors are also assessed and initial uncertainty estimates due to these quantities are presented. Using the same methods as [4], PIV, PLIF, registration and alignment uncertainties are propagated into the Favre-averaged stresses and mass fluxes

Validation methodologies for turbulent variable density flows: A jet case study

Comparisons studies between simulated variable density turbulent flows often consist of direct graphical representations where the level of agreement is determined by eye. This work demonstrates a formal validation methodology using an existing validation framework to examine the agreement between a simulated variable density jet flow and corresponding experimental data. Implicit large eddy simulations (ILES's) of a round jet and a plane jet with density ratio $s = 4.2$ were simulated using the compressible hydrodynamic code xRAGE. The jet growth, characterized by the spreading rates, was compared, and the difference between the simulations and the experiment was examined through jet structure diagnostics. The spreading rates were found to be larger than the experimental values, primarily due to resolution issues in the simulations, a fact that is quantified by the validation metric analysis.Comment: 19 pages, 13 figure

Evaluation of a Desktop 3D Printed Rigid Refractive-Indexed-Matched Flow Phantom for PIV Measurements on Cerebral Aneurysms

Purpose Fabrication of a suitable flow model or phantom is critical to the study of biomedical fluid dynamics using optical flow visualization and measurement methods. The main difficulties arise from the optical properties of the model material, accuracy of the geometry and ease of fabrication. Methods Conventionally an investment casting method has been used, but recently advancements in additive manufacturing techniques such as 3D printing have allowed the flow model to be printed directly with minimal post-processing steps. This study presents results of an investigation into the feasibility of fabrication of such models suitable for particle image velocimetry (PIV) using a common 3D printing Stereolithography process and photopolymer resin. Results An idealised geometry of a cerebral aneurysm was printed to demonstrate its applicability for PIV experimentation. The material was shown to have a refractive index of 1.51, which can be refractive matched with a mixture of de-ionised water with ammonium thiocyanate (NH4SCN). The images were of a quality that after applying common PIV pre-processing techniques and a PIV cross-correlation algorithm, the results produced were consistent within the aneurysm when compared to previous studies. Conclusions This study presents an alternative low-cost option for 3D printing of a flow phantom suitable for flow visualization simulations. The use of 3D printed flow phantoms reduces the complexity, time and effort required compared to conventional investment casting methods by removing the necessity of a multi-part process required with investment casting techniques

FEDSM2008-55151 ROBUST GRADIENT ESTIMATION USING RADIAL BASIS FUNCTIONS

ABSTRACT Utilization of Radial Basis Functions (RBFs) for gradient estimation is tested over various noisy flow fields. A novel mathematical formulation which minimizes the energy functional associated with the analytical surface fit for Gaussian (GA) and Generalized Multiquadratic (GMQ) RBFs is presented. Error analysis of the wall gradient estimation was performed at various resolutions, interpolation grid sizes, and noise levels in synthetically generated Poiseuille and Womersley flow fields for RBFs along with standard finite difference schemes. To test the effectiveness of the methods with DPIV (Digital Particle Image Velocimetry) data, the methods were compared using the velocities obtained by processing images generated from DNS data of an open turbulent channel. Random, bias and total error were computed in all cases. In the absence of noise all tested methods perform well, with error contained under 10% at all resolutions. In the presence of noise the RBFs perform robustly with a total error that can be contained under 10-15% even with 10% noise using various interpolation grid sizes, For turbulent flow data, although the total error is approximately 5% for finite difference schemes in the absence of noise, the error can go as high as 150% in the presence of as little as 1% noise. With DPIV processed data the error is 25-40% for TPS and MQ methods optimization of the fitting parameters that minimize the energy functional associated with the analytical surface using RBFs results in robust gradient estimators are obtained that are applicable to steady, unsteady and turbulent flow fields. INTRODUCTION Digital Particle Image Velocimetry (DPIV) is a noninvasive optical flow diagnostic tool used to spatially and temporally resolve the velocity field across a variety of applications. Several sources of error are present in the DPIV estimation, including imaging errors as well as systematic errors in the velocity estimation. These sources of error are further compounded when computing important flow parameters which require gradient estimation, such as vorticity [1], shear stress Luf

Signal-to-noise ratio, error and uncertainty of PIV measurement

In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The inherent amount of signal mutual information between consecutive images governs the strength of the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the produced PIV measurements. Hence we posit that correlation signal-to-noise-ratio (SNR) metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. In this paper we present a framework for evaluating the correlation SNR using a set of different metrics, which in turn are used to develop models for uncertainty estimation. A new SNR metric termed \u93mutual information\u94 (MI) which quantifies the amount of common information (particle pattern) between two consecutive images is also introduced and investigated. This measure provides a direct estimation of the apparent NIFIFO parameter of an image pair providing an alternative approach towards uncertainty estimation but also connecting the current development to one of the most fundamental principles of PIV and the previously established theory. The SNR metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations and the notion of \u93valid\u94 measurement is redefined with respect to the correlation peak width. These advancements lead to more robust uncertainty estimation models, which are tested against both synthetic benchmark data as well as actual experimental measurements. For all cases considered here, expanded uncertainties are estimated at the 95% confidence level, and the resulting calculated coverages are approximately 95% thus demonstrating the feasibility and applicability of these new models for direct estimation of uncertainty for individual PIV measurements

Particle image velocimetry from multispectral data

Since the adoption of digital video cameras and cross-correlation methods for particle image velocimetry (PIV), the use of color images has largely been abandoned. Recently, however, with the re-emergence of color-based stereo and volumetric techniques, color imaging for PIV has again become relevant. In this work we explore the potential advantages of color PIV processing by developing and proposing several methods for handling multi color images. The first method uses cross-correlation of every color channel independently to build a color vector cross-correlation plane which can be searched for one or more peaks corresponding to either the average displacement of several flow components using a color ensemble operation, or the individual motion of colored particles, each type with a different behavior. In the second case, linear unmixing is used on the correlation plane to separate out each known particle type as captured by the different color channels. The second method introduces the use of quaternions to encode the color data, and the cross-correlation is carried out simultaneously on all colors. The resulting correlation plane can either be searched for a single peak corresponding to the mean flow, or multiple peaks can be used with velocity phase separation to determine which velocity corresponds to which particle type. Each of these methods was tested using synthetic images simulating the color recording of noisy particle fields both with and without the use of a Bayer filter and demosaicing operation. It was determined that for single phase flow, both color methods decreased random errors by approximately a factor of 2 due to the noise signal being uncorrelated between color channels, while maintaining similar bias errors as compared to traditional monochrome PIV processing. In multi-component flows, the color vector correlation technique was able to successfully resolve displacements of two separate flow components with errors similar to traditional grayscale PIV processing of a single phase. It should be noted that traditional PIV processing is bound to fail entirely under such processing conditions. In contrast, the quaternion methods, frequently failed to properly identify the correct velocity and phase and showed significant cross-talk in the measurements between particle types. Finally, the color vector method was applied to experimental color images of a microchannel designed for contactless dielectrophoresis particle separation, and good results were obtained for both instantaneous and ensemble PIV processing. However, in both the synthetic color images that were generated using a Bayer filter and the experimental data, a significant peak locking effect with a period of two pixels was observed. In order to mitigate this detrimental effect it is suggested that improved image interpolation algorithms tuned for use in PIV are applied on the color images before processing, or that cameras that do not require a demosaic algorithm are used for PIV