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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Molecular Tagging Velocimetry in Superfluid Helium-4: Progress, Issues, and Future Development

Helium-4 in the superfluid phase (He II) is a two-fluid system that exhibits fascinating quantum hydrodynamics with important scientific and engineering applications. However, the lack of high-precision flow measurement tools in He II has impeded the progress in understanding and utilizing its hydrodynamics. In recent years, there have been extensive efforts in developing quantitative flow visualization techniques applicable to He II. In particular, a powerful molecular tagging velocimetry (MTV) technique, based on tracking thin lines of He 2 * excimer molecules created via femtosecond laser-field ionization in helium, has been developed in our laboratory. This technique allows unambiguous measurement of the normal fluid velocity field in the two-fluid system. Nevertheless, there are two limitations to this technique: (1) only the velocity component perpendicular to the tracer line can be measured; and (2) there is an inherent error in determining the perpendicular velocity. In this paper, we discuss how these issues can be resolved by advancing the MTV technique. We also discuss two novel schemes for tagging and producing He 2 * tracers. Here, the first method allows the creation of a tagged He 2 * tracer line without the use of an expensive femtosecond laser. The second method enables full-space velocity field measurement through tracking small clouds of He 2 * molecules created via neutron- 3 He absorption reactions in He II.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Visualization of R410A Flow Boiling Inside Horizontal Smooth Tubes under Diabatic Conditions

This article presents a novel approach to visualize the flow boiling in round tubes under “diabatic conditions”. In the visualization test section, a 3D printed round tube is placed inside a glass tube with secondary fluid at a higher temperature flowing in the annulus between the two tubes thus providing diabatic conditions. Experimental work was conducted for evaporating R410A flow in a horizontal smooth round tube with the inner diameter of 6.3 mm. Compared to the traditional adiabatic visualization technique, the more realistic evaporative condition is simulated and the developing evaporation process is captured. New insights for the flow behavior at low vapor quality are brought by this diabatic method. The vapor plug occurs at very low vapor quality, and this is attributed to the coalescence of bubbles generated on the heated tube wall. For the intermittent flow, liquid slug triggered by Kelvin–Helmholtz instability affects the nucleation on the tube wall. It brings the fresh liquid to rewet the dry surface and activate the nucleation sites. Finally, heat flux condition affects the heat transfer mechanisms during the flow boiling, and the heat transfer through the nucleate boiling mechanism increases as the heat flux increases.

3D printed↗
DOE OSTI2026

Holistic energy analysis method for thermal management architectures of data centers

Modern high-performance computing (HPC) data centers (DCs), particularly those supporting energy-intensive artificial intelligence (AI) workloads, face escalating thermal management challenges that degrade performance through thermal throttling and drive up cooling power consumption and operational costs. To address this challenge, many have developed a wide variety of thermal management solutions (single-phase, two-phase, direct, indirect, hybrid, and more) which attempt to cool HPC DCs effectively while attempting to minimize overall system power consumption. However, the analysis of these solutions and methods to effectively compare one with another is lacking. Overall power usage effectiveness (PUE) and total-power usage effectiveness (TUE) provide a metric to quantify power consumption but fail to identify components in the system which require further optimization. To address this, we propose a holistic analytical framework – the waterfall diagram (WFD) – which leverages a waterfall chart methodology, offering a comprehensive visualization of both the thermal management system loop and heat flow pathways from individual server components to the outdoor ambient. Use of the WFD enables graphical estimations of power efficiency and cooling performance across each component of a DC cooling system and complements Sankey-style energy flow visualizations by additionally resolving stage-wise temperature changes and incremental TUE contributions. The framework is used in conjunction with simulation-based approaches, to conduct a detailed pressure drop and flow distribution analysis aimed at identifying the optimal coolant distribution architecture for a single-phase direct-to-chip water-cooled DC, which serves as the baseline for subsequent WFD analysis. Among the evaluated architectures, the 3 U modular coolant distribution architecture is found to demonstrate the best performance, considering minimal pressure drop and uniform flow distribution. In addition, TUE is calculated for each cooling loop component based on its associated pressure drop and corresponding pumping power, which are integrated into the WFD. This correlation between TUE and local temperature offers immediate insight into the power efficiency and thermal performance contributions of individual components, facilitating further development and optimization. Examples of WFD applications are presented under varying thermal loads and ambient conditions, demonstrating reasonable cooling strategies. Notably, the 3 U modular architecture maintains a consistent chip case temperature of 85°C, achieving a TUE of 1.016 at ambient temperature of 47°C, and a TUE of 1.026 at ambient temperature of 52°C. The WFD methodology provides an efficient, holistic, and streamlined framework for DC thermal management architecture assessment and enables design optimization which is important for addressing the thermal-fluidic energy challenges of current and next-generation DCs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. Furthermore, the results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Liquid helium fluid dynamics studies. Final Technical Report

Future high energy physics accelerators depend on a number of advanced technologies to open the many doors of scientific discovery. Among these advanced technologies, superconducting magnets and superconducting radio frequency (SRF) cavities are the backbone of the accelerator and detector systems. But all these low temperature systems depend critically on successful and reliable operation of their supporting technologies, among which the liquid helium cooling system is of the utmost importance. To improve the quality of these systems both in terms of efficiency and reliability, a robust helium cryogenics research and development (R&D) effort is required. The proposed research to be conducted by the FSU cryogenics group aims to produce fundamental knowledge that meets this R&D need. The projects that we have completed over the past grant period at Florida State University consist of experimental research on liquid helium fluid dynamics and heat transfer problems relevant to the development of future superconducting particle physics accelerators. Liquid helium is the coolant used in all such facilities and in many of these facilities He II (the low temperature phase of liquid helium also known as superfluid helium) is preferred due to its outstanding heat transfer characteristics. The work consists of two main experimental studies that probe both fundamental as well as practical aspects of liquid helium cooling. The first is a broad and fundamental study of the heat and mass transfer processes that can occur during a sudden catastrophic loss of vacuum (SCLV) incident in a superconducting accelerator. SCLV refers to the remote but extremely critical accident scenario where atmospheric pressure air is allowed to flood into the insulating vacuum system and impinge on the liquid helium cooled surfaces in the accelerator. Safe performance and recovery from such accidents is essential to the reliable operation of superconducting accelerators. The dynamics of this process is quite complex and so our approach is to conduct a series of well-orchestrated experiments that probe the various physical phenomena that can occur during an SCLV event. The experiments are coupled with analytic and numerical analysis in an effort to develop a general understanding of the process and to assist with future accelerator design and development. The second activity is directed toward fundamental understanding of heat and mass transfer in He II, which is essential to the design of superconducting magnets and radio frequency cavities in accelerators. The work consists of flow visualization of the dynamics of He II using laser assisted techniques. Two complementary techniques are used to study the fundamentals of the turbulent state. The first technique uses neutrally buoyant solid hydrogen particles to probe the flow fields of the superfluid and normal fluid components. The other technique uses laser excited He2* molecules as tracers of the normal fluid motion within the He II. The activities also included an effort to use visualization techniques to locate transient hot spots in radio frequency superconducting cavities. Such work provides valuable information about the heat transfer process in He II and its impact on the performance of superconducting devices. The research effort at Florida State University is not directly in support of a specific high energy physics experiment or facility. Rather, the work is general and coordinated with HEP accelerator laboratories to provide valuable insight that can assist with future accelerator development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Fundamental Understanding of Water Movement in Gas Diffusion Layer under Different Arrangements Using Combination of Direct Modeling and Experimental Visualization

In this paper, direct-modeling-based Lattice Boltzmann Method (LBM) combined with in-situ flow visualization, is used to explore fundamentally the transport of liquid-water inside the gas-diffusion layers (GDLs) used in polymer electrolyte fuel cells. Studies of the water evolution, water saturation, and breakthrough pressure inside a GDL with single and multiple injection points under land and channel geometries are explored. The model and experiment demonstrate good agreement between geometries of GDLs provided in this study which were obtained by a three-dimensional (3-D), reconstructed micro-structure from micro X-ray computed tomography (CT). The overall predictions of water evolution within the GDL agree well with the data visualized from the X-ray CT experiment for all cases studied. It also reveals that the liquid-water saturation profiles inside the GDL and breakthrough pressure are different when the location of the water injection point is altered, thereby providing analysis as to the impact of microporous layers or catalyst-layer functioning. Moreover, the uncompressed GDL undergoes a significantly different mechanism of water transport than that of the compressed GDL. Furthermore, the predictions show that the wettability variation is one of the key factors of the saturation characteristics.

42 ENGINEERING↗
DOE OSTI2020

Velocity Measurements in Channel Gas Flows in the Slip Regime by means of Molecular Tagging Velocimetry

Direct measurements of the slip velocity in rarefied gas flows produced by local thermodynamic non-equilibrium at the wall represent crucial information for the validation of existing theoretical and numerical models. In this work, molecular tagging velocimetry (MTV) by direct phosphorescence is applied to argon and helium flows at low pressures in a 1-mm deep channel. MTV has provided accurate measurements of the molecular displacement of the gas at average pressures of the order of 1 kPa. To the best of our knowledge, this work reports the very first flow visualizations of a gas in a confined domain and in the slip flow regime, with Knudsen numbers up to 0.014. MTV is cross-validated with mass flowrate measurements by the constant volume technique. The two diagnostic methods are applied simultaneously, and the measurements in terms of average velocity at the test section are in good agreement. Moreover, preliminary results of the slip velocity at the wall are computed from the MTV data by means of a reconstruction method

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Experiments and computations of microfluidic liquid–liquid flow patterns

We study two-phase liquid–liquid flow patterns in a 500 μm capillary microchannel for four biphasic systems: ethyl acetate/water, 2-pentanol/water, methyl isobutyl ketone/water, and heptane/water. Flow visualization experiments using laser induced fluorescence (LIF) reveal a total of 7 different flow patterns for all solvent pairs, namely slug flow, droplet flow, slug-droplet flow, parallel, annular, dispersed, and irregular flow. A map of different flow patterns was built to delineate the origin of their formation. We find conventional dimensionless groups are insufficient to uniquely identify the flow patterns. Computational fluid dynamics (CFD) modeling in OpenFOAM shows agreement with the experimental flow patterns for most of the two-phase flows. Principal component analysis reduces the dimensionality of potential descriptors of flow patterns and, unlike prior work using two dimensionless numbers, determines six important features that describe >95% of the variance of the experimental flow patterns. These include the total flow rate, the flow rate ratio between the two phases, the capillary and Ohnesorge numbers of the aqueous phase, and the Weber number and velocity of the organic phase. Lastly, we build a decision-tree model to further regress the data and identify the critical features and demonstrate an accuracy in predicting the flow patterns of up to 93%.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Milestone Completion Report WBS 1.3.5.05 ECP/VTK-m FY17Q4 [MS-17/03-06] Key Reduce / Spatial Division / Basic Advect / Normals STDA05-4.

The FY17Q4 milestone of the ECP/VTK-m project includes the completion of a key-reduce scheduling mechanism, a spatial division algorithm, an algorithm for basic particle advection, and the computation of smoothed surface normals. With the completion of this milestone, we are able to, respectively, more easily group like elements (a common visualization algorithm operation), provide the fundamentals for geometric search structures, provide the fundamentals for many flow visualization algorithms, and provide more realistic rendering of surfaces approximated with facets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Niowave Flow Testing of the High Power Converter - FY 21

Design work for a 100 kW converter to produce a neutron flux via electron impact on a flowing stream of liquid metal lead-bismuth (LBE) was conducted in FY20. In FY21, the focus shifted to a 20 kW converter which was designed in collaboration with Niowave engineers. A flow visualization model is needed to validate model results for the 20 kW converter and ensure adequate coolant flow over containment structures. This work highlights the mockup that was made with quartz side plates by LANL.

42 ENGINEERING↗
DOE OSTI2022

Continuous Emulation and Multiscale Visualization of Traffic Flow Using Stationary Roadside Sensor Data

With the advent of the next-generation traffic monitoring systems, there has been a significant increase in the spatial-temporal resolution of vehicle mobility data in many cities. Effective analysis and visualization of such data can provide transportation planners with data-driven insights, which can facilitate the understanding of multiscale traffic dynamics. In this paper, we present a web-based traffic emulator for emulating and visualizing near-real-time and historical traffic flows on highways using data from road-side sensors. To construct a continuous traffic flow, the emulator adopts an analytical pipeline that can (a) integrate traffic data collected from discrete road-side radar detection sensors, (b) interpolate traffic conditions (vehicle speed and volume) on unmeasured road segments based on traffic flow theory, and (c) generate lane-specific vehicle trajectories and movements using a mathematically optimized representation of the road network. Our app also provides an integrated visual workflow that allows users to explore the interconnected traffic dynamics using an appropriate traffic flow visualization selected based on the level of detail. We devise two innovative geo-visualization techniques that utilize an animated strips-network representation and a lane usage matrix to visualize lane performances. To ensure a smooth emulation of large-scale traffic flow in an easy-to-access web environment, we implement the emulator using client-side GPU-accelerated techniques. Lastly, we close with a case study that visualizes traffic dynamics of two scenarios - an afternoon peak hour and a traffic accident - in Chattanooga, Tennessee. Our app visualizes the responses of traffic dynamics during different traffic conditions, and to the presence of the traffic accident at different spatial scales.

42 ENGINEERING↗
DOE OSTI2020

Deep Learning for Intelligent Bubble Size Detection in the Spallation Neutron Source Visual Target

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) will undergo proton power upgrade (PPU), increasing the proton beam power from 1.4 MW to 2.8 MW. From 2.8 MW, 2.0 MW will go to the current First Target Station and the rest will go to the future Second Target Station (STS). The First Target Station uses a liquid mercury target that is contained in a 316L stainless steel vessel. The proton beam is pulsed at 60 Hz, with a pulse of about 0.7μs. When the proton beam hits the target, the intense energy deposition leads to a rapid rise in temperature in the mercury. This temperature rise creates pressure waves that propagate through the mercury and cause cavitation erosion. The power upgrade will cause stronger pressure waves that will further increase damage because of cavitation. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at 1.4 MW. However, at higher power, additional mitigation is necessary. Therefore, the 2 MW target vessel will be equipped with swirl bubblers and an additional gas injection port near the nose to inject more gas in the target. To develop a gas injection strategy and design, flow visualization in water with a transparent prototypical target (“visual target”) was performed. Bubble sizes and their spatial distribution in the flow loop are crucial to understanding the effectiveness of the bubbles in mitigating pressure waves. Bubbles were generated in the visual target under varied conditions of input pressures with helium and air. Images were captured using a high-speed camera at varied frame rates at different positions away from the swirl bubbler and different depths in the flow loop under varying lighting conditions. Initially, methods such as circular Hough transforms were applied after a series of images processing to obtain a general distribution of bubble sizes. Bubbles smaller than 500 μm are preferred to effectively mitigate the effect of pressure waves, which demands an accurate bubble detection and sizing system. Intelligent detection and identification of bubble sizes alleviate misdetection and improves accuracies. Employing neural networks, intelligent detection of bubble sizes and their distribution was developed and provides a robust alternative to traditional techniques. Human intervention was employed to label in-focus and out-of-focus bubbles in the set of training images. An object detection network using a pretrained convolutional neural network was created that extracted the features from the training images. Data augmentation was used to improve network accuracy through a random transformation of the original data.

Rasheed, Fayaz↗
DOE OSTI2014

Remedial Amendment Delivery near the Water Table Using Shear Thinning Fluids: Experiments and Numerical Simulations

The use of shear thinning fluids (STFs) containing xanthan is a potential enhancement for emplacing a solute amendment near the water table and within the capillary fringe. Most research to date related to STF behavior has involved saturated and confined conditions. A series of flow cell experiments were conducted to investigate STF emplacement in variable saturated homogeneous and layered heterogeneous systems. Besides flow visualization using dyes, amendment concentrations and pressure data were obtained at several locations. The experiments showed that injection of STFs considerably improved the subsurface distribution near the water table by mitigating preferential flow through higher permeability zones compared to no-polymer injections. The phosphate amendment migrated with the xanthan SFT without retardation. Despite the high viscosity of the STF, no excessive mounding or preferential flow were observed in the unsaturated zone. The STOMP simulator was able to predict the experimentally observed fluid displacement and amendment concentrations reasonably well. Cross flow between layers could be interpreted as the main mechanism to transport STFs into lower permeability layers based on the observed pressure gradient and concentration data in layers of differing hydraulic conductivity.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2025

Validation of Pronghorn for Natural-Circulation Molten Salt Loops

This paper presents the development and validation of a high-fidelity thermal-hydraulic model of a molten salt natural circulation flow loop, designed for integration within a digital twin framework. The study evaluates the performance of Idaho National Laboratory’s Pronghorn against experimental data from Texas A&M University Molten Salt Flow Loop (MSFL) four Hitec-salt test benchmark data. Natural circulation of high-Prandtl-number fluids exhibits complex, counter-intuitive flow patterns that make pointwise thermocouple readings unreliable. Experimental work at TAMU’s MSFL provides benchmark data, including flow visualization at a test-section and centerline steady-state temperature measurements along the loop. Validation includes four single-phase natural circulation test cases with Hitec salt. Key metrics include flow profile agreement and steady-state temperature accuracy. Pronghorn results for two-dimensional single-phase agree qualitatively with the experimental flow profile. This paper illustrates the importance of Computational Fluid Dynamics (CFD) in elucidating the behavior of high-Prandtl-number thermal-hydraulics, along with how misleading centerline temperature measurements can be. Pronghorn reproduces the axial and radial stratification that makes single thermocouple readings unreliable. Future research will focus on reduced-order modeling techniques to enable rapid simulation suitable for real-time digital twin applications. The validated cases provide a basis for developing reduced-order surrogates aimed at real-time digital-twin applications.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Dynamic Data Repartitioning for Load-Balanced Parallel Particle Tracing

We present a novel dynamic load-balancing algorithm based on data repartitioning for parallel particle tracing in flow visualization. Instead of static data assignment, we dynamically repartition the data into blocks and reassign the blocks to processes to balance the workload distribution among the processes. Block repartitioning is performed based on a dynamic workload estimation method that predicts the workload in the flow field on the fly as the input. In our approach, we allow data duplication in the repartitioning, enabling the same data blocks to be assigned to multiple processes. Load balance is achieved by regularly exchanging the blocks (together with the particles in the blocks) among processes according to the output of the data repartitioning. Compared with other load-balancing algorithms, our approach does not need any preprocessing on the raw data and does not require any dedicated process for work scheduling, while it has the capability to balance uneven workload efficiently. Results show improved load balance and high efficiency of our method on tracing particles in both steady and unsteady flow.

data repartitioning↗
DOE OSTI2016

Particle-image Velocimetry Sensitivity through Automatic Differentiation

A commonly encountered difficulty in modern experimental fluid dynamics experiments is the need for full-flow visualization and measurement; traditional techniques such as hot-wire probes and laser Doppler velocimetry cannot provide such information without difficult scanning procedures. Particle-image velocimetry (PIV) is a measurement technique which can overcome this spatial limitation to provide real-time three-dimensional fluid velocity vectors for an entire plane within the flow, as opposed to a single point that is provided by other measurement techniques. To accomplish this, a PIV system seeds the fluid flow with tracer particles; these must have nearly the same density as that of the fluid and a high drag coefficient to ensure that they follow the fluid flow without deviation. A laser is sent through optics to expand its beam into a sheet which illuminates the plane of interest in the fluid. The particles reflect more light than the fluid, and their image is recorded using a high speed camera. Due to limitations in bandwidth, video cannot be taken fast enough to be useful, and instead pairs of images are captured with a known separation in time. The illuminated particles will move between the two images taken by the camera, and their relative motion can be used to compute the fluid velocity at that point. When a single camera is used, only two-dimensional velocity vectors can be computed, but with the addition of another camera this can be improved to full three-dimensional vectors. The flow's time evolution can be measured by taking series of image pairs and processing each pair to get the velocity field at the time between each image pair. Only the two-dimensional version will be considered in this work. To compute the velocity vectors of the flow, the images are broken up into interrogation regions, usually in a uniform grid. In the most basic PIV algorithm, corresponding regions in the image pairs are cross-correlated to compute the most likely displacement from one image to the next. This is used since the cross correlation will achieve a maximum value when the two interrogation regions line up the best. The location of the peak in the correlation map and scaling information for the optical setup is used to compute the particle displacement from one image to the next. This process is similar to holding two semi-transparent images and moving one until they match as well as possible. Sub-pixel displacements between images can be obtained by fitting a Gaussian function to the correlation peak. Knowing the displacement vector for each set of interrogation regions in the image pair, it is a simple matter to divide by the time gap between the two images to compute the fluid velocity at the point in time and space. Since there are many interrogation regions in each image pair, the velocity field for a sheet is sampled according to the arrangement of the interrogation regions. The sensitivity of the final computed vector to the input images is difficult to compute, and has led most considerations of uncertainty in the PIV field to apply Monte Carlo methods and correlations to quantify the systematic and random errors which result from application of various PIV algorithms. In this work, automatic differentiation (AD) has been used to trace the dependence of velocity vectors computed using the correlation-peak PIV algorithm back to the input values given to an artificial image generator. These initial results form the foundation for continued work in the application of AD to algorithms in PIV. They demonstrate that AD methods can be successfully applied to PIV algorithms without undue complexity. The derivatives of each individual vector with regard to the coefficients of the velocity field used to create the artificial images can be computed and the statistics of them considered collectively, or correlated between each other to quantify the effectiveness of a PIV algorithm. With the initial implementation complete, adding extra algorithms is relatively simple and considerable data can be generated for analysis. It is hoped that application of these methods can lead to improved PIV algorithms which demonstrate better sensitivity to small variations in particle displacement. While these methods can be used as an analysis tool for refinement of new algorithms, computation of actual resultant vector sensitivities to input images' individual pixels is the next logical step of this work. Such information will be analyzed with experimental data to produce a better understanding of how output vectors' uncertainty relates to the actual image pairs, and lead to automatic bad vector removal. (authors)

42 ENGINEERING↗