Dedicated to the memory of John Furlan. Wear prediction is important in designing reliable machinery for slurry industry. It usually relies on multi-phase computational fluid dynamics, which is accurate but computationally expensive. Each run of the simulations can take hours or days even on a high-performance computing platform. The high computational cost prohibits a large number of simulations in the process of design optimization. In contrast to physics-based simulations, data-driven approaches such as machine learning are capable of providing accurate wear predictions at a small fraction of computational costs, if the models are trained properly. In this paper, a recently developed WearGP framework [1] is extended to predict the global wear quantities of interest by constructing Gaussian process surrogates. The effects of different operating conditions are investigated. The advantages of the WearGP framework are demonstrated by its high accuracy and low computational cost in predicting wear rates.

Fluidized beds are used in a wide range of applications in gasification, combustion, and process engineering. Multiphase flow in such applications involves numerous uncertain parameters. Uncertainty quantification provides uncertainty in syngas yield and efficiency of coal/biomass gasification in a power plant. Techniques such as sensitivity analysis are useful in identifying parameters that have the most influence on the quantities of interest. Also, it helps to decrease the computational cost of the uncertainty quantification and optimize the reactor. We carried out a nondeterministic analysis of flow in a biomass reactor. The flow in the reactor is simulated with National Energy Technology Laboratory’s open source multiphase fluid dynamics suite MFiX. It does not possess tools for uncertainty quantification. Therefore, we developed a C++ wrapper to integrate an uncertainty quantification toolkit developed at Sandia National Laboratory with MFiX. The wrapper exchanges uncertain input parameters and critical output parameters among Dakota and MFiX. We quantify uncertainty in key output parameters via a sampling method. In addition, sensitivity analysis is carried out for all eight uncertain input parameters namely particle-particle restitution coefficient, angle of internal friction, coefficient of friction between two-phases, velocity of the fluidizing agent at the inlet, velocity of the biomass particles at the inlet, diameter of the biomass particles, viscosity of the fluidizing agent, and the percentage of nitrogen/oxygen in the fluidizing agent.

In the manufacturing of metal matrix composites (MMC), liquid-metal reactive infusion with a solid mesh or particles composed of ceramic or metal may be used. The objective of this study is to determine the uncertainty quantification of the modeling of liquid hafnium infusion to expedite the processing and improve properties of MMCs ultimately. Uncertainty quantification (UQ) characterized the uncertainty scientifically especially for high-performance computing with observed physics and/or chemistry of the phenomena and predicted from estimated parameters. In this work, molten hafnium infusing through a boron carbide packed bed is modeled to optimize the manufacturing of components used for a hypersonic vehicle. The creation of molten matrix composites by the infiltration of molten metal represents a formidable challenge to be accurately modeled. First, the structural randomness associated with porous mediums complicates the prediction of the flow passing through it. Secondly, the properties of the molten metal could vary inside our control volume, since the temperature inside the control volume is not constant. Also, there are several chemical reactions and solidification rates occurring in during the impregnation. Given the recent advances in high-performance computing, an in-house pore network simulator are implemented along with Dakota, an open-source, exascale software, to determine the optimal parameters (e.g., porosity and temperature) and uncertainty quantification for the modeling.

Numerical modeling of turbulent mixing is complicated not only by the natural complexity of the flow physics, but by the model sensitivity to the user specified conditions. When aiming to quantify the level of trust in a given model, a validation experiment is often performed to provide data against which confidence comparisons can be made, ultimately evaluating the adequacy of the model assumptions. In the nuclear community, a number of promising Generation IV reactor concepts have been proposed, each requiring high fidelity modeling capabilities to accurately assess safety related issues. The experiment described in this paper is intended to provide a much needed validation data set to assess the use of computational fluid dynamics (CFD) in a complex turbulent mixing scenario relevant to the prismatic very high temperature reactor (VHTR) concept. Over the course of the VHTR’s operation, the reactor’s graphite moderated hexagonal fuel blocks shrink from neutron damage, forming interstitial gaps between adjacent blocks. A significant percentage of the coolant can flow through these gaps, having a substantial impact on the thermal-hydraulic conditions in the core. An experimental facility is presented that uses air as a simulant fluid and includes a unit cell representation of the hexagonal blocks, which accounts for both the intended circular channels and secondary rectangular slot features induced by the bypass gaps. The outlet of the unit cell consists of a collated jet consisting of a central round jet surrounded by three slot jets at relative 120° angles to one another issuing into a stagnant domain. A preliminary test case is proposed in which the collated jet is set to an isothermal and iso-velocity condition. Constant temperature anemometry (CTA) and constant current anemometry (CCA) measurements serve to capture the velocity and temperature inlet quantities (IQs). Particle image velocimetry (PIV) measurements provide the appropriate system response quantities (SRQs), yielding insight into the mean and fluctuating components of the 2-D velocity field. Results are presented in the range of 0–8 diameters downstream of the inlet to the test section. The collated jet inlet region yields velocity profiles that are heavily influenced by opposing pressure gradients between the neighboring round and slot regions. As a result, the velocity peaks found in this area are neither in the centerline of the round jet nor that of the slot, but are towards the outer edge of each. With increasing downstream distance, the collated jet is found to exhibit a more classical round jet profile. The inlet region of the collated jet is thus of particular interest to future modeling efforts to more accurately depict the lower plenum behavior and transition to a self-similar profile downstream. Proper uncertainty quantification is also presented, and aids in assessing the integrity of the experimental results for future CFD validation.

The need for a revised methodology and uncertainty quantification for wire-mesh sensor void fraction measurements in horizontal low void fraction flow conditions was identified. Two-phase flow measurements were performed at a low-pressure, adiabatic and horizontal flow loop using wire-mesh sensors over a range of water superficial velocities from 3.5 to 5.5 m/s, air superficial velocities from 0.05 to 0.9 m/s and volumetric void fractions from 1 to 16% Using this proposed analysis, a corrected trend with average percent differences of 36, 21 and 6% was obtained for the low, medium and high gas flow rate cases, respectively, when comparing the wire-mesh sensor void fractions to two-phase pipe flow models. By combining these measurements of the void fraction with those of the interfacial velocity, the gas superficial velocity was calculated based on the physical theory, and compared to the superficial velocity measured by the flowmeters for validation purposes. An estimation of the uncertainty of these parameters showed that most of the measured parameters agreed reasonably with physical theory within 20%.

Uncertainty quantification for planar PIV remains a challenging task. In the present study, we assess three methods that were recently described in the literature: primary peak ratio (PPR), mutual information (MI), and image matching (IM). Each method was used to calculate the uncertainty in a synthetic turbulent boundary layer flow and an experimental jet flow. In the experimental case, two PIV systems with common fields of view were used — one with a high dynamic range (which was considered as the true solution) and another with a magnification ratio of about four times less (which was considered the measurand). The high resolution PIV system was verified by comparing velocity records at a point with an LDV measurement system. PIV processing was performed with PRANA and Insight4G. In regards to the experimental flow, the PPR method performed best, followed by mutual information, and lastly image matching. This was due to better responses by PPR and MI of uncertainty to the spatially varying error distribution. Similar conclusions were made with respect to the synthetic test case.

In the last decade there has been a growing interest in urban flow CFD simulations. As RANS approaches demonstrated to be not enough accurate to predict urban flows, people focus more and more on LES simulations. Though better results could be obtained with fine grid LES, the complexity of the urban physics seems to vanish the increasing computational resources. A different approach is herein considered, proposing a first uncertainty quantification (UQ) analysis on a single building pollutant dispersion case. A hybrid method merging the anchored-ANOVA and the POD/Kriging-based response surface is proposed to reduce the costs of the UQ analysis. Moreover, simulations are performed by the Lattice Boltzman (LBM) code PowerFLOW. Sensitivity results are presented showing the importance of vortex dynamics and the high sensitivity to the wind angle.

Recent concerns over the safety of oil and natural gas extraction, fracking, and carbon sequestration have driven the need to develop methods for uncertainty quantification for coupled subsurface flow & deformation processes. Traditional monte-carlo methods are versatile, but exhibit prohibitively slow convergence. In this work, we develop an intrusive polynomial chaos expansion method for Biot’s Poroelasticity Equations based on galerkin projection with uniform and log-normally distributed material parameters. We analyze accuracy and efficiency of our method and compare it to monte-carlo and anova based probabilistic collocation methods.

Measurement uncertainty of quantities that are functions of more than one measured variable are usually determined using propagation methods; either the Taylor Series Method or the Monte Carlo Method. Each of these requires critical assumptions that are more sweeping and potentially dangerous than commonly realized. The implications of these assumptions is explained along with some examples of how violation of these assumptions invalidates the uncertainty estimate. A new perspective based on consideration of potential error sources is presented ranging from the physical system being measured, the measurement system, the data reduction system, to the final experimental measurement result. An alternative approach that relies on sampling of error sources, whether known or unknown, is demonstrated through several examples. These examples demonstrate that the alternative approach can provide a more realistic estimate of total experimental uncertainty; one which is commonly much larger than that provided by traditional propagation methods.

Digital in-line holography has been applied extensively to particle field measurement, where the particles can be the tracer particles for flow measurements, droplets in spray diagnostics, or aquatic microorganisms. The particle detection algorithm plays a key role in accurate detection of particle 3D locations and sizes. A hybrid method has recently been proposed for particle field measurement in digital in-line holography. It features automatic determination of the threshold for segmentation of the particle field and the capability to measure particles of arbitrary shapes. Using the hybrid method, the particle 3D location, size and shape information can be extracted. The uncertainty of the hybrid method is characterized using both synthetic and experimental holograms at different particle field conditions. The depth measurement uncertainty is within 2 times the particle diameter for a wide range of particle field conditions.

As the effects of climate change continue to rise with increasing carbon dioxide emission rates, it is imperative that we develop an efficient method for carbon capture. This paper outlines the framework used to break down a large, complex carbon capture system into smaller unit problems for model validation, and uncertainty quantification. We use this framework to investigate the uncertainty and sensitivity of the hydrodynamics of a bubbling fluidized bed. Using the open-source computational fluid dynamics code MFIX we simulate a bubbling fluidized bed with an immersed horizontal tube bank. Mesh resolution and statistical steady state studies are conducted to identify the optimal operating conditions. The preliminary results show good agreement with experimental data from literature. Employing statistical sampling and analysis techniques we designed a set of simulations to quantify the sensitivity of the model to model parameters that are difficult to measure, including: coefficients of restitution, friction angles, packed bed void fraction, and drag models. Initial sensitivity analysis results indicate that no parameters may be omitted. Further uncertainty quantification analysis is underway to investigate and quantify the effects of model parameters on the simulations results.

A robust shape optimization procedure based on a multi-objective genetic algorithm coupled to a non-intrusive uncertainty quantification analysis was applied to a transonic inviscid flow of a dense gas over a plane turbine cascade. The goal was to simultaneously improve the mean turbine performance and the system stability under fluctuating thermodynamic inlet conditions. Despite an elevated computational cost, the optimization procedure was capable of generating a Pareto front of turbine geometries which improved the mean isentropic turbine efficiency μ(η s ) over the baseline profile, while limiting the solution variability in terms of the coefficient of variation of the power output CV ( P 2 D ). In addition to demonstrating an excellent parallel scalability over 1600 processors, the robust optimization revealed that variability of CV ( P 2 D ) depends more on the variation of inlet conditions than turbine geometry. A posteriori stochastic analyses on selected optimized turbine geometries allowed an investigation of flow behavior variability, as well as propositions for the improved selection of robust optimization cost criteria in future simulations.

Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades and military aircrafts with increasing maneuvering capabilities etc. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. The analysis has been put in a stochastic framework and the propagation of system uncertainties have been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection based non-intrusive Polynomial Chaos approach is compared to its classical Galerkin based counterpart, and proven to be more efficient as order of chaos expansion increases. Effect of system randomness on the bifurcation behavior and the flutter boundary has been significant. Stochastic bifurcation results and bifurcation of probability density functions are presented here.

In this article, a method is proposed to study uncertainty propagation on high-dimensional obstacle problems. A greedy algorithm, based on variable decomposition, is used to approximate the solution of regularized problems obtained by penalization of the initial problem. The convergence of this algorithm is a consequence of a more general theorem. Indeed, the algorithm converges for the minimization of a strongly convex functional whose derivative is Lipschitz on bounded sets. We describe how this algorithm was numerically implemented and present the results which were obtained with a one-dimensional membrane problem.

This paper is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are determined from experiments performed on elementary flows and they are subject to uncertainty. The widely used k– ε turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for the flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte-Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise velocity component in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly affected.

A method to estimate the uncertainty of each vector in Particle Image Velocimetry measurements by estimating the parameters which contribute to errors in the computed velocity field is discussed. These parameters include particle image diameter, particle density, particle displacement, and velocity gradient. After PIV processing, our code “measures” these parameters and an estimate of the velocity uncertainty is made for each vector in the flow field.

A major focus for the development of computational fluid dynamics (CFD) technology is the attainment of an acceptable level of credibility of CFD analysis and simulations for the range of fluid flows of interest. Toward this end, a systematic program for CFD verification and validation (V&V) is being developed and implemented to enable Predictive-CFD (P-CFD) capability for use in the industrial design process. This paper provides an overview of a practical approach for CFD V&V that can support the initial use of CFD in the industrial design process and lays the foundation for providing a true predictive capability for CFD in the future. The approach emphasizes a bottom up view of CFD validation. In particular, validation assessments of fundamental, unit and separate-effects physics, flow configurations are performed to develop the large body of knowledge required to implement knowledge-based tools and procedures, e.g. , best practices and design guidelines, for managing uncertainty and improving reliability of CFD analysis and simulations. In this approach, the flow field data obtained from validation experiments require a higher level of fidelity, resolution and documentation, including a complete and thorough description of the boundary and initial conditions driving the flows, the as-built geometry of the validation experiment and an appropriate uncertainty analysis of the experimental data. Datasets which meet these standards are termed validation-level datasets. It is expected that over time, the amount of validation-level data in the CFD V&V archives and the knowledge gained from CFD V&V assessments will be sufficient to assure the accuracy of the associated CFD predictions over a wide range of applications with a minimal amount of additional, confirmatory physical testing. In time, automated and standardized P-CFD methodology with associated best practices, design guidelines, and uncertainty quantification methods will provide a predictive capability in which sufficient confidence can be placed in CFD predictions that CFD analysis can replace large, semi-scale physical testing and allow for designs to be developed using CFD up front in the design process.