Integral Quantities Research Articles

Ocean data assimilation focusing on integral quantities characterizing observation profiles

An observation operator in data assimilation was formalized based on the signatures extracted from the integral quantities contained within observed vertical profiles in the ocean. A four-dimensional variational global ocean data assimilation system, founded on this observation operator, was developed and utilized to conduct preliminary data assimilation experiments over a ten-year assimilation window, comparing the proposed method, namely profile-by-profile matching, with the traditional method, namely point-by-point matching. The proposed method not only demonstrated a point-by-point skill comparable to the traditional method but also provided superior analysis fields in terms of profile shapes on the temperature-salinity plane. This is an indication of a well-balanced analysis field, in contrast to the traditional method, which can produce extremely poor relative errors for certain metrics. Additionally, signatures were shown to successfully represent properties of the water column, such as steric height, and serve as an effective new diagnostic tool. The top-down, or macro–micro, viewpoint in this method is fundamental to the extent that it can offer an alternative view of how we comprehend ocean observations, holding significant implications for the advancement of data assimilation.

A Numerical Study on the Influence of Confining Walls on Drag and Heat Transfer Coefficients in Single‐Particle Lab‐Scale Reactors

AbstractSingle‐particle reactors in lab‐scale are a promising technology to gain an in‐depth understanding of the intricate reaction and transport processes that occur in catalyst particles under operando conditions. It is not described whether the effect of the bounding walls in such narrow flow channels influence the processes at the particle. Therefore, this work applies three‐dimensional (3D) computational fluid dynamics (CFD) simulations to analyze the drag coefficient CD alongside the local and average particle Nusselt number Nup as characteristic local and integral quantities in the range of particle Reynolds numbers 10 ≤ Rep ≤ 103. An equation is derived to correct for the wall effects on CD and Nup and assist the experimenter in the interpretation of measured results.

On the size- and shape-dependence of integral and partial molar Gibbs energies, entropies, enthalpies and inner energies of solid and liquid nano-particles

In this paper the size- and shape dependences of 8 different integral and partial molar thermodynamic quantities are derived for solid and liquid nano-phases, starting from the fundamental equation of Gibbs: i) The integral molar Gibbs energies of nano-phases and the partial molar Gibbs energies of components in those nano-phases, ii) The integral molar enthalpies of nano-phases and the partial molar enthalpies of components in those nano-phases, iii) The integral molar entropies of nano-phases and the partial molar entropies of components in those nano-phases, and iv). The integral molar inner energies of nano-phases and the partial molar inner energies of components in those nano-phases. All these 8 functions are found proportional to the specific surface area of the phase, defined as the ratio of its surface area to its volume. The equations for specific surface areas of phases of different shapes are different, but all of them are inversely proportional to the characteristic size of the phase, such as the diameter of a nano-sphere, the side-length of a nano-cube or the thickness of a thin film. Therefore, the deviations of all properties discussed here from their macroscopic values are inversely proportional to their characteristic sizes. The 8 equations derived in this paper follow strict derivations from the fundamental equation of Gibbs. Only the temperature dependent surface energy of solids and surface tension of liquids will be considered as model equations to simplify the final resulting equations. The theoretical equations are validated for the molar Gibbs energy against the experimental values of liquidus temperatures of pure lead. The theoretical equations for the molar enthalpy are validated i). Against the experimental values of dissolution enthalpy differences between nano- and macro cobalt particles in the same liquid alloy and ii). Against the size dependent melting enthalpy of nano-indium particles. In this way, also the theoretical equations for the molar entropy and molar inner energy are validated as they are closely related to the validated equations for the molar Gibbs energy and molar enthalpy.

Modal Discontinuous Galerkin Simulations of Richtmyer–Meshkov Instability at Backward-Triangular Bubbles: Insights and Analysis

This paper investigates the dynamics of Richtmyer–Meshkov instability (RMI) in shocked backward-triangular bubbles through numerical simulations. Two distinct gases, He and SF6, are used within the backward-triangular bubble, surrounded by N2 gas. Simulations are conducted at two distinct strengths of incident shock wave, including Ms=1.25 and 1.50. A third-order modal discontinuous Galerkin (DG) scheme is applied to simulate a physical conservation laws of two-component gas flows in compressible inviscid framework. Hierarchical Legendre modal polynomials are employed for spatial discretization in the DG platform. This scheme reduces the conservation laws into a semi-discrete set of ODEs in time, which is then solved using an explicit 3rd-order SSP Runge–Kutta scheme. The results reveal significant effects of bubble density and Mach numbers on the growth of RMI in the shocked backward-triangular bubble, a phenomenon not previously reported. These effects greatly influence flow patterns, leading to intricate wave formations, shock focusing, jet generation, and interface distortion. Additionally, a detailed analysis elucidates the mechanisms driving vorticity formation during the interaction process. The study also thoroughly examines these effects on the flow fields based on various integral quantities and interface characteristics.

Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations

Investigation of Atwood number impact is crucial for comprehending the flow dynamics of the evolving hydrodynamic instability. In this paper, the Atwood number impacts on the shock-driven hydrodynamic instability at a backward-facing pentagonal interface in its early stages are explored numerically. The shock-driven pentagonal interface has a unique property in which the incident angle of the shock wave is constant along the interface edge. This property provides the ideal environment for the shock-refraction process. To examine the Atwood number impact, we consider five distinct gases, including sulfur hexafluoride, krypton, argon, neon, and helium, which are filled inside the pentagonal interface and surrounded by nitrogen gas. A mixed modal discontinuous Galerkin method is used to solve the two-dimensional Navier–Stokes–Fourier equations for two-component gas flows for numerical simulations. The simulation results illustrate that the Atwood number plays a crucial role in the flow fields of the shocked-pentagonal gas interface, which have not been reported in the literature. The flow fields are greatly impacted by the Atwood number, leading to complex wave patterns, shock focusing, jet formation, interface deformation, and vorticity generation. Further, the Atwood number effects on the flow fields are also thoroughly examined by a quantitative study based on the integral quantities and the interface features. Finally, a quantitative analysis is performed to examine the intrinsic differences between the evolution of the flow fields at the square and pentagonal interfaces.

Estimation Procedure for the Degradation of a Lithium-Ion Battery Pack

This paper proposes a test procedure for evaluating the degradation of cells in a battery pack. The test can be performed using only the charger’s converters and the battery management system (BMS) without requiring sophisticated instrumentation. The method circumvents the difficulties related to the evaluation of derivative quantities for estimating the state of health (SOH) using integral quantities in the evaluation. The method introduces a 'degradation function' that is calculated with respect to the reference performance of pristine cells. The procedure was applied to the JuiceRoll Race Edition system, an innovative electric vehicle (EV) DC charger with internal storage, made in ENEL X and used during the MotoE championship races. Using this procedure, the degradation of performance in individual groups of cells composing the battery pack was quantified in comparison to the reference group. The procedure helps identify modules that have aged too early or show reliability issues. The method is mature for field operational applications.

Aerodynamic Characterization of the IEA 15 MW Reference Wind Turbine by Code-to-Code Comparison

The consistency of different aerodynamic formulations applied to the analysis of a modern multi-megawatt horizontal axis wind turbine rotor is investigated. The proposed code-to-code comparison involves specific implementations of a hierarchy of solvers based on Blade Element Momentum Theory (AEOLIAN), Actuator Line Modelling (OpenFOAM), free-wake Panel Method (FUNAERO) and blade-resolved Computational Fluid Dynamics (OpenFOAM ). The analysis addresses local and integral aeroloads and flow physical quantities concerning the state-of-the-art IEA 15 MW reference wind turbine in axial uniform flow conditions. The proposed solvers predict consistent rotor performance and blade aeroloads (also in line with data from of IEA Task 47). However, differences emerge close to blade root, where blade-resolved CFD reveals a significant flow separation on the suction side. Furthermore, scattering of induction factors computations is observed, especially in the axial direction. Different methodologies and numerical setup used in blade-resolved simulations allow achieving physically-consistent induction values, especially at blade tip. Finally, flow-field predictions by Computational Fluid Dynamics (CFD) and Panel Method are consistent upstream and close to the disk downstream (except where significant flow separation occurs), whilst a more detailed study on the effect of extending wake refinement zone in CFD simulation is advisable.

Extended Regression Analysis for Debye-Einstein Models Describing Low Temperature Heat Capacity Data of Solids.

Heat capacity data of many crystalline solids can be described in a physically sound manner by Debye-Einstein integrals in the temperature range from 0K to 300K. The parameters of the Debye-Einstein approach are either obtained by a Markov chain Monte Carlo (MCMC) global optimization method or by a Levenberg-Marquardt (LM) local optimization routine. In the case of the MCMC approach the model parameters and the coefficients of a function describing the residuals of the measurement points are simultaneously optimized. Thereby, the Bayesian credible interval for the heat capacity function is obtained. Although both regression tools (LM and MCMC) are completely different approaches, not only the values of the Debye-Einstein parameters, but also their standard errors appear to be similar. The calculated model parameters and their associated standard errors are then used to derive the enthalpy, entropy and Gibbs energy as functions of temperature. By direct insertion of the MCMC parameters of all 4·105 computer runs the distributions of the integral quantities enthalpy, entropy and Gibbs energy are determined.

Geomorphic indicators of continental-scale landscape transience in the Hengduan Mountains, SE Tibet, China

Abstract. Landscapes are sculpted by a complex response of surface processes to external forcings, such as climate and tectonics. Several major river captures have been documented in the Hengduan Mountains, leading to the hypothesis that the region experiences exceptionally high rates of drainage reorganization driven by horizontal shortening and propagating uplift. Here we determine the prevalence, intensity, and spatial patterns of ongoing drainage reorganization in the Hengduan Mountains and evaluate the relative timescales of this transience by comparing drainage divide asymmetry for four geomorphic metrics that operate at different spatial and temporal scales. Specifically, we calculate the migration direction and the divide asymmetry index (DAI) for drainage divides using catchment-restricted topographic relief (CRR), hillslope gradient (HSG), normalized channel steepness (ksn), and normalized channel distance (χ). ksn and χ are both precipitation-corrected to account for the strong precipitation gradient across the region. The different spatial scales of these geomorphic metrics allow us to establish the relative timescales of observed landscape transience in the Hengduan Mountains, where local-scale metrics measure short-term change and integral quantities measure long-term disequilibrium. We find a high incidence of strongly asymmetric divides in all metrics across the Hengduan Mountain region. Although the magnitude of asymmetry varies significantly between metrics, possibly due to a combination of metric-specific thresholds and varying proxy relationships with erosion rate, a majority of divides agree on divide migration direction. Agreement in divide migration direction indicates an actively responding landscape when asymmetry is high and a state of quasi-equilibrium when asymmetry is low. Disagreements between the integral quantity, χ, and the other geomorphic metrics can be explained by different timescales of the underlying geomorphic processes, with χ reflecting a long-term response and CRR, HSG, and ksn capturing short-term perturbations to catchment structure. These perturbations include various transient mechanisms, such as differential tectonic uplift or erodibility, glacial alteration, and river captures. Our work confirms the high incidence of drainage reorganization across the Hengduan Mountains and highlights both transient and stable areas in the landscape with high resolution. We also offer valuable insights into the application of geomorphic metrics that can be generalized and applied to the study of landscape transience and drainage divide asymmetry in other settings.

Concentration Quenching of Fluorescence Decay Kinetics of Molecular Systems.

Fluorescence concentration quenching occurs when increasing molecular concentration of fluorophores results in a decreasing fluorescence quantum yield. Even though this phenomenon has been studied for decades, its mechanisms and signatures are not yet fully understood. The complexity of the problem arises due to energy migration and trapping in huge networks of molecules. Most of the available theoretical work focuses on integral quantities like fluorescence quantum yield and mean excitation lifetime. In this work, we present a numerical study of the fluorescence decay kinetics of three-dimensional and two-dimensional molecular systems. We investigate the differences arising from the variations in models of trap formations. We also analyze the influence of the molecular orientations to the fluorescence decay kinetics. We compare our results to the well-known analytical models and discuss their ranges of validity. Our findings suggest that the analytical models can provide inspiration for different ways of approximating the fluorescence kinetics, yet more detailed analysis of the experimental data should be done by comparison with numerical simulations.

Development and validation of a Bayesian unfolding program using OpenBUGS open-source software for Bonner spheres neutron spectrometry

This study presents the development of a novel unfolding program based on a Bayesian method for Bonner spheres spectrometry. The program incorporates a priori information on the neutron spectrum, employing a linear superposition of three non-negative parametric functions: thermal-Maxwellian distribution, an intermediate region represented by a straight line in lethargy space (1/E behavior), and the Watt fission distribution for the fast region. The effectiveness of the developed program was validated through its application to two reference cases from the EURADOS 2018 exercise (LINAC and Skyshine), followed by its implementation in characterizing the neutron field around an OB26 neutron irradiator at the Secondary Standards Dosimetry Laboratory (SSDL) of the Nuclear Research Center of Algiers (CRNA), Algeria. While validation results for the LINAC case were promising, achieving comparable neutron spectrum shape and integral quantities to the reference, challenges were encountered with the Skyshine case. However, these challenges were partially addressed through sensitivity analysis, resulting in slightly improved outcomes compared to the previous participation and to the reference. Application of the program to characterize the neutron field around the OB26 irradiator yielded satisfactory results when compared to reference data. A two-step sensitivity analysis further enhanced the outcomes, initially substituting the Watt fission distribution with the evaporation distribution, thereby improving spectrum shape and integral quantities. Subsequently, utilizing the obtained neutron spectra as prior information for unfolding codes MAXED and GRAVEL ensured stability and agreement with reference data and preliminary results.

A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

On the spectral wave climate of the French Atlantic Ocean

The accurate description of wave climate at different spatio-temporal scales requires the application of advanced statistical models together with a good knowledge of geophysical processes. Furthermore, accurate modelling of multimodal sea states is of primary importance for most of offshore and coastal activities, such as wave energy device optimization, maritime design practice and for safety at sea. The present manuscript is conceived within this scientific framework proposing to assess wave climate of a complex area of French Atlantic Ocean bordering seas. The main “Spectral Climatology Types” of the area are identified as resulting of defined combinations of wave systems detected through directional spectra and partitioned wave systems analysis. The presence of swell systems is evaluated quantitatively on the whole area, characterized by different regimes of multimodal sea-states at strong regional variability and put into relation with main meteorological forcing active on the area at different spatial scales. Celtic Sea exhibits a marked regional characterization with a prevalence of multimodal conditions given by different combination of wave systems with increasing contribution of swell systems moving from North-West to South. A significant presence of crossing sea states is observed in South Celtic Sea especially in proximity of bathymetric slope. The South Bay of Biscay is influenced by fully developed swell systems enhanced by refraction effects caused by both the coastline and bathymetry gradients. English Channel and North Sea show complex sea-states conditions induced by local topography features together with wind channelling and tide effects able to trigger geophysical processes at a sub-scale responsible for the development of multimodal seas. Crossing and bimodal seas are also found to be influenced by bathymetry gradients acting directly on the directional spectrum shape as well as by tide due to tidal current-induced refraction effect on wave propagation. No generalized significant trends are detected within the investigated spatial domain for the wave spectrum integral quantities; locations sited at northern Celtic Sea show a downward Significant Wave Height, while only locations confined at eastern English Chanel only shows a Peak Period upward trend.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

Assessing the PLEIADES/GERMINAL V3 fuel performance code against transmutation experiments in sodium fast reactors

We present the results of a first assessment of the multiphysics PLEIADES/GERMINAL V3 fuel performance code against integral irradiation experiments of americium-bearing MOX fuel pins irradiated in sodium fast reactors. The pins considered in this work cover a range of americium contents from 2 to 5 weight %, being representative for the homogeneous transmutation path. The code predictions are compared to several post-irradiation examination results on integral (e.g., fission gas release) and local quantities (e.g., actinides redistribution in the fuel pellet), and demonstrate a satisfactory agreement with experimental data. The deviations between calculated and experimental quantities shed some light on modeling developments needed to better calculate the behavior of americium-bearing mixed-oxides fuel pins under irradiation.

Reduced-Order Model Approaches for Predicting Airfoil Performance

This study delves into the construction of reduced-order models (ROMs) of a flow field over a NACA 0012 airfoil at a moderate Reynolds number and an angle of attack of 8∘. Numerical simulations were computed through the finite-volume solver OpenFOAM. The analysis considers two different reduction techniques: the standard Galerkin projection method, which involves projecting the governing equations onto proper orthogonal decomposition modes (POD−ROMs), and the cluster-based network model (CNM), a fully data-driven nonlinear approach. An analysis of the topology of the dominant POD modes was conducted, uncovering a traveling wave pattern in the wake dynamics. We compared the performances of both ROM techniques regarding their prediction of flow field behavior and integral quantities. The ROM framework facilitates the practical actuation of control strategies with significantly reduced computational demands compared to the full-order approach.

Decay of Taylor–Green flow type initial conditions in a two-dimensional domain

Geophysical flows are often two-dimensional (2D) in nature. The decay dynamics of the canonical, symmetric initial conditions defined by the Taylor–Green (TG) flow is simulated in a 2D domain. The standard lattice Boltzmann equation method with the Bhatnagar–Gross–Krook collision model is employed. The vortex dynamics is investigated for bounded and unbounded flows with various sets of Gaussian vortices and varying Reynolds numbers. The formation of thin filaments and the generation of small-scale structures near the no-slip walls are found. To characterize the decay properties, the integral quantities, namely, kinetic energy, E(t), enstrophy, Ω(t) , and palinstrophy, P(t), are tracked as a function of the eddy-turnover-time. The initial vortex population in the domain dictates the decay rate of these integral quantities. The energy spectra, E(k), are computed to investigate the effect of domain boundaries and vortex populations on energy distribution among different length scales for Re=50000 . The evolution of TG flow in a bounded domain shows an exponent close to −3, which may be attributed to the generation of thin filaments and small-scale structures in vortex-wall interactions. Exponent changes with an increase in the vortex populations.

Measurement of secondary neutron spectra induced by 480 MeV proton and 430 MeV/u 4He beams with a thick aluminum target

Knowledge of the characteristics of secondary neutrons produced by the interaction of Galactic Cosmic Radiation with spacecraft shielding materials is becoming increasingly important for predicting and mitigating biological risks of space explorers during deep-space travel. Hadron accelerators for medical applications are well suited to reproduce part of the conditions found in deep-space in terms of ion species and energies. The objectives of this work are to measure the secondary neutron spectra produced by proton and helium ion beams hitting an aluminum target with energies that correspond to the Galactic Cosmic Radiation peak during solar minimal activity and to validate and compare physical models of Monte Carlo simulations. Neutron spectra were measured with the extended-range Bonner sphere system NEMUS at two positions, 0° and 90° relative to the direction of the primary ion beam. The experimental setup consisted of 480 MeV proton and 430 MeV/u 4He beams colliding with a 30×30×63.5 cm3 aluminum target. The experimental neutron spectra were analyzed using the MAXED unfolding code and compared to several Monte Carlo simulation codes. The results show deviations in terms of the shape of the neutron energy distributions ranging between 1% and 14% and of the integral quantities of fluence and ambient dose equivalent ranging between 1% and 5.2%.

Data transfers for full core heterogeneous reactor high-fidelity multiphysics studies

Multiphysics simulations for nuclear reactor analysis are usually performed by resorting to operator splitting and fixed point iterations between single-physics solvers. This enables the separate solution of each physics, such as neutronics, fuel performance, and thermal hydraulics, on meshes tailored to the requirements of the respective numerical discretizations of the equations. As the equations are coupled, several fields must be transferred between singlephysics solves. Projecting fields between meshes while preserving order of accuracy, conservation properties, and mapping non-overlapping geometries is a complex endeavour. This conference paper will present the transfers as implemented in MOOSE, which can handle arbitrary meshes, arbitrary mappings, conservation of integral quantities, and are made to scale with distributed simulations on both ends of the transfers. Their adequacy for advanced nuclear reactor multiphysics coupling is shown through examples and numerical studies.

Evaluation of advection schemes and surface tension model for algebraic and geometric VOF multiphase flow solvers

This paper addresses the validation and verification of numerical models for complex multiphase flows involving immiscible fluids. Specifically, the focus is on the dynamics of the interface between the fluids, which remains a challenge in many applications. Previous studies have primarily examined simpler flows with limited complexity, while real-world scenarios involve intricate interfaces and turbulent dynamics. To overcome this, a representative test case involving the motion of an oil cube within a water cube proposed by [12] is used. Different computational models using volume-of-fluid (VOF) approaches are validated and compared, with particular attention given to the influence of numerical schemes for convective terms. The impact of these schemes on integral quantities and interface dynamics is analyzed. Particular attention is paid at the surface tension contribution to the energy budgets, which is usually neglected in the available literature. Furthermore, it is shown here that, the model adopted for the surface tension is responsible for an additional contribution to numerical dissipation. To the authors' knowledge, it is the first time that a detailed analysis of such aspects is presented.