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The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF. [ABSTRACT FROM AUTHOR]

Different techniques are used to analyze annular flow, but the more interesting ones are those techniques that do not perturb the flow and provide enough resolution to clearly distinguish the interfacial phenomena that take place at the interface, especially the disturbance waves (DW) and the ripple waves (DW). The understanding of these events is important because it influences the heat and mass transfer taking place through the thin film formed near the walls in this flow regime. The laser-induced fluorescence (LIF) and the three-electrode conductance probe are two commonly used techniques to study experimentally annular flow phenomena. In this paper, a set of experiments at different temperatures of 20 °C, 30 °C and 40 °C and different liquid Reynolds numbers have been performed in the annular flow regime, the characteristic of the DW and RW as average height and frequency of these waves has been measured by both techniques LIF and conductance probes. In addition, we also measured the mean film thickness. It was found that the mean film thickness and the DW height are practically the same when measured by both techniques; however, the height of the RW is smaller when measured by the conductance probe and this difference diminishes when the temperature increases. [ABSTRACT FROM AUTHOR]

This paper describes all the procedures and methods currently used at UPV (Universitat Politécnica de Valencia) and UJI (University Jaume I) for the development and use of sensors for multi-phase flow analysis in vertical pipes. This paper also describes the methods that we use to obtain the values of the two-phase flow magnitudes from the sensor signals and the validation and cross-verification methods developed to check the consistency of the results obtained for these magnitudes with the sensors. First, we provide information about the procedures used to build the multi-sensor conductivity probes and some of the tests performed with different materials to avoid sensor degradation issues. In addition, we provide information about the characteristics of the electric circuits that feed the sensors. Then the data acquisition of the conductivity probe, the signal conditioning and the data processing including the device that have been designed to automatize all the measurement process of moving the sensors inside the channels by means of stepper electric motors controlled by computer are shown in operation. Then, we explain the methods used for bubble identification and categorization. Finally, we describe the methodology used to obtain the two-phase flow information from the sensor signals. This includes the following items: void fraction, gas velocity, Sauter mean diameter and interfacial area concentration. The last part of this paper is devoted to the conductance probes developed for the annular flow analysis, which includes the analysis of the interfacial waves produced in annular flow and that requires a different type of sensor. [ABSTRACT FROM AUTHOR]

Abstract: Feynman-α and Rossi-α formulas including multiple α-modes are derived for stochastic and continuous neutron sources. The presented formalism is further developed to achieve spatial correction factors for the single α-mode point kinetics representations of the Feynman-α and Rossi-α formulas. As a natural extension of the multiple α-mode formalism, delayed neutrons are included in the Feynman-α formula. The obtained formulas are validated experimentally in a strongly heterogeneous system obeying multiple α-modes, resulting in good agreement with the presented theoretical framework. [ABSTRACT FROM AUTHOR]

• We study the effect that surface tension changes produce on disturbance and ripple waves in annular flow. • We analyzes the effect of the gas and liquid Reynolds numbers and the surface tension on the interfacial properties. • We study the change of the frequency and amplitude of the disturbance waves with the surface tension in annular flow. • Interface property changes are studied when varying the boundary conditions in annular flow. In this paper, we have performed an experimental study of the effect of changing the surface tension of the water in vertical annular concurrent two-phase flow (air + liquid) by adding small amounts of 1-butanol to the liquid phase. Adding small amounts of this chemical compound diminishes the surface tension of the water, while the dynamic viscosity remains practically unchanged. A set of experiments have been performed in the interval of surface tension values that ranges from 72 10-3N/m to 45 10-3 N/m, and with different values of the superficial velocities of the gas and liquid flows. In this broad range of surface tensions and boundary condition values the average amplitude and frequency of the disturbance waves have been measured for each boundary condition and surface tension value. In addition, we also measured the mean amplitude of the ripple waves, the mean value of the unperturbed base thickness, and the average film thickness. Also, we have obtained a set of correlations expressing all these magnitudes in non-dimensional form in terms of the Reynolds number of the gas, the Reynolds number of the liquid and the Kapitza number. Finally, we have performed a brief discussion and comparison with the results of other authors. [ABSTRACT FROM AUTHOR]

In this paper we perform an analysis of the conductance probes used in two-phase flow applications especially for two-phase flow tomography of annular flow, to measure the waves produced in the interface with different boundary conditions without perturbing the flow, and in addition we examine the holdup applications as measuring the average void fraction in a given region. The method used to obtain the detector conductance between the electrodes is to solve analytically the generalized Laplace equation in 3D with the boundary conditions of the problem, and then to obtain the average potential difference between the detector electrodes. Then, dividing the current intensity circulating between the emitter and the receiver electrodes by the average potential difference yields the probe conductance, which depends on the geometric and physical characteristics of the measured system and the probe. This conductance is then non-dimensionalized by dividing by the conductance of the pipe full of water. In this way a set of analytical expression have been obtained for the conductance of two-plate sensors with different geometries and locations. We have performed an exhaustive comparison of the results obtained using the equations deduced in this paper with the experimental data from several authors in different cases with very good agreement. In some cases when the distribution of bubbles is not homogeneous, we have explored the different alternatives of the effective medium theory (EMT) in terms of the self-consistent EMT and the non-consistent EMT. [ABSTRACT FROM AUTHOR]

This paper investigates non-invasive techniques for annular two-phase flow analysis, focusing on liquid film characterization to understand the interfacial phenomena that are crucial for heat and mass transfer. Limited methods allow the study of the temporal and spatial evolution of liquid film, such as Planar Laser-Induced Fluorescence (PLIF). However, this method possesses optical challenges, leading to the need for improved techniques to mitigate refraction and reflection, such as Refractive Index Matching (RIM). This study utilizes an experimental annular flow facility to analyze both RIM and non-RIM PLIF over a range of liquid Reynolds numbers from 4200 to 10,400. Three configurations—PLIF RIM90, PLIF RIM40, and PLIF nRIM40—are compared from both qualitative and quantitative perspectives. In the quantitative analysis, key variables of the liquid film are measured, namely mean film thickness, disturbance wave height, and frequency. Variations in the analyzed variables indicate minor deviations, which are not likely to be caused by the technique used. However, all three methodologies exhibited errors that are estimated to be within a maximum of 10%, with a mean value of approximately 8%. [ABSTRACT FROM AUTHOR]

In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network. These chemical propensities, at a given time, depend on the system state at that time, and do not depend on the state at an earlier time indicating that we are dealing with Markov processes. Then the Chemical Master Equation (CME) is deduced for an arbitrary chemical network from a probability balance and it is expressed in terms of the reaction propensities. This CME governs the dynamics of the chemical system. Due to the difficulty to solve this equation two methods are studied, the first one is the probability generating function method or z-transform, which permits to obtain the evolution of the factorial moment of the system with time in an easiest way or after some manipulation the evolution of the polynomial moments. The second method studied is the expansion of the CME in terms of an order parameter (system volume). In this case we study first the expansion of the CME using the propensities obtained previously and splitting the molecular concentration into a deterministic part and a random part. An expression in terms of multinomial coefficients is obtained for the evolution of the probability of the random part. Then we study how to reconstruct the probability distribution from the moments using the maximum entropy principle. Finally, the previous methods are applied to simple chemical networks and the consistency of these methods is studied. [ABSTRACT FROM AUTHOR]

This paper investigates the challenges isolated islands face in transitioning from fossil fuel-based electricity generation to renewable energy sources. The Canary Islands serve as a case study, where photovoltaic and wind power are the primary renewables, but their variability requires a deep techno-economic analysis. The island's energy demand is predicted to rise by 100% due to economic growth, electrification and electric vehicles. However, implementing renewable systems encounters obstacles, such as limited suitable sites and protected areas. The study uses Wilks' methodology and Monte Carlo sampling to explore 59 combinations of randomly selected inputs of the uncertain variables, aiming for a 95/95% coverage and confidence level in the results. In most cases, they experience energy shortages, failing to meet electric demand. Even though a new generation mix appears to cover demand under all circumstances, the uncertainty unveils a different reality, leading to an approximate 25% increase in system costs. Surpluses in energy generation, while seemingly positive, can pose challenges. The new system's Levelized Cost of Energy increases from around 14 to 17c€/kWh. These cost increases are contingent upon future performance and the variability of uncertain parameters, leading to excesses ranging from slightly below 25% to over 40%. • Demand coverage scenario designed to meet electric demand through renewable sources. • Uncertainty analysis of a scenario for the complete electrification of the economy. • Best Estimate Plus Uncertainty analysis implementing the Wilks' methodology. • Resizing the system to cover the demand with 95% coverage and confidence levels. • Differences in using deterministic and stochastic methods for electric demand coverage. [ABSTRACT FROM AUTHOR]

The demonstration of the safety, high performance and reliability of any man-made device relies heavily in experimental programs. For nuclear reactor safety demonstration, several experimental facilities are used for both testing the design and the validation of computational codes. In the field of thermal hydraulics, most experimental facilities are built at a smaller scale, thus the scaling analysis is a requirement in the licensing process of the nuclear power plant. This includes the analysis of the scaling capabilities of the computer codes, the scale and design differences with the licensed reactor and the methodologies applied for licensing. In collaboration with the Spanish regulatory Body, several Spanish university groups have contributed considerably to the development and application of scaling methodologies. This article provides an overview of the most relevant contributions presented in the last decades. The activities deal mainly with the use of system codes in scaling analysis. Specifically the works can be classified in the use of K v scaling analyses, analysis of counterpart experiments, plant application and the scaling of uncertainties. Finally, the future challenges that will be addressed in relation to scaling are highlighted with emphasis to the contribution to the safe operation of current and future nuclear power plants. • Spanish contributions to the development and application of scaling methods. • Advances and past applications of scaling analysis such as Kv scaling in Spain. • Future challenges regarding scaling methodologies in thermal hydraulics. [ABSTRACT FROM AUTHOR]

Fossil fuel-based economies must undergo a deep transition for complete decarbonization. To this end, it is widely recognized that all economies must move towards the electrification of energy end uses. Even though there is a part that cannot be electrified, at least at affordable costs; clear examples are heavy road transport, maritime and air transport, and some industrial processes. As a result of the limitations of electrification in certain energy end uses, the potential use of hydrogen as an alternative energy carrier has been examined in recent decades. Hydrogen is seen as a viable option for the medium to long term. Specifically, efforts are being made in the case of the Canary Islands to move towards a carbon-free energy mix. In fact, the aim is to advance the economy decarbonization by 10 years over the date foreseen for both Europe and the rest of Spain. To this end, the HOMER program has been used to analyze the possibility of producing the necessary hydrogen in a scenario applied to the Canary Islands in which the uses of this energy vector have been maximized. This research considers two possible scenarios, together with a sensitivity analysis under the different uncertain conditions associated with the used technologies. The results have been the estimation of hydrogen production costs for high demands, about 230,000 tH 2 /year, in 2040 for an isolated archipelago under two totally different generation scenarios. The first scenario is totally renewable, while the other is based on nuclear generation by means of high-temperature SMRs. The results show, that it would be possible to produce at a cost in the range of 1 €/kgH 2 using nuclear technology and around 4 €/kgH 2 using renewables, with uncertainty cost ranges of around 40%, i.e. costs between 0.85-1.48 and 3.29–4.99 € kgH 2 respectively. [ABSTRACT FROM AUTHOR]

Abstract: Neutron noise measurements based on the Rossi-α and Feynman-α methodologies have been performed in a heterogeneous subcritical system. It is shown that the traditional single alpha-mode formulations of the Rossi-α and Feynman-α methods are not applicable due to the presence of higher alpha-modes. Formalisms taking into account multiple alpha-modes are applied resulting in satisfactory results. Three alpha-modes could be identified using the Rossi-α method, whereas only two could be obtained using the Feynman-α method. In the Feynman-α case, the possibility to obtain the fastest decaying alpha-mode was diminished due to detector dead time effects. It was found that the slowest decaying alpha-mode does not exactly correspond to the prompt decay found in pulsed neutron source measurements, which confirms the results of previous studies. Strengths and weaknesses of the multiple alpha-mode Rossi-α and Feynman-α methods observed in this study are pointed out. [ABSTRACT FROM AUTHOR]