BME is actively involved in the development and comprehensive assessment of the pre-conceptual design of a water-cooled small modular reactor operating at supercritical pressure (SCW-SMR). This innovative design incorporates seven heat-up stages and has been proposed in frame of the EU ECC-SMART project. The development and utilisation of an Apros system code model of the concept has enabled the execution of a series of analyses and the evaluation of its steady-state and transient behaviour and characteristics. This paper presents a detailed assessment of one of the most crucial initiating events, the 200% guillotine break of one of the cold-leg pipelines inside the containment. The primary objectives of these investigations were to examine the cooling and flooding conditions of the proposed complex reactor vessel flow path under such conditions, and to determine the minimum set of safety systems required. The key findings derived from the 27 cases investigated are summarised.

In the frame of the EU ECC-SMART project, the pre-conceptual design of a water-cooled small modular reactor operating at supercritical pressure (SCW-SMR) with seven heat-up stages is under development and assessment. The first part of the two-part paper presented the concept design, the models developed at BME in the Apros thermal-hydraulics system code and in the Serpent 2 Monte Carlo reactor physics code, the developed coupling methodology of these models, and the results of the first coupled calculations. This second part of the paper outlines the approaches adopted by the BME research team to improve the original design, primarily to reduce the high cladding temperatures. The effects of the increased mass flow rate and the introduction of inhomogeneous inlet orifices are thoroughly investigated and presented. Finally, a comprehensive sensitivity analysis has also been performed to demonstrate the robustness of the proposed design.

In the frame of the EU ECC-SMART project, the pre-conceptual design of a water-cooled small modular reactor operating at supercritical pressure (SCW-SMR) with seven heat-up stages is under development and assessment. BME is contributing to this project as a consortium member and is developing several models and coupled code systems to investigate the features and characteristics of the proposed new concept. Following the steady-state analyses conducted previously, the Apros system code model was extended to encompass models of the SCWSMR primary circuit, safety systems and I&C systems. A series of calculations were carried out to investigate the possibility of natural circulation in the proposed core layout. Another objective was to check the feasibility of passive heat removal in the event of a long-term SBO, which was challenging in the predecessor HPLWR design. A detailed comparative assessment and a summary of the lessons learned are provided.

Best-estimate thermal-hydraulic system codes are widely used for the analysis of various postulated events of NPPs, therefore, an extensive verification and validation of these codes is essential. In the current study, an SBLOCA scenario (CL-4.1-03) of the PSB-VVER integral test facility has been investigated using NRC's novel system code, TRACE, and the Finnish APROS, which had already been in long use at our Institution. PSB-VVER is currently the most comprehensive physical model of the VVER-type reactors, particularly VVER-1000, in most of the aspects. The experiment under study was carried out in 2004 in the framework of an OECD NEA benchmark. The obtained results have been compared to the benchmark and to each other both from a qualitative and quantitative point of view. As a figure of merit, the improved FFTBM-SM and the SARBM quantitative methods were used. Furthermore, the main lessons learnt during the model development are also presented.

BME, as a consortium member, is participating in the ECC-SMART project, which has been awarded an EU/EURATOM/H2020 grant in 2020, and is researching the development of a supercritical water-cooled small modular reactor concept called SCW-SMR. This paper summarizes the research work carried out so far at BME within the framework of the project. Firstly, several international benchmarks were modelled by the APROS system code and the Ansys CFX CFD software package in order to demonstrate their applicability for the thermal hydraulics analysis of SCW. Later, a complete reactor vessel and a simplified primary circuit model were built with APROS, and a full-length fuel assembly model was developed in Ansys CFX. All the seven heat-up stages of the SCW-SMR pre-conceptual design were modelled and analyzed with these tools. The Serpent 2 Monte Carlo code and the inhouse SPNDYN finite element code were used for reactor physics benchmarking, for various stand-alone reactor physics calculations and in loosely coupled (with APROS and Ansys CFX) and tightly coupled (with APROS) code systems in order to design and optimize the fuel and the reactor core of the SCW-SMR concept. Many successful calculation series (e.g. the socalled SCWR-FQT benchmark) have been performed with these codes and code systems.

The Hungarian PMK-2 test facility is a scaled-down model of the VVER-440/213 type pressurized water reactors of Paks NPP, on which several measurement series have been carried out since the 80s. One of these series include four Standard Problem Exercises (SPE), primarily small-break loss-of coolant accident (SBLOCA) transients, performed in cooperation with IAEA. New RELAP5, TRACE and APROS models have already been developed and a comparative analysis of the results has been published recently for the PMK SPE-4 experiment. In that SBLOCA scenario, no high-pressure injection system (HPIS) was available, but a secondary side bleed and feed operation has been performed during the transient. This paper is a continuation of the previous one and presents the required model modifications and the analysis of the second SPE. The initiating event, similarly to the SPE-4 experiment, is a 7.4% break located at the top of the downcomer, while the main differences are that one line of the HPIS is available and no secondary side feed and bleed operation is performed in this case. One of the main objectives of the experiment was to verify that these safety measures are enough to prevent core dry-out. In addition to the investigation of this question, a sensitivity study was also carried out with respect to selected parameters that might have a significant impact on the characteristic of the simulated processes. The assessment of the results has also been performed with two quantitative methods, namely the Fast Fourier Transform Based Method with Signal Mirroring (FFTBM-SM) and Stochastic Approximation Ratio Based Method (SARBM).

The Small Break Loss of Coolant Accident (SBLOCA) of a nuclear power plant is a transient that is subject to numerous studies. With the support of both experiments and simulation codes, professionals aimed to gain a deeper knowledge of the process, which would prove invaluable in the design and licensing of nuclear power plants. The comparison of integral test results with simulations serve as basis for licensing code validation. A notable example in its history of research is the series of IAEA Standard Problem Exercises (SPE), which were carried out in the 80s and 90s on the Hungarian PMK-2 facility, a scaled down model of the VVER-440/213 type pressurized water reactors of Paks NPP. This paper presents in detail our RELAP5, TRACE and APROS models that were recently developed for the simulation of the fourth Standard Problem Exercise (SPE-4). In order to assess the reliability and adequacy of these models, both qualitative and quantitative analyses were performed, for which the available measurement results served as reference. Quantitative analysis was performed using the original and the improved Fast Fourier Transform Based Method (FFTBM) and the Stochastic Approximation Ratio Based Method (SARBM). The application of these methods allowed for a thorough evaluation of our models and provided a basis of comparison with previously published results.

Various Wire-Mesh Sensor (WMS) designs have been developed and applied for the single-and two-phase flow studies over the recent years. The design and the construction of the WMS can significantly vary depending on the purpose of the research. Typically, the WMSs installed in pipes and ducts have been located across the flow, to obtain instantaneous cross-sections of the flow area. The traditional approach would not be ideal if the scope of the study is to measure the development or the dynamics of the flow in the axial direction. Hence, the axially-aligned conductivity Wire-Mesh Sensor (named AXE) was designed and constructed to be located in the centerline of the 50 mm pipe in the current study. The paper presents briefly the design of the axial sensor and the HIPE test loop that was used in the experiments. The sensor enables the study of the two-phase flow in high resolution (10,000 frames/s, 3 mm x 3 mm resolution). In this paper, the main emphasis is on the study of the different methods that can be applied for the estimation of the velocity fields from the axial wire-mesh sensor data. Two methods have been tested: traditional Time-of-Flight (ToF) estimation and optical flow method. The Time-of-Flight estimation relies on the cross-correlation of the time series of the void fraction values from the different locations. The velocities can be calculated from the Time-of-Flight estimates and the distances between the particular locations. The optical flow methods can be used to evaluate the motion of the objects between the two sequential images. The estimation of the velocity fields from the axial sensor data is analogous to the calculation of the velocity fields from the Particle Image Velocimetry (PIV) images. Now, the same methods are applied to process the axial WMS data. The paper discusses the pros and cons of the different approaches and gives some general recommendations on how and when they should be applied for the WMS data. The velocity fields from the axial sensor experiments are compared to the experiments conducted with the two cross-sectional WMS (32 x 32 sensors). One aim of the studies on axial sensor is to utilize the sensor in research dealing with swirling flows generated by different mechanisms. (C) 2017 Elsevier B.V. All rights reserved.

In the simplest case, consider a \({\mathbb{Z}^d}\)-periodic (d ≥ 3) arrangement of balls of radii < 1/2, and select a random direction and point (outside the balls). According to Dettmann’s first conjecture, the probability that the so determined free flight (until the first hitting of a ball) is larger than t > > 1 is \({\sim\frac{C}{t}}\), where C is explicitly given by the geometry of the model. In its simplest form, Dettmann’s second conjecture is related to the previous case with tangent balls (of radii 1/2). The conjectures are established in a more general setup: for \({\mathcal{L}}\)-periodic configuration of—possibly intersecting—convex bodies with \({\mathcal{L}}\) being a non-degenerate lattice. These questions are related to Pólya’s visibility problem (Arch Math Phys Ser 2:135–142, 1918), to theories of Bourgain et al. (Commun Math Phys 190:491–508,1998), and of Marklof–Strömbergsson (Ann Math 172:1949–2033,2010). The results also provide the asymptotic covariance of the periodic Lorentz process assuming it has a limit in the super-diffusive scaling, a fact if d = 2 and the horizon is infinite.

The work by Ott et al. (Math. Res. Lett. 16:463–475, 2009) established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where non-random examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of Sethuraman and Varadhan (Electron. J. Probab. 10:121–1235, 2005).

A team kivetelesen eredmenyes munkat vegzett a periodus soran. Young (Annals of Mathematics, 1998) sikbeli szoro biliardokra vonatkozo torony konstrukciojanak tobbdimenziora valo kiterjesztesevel mar 1998-tol foglalkoztunk. Balint es Toth friss es gondolatgazdag eredmenye az első attores. Szasz es Varju a sikbeli konstrukciot alkalmazzak a Brown mozgas dinamikai elmeletenek modelljeire, nevezetesen a Lorentz folyamat sztochasztikajara. Veges, sőt vegtelen horizont eseten is igazoltak lokalis hatareloszlasteteleket, es rekurrenciat. Utobbi esetben mar globalis hatareloszlasteteluk is Bleher nevezetes, 1992-es sejtesenek első szigoru bizonyitasa. Dolgopyattal kozos eredmenyeik Erdős-Taylor ill. Darling-Kac bolyongasokra vonatkozo teteleinek kiterjesztesei periodikus Lorentz folyamatra, ezekkel Sinai 1981-es mely sejtesere szellemes es technikas bizonyitast adnak. Solomyak (Annals of Mathematics, 1995) vegtelen Bernoulli konvoluciok abszolut folytonossagara vonatkozo, attorest jelentő cikket altalanositotta Toth es Simon, majd Toth. Solomyak eredmenye olyan mertekek egy parameteres csaladjara bizonyitott abszolut folytonossagot, melyek stacionariusak az egyenesen ertelmezett IFS-ek egy parameteres csaladjara. Ezen IFS-ek ket linearis -1/2-nel nagyobb - rataju kontrakciobol allnak es azonos valoszinűseggel alkalmazzuk mind ket fuggvenyt. Simon es Toth ezt a tetelt kiterjesztette tetszőlegesen sok fuggvenyre es Toth reszeredmenyeket ert el a kulonboző kontrakciok eseten. | The team had an exceptionally successfull research period. We started the work on the multidimensional extension of Young's tower construction for planar dispersing billiards, published in 1998 in Annals of Mathematics. The fresh result of Balint and Toth, rich in ideas, is the first breakthrough here. Szasz and Varju applied the planar construction to dynamical models of Brownian motion: to stochastic properties of the planar Lorentz process. They obtained local limit theorems, and recurrence as well, in case of finite and even infinite horizon. In the latter case their - weaker - global limit theorem in itself provides the first rigorous verification of Bleher's 1992 conjecture. Their results, joint with Dolgopyat, extend classical results for random walks of Erdős-Taylor and of Darling-Kac to the periodic Lorentz process, which made it possible for them to give a technical and witty proof for Sinai's 1981 deep conjecture. Simon and Toth (2006) and Toth (2008) generalized a breakthrough result of Solomyak (Annals of Mathematics 1995). Solomyak considered a one parameter family of Iterated Function System (IFS) that consists of two linear contractions with the same (> 1/2) ratio of contraction which are applied with the same probability. Simon and Toth generalized this result for arbitrary (but finite) number of contractions. Toth obtained partial results about the generalization of the Solomyak's theorem for different probabilities.

A statissztikus fizika es kvantummechanika matematikai problemaival foglalkozunk. A hidrodinamika mikroszkopikus modelljeinek tag osztalyait vizsgaltuk, kulonos tekintettel hiperbolikus skalazasu rendszerek makroszkopikus viselkedesere a lokeshulllamok tartomanyaban. Levezettuk a rugalmassagtan nemlinearis egyenleteit. Attorest jelentő eredmenyek szulettek aszimmetrikus modellek 1/3 kitevős skalazasaval kapcsolatban (szubdiffuziv viselkedes). Erdős-Renyi-Barabasi tipusu omszervező strukturak kritikus viselkedeset, a graf komponenseinek aszimptokus meretet tisztaztuk. Nem-Markov bolyongasok hatareloszlasat meghatarozva meglepő kulonbseget tapasztaltunk az iranyitott es nem iranyitott elek eseteinel. Leirtuk veletlen matrixok sajatertekeinek pomtfolyamatat. Sinai biliardok es altalanosabb kaotikus dinamikai rendszerek ergodikus viselkedeset tisztaztuk, eredmenyesen targyaltuk a sikbeli Lorentz folyamat rekurrenciajanak es Brown-kozelitesenek problemajat. Meghataroztuk iteralt fuggvenyrendszerek attraktorainak Hausdorff dimnenziojat, veletlen Cantor halmazok kulonbseget. Tisztaztuk a kvantummechanikai allapotter geometriajanak kerdeseit. A kvantumrendszerek allapotbecsleseit vizsgalva azok megbizhatosagat jellemeztuk. Algoritmust adtunk n-szintű rendszer becsleseire, a becslesi strategia szamitogepes vizsgalatara is sor kerult. A folytonos optimalizacio kulonfele algoritmusit konstrualtuk meg, tisztaztuk azok hatekonysagat. | Mathematical problems of statistical physics and quantum mechanics are investigated. Various microscopic models of hydrodynamics are introduced, existence of hyperbolic scaling limits is prroven including the derivation of the equations of nonlinear elastodynamics. Fairly deep results have been obtained on the 1/3 exponent scaling of asymmetric systems (subdiffusive behaviour of the tagged particle). In case of Erdős-Renyi-Barabasi type self-organized systems the size of the graph components has been determined. Investigating the limit distribution of non-Markovian random walks, a considerable difference in the behavior of models with directed and non-directed bonds has been observed. Characterization of the point process of eigenvalues of random matrices was presented. Ergodic behavior of Sinai billiards and of more general dynamical systems has been described, discussion of recurrence and Brownian approximation of the planar Lorentz gas has been completed. Hausdorff dimension of attractors of iterated maps has been calculated, difference of random Cantor sets was also studied. Geometry of quantum mechanical and reliability of estimators for the state of quantum mechanical systems has been investigated. Algorithms for constrained estimation for n-level quantum systems have been introduced and investigated by computer simulations. Various methods of continuous optimalization and their effectiveness was also studied.

Let us modify the scatterer configuration of a planar, finite-horizon Lorentz process in a bounded domain. Sinai asked in 1981 whether, for the diffusively scaled variant of the modified process, convergence to Brownian motion still holds. The main result of this work answers Sinai's question in the affirmative. Other types of local perturbations are also investigated: finite-horizon periodic Lorentz processes in the half strip or in the half plane (in these models, the local perturbation is the boundary condition) and finite-horizon, periodic Lorentz processes with a small, compactly supported external field in the strip. The corresponding limiting processes are Brownian motions with suitable boundary conditions and the skew Brownian motion on the line. The proofs combine Stroock and Varadhan's martingale method in [SVI] with our recent work in [DSV].

First return and first hitting times, local times and first intersection times are studied for planar finite horizon Lorentz processes with a periodic configuration of scatterers. Their asymptotic behavior is analogous to the asymptotic behavior of the same quantities for the 2-d simple symmetric random walk (cf. classical results of Darling-Kac, 1957 and of Erdős-Taylor, 1960). Moreover, asymptotical distributions for phases in first hittings and in first intersections of Lorentz processes are also described. The results are also extended to the quasi-one-dimensional model of the linear Lorentz process. Subject classification: 37D50 billiards, 60F05 weak theorems

As Bleher (J. Stat. Phys. 66(1):315–373, 1992) observed the free flight vector of the planar, infinite horizon, periodic Lorentz process {S n ∣n=0,1,2,…} belongs to the non-standard domain of attraction of the Gaussian law—actually with the \(\sqrt{n\log n}\) scaling. Our first aim is to establish his conjecture that, indeed, \(\frac{S_{n}}{\sqrt{n\log n}}\) converges in distribution to the Gaussian law (a Global Limit Theorem). Here the recent method of Bálint and Gouëzel (Commun. Math. Phys. 263:461–512, 2006), helped us to essentially simplify the ideas of our earlier sketchy proof (Szász, D., Varjú, T. in Modern dynamical systems and applications, pp. 433–445, 2004). Moreover, we can also derive (a) the local version of the Global Limit Theorem, (b) the recurrence of the planar, infinite horizon, periodic Lorentz process, and finally (c) the ergodicity of its infinite invariant measure.

For Young systems, i.e. for hyperbolic systems without/with singularities satisfying Lai-Sang Young's axioms (which imply exponential decay of correlation and the CLT) a local CLT is proven. In fact, a unified version of the local CLT is found, covering among others the absolutely contionuous and the arithmetic cases. For the planar Lorentz process with a finite horizon this result implies a.) the local CLT and b.) the recurrence. For the latter case ($d=2$, finite horizon), combining the global CLT with abstract ergodic theoretic ideas, K. Schmidt, and J.-P. Conze, could already establish recurrence.

The aim of this survey is twofold. First we show how the Markov tower construction is applicable for obtaining finer stochastic properties, like a local limit theorem of probability theory. Here the fundamental method is the study of the spectrum of the Fourier transform of the Perron--Frobenius operator. These ideas and results are applicable to all systems Young has been considering. Second, we survey the problem of recurrence of the planar Lorentz process. As an application of the results from the first part, we obtain a dynamical proof of recurrence for the finite horizon case. Here basically different proofs were given by K. Schmidt, in 1998, and J.-P. Conze, in 1999. As another application we can also treat the infinite horizon case, where already the global limit theorem is absolutely novel. It is not a central one, the scaling is $\sqrt {n \log n}$ in contrast to the classical $\sqrt n$ one. Beyond thus giving a rigorous proof for earlier heuristic ideas of P. Bleher, which used three delicate and hard hypotheses, we can also a) verify the local version of this limit theorem for the free flight function and b) prove the recurrence of the planar Lorentz process in the infinite horizon case.