1,721,026 research outputs found
A finite element implementation of the incompressible Schrödinger flow method
No full textFirst proposed by E. Madelung in 1926, the analogy between quantum mechanics and hydrodynamics has been known for a long time; however, its potentialities and the possibility of using the characteristic equations of quantum mechanics to simulate the behaviour of inviscid fluids have not been thoroughly investigated in the past. In this methodology, the incompressible Euler equations are thus substituted by the Schrödinger equation, turning a quasi-linear Partial Differential Equation into a linear one, an algorithm known in the literature as Incompressible Schrödinger Flow. Previous works on the subject used the Fast Fourier Transform method to solve this problem, obtaining promising results, especially in predicting vortex dynamics; this paper aims to implement this novel approach into a Finite Element framework to find a more general formulation better suited for future application on complex geometries and on test cases closer to real-world applications. Simple case studies are presented in this work to analyse the potentialities of this method: the results obtained confirm that this method could potentially have some advantages over traditional Computational Fluid Dynamics method, especially for what concerns computational savings related to the required time discretisation, whilst also introducing new aspects of the algorithm, mainly related to boundary conditions, not addressed in previous works
Multi-Physics Model Bias Correction with Data-Driven Reduced Order Modelling Techniques: Application to Nuclear Case Studies
Get PDFNowadays, interest in combining mathematical knowledge about phenomena and
data from the physical system is growing. Past research was devoted to
developing so-called high-fidelity models, intending to make them able to catch
most of the physical phenomena occurring in the system. Nevertheless, models
will always be affected by uncertainties related, for example, to the
parameters and inevitably limited by the underlying simplifying hypotheses on,
for example, geometry and mathematical equations; thus, in a way, there exists
an upper threshold of model performance. Now, research in many engineering
sectors also focuses on the so-called data-driven modelling, which aims at
extracting information from available data to combine it with the mathematical
model. Focusing on the nuclear field, interest in this approach is also related
to the Multi-Physics modelling of nuclear reactors. Due to the multiple physics
involved and their mutual and complex interactions, developing accurate and
stable models both from the physical and numerical point of view remains a
challenging task despite the advancements in computational hardware and
software, and combining the available mathematical model with data can further
improve the performance and the accuracy of the former.
This work investigates this aspect by applying two Data-Driven Reduced Order
Modelling (DDROM) techniques, the Generalised Empirical Interpolation Method
and the Parametrised-Background Data-Weak formulation, to literature benchmark
nuclear case studies. The main goal of this work is to assess the possibility
of using data to perform model bias correction, that is, verifying the
reliability of DDROM approaches in improving the model performance and accuracy
through the information provided by the data. The obtained numerical results
are promising, foreseeing further investigation of the DDROM approach to
nuclear industrial cases
Numerical Monte Carlo analysis of the void coefficient in Pavia TRIGA Mark II reactor
Get PDFIn nuclear reactor safety assessment studies, void formation in the coolant, both in nominal operation and in accidental scenarios, must be considered since bubble nucleation can lead to fast reactivity changes, thus putting a strain on the reactor control. The evaluation of such a phenomenon is not trivial due to the non-linearities related to the competing phenomena (e.g. neutron absorption and scattering) and the spatial effects. This work aims to analyse the impact of void formation on the multiplication factor in the Pavia (Italy) TRIGA Mark II reactor, focusing on spatial effects. A model of the TRIGA has been developed using Serpent Monte Carlo code and validated against experimental measurements conducted at the Pavia reactor. Two approaches have been adopted. The first consists of directly evaluating the multiplication factor of several configurations, each featured by a different water density to mimic a homogeneous void formation. The second approach consists of a perturbative procedure, i.e., a first-order sensitivity analysis, which allows the gathering of more information on the aforementioned competing phenomena. Both cases subdivide the core into several radial and axial regions to recover the spatial effect. The two approaches appear to be complementary in the information they provide. The results show that the void coefficient is negative in the core and strongly dependent on both position and void fraction. Moreover, the results show the strong influence of the fuel elements type (101 and 103), their location, and the experimental methods adopted on the void coefficient
Model order reduction of a once-through steam generator via dynamic mode decomposition
No full textOnce-Through Steam Generators (OTSG), as the heat exchanger and the radioactive shield that connecting the primary system and the secondary system, is of vital importance for nuclear safety and economy. Whereas large-scale and coupling simulation models can provide high-fidelity estimations of the flow and heat exchange in OTSGs, there is an extra computational burden when applied to multi-query tasks such as optimization and uncertainty analysis. Model Order Reduction (MOR) methodology provides an alternative for the multi-query tasks. Few studies exist related to nuclear reactor components and to the OTSG using MOR; as such, this paper introduces DMD, which is data-driven and is suitable for any problem without restriction, to build the Reduced Order Model (ROM) aiming to offer accurate and fast estimation for the dynamic operating characteristics of the OTSG. The results show the established DMD model can accurately simulate the system state and improve greatly the computational efficiency
Advection-Diffusion of Scalars with the Incompressible Schrödinger Flow
No full textThe description of fluid motion is typically carried out either considering continuum matter or collision models (Lattice Boltzmann methods), with the former being the most common: in this framework, differential balance equations are derived from conservation principles and are solved to obtain density, velocity, pressure and temperature fields. If viscous forces are neglected, the fluid behaves as inviscid, and it obeys the Euler equations: their direct numerical simulation is challenging because of their mathematical structure, which imposes tight constraints on the mesh size and the temporal discretization. Thus, powerful computers are needed to deal with the long computational times of direct numerical simulations of fluids, and still, computational times are often unsuitable for multi-query scenarios and parameter sensitivity studies. A third approach to dealing with inviscid fluids was born in the 1920s when Madelung proposed its interpretation of quantum mechanics based on an analogy between the Schrödinger equation and the compressible Euler equations obtained by adopting a suitable coordinate transformation. This framework has been recently analysed for simulating incompressible inviscid flows, providing a novel methodology for solving the Euler equations, known as Incompressible Schrödinger Flow. Its different mathematical formulation allows a less tight numerical discretization; investigating this approach can give a new perspective on the description of fluids. This work focused on the application of this method in the advection-diffusion of scalars (e.g., temperature or concentration) in inviscid incompressible flows, adopting as velocity that computed by the Incompressible Schrödinger Flow; furthermore, it will be investigating the possibility of inserting into the “quantum” counterpart equation a potential term related to gravity and buoyancy forces
Data-driven model order reduction for sensor positioning and indirect reconstruction with noisy data: Application to a Circulating Fuel Reactor
Get PDFSensor positioning and real-time estimation of non-observable fields is an open question in the nuclear sector, especially for advanced nuclear reactors. In Circulating Fuel Reactors (CFR), liquid fuel and coolant are homogeneously mixed, and thus these reactors will not have internal structures, making sensor positioning in the primary circuit, including the core, an unresolved problem, making most of the core blind to sensors. Thus, the possibility of estimating the system state in the whole domain using a few local measurements has important implications for safety, monitoring, and control both in nominal and accidental conditions. In this context, the integrated Model Order Reduction and Data Assimilation framework offers intriguing opportunities to reliably combine experimental data and background knowledge from a reduced mathematical model. This work discusses and applies innovative methods within this framework, based on the Generalized Empirical Interpolation and the Indirect Reconstruction algorithms, to a proposed concept of CFR. This work aims to identify the optimal sensor positioning within the core and assess the feasibility of reconstructing the quantities of interest starting only from transient sparse data on fuel temperature, possibly noisy, and testing the predictive capabilities of the discussed methods
Stability assessment of an optimized cooling configuration of a fusion gyrotron resonant cavity through an analytical model
No full textOne of the main issues for the gyrotrons remains an efficient cooling of the resonant cavity, as the high amount of energy released on its inner wall leads to high temperatures, cavity expansion, and subsequent frequency downshifts in the electromagnetic power, reducing the efficiency of the tube, resulting in a multi-physics problem. Moreover, the heat load released is not uniform, causing thermal gradients in the cavity structure and, consequently, thermal stresses. In a previous optimization study, a Biogeography-Based optimization algorithm was used to determine an optimized axial profile for the heat transfer coefficient (HTC) of the cavity coolant. A straightforward engineering solution, based on an annular region for the coolant passage, was designed to achieve the identified HTC profile. However, even with the optimized HTC the cavity wall will still experience displacements, potentially changing the cooling system configuration and, consequently, the expansion. In the present study a stability analysis of the mentioned optimized cooling configuration is performed by means of a 0D model. A linearization of the model is performed, including the linear thermal expansion of the metal, and the stability of the system is verified. Then, the response in time of the linear model is validated through a comparison with the non-linear one
An improved zero-dimensional model for simulation of TRIGA Mark II dynamic response
Get PDFThe primary aim of this work is to improve the analysis of the dynamic behaviour of the TRIGA Mark II reactor at the University of Pavia through a zero-dimensional approach. Besides the coupling between neutronics (point-reactor kinetics with six delayed neutron precursors group) and thermal-hydraulics (two-region model, with fuel and coolant) implemented in earlier works, the new model considers also the time behaviour of the mass flow rate due to natural circulation, of the neutron poisons and of the primary and secondary pool temperature. The system of coupled first-order differential equations is non-linear, as some state variables, such as the mass flow rate and the coolant temperature, multiply each other. The SimulinkTM programming environment for dynamic analysis and control purposes is used to solve the system. A comparison with experimental data collected on-site for different reactor power transients and with measurements of the poison anti-reactivity during reactor shut-down and of the pool temperature allows the validation of the model. The model results and the experimental data reach a remarkable agreement. In addition, a linear stability analysis of the reactor is performed through the root locus and the stability map in terms of the thermal feedback coefficients. This analysis shows how the power level influences the dynamic of the system, and that, for certain values (always negative) of the fuel thermal feedback coefficient, positive values of the one for the moderator still ensures the system stability
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