Laminar free convection in open-ended vertical 7-rod bundles: experiments and porous model

The flow of ambient air induced solely by buoyancy, through a vertical rod bundle has been modelled as a phenomenon in a porous medium. The rods are at uniform heat flux condition and the circular shell adiabatic. The induced flow rate was found to be controlled by a parameter ψ dependent on the heat flux, rod diameter, length, fluid properties and the bundle permeability. Measurements performed on two 7-rod bundles corroborate the theoretical predictions. Longitudinally averaged heat transfer rates from the central and peripheral rods have also been measured and average information generated for the bundle.     

A porous body model for predicting temperature distribution in wire-wrapped rod assemblies operating in combined forced and free convection

Based on a model analogous to that of heat transfer in a porous body, a method for predicting temperature distribution in wire-wrapped assemblies operating in forced convection (negligible free convection) was developed in a previous paper. In this paper the method is extended to assemblies operating in mixed convection (combined free and forced convection). The results obtained from this analysis were found to predict available data with a precision equal to that from presently available more complex analysis methods. A new criterion based on the value of a modified Grashof number Gr_c^* has been developed to determine if an assembly with given geometry and operating conditions is in forced convection or in mixed convection.     

A bounded Monte-Carlo estimator for reaction rates in finite volume elements

The Monte-Carlo calculation of reaction rates becomes unreliable in regions where only very few particle histories contribute directly to the reaction. The integral formulation of the transport equation however, generates a sampling procedure which makes each collision point of a history (in regions near the particle source) contribute to reactions in regions far from the source. Each collisionpoint contribution is an integral over the solid angle under which the detector region is seen from the collision point and its estimator is based on the uncollided flux. For large distances between collision point and flux point this new estimator reduces to the standard point flux estimator with its well known singularity behaviour.     

Neutron transport for pure-triplet scattering in finite planar media with reflective boundaries

Pure-triplet scattering in neutron transport through a finite plane-parallel medium with internal source of energy is considered. The medium is assumed to have specular- and diffusely-reflecting boundaries. The neutron partial heat fluxes for this problem are computed in terms of the albedos of the source-free problem. Pomraning–Eddington approximation is used to solve the source free problem. A weight function is introduced to force the boundary conditions to be fulfilled.     

Some efficient lagrangian mesh finite elements encoded in zephyr for two-dimensional transport calculations

Using a general finite elements formulation in phase-space and an explicit mesh-by-mesh procedure, the time-independent two-dimensional transport code ZEPHYR provides a good alternative to finite differences production codes DOT and TWOTRAN.This is obtained mainly by two very efficient (stable and accurate) discontinuous finite elements involving triangles and quadrilaterals in R-Z or X-Y space.The accuracy is the same for rectangular grids and for irregular Lagrangian meshes.Comparing with finite differences codes and for a given accuracy the number of meshes may be divided at least by a factor of 4 (awkward geometries are easily tractable with fewer meshes) and the number of iterations may be divided at least by a factor of 2.Moreover the stability of discontinuous finite elements makes fine-mesh rebalance very efficient for convergence acceleration.Thus, for a given accuracy, ZEPHYR's storage requirements may be somewhat larger than DOT's or TWOTRAN's but time requirements may be somewhat smaller.     

Development of the finite element method of body fit nodalization for mixed convection analysis in rod bundles

In the reactor rod bundle analysis, mixed convection phenomena are very important after the reactor shutdown. In this paper, the finite element method based on the body fit nodalization are developed to analyze the mixed convection phenomena in a complex geometry. The velocity distribution and the temperature distribution in the reactor rod bundles are obtained using the above two methods. To validate the developed methods, a comparison of the present results with the analytic solutions for a concentric tube is taken. The results show that the mixed convection in a complex geometry can be treated very well with these two methods, and that the finite element method with the body fit nodalization is more efficient than the finite difference method with the body-fitted coordinate system.     

Effect of rolling on the flowing and heat transfer characteristic of turbulent flow in sub-channels

The flowing and heat transfer of turbulent flow in typical 4 rod bundles in rolling motion is investigated with LES and URANS. As the rolling period decreases, the average wall shear stress increases, and the frictional resistance increases. The wall shear stress solved by LES is not good enough, while that of URANS is consistent with experiments. The variation of frictional resistance coefficient, Nusselt number and Reynolds stress with rolling amplitude is very weak. In rolling motion, the biggest frictional resistance coefficient is not located in a constant time.     

Optimal discontinuous finite element methods for the Boltzmann transport equation with arbitrary discretisation in angle

This paper describes the development of two optimal discontinuous finite element (FE) Riemann methods and their application to the one-speed Boltzmann transport equation in the steady-state. The proposed methods optimise the amount of dissipation applied in the streamline direction. This dissipation is applied within an element using a novel Riemann FE method, which is based on an analogy between control volume discretisation methods and finite element methods when integration by parts is applied to the transport terms. In one-dimension the optimal finite element solutions match the analytical solution exactly at each outlet node. Both schemes couple elements in space via a Riemann approach. The first of the two schemes is a Petrov–Galerkin (PG) method which introduces dissipation via the equation residual. The second scheme uses a streamline diffusion stabilisation term in the discretisation. These two methods provide a discontinuous Petrov–Galerkin (DPG) scheme that can stabilise an element across the full range of radiation regimes, obtaining robust solutions with suppressed oscillation. Three basis functions in angle of particle travel have been implemented in an optimal DPG Riemann solver, which include the _PN$P_N$ (spherical harmonic), _SN$S_N$ (discrete ordinate) and LW_N${\text{LW}}_N$ (linear octahedral wavelet) angular expansions. These methods are applied to a series of demanding two-dimensional radiation transport problems.     

GPU-based Monte Carlo simulation in neutron transport and finite differences heat equation evaluation

Graphics Processing Units (GPU) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Since researchers and practitioners realized the potential of using GPU for general purpose, their application has been extended to other fields out of computer graphics scope. The main objective of this work is to evaluate the impact of using GPU in two computational expensive problems in nuclear area: a neutron transport simulation by Monte Carlo method and Poison heat equation resolution for a square thin plate. To accomplish that, GPU and CPU-based (single- and multi-core) approaches were developed. Results demonstrated that the GPU-based approach is damn faster than a parallel 8-core CPU-based approach also developed in this work.     

Investigations on the role of mixed convection and wall friction factor in single-phase natural circulation loop dynamics

The objective of the present paper is to present a 1-D model for simulating the startup from rest of water cooled single-phase natural circulation loops having horizontal heaters. The starting point of analysis is the inability of the 1-D codes to account for natural convection in the heater. Present 1-D models are unable to account for axial diffusion in the fluid caused by natural convection. Start-up from rest and many other characteristics cannot be simulated using classical 1-D models because of the inherent tendency of the predicted dynamics to be attracted by zero flow condition. The paper presents an elegant approach for taking into account both natural and forced convection. The enhancement of fluid motion and thermal mixing by natural convection is an important consideration in the design of nuclear reactors. Hence, the model developed is of direct relevance to nuclear reactor thermal hydraulics. The model developed for natural convection has been validated against the CFD simulations. The model developed has been incorporated in a classical 1-D model developed by the authors previously. The application of model to a rectangular single-phase natural circulation loop show that the model can predict the loop behavior from start-up with fidelity. The model reproduces most of the characteristics like unidirectional oscillation, bidirectional oscillations and chaotic switching reasonably well. Finally, model has been used to investigate the phenomenon of hysteresis observed in experimental loop. The paper also brings out the role of constitutive laws for wall friction in predicting the loop dynamics.     

The pulsing CPSD method for subcritical assemblies driven by spontaneous and pulsed sources

Stochastic neutron transport theory is applied to the derivation of the two-neutron-detectors cross power spectral density for subcritical assemblies when external pulsed sources are used. A general relationship between the two-detectors probability generating functions of the kernel and the source is obtained. This relationship considers the contribution to detectors statistics of both the pulsed source and the intrinsic neutron one. An expansion in α-modes is derived for the final solution, which permits to take into account the effect of higher harmonics in subcritical systems. Further, the expression corresponding to the fundamental mode approximation is compared with recent results from experiments performed under the MUSE-4 European research project.     

A lattice Boltzmann modeling of corrosion behavior and oxygen transport in the natural convection lead-alloy flow

Corrosion of structural materials presents a critical challenge in the use of lead–bismuth eutectic (LBE) or liquid lead as a nuclear coolant in accelerator-driven systems and advanced reactors. Actively controlling the oxygen concentration in LBE has been proved to be effective to mitigate corrosion under certain conditions. For mixing the oxygen uniformly and quickly, natural convection is proposed to enhance the oxygen transport. In the present study, a lattice Boltzmman simulation of coupled natural convection and lead bismuth eutectic flow in a simplified container was carried out to study characteristics of the oxygen transport and corrosion behaviors. It is assumed that the corrosion product (mainly iron) concentration is at its equilibrium level at the wall. The wall boundary condition for the mass transfer of corrosion production was taken based on the active-oxygen-control model. To examine the effect of different nature convection flow patterns on corrosion behavior and oxygen transport, three heating cases, which correspond to one-, two- and four-vortex flow patterns, are examined. Both of the local and average Sherwood number at the wall, distribution of corrosion product and oxygen, and oxygen diffusion time are analyzed. Some useful information was obtained to understand the mechanism of corrosion behavior and oxygen transport in the LBE system.     

空气中~(222)Rn、~(220)Rn子体水平的α能谱数据重建测量法

研究了一种能获取总测量周期内任意时段任意能区α能谱数据的α能谱数据重建测量方法,应用该方法解决了空气中222Rn和拟220Rn子体水平优化测量中时间段重叠的问题,并在ORTEC八通道α谱仪上实现了空气中222Rn和220Rn子体水平自动、快速及可靠的测量.     

Calculation of leakage areas and leak rates for wall penetrating cracks in pipes loaded with internal pressure and bending moment

In this paper calculations on the leak opening and leak rates of piping components with through cracks are presented. Mostly the analyses are post-calculations to experiments in order to verify the models used in the calculations. The experiments under consideration were performed at MPA-Stuttgart, Siemens-KWU and at the HDR-facility, located in Karlstein/Germany. Straight pipes, pipe bends and branches with different crack locations were considered. As far as possible numerical and experimental results are compared.     

CFD methodology and validation for single-phase flow in PWR fuel assemblies

This paper presents the CFD modeling methodology and validation for steady-state, normal operation in a PWR fuel assembly. This work is part of a program that is developing a CFD methodology for modeling and predicting single-phase and two-phase flow conditions downstream of structural grids that have mixing devices. The purpose of the mixing devices (mixing vanes in this case) is to increase turbulence and improve heat transfer characteristics of the fuel assembly. The detailed CFD modeling methodology for single-phase flow conditions in PWR fuel assemblies was developed using the STAR-CD CFD code. This methodology includes the details of the computational mesh, the turbulence model used, and the boundary conditions applied to the model. The methodology was developed by benchmarking CFD results versus small-scale experiments. The experiments use PIV to measure the lateral flow field downstream of the grid, and thermal testing to determine the heat transfer characteristics of the rods downstream of the grid. The CFD results and experimental data presented in the paper provide validation of the single-phase flow modeling methodology. Two-phase flow CFD models are being developed to investigate two-phase conditions in PWR fuel assemblies, and these can be presented at a future CFD Workshop.     

Flow transport and mixing induced by horizontal jets impinging on a vertical wall of the multi-compartment PANDA facility

In the frame of the OECD/NEA SETH project an experimental campaign has been carried out in the PANDA facility to investigate gas transport and mixing induced by a plume or a jet in the large-scale multi-compartment PANDA facility. The paper summarizes the results of the horizontal jet test series consisting of eight tests. Horizontal jets impinging on a vertical wall of one of the cylindrical PANDA containment vessels have been generated by changing various parameters, such as: type of injected fluid (steam or a mixture of steam and helium), fluid injection velocity, elevation (with respect to the containment vessel) of the injection exit, initial fluid composition in the vessels, and location of the vent line. The initial jet Froude number has been varied between 17 and 36 and in one of the test condensation occurred. The paper shows the effect of these parameters variation on the test evolution with respect to jet impingement location in the vertical curved wall and variation of impingement location as a function of buoyancy variation. Fluid mixing and stratification, characteristics of gas transport between the compartment and the effect of condensation on the overall phenomena evolution are analyzed in the paper.     

A finite element method for neutron transport—VI. Upper and lower bounds for local characteristics of solutions

Finite element methods for neutron transport are being developed because they have the potential to achieve the full geometrical flexibility of the Monte Carlo method, and they are faster in computing global solutions. It is shown that the finite element method also shares with Monte Carlo the capability to bracket local characteristics of a solution, such as the reaction rate for a small locality. The bracketing bounds for the Monte Carlo method have a statistical error, whereas these bounds are rigorous for the finite element method. The latter bounds for a locality of a system are obtained by a bi-variational method with the aid of an associated system.For cell problems very tight bounds can be computed, but in deep-penetration problems for shields there are some difficulties to be overcome. Reasons are advanced for the difficulties.     

A wide-range reactimeter for research reactors and critical assemblies

Translated from Atomnaya Énergiya, Vol. 69, No. 3, pp. 150–153, September, 1990.     

Forced convection heat transfer in rectangular ducts—general case of wall resistances and peripheral conduction for ventilation cooling of nuclear waste repositories

A numerical solution for laminar flow heat transfer between a flowing gas and its containing rectangular duct has been obtained for many different boundary conditions which may arise in nuclear waste repository ventilation corridors. The problem has been solved for the cases of insulation on no walls, one wall, two walls, and three walls with various finite resistances on the remaining walls. Simplifications are made to decouple the convective heat transfer problem from the far field conduction problem, but peripheral conduction is retained. Results have been obtained for several duct aspect ratios in the thermal entrance and in the fully developed regions, including the constant temperature cases. When one wall is insulated and the other three are at constant temperature, the maximum temperature occurs in the fluid rather than on the insulated wall. This maximum moves toward the insulated wall with increasing axial distance. Nusselt numbers for the same constant flux on all four walls with peripheral conduction lie in a narrow band bounded by zero and infinite peripheral conduction cases. A dimensionless wall conduction group of four can be considered infinite for the purpose of estimating fully developed Nusselt numbers to within an accuracy of 3%. A decrease in wall and bulk temperatures by finite wall conduction has been demonstrated for the case of a black body radiation boundary condition. Nusselt numbers for the case of constant temperature on the top and bottom walls and constant heat flux on the side walls exhibited unexpected behavior.