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In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient. [ABSTRACT FROM AUTHOR]

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module Conical (Gil et al., 2012) for the computation of conical functions. Specifically, the module includes now a routine for computing the function R − 1 2 + i τ m ( x ) , a real-valued numerically satisfactory companion of the function P − 1 2 + i τ m ( x ) for x > 1 . In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided. The module also improves the performance of our previous algorithm for the conical function P − 1 2 + i τ m ( x ) and it includes now the computation of the first order derivative of the function. This is also considered for the function R − 1 2 + i τ m ( x ) in the extended algorithm. Program summary Program Title: Module Conical Program Files doi: http://dx.doi.org/10.17632/rpw5d8gdkg.1 Licensing provisions: CC by 4.0 Programming language: Fortran 90 External routines/libraries: The module Conical uses a Fortran 90 version of the routine dkia (developed by the authors) for computing the modified Bessel functions K i a ( x ) and its derivative. This routine is available at http://toms.calgo.org . Nature of problem: These functions are the natural function basis for solving, for example, the Laplace’s problem in spherical coordinates for two intersecting cones or for regions bounded by two intersecting spheres, or by one or two confocal hyperboloids of revolution when using toroidal coordinates. The conical function P − 1 2 + i τ m ( x ) is also used in the Mehler–Fock integral transform for problems in potential and heat theory, Solution method: The algorithm uses different methods of computation depending on the function under consideration ( P − 1 2 + i τ m ( x ) or R − 1 2 + i τ m ( x ) ) and the values of x , τ and m : numerical quadrature, asymptotic expansions in terms of elementary functions, asymptotic expansions in terms of Bessel functions, asymptotic expansions for tau large and backward/forward recursion of three-term recurrence relations. Restrictions: In order to avoid underflow/overflow problems in standard IEEE double precision arithmetic, the admissible parameter ranges for computing the conical function P − 1 2 + i τ m ( x ) in the routine conicp are: − 1 < x < 1 , 0 < τ < = 100 , 0 ≤ m ≤ 40 1 < x ≤ 100 , 0 < τ ≤ 100 , 0 ≤ m ≤ 100 . When using the routines conicr and conicpr , the admissible parameter ranges for computing the functions P − 1 2 + i τ m ( x ) and R − 1 2 + i τ m ( x ) are 1 < x ≤ 100 , 0 < τ ≤ 100 , 0 ≤ m ≤ 100 . [ABSTRACT FROM AUTHOR]

The efficient operation and in-core fuel management of PWRs are of utmost importance. In the present work, a core reload optimization using Shuffled Frog Leaping (SFL) algorithm is addressed and mapped on nuclear fuel loading pattern optimization. SFL is one of the latest meta-heuristic optimization algorithms which is used for solving the discrete optimization problems and inspired from social behavior of frogs. The algorithm initiates the search from an initial population and carries forward to draw out an optimum result. This algorithm employs the use of memetic evolution by exchanging ideas between the members of the population in each local search. The local search of SFL is similar to particle swarm optimization (PSO) and applying shuffling process accomplishes the information exchange between several local searches to obtain an overall optimum result. To evaluate the proposed technique, Shekel's Foxholes and a VVER-1000 reactor are used as test cases to illustrate performance of SFL. Among numerous neutronic and thermal-hydraulic objectives necessary for a fuel management problem to reach an overall optimum, this paper deals with two neutronic objectives, i.e., maximizing effective multiplication factor and flattening power distribution in the core, to evaluate the capability of applying SFL algorithm for a fuel management problem. The results, convergence rate and reliability of the method are quite promising and show the potential and efficiency of the technique for other optimization applications in the nuclear engineering field. [ABSTRACT FROM AUTHOR]