In the event of a nuclear reactor accident, large amount of radioactivity in the form of fission products may get released to the piping assembly of primary heat transport system. These fission products mostly in the form of aerosol particles get deposited on the inner surface of the piping system due to various depositional processes. The removal processes in the complex piping system are controlled to a large extent by the thermal-hydraulic conditions like temperature, pressure and flow rates. These parameters generally vary with time and therefore must be carefully monitored to predict the aerosol behavior in the piping system. Experimental determination of the deposition fraction, interpretation of the role of controlling parameters and development/validation of theoretical models are key areas gaining constant attention among researchers. In the present work, experiments were conducted in a piping assembly consisting of bends and horizontal-vertical orientation at two different carrier gas flow rates. Deposition fractions in the test assembly were estimated and the role of different dynamical processes (thermophoresis, gravitation and bend impaction) was interpreted. The computational fluid dynamics modeling approach is used for theoretical simulation in this work. Aerosol behavior in terms of number concentration, particle size distribution, and particle deposition in the piping system was simulated with the computational fluid dynamics software ANSYS Fluent 16.0 and the results were compared with experimental measurements (wherever applicable).

A meshless method based on fundamental and particular solutions (MFS–MPS) has been implemented for the current-hole simulation in cylindrical tokamaks. We first benchmark the method by solving the Grad–Shafranov (GS) equation for zero as well as nonzero inverse aspect ratios and noncircular cross-sections. Thereafter, the method is implemented to solve the time-dependent reduced resistive MHD equations for the current-hole simulation. The initial current density profile with a negative current density near the center is chosen and the corresponding equilibrium magnetic flux profile is first computed using the GS equation. These profiles are then used to solve the coupled nonlinear system of MHD equations using MFS–MPS and a semi-implicit time differencing scheme. After an initial linear phase extending up to a few thousand Alfvén times, the nonlinear oscillations are observed which continue for several Alfvén times. This oscillating behavior is in agreement with the previous simulations using other numerical methods. It is also found that these oscillations are damped out at higher resistivity.

We investigate the anisotropy in turbulent convection in a three-dimensional (3D) box using direct numerical simulation. We compute the anisotropic parameter A = u(perpendicular to)(2)(2u(vertical bar vertical bar)(2)), where u(perpendicular to) and u(vertical bar vertical bar) are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number Pr approximate to 1, but the anisotropy increases with the Prandtl number. For Pr = infinity, A approximate to 0.3, anisotropy is not very significant even in extreme cases. We also observe that u(vertical bar vertical bar) feeds energy to u. via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014)] for turbulent convection.

In this paper a meshless method based on fundamental and particular solution (MFS–MPS) is implemented to numerically solve the time-dependent Navier–Stokes equations in stream function–vorticity form for lid-driven cavity flows. Further, the method is applied to natural convection problem in a cavity where an additional temperature equation and mixed boundary conditions are involved. Finally the MHD equations in stream function–vorticity–magnetic field-current density form are solved for MHD flows in a lid-driven cavity. A semi-implicit approach is used for the time advancing in which the time derivative is discretized using first order forward-difference approximation, the Laplace operator is taken in next time level, and rest of the terms are taken in the current time level. We take the number of boundary collocation points more than the source points and solve the overdetermined system of equation in a least squares sense at each time step. The least squares approach alleviates the problem of ill-conditioning to a certain extent. The results obtained are in good agreement with the previous numerical works where available. We find that the meshless method based on MFS–MPS is simple and effective, and can easily be applied to the coupled time-dependent nonlinear system of equations.

The coupled nonlinear steady state Navier–Stokes (N–S) equations in the stream function–vorticity form for a lid-driven cavity are solved by a one-stage Method of Fundamental Solutions (MFS) and the Method of Particular Solutions (MPS). This method has been earlier used for linear Poisson-type problems and has not been applied to coupled nonlinear equations. In this method the steady state N–S equations are first put in the form of two nonlinearly coupled Poisson equations and the solution is sought as the sum of their respective homogeneous and particular solutions. The homogeneous solution is obtained using the MFS and the particular solution is found with the help of Radial Basis Functions (RBFs). Both the operations are accomplished in a single stage. The nonlinear coupling of the N–S equations is tackled by iteration and successive relaxation. We find that the method is easy and effective when compared with the boundary element method (BEM) or the two-stage MFS-MPS, due to its meshless, singular integration free qualities and the single stage operation. The results are obtained for the moderate Reynolds numbers by varying the relaxation parameter. The convergence of MFS-MPS scheme for the present nonlinear problem is numerically demonstrated.

In this work a meshless method based on the approximate particular solutions is applied to the computation of fixed boundary tokamak equilibria using Grad–Shafranov (GS) equation. The GS equation is solved for different choices of the right hand side of the equation: (i) when it is not a function of magnetic flux (i.e., Solov’ev solutions), (ii) when it is a linear function of magnetic flux, and (iii) when it is a nonlinear function of magnetic flux. For all these cases the first order derivative term in the GS equation is transferred to the right hand side such that the left hand side consists only the Laplace operator. This enables us to use the Radial Basis Functions (RBFs) in the calculation of approximate particular solutions. A linear combination of these particular solutions is taken as the solution of the GS equation and the resulting system of algebraic equations is solved iteratively because of the presence of the magnetic flux on the right hand side in all three choices. Furthermore, we use least squares approach in solving the overdetermined system of algebraic equations which alleviates the problem of ill-conditioning to a certain extent. The numerical results obtained using this method are in good agreement with the analytical solutions (where available). We find that the method is convergent, accurate and easily applicable to the irregular geometries due to its meshless character.

In this paper, we present the results of numerical simulations of the turbulent convection in the Argon gas present in the annulus of a fast breeder reactor. We employ RANS scheme with k-is an element of model and solve the equations using an open-source software OpenFOAM. The Rayleigh numbers Ra of our simulations lie in the range of 10(8) to 10(10). We observe a pair of rolls with a hot plume rising from one end, and a cold plume descending from the opposite end of the annulus. This feature results because the aspect ratio of the geometry is near unity. We also find that the circumferential temperature difference (CTD) is proportional to Ra. (C) 2013 Elsevier Ltd. All rights reserved.

In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

The presence of strong magnetic fields in magnetically confined thermonuclear fusion plasmas introduces a considerable anisotropy in the ion velocity distributions. Drifting or streaming of ionic species is another source of anisotropy in fusion plasmas. To account for these anisotropies, we consider in the present work a generalization of the equilibrium Maxwellian distribution in the form of a drifting tri-Maxwellian distribution function. It is shown that the calculation of thermonuclear reactivities for these distributions is best carried out in a transformed velocity space. Computational results for gyrotropic velocity distributions with drifts parallel and perpendicular to the magnetic field are presented.

Pseudospectral Direct Numerical Simulation (DNS) has been performed to simulate dynamo transition for nonhelical magnetohydrodynamics turbulence. The numerical results are compared with a recent low-dimensional model [Verma etal. [13]]. The forcing in DNS is the same as that used in the low-dimensional model. Dynamo transition is observed in DNS, but the forcing required for the transition is higher than that for the model. A qualitative similarity is observed between DNS and model results. The difference is due to the presence of large number of modes present in the DNS.