br Acknowledgment The study has been sponsored by a

Acknowledgment The study has been sponsored by a Russian Science Fund grant (project no. 15-19-00091).
Introduction The issue of the flow and heat transfer in cross-flowed tube bundles is among the most practically important ‘canonical’ cases [1,2] of the problem on liquid metal coolant thermohydrodynamics. This problem was extensively studied experimentally in the 1950s and the 1960s in the laboratories of the Central Boiler and Turbine Institute named after I.I. Polzunov (CBTI) [1,3] and of the Institute for Physics and Power Engineering named after A.I. Leypunsky (IPPE) [2,4]. The subjects of the research were the intensities of the local and the average heat transfer of inline and staggered tube bundles of various configurations in cross-flow, as well as the flow of heavy and alkali liquid metals around isolated cylinders with the Péclet number varying over a wide range. Measurement procedures were developed, and the effects of various factors on the heat transfer processes were studied, in particular, the operating parameters, the number of tube rows in the cross direction, bundle configurations, etc. In the last decade, there has been a renewed interest towards this mek162 area of research, primarily, due to the large-scale projects in building nuclear power plants with new-generation high-safety fast reactors providing opportunities for implementing a closed nuclear fuel cycle. The results of the studies on the problem of heavy metal thermohydrodynamics (the metals in question were molten lead and lead-bismuth eutectics) in tube bundles in cross-flow that have been recently carried out in IPPE are partially described in Refs. [5,6]. The experimental approach to studying the flow structure and the thermal state of metal melts involves considerable costs and overcoming a number of intrinsic difficulties. Currently, numerical simulation based on the unsteady equations of motion and heat transfer is considered the most promising area of research for gaining more knowledge required for developing new projects. The computation techniques that are used nowadays can be classified into two groups, the engineering type (which is relatively cost-effective) based on the Reynolds-averaged Navier–Stokes equations (RANS, URANS); and vortex-resolving techniques (DNS, LES, DES); the latter are highly accurate but demand a lot of computational resources. The computations of turbulent flow of liquid sodium around an isolated circular cylinder with significant buoyancy effects can serve as an example of applying the direct numerical simulation method to a similar problem [7]. The experience of numerical simulation of turbulent flow and heat transfer in tube bundles in cross-flow described in literature mostly concerns the media with Prandtl numbers around unity. Early computations were based on the assumption that the flow field was periodic in the streamwise and the cross directions, which corresponded to the infinite bundle model [8,9]. However, when setting up laboratory experiments, researchers prefer to use bundles with the least possible number of tubes, especially for costly experiments with liquid metal flows. Consequently, this raises the question about the influence that the boundary effects have on the flow structure and the heat transfer characteristics. When carrying out numerical simulations whose results are compared to the experimental data, it is reasonable to eliminate (or at least substantially reduce) uncertainties of this sort. This can be done by rejecting the assumption that the flow is periodic, i.e., by using a computation domain comprising all of the tubes forming the bundle in the experimental prototype (see, for example, Refs. [10,11]).
Problem setting and the computational aspects Unsteady turbulent flow with a small Prandtl number (Pr = 0.023) has been examined in the two-dimensional formulation applied to the problem of inline tube bundles consisting of round tubes in cross-flow. We used the model of the incompressible Newtonian fluid with constant physical properties, without the buoyancy effects taken into account. Numerical simulation was based on solving the unsteady Reynolds-averaged Navier–Stokes equations (URANS) combined with the energy equation. The SST turbulence model was used to close the Reynolds system of equations [12].