The computations were carried out for the experimental

The computations were carried out for the experimental conditions of Ref. [3], where inline tube bundles with various distances (steps) between them were studied in cross-flow of liquid alkali metals. The operating chamber of the experimental installation was a rectangular box with an inlet diffuser and an outlet confuser. In the experiments of Ref. [3], the central tubes of the first and the sixth rows of the bundles were heated successively by passing the electrical current through them. The rest of the tubes were not heated and served only to create a hydrodynamic similarity. Only the case of heating the sixth-row tubes was taken for carrying out the computations in this PR-171 investigation . Numerical simulation was done for two tube bundles:
The velocity V* in the minimal cross-section normal to flow, determined by the ratio where Vin is the velocity at the computational domain inlet, is taken as the velocity scale. The computational domains consisted of a number of tube rows in the direction normal to the flow, and two rows of semicircular ‘displacers’ and arranged on the side boundaries (the same as in the experiments of Ref. [3]). One, three or five tube rows were set in the direction normal to the flow in the computations for the closely packed bundle. The computations for the widely packed bundle were carried out for one configuration consisting of three complete tube rows. Ten tube rows were placed along the depth of both bundles. The values of the geometrical parameters used for the simulation are listed in Table 1. Fig. 1 shows, as an example, the computational domain for the closely packed bundle with one complete tube row. Constant values of the normalized velocity were set at the domain inlet: Vin = 0.185 for the closely packed bundle and 0.408 for the widely packed one; the reduced temperature at the inlet was assumed to be zero, Tin = 0. The reduced pressure at the outlet boundary was assumed to be zero. No-slip conditions were imposed on the tube walls. The walls themselves were taken to be adiabatic except those of the sixth-row tubes where a constant-rate heat flux was set. The walls with semicircular displacers limiting the flow domain in the cross direction were regarded as adiabatic, and a no-slip condition was set for them as well. The basic series of computations were carried out for each specific geometry for the following set of the Péclet number values, Pe =V*d/a: 600, 800, 1000 and 1200 (a is the thermal diffusivity). The Reynolds number values ranged from 26,200 to 52,400. Unstructured computational grids included, depending on the bundle configuration, from 160 to 500 thousand nodes. An additional computational series was performed for a closely packed bundle with three tube rows (across the flow) on a coarser computational grid, as compared to the basic one (the total number of grid nodes was reduced to about a third). Grid clustering to the cylindrical walls maintained a normalized size of the near-wall cell y+ not exceeding unity for all the computed variants.
Computational results and discussion Moving on to presenting and discussing the results, we should first and foremost note thorax the numerical solution was reduced to a steady one during the computations for the closely packed bundle with one tube row at all the examined values of the Péclet number, and also at its minimal value (Pe = 600) for the variants of 3 and 5 rows. In other cases, the flow field computed was unsteady and non-periodic, which required obtaining a substantially large time sample for subsequent averaging. Figs. 2–4 show general pictures and enlarged fragments (in the vicinity of the sixth-row tubes) of the instantaneous distributions of the total dimensionless velocity and the normalized temperature, obtained for the closely packed bundle with different numbers of cross-flow tube rows at the highest Péclet number (Pe = 1200) of the examined ones. The temperature was normalized to the difference between the outlet bulk temperature and the inlet temperature.