In Pressurized Water Reactors (PWR), Steam Generator (SG) tubes constitute one of the three barriers which preserve the environment from radioactivity. Excessive tube vibrations under fluid forces, due to the steam-water mixture flow across the tube bundle, can lead to the failure of some tube. Several methods have been proposed to estimate some upper bounds for these forces. These bounds are applicable at the design stage and are helpful to avoid tube failures. Most of the available methods are based on experimental results that have been obtained on tube bundles installed in scaled test-facilities. Unlike this popular test-based approach, one combines here Computational Fluid Dynamics (CFD) to High Performance Computing (HPC), in order to estimate fluid forces in a simple case by applying the Direct Numerical Simulation (DNS) method to solve the Navier-Stokes equations. In the first paragraph, one summarizes the general standard method which allows one to derive the auto-power spectral density of the displacement response at any point of an SG tube, departing from the cross-power spectral densities of fluid forces between any two points along the tube. In the second paragraph, one recalls the equivalent dimensionless spectrum, which was proposed by Axisa et al. in the early nineties, and which still remains a useful reference in the domain. One then applies DNS to the test case of a single infinite cylinder, which is submitted to a single phase cross-flow in a rectangular channel. The Reynolds number is equal to 3900. One presents the time dependent tensors of fluid pressure and viscous stresses, and uses this tensor to estimate the field of non stationary forces that are applied by the fluid, per unit length, at a set of equidistant locations along the tube. Even if they do still require experimental validations, our computation results are more abundant and detailed than standard experimental results, as well as more flexible to use. They therefore provide an interesting additional source of information. They already allow us to try to get new insights into quantities that would be, in any case, very difficult to obtain experimentally. Lift, drag, and even the forces acting in the direction of the tube axis, are computed, and can be distinguished one from the other. Fluid forces due to viscous stresses can also be compared to the ones caused by pressure. The degree of correlation of the forces along the tube can also be examined.

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