Determination of the Thickness of a Boundary Layer on a Submarine Hull Using Computational Fluid Dynamics

In this study, a numerical model based on computational fluid dynamics (CFD) is proposed to determine the boundary layer thickness on the hull of a three-dimensional submarine on its three axes (x, y, z). Five three-dimensional models of a submarine with different scales have been considered for ten different values of velocity. Hence, the thickness of the boundary layer could be calculated for 50 study cases. These calculations have been performed by using a non-structured mesh of the type “Fluent Mosaic”. This study does not use the functions of the wall to solve the boundary layer, but the value of \(y^{ + } \approx 1\) is fixed in order to solve the flow equations in the viscous layer. Analyzing the numerical results has led to a mathematical formula that helps evaluate the maximum thickness of the boundary layer as a function of submarine parameters. Depending on this mathematical formulae, the exact domain dimensions in which Navier–Stokes equations should be solved is defined. Thus, Euler equation can be solved in the rest of the domain far from the boundary layer, this approach of dividing the flow domain has decreased the time calculation by 60% in comparison to the case where viscous flow equations are solved in the entire domain. On the other hand, this study shows that if the submarine is equipped with a cavitator in order to generate a vapor around the hull, the optimum dimensions of this cave will be equal to the thickness of the boundary layer calculated by the proposed mathematical formulae.