As an alternative to full potential solvers for transonic inviscid flows, a numerical method is proposed that solves the mass and momentum conservation equations for inviscid compressible flows in combination with the polytropic equation for isentropic flow. It is shown that simple wave solutions for shear flow exist for those conservation equations. This allows the method to evaluate the lift force reasonably well over two-dimensional (2D) airfoil as well as three-dimensional (3D) isolated wing without enforcing the Kutta condition at sharp trailing edges and along wake meshes. Furthermore, it is shown that viscous effects can be evaluated with reasonable accuracy simply by introducing viscous terms in the momentum conservation equations. The dissipated kinetic energy is then drained from the computational domain because the energy conservation equation is replaced by the polytropic equation. The usefulness of the isentropic flow assumption in compressible flow simulations focusing on a possible alternative to the full-potential formulation is discussed by presenting computed results for typical transonic flows in aerospace engineering.

To contribute to achieving global “Net Zero” emissions by 2050, it is necessary to improve the environmental performance of aircraft. A natural laminar flow design, which is one of the most effective technologies for achieving this goal, was applied to the vertical tail of a narrow-body aircraft. The design effect was demonstrated in the European Transonic Windtunnel, which allows testing at flight Reynolds numbers. The transition location on the high-precisely manufactured laminar flow vertical tail model was detected by a temperature-sensitive paint. Significant laminar effects have been confirmed in a wide range of Reynolds numbers, including the design point, in the previous paper. In this paper, we focus on the variation in the transition location depending on the Mach number and sideslip angle. The variation in the transition location with the Mach number and sideslip angle was analyzed based on linear stability theory, and the correlation with the pressure gradient was clarified. It is also shown that Tollmien-Schlichting instability tends to be dominant on the inboard, and crossflow instability tends to be dominant on the outboard. In conclusion, it is shown that the laminar flow vertical tail is experimentally robust to variations in the Mach number and sideslip angle.