Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions for Flat Plate without/with Suction

In this work, we investigated the problem of the boundary layer suction on a flat plate with null incidence and without pressure gradient. There is an analytical resolution using the Bianchini approximate integral method. This approximation has been achieved by Lambert or Error functions for boundary layer profiles with uniform suction, even in the case without suction. Based on these new laws, we brought out analytical expressions of several boundary layer features. This gives a necessary data to suction effect modeling for boundary layer control. To recommend our theoretical results, we numerically studied the boundary layer suction on a porous flat plate equipped with trailing edge flap deflected to 40°. We showed that this flap moves the stagnation point on the upper surface, resulting to avoid the formation of the laminar bulb of separation. Good agreement was obtained between the new analytical laws, the numerical results (CFD Fluent), and the literature results.

Critical Mach Numbers of Flow around Two-Dimensional and Axisymmetric Bodies

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

Optimization of Lift-Curve Slope for Wing-Fuselage Combination

The paper presents results obtained by the author for wing-body interference. The lift-curve slopes of the wing-body combinations are considered. A 2D potential model for cross-flow around the fuselage and a discrete vortex method (DVM) are used. Flat wings of various forms and the circular and elliptical cross sections of the fuselage are considered. It was found that the value of the lift-curve slopes of the wing-body combinations may exceed the same value for an isolated wing. An experimental and theoretical data obtained by other authors earlier confirm this result. Investigations to optimize the wing-body combination were carried within the framework of the proposed model. It was revealed that the maximums of the lift-curve slopes for the optimal midwing configuration with elliptical cross-section body had a sufficiently large relative width (more than 30% of the span wing). The advantage of the wing-fuselage combination with a circular cross section over an isolated wing for wing aspect ratio greater than 6 can reach 7.5% at the relative diameter of fuselage equal to approximately 0.2.