http://hdl.handle.net/11422/119 Thu, 09 Apr 2026 10:51:40 GMT 2026-04-09T10:51:40Z http://hdl.handle.net/11422/9066 Title: Application of the boundary-value technique to singular perturbation problems at high Reynolds numbers Author(s)/Inventor(s): Qassim, Raad Yahya; Freire, Atila Pantaleão Silva Abstract: The boundary-value technique, advanced by Roberts for the solution of singular pertubation problems of ordinary differential equations where the small parameter multiples the highest derivative, is extended to the solution of the Navier-Stokes equation at high Reynolds numbers. Three standard flows—uniform flow past a plate, flow with a linearly adverse external velocity, and shear flow past a flat plate—have been chosen as test problems with a view to evaluating some of the features of the boundary-value technique, particularly in comparison with coefficient matching techniques as examplified by the method of matcher asymptotic expansions. Publisher: Elsevier Type: Artigo Wed, 30 Jun 2004 00:00:00 GMT http://hdl.handle.net/11422/9066 2004-06-30T00:00:00Z http://hdl.handle.net/11422/9065 Title: An asymptotic solution for transpired incompressible turbulent boundary layers Author(s)/Inventor(s): Freire, Atila Pantaleão Silva Abstract: In this work perturbation techniques are used to study the equations of mean motion for transpired incompressible turbulent boundary layers. One of the features of this approach is the use of multiple scales. Indeed, the solution of this problem requires the use of three distinct scales associated with the three flow regions : the inviscid region, the defect layer and the wall layer. In the construction of the wall and defect solutions, a new law of the wake is determined by comparison of these two solutions in an interval of common domain of validity. The matching conditions also yield a skin-friction equation for transpired turbulent boundary layers. The velocity profiles obtained from the law of the wake expression, and the values of the skin-friction coefficient predicted by the skin-friction equation for flows with both injection and suction of fluid, are compared with experimental data showing good agreement. Publisher: Elsevier Type: Artigo Fri, 28 Feb 2003 00:00:00 GMT http://hdl.handle.net/11422/9065 2003-02-28T00:00:00Z http://hdl.handle.net/11422/9064 Title: An extension of the transpired skin-friction equation to compressible turbulent boundary layers Author(s)/Inventor(s): Freire, Atila Pantaleão Silva Abstract: The injection or suction of fluid into the turbulent boundary layer has proved over the years to be an effective means of controlling the properties of fluid flowing over a surface. The result of this injection or suction of fluid is to modify the velocity and temperature distributions through the boundary layer so that the drag and the heat transfer are either reduced or increased. Most of the studies on this topic, however, deal with incompressible flow. The majority of the results on supersonic flow comes from the work of Squire and his students at Cambridge University [l-S]. These results are given for Mach mtmbers up to 3.6 at various injection rates. Full tables of measured profiles are presented and expressions for the law of the wall and the law of wake are proposed. As for the incompressible case, the law of the wall is obtained by straightforward application of the mixing-length theory [l]. Unfortunately, in those works the skin-friction coefficients are evaluated by means of the momentum-integral equation which tends to be very inaccurate, thus definitive checks on the proposed law of the wall are impossible. In a previous paper [6], the present author has proposed a skin-friction equation for transpired incompressible turbulent boundary layers. This equation is much less sensitive than the momentum-integral equation to small variations in the flow parameters so providing much more reliable results. The aim of this work is to extend this skin-friction equation to compressible flow. Publisher: Elsevier Type: Artigo Fri, 28 Feb 2003 00:00:00 GMT http://hdl.handle.net/11422/9064 2003-02-28T00:00:00Z http://hdl.handle.net/11422/9063 Title: An asymptotic approach for shock-wave/transpired turbulent boundary layer interactions Author(s)/Inventor(s): Freire, Atila Pantaleão Silva Abstract: In this work perturbation techniques are used to study the problem of the interaction between a shock wave and a transpired turbulent boundary layer at transonic speeds. In the case considered here, the Mach number is assumed to be high enough for the sonic line to penetrate deep into the boundary layer so that it ends close to the wall. The flow region is divided into a region of strong interaction and regions of weak interaction. For the regions of weak interaction, upstream and downstream of the shock, a classical two-deck structure is assumed to hold for the boundary layer. Solutions chosen for these regions must account for the effects of blowing or suction. The strong interaction region on the other hand is shown to consist of three decks. A detailed analysis of the whole flow field is carried out and solutions valid in the double limit as Reynolds number tends to infinity and Mach number tends to one are proposed. Solutions of adjacent layers are shown to match so providing a smooth solution for the entire flow region. The analysis yields solutions for the pressure and skin-friction profiles. Publisher: Elsevier Type: Artigo Fri, 01 Jul 1988 00:00:00 GMT http://hdl.handle.net/11422/9063 1988-07-01T00:00:00Z