scholarly journals Улучшение несущих свойств крыла на взлетно-посадочных режимах с помощью системы управления пограничным слоем с использованием актуаторов эжекторного типа

2018 ◽  
Vol 44 (15) ◽  
pp. 71
Author(s):  
А.В. Воеводин ◽  
А.А. Корняков ◽  
Д.А. Петров ◽  
А.С. Петров ◽  
Г.Г. Судаков
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Gas Jet ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Edge Based

AbstractA device making it possible to control of the flow past a wing at low flight speeds is proposed. The device comprises an ejector-type actuator that simultaneous sucks the boundary layer on the upper surface and blows a gas jet in the vicinity of the trailing edge. Based on the Reynolds-averaged Navier–Stokes equations, a mathematical model of an ejector-type actuator is developed and experimental studies are carried out.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

Dynamical Study of a Molten Boundary Layer Ejected by Laminar Gas Flow

2014 ◽  
Vol 348 ◽  
pp. 88-93 ◽  
Author(s):  
S. Aggoune ◽  
El Hachemi Amara
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Gas Flow ◽  
Stokes Equations ◽  
Gas Jet ◽  
Navier Stokes ◽  
Dynamical Study ◽  
Navier Stokes Equations ◽  
Finite Differences Method ◽  
Layer Increase

We consider in the present work the fusion laser cutting of stainless steel sheets under a nitrogen laminar gas jet. The molten metal is treated as a laminar and steady viscous incompressible fluid. The mathematical model describing our problem is set in terms of Navier-Stokes equations, solved numerically using the finite differences method, where the effect of the gas jet velocity on the molten boundary layer is considered. The generated shear stress occurring on the gas-liquid interface and its contribution in the momentum is carried out, and it is found that when the skin friction and the shear stress decrease, the thickness and the velocity at the edge of the molten boundary layer increase along the kerf surface. The layer thickness reduces when the assisting gas velocity is increased.

Asymptotic analysis of a linearized trailing edge flow

1972 ◽  
Vol 6 (3) ◽  
pp. 327-347 ◽  
Author(s):  
K. Capell
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wake Region ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Appl Math ◽  
Edge Flow

An Oseén type linearization of the Navier-Stokes equations is made with respect to a uniform shear flow at the trailing edge of a flat plate. Asymptotic expansions are obtained to describe a symmetrical merging flow for distances from the trailing edge that are, in a certain sense, large. Expansions for three regions are found:(i) a wake region,(ii) an inviscid region, and(iii) an upstream lower order boundary layer.The results are compared with those of Hakkinen and O'Neil (Douglas Aircraft Co. Report, 1967) and Stewartson (Proc. Roy. Soc. Ser. A 306 (1968)). They are further related to the results of Stewartson (Mathematika 16 (1969)) and Messiter (SIAM J. Appl. Math. 18 (1970)).

On the development of the wake behind the trailing edge of a flat plate

1970 ◽  
Vol 42 (3) ◽  
pp. 627-638 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Constant Velocity ◽  
Stokes Equations ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations

A stream with constant velocity U is impulsively started at time t = 0 past the trailing edge of a semi-infinite flat plate. According to boundary-layer theory, it is found that the flow at a distance x downstream from the trailing edge is unaware of the presence of the plate when x > Ut; at time t = x/U there is then a discontinuity in the velocity normal to the plate. It is the neglect of diffusion parallel to the axis of the plate that introduces the discontinuity, and when the complete Navier–Stokes equations are considered for t ≃ x/U, a solution is found that can be matched with that gained from boundary-layer arguments.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

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