scholarly journals An Explanation and Understanding of Aerodynamic Lift by Triple Deck Theory

2021 ◽  
Author(s):  
Alois Schaffarczyk
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Kutta Condition ◽  
Cfd Models ◽  
Definition Of ◽  
Aerodynamic Lift

An explanation of aerodynamic lift still is under controversial discussion as can be seen, for example, in a recent published article in Scientific American [1]. In contrast to an approach via integral conservation laws we here review an approach via the classical Kutta-Condition and its relation to boundary layer theory. Thereby we summarize known results for viscous correction to the lift coefficient for thin aerodynamic profiles and try to remember the work on triple-deck or higher order Boundary Layer theory, its connection to interactive boundary layer theory, viscous/inviscid coupling as implemented to well-known engineering code Xfoil. Finally we compare its findings to simple 2D numerical solution of full Navier Stokes equations (CFD)models. As a conclusion, a clearer definition of terms like understanding and explanation applied to the phenomenon of aerodynamic lift will be given.

scholarly journals Review of an Explanation of Aerodynamic Lift by Triple Deck Theory

2021 ◽  
Author(s):  
Alois Schaffarczyk
Keyword(s):  
Boundary Layer ◽  
Computational Fluid Dynamic ◽  
Recent Article ◽  
Fluid Dynamic ◽  
Lift Coefficient ◽  
Higher Order ◽  
Boundary Layer Theory ◽  
Cfd Models ◽  
Definition Of ◽  
Aerodynamic Lift

Inspired from a recent article by Regis , earlier publised work of McLean , , and informal discussions much earlier with members of the Danish Technical University and KTH, Sweden we summarize known results for viscous correction to the lift coefficient for thin aerodynamic profiles. We thereby try to remember [d=1]theto work of on triple-deck or higher order Boundary Layer theory and compare it to simple 2D Computational Fluid Dynamic (CFD) models. As a conclusion, a clearer definition of terms like understanding and explanation applied to the phenomena of aerodynamic lift will be given.

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.

On the flow downstream of separation in an incompressible fluid

1953 ◽  
Vol 49 (3) ◽  
pp. 561-569 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Theoretical Explanation ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Main Stream ◽  
Navier Stokes Equations ◽  
Narrow Region

When a stream is flowing along a wall against an adverse pressure gradient, the skin friction at the wall decreases to zero, at which point or at least very near it the flow seems to leave the surface altogether. Between the main stream and the wall there may be a slow back-flow. Upstream of separation the influence of the wall on the flow is satisfactorily explained by the boundary-layer theory, which among other things presupposes that this influence is confined to a narrow region near the wall. Such a theory is clearly inadequate downstream, however, because this layer rapidly increases in width and, further, the main stream is seriously affected, and consideration of the Navier-Stokes equations would seem to be necessary before a full theoretical explanation of separation could be given. Apart from a note by Dean (2) on the relations between the pressure and velocity at separation, there has, however, been no relevant attack on these equations.

Laminar boundary layers

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Momentum Integral ◽  
Aerodynamic Lift

This chapter starts by introducing the concept of a boundary layer and the associated boundary-layer approximations. The laminar boundary-layer equations are then derived from the Navier-Stokes equations. The assumption of velocity-profile similarity is shown to reduce the partial differential boundary-layer equations to ordinary differential equations. The results of numerical solutions to these equations are discussed: Blasius’ equation, for zero-pressure gradient, and the Falkner-Skan equation for wedge flows. Von Kármán’s momentum-integral equation is derived and used to obtain useful results for the zero-pressure-gradient boundary layer. Pohlhausen’s quartic-profile method is then discussed, followed by the approximate method of Thwaites. The chapter concludes with a qualitative account of the way in which aerodynamic lift is generated.

A numerical study of laminar separation bubbles using the Navier-Stokes equations

1971 ◽  
Vol 47 (4) ◽  
pp. 713-736 ◽  
Author(s):  
W. Roger Briley
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Reynolds Numbers ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Separation ◽  
Boundary Layer Equations

The flow in a two-dimensional laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow. The study was motivated by the need to analyze high-Reynolds-number flow fields having viscous regions in which the boundary-layer assumptions are questionable. The approach adopted in the present study is to analyze the flow in the immediate vicinity of the separation bubble using the Navier-Stokes equations. It is assumed that the resulting solutions can then be patched to the remainder of the flow field, which is analyzed using boundary-layer theory and inviscid-flow analysis. Some of the difficulties associated with patching the numerical solutions to the remainder of the flow field are discussed, and a suggestion for treating boundary conditions is made which would permit a separation bubble to be computed from the Navier-Stokes equations using boundary conditions from inviscid and boundary-layer solutions without accounting for interaction between individual flow regions. Numerical solutions are presented for separation bubbles having Reynolds numbers (based on momentum thickness) of the order of 50. In these numerical solutions, separation was found to occur without any evidence of the singular behaviour at separation found in solutions to the boundary-layer equations. The numerical solutions indicate that predictions of separation by boundary-layer theory are not reliable for this range of Reynolds number. The accuracy and validity of the numerical solutions are briefly examined. Included in this examination are comparisons between the Howarth solution of the boundary-layer equations for a linearly retarded freestream velocity and the corresponding numerical solutions of the Navier-Stokes equations for various Reynolds numbers.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

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.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

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