scholarly journals Measurement and modelling of the turbulent boundary layer near the attachment line of a swept wing

2017 ◽  
Vol 121 (1240) ◽  
pp. 746-769
Author(s):  
E. R. Gowree ◽  
C. J. Atkin
Keyword(s):  
Boundary Layer ◽  
Inviscid Flow ◽  
Swept Wing ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Alternative Approach ◽  
Ill Posed ◽  
Layer Velocity ◽  
Swept Wings ◽  
Attachment Line

ABSTRACTThis work is motivated by the need for low-order aerodynamic models to predict accurately the effect on profile drag of controlling attachment line transition. Head's entrainment method(1), a rapid integral boundary layer technique used for design studies on swept wings, suffers from the governing swept-tapered turbulent integral boundary layer equations being ill-posed in the vicinity of the attachment line. This singularity has been treated using crude extrapolations of the attachment-line similarity solution for over half a century, but this approach is unlikely to deliver accurate predictions of the effect of changes in the attachment line flow on profile drag. An experimental study has been carried out to explore the nature of the turbulent flow in the vicinity of a highly swept swept attachment line and has revealed a quite complex, non-monotonic development of the momentum thickness in this region. It has also revealed lower levels of twist in the boundary layer velocity profiles than anticipated from the highly curved character of the inviscid flow streamlines. These observations have prompted an alternative approach to the modelling of the flow in this region which not only successfully eliminates the lack of robustness in the swept-tapered equations but which also matches the experimental results to within ±5%.

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

1967 ◽  
Vol 89 (4) ◽  
pp. 281-288 ◽  
Author(s):  
V. D. Blankenship ◽  
P. M. Chung
Keyword(s):  
Boundary Layer ◽  
Shock Tube ◽  
Inviscid Flow ◽  
Perturbation Parameter ◽  
Entrance Region ◽  
Compressible Boundary Layer ◽  
Internal Flows ◽  
Flow Equations ◽  
Boundary Layer Equations ◽  
Interaction Problem

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

Investigation of Formation and Development of Stationary and Secondary Disturbances in the Favourable Pressure Gradient Area on the Swept Wing

2013 ◽  
Vol 8 (2) ◽  
pp. 55-69
Author(s):  
Stepan Tolkachev ◽  
Vasily Gorev ◽  
Viktor Kozlov
Keyword(s):  
Boundary Layer ◽  
Roughness Element ◽  
Swept Wing ◽  
Liquid Crystal Thermography ◽  
Natural Case ◽  
Turbulent Transition ◽  
Stage Transition ◽  
The Moment ◽  
Combined Technique ◽  
Attachment Line

In this work the combined technique of liquid-crystal thermography and thermoanemometry measurements is used to trace the stationary disturbance development from the moment of formation to the nonlinear stage transition. It has been shown that the pair of stationary vortices are formed after the cylindrical roughness element. These vortices modify a boundary layer and destabilize it. There is the area of maximal receptivity to the roughness location, which in the experiment was distant from the attachment line. If the stationary disturbance has enough magnitude in its core the secondary disturbances excite and lead to the laminar-turbulent transition. Secondary disturbances are sensitive to the acoustics and achieve the magnitude in hundred times higher than for the natural case

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part II: Attachment-Line Flow on an Infinite Swept Wing

1967 ◽  
Vol 18 (2) ◽  
pp. 150-164 ◽  
Author(s):  
N. A. Cumpsty ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Cross Flow ◽  
Swept Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow ◽  
Momentum Integral ◽  
Attachment Line

SummaryAn earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

Optimization of Steady Suction for Disturbance Control on Infinite Swept Wings

2002 ◽  
Author(s):  
Jan O. Pralits ◽  
Ardeshir Hanifi
Keyword(s):  
Boundary Layer ◽  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Transition Control ◽  
Boundary Layer Equations ◽  
Medium Range ◽  
Gradient Based ◽  
Swept Wings ◽  
Commercial Aircrafts

Theory and results are presented on transition control using steady suction to suppress convectively unstable disturbances in a growing boundary layer on infinite swept wings. The suction profiles are computed using optimal control theory and the optimization process is gradient based. Here, the gradient is evaluated using the adjoint of the parabolized stability equations and the adjoint of the boundary layer equations. Results are presented for an application of the theory on a wing-profile designed for medium range commercial aircrafts.

Receptivity and sensitivity of the leading-edge boundary layer of a swept wing

2015 ◽  
Vol 775 ◽  
Author(s):  
Gianluca Meneghello ◽  
Peter J. Schmid ◽  
Patrick Huerre
Keyword(s):  
Boundary Layer ◽  
Flow Instability ◽  
Cross Flow ◽  
Leading Edge ◽  
Open Loop ◽  
Base Flow ◽  
Local Instability ◽  
Swept Wing ◽  
Global Mode ◽  
Attachment Line

A global stability analysis of the boundary layer in the leading edge of a swept wing is performed in the incompressible flow regime. It is demonstrated that the global eigenfunctions display the features characterizing the local instability of the attachment line, as in swept Hiemenz flow, and those of local cross-flow instabilities further downstream along the wing. A continuous connection along the chordwise direction is established between the two local eigenfunctions. An adjoint-based receptivity analysis reveals that the global eigenfunction is most responsive to forcing applied in the immediate vicinity of the attachment line. Furthermore, a sensitivity analysis identifies the wavemaker at a location that is also very close to the attachment line where the corresponding local instability analysis holds: the local cross-flow instability further along the wing is merely fed by its attachment-line counterpart. As a consequence, global mode calculations for the entire leading-edge region only need to include attachment-line structures. The result additionally implies that effective open-loop control strategies should focus on base-flow modifications in the region where the local attachment-line instability prevails.

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