Infinite Swept Wing Research Articles

Computation of leading-edge contamination

The leading-edge contamination (LEC) problem of an infinite-swept wing is computed by solving the full two-dimensional Navier–Stokes equation using a very high spectral accuracy compact scheme. The initial condition is given by the steady attachment-line boundary layer forming over the leading-edge of an infinite swept wing or a yawed cylinder. The contamination is shown as due to either a convecting or a stationary vortex far outside the attachment-line boundary layer at the leading edge. This mechanism is proposed to account for the sub-critical instability onset observed for attachment-line boundary layer. (The criticality is for Reynolds number (based on momentum thickness) exceeding 100––an empirically suggested value based on earlier experiments.) The presented results show the problem to be essentially two-dimensional. Inflow and outflow of computational domain are chosen so that we consider cases of both sub- and super-critical instabilities. The receptivity mechanism of leading-edge contamination for both cases is investigated with respect to different parameters. Finally, we have also analyzed the computed solutions by proper orthogonal decomposition (POD) to highlight the low-dimensional nature and to provide a quantitative measure of leading-edge contamination events.

Optimization of steady suction for disturbance control on infinite swept wings

We present a theory for computing the optimal steady suction distribution to suppress convectively unstable disturbances in growing boundary layers on infinite swept wings. This work includes optimization based on minimizing the disturbance kinetic energy and the integral of the shape factor. Further, a suction distribution in a continuous control domain is compared to an approach using a number of discrete pressure chambers. In the latter case, the internal static pressures of these chambers are optimized. Optimality systems are derived using Lagrange multipliers. The corresponding optimality conditions are evaluated using the adjoint of the parabolized stability equations and the adjoint of the boundary layer equations. Results are presented for an airfoil designed for medium range commercial aircraft. We show that an optimal suction distribution based on a minimization of the integral of the shape factor is not always successful in the sense of delaying laminar-turbulent transition. It is also demonstrated that including different types of disturbances, e.g., Tollmien–Schlichting and cross-flow types, in the analysis may be crucial.

Linear compensator control of a pointsource induced perturbation in a Falkner–Skan–Cooke boundary layer

We focus on the problem of controlling pointsource induced perturbations on an infinite swept wing using linear control theory. Based on wall measurements in a spatial simulation of localized disturbances in Falkner–Skan–Cooke boundary layers, an extended Kalman filter is used to estimate the full three-dimensional wave packet. The estimated field is in turn used to calculate a feedback control which changes the growth of the disturbance into decay. This is the first time that optimal control and estimation concepts are successfully applied to construct a dynamic output feedback compensator which is used to control disturbances in spatially developing boundary layers.

Turbulent structure in the three-dimensional boundary layer on a swept wing

Abstract The effects of mean flow three-dimensionality on the turbulent structure of the boundary layer on a swept wing are investigated experimentally. The configuration of the test model used to simulate the infinite swept wing condition is similar to that used by Van den Berg, B., Elsenaar, A., Lindhout, J.P.F., Wesseling, P., 1975. Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory. J. Fluid Mech. 70 (1), 127–148. Mean flow measurements show that the location of the maximum cross-flow velocity is within the log-law region for the streamwise velocity profiles. In the near-wall region, the streamwise turbulence intensity, u 2 /U τ , decreases with increasing three-dimensionality. A four quadrant analysis is applied to the fluctuating velocity components in the local mean flow and wall-normal directions. At downstream stations, the contributions to the turbulent shear stress from quadrant 4 (sweeps) are predominant in the region near the wall. It is thus revealed that strong ejections are suppressed by the effects of increased three-dimensionality.

Wing tunnel model for simulating an infinite swept wing

Wing tunnel model for simulating an infinite swept wing

Three-dimensional application of the Johnson-King turbulence model for a boundary-layer direct method

Abstract The Johnson-King turbulence model[1; AIAA Paper 84-0175 (1984)] as extended to three-dimensional flows was evaluated using a finite-difference boundary-layer direct method. Calculations were compared against the experimental data of the well-known van den Berg-Elsenaar[2; Report NLR-TR-72092U (1972)] incompressible flow over an infinite swept-wing, as well as with some other boundary-layer methods. The Johnson-King turbulence model, which includes the non-equilibrium effects in a developing turbulent boundary layer, was found to significantly improve the predictive quality of a direct boundary-layer method. The improvement was especially visible in the computations with increased three-dimensionality of the mean flow, larger integral parameters and decreasing eddy-viscosity and shear-stress magnitudes in the streamwise direction; all in better agreement with the experiment than simple mixing-length-based methods.

Numerical computation of three-dimensional turbulent boundary layers for the infinite swept wing

A numerical scheme for turbulent incompressible boundary layer is proposed. The formulation of the problem assumes translation invariance in cartesian coordinates. An anisotropic eddy viscosity model is considered. Numerical experiments show good agreement with a streamline coordinate formulation on the one hand and experimental data on the other hand.

Analysis of transitional separation bubbles on infinite swept wings

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

Analysis of three-dimensional separated flow with the boundary-layerequations

An analysis based on the boundary-layer equations is presented for the p rediction of threedimensional separated flow. In this analysis, t he boundary-layer equations are solved with finite difference techniques in four i nverse (pressure is unknown) modes. One inverse mode, in which the component of vorticity normal to the surface is specified at the boundary-layer e dge, is shown to result in an elliptic system of boundary-layer equations which has departure solutions when solved with a f orward marching technique. The accuracy o f the p resent analysis in the other t hree inverse modes using forward marching techniques is demonstrated for: (1) separated flow over an infinite swept wing which has been rendered three dimensional with a rotated coordinate system; and (2) a three-dimensiona l separated flow problem analyzed by Smith. The principal conclusion o f this paper is that the methodology is now in place to solve the boundary-layer equations for three-dimensiona l separated flow and hence work should now be focused on the development of three-dimensiona l viscousinviscid interaction procedures.

Attachment-Line Flow on an Infinite Swept Wing

A proposed method for calculating three-dimensional incompressible laminar and turbulent boundary layers is investigated with respect to its applicability to incompressible attachment line flow on an infinite swept wing. The calculation results obtained exhibit satisfactory agreement with experimental data.

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

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.

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part I: Flow over the Rear of an Infinite Swept Wing

SummaryA method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.