Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

A new laminar–turbulent transition model for low-turbulence external aerodynamic applications is presented that incorporates linear stability theory in a manner compatible with modern computational fluid dynamics solvers. The model uses a new transport equation that describes the growth of the maximum Tollmien–Schlichting instability amplitude in the presence of a boundary layer. To avoid the need for integration paths and nonlocal operations, a locally defined nondimensional pressure-gradient parameter is used that serves as an estimator of the integral boundary-layer properties. The model has been implemented into the OVERFLOW 2.2f solver. Comparisons of predictions using the new model with high-quality wind-tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model, as well as its improvement over the current state of the art in computational fluid dynamics transition modeling at approximately half the computational expense.

Computational Fluid Dynamics Compatible Transition Modeling Using an Amplification Factor Transport Equation

The rationale used for the aerodynamic wing design of the prototype long-range human-powered aircraft Light Eagle is presented. Three different airfoils, designed for chord Reynolds numbers of 500,000,375,000, and 250,000 were used across the wingspan. The airfoil design rationale centered on minimizing the losses in the transitional separation bubbles typically occurring on airfoils at Reynolds numbers of less than 1 million. Structural and manufacturing constraints were also a consideration in the airfoil design, although to a lesser extent. Airfoil performance prediction during the design process was done entirely through numerical simulation. The numerical model employs the Euler equations to represent the inviscid flow, and an integral boundary-layer formulation to represent the viscous flow. Strong viscous-inviscid coupling and an amplification transition criterion included in the overall equation system permit calculation of transitional separation bubbles and their associated losses. Flow visualization tests performed on the Light Eagle at various lift coefficients in towed flight revealed transition occurring very near the intended position on the wing surface except within a few chords of the tip, where the flow appeared to be turbulent over most of the upper surface. Total drag aircraft polars obtained from the measured aircraft energy time history in glide contained too much scatter to be used as quantitative test data but did reproduce the basic trends of the calculations, including maximum lift coefficient levels.

Low-Reynolds-number airfoil design for the M.I.T. Daedalus prototype- A case study

In this paper, wind-tunnel results of a real time optimization of a morphing wing in the wind tunnel for delaying the transition toward the trailing edge are presented. A morphing rectangular finite aspect ratio wing, having a wind tunnel experimental airfoil reference airfoil cross section, was considered, with its upper surface made of a flexible composite material and instrumented with Kulite pressure sensors and two smart memory alloys actuators. Several wind-tunnel test runs for various Mach numbers, angles of attack, and Reynolds numbers were performed in the 6' x 9' wind tunnel at the Institute for Aerospace Research at the National Research Council Canada. Unsteady pressure signals were recorded and used as feedback in real time control while the morphing wing was requested to reproduce various optimized airfoils by changing automatically the two actuators' strokes. This paper shows the optimization method implemented into the control software code that allows the morphing wing to adjust its shape to an optimum configuration under the wind-tunnel airflow conditions.

Real Time Morphing Wing Optimization Validation Using Wind-Tunnel Tests

This paper presents the modeling and experimental testing of the aerodynamic performance of a morphing wing in open-loop architecture. We show the method used to acquire the pressure data from the external surface of the flexible wing skin, using incorporated Kulite pressure sensors and the instrumentation of the morphing controller. The acquired pressure data are analyzed through fast Fourier transforms to detect the magnitude of the noise in the surface airflow. Subsequently, the data are filtered by means of high-pass filters and processed by calculating the root mean square of the signal to obtain a plot diagram of the noise in the airflow. This signal processing is necessary to remove the inherent noise electronically induced from the Tollmien-Schlichting waves, which are responsible for triggering the transition from laminar to turbulent flow. The flexible skin is required to morph the shape of the airfoil through two actuation points to achieve an optimized airfoil shape based on the theoretical flow conditions similar to those tested in the wind tunnel. Two shape memory alloy actuators with a nonlinear behavior drive the displacement of the two control points of the flexible skin toward the optimized airfoil shape. Each of the shape memory actuators is activated by a power supply unit and controlled using the Simulink/MATLAB® software through a self-tuning fuzzy controller. The methodology and the results obtained during the wind-tunnel test proved that the concept and validity of the system in real time are discussed in this paper. Real-time acquisition and signal processing of pressure data are needed for further development of the closed-loop controller to obtain a fully automatic morphing wing system.

Modeling and testing of a morphing wing in open-loop architecture

The linear stability theory was applied to the problem of boundary layer transition in incompressible flow. The theory was put into a form suitable for three-dimensional boundary layers; both the temporal and spatial theories were examined; and a generalized Gaster relation for three-dimensional boundary layers was derived. Numerical examples include the stability characteristics of Falkner-Skan boundary layers, the accuracy of the two-dimensional Gaster relation for these boundary layers, and the magnitude and direction of the group velocity for oblique waves in the Blasius boundary layer. Available experiments which bear on the validity of stability theory and its relation to transition are reviewed and the stability theory is applied to transition prediction. The amplitude method is described in which the wide band disturbance amplitude in the boundary layer is estimated from stability theory and an interaction relation for the initial amplitude density of the most unstable frequency.

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L. M. Mack

Papers

Transition and laminar instability