Hsun Chen

An Inviscid-Viscous Interaction Approach to the Calculation of Dynamic Stall Initiation on Airfoils

An interactive boundary-layer method is described for computing unsteady incompressible flow over airfoils, including the initiation of dynamic stall. The inviscid unsteady panel method developed by Platzer and Teng is extended to include viscous effects. The solutions of the boundary-layer equations are obtained with an inverse finite-difference method employing an interaction law based on the Hilbert integral, and the algebraic eddy-viscosity formulation of Cebeci and Smith. The method is applied to airfoils subject to periodic and ramp-type motions and its abilities are examined for a range of angles of attack, reduced frequency, and pitch rate.

Calculation of multielement airfoil flows, including flap wells

A calculation method for multielement airfoils based on an interactive boundary-layer approach using an improved Cebeci-Smith eddy viscosity formulation is described. Results are first presented for single airfoils at low and moderate Reynolds numbers in order to demonstrate the need to calculate transition for accurate drag polar prediction and the ability of the improved Cebeci-Smith turbulence model to predict flows with extensive separation, and therefore to predict maximum lift coefficient, (cl)max. Results, in terms of pressure distributions and lift and drag coefficients, are presented for a series of twoelement airfoils with flaps or slats. The method is extended to the computation of configurations with flap wells. Results show that the same accuracy can be reached as for faired geometries. A slight compressibility effect was accounted for by introducing compressibility corrections to the HessSmith panel method. Again, the importance of the compressibility effects and the turbulence model on stall, and the need to calculate the onset of transition, are demonstrated. Recommendations are then made for the preferred approach to predicting the aerodynamic performance of multielement airfoils for use as a practical and efficient design tool.

Physics of Unsteady Flows

Standard textbooks on aircraft aerodynamics either omit any discussion of unsteady aerodynamic effects or, at most, devote a. single chapter to it. A more detailed discussion of unsteady aerodynamics is usually found in textbooks on aeroclasticity. as for example in the books by Dowell et al. [1] and Bisplinghoff et al. [2]. This is because a complete understanding and analysis of aircraft flutter and dynamic response phenomena cannot be attained without the proper unsteady aerodynamic analysis methods. This state of affairs is somewhat unfortunate because it generates the impression that unsteady aerodynamics is a highly specialized discipline which is needed only for the prediction of aeroelastic phenomena.

Boundary-Layer Methods

This chapter is concerned with the solution of the boundary-layer equations of subsection 2.4.3 for boundary conditions that include a priori specification of the external velocity distribution either from experimental data or from inviscid-flow theory (called the standard problem), a priori specification of an alternative boundary condition which may be a displacement thickness distribution (called the inverse problem), or the determination of the freestream boundary condition by iteration between solutions of inviscid and boundary-layer equations (called an interaction problem).

The Differential Equations of Fluid Flow

The differential equations of fluid flow are based on the principles of conservation of mass, momentum and energy and are known as the Navier-Stokes equations. For incompressible flows and for flows in which the temperature differences between the surface and freestream are small, the fluid properties such as density ϱ and dynamic viscosity μ in the conservation equations are not affected by temperature. This assumption allows us to ignore the conservation equation for energy and concentrate only on the conservation equations for mass and momentum.

Navier-Stokes Methods

Numerical methods for the solution of boundary layer equations were discussed in Chapter 5 and here the discussion is extended to the Navier -Stokes equations for incompressible and compressible flows. Forms of the equation appropriate for numerical methods are presented in Section 8.2 and turbulence models including those based on algebraic and one and two transport equations are introduced in Section 8.3. Brief discussions of the numerical methods for incompressible and compressible flows are provided in Sections 8.4 and 8.5 respectively and the reader is referred to [1,2] for further information.

Applications of Navier-Stokes Methods

Navier-Stokes (NS) methods are more general than those based on interactive-boundary-layer (IBL) theory and can be used to solve some airfoil flows that IBL methods cannot. For example, as discussed in Chapter 7, the IBL method can predict the initiation of dynamic stall of an airfoil but cannot predict the details of the downstream separated flow and, therefore overall lift and drag. Also, the prediction of airfoil dynamic stall for oscillatory, ramp and more complex motions at various freestream speeds and Reynolds numbers requires the use of NS methods.

Applications of Boundary-Layer Methods: Flows Without Separation

In this chapter we discuss the applications of the boundary-layer method to laminar and turbulent flows without flow separation; flows with separation are addressed in the following chapter. In Section 6.2 we discuss laminar and turbulent flows on a flat plate with fluctuations in external flow and in Section 6.3 the development of unsteady laminar boundary-layers when the body is given, impulsively, a free-stream velocity. We consider two cases, the first corresponding to impulsive motion of a flat plate and the second a circular cylinder. The latter has been used extensively as a model problem to study the nature of solutions in the presence of flow reversal, flow singularity and separation.

Applications of Panel Method

In this chapter the panel method described in Chapter 3 is applied to the basic unsteady aerodynamic problems described in the first chapter, namely the problems of lift and thrust generation, airfoil flutter and gust response. However, before discussing these applications, it is instructive to recall the need to differentiate between streamlines, path lines and streak lines in unsteady flows in contrast to steady flows where all three lines collapse into a single line. A streamline is a curve whose tangent at any point is in the direction of the velocity vector at that point. If the flow is unsteady, the streamline pattern is different at different times because of the change in velocity vectors with time. The path line is the trace of the fluid particle as it moves downstream with the local flow velocity whereas the streak line is obtained by connecting the location of those particles which moved through a given point in space at consecutive times. Smoke particles released at a given point at different times for the purpose of flow visualization therefore represent streak lines. Figure 4.1 shows the panel method computed streak lines, streamlines and path lines due to a ramp- type change in angle of attack of a symmetric airfoil. Note that the formation of the starting vortex is most clearly visible using streak lines.

ON THE CALCULATION OF INITIAL CONDITIONS FOR PARABOLIZED STABILITY EQUATIONS FOR PREDICTING TRANSITION

The generation of initial conditions for stability based -transition methods for t hree -dimensional flows is addressed. By using the zarf concept used in the saddle -point method of Cebeci -Stewartson, a “critical” Reynolds number is determined for crossflow dominated flows. This number corresponds to the minimum Reynolds number for which the eigenvalues r r �