Analysis of Low-Speed Unsteady Airfoil Flows | springerprofessional.de

Springer Professional

nach oben

2005 | Buch

Kapitel lesen Erstes Kapitel lesen

Analysis of Low-Speed Unsteady Airfoil Flows

verfasst von: Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

The standard textbooks on aerodynamics usually omit any discussion of un steady aerodynamics or, at most, consider it only in a single chapter, based on two justifications. The first is that unsteady aerodynamics should be regarded as a specialized subject required "only" in connection with understanding and an alyzing aeroelastic phenomena such as flutter and gust response, and therefore should be dealt with in related specialist books. The second reason appears to be reluctance to discuss aerodynamics with the inclusion of the time-dependent terms in the conservation equations and the boundary conditions for fear that added complications may discourage the reader. We take the opposite view in this book and argue that a full understanding of the physics of lift generation is possible only by considering the unsteady aerody namics of the starting vortex generation process. Furthermore, certain "steady" flows are inherently unsteady in the presence of flow separation, as for example the unsteady flow caused by the Karman vortex shedding downstream of a cylin der and "static" airfoil stall which is an inherently unsteady flow phenomenon. Therefore, it stands to reason that a unified treatment of aerodynamics that yields steady-state aerodynamics as a special case offers advantages. This rea soning is strengthened by the developments in computational fluid dynamics over the past forty years, which showed that accurate steady-state solutions can be obtained efficiently by solving the unsteady flow equations.

Anzeige

Inhaltsverzeichnis

Frontmatter

1. Physics of Unsteady Flows

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

2. The Differential Equations of Fluid Flow

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

3. Panel Methods

Abstract

Panel methods are ideal for calculating the flowfield over an airfoil executing unsteady time-dependent motion in an inviscid incompressible medium. The unsteady motion on the airfoil causes continuous vortex shedding at the trailing wake, which distinguishes unsteady flows from steady flows. Therefore, before we discuss panel methods for unsteady flows, it is useful to discuss panel methods for steady flows.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

4. Applications of Panel Method

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

5. Boundary-Layer Methods

Abstract

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).

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

6. Applications of Boundary-Layer Methods: Flows Without Separation

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

7. Applications of Boundary-Layer Methods: Flows with Separation

Abstract

The calculation method of the previous chapter is limited to flows without separation. As discussed in Section 5.2. the boundary-layer equations for steady flows become singular at the vanishing of wall shear, and the solutions break down. To avoid the singularity and be able to obtain solutions of flows with separation, it is necessary to solve the equations in the inverse mode.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

8. Navier-Stokes Methods

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

9. Applications of Navier-Stokes Methods

Abstract

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.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

10. Companion Computer Programs

Abstract

In this chapter we describe two computer programs. The computer program of Section 10.2 is for steady airfoil flows based on the Hess-Smith panel method (HSPM). The computer program in Section 10.3 is based on the interactive boundary layer method discussed in Chapters 4 and 5 and is applicable to both steady and unsteady laminar and turbulent flows, including separation. Several sample calculations for steady and unsteady airfoils are also presented. Both computer programs arc given on the accompanying CD-ROM.

Tuncer Cebeci, Max Platzer, Hsun Chen, Kuo-Cheng Chang, Jian P. Shao

Backmatter

Titel: Analysis of Low-Speed Unsteady Airfoil Flows
verfasst von: Tuncer Cebeci
Max Platzer
Hsun Chen
Kuo-Cheng Chang
Jian P. Shao
Copyright-Jahr: 2005
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-27361-5
Print ISBN: 978-3-540-22932-2
DOI: https://doi.org/10.1007/b138967

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht