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2017 | Buch

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Boundary-Layer Theory

verfasst von: Hermann Schlichting (Deceased), Klaus Gersten

Verlag: Springer Berlin Heidelberg

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

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Über dieses Buch

This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.

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Inhaltsverzeichnis

Frontmatter

Fundamentals of Viscous Flows

Frontmatter

Chapter 1. Some Features of Viscous Flows

Abstract

Theoretical investigations into fluid mechanics in the 19^th century were mainly based on the ideal fluid, i.e. a fluid which is inviscid and incompressible. It is only since the 20^th century that the effects of viscosity and compressibility have been taken into account in any great way. In the flow of inviscid fluids, no tangential forces (shear stresses) exist between adjacent layers; only normal forces (pressures) do. This is equivalent to saying that an ideal fluid does not oppose a change in its shape with any internal resistance.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 2. Fundamentals of Boundary–Layer Theory

Abstract

Flows of fluids with low viscosity values and thus very high Reynolds numbers occur in many technical applications. As was shown in the examples from the last chapter, the limiting solution Re = ∞ is often a good approximation. A notable shortcoming of this limiting solution is that the no–slip condition is not satisfied, i.e. the velocities at the wall are not zero but are finite. The viscosity must be taken into account in order to satisfy the no–slip condition.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 3. Field Equations for Flows of Newtonian Fluids

Abstract

The equations of motion for a general (Newtonian) fluid will now be established. In doing so the fluid will be considered to be a continuum.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 4. General Properties of the Equations of Motion

Abstract

Before we discuss solutions of the equations of motion in the next chapter, some general properties of these equations shall first be discussed. First we will examine which quantities enter into the solutions of the equations of motion.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 5. Exact Solutions of the Navier–Stokes Equations

Abstract

The task of finding exact solutions of the Navier–Stokes equations is generally extremely difficult. The nonlinearity of these equations forbids the use of the principle of superposition which served so well in the case of inviscid incompressible potential flows.

Hermann Schlichting (Deceased), Klaus Gersten

Laminar Boundary Layers

Frontmatter

Chapter 6. Boundary–Layer Equations in Plane Flow; Plate Boundary Layer

Abstract

We now wish to treat flows with very small viscosity or very high Reynolds numbers. An important contribution to the science of fluid motion was made in 1904 by L. Prandtl (1904). Prandtl showed the manner in which the viscosity has its effect for high Reynolds number flows and how the Navier–Stokes differential equations can be simplified to yield approximate solutions for this limiting case. We shall now derive the simplifications which arise for the Navier–Stokes equations in the case of very small friction forces in a physically illustrative manner.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 7. General Properties and Exact Solutions of the Boundary–Layer Equations for Plane Flows

Abstract

Before further examples of the calculation of boundary layers are treated in the next chapter, some general properties of boundary–layer equations will be discussed. We will confine ourselves to steady, two–dimensional, incompressible boundary layers.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 8. Approximate Methods for Solving the Boundary–Layer Equations for Steady Plane Flows

Abstract

In order to calculate the flow in the boundary layer, in general partial differential equations must by solved. Today there are many very effective and precise numerical methods available, as will be shown in Chap. 23.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 9. Thermal Boundary Layers Without Coupling of the Velocity Field to the Temperature Field

Abstract

Our considerations of boundary–layer flows up until now have referred only to the velocity field. These will now be correspondingly extended to include the temperature field. It will be assumed that heat is transferred to the flow field through the surrounding walls, so that a temperature field forms together with the velocity field.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 10. Thermal Boundary Layers with Coupling of the Velocity Field to the Temperature Field

Abstract

In the treatment of thermal boundary layers until now, we assumed constant physical properties and so the velocity field was independent of the temperature field. In this chapter we will investigate the effect of variable physical properties.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 11. Boundary–Layer Control (Suction/Blowing)

Abstract

It emerges from the previous discussions of boundary–layer flows that the boundary conditions, i.e. the distributions of the outer velocities U(x) or u _e(x) and the wall temperature T _w(x) or the wall heat flux q _w(x), determine the behaviour of the boundary layer.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 12. Axisymmetric and Three–Dimensional Boundary Layers

Abstract

In the previous chapters, the calculation of boundary layers was restricted to the plane case, where the two velocity components depended only on two spatial coordinates. There was no velocity component present in the direction of the third spatial coordinate.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 13. Unsteady Boundary Layers

Abstract

The examples of solutions of the boundary–layer equations treated up until now have been those for steady flows. Although it is steady flows which are by far of greatest importance in practical applications, in this chapter we will treat some cases of boundary layers which vary in time, that is, unsteady boundary layers.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 14. Extensions to the Prandtl Boundary–Layer Theory

Abstract

In the previous chapters we have already made mention of higher order boundary–layer theory on some different occasions. This theory treats the effects which were not taken into account in the boundary–layer equations used up until now. They will now be included in an extension to the Prandtl boundary–layer theory to a higher order boundary–layer theory. In acquiring this theory we will simultaneously be able to achieve statements about the region of validity of the Prandtl boundary–layer theory.

Hermann Schlichting (Deceased), Klaus Gersten

Laminar–Turbulent Transition

Frontmatter

Chapter 15. Onset of Turbulence (Stability Theory)

Abstract

In many cases, real flows deviate considerably from the laminar flows treated in the previous chapters. They demonstrate a characteristic feature called turbulence. As the Reynolds number is increased, both internal flows through pipes and channels and external boundary–layers flows past bodies exhibit a noticeable change from a laminar flow form to a turbulent flow form. This transition from laminar to turbulent flow, also called the onset of turbulence is of fundamental importance for the whole science of fluid mechanics.

Hermann Schlichting (Deceased), Klaus Gersten

Turbulent Boundary Layers

Frontmatter

Chapter 16. Fundamentals of Turbulent Flows

Abstract

Most flows which occur in practical applications are turbulent. This term denotes a motion in which an irregular fluctuation (mixing, or eddying motion) is superimposed on the main stream.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 17. Internal Flows

Abstract

Fully developed Couette flow is a simple shear flow where the shear stress has a constant value everywhere in the flow field. It is our intention to treat turbulent Couette flow particularly comprehensively in this section, since it is of fundamental importance for turbulent flows close to walls in general, far beyond this particular example.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 18. Turbulent Boundary Layers Without Coupling of the Velocity Field to the Temperature Field

Abstract

In this chapter we will look at turbulent plane flows with constant physical properties. As has already been explained in Sect. 16.6, turbulent flows also have boundary–layer character at high Reynolds numbers, i.e. the entire flow field consists of the inviscid outer flow and the thin turbulent boundary layer close to the wall, for which the boundary–layer equations (16.34) to (16.36) hold.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 19. Turbulent Boundary Layers with Coupling of the Velocity Field to the Temperature Field

Abstract

As Sect. 10.1 showed for laminar boundary layers, the velocity field is coupled to the temperature field if the physical properties are no longer constant but rather depend on the temperature.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 20. Axisymmetric and Three–Dimensional Turbulent Boundary Layers

Abstract

In Chap. 12 we treated axisymmetric and three–dimensional laminar boundary layers. The boundary–layer equations given there are also valid for turbulent boundary layers, as long as the friction terms are extended by corresponding terms of the Reynolds stresses. Therefore, compared to Chap. 12, we have to deal with the additional problem of turbulence modelling.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 21. Unsteady Turbulent Boundary Layers

Abstract

Turbulent flows are by definition unsteady, and so we need to explain what is meant by “unsteady turbulent flows”. Up until now, turbulent flows were decomposed into the flow obtained after time averaging (which was therefore time independent), and the fluctuations which varied in time.

Hermann Schlichting (Deceased), Klaus Gersten

Chapter 22. Turbulent Free Shear Flows

Abstract

Turbulent free shear flows occur if there are no walls directly at the flow. Figure 22.1 shows some examples: a free jet, a buoyant jet, a mixing layer with the free jet–boundary flow as a special case, and a wake flow. The corresponding laminar flows are treated in Sects. 7.2, 7.5, 10.5.4 and 12.1.5. The flow of a turbulent wall jet, which is a jet bounded on one side by a wall, is treated in Sect. 22.8 (the laminar wall jet is discussed in Sect. 7.2.7).

Hermann Schlichting (Deceased), Klaus Gersten

Numerical Methods in Boundary–Layer Theory

Frontmatter

Chapter 23. Numerical Integration of the Boundary–Layer Equations

Abstract

Numerical solutions of the boundary–layer equations are based on the assumption that the differential expressions in the partial differential equations can be approximated by difference expressions. This approximation, called discretisation can be obtained from a series expansion for the velocity components in the coordinate directions. These series expansions do not necessarily have to consist of Taylor series. Since only a certain number of terms in any expansion can be taken, there is a discretisation or truncation error, and this is dependent on the number and size of the terms neglected.

Hermann Schlichting (Deceased), Klaus Gersten

Backmatter

Titel: Boundary-Layer Theory
verfasst von: Hermann Schlichting (Deceased)
Klaus Gersten
Copyright-Jahr: 2017
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-662-52919-5
Print ISBN: 978-3-662-52917-1
DOI: https://doi.org/10.1007/978-3-662-52919-5

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