Boundary Layer
The boundary layer refers to the thin layer of fluid near a surface where the effects of viscosity are significant. In engineering, it is crucial for understanding the behavior of fluids around objects such as aircraft wings and turbine blades. The boundary layer's characteristics, such as its thickness and velocity profile, have a significant impact on the overall performance and efficiency of engineering systems.
5 Key excerpts on "Boundary Layer"
- Amithirigala Widhanelage Jayawardena(Author)
- 2021(Publication Date)
- CRC Press(Publisher)
...Chapter 7 Viscous fluid flow – Boundary Layer 7.1 Introduction Fluids, in general, can be classified as ideal fluids and viscous or real fluids. Ideal fluids are assumed to have no viscosity although all fluids, in reality, have some viscosity. The viscous effect in fluid flow is confined to a thin layer near the boundary of flow, which is known as the Boundary Layer. Outside the region of the Boundary Layer, the fluid is assumed to be ideal, and the flow is sometimes referred to as potential flow. The general concept of Boundary Layer was introduced by Prandtl in 1904. It is an important and significant concept in Fluid Mechanics and provides a useful link between ideal fluids and real fluids. For fluids having relatively small viscosity, the effect of internal friction in a fluid is appreciable only in a narrow region surrounding the fluid boundaries. In the case of a flat plate placed in a flow field, the velocity (relative to the boundary) of the fluid at the boundary is zero. This is called the no-slip boundary condition. The flow velocity across the flow, therefore, varies from zero to its full value with a steep velocity gradient. Because of the viscosity of the fluid, this velocity gradient gives rise to shear stresses, which retard the flow flowing near the boundary. The region affected is called the Boundary Layer, or friction layer. The velocity in the boundary-layer approaches the velocity in the main flow asymptotically. The Boundary Layer is very thin at the upstream end of a streamlined body at rest in an otherwise uniform flow. As the layer moves downstream, the continual action of shear stress tends to slow down additional fluid particles causing the thickness of the Boundary Layer to increase in the downstream direction. For smooth upstream boundaries, the Boundary Layer starts as laminar. As the thickness increases, the flow becomes turbulent and transforms into turbulent Boundary Layer...
eBook - ePub- Keith J. Moss(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...The building services engineer is mainly concerned with a limited number of applications such as the flow of air in ducts and the flow of water in pipes and channels. If a flat plate is positioned in a stream of flowing fluid which is unaffected by solid boundaries, the development of the Boundary Layer from the leading edge of the plate can be identified, one side being considered. Refer to Figure 6.7. The following points can then be observed: Figure 6.7 Formation of the Boundary Layer on one side of a flat plate. • Fluid velocity under the Boundary Layer starts at zero at the leading edge of the plate and reaches a maximum at the boundary limit. • The thickness of the Boundary Layer is very small compared with its length L. • There are three discrete regions. • Laminar and transition lengths are very short; flow therefore is often considered turbulent throughout the whole Boundary Layer. • During transition Re has critical values. • The plate imposes a resistance to flow causing a loss in fluid momentum. The plate experiences a corresponding force called skin friction. • The Boundary Layer increases in thickness to a maximum value as the length L from the leading edge of the plate increases. • At points close to the solid boundary of the flat plate, velocity gradients are large and the viscous shear mechanism is significant enough to transmit the shear stress to the boundary such that the layer adjacent to the boundary is in laminar motion even when the rest of the Boundary Layer is turbulent. This is the laminar sublayer which you will notice becomes extremely thin downstream of the leading edge of the flat plate. • A pipe may be considered as a flat plate wrapped round to reform itself. Thus fluid velocity starts at zero at the pipe wall and reaches a maximum value at the centreline of a straight pipe. It then returns to zero velocity at the opposite wall of the pipe forming the velocity profile which is bullet shaped...
eBook - ePub- Rose G Davies(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...There would be more terms of second-order cross derivatives to describe the friction stresses in different directions around a fluid particle, as shown in the terms in the brackets of Equations (3.5) and (3.6). It is difficult to solve those equations for a turbulent Boundary Layer analytically, and it can be solved numerically with a standard PDE solving program. The details of the turbulent model and the principle of solving the equations of Boundary Layer can be found in Boundary-Layer Theory (Schlichting, 1978). We can treat the airflow over an aerofoil as the fluid flow over a flat plate. For simple practicable purposes, we adopt the approach described by Shandong Engineering College (1979), which is that viscous friction causes the change of fluid momentum within the Boundary Layer. So the thickness of a Boundary Layer at any location along the surface of a flat plate, and the friction force, which is between the fluid and the surface, are estimated and are shown here: The thickness of the laminar Boundary Layer δ : δ = 4.64 × Re x − 0.5 (3.8) where Re x = local Reynolds number on the surface/aerofoil, and x is the distance from the leading edge of plate/aerofoil to a location on the surface. The friction coefficient C f on the surface in the laminar Boundary Layer : C f = f 1 2 ρ v 2 b c = 1.372 Re c − 0.5 (3.9) where R e c = ρ v c μ, the overall Reynolds number of the surface/aerofoil; f is the viscous friction force; c is the length of the surface/chord of the...
eBook - ePubTransport Phenomena
An Introduction to Advanced Topics
- Larry A. Glasgow(Author)
- 2010(Publication Date)
- Wiley(Publisher)
...In fact, a shockingly advanced aircraft was constructed by Germany during the war, which owed more to Willy Messerschmitt, his design team, and serendipity than to Schlichting' exposition of boundary-layer theory. Interested students of aviation should see Messerschmitt Me 262, Arrow to the Future by W. J. Boyne (1980). Similarly, after World War II (1947–1948), the Soviet Union (specifically the Mikoyan–Gurevich OKB) produced the MiG-15; this aircraft completely stunned United Nations forces when it first appeared in the Korean conflict in November 1950. Neither the Me 262 nor the MiG-15 was affected in the least by efforts to limit the distribution of boundary-layer theory. 4.2 The Flat Plate Ludwig von Prandtl established the foundation for a major advance in fluid mechanics in 1904 when he observed that the effects of viscous friction are confined to a relatively thin fluid layer immediately adjacent to the immersed surface. Prandtl (1928) employed a simplified version of the Navier–Stokes equation in the Boundary Layer and the appropriate potential flow solution outside. Of course, the distinction between these two layers is quite fuzzy; it is a standard practice to assume that the boundary-layer thickness (δ) corresponds to the transverse position where. Let us consider a steady two-dimensional flow in the vicinity of a fixed surface. The appropriate equations are (4.1) (4.2) and (4.3) Now suppose the surface in question is a flat plate, and the origin is placed at the leading edge as shown in Figure 4.3. The characteristic thickness of the Boundary Layer (in the y -direction) is δ and the length of the plate is L. Figure 4.3 The Boundary Layer on a flat plate. We recognize that, in general, and, except for the region very near the leading edge of the plate...
eBook - ePubUnderstanding Aerodynamics
Arguing from the Real Physics
- Doug McLean(Author)
- 2012(Publication Date)
- Wiley(Publisher)
...Farther from the wall, the vorticity gradient weakens, the rate of diffusion decreases, and eventually the flow becomes effectively irrotational far from the wall.This is a general pattern that characterizes flows past bodies when the viscosity is small. Near the solid surface, there is formed a viscous, vortical Boundary Layer outside of which the flow remains effectively irrotational, as if it were inviscid. Note that no matter how small the viscosity is, a viscous Boundary Layer will form along the surface as long as the no-slip condition prevails, and there will always be at least this thin layer where the effects of viscosity are important. We'll consider this general flow structure further, including more details of the behavior of Boundary Layers, in Chapters 4 and 5. Also note that “small viscosity” is usually referred to as “high Reynolds number,” where the inverse of the Reynolds number (1/R) is a dimensionless parameter that multiplies the viscous terms in the nondimensional form of the momentum equations. We discuss the Reynolds number and what it means in some detail in Section 3.9.2.3.7 Turbulence, Reynolds Averaging, and Turbulence ModelingAt the high Reynolds numbers typical of engineering applications, Boundary Layers usually transition from laminar to turbulent before reaching the back of the body, and the viscous wakes behind bodies are always turbulent. Turbulence is a complicated beast that is highly random but at the same time displays a surprising degree of organized structure over ranges of length and time scales that depend on the situation. In Chapters 4 and 5, we'll look at some of the details of turbulent structures and their consequences in Boundary Layers and wakes. In this section, our focus will be on the effects that turbulence has on the flow that are important in applications and how these effects can be practically handled in the framework of the NS equations...
