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8.1 Introduction
The study of external flows is of importance to the engineers in the analysis of flow around an aircraft, turbine blades, automobiles, buildings, smokestacks, bridge abutments, and so on. To discuss the external flows, we can divided the flows into low-Re-number flows (Re < 5, or so) and high-Renumber flows (Re >1000).
The separation on the flat surface occurs as the flow is approaching a stagnation region where the velocity is low and the pressure is high
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8.1 Introduction In the study of external flows, the drag and lift are interested, the details of the flow field are seldom of interest. • Drag(阻力) (曳力) : the force of the flow exerts in the direction of the flow Projected area (projected of plane • Lift(升力): the force on athe flow exerts normal to the Drag force normal direction of the flow.of to the direction the flow)
The flow can become significantly influenced by the presence of a boundary or another object. These flows should not be discussed in this curriculum.
8.2 Separation
Separation occurs when the main stream flow leaves the body, resulting in a separated region of flow. For blunt bodies, separation is unavoidable at high Re numbers and its effect must be understood.
the laminar and turbulent boundary layers. The boundary layer that develops on a plane streamlined surface is usually sufficiently thin that the curvature of the surface can be ignored, so the problem can be treated as a flat plate. Outside the boundary layer there exists an inviscid, freestream flow. 2013-11-15 9
For due to the The boundary layer near The separated region is For blunt body, the flow Shear stresses streamlined body,region This the stagnation point is aflow simply leaves the region may separate from the viscosity are concentrated closes; wake eventually in the the wake body and form a streamlined body atthe main the laminar the thin boundary layer, the intoformed. boundary layer, keeps diffusion separated region. trailing and undergoes transition flow the edge. separated region, and and eventually downstream to a turbulent disappears as its area wake. Outside these regions boundary layer.approximateexceedingly large. the flow is becomes by an inviscid flow.
• Low-Re number flows, called stokes flows, seldom occur in engineering application (lubrication flow and flow in porous media) and is not discussed in this curriculum. We will direct our attention to high-Re-number flows in this curriculum only.
abrupt change in geometry, separation will occur at, or near, the abrupt change. reattachment will occur at some location.
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8.2 Separation
Downstream of the Upstream of the separation separation point, the xpoint, the x-component component velocity near the velocity near the wall is in the wall is in the negative xpositive x-direction, so u/y direction, so u/y at the at the wall is positive. wall must be negative. Consider the flow on the flat surface just before the step, the region near the forward separation point is enlarged..
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8.1 Introduction
We will focus our attention on this category of flows.
High-Re-number flows can be subdivided into three major categories:
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If the flow in the boundary layer on a For streamlined object, the streamlined bodythe separated can region is be determined, insignificantly small or nonexistent, so it is need to study drag can be calculated.
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Incompressible immersed flows (involving such automobiles, helicopters, submarines, and buildings); Flows of liquids that involve a free surface as a ship or a bridge abutment; Compressible flows involving high-speed object (V > 100 m/s) such as aircraft, missiles, and bullets.
drag coefficient : C D FD
Lift force
lift coefficient :
1 V 2 A 2 FL CL 1 V 2 A 2
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8.1 Introduction
For blunt object, the drag on a blunt is dominated by the flow in the separated region, hence there is little interest in studying the boundary layer growth on the front part of a blunt body and the associated viscous shear at the wall. The interest is focused on the empirical data that provide the drag coefficient.
Chapter 8:
External flows
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Outline
8.1 Introduction 8.2 Separation
8.3 Flow around immersed bodies