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Environmental Fluid Mechanics - Chapter 4

Dòng chảy Inviscid và lý thuyết lưu lượng tiềm năng Các hình thức xoáy của Eq Navier-Stokes. (3.1.3) có nghĩa là nếu dòng chảy của chất lỏng với mật độ liên tục ban đầu có không xoáy, và độ nhớt của chất lỏng là số không, sau đó dòng chảy luôn luôn là irrotational. Dòng chảy như vậy được gọi là một dòng chảy, lý tưởng, irrotational, hoặc inviscid, và nó có một vận tốc khác không tiếp tuyến với bất kỳ bề mặt rắn. Một chất dịch thực sự, với độ nhớt khác không là tùy thuộc vào điều kiện. | 4 Inviscid Flows and Potential Flow Theory 4.1 INTRODUCTION The vorticity form of the Navier-Stokes Eq. 3.1.3 implies that if the flow of a fluid with constant density initially has zero vorticity and the fluid viscosity is zero then the flow is always irrotational. Such a flow is called an ideal irrotational or inviscid flow and it has a nonzero velocity tangential to any solid surface. A real fluid with nonzero viscosity is subject to a no-slip boundary condition and its velocity at a solid surface is identical to that of the solid surface. As indicated in Sec. 3.4 in fluids with small kinematic viscosity viscous effects are confined to thin layers close to solid surfaces. In Chap. 6 concerning boundary layers in hydrodynamics viscous layers are shown to be thin when the Reynolds number of the viscous layer is small. This Reynolds number is defined using the characteristic velocity U of the free flow outside the viscous layer and a characteristic length L associated with the variation of the velocity profile in the viscous layer. Therefore the domain can be divided into two regions a the inner region of viscous rotational flow in which diffusion of vorticity is important and b the outer region of irrotational flow. The outer region can be approximately simulated by a modeling approach ignoring the existence of the thin boundary layer and applying methods of solution relevant to nonviscous fluids and irrotational flows. Following the calculation of the outer region of irrotational flow viscous flow calculations are used to represent the inner region with solutions matching the solution of the outer region. However in cases of phenomena associated with boundary layer separation matching between the inner and outer regions cannot be done without the aid of experimental data. The present chapter concerns the motion of inviscid incompressible and irrotational flows. In cases of such flows the velocity vector is derived from a Copyright 2001 by Marcel Dekker Inc. All .