Technology & Engineering
Inviscid Fluid
An inviscid fluid is a theoretical concept used in fluid dynamics to describe a fluid with zero viscosity. Inviscid fluids do not experience internal friction or resistance to flow, allowing for simplified mathematical modeling of fluid behavior. While real fluids have viscosity, the concept of inviscid fluids is useful for understanding idealized fluid dynamics and aerodynamics.
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eBook - PDFBasic Aerodynamics
Incompressible Flow
- Gary A. Flandro, Howard M. McMahon, Robert L. Roach(Authors)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
309 8 Viscous Incompressible Flow External aerodynamics was a disturbingly mysterious subject before Prandtl solved the mystery with his work on boundary layer theory from 1904 onwards. L. Rosenhead Laminar Boundary Layers, Oxford 1963 8.1 Introduction This chapter examines the role of viscosity in the flow of fluids and gases. Although the viscosity of air is small, it must be included in a flow model if we are to explain wing stall and frictional drag, for example. The four preceding chapters are con- cerned with the analysis of airfoils, wings, and bodies of revolution based on an assumption of inviscid flow (i.e., negligible viscous effects). The inviscid-flow model allowed analytical solutions to be developed for predicting, with satisfactory accu- racy, the pressure distribution on bodies of small-thickness ratio at a modest (or zero) angle of attack. However, the inviscid-flow model leads to results that are at odds with experience, such as the prediction that the drag of two-dimensional air- foils and right-circular cylinders is zero. This contradiction is resolved by realizing that actual flows exhibit viscous effects. Viscosity is discussed from a physical viewpoint in Chapter 2. In Chapters 5, 6, and 7, the existence of viscosity is acknowledged when it is necessary to advance an analytical derivation for an inviscid flow. Also, viscous effects are called on, with words like viscous drag and separation, when comparing the predicted and observed behavior of airfoils and wings. However, no analysis in this textbook has been developed thus far that provides the required detailed physical basis for these effects . The focus of this chapter is a detailed study of the role of viscosity in an incom- pressible flow, particularly regarding modifications to the behavior of airfoils and wings that was predicted based on an inviscid-flow model.
eBook - PDF- J. J. Connor, C. A. Brebbia(Authors)
- 2013(Publication Date)
- Newnes(Publisher)
5 Inviscid Fluids 5.1 BASIC PRINCIPLES In this chapter we will specialise the governing equations of fluid flow for the case of inviscid flow. We will define a steady flow as the case for which the velocity at any point is independent of time (i.e. dv/dt = 0). A steady flow problem requires spatial boundary conditions but not initial conditions. Let us summarise the governing equations for a fluid, previously deduced : Equation of motion Continuity dp dv h Constitutive equations (Stokes type flow) o t j = -P*ti + Men -k'Av) ( 5 · 3 ) Equation of state (barotropic flow) f(p,p) = 0 (5.4) Strain rate-velocity relationships = ljdvi dvj) 11 2dxj + dx,j p · 3 ' 174 Inviscid FluidS 175 For a liquid with zero viscosity the constitutive equations reduce to <*a = ~Ρ δ α ( 5 · 6 ) or simply σ= -p (5.7) The state of stress is then defined by a single variable p. The equilibrium equations are now with boundary conditions Pn = -P or v n given (5.9) but p s = 0, v s not necessary which implies that we cannot apply a tangential boundary force to an Inviscid Fluid. Incompressibility (p = constant = p 0 ) implies that the con-tinuity equation gives ^ = 0 (5.10) dx k RELATIONSHIP BETWEEN VISCOSITY AND VORTICITY Consider a sphere of incompressible, Inviscid Fluid initially at rest. When the forces are incremented in the fluid they will produce certain surface forces on this sphere. These surface forces must act normally to the surface since the fluid is frictionless (i.e. it would not resist tangential forces). Thus, their component is applied at the centre of the sphere and the body forces at the mass centre. The sphere then cannot rotate as no couple can be applied to it. In order to define this irrotationality condition mathematically, let us consider the equation of motion in terms of velocities. We have dxj Po j dx k ' Ot or H / P1 , ..„2.-Î . t D * -V. — + vV 2 ? + 6 = ^
eBook - PDF- Frank H. Berkshire, Simon J. A. Malham, J. Trevor Stuart(Authors)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
Part I Inviscid Flow 1 Flow and Transport 1.1 Fluids and the Continuum Hypothesis A material exhibits flow if shear forces, however small, lead to a deformation which is unbounded – we could use this as a definition of a fluid. A solid has a fixed shape, or at least a strong limitation on its deformation when force is applied to it. Within the category of ‘fluids’, we include liquids and gases. The main distinguishing feature between these two fluids is the notion of compressibility. Gases are usually compressible – as we know from everyday aerosols. Liquids are generally incompressible – a feature essential to all modern car brakes. However, some gas flows can also be incompressible, particularly at low speeds. Fluids can be further subcategorised. There are ideal or inviscid fluids. In such fluids, the only internal force present is pressure, which acts so that fluid flows from a region of high pressure to one of low pressure. The equations for an ideal fluid have been applied to wing and aircraft design (as a limit of high Reynolds-number flow). However, fluids can exhibit internal frictional forces which model a ‘stickiness’ property of the fluid which involves energy loss – these are known as viscous fluids. Some fluids/material known as ‘non-Newtonian or complex fluids’ exhibit even stranger behaviour, their reaction to deformation may depend on: (i) past history (earlier deformations), for example some paints; (ii) temperature, for example some polymers or glass; (iii) the size of the deformation, for example some plastics or silly putty. For any real fluid there are three natural length scales: 1. L molecular , the molecular scale characterised by the mean-free-path distance of molecules between collisions; 2. L fluid , the medium scale of a fluid parcel, the fluid droplet in the pipe or ocean flow; 3. L macro , the macro-scale which is the scale of the fluid geometry, the scale of the container the fluid is in, whether a beaker or an ocean.
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