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CFDa.3.potential

CFDa.3.potential - Fluids Review TRN-1998-004 Potential...

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© Fluent Inc. 12/05/10 C1 Fluids Review TRN-1998-004 Potential Flow
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© Fluent Inc. 12/05/10 C2 Fluids Review TRN-1998-004 Outline Introduction What is a potential flow? Governing equations for potential flow Boundary conditions for potential flow The stream function Bernoulli’s equation Total pressure Application of Bernoulli’s equation Solving potential flow problems Example: Flow over a circular cylinder Potential flow and lifting bodies Summary
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© Fluent Inc. 12/05/10 C3 Fluids Review TRN-1998-004 Consider a low speed (but Re is reasonably high) flow over a streamlined object Viscous effects confined to narrow region (boundary layer) near body A useful approximation of this type of flow is to neglect viscous effects entirely! Introduction
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© Fluent Inc. 12/05/10 C4 Fluids Review TRN-1998-004 What is Potential Flow? A potential flow is a simplified model of fluid motion which assumes the flow is... irrotational - vorticity is zero inviscid - viscous effects are neglected incompressible - density is constant the force field is ``conservative’’ isothermal - temperature is uniform When are the potential flow assumptions reasonable? Steady flow of liquids and gases at relatively high Reynolds numbers Upstream flow is vorticity-free (e.g. undisturbed) Example: flow of air around an airplane in an undisturbed atmosphere
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© Fluent Inc. 12/05/10 C5 Fluids Review TRN-1998-004 Governing Equations for Potential Flow For an incompressible flow, the continuity equation reduces to For an irrotational flow field, we can define the velocity as follows: where ϕ is called the velocity potential . This is due to the vector identity 0 = V ϕ = V
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© Fluent Inc. 12/05/10 C6 Fluids Review TRN-1998-004 Governing Equations for Potential Flows (2) Combining the continuity equation with the definition of the velocity in terms of ϕ yields This is the governing equation for potential flow. It is Laplace’s equation , one of the most famous and well-studied equations of mathematical physics.
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