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Ebook Computational fluid dynamics for engineers: Part 2

(BQ) Part 2 book "Computational fluid dynamics for engineers" has contents: Inviscid flow equations for incompressible flows, boundary layer equations, stability and transition, grid generation, inviscid compressible flow, incompressible navier stokes equations, compressible navier—stokes equations. | Inviscid Flow Equations for Incompressible Flows 6.1 I n t r o d u c t i o n In this chapter we address the solution of the inviscid flow equations for incompressible flows and postpone the discussion on compressible flows to Chapter 10. For incompressible irrotational flows the Euler equations of subsection 2.4.1 simplify further and, in terms of either velocity potential, 0, or stream function, i\), they reduce to the Laplace equation in allows the equation resulting from the irrotationality condition, du dy dv dx (6.2.5) V2^ = 0 (6.2.6) to be written as Laplace's equation in ^ , The assumption of an irrotational flow is a useful one in that it removes the nonlinearity in the momentum equations and allows them to be replaced by the Bernoulli equation (2.4.16), which provides an algebraic relation between velocity and pressure. For a two-dimensional flow, it is given by P + ^Q(u2 + v2) = const. (6.2.7) Equations (6.2.2) and (6.2.6) apply to any incompressible irrotational flow and can be used to compute the velocity field about a given body. What distinguishes one flow from another are the boundary conditions. For example, to predict the flowfield about a body at rest in an onset flow, V^, moving in the increasing x-direction (an onset flow is the flow that would exist if the body is not present), it is necessary to impose the condition that the surface of the body is a streamline of the flow, that is, %b — constant — = 0 — (6.2.8) on at the surface on which n is the direction of the normal, and that far away from the body. The velocity components are » = ! = ! or = " - «=£=-£=• v = - ^ 0 (6.2.11) 182 6. Inviscid Flow Equations for Incompressible Flows Linos of equipotential Fig. 6 . 1 . Equipotential lines and streamlines for a source flow. Equipotential lines Streamline Fig. 6.2. Equipotential and streamlines for a potential vortex flow. where r is the strength of the vortex. The minus sign on the right-hand side of Eq. (6.2.11)