Inviscid Flow

What is Inviscid flow?

The inviscid-flow assumption means physically that viscous-shear and normal stresses are negligible. Thus, all of the viscous shear-stress terms on the force side of the momentum equations drop out, as well as the normal stresses due to viscosity. As a result, the only stresses acting on the body surface are the normal stresses due to pressure. While for viscous fluids, the viscous-shear stresses are assumed to be proportional to the rate of strain of a fluid particle, with the constant of proportionality as the coefficient of viscosity. Thus, an assumption equivalent to that of negligible viscous stresses is that the viscosity coefficient is essentially zero.

Such a flow is termed inviscid (i.e., of zero viscosity). In effect, the boundary layer on the body’s surface is deleted by this assumption. This implies that the boundary layer must be very thin compared to a dimension of the body. The presence or absence of the boundary layer has a negligible effect relative to modifications to the body geometry as “seen” by the flow. The inviscid, incompressible-fluid model is often termed a perfect fluid (not to be confused with an excellent or ideal gas). The boundary layer in many practical situations is extremely thin compared to a typical dimension of the body under study. The body shape that a viscous flow “sees” is essentially the geometric shape. The exception is where the flow separates, and the boundary layer leaves the body, resulting in a significant change in the effective geometry of the body. Such separated regions occur on wings, for example, at large angles of attack.

However, the wing angle of attack of a vehicle at a cruise condition is only a few degrees, so that the effects of separation are minimal. Thus, the inviscid-flow assumption provides useful results that closely match the experiment for conditions corresponding to cruise. The inviscid-flow model breaks down when large regions of separated flow occur. Because the presence of the boundary layer is neglected in perfect-fluid theory, the theory does not predict the frictional drag of a body; that must be left to viscous-flow theory. However, predictions for low-speed pressure distribution, lift, and pitching moment are valid within the framework of incompressible inviscid flow.

Inviscid Flow

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