Unsteady Flow Categories

As derived above, unsteady potential flow introduces three basic new effects not present in steady flow: unsteady Vp ■ n due to body motion U(t), O(t), the additional pdp/dt term in the Bernoulli equation for the pressure, and the generation of shed vorticity yshed. Only some of these effects may be important in any given situation, giving a natural categorization of unsteady flows summarized in Table 7.1.

Table 7.1: Unsteady flow regimes and retained or discarded effects

d(Vp ■ n)/dt

pdp/dt

yshed

Steady

0

0

0

Quasi-steady I

V

neglected

neglected

Quasi-steady II

V

neglected

estimated

Unsteady

V

V

V

The quasi-steady approximation is employed for defining the aerodynamic loads in flight in Chapter 6, where the unsteady forces on a maneuvering aircraft are assumed to be the same as those in steady flight at the same instantaneous flight condition defined by the parameters а, в, p, q, r. In the “Quasi-steady II” case a slight refinement is made by estimating the shed vorticity effects via the additional a parameter.

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