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By Poisson, Eric

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For a larger pipe diameter or a faster flow speed, the flow will become turbulent. Most flows that we experience in everyday life have a Reynolds number of 104 or greater, and thus most flows are turbulent. 1)) are valid for both laminar and turbulent flows, however, the detailed flow fields for laminar and turbulent flows are very different. Since the stream lines in laminar flow are parallel each other, a coordinate axis is taken parallel to the flow direction, and the convective acceleration, the second term on the LHS, becomes exactly zero or leaves only the term u (duldx) like the one dimensional Euler equation.

Figure (a) shows the instantaneous flow field as the wing just starts to move. This flow field is nearly identical to Fig. 8 (a flow pattern around an inclined flat-plate), which was already described in the previous chapter for an ideal fluid. Initially, circulation does not exist in the fluid or around the wing, and the fluid flows as if it is an ideal fluid that generates neither lift nor drag. Point A in the figure is the front stagnation point and point S is the rear stagnation point. The fluid particle initially existing at the trailing edge of point B flows upstream to the point S on the wing.

This unsteady state naturally affects the characteristics of the wing, and there is no guarantee that the generated lift on the wing has the same magnitude as the lift in a steady flow. For a two-dimensional oscillating wing, if the fluctuating speed V is small compared to the main speed U, there is an analytical method. However, in the case of large amplitude oscillations that may be accompanied by flow separation there is no general solution to date. Thus, computer analysis seems to be suitable for such flow fields, and these kinds of research have been performed.

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