By Kirill V. Rozhdestvensky
This publication describes a mathematical version of circulate prior a lifting process acting regular and unsteady movement in shut proximity to the underlying reliable floor (ground).
The writer considers a number of approximations in keeping with the final approach to matched asymptotic expansions utilized to lifting flows. specific significance is hooked up to the case of utmost flooring results describing very small relative floor clearances. Practitioners thinking about the layout of wing-in-ground impression autos will locate during this ebook all of the appropriate formulae and calculated info for the prediction of aerodynamic features during this very important restricting case. extra more often than not, this publication is acceptable for graduate scholars, researchers and engineers operating or lecturing within the sector of theoretical aerodynamics.
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Additional info for Aerodynamics of a Lifting System in Extreme Ground Effect
11) for the channel flow potential IPl evaluated for v = hieii -+ 0, that is, IPl V h le ~o + IPla ho IPi = IPh + IPl 2 ho In f'V 1) + --* a2dlh~(1v2 - ---;;- - = alho ( --;;- - - 2 h le h le 7r V) - 7r 2V +a3ho--;;- +a4 ho. 22) on the line h whieh corresponds to the leading (side) edge. 76) The boundary conditions written above must be fulfilled on the line h, which corresponds to the leading (side) edge. Note that one of the results of matching in the second stage is the determination of the strength Q(l, t) of the sources distributed along the lines hand b.
Therefore, one has to analyze a loeal flow near the hinge. First of all, use the local coordinate system Xf = bf - x, Yf = y. Introduce stretched coordinates Yf = yr/h, Xf = xr/h. After stretching, the local region near the hinge transforms into a strip (0 :s: Yf :s: 1,lxfl < (0), on the boundary of which a normal derivative of the flow potential is known. Mapping the strip onto a half plane and using the Schwartz formula (see Fuks and Shabat (131]), one can write the expression for the flow perturbation veloeity on the lower surface of the foil near the hinge as dCPf () dx = - 7Th [ln 11 - exp( -7TXt) I + 7TXtl + R, where R is a eonstant.
60) that Ube = CPbe -[(eu - el) In 11 + ~I =;' [v(7rcpae -1) - ~7rCP;el. 56) by replacing du,l by eu,l and hie by h;e' Note that the solutions of local fiow problems, presented above, lose validity in the vicinity of the order of O(h o ) of the corner points of contours h, h, where the fiow is essentially three-dimensional. Near such corner points, additional solutions should be constructed, but this question will not be discussed here. 22) of the channel fiow, it is necessary to match these expansions in the overlap regions.