The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Pressure Transients in Transitional Boundary Layer over a Solid Surface
Pressure Transients in Transitional Boundary Layer over a Solid Surface
Pages 269-284
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From page 269... ...
, a velocity potential ~ with Ui = vie = B/3xi ~ is introduced for an irrotational (w = v x u = 02 flow, the continuity equation is reduced to v' = 0 which can be solved without any reference to pressure under suitable boundary formulation. For steady state potential flows, 2the Bernoullis relation p + pu /2 ~ B as an integral of the momentum equation enables us to find p where B can be evaluated from the boundary data.
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From page 270... ...
Thus the pressure transients cannot be determined with such stream function vorticity formulation even for flows in two space dimensions. For flows in three space dimensions, the flow field evolution is generally visualized according to equation (5)
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From page 271... ...
The popular approach of considering vorticity transport and interaction in discrete form without due attention of retaining solenoidal velocity and vorticity fields is fundamentally questionable. It is often tolerated in the construction of approximate solutions if the residual divergences could be controlled to remain small, and the global mass conservation can be monitored and likewise maintained.
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From page 272... ...
and (10) with some preassigned small values of and Fi =pui^/2 for different simple test problems have rendered highly successful approximations to the corresponding incompressible flow velocity fields (5,6)
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From page 273... ...
In otherwords, an equal and opposite set of associated impulsive forces would annihilate the local residual divergence to leave a solenoidal velocity field, being disturbed by the set of associated impulsive forces. This concept has been little developed; but gives equations (9)
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From page 274... ...
with the vorticity transport equation (S) under some approximate boundary formulation.
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From page 275... ...
Thus, the magnitude of the artificial impulse appears irrelevant as a measure of disturbance "strength". The peak magnitudes of the equilibrated pressure disturbances correlate well with the eventual course of evolution as is described above despite that they are much less than those of the associated solenoidal velocity disturbances.
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From page 276... ...
The two distinct high pressure regions over the plate surface appear to be two ne ighbouring isolated globules or half domes encased in a low pressure valley in the shape of some semispherical caps in three space. This is typical of "large" initial disturbances that promptly evolve into propagating local turbulent regions.
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From page 277... ...
for studying the global qualitative aspects of the pressure evolution in a transitional flow field as mentioned in the previous section. To better appreciate the three dimens tonal aspects of the pressure bans tents next to the plate surface we give in Fig.
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From page 278... ...
The multiple of such convecting pressure quadruples in a local turbulent region is thus a powerful "acoustic" source, with identifiable characteristics, directionally, spectrally and/or in selected correlation functions to distinguish itself from the prevailing noisy environment. Better understanding of the quadruple structure of the propagating local turbulent region in a transitional flow field could have far reaching implications.
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From page 279... ...
The evolution of the pressure field can be described by a three dimensional analog of the dissipative KDV equation possessing the different limiting properties described above. As such the propagating large pressure disturbances are likely dispersive waves whose "convective" velocity can be much different from the local instantaneous velocity of the fluid.
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From page 281... ...
~ ~~ ~ ~ z ~ ~~ ~ ~ z ~1~ ~~ ~ 0.~1~-~ Fig.
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From page 284... ...
a. Temam, R., "Navier Stokes Equation", North STREAMLINES RT I- 20 Holland Elseviers, (1978)
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