The boundary-layer flow over a permeable surface through which suction is applied

Abstract

A brief review of existing work is given and the possibility of certain simple solutions for velocity distributions of the type U = kxpowerm with their appropriate suction distributions is indicated. An improved approximate calculation of the 'entry flow' along a flat plate, through which constant suction is applied, is given in some detail. Also Prandtl's original calculation (based on the momentum equation) for boundary-layer flow with constant suction and a constant adverse Velocity gradient is repeated, using Howarth's accurate solution for flow without suction. It is also demonstrated (subject to the accuracy of the approximations) that distributed suction should be much more economical in quantity than suction flow through the minimum number of isolated slots required to prevent separation in the flow under a constant adverse velocity gradient. Practical applications of porous suction are then considered and illustrated by simple examples. These fall under two headings :--(a) the stabilisation of laminar flow against disturbances, (b). the prevention of separation. If the stability calculations made by Pretsch are correct, then a suction velocity vl, given by v1/U>= 1.82 × 10power-5, where U is the free-stream velocity, should make the boundary-layer flow past a flat plate stable against all small disturbances. Thus by use of a very small suction flow it may be possible to stabilise the flow over a laminar flow type wing against the adverse effects of waviness. The prevention of laminar separation, coupled with the increase of stability, makes possible a wing with 100 per cent. laminar flow. Bluff shapes as extreme as a circular cylinder require only a comparatively small suction flow to overcome laminar separation. The application of porous suction to the attainment of a high CL MAX is also considered, and it is demonstrated that, even for a thin wing, a very high CL MAX should be made possible by a surprisingly small suction flow applied over less than 10 per cent. of the chord. It is also suggested that porous suction could be used as a valuable research tool to thin the boundary layer and thus simulate high Reynolds number conditions at small test Reynolds numbers for both incompressible and compressible flOW. Some consideration is given to the practical realisation of a porous surface which approximates to the mathematical concept. It is concluded that porous bronze, made by sintering metallic powder, is the most suitable existing material for laboratory experiments. There seems to be no reason why a similar 'surface' should not be made in light alloy for the flight applications. It is considered that the simulation of a porous surface by the use of isolated slots is not suitable unless their spacing and width are small compared with the boundary-layer thickness. It is concluded therefore that porous suction may have important practical applications to flight at both small and large CLs. Experiments are needed to confirm the ideas put forward in this report. Also accurate solutions of the boundary-layer equations for the flow under an adverse pressure gradient with porous suction are required to check the approximate treatment used herein.