Wind-tunnel-wall corrections

When the wind tunnel was f i r s t developed as a p r a c t i c a l approach t o experimental aerodynamics, it was recognized t h a t the flow about a body i n a wind tunnel was not the same a s the flow about the same body i n f l i g h t .Since t h a t tw, m a i n l y during the p a s t 30 years, there has appeared a steady stream of research papers, some offering i ~r o v e m e n t s i n recognized corrections in keeping with the improvements i n wind-tunnels, equipment , t e c h i que s , and general understanding of aerodynamics and other s deriving necessary corrections f o r new types of aerodynamic configurations o r new types of measuring techniques.The problem a r i s e s from the f a c t t h a t , although the d i f f e r e n t i a l equations of the flow a r e the same i n the tunnel as in f l i g h t , the outer boundary conditions a r e d i f f e r e n t .I n f l i g h t , the condition i s simply t h a t the flow a t i n f i n i t y i s uniform; i n the tunnel, c e r t a i n other conditions, depending on the type of tunnel, must be s a t i s f i e d a t tEe tunnel boundaries.For the closed tunnel, the condition i s obviously that the velocity component normal t o the w a l l bs zero.For the open tunnel, where the j e t traverses a region of comparatively quiescent air, the condition i s t h a t the pressure a t t h e boundary be miform.By Bernoulli's l a w , it follows t h a t the tunnel v e l o c i t y must be uniform on the boundary.I f t h i s velocity i s considered a s the swn of the undisturbed tunnel velocity U and a small perturbation v'ePoci t y (up v, w) r e s u l t i n g from the presence of the body i n the Jet, the conditf on i s then t h a t (U + u ) 2 + v2 + w2 Z u2 + 2Uu be constant, from which it follows t h a t u is constant over the e n t i r e surface.Furthermore, since u i s obviously zero f a r i n f r o n t of the body, it must be zero over the e n t i r e surface, whence it can be e a s i l y shown t h a t the perturbation p o t e n t i a l i t s e l f i s constant over the e n t i r e surface.The somewhat obvious condition t h a t the perturbation velocity (u, v, w) i s zero f a r i n f r o n t of the body may need s p e c i a l emphasis; neglect of t h i s condition has i n the p a s t sometimes l e d t o erroneous r e s u l t s (reference 1 ) .Some a t t e n t i o n has been directed recently t o a t h i r d case; namely, t h a t of an open tunnel i n which.the body i s so f a r forward i n the j e t t h a t the presence of the closed entrance b e l l cannot be neglected.This case involves a mixed-boundary-value problem i n which the normal velocity i s zero on the closed portion of the boundary and the longitudinal perturbat i o n velocity u i s zero (or constant) over the open portion of the boundary.An i n t e r e s t i n g f u r t h e r boundary condition a r i s e s here, namely, t h a t the flow v e l o c i t i e s be continuous a t the edge of the entrance b e l l .This condition i s similar t o the Kutta condition a t the t r a i l i n g edge of an a i r f o i l .It a r i s e s because of the f i n i t e v i s c o s i t y of a i r , and it provides u n i q ~e n e s s where otherwise an i n f i n i t y of solutions would e x i s t .