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THE iJNI'E3RSIfP OF XP&HINGTON SEATTLE, WASRINGTON 98105 PROGRESS REPORT NO. 3 f o r fo r The P e r i o d f r o n Ee2;itember 16, 1965 t o March 15, 1906 NASA Grant NGB-48-OQ2-010 R. G. Joppa Prinelpsl Investigator June 2, 1966 * f i e l d exists Elhead or' the contPaetio d has t h e e x p e c t e d r e s z r l t on pitching nonents.
n- iriese tests w i l l b e eon",xued a t other locations i n +he t e s t .
section to d e f i n e the region of f l o w convergence that can g i v e n o t i c a b l e remits and t.0 rlom-psre t h e ~ e efrectr; - * A L U I C i L l A che c a i c u l a i e r i f l o w f i e l d s .
INTXRHAL FLOW FIELD ANALYSIS The anal:--sis o f internal f l o i f i e l d s in a two-test s e c t i o s tunnel by the V o r t e x r i n g m e t h o d was extended and essentially completed d u r i n g t h i s r e p o r t i % period. The v o r t i c i t y o f t h e die- crete rings has been d i s t r i b u t e d in a l i n e a r piece-vise continuous mariner and then used to c a l c c l a t e the 3nterriaI flow f i e l d s with
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inprowed results near the t u n n e l valler. Mechanical d i f f i c u l t i e s eccountered earlier have been overco,mme and v e l o c i t y p r o f i l e s can 201 be conputed at sections 30% cootainin;: the c e n t e r line.
A n extension of t h e nethod has been made t h a t i s more suitable f o r caltlulatfng f l o w t h r o u g h an open c i r c u i t wind tunnel. I n this application, the remote airstream VeZocfty is s e t to zero, the Kuttr oondition abandoned at the t u n n e l e x i t , and one vortex strength chosen a r b i t r a r i l y . The method has been lzsed to d e s i g n an intake section now being b u i l t as a part of t h e experirnental prograa.
final. report is being w r i t t The rtext s t e p taken a f S e r o b t a i n i n g a solution f o r t h e tralec- t o r y of t h e vortex wake of E lifting s~siern i n € m e air, a s PB- por+,ed previously, was t o approach t h e o a l c u l a t i o n of t h e nake trajectory i n a closed wind t u n n e l .
The t u n n e l w a l l s were represented by a pattern of s q u a r e :a, .
v o r t e x r i q s l ~ i ~ r i g i n t h e 2larte o f the t u n n e l walls. b r x t h the l i m i t a t i o n of square riEg,s, only t u n n e l s of constant c r o s s sec:iion and f l n i t e length can be represented. The c r o s s section can be conporred of any number of s i d e s of equal l e n g t h arranged i n any polygon. A c o n t r o l p o i n t wag l o c a t e d i n t h e c e n t e r of each aquare, and the boundary c o n d i t i o n o f no flow through the wall was s a t i s f i e d at e a c h such control p o i n t . A wing in the tunnel is represented by s bound and trailing vortex sgt;tem, i n i t i a l l y t r a i l i n g s t r a i g h t downstream. This system q f simultaneous equa- tions is s o l v e d on t h e computer f o r the unknown s t r e n g t h s of each of the v o r t e x rings.
The mill v o r t e x rings are u s e d to calculate the v e l o c i t i e s a t the w i n g t r a i l i n g system and t h f a system ie relocated such t h a t i t is everywhere p a r a l l e l to the l o c a l f l o w . Then the f i r s t calculation o f wall. v o r t i c i t y i s r e - i t e r a t e d and the p r o c e s s c y c l e d t o convergence.
It has been shown t h a t the proceso does converge and t h a t the m.
wake t r a j e c t o r y can b e found i n the wind tunnei. ine a r i g i a a i h y p o t h e s i s , t h a t t h e wake vortex would change i t s p o s i t i o n s i g n i f - j c a n t l y . w f t h r e s p e c t t o its free a i r position, ha8 been confirmed.
E f f e c t s on p i t c h i n g moments had not been oalculated at t h e closing d a t e o f t h i s r e p o r t i n g p e r i o d , b u t l a t e r c a l c u l a t i o n s have already shown t h a t i n some c e s e s t h e i n f l u e n c e o f t h e ehiPting v o r t e x wake on a t a i l a t t h e 3unrrel. c e n t e r l i n e ban more than c a n c e l t h e p i t c h i n g nornent i n t e r f e r e n c e due t o t h e walls.. A najos e f f o r t i n t h e n e x t period sill be t o complete t h e c a l c u l a t i o n of r i n d tunnel w a l l i n t e r f e r e n c e s , i n c l u d i n g the e f f e c t o f t h e relotlation of the wake on the t a i l .
I n o r d e r t o check t h e zclequacy of t h i s representation, the c l a s s i c a l c a s e of ~i simple wing w i t h undeflected wake i n a c r r c u - lar tunnel was s o l v e d . The r e s x 1 - h agree e x a c t l y w i t h those of' P r a n d t l and Gle-rt at t h e wing. The vorticity i n t h e w a l l agrees i n the limiting c a s e a8 t h e span o f the ring approaches z e r o w i t h t h a t found in closed form for a d o u b l e t in the center of a c i r - cular'tunnel. The downraoh interferenue along the tunnel c e n t e r l i n e was calculated as w e l l , b u t no t h e o r e t i c a l s o l u t i o n is airail- a b l e for comparison. The b e s t one found Pa an approximate s o l u t i o n by Lotz In TU 801.
This r e c u l t I s b e i n g w r i t t e n up f o r publication.
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