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R . & M . N a . 3 6 4 9

M I N IS T R Y O F T E C H N O L O G YA E R O N A U T I C A L R E S E A R C H C O U N C I L

R E P O R T S A N D M E M O R A N D A

W a k e B l o c k a g e C o r r e c t io n s in a C l o s e d W i n d T u n n e lfo r O n e or T w o W a l l - M o u n t e d M o d e l s S u b j ec t to

S e p a r a t e d F l o wBy R. W. F. GOULD

A e r o d y n z m l ic s I ) i v i s io n . N . P . L .

L O N D O N : H E R M A J E S T Y 'S S T A T I O N E R Y O F F I C E1970

PRICE 12S 0d [60p] NET


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W i th B l o c k a g e C o r r ec ti o n s in a C l o s e d W i n d T u n n e lfo r O n e o r T w o W a l l -M o u n t e d M o d e l s S u b je ct to

S e p a r a t e d F l o wBy R. W. F. GOULD

Aerodynamics Division, N.P.L.

Reports and M emoranda N o. 3649*February, 1969Summary.Measurements described show that Maskell's wake blockage corrections apply to rectangular plates

normal to the flow, over the range 1/3/> h/b >/3 tested, whether the plates are mounted on the tunnelaxis or adjacen t to a wall. Only small non-linear effects were found even when the corrections approached100 per cent.Blockage correction formula are developed for use when two models are present in the working sectionat the same time (but each outside the wake o f the other).The method of determining the required blockage factors is described with examples from measure-ments on flat plates mounted normal to a wall and on lattice models.

LIST OF CONTENTSSection.

1. Introduction2. Preliminary Measurements

2.1. Theoretical background2.2. Experimental method2.3 . Discussion of results of preliminary measurements

3. Main Programme of Tests3.1. Introduction3.2. The measurements3.3 . Discussion of results

4. ConclusionsList of SymbolsReferences

*Replaces N.P.L. Aero Report 1290--A.R.C. 31 007.


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A p p e n d i x AA p p e n d i x BA p p e n d i x C

T h e S e p a r a t i o n o f G e n u i n e W a k e B l o c k a g e Ef fe c ts f r o m S p e e d M e a s u r e m e n t E r r o r sW a k e B l o c k a ge I n te r f e re n c e B e tw e e n T w o M o d e l sT h e M e t h o d o f E v a l u a t i n g W a k e B l o c k a g e F a c t o r s

I l l u s t r a t i o n s - - F i g s . 1 t o 9D e t a c h a b l e A b s t ra c t C a r d s

1. Introduction.M a s k e l l ' s t h e o r y o f w a k e b l o c k a g e i n c l o s e d t u n n e l s 1 w a s o r i g i n a l ly i n t e n d e d f o r u s e w i t h a i r c r a f t

m o d e l s . H o w e v e r , i t a p p e a r e d a t a t i m e w h e n i n t e r e s t w a s g r o w i n g r a p i d l y i n th e t e s t i n g o f b l u f f m o d e l sr e p r e s e n t i n g b u i l d i n g s t r u c t u r e s a n d w a s t h e r e f o r e o f v it a l c o n c e r n i n n o n - a e r o n a u t i c a l t e s t in g .

T h e w o r k d e s c r i b e d i n th i s p a p e r b e g a n a s s i m p l e e x p e r im e n t s t o f i n d t h e l im i t a t i o n s o f t h e n e w t h e o r yw h e n a p p l i e d t o t h e l a rg e b l o c k a g e s a r i s in g i n t h e t e s t i n g o f b l u f f m o d e l s , p a r t i c u l a r l y t h o s e m o u n t e d o nt h e f lo o r . T h e r e s u lt s o f t h e i n i ti a l te s t s p r o v e d v e r y e n c o u r a g i n g a n d t h e w o r k w a s e x t e n d e d t o c o v e ri n t e rf e r e n c e e f fe c ts b e t w e e n m o r e t h a n o n e b l u f f m o d e i n t h e s a m e t u n n e l . T h e o n l y t u n n e l a t N P L h a v i n ga s u i ta b l e b a l a n c e c o m b i n e d w i t h a w o r k i n g s e c t i o n o f a d e q u a t e l e n g t h w a s t h e 7 ' x 7 ' t u n n e l , a n d t h isw a s u s e d fo r m o s t o f t h e m e a s u r e m e n t s . S o m e c o n f i r m a t o r y e x p e r i m e n t s w e r e u n d e r t a k e n i n t h e 1 3 ' x 9 't u n n e l .

T h i s r e p o r t d e s c r ib e s a l i n k e d s e r ie s o f e x p e r im e n t s w h i c h p r e s e n t a f a i rl y c o h e r e n t p i c t u r e o f o n e t y p eo f i n te r f e r e n c e e f fe c t a m o n g t h e m a n y s ti ll n e e d i n g i n v e s t ig a t i o n .

2. Pre l iminary Measu rements .3.1 . T he ore t i c a l Bac k ground .

M a s k e l l 1 h a s d e r i v e d e x p r e s s io n s f o r t h e c o r r e c t i o n o f fo r c e a n d p r e s s u r e c o e f f i ci e n ts m e a s u r e d i nc l o s e d w i n d t u n n e l s o n b l u f f m o d e l s s u b j e ct t o s e p a r a t e d f lo w . F o r s y m m e t r i c a l m o d e l s , n o r m a l t o t h ewi n d d i r ec t i o n , ( s u ch a s f l a t p l a t e s ) t h e r e l a t i o n s h i p s g i v en a re

CD qc 1 -- UpCoc q 1 - Cpo = l + n C D S / C (1)

wh ere t h e s u b s c r i p t c r e f e r s t o co r r ec t ed v a l u es , CD a n d Cp a re co e f f i c i en t s o f d rag an d p res s u re , t h ed y n a m i c p r e s s u re q f a r u p s t r e a m b e c o m e s a v a l u e qc i n t h e p l a n e o f th e p i a t e d u e t o b l o c k a g e , S is t h ef r o n t a l a r e a o f t h e p l a te a n d C t h e c r o s s - s e c t io n a l a r e a o f t h e t u n n e l .

T h e t h e o r e t i c a l v a l u e o f t h e b l o c k a g e f a c t o r n i s - 1 / C p b , , w h e r e C pb o is t h e c o r r e c t e d v a l u e o f t h es e p a r a t i o n p r e s s u re c o e f f i c ie n t o f t h e m o d e l ( w h i c h h a p p e n s t o b e e q u a l t o m e a n b a s e p r e s s u r e c o e f f i ci e n ti n t h e cas e o f a f l a t p l a t e n o rm a l t o t h e w i n d ) .S nDI f w e r e w r i t e t h e b l o c k a g e t e r m n Co -~ a s ~ t h e n , f o r a g i v e n a p p r o a c h d y n a m i c h e a d q, t h e b l o c k a g ee f fe c t v a r ie s d i r e c t l y w i t h t h e d r a g p e r u n i t a r e a o f tu n n e l s e c ti o n . F u r t h e r m o r e , s in c e t h e se e x p r e s s i o n sw e r e d e r i v e d w i t h o u t t h e u s e o f m a t h e m a t i c a l d e v ic e s s u b je c t t o i m a g e i n t e r f e r e n c e f r o m w a l l s (e .g .,s o u r ce s ) th e r e w o u l d a p p e a r t o b e n o i n b u i l t li m i t a t i o n o n t h e p o s i t io n o f t h e m o d e l .

T h e p r e l i m i n a r y e x p e r i m e n t s w e r e d e v i s e d t o c h e c k t h e v a l u e o f t h e b l o c k a g e f a c t o r n , a n d i ts v a r i a t i o nf So v e r a w i d e ra n g e o ~ v a l u e s f o r t h e e x t re m e p o s i t i o n s re p r e s e n t e d b y a x i a l l y - m o u n t e d a n d w a l l - m o u n t e d

m o d e l s .


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2.2. Experimental Method.The 7' x 7' tunnel at N PL has a balance midway along its 24 ft (7.31 m) long working section. The

corner fillets to the working sections decrease slightly in size with distance downstream to compensatefor boundary layer growth, and the sect ional area in the plane of the balance is exactly 45 sq. ft (4.18 m2).For the purposes of the present investigation it was necessary to check and, in consequence, modify thewindspeed measurement system as described in Appendix A.The models used in these measurements were plates of 7/8 in. (22 ram) plywood having sides in theratio exactly 2:1. The reason for this choice of side ratio was that in tests on plates normal to the windFail, Lawford and Eyre2 had showed that the base pressure for 2:1 plates was very close to that for squareplates. Provided therefore that the tunnel boundary layers were thin, it seemed reasonable to argue tha t aplate with b = 2h mounted within 1/8 in. (3 mm) of the roof(so that the plate and its image in the roof wereequivalent in some respects to a square plate in midstream) would be almost unaffected by the slightleakage through the gap between the plate and the roof.

Initia lly a 22 in. x 44 in. (55.9 x 111.8 cm) plate was mounted on the balance normal to the wind inthe centre of the tunnel. The relative proportions of the plate and balance support guards within thetunnel are shown in Fig. 1.The drag was measured at 90 ft/s (27.4 m/s) in this condition and then measured again with dummysupport guards mounted on the floor. The difference between these readings (about 3 per cent) wassubtracted from the first reading to give a close approximation to the drag of the centrally mounted platein the absence of any suppor t interference.The plate size was reduced to 10 in. x 20 in. (25.4 x 50-8 cm)in stages, while maintaining the ratio between the sides, and the same drag measurement procedure wasfollowed at each stage.Next a 22 in. x 44 in. (55.9 x 111.8 cm) plate was mounted on the balance normal to the wind andwith a 1/8 in. clearance between the plate and the roof. This time the thin steel plate supports were entirelyin the wake immediately behind the board and no support correct ions were necessary. This plate was alsoprogressively reduced in size and a series of drag measurements were made.

2.3. Discussion of Results of Preliminary Measurements.Figs. 2 and 3 show the values of the measured drag coefficients plot ted against the blockage parameter

CD S/C (evaluated more simply as D/qC). Although straight lines could be fitted to the results withoutserious deviation, careful analysisshowed that the points were better represented by quadratic curvesover the range of measurements. The expressions suggested are :For centrally-mounted plates with 0 < CD S/C


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T h e i n t e r e s t i n g c o n c l u s i o n s f r o m t h e p r e l i m i n a r y t e s t s a r e t h a t :( a) P o s i t i o n o f t h e m o d e l i n t h e t u n n e l h a s n o s i g n i f i c an t ef f ec t o n t h e w a k e b l o c k a g e c o r r e c t i o n .( b) M e a s u r e m e n t s m a d e t o d e t e r m i n e b l o c k a g e c o r r e c t io n s w i t h l a rg e m o d e l s s u b j e c t to s e p a r a t e d f l o w

(i .e . w h e r e a l a r g e e ff e c t i s a v a il a b l e f o r m e a s u r e m e n t ) c a n b e u s e d b y l i n e a r i n t e r p o l a t i o n t o d e d u c ew i t h s u f f ic i en t a c c u r a c y t h e b l o c k a g e c o r r e c t i o n s o n s m a l l e r g e o m e t r i c a l l y s im i l a r m o d e l s , s i n c e t h ed e p a r t u r e o f t h e c u r v e s o f F i g s. 2 a n d 3 f r o m l i n e a r i t y a r e s m a ll .

3 . M a in Pro g ra mme o f Tes t s .3.1. Introduction.

M a s k e l l ' s p a p e r t i s b a s e d o n h i s c o l l e a g u e ' s t e s ts 2 o n c e n t r a l l y - m o u n t e d t h i n f l at p l a te s u s e d s i n g l yi n a c lo s e d w i n d t u n n e l . T h i s w a s a l m o s t c e r t a i n l y t h e f i rs t p a p e r g i v i n g i n f o r m a t i o n o n s u c h p l a t e s f u l lyc o r r e c t e d f o r b l o c k a g e e f fe c ts . T h e c o n n e c t i o n b e t w e e n a s p e c t r a t i o , d r a g c o e f f i c ie n t a n d b l o c k a g e c o r -r e c t ion i s c l e a r ly e s t a b l i she d in t he se pa pe r s .

H o w e v e r , in n o n - a e r o n a u t i c a l t e st in g , m u c h o f t h e i n t e re s t is c e n t r e d o n w a l l - m o u n t e d m o d e l s r e p re -s e n t in g s t r u c t u r e s i n a n a t u r a l w i n d . E a r l y w o r k b y I r m i n g e r a n d N o k k e n t v e d 3 s u g g es t ed t h a t t h e d r a gc o e f fi c i en t s o f w a l l - m o u n t e d p l a t e s w e r e a l m o s t c o n s t a n t f r o m h /b = 1 to h/b -~ 0 a t a v a l u e a r o u n d 1 .2 .T h i s i s m a r k e d l y i n c o n t r a s t w i t h t h e c o r r e s p o n d i n g v a l u e s f ro m 1 .1 5 t o 1 " 86 f o r c e n t r a l l y m o u n t e d p l a t e s,w h i c h c o u l d b e r e g a r d e d a s e q u i v a l e n t t o w a l l m o u n t e d p l a te s o f h a lf t h e h e i g ht w h e n c o n s i d e r e d w i t ht h e i r i m a g e s i n t h e w a l l . T h i s r a i s e d d o u b t s t h a t b l o c k a g e f a c t o r s o n w a l l - m o u n t e d p l a t e s s h o u l d b e t h es a m e a s t h o s e o n c e n t r a l l y - m o u n t e d p l a t e s, e v e n w h e n t h e a s p e c t r a t i o o f th e f l o o r - m o u n t e d p l a t e is b a s e do n 2h/b t o i n c l u d e t h e i m a g e .

A f u r t h e r to p i c o f in t e re s t w a s t h e p r o b l e m o f b l o c k a g e c o r r e c t i o n s o n o n e s t r u c t u ra l m o d e l w h e na n o t h e r m o d e l w a s i n t h e t u n n e l ( n o t n e c e s s a r i ly i n th e s a m e p l a n e ) t o s i m u l a t e a f u l l s c a le s i te g r o u p i n ga r r a n g e m e n t . F u n d a m e n t a l t o s u c h a p r o b l e m w a s t h e q u e s t io n a s t o w h e t h e r t h e ' a c t i v e ' b l o c k a g e e f fe c te x p e r i e n c e d b y a m o d e l d u e t o i ts o w n p r e s e n c e in a w i n d t u n n e l w a s t h e s a m e a s t h e ' p a s s i v e ' b l o c k a g ee f fe c t e x p e r i e n c e d b y a n o t h e r m o d e l e v e n o f i n f i n i te s m a l a r e a , in t h e s a m e p l a n e , a n d h o w t h i s d e p e n d e do n t h e s i z e o f th e m o d e l s .

T h e s e s u b j e c t s w e r e s t u d i e d b y a s s u m i n g t h a t t h e t o t a l b l o c k a g e e f fe c t i n a t r a n s v e r s e p l a n e w a s d e -p e n d e n t o n t h e t o t a l d r a g i n t h a t p l a n e p e r u n i t a r e a , t h a t a c t i v e a n d p a s s iv e b l o c k a g e e f f ec t s w e r e t h e s a m eb e t w e e n i d e n t i c a l m o d e l s i n t h e s a m e p l a n e s o t h a t t h e e f fe c t c o u l d b e c o n s i d e r e d s e p a r a t e l y a n d s u p e r -p o s e d . F r o m s u c h c o n s i d e r a t i o n s i t w a s p o s s i b l e t o d e r i v e a n e x p r e s s i o n f o r th e r a t i o o f t h e d r a g o f o n ep l a t e i n th e p r e s e n c e o f a n o t h e r t o t h e d r a g o f t h i s p l a t e a l o n e i n t h e t u n n e l . F o r t h e p a r t i c u l a r c a s e w h e nb o t h p l a t e s w e r e in t h e s a m e p l a n e , t h e b l o c k a g e f a c t o r o f o n e p l a t e , as d e r i v e d f r o m t h e c h a n g e i n d r a go f t h e o t h e r , s h o u l d h a v e b e e n t h e s a m e a s t h e b l o c k a g e f a c t o r o f t h e s a m e p l a t e , a s d e r i v e d f r o m t h ep r e v i o u s s i n g l e- p l a t e m e a s u r e m e n t s i n t h e p r e l i m i n a r y p r o g r a m m e . I f t h i s w a s f o u n d t o b e t r u e t h e n . i tw a s a r g u e d , t h e i n it i al a s s u m p t i o n s w e r e v a li d a n d t h e m e t h o d c o u l d b e u s e d t o i n v e s ti g a t e th e b l o c k a g ef a c t o r s w h e n t h e p l a te s w e r e n o t c o p l a n a r . T h e t h e o r e t i c a l b a s is o f th e m e t h o d is d e s c r i b e d i n A p p e n d i x B .

3.2. Th e M ea su remen t s .A p l y w o o d p l a t e 2 6 in . w i d e a n d 1 3 i n . h i g h ( 6 6 x 3 3 cm ) c h a m f e r e d a r o u n d t h e p e r i m e t e r a t th e r e a r ,

w a s m o u n t e d o n t h e b a l a n c e w i t h i n 1 /8 in . ( 3 ra m ) o f t h e r o o f , n o r m a l t o t h e w i n d d i r e c t i o n . T h i s p l a t ew a s u s e d t o m e a s u r e t h e b l o c k a g e f a c t o r o f a n i d e n t i c a l p l a t e n o r m a l t o t h e f l o o r , o v e r a r a n g e o f d i s t a n c e su p s t r e a m a n d d o w n s t r e a m o f t h e u p p e r p l a t e. T h e m e t h o d is d es c r ib e d i n d e ta i l in A p p e n d i x C .

T h e u p p e r p l a te , t h u s c a l ib r a t ed , w a s t h e n u s e d t o d e t e r m i n e t h e c o r r e s p o n d i n g b l o c k a g e f a c t o rs o fo t h e r p l a t es o f v a r y i n g s iz e s a n d h e i g h t / b r e a d t h r a ti o s . T h e n a n o p e n g r i d s t r u c t u r e ( o p e n a r e a r a t i o 0 -4 6)w a s u s e d i n s t e a d o f t h e l o w e r p l a t e a n d i ts b l o c k a g e f a c t o r m e a s u r e d o v e r t h e s a m e r a n g e o f p o s i t i o n s .T h e o p e n g r i d s t r u c t u r e w a s a u g m e n t e d b y a n i d e n t i ca l s t r u c t u r e w i th c o n n e c t i n g b a r s t o f o r m a n o p e nbo x s t r u c tu r e ( F ig . 5) a nd th i s w a s t e s t e d in t he s a m e w a y .

3.3. Discussion of Results.A s d e s c r i b e d i n A p p e n d i x C o n e o f th e s t a g e s i n t h e m e a s u r e m e n t o f t h e b l o c k a g e f a c t o r o f a p l a t e i s


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t h e m e a s u r e m e n t o f i ts d r a g i n t h e t u n n e l . A f t e r t h e m e a s u r e m e n t o f th e b l o c k a g e f a c t o r it i s p o s s i b let o c o r re c t t he d ra g c oe f f i c i e n t t o a f r e e -a i r va l ue . The u ppe r g ra ph i n F i g . 6 show s how t h e c o r re c t e d d r a gc o e f fi c ie n t s o f a s er ie s o f w a l l - m o u n t e d p l a t e s v a r i e d w i t h t h e i r h e i g h t t o b r e a d t h r a t io . T h e d o t t e d l in ec o m p a r e s t h e d r a g c o e f f ic i en t s o f c e n t r a l l y - m o u n t e d p l a te s * h a v i n g t h e p r o p o r t i o n s o f t h e f l o o r - m o u n t e dp l a t e a n d i ts i m a g e i n t h e f l o o r . T h i s s h o w s t h a t t h e d r a g c o e f fi c ie n t s o f ta l le r g r o u n d - m o u n t e d p l a te s a r ec o m p a r a b l e w i t h c e n t r a l l y - m o u n t e d p l a te s b u t a s I r m i n g e r a n d N o k k e n t v e d 3 s u g g e s te d t h e d r a g c o -e f fi ci e nt s o f v e r y b r o a d f l o o r - m o u n t e d p l a t e s m i g h t w e l l t e n d t o a c o n s t a n t v a l u e.Th e l ow e r g ra ph i n F i g . 6 show s t he va l ue s o f no, t he b l oc k a ge fa c t o r i n t he p l a ne o f t he p l a t e , fo r wa l lm o u n t e d p l a te s o f d i f fe r i n g a s p e c t r a t io s . T h e v a l u e s p l o t t e d a s c ir c le s w e r e e v a l u a t e d f r o m b a l a n c em e a s u r e m e n t s b y l i n e a r e x p re s s i o n s d e r i v e d in A p p e n d i x B . H o w e v e r t h e a r e a s o f th e p l a t e s t e s te d v a r i e do v e r a r a n g e o f n e a r l y 5 :1 s o t h a t s o m e p o i n t s w o u l d b e a f fe c te d m o r e t h a n o t h e r s b y t h e n o n - l i n e a re f fec t s e xpe r i e nc e d by l a rge p l a t e s . S i nc e t he va l ue s o f no c a l c u l a t e d i n t h i s w a y va r i e d so l i t t le ove r t her a n g e o f a s p e c t r a ti o s f r o m 1 /3 t o 3 , i t se e m e d r e a s o n a b l e t o e x p e ct t h e m a g n i t u d e o f th e n o n - l i n e a r i t yt e r m s a l s o t o v a r y l i t tl e w i t h a s p e c t r a ti o . T h e m e a s u r e d v a l u e s o f n o w e r e m o d i f i ed b y a d d i n g v a r y i n ga m o u n t s c o r r e s p o n d i n g t h e t e r m 1 . 1 2 C D S I C wh i c h e xp re s se d t he non- l i ne a r i t y fo r b = 2h p l a t e s ( seeF i g . 3 ). T h e m o d i f i e d v a lu e s o f n o w e r e t h e n c o n s i d e r e d a s r e p r e s e n t i n g s m a l l - m o d e l c o n d i t i o n s f o r t h ev a r i o u s a s p e c t r a t i o s r e p r e s e n te d .T h e c o r r e c t e d v a l u e s a r e c o m p a r e d w i t h t h e b l o c k a g e f a c t o r s o f c e n t r a l ly m o u n t e d p l a t es r e p r e s e n t i n gt h e w a l l - m o u n t e d p l a t e a n d i ts i m a g e , w h e r e t h e b l o c k a g e f a c t o r n o i s t a k e n a s - 1/Cpbc. I t w o u l d s e e mt h a t s m a l l w a l l - m o u n t e d p l a t es w i t h a s p e c t r a t i o s f r o m 1 /3 t o 3 h a v e i d e n t i ca l v a lu e s o f no w i t h i n t h ea c c u r a c y o f t h e se e x p e r i m e n t s .O f pa r t i c u l a r i n t e re s t wa s t he e nc oura g i ng a g re e me n t be t we e n t he va l ue s o f nn , fo r t h re e p l a te s o fd i f f e r i ng s i ze bu t e a c h w i t h b = 2h , de du c e d i n one c a se f rom t he c ha ng e s i n d ra g o f a n up pe r p l a t e ont h e b a l a n c e , i n t h e o t h e r f r o m t h e m e a s u r e d d r a g c o e ff i ci e n ts o f th e p l a t e s a l o n e .

The fo rme r va l ue s , c o r re c t e d t o sma l l -p l a t e c ond i t i ons a ve ra ge d 2 .84 (a s s e e n i n F i g . 6 ) whe re a s t hel a t t e r we re r e l a t e d t o t he sma l l -p l a t e va l ue 2 .79 (F i g . 3 ) . Th i s a g re e me n t wa s f e l t t o i nd i c a t e t ha t t hea s s u m p t i o n s u n d e r l y i n g t h e t h e o r e t ic a l b a si s o f t h e m e t h o d w e r e s o u n d .T h e m e a s u r e m e n t s o f b l o c k a g e f a c t o r f o r a s e ri es o f w a l l - m o u n t e d p l a t e s o v e r a r a n g e o f d i s t a n ce su p s t r e a m a n d d o w n s t r e a m o f t h e p l a t e w e r e i n it i al l y d i ff i cu l t t o u n d e r s t a n d . W h e n p l o t t e d o n t h e b a s iso f a c tu a l a x i a l d i s t a n c e x f r o m t h e p l a t e t h e r e s e e m e d a r e m a r k a b l e s i m i l a r it y b e tw e e n b l o c k a g e f a c t o r sf o r d i f f er e n t p l a te s f o r d i s t a n c es u p s t r e a m o f t h e p l a t es , b u t w i d e d i s p a r i t y b e t w e e n v a l u e s d o w n s t r e a m o ft he p l a t e s . Th i s s e e me d su rp r i s i ng i f t he u ps t re a m e f fe c ts we re t o d e pe n d on p l a t e s iz e, s inc e t he me a ns i de (x / ~ ) o f t he p l a t e s i nvo l ve d va r i e d be t we e n 13 i n . a nd 22 .5 i n . (33 a nd 57 .1 c m) , a nd ye t t he up s t re a mre su l t s s e e me d t o be i n de p e nd e n t o f t he p l a t e s i ze . Af t e r tr i a l me t ho ds o f p l o t t i ng , it wa s foun d t ha t t heu p s t r e a m e f fe c ts v a r i e d a c c o r d i n g t o x a n d t h e d o w n s t r e a m e f fe c ts a c c o r d i n g t o x / \ , , ~ . Thi s sugge s t e dt h a t t h e u p s t r e a m n o n - d i m e n s i o n a l p a r a m e t e r w a s p r o b a b l y x/x//--C.

T o c o n f i r m t h is s o m e f u r t h e r t es t s w e r e m a d e i n th e N P L 1 3 f t x 9 ft t u n n e l , w h e r e x / ~ w a s 1 2 2 . 8 i n.(3 .12 m) ins tea d o f 80 .5 in . (2 .05 m) as in th e 7 f t x 7 f t tunn e l . Th e tes t s w ere ov er a l imi ted range ofd i s t a nc e s (be c a use o f t he sho r t wo rk i n g s e c t i on ) a nd on t w o p l a t e s i ze s on l y .

T h e r e s u lt s o f t h e c o m b i n e d m e a s u r e m e n t s a r e s h o w n i n F i g s. 7 a n d 8 .T o e l i m i n a t e th e c o m p l i c a t i o n o f t h e s l ig h t n o n - l i n e a r i t y a l r e a d y f o u n d i n v a l u e s o f n o ( a n d p r e s u m a b l ys i m i l a r ly p r e s e n t i n v a l u e s o f n ) v a lu e s o f t h e a t t e n u a t i o n f a c t o r n/no we re use d fo r p l o t t i ng . I t shou l d be

* T h e d a t a f o r c e n t r a l l y - m o u n t e d p la t e s w e r e d e r i v e d f r o m t a b u l a t e d r e s u lt s b y F a i l, L a w f o r d a n d E y r e 2.T h e p r e s e n t a u t h o r h a s f o u n d t h a t t h e s e t a b u l a t e d r e s u lt s c a n b e s u m m a r i s e d b y t h e e x p r es s i o n s :

a n d 'CDo = 1.103 +0 .01 98 (h/b+b/h) ( 4 )

- Cp,,c = 0.333 + 0.01735 ( h / b + b / h ) (5 )for 1/40 ~< h/b


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n o t e d t h a t F i g . 7 i n c l u d e s r e s u l t s f o r w a l l - m o u n t e d m o d e l s r a n g i n g f r o m p l a t e s w i t h 3 1 > h / b > > . 1/3, tot h e s in g l e g r i d a n d d o u b l e g r i d m o d e l s . B y l o g a r i t h m i c p l o t t i n g i t w a s f o u n d t h a t t h e p o i n t s w e r e b e s tr e p r e s e n t e d b y a c u r v e o f t h e f o r m

1 "l _ x / ~ 7 0 = e - ( ~ 2 x 2 / 4 c }

T h e o n l y t h e o r e t ic a l w o r k k n o w n o n t h e u p s t r e a m e ff ec ts o f b l o c k a g e i s t h a t b y A l l en a n d V i n c e n t i 4w h i c h r e l at e s to t w o - d i m e n s i o n a l m o d e l s . T h e a t t e n u a t i o n f a c t o r f o u n d b y t h e se a u t h o r s t a k e s t h e f o r m

n _ x / n o = 1 - c o th ( z ~ x / x / / - C ) + ( x / /- C / r c x ) (7 )

i n t h is c a s e x / ~ i s t h e h e i g h t o f t h e t w o - d i m e n s i o n a l t u n n e l . V a l u e s o f n _ , , / n o c a l c u l a t e d f r o m e q u a t i o n ( 7)d e c a y e d m u c h m o r e s l o w l y w i t h u p s t r e a m d i s t an c e ( - x ) th a n t h e p r e s e n t e x p e r i m e n t a l r e su l ts a n d h a v en o t b e e n p l o t t e d i n F i g . 7 . P e r h a p s t h e o r e t i c a l w o r k i n t h e f u t u r e w il l s h o w t h e l i n k b e t w e e n t h e p a r a m e t e r s( g x / 2 x / ~ ) a n d ( ~ x / x / ~ ) i n t h e t w o e x p r e s s i o n s . O n e o b v i o u s c o n n e c t i o n w o u l d s e e m t o b e in a t h e o r e t i c a ls y s t e m i n w h i c h t h e f l o o r - m o u n t e d m o d e l a n d f l o o r w e r e t r e a t e d a s a c e n t re l i n e m o d e l o f t w i c e t h e h e i g h t ,i n a t u n n e l o f t w i c e th e h e i g h t . F o r p r e s e n t p u r p o s e s , h o w e v e r , a n e m p i r i c a l s o l u t i o n w o u l d s e e m s u f fi c ie n t .

W i t h i n t h e a c c u r a c y o f t h e e x p e r i m e n t t h e r e s e e m e d s u f fi c ie n t d i s t i n c t i o n b e t w e e n r e s u l t s f o r t h e v a l u e so f b l o c k a g e f a c t o r d o w n s t r e a m o f d i f fe r i n g a s p e c t r a t i o p l a t e s t o m e r i t s e p a r a t e c u r v e s a s s h o w n i nF i g . 8 . T h e r e l a t iv e l y r a p i d a t t e n u a t i o n f o r s u c h p l a t e s in t h e d o w n s t r e a m d i r e c t i o n m u s t b e c o n n e c t e dw i t h t h e m i x i n g e ff e ct d u e t o t h e s t r o n g t u r b u l e n c e o f l a r g e s c al e in t h e w a k e o f t h e p l a t e s.

I n F i g . 9 it w il l b e s e e n t h a t n o s u c h a t t e n u a t i o n w a s p r e s e n t b e h i n d t h e o p e n g r i d m o d e l s , w h e r e t h et u r b u l e n c e s c a le w ~l~ o b v i o u s l y m u c h s m a l l e r a n d r e l a t e d t o t h e m e s h s iz e a n d t h e w i d t h o f t h e b a r s .I n t h i s f igu r e t he o r ig in f o r p lo t t i ng the b loc ka g e f a c to r s f o r t he do ub l e g r id m ode l w a s a n e f f e c t ive pos i t i on ,a t d i s t a n c e s f r o m e a c h g r id p l a n e i n v e r s e ly in p r o p o r t i o n t o t h e d r a g s o f t h e t w o c o n s t i t u e n t p l a n e g r i d sw h e n i n t h e a ss e m b l e d p o s i t i o n . T h e s e s e p a r a t e d r a g s w e r e d e d u c e d f r o m d i f fe r e n c e s b e t w e e n t h e d r a g so f a s i n g le g r id a n d t h e c o m p l e t e m o d e l . T h e e f fe c ti v e c e n t r e w a s a b o u t o n e - t h i r d o f t h e o v e r a l l d e p t ho f t h e m o d e l f r o m t h e f r o n t f a c e .

T h e d o w n s t r e a m s e c ti o n o f t h is g r a p h c o u l d n o t b e p l o t te d o n F ig . 8 fo r w a n t o f a n a r e a p a r a m e t e rx / ~ a p p r o p r i a t e t o t h e w a k e d i m e n s i o n s . T h e u p s t r e a m s e c t i o n f i t t e d F i g . 7 e x a c t l y w i t h t h e e s s e n t i a ld i f f e r e nc e tha t no w a s on ly 1 .28 .

I t i s i n t e r e s t i n g t o c o n s i d e r t h e g r i d m o d e l s a s b a r s m o u n t e d i n t h e f r e e s t r e a m ( a s d i s t i n c t f r o m t h ew a l l - m o u n t e d p l a t e s c o n s i d e r e d s o f ar ). C oo f o r t h e s i n g le g r id , b a s e d o n t h e f r o n t a l a r e a , w a s m e a s u r e d a s1 .6 9. F r o m e q u a t i o n (4 ) i t is k n o w n t h a t t h i s d r a g c o e f f i c ie n t a p p l i e s t o t h i n r e c t a n g u l a r p l a t e s o f a s p e c tra t i o 29 .6 . Al te rna t i ve ly , s ince no = - l / C p b c f o r t h i n p l a t e s, a b l o c k a g e f a c t o r o f 1 .2 8 c o r r e s p o n d s t o ab h s e p r e s s u r e c o e f fi c i e n t o f 0 .7 8 , w h i c h f r o m e q u a t i o n (5 ) ap p l i e s t o a p l a t e o f a s p e c t r a t i o 2 5 "8 . T h u s o nt h e e v i d e n c e o f b o t h d r a g c o e f f ic i e n t a n d b l o c k a g e f a c t o r t h e o p e n l a t ti c e g r i d b e h a v e s l i k e a t h i n f i a t p l a t eo f a s p e c t r a t i o r a t h e r l e s s t h a n t h e i n f i n it e v a l u e u s u a l ly a s s u m e d .

I t is i n t e r e s t in g t o n o t e t h a t t h e b l o c k a g e f a c t o r f o r th e c o m p l e t e g r id m o d e l i s a l m o s t u n c h a n g e d e v e nt h o u g h s o m e o f t h e d r a g o n w h i c h i t is c a l c u l a te d h a s b e e n s e r i o u s l y af f e c te d b y s h i e l d in g f r o m t h e u p -s t r e a m e l e m e n t .

I t h a s b e e n e m p h a s i z e d t h a t t h e d i s t i n c t i o n b e t w e e n t h e o p e n l a t ti c e m o d e l a n d t h e s o l id p l a t e s w a s t h a tt h e o p e n a r e a r a t i o w a s s u f f ic i e n tl y h i g h ( 0.4 6) f o r t h e l a t t ic e m o d e l t o b e c o n s i d e r e d a s i n d i v i d u a l l o n g b a r s .F o r a l a t t ic e m o d e l w i t h a m u c h h i g h e r o p e n a r e a r a t i o i t is p o s si b l e t h a t t h e f l o w a s s o c i a t e d w i t h t h ei n d i v i d u a l b a r s c o u l d b e c o m e m o r e n e a r l y t w o - d i m e n s i o n a l , s o t h a t t h e v a l u e o f n o w o u l d l i e s o m e w h e r eb e t w e e n t h e m e a s u r e d 1 .2 8 a n d a t h e o r e t i c a l , b u t i m p r o b a b l e , 0 . 9 4 f o r t h e t w o - d i m e n s i o n a l c a s e( C p b ~ = - 1 - 0 8 ) . U n d o u b t e d l y a l s o , a s t h e o p e n a r e a r a t i o d e c r e a s e s t o w a r d s z e r o n o w i ll ri s e t o w a r d s2 .7 9. F o r a l l o p e n a r e a r a t i o s t h e u p s t r e a m b e h a v i o u r w i ll b e i n a c c o r d a n c e w i t h F i g . 7. T h e d o w n s t r e a mb e h a v i o u r w i ll b e i n t e r m e d i a t e b e t w e e n t h a t r e p r e s e n t e d b y F i g . 9 a n d F i g . 8 i f t h e o p e n a r e a r a t i o isl es s t h a n 0 -4 6, b e in g g o v e r n e d b o t h b y t h e o p e n a r e a r a t i o a n d t h e s i ze o f t h e m e s h .


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T h u s i t w o u l d s e e m r e a s o n a b l e t o u s e a b l 0 c k a g e f a c t o r n o o f a b o u t 1 -2 8 f o r a n y o p e n l a tt i ce m o d e lw i t h a n o p e n a r e a r a t i o o f a b o u t 0 .4 o r m o r e c o n s i s t in g o f th i n e l e m e n t s , c a l c u l a ti n g t h e b l o c k a g e c o r r e c t -i o n o n t h e m e a s u r e d d r a g o f t h e w h o l e m o d e l . T h i s o ff e rs a m o r e a t t r a c t i v e m e t h o d t h a n t h e u s e o f as e p a r a t e b l o c k a g e f a c t o r f o r t h e s h i e l d e d e l e m e n t s c o u p l e d w i t h v e l o c i t i e s r e d u c e d i n a r a t i o o f o t h e re mp i r i c a l sh i e l d i ng fa c t o r s , a s s e e m e d l i ke l y be fo re t he se t e s t s we re ma d e .

4. Conclusions.F o l l o w i n g t h i s i n v e s t i g a ti o n , t h e a u t h o r c o n c l u d e s t h a t :(1 ) M a s k e l l ' s w a k e b l o c k a g e c o r r e c t i o n s f o r a m o d e l s u b j e c t t o s e p a r a t e d f l o w a p p l y r e g a r d le s s o f th ep o s i t i o n o f t h e m o d e l r e l a t iv e t o t h e t u n n e l a x is .(2 ) T h e s e c o r r e c t i o n s n e e d o n l y m i n o r m o d i f i c a t i o n f o r n o n - l i n e a r i t y e v e n w h e n t h e c o r r e c t i o n o n d r a ga pp roa c he s 100 pe r c e n t.(3) Th e wa k e b l oc ka ge e f fec t e xpe r i e nc e d by a s e c ond m ode l due t o t he p re se nc e o f a c o -p l a n a r m ode l i na t unn e l o f c l o se d s e c t i on is the s a m e a s t ha t e xp e r i e nc e d by t he f i r s t mo de l a nd vice versa.

(4) I t is pos s i b l e t o supe rp ose t he a c t ive a nd pa s s i ve wa ke b l oc ka ge e f fec t s due t o t w o o r m ore m ode l si n t h e t u n n e l a t t h e s a m e t i m e , p r o v i d e d e a c h m o d e l i s w e l l c l e a r 0 f t h e w a k e o f t h e o t h e r s. O n t h i s b a s ise q u a t i o n s h a v e b e e n d e r i v e d f o r th e o v e r a l l w a k e b l o c k a g e e f f ec ts o n t w o m o d e l s i n th e t u n n e l a t t h es a m e t i m e . ( A p p e n d i x B ) . A m e t h o d o f d e t e r m i n i n g t h e r e l e v a n t b l o c k a g e f a c to r s f o r t h i s p u r p o s e i s a l s od e s c r i b e d ( A p p e n d i x C ).(5 ) W a l l - m o u n t e d r e c t a n g u l a r p l a t e s w i t h h > b t e n d t o b e h a v e f o r d r a g p u r p o s e s a s c e n t r a l l y - m o u n t e dp l a t e s w i t h s id e s in t h e r a t i o 2 h : b, p r o v i d e d t h e w a l l b o u n d a r y l a y e r is t h i n .

( 6 ) S m a l l w a l l - m o u n t e d r e c t a n g u l a r p l a t e s w h e r e h < 3 b ( a n d p o s s i b l y f o r h i g h e r v a l u e s o f h /b n o tt e s te d ) a ll h a v e t h e s a m e w a k e - b l o c k a g e f a c t o r s p r o v i d e d t h e w a l l b o u n d a r y l a y e r is t h in . L a r g e r p l a t e sh a v e s l i g h t ly r e d u c e d b l o c k a g e f a c to r s . I n t h e N P L 7 f t x 7 ft w i n d t u n n e l t h e v a l u e o f t h e w a k e b l o c k a g efa c t o r no fo r b /h = 2 w a l l -m oun t e d re c t a ngu l a r p l a t e s wa s found t o be no = 2 .79 - 1 .12 (CD S/C ).( 7 ) T h e w a k e b l o c k a g e f a c t o r f o r w a l l - m o u n t e d m o d e l s i n a n y p l a n e d e c r e a s e s w i t h d i s t a n c e a h e a do f t h e m o d e l . T h e a t t e n u a t i o n f a c t o r a p p l y i n g t o r e c t a n g u l a r p l a t e s a n d l a tt i ce m o d e l s w a s f o u n d t o f it t h ee m p i r i c a l e x p r e s s io n

n- x/n o = e - (~2x2/4c)T h e a t t e n u a t i o n f a c t o r a t p l a n e s d o w n s t r e a m o f t h e m o d e l s i s p r o b a b l y r e l a t e d t o t h e s iz e o f th e i r w a k e sa n d i s c lo s e t o u n i t y f o r a c o n s i d e r a b l e d i s t a n c e b e h i n d o p e n l a tt i ce m o d e l s . E x p e r i m e n t a l v a l u e s o f t h isf a c t o r f o r s o m e w a l l - m o u n t e d p l a t e s a n d l a tt i ce m o d e l s a r e s h o w n i n F i g s . 8 , 9 .


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bC

CDCpCpbD

D 'hmn

PphPqRR '

SX

Z

Suffix cSuffix o

Suffix (+ x)Suffix ( - x)

Suffix

LIST OF SYMBOLSWidth of plateCross-sectional area o f working sectionDrag coefficient D/qSPressure coefficient (p-P)/qSeparation-pressure coefficient (Pb - P) /qDrag of plate A alone in tunnel for dynamic pressure qDrag of plate A in presence of plate B for dynamic pressure qHeight o f plateBlockage factor in general : blockage factor for plate ABlockage factor in general : blockage factor for plate BSurface pressure at any position on model

Equation 1

Surface pressure at separalion poim. I:~asc-pressurc for thin plalc normal to streamStatic pressure in undisturbed streamDynamic pressure o f undisturbed streamDrag of plate B alone in tunnel for dynamic pressure qDrag of plate B in presence of plate A for dynamic pressure qArea of model chosen to define drag coefficientDistance from plane of model, positive downstreamDistance from floor or roofCorrected for blockageIn own plane (x = o)At distance x downstream of own planeAt distance x upstream of own planeValue which would have obtained in the absence of tunnel walls


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No. Author(s)1 E.C. Maskell . . . .

R. Fail, J. A. Lawford and ..R. C. W. Eyre

J. O. V. Irminger and ..C. H. R. Nokkentved

4 H. J. Allen and W. G. Vincenti

5 C.F. Cowdrey . . . . . .

REFERENCESTitle, etc.

A theory of the blockage effects on bluff bodies and stalled wingsin a closed wind tunnel.R. & M. 3400, November, 1963.

Low speed experiments on the wake characteristics of flat platesnormal to an air stream.

R. & M. 3120, June, 1957.Wind pressure on buildings

series).Chapter 4 Kopenhagen, 1936.(experimental researches second

Wall interference in a two-dimensional-flow wind tunnel withconsideration of the effect of compressibility.

NACA Report 782, 1944.The application of Maskell's theory of wind-tunnel blockage to

very large solid models.NPL Aero Report 1247, October, 1967.

APPENDIX AThe Separation o f Genuine W ak e Blockage Ef fec ts f rom Speed M easurement E rrors .

The presence of a large model in a wind tunnel will produce genuine wake-blockage effects. It may inaddition affect the static pressure in the region of wall-pressure tappings used to measure wind speed(e.g. in a contraction ahead of the working section). Thus unless steps are taken to eliminate errors in themeasurement of tunnel speed, genuine wake blockage effects cannot be studied separately.For models in the balance plane of the NPL 7 f t x 7 ft tunnel the approach dynamic head had previouslybeen measured in terms of the pressure difference between sets of static holes at each end of the 7.15:1contraction. For the present tests three further static holes were fitted on the contraction wall fillet atpositions where the sectional area was about 12, 18 and 28 per cent above that at the end of the con-traction. The pressure difference between each of the new holes and the upst ream set of holes was measuredboth in the empty tunnel and with a floor-mounted 20 in. x 40 in. (50.8 x 101:6 cm) plate normal to thetunnel axis at 2 ft (61 cm) downstream of the end of the contraction, representing the extreme limits ofany possible interference effects. The ratios of each of the pressure differences with the board in place tothe corresponding pressure differences with the tunnel empty were evaluated. Even for the combinationusing the nearest of the new holes the ratio was found to be within 0.5 per cent of unity. On the evidenceof these measurements the downst ream hole was selected for use with the holes upstream of the con-traction to monitor the approach dynamic head in all the subsequent experiments on blockage. In thisway it was ensured that errors in measuring the approach dynamic head were not mistaken for genuineblockage effects.


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A P P E N D I X BW a k e B l o c k a g e I n t e r f e r e n c e B e t w e e n T w o M o d e l s .

(a ) P l a t e - t y p e m o d e l s.L e t u s c o n s i d e r a w i n d t u n n e l w i t h a c lo s e d s e c t i o n o f a r e a C , h a v i n g t h i n b o u n d a r y l a y e r s a n d o n e

b a l a n c e , fo r t h e s a k e o f a r g u m e n t a r o o f - b a l a n c e a s i n t h e 7 f t x 7 ft t u n n e l . L e t t h e t u n n e l b e r u n a t ac o n s t a n t a p p r o a c h d y n a m i c h e a d q ( fa r a h e a d o f t h e m o d e ls ) .L e t u s s u p p o s e t h e r e a r e t w o f l a t p l a t e s a l w a y s m o u n t e d n o r m a l t o t h e w i n d w h o s e f r e e - s t r e a m d r a g sf o r a d y n a m i c h e a d q a r e D ~ , R ~o . I f t h e s e a r e p l a c e d s e p a r a t e l y o n t h e b a l a n c e t h e d r a g r e c o r d e d w i l l b eD a n d R , d u e t o t h e i r r e s p e c t iv e b l o c k a g e f a c t o r s m o a n d n o ( w h e r e t h e s u ff ix o d e n o t e s i n i ts o w n p l a n ei . e . , x = 0 f rom the pla t e )?

I f t h e f ir s t p l a t e is fi x ed t o t h e r o o f b a l a n c e a n d t h e s e c o n d m o u n t e d n o r m a l t o t h e f l o o r a t a d i s t a n c ex u p s t r e a m , t h e d r a g o f t h e r o o f - m o u n t e d p l a t e w i ll i n c r e a s e to D ' d u e t o i t s o w n b l o c k a g e f a c t o r m oa nd t o t he b l oc k a ge f a c t o r o f t he o t h e r p l a t e n (+ x ), t he l a t t e r r e p r e se n t i ng t he b l oc k a ge e f f ec t o f t he se c ondp l a t e a t a d i s t a n c e x d o w n s t r e a m o f i ts o w n p l a n e ( s e e F i g. 4 ). S i m i la r ly t h e d r a g o f th e f l o o r - m o u n t e dp l a t e w il l i n c r e a s e t o R ' d u e t o i ts o w n b l o c k a g e f a c t o r n o a n d t o t h e b l o c k a g e f a c t o r o f t h e r o o f - m o u n t e dp l a t e , m ~_x) a t a d i s t a n c e x u ps t r e a m o f it s own p l a ne .

W e m a y c a l c u l a t e t h e s e e f fe c ts f r o m M a s k e l l ' s e x p r e s s i o n s a s l o n g a s w e a s s u m e t h e p r i n c i p le o f s u p e r -p o s i t i o n t o h o l d f o r p l a te s e a c h o u t s i d e t h e w a k e o f t h e o t h e r .F or a s i ng l e p l a t e i n t he t unne l :

D = D~o (1 + m o D / q C ) ( 8 )R = R ~ ( l + n o R / q C ) . (9 )

W i t h t w o p l a t e s in t h e t u n n e l :

R e - a r r a n g i n g ( 8) ,

a n d f r o m ( 1 0)

Di v i d i ng ( 13 ) by ( 12)

D ' = D~o (1 + to o D ' / q C + n ( + x ) R ' / q C )R ' = R ~ (1 + n o R ' / q C + m ( _ x ) D ' / q C ).

D ( 1 - m o D ~ / q C ) = D ~o

D' (1 - m o D ~ / q C ) = D ~ (1 + n ~+ x) R ' / q C ) .

D ' / D = 1 + n { + x ) R ' / q C .

( 1 o )( 1 1 )

(12)

{ 1 3 )

(14)t i t is c o n v e n n o n a l t o c o n s i d e r b l o c k a g e e f fe c ts i n t e r m s o f a r is e in u p s t r e a m d y n a m i c p r e s s u r e f r o m

q a n d q c. I n t h e p r e s e n t t r e a t m e n t t h e a u t h o r h a s f o u n d i t m o r e c o n v e n i e n t t o c o n s i d e r q u n c h a n g e d a n dt h e d r a g i n c r e a s e d f r o m D oo t o D b y t h e p r e s e n c e o f th e t u n n e l w a l ls . T h e t w o s y s t e m s a r e l i n k e d b y t h e

D Do~e xpr e s s i ons C Dc - - - -qcS q S "

10


12/22

Similarly,

Hence

This may be re-arranged to give

In an alternative form

R ' / R = 1 + m ( _ x ) D ' / q C .

= ' CD ' / D 1 + n(+ x ) (R + m (_: ,) RD / qC ) / q .

D ' 1 + n(+x) R /q C--D - 1--n(+ x) m(- x) RD /q 2C2"

(15)

(16)

(17)

( D ' / D ) - 1 ( 1 8 a )n(+x) R /q C = 1 + (D ' /D) m(_x) (D/qC)

or when the lower plate is downstream of the upper plate,( D ' / D ) - 1

n(-x ) R/q C = 1 +(D ' /D) m(+x) (D/qC)" (18b)

These relate the increase in drag of the balance-mounted plate, when the second plate is introduced, tothe measured drags of the plates placed in turn in the tunnel, and to the blockage factors of the two platesas each affects the other. This equation is most useful for determining the variation of the blockage factorof a model over a range of distances upstream and downstream.For the correction of wind-tunnel measurements a more convenient form is

Do~ 1 - n(+ x) m o R D / q 2 C 2D' (1+ n(+ x) R/ qC ) (1+ m o D / qC) (19)

I(b) Block- type mode ls .The above treatment for pairs of flat plates normal to the wind is only possible because the separation

drag (responsible for wake-blockage effects) is equal to the total drag of such models measured with abalance.For a model of rectangular-block form, arbitrarily inclined to the wind, the drag measured on a balanceconsists of the separation drag modified by drag components dependent on the lateral force and on thepressure field within the wake enclosing the model.

One can determine the separation drag coefficient approximately for such a model from a graph of themeasured drag coefficient versus the square of the lateral-force coefficient over a range of inclinations to thewind. Such a procedure is mentioned by Maskell t in connect ion with lifting aircraft models.However, Cowdrey5 has shown that the blockage effect of a single rectangular-block model, which isneither sufficientlydeep (in the wind direction) nor sufficiently inclined to the wind to cause re-attachmentof the separated wake on the model, is identical to that for the plat plate corresponding to the forwardface of the model bounded by the separation line.This fact enables the blockage correction on one such model in the presence of another to be calculatedwith reasonable accuracy.Consider the two flat plate models equivalent to such a pair of models.

11


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E qua t i ons ( 10 ) . ( 11 ) c a n be c om bi ne d i n t he f o r m

D 'D~ ( 1 - m 0 D o ~ / q C ) (1 - n o R ~ / q C ) - n ~+ ~) m (+ x ) R o D J q 2 C 2

1 - (n o - n I + x , ) R ~ / q Cor . i n coef f i c i ent form xvi th suf f i ces A. B for the tw o p la t es


14/22

For the first, equation (18a) gives1 + n(+x)R / q C

( D '/ D )I = 1 - n ( + x ) n ( - x ) R 2 / q 2 C 2 (21)

and for the second reading, equation (18b) gives( D , / D ) 2 = 1 + n t - x ) R / q C (22)1 - n(+x) n(-x) R 2 / q 2 C 2

leading to the useful result,tD__3_t = 1 + n( +x) R / q C (23)

D'2 1 + n(-x) R /q C "Initially by assuming that n(_ x~ ~ 0, an approximate value of n(+ x) was obtained. Then subst itution of thisvalue into equation (22) a better value of n-x) was obtained. This process was repeated, using each ofequations (21), (22) and (23) in turn to give values of n~+x) andn(-x ) which satisfied all three equations.

This procedure was repeated when the lower plate was moved into other pairs of positions each closerto the plane o f the upper plate. As the process continued the provisional graph of results made it possibleto make better estimates of the approximate values of n(_ x) and thus to shorten the iterative process.In this way a complete series of blockage factors was obtained for the identical pair of plates chosen.

One of these plates was used on the balance in all subsequent tests with a variety of other plates andmodels on the floor. From this stage onwards it was possible to cover the range of positive and negativevalues of x in single positions, and since m(+x), m~-x), and D / q C were all known for the calibrated plateequat ion (21) or (22), as appropriate, enabled values ofn~+x), n~-x) to be estbalished for each of the othermodels.It is worth emphasising at this stage that there is an implicit assumption that the area of tunnel con-taining the upper plate has the same approach velocity in the empty tunnel as that containing the lowerplate.* However, small discrepancies between roof and floor distributions can be nullified by the modi-fication of the value of the term D / q C , associated with the drag of the upper plate in equations (18a, 18b),in the ratio of the mean dynamic head at the upper plate to that at the lower plate. For this purpose themean dynamic head may be taken as ~ u z dz, where h is the height of a plate, and the integration covers

0

the position of each plate with the tunnel empty. This method has been found to give identical values ofdrag coefficients for floor mounted plates in a uniform stream and in a deliberately induced thick boun darylayer deeper than the model. Since the air flows over sharp-edged bluff models are not very sensitive toscale effects, precise wind speed setting is unnecessary so tha t time can be saved if values of D / q C andsuch terms are obtained from simultaneous readings of drag and dynamic head whenever steady con-ditions exist.

*A common, but not always detected source of maldistribution of velocity in a wind tunnel is theuneven choking of screens by dust, etc.

13


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14


16/22

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R . & M . N o . 3 6 4 9

Crown copyright 1970Published by

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