Correlation and Decay of Turbulence Produced by Various Grids in a Wind Tunnel

Citation

Atsumi, John Shoichi (1939) Correlation and Decay of Turbulence Produced by Various Grids in a Wind Tunnel. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yq2d-wt47. https://resolver.caltech.edu/CaltechTHESIS:12092024-180737116

Abstract

No abstract.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	(Aeronautical Engineering)
Degree Grantor:	California Institute of Technology
Division:	Engineering and Applied Science
Major Option:	Aeronautics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	von Kármán, Theodore (advisor) Millikan, Clark Blanchard (advisor)
Thesis Committee:	Unknown, Unknown
Defense Date:	1 January 1939
Record Number:	CaltechTHESIS:12092024-180737116
Persistent URL:	https://resolver.caltech.edu/CaltechTHESIS:12092024-180737116
DOI:	10.7907/yq2d-wt47
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	16910
Collection:	CaltechTHESIS
Deposited By:	Benjamin Perez
Deposited On:	11 Dec 2024 00:32
Last Modified:	18 Mar 2025 23:59

Thesis Files

PDF - Final Version
See Usage Policy.
56MB

Repository Staff Only: item control page

CORRELATION AND DECAY OF TURBULENCE PRODUCED BY VARIOUS GRIDS IN A WIND TUNNEL Thesis by Shoichi Atsumi In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Aeronautical Engineering California Institute of Technology Pasadena, California 1939 TABLE OF CONTENT S Acknowledgment 1 Summary 2 Introduction 4 Design of App a ratus and Equipment 7 Velocity Survey 10 Influence of Initial Turbulence 12 Measurements of Correlation and Decay of Turbulence 15 Results and Discussion 19 Conclusion 30 Appendix l Detail Description of the Various Parts of the Wind Tunnel 31 Entrance 31 Working Section 32 Exit Diffuser 33 Propeller and Lotor 34 Appendix II Hot Wire Ane mome ter and Electric Equipment 35 Hot-Wire Technique 38 Appendix III An a lyses of Exper i mental Res ults a. 39 Grid.= l½ in. Calculation of 'A...2 39 Calcul ation of ~ 40 Ca lculation o f Coefficient C in U . X u' = C ( M) sot. 41 Calculation of Coefficient Bin 1-S"d.. BC2 X L = • ( l-5ct) 42 Calculation of A a nd B 43 Calculation of L, :g: u'' and x_ using ~ A and B b. 44 Grid~ 1 in. Calculation of 'l\..2 45 J 46 Calc ulat ion o f Calculation of Coefficie n t C in U X S°C{. u' == c (M ) Calculation of Coefficient Bin L _ BC.a X ,-set. 47 ( 1-bcx) 48 Calculation of A 49 - • 2 Calculation of L, u -U I , and I'\.. ~·using A and B 49 Appendix IV Equation for De termin g A.2 50 Equ a tion for De terming d.. 51 Equation for u 51 Equa tion for Scale of Turbulence 52 Mat h ematical Deriva tion o f A 53 Ma thematical Derivation o f B 54 Equa tion for Scale of Turbulence 54 Equation for u u:, 54 E quation for A.2 54 u:, Appendix V Effect of Hot-Wire Length 55 INDEX IJ.1 0 TABLES 1. Dimensions of Grid for Producing Turbulence. 2. Survey o f Dynamic Pressure in the Working Section 3. Superposition of Two Types of Turbulence using Grids # 2 and f/-.r 3 . 4. Superposition of Two Types of Turbulence using Grids f/ 3 and # 4. 5. Superposition of Two Types of Turbulence using Grids l½ .in. and # 4. 6. Superposition of Two Types of Turbulence using Grids # 4 and // 3. 7. Superposition of Two Types of Turbulence using Grids #1 and #3. 8. Decay of Turbulence Produced by l½ in. Grid at U = 29.8 ft. per sec. 9. Decay of 'I 'urbulence P roduced by l ½ in. Grid at U = 38 ft. per sec. 10. Decay of Turbul ence Produced by l½ in. Grid at U = 53.5 ft. per sec. 11. Correlation of Turbulence Produced by li· in. Grid at U = 29.8 ft. per sec. 12. Correlation of Turbulence Produced by l½ in. Grid a t U = 38 ft. per sec. 13. Cor relation of Turbulence Produced by l ½ in. Grid at U = 53 . 5 ft. p e r sec. 14. Decay o f Turbulence Produced by 1 in. Grid at U = 29. 9 f t./sec. 15. Dec ay o f Turbulence Produced by 1 in. Grid a t U = 42.25 ft./sec. 16. Decay o f Turbul e nce Produced by 1 in. Grid at U ~ 59.7 f t./sec. 17. Correlation of Turbulence Produced by 1 in. Grid a t U = 29.9 ft ./s ec . 18 . Corre lation of Turb ulen ce Produced by 1 in. Grid at U = 42.25 f t./sec. I NDEX TO FIGURES l. Schematic Diagram of the Wind Tunnel. 2. Sup erposition of 'l'wo Types of Turbulence Produced by Grids .# 2 and # 3 . 3. Su perposition o f Two Types of Turbulence Produced by Grids # 3 and # 4. 4. Superposition of Two 'l'ypes o f Turbulence Produced by Grids l ½ in. and # 4. 5. Superposition of Two Types of Turbulence Produced by Grids #4 and # 3. 6. Super position of Tw o Types of Turbulence Producec by Grids f/ 1 and ;,13. 7. Decay o f Turbulence Produced by l½ in. Grid. 8. I ncrease of 10. Variation of R IC with ~ . lV1 with Y for Different Values of jX • 2 Wind Spe ed = 29.8 ft ./sec. Grid = 1-½ in. 11. Correlation curve at X = 38.6 u == 29 . 8 ft . /sec. 12. Corre l a tion curve at X u = 29 . 8 ft./ sec . M 14. = 51 M Corre l a t ion curve at X = 66. 4 M X Variation of L with 15. R2 vs y 13. fil . y u = 29.8 f t./sec. u = 2£) . 8 ft./sec. u = 29 . 8 ft./ sec . R2 == -2 y 16. Variation of R2 with Y for Different Values of~ I\1 • U == 38 ft ./sec. Grid = l ½ in. 17. Correlat i on c urve at X = 36.4 . u = 38 ft./sec. 18. Correl atj_on curve at 50 . 85 u = 3 8 ft./sec. 19. Correl a ti on curve at X 66. 4 . u ::: 38 f t /sec 20. Variation of L wit h ! 21. R 22. M X M= M = 2 vs u = 38 f t ./sec. y u = 38 ft./ sec. Y R.2 =-· 2 Vari ation of R2 with Y for Differ ent value s of! M• u = 53.5 f t ./sec . Grid = l½ in . 23 . Correlat i on curve at X = 34.7 u = 53.5 ft ./s ec. 24 . Correla ti on curve at u = Q3.5 f t . / se c . 25. 26. Correl ati on c urve a t lVi -=:- 66.2 Vari ation of L with x. 27. R Tuf X =: 50.85 M X u ::: 5 3 .5 ft . /se c . u = 53 . 5 ft ./sec. M 2 U = 53.5 ft. / sec . vs Y Y R2 c=. .2 28 . Increase of the Sc ale of Turbu l ence with ~ - 28 a . Sup erposition of Corre l ati on Curve Ta ken at X 29. Variat i on of ~ with X. 30. De c ay of Turbul ence Produc ed by 1 in. Gr i d 31. Variation 0 f /I.._ .,. 2 W _L-· th X• _ M 32 . • _._ i on V aria~ IVI L o f Corre 1 a ti on uurve wi th X in• U = 29.9 f t ./sec. 33 . M ('I • ]\ ; Grid = 1 in. V Variat i on o f Correlati on Curve wit h ~. M U = 42.25 ft./s ec. Grid == 1 in. = 51. 3 4. Increase of the Scale of Turbulence with ~ . Grid = 1 in. 35 . I nput Circuit for Corre l a tion Amp lifier. 36. Pr eamp li f ier Di agr am . 37. Power Ampl ifier Di a gr am . 38 . Ef f ect of Hot~Wi r e Length. INDEX TO PHOTOS 1. Wind Tunnel. 2. Front View of the Entrance. 3. Working Section. 4. Diffuser and Propeller with Motor. 5. Potentiometer, Hot-Yvire .Amplifi er, and Galvanometer. 6. Hot Wire behind the Turbulence Producing Grid for the Measurements of the Decay. 7. Upper portion of the Traversing Mechanism. 8. Lower Portion of the Traversing Mechanism. 9. 1 inch Grid. 10. Grid #1. 11. Grid #3. 12. Grid #4. 13. Grid #2. NOT A'l1 ION u' ~ == Constant. A = y-L B = 1 dL u' dt = Constant. B.P. = Barometer pressure. f = Frequency of vibration. I= Intensity of altern ating current out put. L f = 00 R dy = Scale of turbulence. 0 M = Mesh l ength of a grid. R1 = Longitudinal correlation factor. R2 = Transverse correlation f actor. R = ulu2 --· u2 RC = Comp ensating resistance in ohms. T = Te mperature in de gree Centigr ade. t = Time. u ~ Velocity fluctuations. u'::::: Root mean square of velocity fluctuations. U = Mean stream veloc~ty . u' U Intensity of turbulen ce. X Distance fro m a grid. Y = r == Dis ta.nee b etween t wo hot wires. 1 ~ [d::: L: [d::~ Lo 21 == Dens i t y o f alcohol. , = Kinema tic viscosity. e Density of .air . == L::. = Amplitude o f vibr a tion s. -1- ACY::NO'i"J LEDGMENT The aut hor wishes to thank Drs. Th. de Karman and Cla r k Millikan for t h eir c onstant interest and guidance in t he exp erimental program, Drs. A. L. Klein and E. E. S echl er f or t heir many helpful suggestions on th e de sign of t he appar·atus, and Ivlr. Carl Thiele for his help in using the hot-wire anemomet er - 2- SUMMARY There is 8. di screp t~ncy between the assumptions made by Th. de Karman and G.I. Taylor in t h eir Statistical Theory of Isotro p ic Turbulence. The present tests were underta k en to invest iga te t h e correl s. tion and decay of t he turbule n ce p roduce d by t ne grid s o f various mesh leng ths so th a t t h e assumptions i~ the theorys could be ev a lu a te d . As no wind tunnel wa s suitable for t h is work, a new tunnel wit h 12 feet worl::ing section was built. The en- tr a nce was especially d e signe d to maintain ::i u n i f orm f low and to reduce an initial turbulence in the working section. Three t y pes of me a surements were made: 1. Measurements wer·e ma de with · a hot wire a nemomete r to d et e rmine t h e decay of turbulence at various mean speeds of air s tream. 2. Traverses were made with two hot wires to deter- mine the scale or " a verag e eddy size" at various p ositions behin d t h e g rids. 3. The initial turbulence inten sities of various de g re e s was p roduced u ps tream o f t h e g rids of various me s h l engths. Measureme nts were ma de to determine the effect of t b e i n iti a l tu r bulence on t he turbu len c e p roduce d by the p rids. The results of the test gave the following facts: 1. The decay of tur·bulence is indep endent of me an speeds of air stream and i s p ro1) ortional to the ne gative - 5 fi.. power of x. M 2. The scale or "aver a ge eddy size" increases downstream. The i ncrease of t h e scale is p ro p ortional to t h e l-5o( power of X. - 3. iVl The scale at a fixed point is nearly independeent . of mean speeds of air stream. 4. u'l\.2 The quan tity YL is constant. 5. ( 5-tAB) X -r u 6. 7. u' is proportional to dL dt 8. The effect of a s me.11 a mount of large scale tur- bulence on turbulence produced by the g rids was ne g lig ible. -4- INTRODUCTI ON Turbulence involves in many ensi n ee ring problems con cern ing a moti on o f f luid, namely mo tion o f a body, dissipation o f energy , mixing , evap oration, and heat transfer, yet comp lete solutions o f t :r-1ese p roblems c a n only be achieved b y solving first the mechan ism of turb ulenc e itself. Unfo rtunate l y t he me chanis m o f turbulence is extre me ly compli c atedin it s nature so that the mathematic a l t reatment is very difficult. Howev e r, in recent y e ars it bec c me t he fo cus o f the flui d dynamicists to solve st a ti s tically the proble m of isotropic turbulence. It has been lrnm-:m that when a ir f l ows past a g rid, a conside rable a mount o f vortices is for med in the wake of the wires or rods o f t h e g rid and is carri e d down s t re am. At sufficiently f a r downstream the re- g ular c h aracter of the vortices disa pp ears due to t he mixing and interming ling of the vortic es , and velocity and velocity f luctuations a pp e a r to be uni for ml y dis tr ibuted over t he cross section of t h e stre am . I n this field of fluctu a ting velocity, t he veloci ty f luctua tions are st atistically t h e s ame a t ev e r y p oin t over t he cros s section of t h e stream; in 6th br words , t h e root me a n square o f t h e v el ocity - 5- fl u ctua tions is ind epe n d e n t o f a d irecti on over t h e cross section. If a n ob server moves wit h t h e me a n a ir strean: , t h e vel ocit y f l u ctuations ar e t h e s a me re gardless o f directions over t h e wh ole cross section of the stre a m. This type of turb ule n t motion is c a lled "iso- trop ic turbule n c e . 11 I n the fiel d o f isotro p ic tur bulence exists a definite corre lati on b e t we e n tw o points s epara ted b y a Y.:novm d is t a n c e . ll,l/2 R~2 = - - u.2 where R Correla tion factor is d efin ed as 1 is c a lled the long~ itud i nal cor r ela tion factor, while R t h e tr ansve rse correla tion f a ctor, a nd 2 u ar e velocit y fluctu a tions. Correlation factor 2 b et ween t wo points is t h en a function o f t h e distance 1 and u s e p a r a ting t h e m, a n d i s a unity when t wo points coincide eac h other, and i s zero when t h e d istance is far ap a rt so t hat no relat ion be t ween t wo p oi n ts exis t s. Correla - tion factor between t wo p oints in a turbulent f low c a n be ob tai n ed by rneans o f a hot wire a_ne mome ter . In a strict sense, correlation fa c to r betwee n t wo s h ort and pa r a l le l lines inste ad o f two points i s me c,. su r ed by means of a hot wire a nemometer, s i nce each hot wire h a s a finite leng t h . Th e co r r e l a tion curve s correspond fairly well to the erro r l aw . The widt h of eac h correlation curve g ives -6- an i d ea of t h e average size of t h e eddies. Hence the comparison of correlation curve s observed under dif f erent conditions give a relative me asure of the tlphysical size" of t he eddies. The average size of the eddies in the stream is called t h e scale of turbulence. Statistical theories of isotropic turbulen-0e were developed indep endently by G.I. Taylor, Th. de Karman, a nd H.L. Dr yd en with their own assumptions, y et a complete exper i menta J_ proof of t h e assumpt ion s ha s been lac king because of t he difficulties involving in building an ac cu rat e measuring appar a tus and of t h e d iff iculty in exp erimen tal techn ique. The author investigated t h e decay and scale of turbulence produced by g rids in a s p e c ial ly constructed tunnel by means of a hot-wire anei-nometer so t hat the exper i mental evaluation of the assump tions made by de K.arman and Tay lor could be mad e . The resu lts for the d ecay and correla tion with various mean speeds of air stream as well as the equa tions for the decay, scale and A. were obtained. The discussion on the validity of t h e assumptions made by de Karman and Tay loi" is also included in this thesis. -7- DESIGN OF APP ARATUS AND EQUIPMENT When this work was started , t wo design problems had to be solved: a wind tunnel and a traversing mechanism which would carry hot wires for the mea sure ments of correlation of turbulence. A gre a t deal o f thought was g iven to the desig n of t he tunnel in order to obtain const ant and uniform velocity distributions with a turbulence level as low as p ossible and to the desi gn o f the traversing rnechanism which would not c a use much air d isturbance around it. ' ifith these in mind, it was decided to build a wind tunnel of Eiffel type wit h t h e working section of 12 ft. long and the cross section approxima t e ly 20 i n . s quare. (See Fig . 1 and for detail see Appendix 1.) To take care t h e acceleration of air stream in the working section because of the incre as e in the boundary lay e r thickness along· the inside walls, the two side walls . were made adjustable. The tr aversing me chan ism was mounted on a pair of st e el r ai ls under t h e tunnel, and the upper p ortion of the me chani sm was inserted into the working section throug h a slot of 2 in. wide running along the bottom wall of the tunnel. The o p ening o f t he slot was closed with a movable belt made of a shim sheet wh ich was supported by four rollers. Hence t he traversing mechanism could be moved -8- to any desired position alonE the working section of the tunnel. In order to obtain a constant and uniform flow in the working section, the design of the entrance met a great difficulty. However, by making the entrance with a contraction ratio in area of 16 to 1 and by designing the entrance in such a way that acceleration of air flow be constant, the difficulty was overcome. ( For· detail see Appendix 1.) At the beginning of the entrance were placed two layers of cheese cloth which served to damp out the large eddies gave a uniform flow of very fine scale turbulence which damped out before the air reached the worldng section. The cheese cloth caused some loss of kinetic energy, however this loss was well compensated by obt aining a steady flow with a low turbul ence level in t he working sectj_on.Behind the working section was placed a diffuser into which were built the vane s which s erv ed to e l iminate the rotary compenent of velocity induced by t he t wo bladed wooden prope ller. The pro- peller wa s mounted directly on the s ha ft of a 4 h. p . D.C. motor. The tunnel vibration s we re e l iminated by sep aratj_ng the last portion of t h e tunnel, where the propeller was inserted, from t he rest of the tunnel. The gap wa s -9- covered wit h a el a stic rubber b a nd . The v a rious g rids listed in Table 1 were used to produce t111"bulence. Bec aus e of slight deviation in mesh size, a mean value o f t he mesh size wa s determined and tabul ated tog ether with t h e maximum de vi a tion from the mean value. The mean me sh siz e was used as the leng t h c haracteristic of each g rid. For t h e meas ur ement s of corre l ation, t he trav e rsing mechanism to measure accurately a distance o f separation of two hot wires wa s built. The me chani sm equipped with a symmetric a l airfoil to which attached t wo vertically ext e nded arm s e a c h of which served to carry a hot wire. On e arm could be s lid a long t h e a ir f oil by means o f thre a ds rotated by a handle loc a ted below t he me chan ism . The mec hanis m wa s d es i g ned in suc h way s t ha t t h e di stance be t we en t wo h ot wires was recorded on a counter, tha t t h e a ir fo il could be mo v e d vertically in the v or k ing sectio n , and t hat t h e whole mech anism could b e slid along t h e working section. For me as urement of the correlation and decay of turbulence was used a hot wi r e anemometer built by D. Knobloc k a nd C. Thiele. ( For detail see Appendix II.) -10- VEL OCITY SURVEY As bound a ry layer s along the walls of the working secti on incre a se in t .hic k.L"l.ess, the ma in stre a m will accelerate in t h at section. This condition is undesir- able for t h e present test. The cond ition nece s sary for t h e stream is to have constant and uniform ve l ocity distributions in the whole work ing s e ction, so t h at when a g rid is inserted at t h e beginn i ng of t h e 0o r k i ng s e cti on, isotropic turbulence can be produ ced in t h at sect i on. To obtain such a cond i tion of the stream, t h e side walls of the working section ,,v ere carefu l ly ad justed while t h e p itot survey was being done. After 't h e wa lls vve re a djus ted in plac e, t h e comp lete ve l ocit y survey s we r e made a t various cross section s. The results of the survey s h o wed that t h e stream was quite cons t ant and uniform e x cept near t h e walls. The results are tabulated in Table 2. The e x tensive vel6city survey s in t h e re g i on near the airfoil of t h e tra v e rs e mec h a n ism were also made by mean s of a p itot tube and yaw me te :c· i n ord er to determine a b est loc a ti on for t h e h ot wires. The best location for t h e hot wires was found to be 1 .5 in. in front of the air foil and 4 in. above the c h ord line of t h e a ir -11- foil. In that location velocity distributions were uniform, and the air velocity was two percent higher t h an the tunnel velocity. was negligibly small. The inclination of t h e stream Hence tha t location was chosen for the hot wire s to be placed for t h e measurements of correlation. The leng t h and s h a p e of t h e hot-wire carry- ing arms wei-'e designed according to the results of the velocity survey. -12- I NFLUENCE OF I NI'I'IAL TURBULEN CE When the test was inaugurated, no reference concerning an experimental result on a superposition o f two t yp es of turbulence h aving dif f erent ma gnitudes of intensity and scale was available. Previously G.I. Taylor* mentioned t h e i mp ortance of an initial turbulence on the measure ments of the correlation and decay of turbulence produced by a grid, however his s t atement was based on his intuition and not on experime ntal facts. It was therefore urg ed to investiga te this problem first. To do the investigation, at the beginning of the working section was inserted a grid for t he purpose of producing an initial turbulence, t he dec ay of which was then mea sured. At some distance behind the position of the first grid, was placed a second grid a lone, and the decay of turbu lence produced by the second grid was measured. Finally two grids were pla ced at their respec- tive positions, and t he me a surements were made to obtain the effect o f t h e initial tu r bulence on the second. Five sets of the g rids were used; namely l ½" and #4, # 1 and # 3, #3 and # 4, and #4 and # 3. * Taylor, G.I., Statistical Theory of Isotropic Turbulence, Journal of t he Aeronautical Sciences, Vol. 4, No. 8, pa g e 314, June, 1937. -1 3 - The results o f the tests s h own in Fi g s. 2, 3, 4 , 5, and 6 , il l u s t ra t ed int e r e sting phe nomena : The st ri k ing featu r e of the r esul t s was tha t whe n t h e a i r in 8 v1 ind s t ream had a}.re ad y e ven a lar ge amount o f l arge or s ma l l sc al e turbu lenc e , t h e eff ect o f t h e initial tur bul en c e u p on t he t urb u len c e prod u ced by t h e g r id (re fe r red to t h e s e cond grid ) wa s n egl i g i ble, p rov ided t hat the int ensi t y o f t h e i n i t i a l turb ulence W c).S l ovver t han tb.a t o f t he g rid. For in s t anc e , as s h ovm i n Fi g s . 2 a nd 3 t he wind stream p os se ss ed lar g er sc a le turb u l enc e t han the me sh o f the turbulenc e p roducing g rid, y et t h e initial turbul enc e did not affec t d e c ay of t he turbul en ce p ro d uc ed by g rid. the The s a me wa s t 1,1~ e when t h e wi n d st r eam alre a dy had ev en a l ar g e amoun t o f sma l l s c a l e tu rbulen c e . ( S e e F i g . 5 .) In t he case wh e n t he me s h o f a g rid wa s c onsiderab ly s ma l l er t han t h e s c ale o f t h e initi a l turbu l enc e , t bB i niti a l turb ul ence even t h e intensity o f wh ic h was h i gh h a d no effe ct on t h e t u r bu l enc e prod uc ed by t h e g rid as s h own in Fi g . 4. By t h i s t e st it was l earn ed t h a t the init i a l turbu- l e nce d ec ayed qu ic k l y when i t st r uc k t he g r i d d ue to mi x ing and int e rmi n g ling o f t h e e dd ies, h owe v e r wh en the airs t r eam h ad a h i g he r intensit y o f initia l turb ul en ce t han -14- tha t of t he turbulence produc ing gr i d and the sc ale o f t he initi al tur bulence wa s app ro ximately t he same order o f t h e mesh leng t h o f the g rid, a portion o f the ini tial tur·bulence passed thr o u gh the grid. as shown in F i g . 6. r he free tunnel turb u lence wa s found to be 0.3 o f one p ercent which vms v e ry low compa re d -r.'it l1 the initial turbu lence used for the te st. The sc al e o f the free tunnel turbulenc e wa s, no doubt, v e r y smal l since two lay ers of very fine cheese cloth wer e used to damp out t h e large eddies in front of the entr a nce. For t h is re a son the author e xp e ct ed t ha t t h e ef f ect o f the initial turbu l ence existed in the free vrind s t re am on t he turbulence p roduced by t he g rid was ne g li g i ble, and t hat the results o f t he decay a nd correla tion of turbulence, whic h menti oned later, were high l y reli ab le. -15- MEASlfrlElVlENTS OF CORRELA'rION AND DECAY Of ' TURBULENCE Main objects of the me1.rnurements were to investigate the following phenomena: 1. Variation of the scale of turbulence be h ind the differ ~ t turbulence producing g rids. 2. Variation of t h e intensity o f turbulence b~hind the differnet grids. 3. Variation of the decay of turbulence wi th respect to c hange in a mean velocity of the stream. 4. Variation of the scale o ~ turbulence wit h res pe ct to change in a mean velocity of the stream. For these investig ations two g rids namely 1.5 in. g rid and 1 in. g rid wer e individsually used to produce turbulence o f diff erent scales and intensities. Before the me asure ments were begun, it was necessary to c a librate eac h hot wire in t h e calibration tunnel at an air velocity exactly the Sarne a s that in t h e working se c tion of the turbulence tunne l . The hot wire and holder we re v ibrated by means o f a cross wire suspension with the known amplitudes and frequencies so that the calibration gave the output re ad ing corres p onding to a calcul ab le level of "artificial" turbulence. (For detail see Append ix II.) After two hot wires were car·efully calibrated so that the wires gave approximately the same output reading s, -16- they we re pla ced at t h e up p er ed g es of t h e arms provided on the traversing mechanism as shown in Photo 8. The h ot wires were cautiou s ly alined paralled to each ot h er in suc h a way t hat one wire could bare ly pass d irectly behind the ot h er. The initial gap between the wire s was made as s ma ll as pos.sj_ble by me a ns of t he screws provid ed on t he a r ms for the adjustment of the hot wire holders. The hei ght of t h e trav ersing me chanism were adj usted such as to p lace the wi res in the cente r o f t h e work i ng section. At this stage t he tunne l wa s o p erat ed at the const ant mean velocit y of the a ir stream. The hot wires wi t h a v,:nown d is tanc e apart we re t h en h ea t ed by me a ns of known electric currents . Rate o f cooling of eac h wire was c a used to c hange by t h e velocit y fluctuations, henc e e lectr i ca l r es ista n c e of t h e wi re was changed . The c hange in electrical resistance o f t he hot wi re caus ed t he v a ri a tion in t he p ote n ti a l drop acros s t h e wire, whic h was properly amplifj_ed and p a ssed thr ou g h the thermocoup le and then connected to the v1a ll t y pe g alv anome te r . The output reading on the g alvano me ter indic ate d the average i ntensity o f t h e squa re of t h e alterna ting current out put, whic h wa s prop ortional to t h e me a n of -17- the squa re v alue o f t h e velocit y f luclua tion s. Hence the i ntensity o f t h e turbulen ce could be co mputed fro m the out put re a ding and the c a lib ration dat a . When two h ot wire s were conne cted by means of a switch in such a wa y t h a t t h e c han g e in volta g es a cross t h e wi r es was added, t he re s ult ing output readi nr, M+ , was proportional to t h e quanti t y (urt- u ) 2 . 2 When they we re conn ect ed so t ha t t h e volt age s opp osed one an ot h er, the resultin~ output re ad ing , Iv'I _ , wa s pro p ortional to (u 1-u 2 ) 2 . M+ = K ( u 1+ u ) 2 Thus 2 M where K is a cons t ant o f p ro p ortionality . The me a sure ments o f M+ s and M_ s were made until the value for M_ e x c e eded the value for M ;- as t he distance between t h e h ot wires incr e a se d . By ob t a ining these v a lues, correla tion f a ctor a s a function of t he distance could b e c omput ed by t he relation, J'.1+- IvL M+-t- WL fro m which a co r rela ti on curv e could be ob ta jned. A series o f tes ts wa s r epea ted with t he hot wire trav e rs :lng me chan is m b e ing moved to v arious secti ons in t he wor k ing s ec ti on and the n t he me an velocit y o f the a ir stream b e ing v aried . -18- The resul ts of t he tes t are g ive n in Tab l es llab c, 12abc, and 1 3abc, and F i g s. 10, 11, 12, 13, 1 6 , 17, 18 , 19, 22 , 23, 24, and 25. The measurenient s for the decay of turbulence were made by mov ing t he ho t wir e along t h e long itudinal axis of t h e wor k ing section a t t he air spe ed co rresponding to t hat of t he correlation test . The ho t wire holde r was p l a c ed a t t h e edge of a long a r m especially made for t he decay test. The results of t h e test were plotted against X as shown in Figs. 7 and 30. Ivl Among t h e features to be noted a re: first, the decay of turbulence is not d ep ended on varying U and, second, t he widt h of t he correlation curve inc rea s es down strearµ. The a bse nce o f e xp erime nt a l point at t h e top of the co rre lation curves is due to t wo reas on s: first, t h e initial gap between t wo hot wi res vrn s g iven to allow one h ot wire move directly behind the other and , second, the ho t wires introduced a mutual interference when t h e di stance betw e en t hem became s h o r t. -19- RESUL'l'S AND DISCUSSION The me asurements or he decay o f turbulence showed u' was inde p e ndent of U and t hat -U c ur v e s were p rot hat -U u' X p ortional to some ;; m': e r o f -• In this res pe ct t he measlvi ure men t s wer e in good agreement wi th t b o s e obtained by E . L . Dryden . .,:. However, the me a sure ni e n t s o f t lJe s c a le of tu rbulence tak en by t he auth or gave fo:c th e .fir st time enough experimental evidences which could evaluate the assumpti ons in t h e t he orys d evelop ed i nde pend ently by G.I. Tay lor and Th. de Karman . The aut h o r wa s fir st concern ed to e v a lute p ro p erly t he foun c amenta l e quation for the d e cay o f t urbu l ence, du 2 -y uz at =- 10 - /\..2 - 0 F'rom t l1 is e qua tion l( was solved. Ap p, n d i x IV.) ................... ( 1) ( F or detail se e 'rhe values for ~ was t hen computed fro m t he decay curves whic h are s h own in F i gs. 7 and 30. and t he c omputed i'( s we re p lotted in Figs. 8 and 3 1. '11he evid ences s h owed t hat le a t a g iven U i n cre as ed l ine a rl y wi th ~ and that t h e increase of ~ wa s proportional S ince the l\! curves were line a r wi th M ~, the -,:. Dryd e n , H. L ., " Measurements of Intensity and Scale of Wind Tunnel Turbulence and Their Relat ion to the Critical Re y nold s Numb er o f Sp heres" N. .A . C. A. Report No. 581. -20- 2 values for U~ could be computed. X 7 The result of the 2 computation gave that lL.il was a constant which was des7 X i gnated b y <X,. culat ion o f (For detail se e Ap p endix III und er ncal- i:. 1t) It e n abled then to obtain the equa tion f or the decay in a form given by u' u = ............ ( 2 ) where C is a constant. This equation wa s ev a luated with u' and C(. the measured U The result showed that the com- pute d v a lue-s were the same within the experimental a ccurac y , thus the equa tion (Se e Ap p endix III.) (2) was proved to be s a tisfacto~r - Therefore, the e xperimental results of the decay of turbulence d efinitely proved de Karms.n I s as s ump tions that l~ increases proportional to t h e time and that ~'is p rop ortional to ne g ative 5a power of;G. I. Taylor I s statement,"'~ "The linear law f o r the decay can only be applied when a very definite scale can be ascribed to the turbulence. If the air in a wind stream has already a s ma ll amount of large scale turbulence when it stri k es a screen of small mesh the linear law could not be expe cted to apply," is not fully affirme d * Taylor, G.I. Statistical Theory of Isotropic Turbulence, Journa l of Aeronautical Sci ences, Vol. 4, No. 8 , Page 314, Jun.e, 1 9 37. -21- by the author b ec a us e t he e xt e nsi ve research on the superp osition of t wo types of turbulence showe d tha t t he effect of a s mall amount o f large sc a le turbulence u pon t h e turbulence produced by g ri d s o f s mall mesh wa s ne g li g ible. As wa s learned l a ter, the linear law for t he d ec ay is a s pe ci &l case o f the g e n er a l equa t ion for the d ec ay . The scales of the turbulenc e shown in F i gs . 1 4 , 20, and 26 are t he g r aphi c al i n ter g rat ion s of t he co rres p onding correlation curve s . It was convenient to use the ~ sc a l e in suc h a form as L = j Rd!f , whic h was introduced 0 first by G.I. Tay lor, because the exa'c t "width" of each correlation curve a t R from experiment. 2 = 0 wa s very cfifficult to obtain Among the features in the sc a l e curv es , s hown in Pigs. 14, 20, 26, and 2 8 , to be n ot ed are: first, the scale o f the turbulence increases p ro por tion a l to some power o f X and, second, the sc ale is p rac t :tc::.dly independent of U. The second feature agrees vvi th that obt ained by H. L. Dryden. For the relation b etwe en u 1 and L, de Ka r man ma d e t h e a ssump tion that u 1 is.prop ortional to d L so that 1 at Bu' = dL Bu' dL dX dt or U - . . . . . . . . . . . . . . . . . (3) - 22 - whe r e B is a co n s tant o f pr op ortional it y . The equation for L was solved after substituting equat ion (2) in (3). The equation t h us obtained i s L _ BC X - 1-v c:; CX.. J-S"d. .................... 4) ( where C i s a _constant whi ch is the same as in t h e equation ( 2) . '.rhe equ i:, t ion ( 4) was t h en eva1ua ted by subs ti tut ing the known q uantities into t he equation. under 11 Ca l culaticn o f C and B . 11 ) ( Se e Appendix III The result o f t h e evalua- tion showe d t h at de Kannan's ass ump tion that u' is p ropor t l·o na 1 t o dL dt gav e a p;oo a- &gre emen-t wit h th e e xp erimental fact. It was u ossi b l e at t hi s J oint to evalu nte the quantit y u·' "A..2. YL = constant A .......... ( 5 ) This equatl on is one of i mp ort ant parameters wh ic h invo lve in t he study of turbulence. The equation (5) is he l d s a tisfact o rily b y both t he or ie s d e v elo ped b y de Ka rma n and 'l' a y lor al though t h ei r a s s ump tions on the sc a l e and t h e decay o f turbul ence are different. de Karman 's a ssump tion that enables to h old the equation ( 5 ) is the rel a tions h ip between u' and L g iven in the equa tion ( 3), wh ile 'I'aylor 1 s a ssumptions wh ic h h old t h e e qu a tion ( 5 ) are t h at t he de c ay curv e is -23- lin ear and that the scale Lis constant re ga rdless of X I n Tay lo r 's case t h ere is no relationship betwe en u' and L. The equa tj_ons ( 3 ) and (5) we re substituted in the equation (1) in order t o de rive the fo l l owing equations: 5' U u'° C 5 -t-AR X s+AE3 3 A ., •..... .. ...... (6) AB L == Cl X !i+AB. . . • • . . • . . . . . . . . . ( 7 ) ...... ......... ( 8 ) Comparing the equations ( 6 ) and (2) and also ( 7) and ( 4 ), the p oint of i nterest to be noted is that the corres p ond ini;.: equations are si milar in their forms , The e v aluations o f the equations ( 6), (7), and (8 ) were then made. ( F'or detail see Appei1dix I I I under 11 Ca lculat ion of L, -, U , an d ;'-')\ ~ b y using • A• an d. B . ) The re sults showed u t hat e quations were comp letely s a tisfactory . 'I1he most imp ortan t re la tionship discovered during these evaluations was that 1 c(_ d l og U = 5 +AB = •• u' X 5M -2 4 - or l-5c(_ = 5!!B This relations h i p enabled t h e aut h or to p r edi ct t ha t the va l ue for 1 is 5 or g reater t han 5 for is otrop ic tu rbuOI- le n c e since the v alue for AB never be comes ne g ative. Hence, the p r e ceding results lead to con Blus ion t hat t h e e qu ation (2) is identical with th e equat ion ( 6), t hat t he equation ( 4 ) is identical wit h t h e equation ( 7), and that t h e e qu ation (8) is a ga in' i de n tic a l with the equ ation (4) g ive n in Append ix I V. The p o int o .f interest was then to verify t he equations (2), ( 4 ), (6), a n d (7) fro m a ma t h emat i c a l p o int o f view. S ince +AB X x:_2 = 5u )' 5 M Y :::; d lo g u u d lo g u:, X u u:, } X d (M) 5M ( 5+AB ) X - d ( ;~1 ) The i n te g ration o f t h is e quat i on g ives 5 Q u' But ex.. =: 1 5 -t-AB C X 5+A.B . . . . . . . . . . . . . . . . .. . ( 6a) so that t h e e qu a tion ( 6a) b e come s U = C X 5ot.. u:, ................... , 2 l -25- It is e a sily provable that the constant C in the equation . 5-t-AB (2) is the same as 0 3 7 - in the equation (6); therefore, the equation {2) is identical with the equation {6). Now inserting 5-tAB in place of~ in the equation (4), the equation for L gives in the form L = 02 { 5+AB) A AB X S-+AB 5-t-AB) = O , t 'nere f ore But 02 ( A 1 . . . . . . . . . . . . . ... <: :. .c. (7) i( = 5+AB X -,, -u................. . ( 8) The equation {8) leads to conclusion that "A= -,,t c;::(. ••••••••••••••••••••••• ( g ) Hence all equations are consista.nt with one another. The exp erimental evidence showed that the scale of the turbulence was nearly independent of U. } 7 i g . 28.) ( Se e But, a s explained before, the scale definitely / increased downst r eam from th,t rid 7 obeying the equation, AS L = const. X s-+-A.£3 The superposition of three correlation curves taken at a g iven distance behind the 1.5 in. g rid but at three different Us showed that the correl ation curves -26- were nearly i dentical as shown in Fi g . 28a . The curvature at the vertex of the co 1·relation curve should h a ve been theoretically incre a sed as U increased, howe ve r t he variation of t he curvature at the vertex of th e correlation curve was not obtained because of the mutual interference of two hot wires. For this re as on, the curv 8ture a t the verte x of each correlation curve vva s drawn in such a way that the parabola which touched correlation curve met with the axis at Y == .I\.. where ')\__ is ca l culated fro m the decay curve. See Figs. 11, 12, 13, 17, 18, 19, 23, 24, and 25. The variation of the shape ?f the correlation curve with t he 'increase in distance from the grid was then investigated. F'irst, the ratios between the various widths Ys of each correlatj_on curve and the width Y at R 2 = . 2 were determined and, second, the ratios were plotted against the corresponding R as shown in Pi gs. 2 15, 21, and 27. The striking feature of these figur e s is tha t the correlation curves are nearly the same shape, although there is very slight variation of the curvature near the vertex of the curve. The variation o i ' the cur- vature near the vertex of the curve was so small that it was not well shown in the fi gures. According to the experimental results,)\__ was proportional to u-½ and L wa s constant as U varied. -27- Consquently A. was pro p ortion al to L u½. The equa tion for A. is L AL S ince rx.. was an order of~' the vari a tion of~ with Xis very g r a dua l as s hown in Fig. 29. Now consider the Tay lor's assump tions in re l ation with those of de Ka r man. t h e ass ump tion t ha t - Both Tay lor and de Karman made I ls~ _u_i~_: 7 L canst. A, h owever Taylor a s ~ sumed that Lis a constant, while de Karman assumed that Lis pro portioh al to some power of X . These two diff er- ent assump tions on L le ad to a n ext r emely interesting conclusion. Prom the equation L = ~ -::;, one obtains 1 S" 1-- L :::: 1 C3 X s+AB ........... de Karman ................... Taylor In the case of Taylor's L, AB must be zero, i.e., AB= -,, L u.'d-c because ~ = 0 or B = O. The equations for t h e decay of turbulence are -28- .r = C 5-t-AB X 7MB U u' 3 A ,r ......... ae na r man ~ ••••••••••••••••• ra;/lOr 1 Solving lL.2 from t h e equa tion for the decay, du' -ru' dt = -5 -ll.it. ) u:, by using Karman 1 s U ,one obtains i'L = ( 5+-AB) -r X U •••••••·••••· Karma n According to Ta y lors U du' = dX u2 K x2 2 Putt i ng these equation in the equation (1), ) . . . . . . . . . . . . . . . . . Taylor U I 11..2 Now inserting Tay lor~ l\...z and L in -,, L = A and solving for u' one obt a ins U' u'= AYL l\...2 u' U AK1 - , 1 2 5X - K X ' -29- AK 1 5 where K = L. 1 Hence U u' 1 = K2 Therefore K - .£_ 2 - AL = AL 5 x Taylor s~uMnarizing Karman 1 s and Taylor's equations, de Karman Tay l or 5 L = 1 X / - s-+AB L Cg I\..=(5+AB) X u 7 = Kl K= u5 )' X 5 U C (5+AB) X S+AB u' - 3 A u u:, = K5A X 1 The c omparison oft he corresponding equations give definitely that the Ta ylor's theory is a special case of the g eneral theory developed by de Karman. - 3 0- CONCLUSION As far as the author knows, the present investig ation is t h e first to reveal the following facts: 1. The decay of the turbulence is p roportional to t he ne ga tive 5 o( power of X M. 2. stream. The scale o r II ave r a g e eddy s iz e II incre a ses down- The increase of t h e scale is p ro p orti onal to the neg a tive 1-5 d... p ower of X M" 3. The scale s t a fixed point is nearly independ ent 4. The quantity of u-Y' ~ is constant. 5. u' 6. I\_ of U . is p rop_ortional to dL dt" -x z. = I' t = ( 5+AB) 7. C( = 5+AB or 8. The ef f ect of a small amount of initial turbul- ! 1 o(_ u ,x dL dX ence on t h e deca y of turbulence produced b y t h e gr i ds is ne g l i g i b le. 9. de Kar-man's assumptions related to (1) to (7) inclusive a re comp letely satisfied by the experimental results. - 31 - i-U:' PEkuIX I. DETAIL DES CRIPTION OF 'l'RE VAR IOUS PAR'l' S OP n rn WIND TUNN E L. EN'rRANCE ( See Fi g . 1 and ;>hoto 1) Three i mp or tant and necessary requirements for a wi nd tunnel are: ( 1) Constant and p arallel direction of air flow. (2) Constant and un iform velocity d istri butio n s acro ss t h e wo r k inr sections. (3) J. U nimurn. amount of turbulence in air f low. 'l'o s ati sfy t l-J ese r e quir ements t h e author found a simp le :w.eth od to de si r,n a p rop er· ei1trance. 'l' he s at isfac- tory way for an entra nc e design is to ma ::.ntain a ir f lov; in suc h a way to have un i fo r m a cceleration. With t h is in mind , t he ratio of air velocities a t t he two .extreme ed ges of t he entrance are first determined; need l ess to say tha t t he r a tio is the same as the contraction ratios of areas. The inte ~med iate ve locities are then obt a i n ed by a s tr ai ght line variat ion . By using Q == VA == con stan t , the a re a at any section can be d e t ermined, from wh ich t h e curvature is e as ily ob taine d . Q i s t h e qua ntity of air, V. is t h e v elocity, and A is the cros s s ectj_ on a rea. This met h od wa s used to d e si gn t h e entrance. The forwar d end of t he entrance was 80 in. by 80 i n . i n area and con tracted to 20 i n . square over t h e distance of 9 ft . -3 2 - The inner walls were made o f 22 gag e galv a nized steel sheets which were nailed against a numbe r of wooden ribs and fra mes. Yet t he surface of t he wa lls wer e kept as s moot h as possible. The joints of the wa lls were solder- ed tog ether and mad e air tight. At the re ar end of t he entrance a straight plywood section 2 ft. long was adde d . Two laye rs of c hee se clot h with mesh size of about .016 in. square were placed at the beginning of the entrance in order to damp out the motion of l ar ge eddies in t he incoming a ir. WORKI NG SECT ION ( See Fi g . 1. and photo 2) The working section was 12 feet long with a cross section being approximately 20 i n . square. The top and bottom wa lls consi sted of .75 in. plyw ood stiffened by 2 in. by 4 in. lumber. Each of t he sid e wall s cons isted of t hree plywoods 3 ft. long , the end o f which being hinged to g e ther, was mad e ad j ustable in or out in order to obtain constant and uniform air flow along t h e working section. Eac h side wall was equipped with observa tion sindows, and was s tiffene d with 2 in. by 3 in. ang le iron which was connected to the top and bottom wal l s by me ans of wood.en screv✓ S. The bot tom wall was equipped with a slot 2 in. wide along its entire length for t he movement -33- of the traversing mechanism. The slot wa s closed by a shim sheet of .0005 in. thick. The sheet was rolled around four rollers of 6 in. in diameter, so it could be moved with the traversing mechanism. The whole working section was made rigid by 4 in. by 4 in. wooden columms and frames. EXIT DI FFUSER The exit diffuser w2s added to the rear end of the 'N orking section. The diffuser was built in such a way as to transform a rectangular section 20 in. by 21 in. to the cylindrical section 30 in. diameter over the distance of 5 ft. 2 in. Consideration was given for the design in order to avoid separation of air flow from the walls. It was made of 20 gauge galvanized steel s he ets stiffened by angle iron and the center lines of the walls. A rectangul ar fra me made o f 2.Dgle iron and an iron ring were rivetted to the extreme edges of the diffuser. A circul ar cylinder 30 in. diam. was added to the rear end of the diffuser with a gap of l in. The cylin- der was made of 16 gauge steel sheet reinforced by two steel rings at the ed ges of the c y linder. A counter propeller consisted of four sheet me tal v anes, p laced in the cylinder, served to eliminate the -34- rotary comp onent o f velocity induced by t h e propeller. PROPELLER Ai,m MOT OR ( S ee photo 4 .) The prop elle r consisted of two wooden b l a des, mount e d directly on the shaft of 4 h.p. D.C. shun t motor The propeller 29 in. diameter was insert e d about 5 in. into t he c y lind e r as s h own in Fig. 1. -35- APP END I X II. BOT VJIRE ANEMOMETER ANL EU2'. CT HI CAL f~QUIPMEN'l' The hot wire anemometer is a wire of small dia meter through whic h is heated by passing an electric cur rent t hrough it. Two types o f wires may be used: first, pure p l a tinum ·,dre o f about .000 5 in. in diameter and, second, v\i ol la ston wi r e which is pl a tinum wire of .0005 in. in diameter with a .0045 in silver covering . Wollasto n wire is gener a lly used for a hot wire because of two adv a nta ge s: t h e wire is easily handled and the silver coating may be etched to obta j_n any desirab le leng th o f the p l atinum wire. The \!'J ollaston wire is soldered to two s p ind les, made o f sewing needles, which form the ti ps of the holder. Th e silver . coa ting is et c he d away for a shor·t leng t h in the center of the Wollaston wire. When the hot wire is heate d , velocit y fluctuati on s cause ch 8n ges in the rate o f coo l ing of the wire, hence in its temper ture and in its re s istan c e . The resulting variations in the p otential drop a c ross the wire may then be amplified and passed through a t h ermocoup l e a nd applied to a wa l l type g alvan ometer whic h indicates tb.e intensity of square of the alternating current out put. The v ariation of the wires temp er a ture is mainly a f fected by t he comp onent of the velocity flu ctua tion parallel to t he direction of mean -36- flow, the other components p roducing only second order affects. If t h e velocity f luctu ations are low, t he out- put reading is proportional to the mean-square of the veloc i ty fluctuations. The instrv.ment in this form is not app licabl e when velocity fluctuations become r ap id becau s e the electric current is not able to supply sufficient energy to raise the temp erature of wire fast enough to corres pond to t h e equilib rj_um temperature. The theoretj_cal study of this prob lem shows that a sinusoidal fluctuation of fre qu e ncy f has its amp litude diminis tie d in the ratio I where M is a time constant depending on the physical prop erties of t he wire and the mean temp erature and heating at wh ich it is ope rated. In order to resotre the amplitude and compensi:~te for the lag the method adopted by D. Knoblock and C. rr hiele was to insert in the ampl i f ier ci r cuit a volta ge divid er con sisting of an induct ance and adjustable resistance in series. The amp lifier then ampli- fies the high frequencies more than the low frequencies. If the ratio of inductance to adjustable r es istance is made equal to the time constant of the wire, a sinusoidal fluctu a tion of fr equency f has its amplitude increased proportional to Vl + ( 1Tf / M 2 2 , so that with this arrange- ment the a rnplii'ier co mpensates for the l ag of the wire -37- u p to frequencies at which the unavoidable distributed capacity of the induct a nce begins to short circuit the volta g e divider. The lower and upper frequency limit in the equipment used for the turbulence test is 5 and 8000 cycles per sec. re spe ctively. 'rhe maximum sensitivity of the apparatus is that 1 10,000 of a volt gives full scale reading on the wal l typ e galvanome ter. The amp lifiers and input circuit for correlation amplifier are shown in Pigs.35., 3~,a.nd. ~1- -38- HOT-WIRE TECHNI QUE The hot wire is made of .005 in. Woll a ston wire which is a .0005 in. p latinum wire with a .0045 in. silver covering . The wire wa s soldered to two spindles made of sewing nee dles b y means of so f t so ld er. While sold ering , t he s p indles were p ressed slight y inward so vi hen r e le a sed, the s p indle s s prang and g ave a s l igh t tension to t h e wire. The slight tension in t he wi re was necessary to p reve n t wa rp age of t h e wir e wlien it was heated during t he test. Afte r t he wir,:: was soldered in place, about 2 mm. of silver in t h e ce n ter was et c h ed off by me ans of a bubble o f 60 percent diluted nitric acid for med at t h e end of a c api llary tube . For etc h ing s i lver off a va luable p oint of t e c hnique wa s discovered. The best re s u l t was pbtained by t h e aid of el e ctric curre n t. The Wollaston wire was conn ected to t he po sitive terminal of one-volt dry cell and t h e n e ga tive terminal was conne ct ed to a carbon rod wh ich was dipped into t h e nitric acid . i hen t h e wire was placed in t he b ub bl e o f t :·1e nitric acid, e lee tric current b e gan to flow t h rough t h e ac i d . made very quickly . Thu s etc hing o f silver wa s It too k approximately t wo mi n utes to etc h 2 mm. of silv e r b y this met h od, whil e without t h e aid of t h e dry ce 11, it mi g ht have ta k en as long as two h o u rs . -39- APP ENDIX III Calculation of J( = 5 M Y U d log ~r X d (M) X M d lo g Q u' u = 29.7 ft./sec. d (~) tt ( sq. in.) u -:=: 38 ft ./sec. ?L( sq. in.) 26.09 .0220 .0221 .01736 34.10 .0164 .02965 .0233 42.10 .0131 .0372 .0292 50.06 .0110 .04425 .0347 58 .10 .0095 .05125 .04025 66 .08 .0084 .0579 .0455 X ivI d log U u' - · -·-x ·- d (M) u === 53.5 ft./sec. K 26.09 .0220 .01250 34.10 .0164 .01676 42.10 .0131 .02100 50.06 .0110 .02500 58.10 .0095 .028 96 66.08 .0084 .03270 - 40- I Calculation of o<.. - 1.5 in. grid(½ in. dowel) U = 29.8 ft./sec. -Y= .02 31 sq. in. / sec. A.2 <I = n:-61-r(-.0-::--,2:,-, :3,-:-1-,-)--, -x / 356 :: (356) (.05275) ( L 5) ( • 0231 )( 60 )- = 9 • 0 25 M U ::: 38 ft ./sec. .J.._ (456) ~ U 7= .02322 s q. in./sec . (.0 413) - IT.51"(. 02322 )( 60) = 9.01 53.5 ft./sec. J.. _ ( 642. 5) ( • 029 8 5) ~ - ( 1. 5) ( • 02354 ( 60) 7 = .02354 sq. in . /sec. = 9.06 -41.:_ Calculation of coefficient, C, in :Q u' M 35 40 45 50 55 60 65 u' X 35 40 45 50 55 60 65 u ::; u M u:, ( fro m exp.) 7.14 7.71 8.20 8.70 9.175 9.63 10.06 37.5 40.3 43.0 45.5 48.0 50.5 52.8 X 35 40 45 50 55 60 65 C 5.25 5.23 5.24 5.23 5.235 5.24 5.25 Average 5.24 u = C {~)-555 u:, ( ~). 555 M u (from exp.) u:, 7.19 7.76 8.27 8.77 9.25 ~ .72 10.14 37.5 40.3 43 45.5 48 50.5 52.8 C 5.22 5 .2 5.2 5 .19 5.19 5.2 5.21 Average 5.21 u ( X) . 5425u' =C M 53.5 ft ./sec. M 1'11 M ( ~).55 4 u = 38 ft./ sec. M C {~)5~ :Q = C ( X). 554 U= 29 . 8 ft./sec. X ;::: (~ ). 5425 11, u ( from exp.) u:, 7.12 5 7.675 8.180 8.670 9.160 9.600 10.050 37.5 40.3 43 45.5 48 50.5 52.8 C 5.265 5.260 5.260 5.250 5.240 5.265 5 .260 Average 5.26 -42- ,-sa.. Calcula tion of Coefficient, B, in L = .446 - (l- 5 Gl) U :::: 29. 8 ft./ sec. 1.5 in. grid( ½ in. dowel) L = B. 239 B.C.2 X X . 446 """ B ( • 526 ) X. 446 X M X 40.0 46.7 53.3 60.0 66.7 60 70 80 90 100 .526X 0446 L (from B exp .) .5575 .605 .641 .670 .695 3 .26 3.495 3 .71 3 .92 4 .10 L = ( .1714)(526) x· 446 - .0902 x· 446 L = .54 B X• 445 U = 38 ft./sec. X .1'71 .173 .1726 .171 .1695 Average .1714 .54 x -445 L (from B exp.) 60 70 80 90 100 3.34 3 .58 3.80 4.005 4.19 .574 . 616 . 652 .683 .716 Aver ag e L .172 .172 .1715 .1705 .1705 .1713 = . 0925 x • 445 L = .532 B x • 445 U ~ 53.5 ft./sec . X . 532X • 4475 L ( fro m B exp.) L = 60 3 .316 70 3 .6 40 80 3 .770 90 3.948 100 4. 175 .08825 x• 4475 .557 .600 . 634 . 661 .680 Aver ag e .1678 .1650 .168 0 .1674 .1630 .166 -- o cz f' '? / -43- Calculation of A and B 1.5 in. g rid ( .5 in. dowel) U UI = 29.8 ft./sec. = ( • 239) UX - S"d.. L = (.1714)( .526) X ) ( • 44 6) _ 239 A -_ ( • 0902. 0902 • dL dt == Bu ' = B( .239)U X B === ( • 0902 ~s ~ 446 ) • vv 2 :;:o -. 554 dL ss4 = U dX = U ( .0902)( .446) x -· = _1 683 u 1 = (.2 404) U X U = 38 ft./sec. L = (.0925) X A A_ ( .2404)(9.01) .0925 -. '5'5:s B ::: ( .092~ ~ics{J5) - U - - . 555 45 :: 23 • 4 dL dt = B U ( .240 4 )X t-5ol = (.0925)(.445) U X -. sss .1713 53. 5 ft./sec. u' = (.2 38 ) U X - • S:SD5 • L = ( .166)( .532) x ·4475 ( . 238 )( 9. 06 ) A = T:-166 n-:-532) = 24 • 4 dL -.ss2s dt = BU (.238) X = B = .166 (.116)(.532)(.4475) U X -.ss2s -44- Calculation of L, ~, and ,>{ using A and B •. gri"d 1 21 in. i n. dowel) ( 2l U = 29.8 ft./sec. B = .1683 A = 23.9 AB = 4.025 AB L = ex T+AB = c x -446 u = c5+AB x ..r-r.t1.a _ I c, = . 0902 I 5" u' , A - 025 x· 554 0' 9.23. 9 - (9.025 ) (.0231 ) u == 38 ft./sec. . 3775 ex· 554 :1 3 56 X ==- . 0 00 586X A = 23. 4 B = .1713 AB = 4. 01 AB L == et x s+As= cx-445 I u u' - C5+AB X t A >. 2 == ( 5 -t-AB U) y X 'l 5 5+AB c, = .0925 = • 3 B5ciix· 555 C3 = 10.8 = . 000459X U = 53.5 ft./sec. A= 2 4. 4 B = . 1 66 c , = . 08825 !, U _ c5 +AB X HAB _ •3710vx· 5525 u' A 3 ;\z __ 'L 3 (5 -t-AB) ;r X U == . 000332X AB = 4. 06 -45- Calculation of Jt::: 5 M Y u d log u0 , X d ( M) Grid U = 29.9 ft./sec U = 42 .25 fi( /4,ec. ~ (Sj.,i?.) ;<- 35 3. 893 \ . 018 .01272 40 3.9 8 .01995 .0141 45 4. 0 6 .0228 .01615 50 4.125 . 02645 . 0 187 \I 4 . 24 .03175 . 0229 \ 4.325 .0377 .0266 \ 4 .41 .0 421 .0298 . 04625 .0327 60 \ 70 i 80 ! ( 1{ , 90 . ·,. 4. 49 \ ) X M d lo g u ) I u:, '! U - 59.7 ft . /sec. X ~ 35 3. 8 93 .01084 40 3.98 .012 4.06 .0137 5 50 4.125 .0159 60 4.24 70 4.325 d ( Ivl ) 45 80 \ \ \ \·, i ' I .0191 .0227 4.41 .0253 4.49 .0279 ·,~ 90 - 46- -"' 1 YX Calculation OJ. cX_ = U ~ ~- Grid = 1 in. u e::: 29.9 f t./sec. I c:(. U = ~11 ·\ff / 1/ 29 . 9 X 12 .04 45 >< 85 = 8. 08 .02324 = 42.25 ft./sec. L = 42 . 2 5 x 12 ¢<.. .0232 4 ~ 0335 90 = 8.125 0 I -47- Calculation of C in U u' Grid = 1 in. U = 29 . 9 ft./sec. X . 619 u M X ( M) 35 9.035 48. 75 5.39 40 9.825 53.25 5. 425 45 10.60 57.20 5.39 50 11.27 61.30 5.44 60 12.60 6 9 .00 5.475 70 13.90 75.25 5.410 80 15.07 81.30 5.40 90 16.20 88.50 5.46 u' ( actual) Average C 5.41 -48- I -SCL Calculation of B from L = ~CaX ( 1-5~) Grid= 1 in. L = B . 485 X. 381 X M .48 5 x .381 L (actual) B 40 1.98 .3525 .178 50 2.15 .383 .178 60 2.31 .412 .178 70 2.45 .436 .178 80 2.575 .456 .177 90 2.695 .476 .165 100 2.805 .495 .166 Average L = ( .117)( .485) x · 3 81 = .0858 x.381 .177 -49- Calculation of A Grid = 1 in. A = u' K 7 L u' = .185 u x-· L = .0858 x· 381 where 619 A: = <:(-Y UX A_ .185 x 8 .08 _ 1'7 4 .0858 • ,t:/8 Calculation .of C in L = c, X s-t- ~8 AB = 1'7.4 x 1.77 = 3.08 AB 381 L = c, x 5'+AB = o,x· Therefore C, = . 0858 5 Calculation of C in U 5+AB u' = -A u = C .4645 x-619 = 5.41 x.619 u:, 3 1'herefore c., = 11. 65 Calculation of ~ where -Y = .02324 sq. in./sec. ex J 5+-AB -50- APPENDIX IV. 'K:_ EQUA'11 ION FOR.,, DETERMINING de Karman' s equation for the decay of energy of ~ turbulence is in the form: If the condition downstream of a grid in the wind tunnel is t= x, u du 2 dt == U du' or du 2 dx =:: -10 Y uz. /\....2 •.••.•• (la) u' U dx = -5 7' .>..2. 1 U , \... l\:: = - 57 u' du' dx . . . . . . . . . . . ( la ) . . . . . . . . . . . ... ( 2 ) For more convenient form, let U y, then u' log U = log u 1 +- log y By differentiating with respect to X, d log U dx But = d log u' dx + d lo.E....,X. dx d lo_g_ ![ _ O dx ' d log u' == _ d log y dx dx .........• ( 3) Substituting the equation (3) in (2), -51- I\. = 5 M -Y U d log u, u ............... ( 4) which is the equation for~, introduced as a leng th for a smallest eddy by G.I. Taylor. EQUATION PO R DE'l1 ERMI NI NG CL du 2 dt __. , u2 = - 10 ✓ - 1\!: FOR THE DECAY OF' TURBULENCE = - 10 u.zcx.. t ........ (5) Hence ............... ( 5a) .............. ( 6 ) EQUA'l1 ION FOR u u' From t h e equation (4), . ......... ( 7) Subst i tuting t h e equa tion (6) in (7), d log U __....,x_u' - x5<X. d ( M) M . .. ........... ( 8 ) Inte\rg r a t ing t h e equa tion ( 8), \ U _ G ,X ) 5C(_ • M , ............... ( 9) u' - -52- where C is a numerical constant for a given grid. EQUATION FOR SCALE OF TURBULENCE dL dt is proportional to u' dL dt Hence = Bu' where B is a numerical constant. From the equation (9) C U x- 5 a'... :L u' - U dL dX L = BC.2. 1-5~ xl-5ct. ......... ( 10) ............. (11) where B can be determined from the measurements of Land t h e decay of turbulence. -53- POSSIBLE SOLU'rION POR LARGE REYNOLDS l\TUMBER S. de Karman derived the equation for the propagation of the correlation: c}(fiizJ+ c(iiz)-f(dh--,. 4h) ;;rt .)~ -1:. 2 = .:2 Ytt.2 (d -f + 4 df) . ... .. . (Jc) -t J~ d-'t, 2 For large Reynolds numbers the assumptions were made t hat the correlation fun c tions wouid preserve t heir shap e s and only their scale would charge. These assump- tions mean t hat both f (r, t) and h (r, t) are f1mctions of one variable If=~ only where Lis a function of M and Ut. By introducing f (<p) and h {If) in equation (12) de Karman obtained the expression: ---2- - d - f elf/ ~ ~ dL + f clti2 + c (az) L cl~ L cir 2 ( d h -t- 4h) df 'F = 2 -y 1.i. (cl'f, -t- elf) .... (, L 2 df 2 yr/ 4f" '/ 4 2 , 3 For large Reynolds number,. u'L the term of the )' , right side vani shes. or - df 11/ ( / clL) Cl'p 'l2tt' cit; - f (s )'L) + dh 2 1 tl.- / \ d'f + 4 h ljl =0 The equation (14) can be satisfied if t h e coeffi c ients which are function oft without being functions of~ arc constant s. Hence de Karman obtained the relationships: u t 7\.2 L7'=A . . . ... . . . .. . . . . . (J5) - 54- dL dt = Bu' . . . . . . . . . . . . . ..( 16 ) where A and Bare numerical constants. By eli!l'l inating u' from the equation (15) and { 16 ) the different ial equation for L (t) is ~B (ddtL { ....... ( 17) or when t = X: u' 2 d L 5 dL 2 L dt2 = - AB (dx ) . . . . . . . . ( 18) The solu~tion of the equation (18 ) is AB L = ex 5t-AB I • • • • • • • • • • • • • • • ( 19 ) where C is a nwnerical constant. Introducing the equation (19) in (16) 5 U - u1 - C 5+AB X 5t-AB 3-A- .i .......... '20) Sub stituting t he expression (20) in (la) . . . . . . . . . . . . . . ( 21) It is interesting to notice that the . equation s (19) and (20), and (21) with ct.= -,c--l~ 5tAB are indentical with the corresp onding equations (9), (5a) a:rxi (11), for t h e case of s mall Reynolds number. -55- AP PEND I X V. EFF'EC 'l1 OF HOT-WIRE LENGT H The author investiga ted experimentally t he effect of hot-wire length on the measurements of~, at a fixed point fro m t he g r ids . long were used. u' The h ot wir e fro m 1 to 5 nm . 'l1he results wer e p lott ed in lv i g . 38. increased to its maximum value as t h e wire leng t h de c r e a sed down to about 2 mm., a nd t he ~, decreased u . At' the slig htly as the wir e leng t h decre as ed to 1 mm . wir e leng th of 1 mm . t h ere existed a h i gh temperature g r adient over the wir~ so t ha t it was dif fi cult to co mpen sate the a mplifier for t h e lag o f the wire. For this re a son, it was de cide d to use the wire leng th of 2 mm. for the measurements of the corr e lation and decay of turb u lenc e . It ha s been known that t h e variation of correla tion with distance a cross th e stream makes so me e r ror in hotwir e resu l ts due to t he lac lf of comp l e te corre l ation over ('.t, t he le ngth o f the wire. The theor e tic al co r re;La-t d: 0B- for this effect wa s done by W.C. Mock, J r.* By using Moc k 1 s correction for mula, t h e , error in t h e corre l a t i on re ad ing s in the present rese a rch was less than 5 percent in a ny case. * Moc k , J r ., W.C. "The Effect of Wire Leng th in Measurement s of Intensity and Scalff of Turbulence By 'l'he HotWire Method ." N. A . C .A. Rep ort 58 1, 1937. TABLE 1 DIMENSIONS OF GRIDS FOR PRODUCING TURBULENCE No. Nominal mesh length, in. Ave r age measured mesh length, in. Deviation of individual meshes from average, in. Average measured wire diameter, in. Material 1 .50 .4956 .0156 .23 Iron wire 2 .50 .50 .105 Iron wire 3 .50 .507 .031 .035 .084 Iron wire 4 .125 .125 .006 .003 .054 Iron wire 1.5 1.5 .50 Wooden dowel 1.0 1.0 .25 Wooden dowel TABLE 2 SURVEY OF DYNAMIC PRESSURE I N THE WORKI NG SECTI ON Pos. 6 i n. 4 in. 2 in. C. L. 2 in. 4 in. 6 in. q (cm. ) alcohol 6 in. 4 . 324 4.341 4 . 340 4 .338 4 .338 4 . 342 4 . 3 53 5 i n. 4.33 9 4 . 346 4 . 355 4 . 3 58 4 . 35 5 4 . 342 4 , 3 62 in. 4 . 3 45 4. 3 60 4 . 355 4 . 3 58 4 . 3 55 4 .360 4 . 3 62 3 in. 4 . 34 5 4 . 360 4 . 3 55 4 . 358 4 .3 55 4 . 3 60 4 . 370 2 in. 4 . 345 4 . 3 60 4 . 360 4 .360 4 .360 4. 3 60 4. 370 1 in. 4 . 345 4 . 360 4 .360 4 . 360 4. 3 60 4 .360 4 . 370 C. L . 4 . 345 4 .360 4 . 360 4 . 3 60 4 . 360 4. 360 4 . 3 70 1 in. 4 . 3 56 4.365 4. 365 4 .360 4. 363 4. 3 65 4 . 38 5 2 in. 4 . 356 4 . 370 4 . 370 4 . 3 65 4. 370 4 .375 4.38 5 in. 4 . 3 56 4 . 371 4 . 371 4. 3 65 4 . 370 4 . 380 4 . 385 4 in. 4. 367 4 . 384 4. 38 9 4. 380 4. 38 4 4 . 38 6 4 . 392 5 in. 4 .367 4 .39 0 4 . 395 -- 4 . 392 4 .39 3 4. 397 4 .399 6 in. 4 . 37 3 4 . 400 4 . 39 4 4 . 407 4. 409 4 . 400 4. 410 L1 3 Pos .:::: Pos i tion C . L.:::: Cent er line TABLE 2a SURVEY OF' D:{.NAN! I C PRESSURE I N TI-i:::E WORKING SEC'l ION 1 Pos. 6 in. 4 in. 2 in. C. L . 2 in. 4 in. 6 in. 4.318 4 .313 q ( c r,1 . ) alcohol 6 in. 4 . 310 5 in. 4.334 4 in. 4 .33 7 3 in. LJ:. 340 2 in. 4 .343 1 in. 4 . 345 C. L . 4 . 355 1 in. 4 . 3 55 2 in. 4 . 3 55 3 in. 4 . 363 4 in. 4 .365 5 in. 4.368 6 in. 4 .373 4.31 4 . 335 4 .336 4 .340 4.345 4 .356 4 .36 3 4 . 306 4 . 3 15 4 . 317 4 .330 4 . 327 4 . 321 4 . 340 4 . 340 4 . 336 4 . 340 4 . 345 4 . 343 4 . 340 4 . 345 4 .343 4 .345 4.345 4 .350 4 . 340 4 . 3 50 4 . 350 4.345 4.345 4 .354 4 . 3 50 4 .355 4 .360 4.355 4.355 4 .366 4.365 4.365 4 .366 4. 371 4.370 4 .366 4.3'71 4 . 380 4 .372 Pos. = Position C.L.::: Center line 4 .324 4 . 33 5 4 .3 3 3 4. 345 4 .345 4.346 4 . 346 4. 350 4.350 4 .350 4 .356 4 . 3 50 4.355 4. 3 62 4 . 3 60 4 .365 4. 374 4.365 TABLE 2b SURVE.'Y OF DYNAMIC PRESSURE IN THE WORKI NG SECTION Pos. 6 in. 4 in. 2 in. C. L. 2 in. 4 in. 6 in. q ( cm. ) alcohol in. 4.305 4 . 300 4.305 4.305 4 . 3 10 4.305 4 . 310 5 in. 4.310 4 .300 4 .315 4 .315 4 .320 4.315 4.320 4 in. 4.320 4 . 305 4 . 315 4.320 4.320 4.320 4.330 3 in. 4.320 4 . 310 4 .320 4 .32 5 4 .325 4.325 4.330 2 in. 4.325 4.315 4 . 325 4.330 4 .330 4 .325 4.330 1 in. 4.325 4 .320 4 .325 4.330 4.330 4 . 325 4 . 3:30 C ,. L1. 4 . 3 25 L1 • 320 4 .330 4 .330 4 . 330 4.325 4.330 1 in. 4. 32 5 4.320 4 . 330 4 . 335 4.330 4 . 325 4 . 330 2 in. 4 . 327 4 . 320 4 .330 4.335 4 . 335 4. 330 4.340 3 in. 4 . 335 4 .325 4 .330 4.340 4 .345 4 . 335 4.345 4 in. 4 .340 4 .330 4.335 4 .340 4.350 4.340 4 .350 5 in. 4 . 3 45 4 .335 4 . 340 4 . 3 50 4 . 350 4.345 4.360 in. 4 . 345 4 .33 5 4.350 4.350 4.360 4.350 4 . 3 60 6 1 6 C. L. == Center Line Pos.::::: Position 11 !: I 80'' I 2 L I t., r I 120 q I.' \SLIGHTLY EXPANDED I I• I ~ SIDE VIEW I FIG. 1 I 2 9 II I !j_ ,, u-.,,,I VANE t t 30 I IIJ] ~: +· L ~UBBER JOINT SCHEMATIC DIAGRAM OF THE WIND TUNNEL L20" I GRID POSITION ' ' - - - ~' I. ,- - - - II - - - - - - - - - - - - - - I 2' - - - - - - , ~ 2 ' , I~ 3' 2" ~ TOP VIEW :~ - ~ CHEESE CLOTH 1 Ti ---- 1 1: 80 -:r ', • ' ', , ·1 ' 1 -, 1·: ' t--_:_:._ _!' ! -T ; t : i ~-•-·I ~ ~ L: t- 6 -[tl~"i~I:-~-~-~~ t,·.~1-:·' - r· ·-1 - \ ~ ·-· '.::.-.: L ~. ~ •..,.+I d,1;_1iy: 5 ;.J:;:r .~ __i~~ 'i , :·T: ; :·:~r,· 4 : :.\~: <.!; • • ll' u - (%) 3 ~- ;-; ::c: i ,. ~~;·r; .·;_: l" 11: .s.1±1 2 ,+; ; · ~ -;+..,.,.-, -'-,.+--•+4-,_...;. , . .•. ; .., . ;. 0 2 4 6 13 IO 12 X 14 16 18 20 22 24 26 28 'l' AE Ll!: 3 a SUP }•.'.HPOS I'l'ON 01< T'NO T:tP ~'S Oli' TU : :3ULT":N'.)E -x B == '74,5 . 3 mm. T::. 22 deg •. C. E . W. length,.,.., 3 .5 mm.'.( .0005 in. dia;n .) . V A (in . ) u'/u (pe rcen t} '( _I • 3 G. ,1 3 6 3.98 9 2.-92 12 2 .-32 15 .19'7 18 1.73 21 1~57 24 1.44 27 1.34 ?, } 3-gi ('1 fl\ /\ B .LIJJ 'l•' .L . "l. J ...,J b , -x I I B == '745.3 mm. H . VJ . l enp:th ~ 3. 5 rr.ra . { .0005 i n . diam.) X ( i .n. ) u'/U ( percent) 3 1.84 6 1.63 9 l,5J. 12 1.43 15 1.32 18 1.2:/. 21 1.21 24 1.13 2? 1.08 B='745.3mm. • B . W. T == 2 2 deg. C. ~ =. 794 length C--? 3. 5 mm. ( .0005 i n . d:i. r,m J X (in.) u•/u (p e r c ent) 3 6.04 6 3 .91 9 2.85 12 2,26 15 1.94 18 1.64 21 1.47 24 1.56 27 l.26 ~ "~: -~ u,~-" c:: ·:: :-; i" ~ ';. ~ 0 ~ -:·_ c :: "': s .. 0 '!,; 5 4 u' ,. ·•· -·-•-+: ..:__ • - • .. ' 3 _:'-'. -:-/J1 +- ~~ .....,..,...~ ...... ~--!.!· ) t::if2 rL-, :: ➔ .Jl • -' !.~=i.J:- •-r ;:; 1 : J:if r -+--" ):-+ __ :-r+t-r""i+-.;...+;---+-;--'---+-,-r+ir+ ~ -4-'-i-·~~+H-i--l-'-'---H l\~'-:·:}i H~ ; r; . . _; f-i; t :a;-+1 illI~:::_~~trj 1:m ,t: +-~+'"-...-1---~-1--.:....4,....-+,---+----+~.;...1_:-----1--.;...-,+.....;....,1-1-1......-l 1!:f~-: l-'-+-Hf-1-'+'-i-++-,-.;.....,. :p 0 1-r--,+-----1-.;--,-,-t ;-t : ht(\if-j;.~;} 1 __ '.~ -~ l~~ :·-:::··!; -;+rr tf' -i , ', - ., r· 4 12 -"t-isl::i+r-i-+-i-h-i--.c+-:-+-i-+-i 16 20 24 X 28 ( INCHES ) 32 .:J6 40 44 TABLE 4a., S UfERPOSI'l'ON OF 1'W O TYPE S OF TUlrnULENCE ,--x -I 20" B = 744.5 •mm. H.W. IT = 25 deg . C. length ...... 3 mm. ( .0005 diam.) " .i\. (in.) U = 11.6 m/s. u'/U ( per·cent) 3 4 .31 9 2 .26 15 1.81 21 1 .. 56 27 1.44 33 1.29 39 1.19 45 1.09 51 .999 TABLE 4h S D1-'EHf Ui3 l'l'ON OF' 11'\rn 'T Y.d ~S 'OF' 'l1U.KBULJ::'NCE I •I·- x -l 20" 1B = ? 44. ;5 lTIL1. H.W. a T = 25 deg. C. length C----7 3 mm.( .0005 diam.) f=.118 U :::oll.6 m/s. X (in.) u'/U (nercent) 5 1.47 9 1.28 15 1.14 21 1.05 27 .95 33 .,878 39 .828 45 .796 51 .765 TABLE 4c ---x 11 --, 20 B = 744.5 mm.• ~ T = 25 deg. C. d=.793 H .'N . 1eng th C---? 3 mm. ( .0005 diam.) '" .A. (in. ) U = 11.e m/s. u' /u ( p ercent) 3 4.28 9 2.27 15 1.81 21 1.56 27 1.41 33 1.29 39 1.17 45 1.095 51 1.02 ~=.118 (!:?!ION!) X OF 0/7 0~ Oc? 0/ 0 0 I .-• ~ ··. · ; : ; _,· -i-:tt -----;,-t · •. l· : ·:-_ - +-:--;- ·:-n~: 1-:, ..1 - ,-,-_ c l :-:~ -~i:Ji f' _:~:J ::n~~ '· / - t-1-~ ~~:aj ,,,,_, i• __ J.~Jtl 'I,, f! % fl ,n p; ; : .!JU v 1 --!:Li ; ~·r- q '. f ' ' ' 1::;cre ::1" -- 11 i :c1::rn-•·-'.F. fH:·: " 1:-. ··-~ -·~ · j '• 111.: I ' ·'"" '·1-f "' 'TITiht~i 1~-=c1 1 ~ i m~l!~Ll]1 ;~~fa;mif:Jt.!mfjJt f ~ ~ ·i- {\) c ' " )- -: :-..: :.,: $ 0 u :x, :..1 ·: ;.,~. C " -, ! -i+ ;---4,,-,-;-,-t+ . . . ~;;;d1t~iRBFi; • • .. - , _ , _ , ;.., -..+ ,,., , H,r "I~,:;=.-rtitl: , ." ,1,, t,r, ,cµ - • ' +-'--+~h-:--f ----,-+,-i-i-'--1~+-+-:-r-:-:,--,-;--,--t-t~ .. Jli! -•irt=t:-'-:·:j TABLE 5a .-x B:=746.4 T=23.5 de g . C. ,d =. 795 H. W. length .,_, 3 rmn. ( . 0005 in. diur1-. ) X ( fn.) u.'/U (percent) 3 4.95 ? 3.26 9 2. 46 12 2.09 18 1.71 24 1.54 36 1.29 48 1.15 . f= .118 7 5 U = 11. 56 m/s. TABLE 5 b .SUPE.u ' O::, JT Ol: OF 'J.Yrn TYfES O:? '11v.!.IBULENCE ,-x I B = 746 .4 ~=.118 '75 T=23.5 der;. C. H .-/; . lengthc.-.. 3 mm.{.0005 in. diam.) X {in .) u'/U 3 2. ;55 6 2.28 9 2 . 24 12 2. 18 18 2.08 24 2. 00 36 1. 35 48 1.77 ( percent) U =11. 56 m/ s. 'l'AB IB Sc ~3U?EH.i:'O3 ITON OF 'J."!iO 'l'Yl'E:3 OF 'rURBULENCE -x B = 746.4 f=.11 8?5 T = 23 .5 de g . C. H .w. length .,_ 3 mm. ( .0005 in. diam.) V A ( ....i. r~.I • )' u'/U (p ercen t) 3 4 .95 6 3 .33 9 2 .45 12 2.07 18 1. 66 24 1.46 36 1.25 48 1.085 U 11.56 m/s. "y -" "'1 ~~ "'"' -~~ 0:: ..... 0 0~ .. , ~ s; ~ -:-.:. ~ ~ '? -:: :.: 1 ~ ~ I [T (%) WJ 4 .!~ j;; riii i#i f;~ 1 ~~ 1 1 tiiI ~t,1t; ~•ti~;~;•·:;lmi;~~I;t1i itli j;f1t,liJ}I~,:~r~i 1~ ; tr11=rt: f u~v ~~~t :rrr}1t:J }r:: J-f!t1~tI1n }~;::rt:lJ gJ}=·:}rt:T~l r~t lJJ,~~~~-ltfU! =~JI! ur:fif :-:/Tm H·'·-ttR 1Wita;-llJ:. ?t· ;~-u- T.-L] :i:; t;~i 3 1 1 U•-Hl, 1 !F n~\ 01 '-f +}'j 'c··i ~.+: ;3,t:;: H, t ~'"}~~· ~:'.l!f~{ !11{ 1 1t· + r+ Lf3 -H Ii: •+'--,: ; i' ,,;,- ,!,, ~t.;1~ ~t :ll\i ~lii}f Wji~~{tj lj\~~ 1 1 1~ ,,. , i , .. ,a· -:.l "" :i-rj;'.' ' c,L\ ,. ,,. N:-J. , - !i -' ~ c r'H , : -:-',, , .. 1,tf l .. jl:j; , ·-, J._;1~ -=Ji-A ,.-1 1 .. , .,j_rJ}\, •·+, ,.if _:-rJ.i : . 1~ :-, 2 •·it'•· • • •➔ J};: : :.,:i Jh1'· .!-:it( f.1:/"J_i:j+i1f i:rF-- i.H1·· tjtt ~-=·· - · ·, ·! i "1 ~: l : · : :: .~ _; · ~:~;·; .; · j J r -; - · r r+l--r-~-r - ~~~:;-_ -_F 1 j.tj::- :1::U tr:J::-- ·•·1 :L ·1i_ t'jr h r '- -;., ' ' : ,. '; ,-,-, ,_ : '' ' L!' : : , ; ! ,·1 : :u I I I ' f;"r-'-!-+) '• __[-, -=[-; -+!•f;:·b-;-1 .'. ;~~ -! ; ; : ;. ti : ·(LU I;. · • · : ➔ i , r: .: :;· : !-! '. L:i~~ :;::,I ;i:_/ 1 rt~;: ·1.fu ; ;:, ;:-tr-l:_- _ \·-:_1,_-. :., •_-rd,_~:_;/: ·__;, .;i,_:~.,-:;,, ~,1:·:,._+;I:+·; 1.,:_.,---ii .. i ,.: ~ ~_:_ Hi+~~-i i '.; i '. 1 ' ' ,1--➔ •-r t· ➔ -t· h ----t;-qj1 -i-t-l7 _; ~,F l; ~ nn ;}; ~~tl~~:-iI;~- 1 ; : ' r j ~:rL:;J:. ,, . ,tt•·' rJ-t:irr .. , "~lf -1-J• 1 1F •l• -l -1 ,· , , , , . It H _;s.; I :. ·. . ., ~ '.fJh • c·, t i Jt; iJ 'ill, ' :; !' jff : 1 •1· . '·:. ;~~~ . , .... ~. ::,C- :- _·-r;,, : i : i ! : ! ,; _ 1 ,., I H:i-_'._,-i_-_,·_ :'.'.:. ;'.·;~r+.:.+\_ :+ :' ~ :: 1;, ,~ ~; ; :·: : ~ ; : ''. '. i: : # ·--~ •:r;, -,'-- _••-t ffl llit H L, j-, ,- ,, j'-H • _ r1. , ·-t- [" •-• ;,lj :,-! i , I. : Id : : , ; ; ; , , , I-+ . ):ii '.lrn l:tff. +"i j~ i(f( -1:J •!1=11. =ti ~ t;r ~;r-rif~r !:; ::.~1 jt.,,-:T:-r~ j14ii:-~1'. ::f <t \r t\; :ii/...;, iii:.. t- :r'.! m~t-'!,:::--....~-:-;,..4+~,;-i-·ii... --:r 't· ,,... , i 1 1 1( ·:t:.i. •·'·!-, , •• ,, , Ii, · •• 1•. ..., •• , .,1 ; . 1 T:GT 1 .,,. 1-··-- ,,1 ,1 ,::, 1 : :,i :1:: oh*liilitlft1tfl1:iIT·4ff flITitl'.111U~: .,::t+%r.:fr ~n:·+¥.]F.cfrfr:+: ·•:' ,~: ei• <i:7: •;~'. 2 4 8 10 16 18 20 22 26 ri' AB IB 6a -j s'' r- B =; 7 42. 4 m..·-n . T := 26 deg. C. H . w . length~ 3 :nrr.1 . ( .0005 in. diam.) ' X (in.) u'/U (percent) 3 6.8 6 4 9 2.88 12 2.30 15 2 18 1.81 21 1.66 24 1.55 27 1.41 f=.117 TABLE 0 b I ---+ I -is" X I- B=742.4 nnn. T = 26 de g . C. H.W. length c.-... 3 nm!". { • 0005 in. diam.) X (in.) u•/u (percent) 3 2.12 6 1.9 9 1.68 12 1.57 15 1.48 18 1.42 TABLE 6C 3U PERiOSITON OF ~ JO TYPES OF TUfiB~ LENCE -l 5" 1B = 742.4 mm. 11 =.26 de g . C. • H . 1.'.i . leng th c:.--.,3 mm .( .000 5 in. diar11.) X (in.) u'/U ( percent) 3 '7. 6 6 4 . 25 9 3 .01 12 2.39 15 2.02 18 1.77 21 1.55 24 1.46 27 1.34 f= .117 8 {fJ~ --lfr; qt 1• \;:t j .1.; '. ~ Tf-1-.+_ ---t-'-H--r-,-'--1•++++++!-l-·Y : f: ., •·:-~-.: T [TI. 1. 117 ~:;.>: l ; i 4 J!iJL :HtfftrH: ~t·r-.+-;;-;,;" . . i+}-.~.,. .,. ,.~:;. . ~~ . . -+~:..-~::~~:~~-L:_..,:.........-,_..,_-+...-_-_+: ::. . :::.L . ...c.;:...-1+--_..._+,:_,+,.....~-< j,-~·~_ i:·-:_.l_ ·~.1 l l_.i~,t _:,:~_-_], , -'~- :-; :..~ . J,, _c llf i/.l~ Jffj4:]j_, ,J- -;-..,t =~1 I[ll ~r(i-:ti~~ ..,........,"....-~--r+- li ]r!; ~ jfjrij ¾ 3 I,~:.-_:.~.•:_ ,ri~-+;+_-,-, --.-,\:;-\---'-j---, r _-_ t:_~--:r·r• : :.·_ !:: • f _;_:r::r_:_ J: lJF ·r:t 1Fl:f,- _:-i~tt: r++r- ii• J ,.: !- 1:r_... l:= _~_ ! ,:_?_~ ,l -.-_:1·,·_ .r '" rHT :;~1t: w;1/1 t {F \ ( ~:fft t;: ·+·-. ....;...a+'--'-'-i--1 .:~.J: J-.J-i;,. - 1 ·: r,. ......,_,_,.+'-.-'-,+,-'-;..;..,f-'+ tt'. :l 1 1 ! ~_.............,., +'-?""i-~l>,-/ :~➔- ~-:: ·!~.Ji -_f}~i-~]:j: L +cs-~+r• ...;....:t_-l,,· ,-;- c..._µ ._....;,.+....,...;..+1 Wl ~Tr; :lr~ r: :\J~- 2 -· :.,.' • ; 'I -•·" i· - . :·. i f :-f : ---+-f-t--+-,-,+--,- ·rj:t'.: . i: (; :., , : • • _;i ;··! - ..L:. f - n·•, :Ld ! 1.i-u~r ff9~::t1+=i=;;:;;:t:::rtt~c:'-tt:-:-:rt:-t::ct~.-: 1Tl F7 t ;) +t-'-:'"""t--,~::h I 10 20 X 30 (INCHES) ::JI:hi_ 40 .5V 60 TAB LE 7a ~ so"-1 B== 747.8 H. 'f;! . T =25 deg. C. ~= .1185 d"' • 795 length .....-. 3 mm. ( • 0005 ,diam. ) U = 11."6 m/ s. X (in.) u'/U (percent) 3 7.53 6 4.22 9 3.14 12 2.66 18 2.16 2 .4 1.8'8 30 1.68 36 1.57 48 1.43 60 1.33 TABLE 7 b B = 7 47. 8 · T == 25 dep;. C. B .',': . l enr.-;th c_.----. 2)== .'795 3 min. ( .0005 diam.) ~= .1185 U = 11.6 m/s. X: (in. ) u'/U (percent) 3 2.53 6 2.46 9 2.39 12 2.32 18 2.22 24 2.10 30 2.04 36 1.92 48 1.82 60 1.70 '11 ABLJ< 7C • SUPERl' OSI T ON OF ~\\ O rJ:YP}'.S 0 :8' TU!:WULENCE ~e = 25 de g . c. f=.11 85 TT == 11. 6 m/ s . X (in. ) u'/TJ ( perce n t) 3 7. 62 6 -- · 4 .06 9 2 .90 12 2 . 38 18 1.84 24 1.55 30 1.36 36 1 .24 48 1.07 60 . 9 35 ... .. ::: , f :;: : -~~~ ~:..:. __ • :_ t '. ~ 0 z 0 - u 30 70 ' q -;-;-r-·' ' : j 1 ' J ! •• · ' •1 j~ l ' _J -n--r-,-1-i-.,..'--,..,h-i-f-°'•j l J L - I : , ;i"i-'T71 1-rJ-'- •· ..,,_ • t' -½-'-+T-'--+,,-H++- I l.+ j..J. J ' • • ~If ~ I: ·l : T~:+:__H ' L::_ _·-~ :·H , -'-i-~..+-•4+ r , ., ., -~ _1-;:-· ., ·!: • 1·. 1_· 1t~ ~ --~ ----I-'-~.....,....,......-.,_,.............................. .....--......,_,...... ..................................,..;........_............ ................~ + - - - - + -. ..,.,... .......... -lft1 \' 1+,t~ ~I · -; , : . ~ ~ ~ ~ ! .,:~ -,-+l, -,-'"t-,- lfr _:J~~: ' !-lG-i:i in-~ 1 ' ' ·H-• ~ - , ~ ~ + - + + r l -! H-i-l-+-:-l+;-;-++i-+'..;..i-:+_;,+i+,-,+;-++++H+H+imA-+-t-'.;,.f",.-rrl-:+~,j,,:-:i:1tµ~,,..~'r~~+-P;..J,l,.-!•4i-+-l+i-;+l+i-i· A 07 !f'Tlt,:,1j~JH,f--!'i·~:[-~-++--.,.-.,.++-+-~;::::~;: .,~~~:+frit+4i:-l=!+f+1+!+t+t+ttt++FiH-i+:+:inttt+µ_::~::j=1~µ+ttt .;+-,+-'-,-'-i-b c-ri l+,-'-'I-H-H..;..!+;-++H-H--H ~ -~ ~ :f J ,,+J 1t· ' 1f=j ,' · t :p-; ! Jii; 111 fa,;' ,. + s__~ ~ ~r 06 '.tl l .05 iT 1 -+•, . -..,•... ~ i.................... ,,..;.-4-,.,..:..,++-,--;-;-H-;-;++-'--++l-iH+H+++;-l++-41H+H+++t+l-i-++H+H.J.+++--t-MH+4+++t+h-41H+H+++t+H-4+f-i++ ;+f ' ' ' :1 i:· .04 .03 J l~j j ~~%21 ,1t-[,•-~,0..~.....,t-,~+ l!J qjf,f 1W[f(i I~l~ r;· :-· ··. - .. . .'....:., 1- ; · · ·;~:- ··: i. ; • ., ... _. ;::·:j: .tll-:-fi 02 ·_-)~.: j_;:i-l;+. •·: T" • /}I:[ -: : ;_:i- .: .0/ 1 ·i- ; •· ;- . -~: t!./-! :::~ t !.. ~-,.,;.to;-,;.---i-,h-,-,-'+-+r-r!-+-i-i+h-4<+;+..:.+-++-i-h-;.....1+""-'++-+-'---h-,+.+ ·; j. J ,.... ·1 ·!-~ 0 .,· .1.:,- 10 20 30 X M :-:+-: · i,T!:l ·,:'.,:: .!,·• 40 5{) 60 70 i 'I l~ttT •j "' -~ •. . :> fl) ; -~ :j .24 22 .20 ./8 ./6 ./4 ./2 . IO ~-.......,__.__......_ .0 · r · , ;... • .06 - ~frt • j. I ~ •• -~ 1 f1t( j ) .,.++-;..+J+f-H..;...;+!...+'-t-'-++,..µ ~13~/~. :;~: .04 ~~~r+h-++.-h-+'-H+-,+.1+;-,-;H+H,+.+,.-~-4,-;-.:..+:-f++++H+++---"11-~-l--'-4-:+!+i-H+'-.,..;+,-,,..,...+~,...+-..;.._.j-~+;-:------1--c._+--,.c..+-.:..:..-H-4+-l 0 0 10 20 30 X !v1 40 50 60 70 ) i- !. . ' '~ I I i: -: . , . . J : •- • I_ ·· . T--:-·: "j f ' ·t· , ' ~ I · -·- :~,-1s--1-~"-¼-...-~1--.~+--'-'-..+J..J....;...H-,..w+,+,...+-i-'-"'-'-+-,-4,+_....+-.;..,..+-,---,+----'-l-----+,-.;...,.++n-l-i_-i,,- '- ,.,.+-.;.+-;.-,.;.... ' ' ' • t , Jli1J~r _,,_: Ii ;:,.'c:i-- -·rt 1lf}ft! iffl i11: J:J~rlt# ·~ ·',,~ ~Hli1"t :Jlj 1 ;, 'u c ~ ~ ,: i; ~· ;:. 2 :; : • • • ('J ~.':'. (U l~ F, ~ ,;. 1-'~ :~ X ~ ;~ j C ,, " ,I :J. "'" M l'J " I: ; ' I tt . I , J 1 r· : 1~-:·1 --: .. , ~-::: I • !. ' -i . ·•- •·--- - · • - • : 1 • •I • - · · -- •-· •-•- · i- • -- - - •- .... "i' . ...... l•-----~ -- - I. I 1 .•r · r. . I . . : ; • t 1 I .t • -l ~t -~TTTTTT r~~ TTfj:rJ&~ -l>,-- -+--,,s - ·_=+ . [=t---=~:.' Lf.. - -:i- i . --:-:--1 -- •I '1:i::; -..:~;_~ . .• ::I : i J_:__:. • I ,:, ~ '.::t ~ :~ 'I l>)C I ! . 710._ ---1-· :- ~- I :- : • 1- ---- --.. --- I ' - - -- - t--- ---; -· • . ,. . ,l!_t J-·;_~m+: --r--- -- _:. , li,' i .. 1--.--:- --+-,-...;- - + - - - - ,i..;.___-+-------l,,"-'---,i"--"'~+---'f---+---'-f - -~ - f - - ~- f - --+--- + - --+---· tt-l~~Af? ':\\ T; -~ - , .. ..... , ...., .. , ... . . .. ; ., • • ·; :!.. •• -- 1 1: -:: .• 88+ ,. ~ -·___, >f-"••:: :•_;..+- :·::- • I * -P+:ccf~: ·- r' ~----+-----+-------+----1-- ··-- ,. 1 • • •• •• ·· 1· .- _ : : ••- . · -r I '· ·· · -~ j~: : :>):- •r. -~i",";~-1. --- J~ .. -------- · ·1 +-: :-i-7 · - ·· -+-...--:· I· ·,·_ ~-l·:·---f ... _,,_ · ::·-•• :1:,:: 1,:·. ; : · I ..............,· ·!·· t---------,--t--+- -_ - ~ fc~1t _-~ . '. . _ . ,·: _J _ : -~ r ~: . . . .: iJ __Tt~~ __ __i\ :! , • : •• · >: •T :D : ; ij ! J 'J: ·• :1-- -:--: .ft· .. ~ J - _ :. :_T~ :,71__ ._ r1---r-:: ', ~?- .•• , .-~r-,' ·,-- -·-: ·~-' . . .... !...... ... . ·-4-- ;- - ' , .:· 1' t.......... ~ l~--1 t !~ ..:...--- 1 -I ; - ••• , l .• ' 1 -~ ·,-+-------,......... -. - - l • -- -, • 1 ---f~- ~+-++--,-+ ~ , 1::).... -•-~ .-. L/l ' ---- r - I' _, • ' j !! l1 , '' I 1 ' 1 l ' l I j ' - [-0-+1 ' i ., I J ,, 1 ;I• : '. . : '.~ ·: ,) • • • ~ ,· , ! ~ -~ - j..... ... _:_ .... ~ .>< -- __ :_, ....L.:1.. ~',' ..:.Ll..'. - · I' - , ,I ', I · ; .L: ti ', . h , , - rl -+1-----t--·- +.-- , I 11 t ! 1 • I ' '' --' ! ' .. - ... . . .•I I I ' .... .. .... , ...... . • • • • 1 •-- - ' I • ' i-1--r·. :-+,··,'j 'i. • I l '.... .... ·-- __ _; _~ 1--•1 _ __; -·-- l.. ' ' . I • ' , ,•I , i I ; ;, ; ,, ! j ~ - + - --+--j . . . :.. ---,~I· -j '-~, l '\ ·I :-'- :1- " .i .. --- j ___ '. _ ' .1·:, -+---LI _ _! !!--• It r-;·; ~~),·-I ~~; ~.~• ;--; -~ -i:--- :J.. ... ..'. .... '. , , , :..'..-w•·-- 1-·....'...f--'.· -1·--· ! ~-- • -- --- - ·- · r--....1 - - r --::':-:-{ ' ' ,,, -t I !Tl-- , -t--+---, /q ,·:·, ;~t '., ,r ~ ,. ' , • . - • · - , . • 7---- -- -,-· t • · •, · , , --,...:..11_ - 111 ~ -1-- ' I'',• • I ' • ·1 ; 1i1L • ' 1 j JI 0 ' I 1 1 I ~ '·' - ' ~ 0 t, n ~--~:-1'-·---r- · ~....... V) I ! ~ ~-'· \ - _ +-:-~ ·: . . I, [ j i+2 ,( I 1 - 1~_:__ _: --- ' i I l , I ' ' ·- - 1-l....... ' ~ '-- T :-' --+-I --l-1.-··. -. L-;!: -- -- ~--~---!--+! I I -- -.:..i-- -----L --!-- · 7·- -1-·--- - 1- -+ - ... , ...... :I I -- , ·· I ! i 1 ; , __ t I I l - • -, i I j , , b j~ . ' I~~ -++++-r11+++-h I' J _. __ - - -1. ........ .. 1· i ' I I ! l .::1 • !' :' . ~J·:· !'. :1 j : ' '! ji - I .--· .,'-T --:-:-·-· I ' -- --1I ·: ·•7 ...... r --t-, -·--;-;--,-;-;- ;-:- ...,. . :~; ij ;;-· . . . . --- -- ,IT •-·1·: ---1. : -- --l ...i,',.,:· ...: ~1--I •---r ------• • • j· 1 ! !!i . 1 ,, - - - _ )'i___ __ -, ___ ·-,-------~ - ~-i+........,..,....._ "'1 ' ! .. ' '4 l • ' ' ,· , t ' , .. ·· . , , · ' ' ' ~ • :..:..L.::....... '• I ' 1 - .1 .... 7:r- -1. 1 : . i'.: ;,, : ' .: : ; -~ • '• I , •' : ; '· - --:- -;- ' .. I ( - - , •-+- •--- - ...... - ---:-~--- ·- 1· ; ' -; I t I l I ' ' I --'-- ---i---··- • I •-- - ~ ---,--·-·,--- -- + - ±·-1- ' 7 --· .. ......... I l i - -l -~-:-- \ --- ·~-~-,. ~- - •--~~--:+_- -_~ : :---- ~-'.-- !-;- ~- - . ·-: i _____'T : I ...:-1--- • -, ~-- ·/ 1---- -- r--~- _I _____ 1- ---- - ---1-- ·1 t-- -·-wL........ - r- - I , ,---~------r -;- -- ----·1 .. .) iI --!. -- :7·....t..-~~ ·.: ···-:· -=-·:~~..'...~:- :'.~', ...:,7-· __11-:-: • _· -<sjl -- 1-1~-- --: _--i ___ ---r· --~ .i-:- 1----- l·---1 :,., .... ·. ~ -· · r+·· · · . . !. . . -1~1·-I __ ,: . l : . . , j . .. .. I· i ; i -'. ; . .:. · ·•· · ·· . . .; . : :i :-i . -:--:, i :: . : ( -..f ·-, ~ ,- •r~r--: ::::~j·:::-~,r::::-r] : , .. --i ____ __:..: . ~: ___ _;__ ___ ;· r1 -• .:. . ... 1 , ....,.... - - !----;- • . . [:.. : _ .. .:. . : !.'...: ... : .. .:.·.L .. .:.~~r. ... 1- -- - +-- :,_;__..:_: __ !_: _i ·----1· •·..:....: :..: ..... ,.: ...~~'- .:. :.. i ____;____ ;•:• :::: i :·:. !:: I: · :L ~LLJlI. . •-•·! :·•· I I ---·:-.--L •--- :•-- .: _! ·~ ,;- , '-, -. ,. . :J~: •:•_L _i _~l J~. :. . :. :L. . .:. 1 w '" "w • . ~ w C ,.w 0 '\ ,.r. 0 7 -:~zl:t :'- k~• • • : 1 ri I,;, I l· • }f- :- C*~L-f .,:· ;'; :J· · : SIT . · - Sf, '~t::: . . . :. --:-P·- r :- - ' " 1 j ~; . I.. I r,7:-~.:... :-::..,-._ J~ :•• I?~ .. - i ' . ; -_-1--,1: i I I I r- · 1• I: . i"J- :,..~_':.'.._: _I .. 1 i •• ··--:- f --:.--:':-1·1:-::--J-----'....:..;.L :..::. t· . ..:..::.: _l.- T - - ---r --~ . - ~1 : i . _ : :. , I , ,; ' : I 1-:-H . :-, I . i- - f'~' '· ~ ::. ~ -· .'. I 'I -+-1 ---- ' J· ~· r_:-:-- •Tt:-itl+P~Lll ~ - J -1~__:_ 0 - '"I :- · -:-·:-i·r1 • l 1 :1! 0 /0 20 30 X M 40 50 60 70 i-;-;T: I ,[ _: !: •_:_ I ,., i r~J- -,--~ r , 1 ,, ! ., ,. ', ' ~ ., --7-:·--i--- i--- :--1~~--; •••-:~---- , , ,: , • 1 , • 7--r-:-:-~·--1-! ~ I .- -1: -: ·I~ 7 ': :: , _ l • :1·::: I -~1~ 1• ;~ , ·i t-"""1··r~·.--.t·..-~ t. ,::::J _ r ·: ~- 1.2I - , .. -,-. . -:l .,-, _ , ,1 . -- . j I' , ! .-- I J I - ;--- ---- 1-;~·. --~- :__: - -----·r-- - - ,' I ·- - : - - e - --1------ f- - ·- ·-7 .. ;, ! I l 1 • r J ,;i . ~- a: -:- ~.; ": _ . i I . ·'· I I ' --7~7-+ -:- . ! ' I- l 1 . , , ~ 1 - 1', ••• . J .,' I ' '. 1..- ••• ' ! ' •• ' , .L i ,: ' .. i ' - 1 . , ~~ . ... i 1 , .. - I: ~ ' , ! - e - ' •1 ' -----; ~-l-:~:- I- - '; - <J . . •• •• .: 1 · • :j~ ! , · -~' ~ ~ ··r (f . . I ·::~:~rt rv:--· ·: ~ ::·· :~ :-: • : : , ·-· ! i r r · 1· : , I -~-T, :~--1-.·· - ·' ': ' ! / , l , .·: ··,; ;_: .: ' I - - I . :l j , ·•·i- , . ,, 1 '• •I 1 . i.:-- - -·-i · -~ ~ 4 ; :·' · • ~ ,. , : -~ : 1: i :.~- : _ 1__:__ <. • . •~~~ •·,<:,___ . --~7i;~ .cl , k_l~ , 1.-: :,··+:·-~e r~ ·•+r -~ , · ·" _ -~-~L-~--1 -~~ t=rsr ~··:.-~- ~~--1' :_:~.. _j __/.__ -~ '~ j_:r -·,. --~-:·•-:~ •.~~ _-~~~J~~:. - I~.. 2~j ·~ t--i -/ TS ,4 -1. •~.n-i~ ;t _ _ , • _ _ _ : __ ; :..:_ t ' ' ' _ • •• ' , 1 , ; ' , 1·; : • , j '. .• I ' I • ' I ±' · ' . l •, : ' I ' . • I , { :1 • _- \ . . 1 : : I ' '·· i _ , - ~- - -··· 1·~-r--·- ~-r~~-1~~- ~--~ - ·-•··•-~-· ·--:- - :-- i-:- I • I j: .-_-: j , ' • • I : j :- : ' ---1-,• : '. ·, ./ ,. ' . [ --~ - ~ • . .: : _ _,___ - ~ ; -,- ' ' :~ 'I ' J....;..; ' · / j_ •. ,V)I: : 'I . ., 'I ~ --,C.:+-AJ ·- '-. . IV\ftj · i . Y, -: N~- :-: lt -1 ·-n·~M~ · : -~-1 ~-r,~ ·1 .-:- ,. • [ .-~~~- --~-=-; ~~-~~-~ ~fg__ ·-sr ~ <t - : : I ~ L.. 9J :0..-. • • ·H ·; ' • j • j ·i~~t t r· ,--,, i•-•· • • • ;;a • ; . ,·- ~~:i ·-r-.-;•· i .;r1I!~ 1·• ! 1-:...f--1•-· -1 ,~·~-~--·-r+ :1· -• ·1~ t= -~!;: ::: .,: ·f· . ! -~ 1 ·, · . i + -~r r :- ·1--· -+ -1T-t ( ;:f- -~-t-----l--~--l"-- - -:--- ·-r~ --___; ' - : 1 • 1 I ---,..--,-·-t r -I I ·l ,--,----, • I i ' -· ' ' ' :· .,,. 1 ' I Lr O -' I · cc-. 1 • : . 1-:--··-i-~ -- c_ ____.,__ -- ___ J_~ ---7- - - _- L - - - 1---t· :, 11 - 1 I --·-·--r---+:.,:--- •• · :~ - I ✓, I -- -::-·+-----+- • " 4') ! J: 1 l • • • +-- I"--" 1 - . ' . .. . ·_. ~ -, . . . . .-~ . . ·.....--:- ..• ;' ... . l ., ·:;. .• :'I · •, \; • a. ~: ., .: •. ;) 0 . .1-:--T~F.7":-;-! ' +t r-__r_F . • I I: . I ' I •-r=t11-: --l ! . . - I I I "' ,\ ' ,.,n ;.; ., , _:, ! .., .. ( l L• • - ' f- ---i ____ _j_ _ I I t .. 1". ! L .. . I ,,..-.. ·- £ 8 F C O O O O 0 TO POTENTIOMETER o ·o o o o BA C D POTENTIOMETER SELECTOR SWITCH AHWl B INPUT SELECTER SWITCH A 0 E Co Do B C HW2D oD oc oA OA 0 Sow .Fow 50 w Q: lJJ - ~ ~ ~ ~ ~ 12 V ~ II . I------'-------' FIG 35. Cl.: {2 12V /1~ INPUT CIRCUIT FOR CORRELATION AMPLIFIER FIG 3G. J... /80 V -r- • -Iv ,/,I. 250M ; M= f /OOOw / -/ V STEP.5 =2:/ ATTENUATION /tJOOM ,, 6£6 8,uf I I O- I OM G VOLT FILAMENTS PREAMPLIFIER -BATTERY OPERATED -8ftf /603 • '-... -Iv + -: 270V "OOOM ~OOOM FIG 37 4mf 6£6 M =IOOOw -3v 250M 6J5G BM 5M TO WALL GAL V: RECTiFIER METER. !Om.a. CAPACITY THERMOCOUPLE ~NERAL RADIO ~ 24ftf fOWER AMPLIFIER - BATTERY OPERATED 6 VOLT FILAMENTS 250M 2Af I ' I ·: -:- 1 I - --1 --, _ 1 ,---:--:-r - -r--,--,I. I I I ' _: _ ,__!-_ _-~- _, r -,--' ! - l , 1 1-- --- ''T _ 1 I L __ 1__ _ _ __ _ ! , I • i i -+--~--~---+- _:__._-; - •1- - l --1 ·· 1 -r· 1 L __ I ' ' - -1i•--·--;I ·- .' . I;. -! [___, - -~- - -- - -- I : ; - -: -- It- I l : l - 1- : , -- - ;- - -- -~ i t- 1:-+- - I .. l 1~--i--_ I"--: _ ., . ·: '. :i -/ --+-·--\ l -+--~-+- --~ -:., s 0 . I I! .:.I - ' ,'.~'.~_ ",:,·:_-~I ,-~-•. J·_=L.~.:-~l;,J--L ···' '• - --~- ' 'i 7 ·- l ---,- ---i--- . i. .::.....• ,-~-..'. . . __Y,5/Af... (JR/D~- i. -- . . : L: . : • : . l : j .--~--I. I : • l --··1···· - '. " j" \ •. ;_ . . · - ,- · - · - ----;- ---! - ---- ' --- - ! 1· ' . i, i ' - ;·----r -;- • 1-··--' - i i- ➔ I 1 ., ' --+~--t -·t: ·- --•l:- --: --r- ·1- - 1---t ' I "--' -:. __ _·--J - ,. l : : I II • ! i 1 ID . r·- - '. !j . -- ; •• .• ! - - : I ; ·. .- ... .-------,j ~ I I -I • ~ I ···., h - i ... I : -- - -- l ' I ™~• i- I : - .. -· I l ! r.___;___I I - I-1 ' -- l . : _, I ' I : - i - '. - - ,: I I I I ;, I ' l I I ' ' ~j I I I ' i- - T-r~!~=l---t·-+- ' 1·•-• ·_- ' ' ' +- t - ;- -t-1·---- _ + 11·· ···11_ i J ·'I·· ~~-~~-~~~~-~~'--'--'---~L.l.c · I ·· ·',1 l I l ' ' ' ; l I •i i ' I ! l ' I 1 I ' : ' ~---!f- -++: ' I • :sd7ftrJFlio7f1-wJRE-.t i t :i - ' I I ]_ ! I 1' t I ,II · I I I - -- - - ------ -t- - ---- 1 -> - -I- -: - ·1·-·· ·:-··- 1---~ -- : I :I ; I I :· :I .! - 1' : • I I I 1· , l--7 -t----\--- -i--t--i-I ( l I I I : I , I I I ' : ' ' I ' ·· i- - - ,-·--'--- '-- ' ---i - : !- !· I I ..,1_.. • , • •1- • • I J' l-:rr;7:R ' I -------- ' ' f :,! :i ! r1 · 1 1·1 rr1 't~~ l .. I I ---! --i~ :-1·-·:1:- -1- ---i i. r 1 I _:_l____ , _ _L_;.._ . :, ! :: l ... 1_ i : ··1· !: • !. · .i ' .: ----i I : ' ! ' ---~-- r '. i' I ! .. i J . , _J__j__J ~_l__L_cLj__c_L ___ _L____ 1 • . • • I : I I , : --1--- ;-----1 I ' - : .: ,i__~LLJ 8 TABLE CA LIBRATION OF HOT WI RE u = 29. 8 ft./sec. T = 19 deg. C B. P . = 7 48 m,_j1 • / b= . 805 f 90 180 ,6( nun . ) TAP I.2. Re I 1150 1150 2 . 66 2.66 6 3 7 3 3 7 _ '7. u' - 2 • 22 X 540 X 10 O = 13 .22% 9.085 u ---- on tap 3, on I= 2.66 DECAY OF' TURBULENCE I .3 ti' 10.50 1 . 2 25 6.1 13. 37 . 945 4 .7 18.05 .795 3.95 22.10 .700 3.48 26.05 . 636 3 .16 30 .05 .576 2.865 38 . 05 .500 2. 49 46 .10 . 439 2.183 54.10 . 40 4 2.01 62 . 10 . 375 1 . [3 65 70 .10 . 351 1.745 --;r .r.. M u ( o/o ) TABLE 9 CALIBRATION OF HOT WIRE u = 38 ft ./sec. B .P. = 748.6mm. T = 21 deg. c. E> == .1196 ( mm.) f TAP IG Re I 2.61 90 6 2 6.75 1050 180 3 2• 6.90 1050 uu' = 10. 4 % on I 2 = 2 . 61 DECAY OF TURBULENCE ( 1. 5 in. grid) X I2 M u'/U (percent) 10.80 1.55 6.17 14.085 1.2025 4.78 18.085 1.005 4.0 22.09 .876 3.49 26.09 .808 3.11 34.10 .684 2.72 42.10 .596 2.37 50.06 .552 2.20 58.10 .505 2.02 66.08 .471 1.875 TABLE 10 CALIBRATION OF HOT WIRE U == 53.5 ft./ sec. B.P. = 747.4 mm. T = 18.8 deg. c. f'= .1208 ~ == .804 (mm.) f TAP I2 Re I 90 6 3 6.3 950 2.51 180 3 3 6.3 950 2.51 u' u = 7.37 % on I.3 == 2.51 DECAY OF TURBULENCE ( 1. 5 in. grid) u'/U (percent) X M 10 2.096 6.15 12.76 1.815 5.325 16.65 1.47 4.32 20.70 1.279 3.76 24.65 1.192 3.5 28.65 1.06 3.11 32.65 1.00 2.93 39.3 .865 2.54 46 .813 2.39 52.6 .738 2.17 59.4 - 7025 2.06 66.0 .68 1.99 72.7 .605 1.775 / - TABLE lla Correl a tion of tur bulen ce prod uced by 1. 5 in. grid X = 38 .6 u = 29 . 8 ft. / sec. T B.P. M = 22 de g . C ~: y (in.) :M t- .02 .05 .10 .. 15 .25 .35 .55 .85 1.15 1.45 1.75 2.05 2.35 20.30 19.78 19.22 5 18.75 16.875 16.075 14.635 13.56 12.05. 11.75 11.30 11.30 11.25 = 748.2 mm . .8055 M- R2 .98 25 .947 .862 .78 1 .645 .560 .388 .2615 .1363 .0755 .0143 5 .0087 -.0088 2 0. 1 85 0.555 1. 43 2.30 3.65 4.525 6.45 7.935 9.15 10.10 10.98 11.105 11.~5 TABLE llb Cor r ela tion of turbulence produced by 1.5 in. g rid u = 29.9 f t./sec. T X Ii! - 51 = 17.5 deg . c. . B .P. = 749.5 mm.• 6- .805 y (in.) M+ M R2 .02 .04 .09 .14 .24 .34 .54 10.70 10.60 10.20 9.625 9.10 8 .275 7.725 6.75 6.15 5.80 5.60 5.35 5.475 5.30 5.175 5.075 .12 .20 .59 .98 1.725 2.20 2.925 3.725 4.30 4.75 5.025 5.15 5. 45 5. 40 5.375 5. 25 ·~ .• 9775 .963 .891 .829 .681 .580 .451 .289 .177 .0995 .05 42 .01905 .00275 -.00935 -.01895 -.01695 .84 1.14 1.44 1.74 2.04 2.3 4 2.64 2.94 3.24 TABLE llc Corr e l a tion o f turbu l en c e produced b,r 1. 5 g r i d ,J X u = 29 . 9 f t. / s ec . T :NI = 66 . 4 B. P . - 7 49 . 5 mm. ~ = . 8 05 = 17. 5 °C y (in.) M+- M_ R . 02 7.8 .10 .975 .04 7.85 .16 .961 .09 7.825 . 40 .903 .14 7 ~'625 . 70 .8235 .24 7.15 1.225 .703 .34 6.825 1.60 .620 .54 6.325 2 .575 .422 .84 5.7 2.925 .322 1.14 5.45 3. 40 .2315 1.44 5.125 3.80 .1485 1. 74 4 .85 4.10 .0878 2.04 4.70 4 .55 .01623 2 . 34 4.60 4.55 . .00547 2.64 4 .60 4 .70 - .01095 2.9 4 4 .55 4 .725 .01886 3.24 4.60 4.775 .018 67 3.54 4.675 4 .775 .01058 2 TABLE 12a Cor relati on o f tur bul ence produced by 1. 5 in. grid X u = 3 8 f t.se c . T M -- 2 1 d eg . C. = 36 . 4 B. P- . = 749 mm. 2:>= . 807 y (in.) M+- M- Rz .0 2 6.70 .05 .985 .04 6.65 .15 .956 .10 6.24 .55 . 839 .15 .6.00 . 89 .742 .25 5.5 5 1. 26 .630 . 45 5 .05 1 .825 .469 . 75 4 . 40 2 .35 . 30 4 1.05 4 .10 2 . 875 .1755 1. 35 3. 87 5 3 . 20 .0955 1.65 3 . 45 3. 27 5 . 02 6 1.95 3. 45 3 . 45 .ooo 2. 25 3 . 45 3. 5 0 -.0062 2. 55 3. 37 5 3. 40 -. 0037 TABLE 12b Correlation o.f turbulence produced by 1.5 in. grid u -- 38 ft ./sec X = 51 M a = .806 0 T B. P. = 748.3 mm. = 20 C y ( in. ) M ..- M_ Rz. .022 8.37 .055 .987 .037 8 . 50 .100 .9775 .082 8 . 30 . 400 .908 .132 7 .94 .7 60 • . 8 26 .182 7.70 1.100 .750 .282 7 . 23 1.600 .638 . 4:32 6 . 83 2 .150 . 522 .582 6.32 2.600 . 4175 .882 5 .70 3.270 . 27 1 1.182 5 .27 3 . 620 .1856 1.482 5 .13 4.100 .1115 1.782 4 .83 4 . 320 .05575 2.082 4 . 67 4.500 .,01855 2.382 4 .55 4.520 . 003 31 . 2 . 682 4 . 45 4.600 -.016 6 2 . 982 4 . 52 4.55 -.0033 3 . 282 4 . 50 4 . 60 -.0110 - TABLE 12c Corre lation of turbulence produced by 1. 5 in. grid. X u = 38 f t . / sec. T M = 20 deg . ,.... -- 66 .4 B.P. = 750. 4 mm . 2) = .806 \J. y (in.) M+ M_ R2 .022 6.38 .06 . 970 .037 6.23 .10 . 969 .082 6 . 10 .26 .919 .132 5.95 . 475 . 852.5 . 182 5.65 .700 .780 .28 2 5. 40 1.070 .670 . 43 2 5.10 1. 450 . 5575 .582 4.92 1.7 3 0 . 480 . 882 4 .25 2 . 300 .298 1.182 4 .00 2.570 .218 1.482 3 .70 2 . 930 .116 1.78 2 3.60 3 . 130 . 0698 2.082 3 .55 3 . 220 . 048 75 2 . 382 3. 40 3.250 .02 255 2 . 682 3.40 3 .300 .01 49 2.982 1 4 .00 14.3 30 -.0180 3 . 282 13 .42 1 4 .720 -.01655 ' TAB LE 13a Correlation of turbulence produced by 1.5 in. grid. u = 53.5 ft. per sec. T = 19.5 deg. c. X M -= 34.7 B .P. == 748.2 J11.m. ~= .806 f= .12075 y (in.) R2 .02 .982 .045 .938 .070 .907 .095 .849 .145 .759 .245 .623 •. 445 .4475 .745 .269 1.045 .1625 1. 345 .07575 1.645 .0465 1.9 4 5 .00375 2.245 -.00833 2.545 -.0264 2. 845 -.0201 3.100 -.0154 3.400 -.0124 TABLE ,1 3b Correlation of turbulence produced by 1.5 in. g rid. U = 53.5 ft. per sec. _X = 50.85 M T == 19 deg. C . B. P . = 749.6 mm. ~= • 805 Y (in.) ~.02 .997 .045 •. 973 .095 .. 8'74 .145 .789 .245 .663 .345 .56 .645 .375 .945 .255 1.245 .1665 1.545 .975 1 .845 .414 2.245 .2695 2.545 0 3.445 -.01425 3.645 -.01434 3.945 -.0186 f TABLE 13c Correlation of turbulence produced by 1.5 in. g rid. U = 53.5 ft. per sec. x_ M _ 66.2 B . P .= 7 4 7 . 3 mm. T = 20 de g . C. Y (in.) .02 .045 .958 .095 .873 .145 .806 .245 .695 .445 .543 .745 .361 1.045 .262 1.345 .1686 1.645 .0978 1.945 .06025 2.545 .00346 2.845 -.00733 3.145 -.0281 TABLE 14 THE DECAY OF TURBULENCE P RODUCED BY 1 I N • . GR I D ( ¼ I N. DOWEL) B = 7 47 .1 mm. T= 20 deg . C. ~ = • 805 ~= .1204 Wollaston H .W. length c..-. 2 mm . ( . 0005 in. diam.) U = 29. 9 ft. per sec. X (in.) ufu (percent) 10 . 25 4.5 16 3.32 22 2.725 28 2.363 34 2.09 40 1.885 50 1.665 60 1 . 46 4 70 · 1.336 80 1.244 90 1.15 100 1.05 110 1.013 TABLE 15 THE DECAY OP TURBULENC E PR ODUCED BY 1 I N. GRID (¼ IN. DOWEL) B =747 .1 mm. T = 20 deg. C. ~ = .805 P==.1204 Wollaston H.W. leng th<--> 2 mm. ( .0005 in. diam.) U = 42. 25 ft. per sec. X (in.) u'/U (percent) 10.25 4.82 16 3.5 22 2.86 28 2.45 34 2.16 40 1.924 50 1.692 60 1.495 70 1.353 80 1.243 90 1.15 100 110 ' 1.08 1.02 TABLE 16 THE DECAY OF TURBULENCE PRODUCED BY 1 IN. GRID ( ¼ I N. DOWEL) B =7 48. 7 mm. T =19 deg. C. ~ =-. 805 f= .121 Wollaston H.W. length...,., 2 mm. (.0005 in. diam.) U=59.7 ft. per sec. X (in.) u'/U (perce nt) 10.25 4.53 22 2.71 34 2.025 50 1.575 62 1.395 74 1.24 86 1.11:5 100 1.06 110 .98 TABLE 17a Correlation of turbulence produced by 1 in. grid. u = 30 ft./sec. T = 23 deg. c. J '( '' X M = 41.. 875 B.P. = 747 mm. ~ = .119 M+ M .02 13.985 .15 98.00 .04 13.525 .35 95.00 .08 12.975 .925 86.75 .13 12~100 1.775 74.50 .23 11.300 3.075 57.50 .43 10.00 4.65 36.50 .73 8.220 6.125 1 4 .65 1.03 7.075 6.70 2.72 1.33 6.925 7.00 -0.538 1.63 6.925 7.30 -2.735 R (percent) TABLE 17b C-orrelation of turbulence produced by 1 in. grid. u = 30 ft./sec. X = 69. 875 M mm. T = 22.2 deg. c. f = .1195 y ( in. ) M+ Ivl _ R .02 7.225 .08 97.9 .04 7.50 .15 96.0 .08 7.00 .425 88.7 .13 6.925 .80 79.3 .23 6.15 1.45 61.9 • 4;5 5~ 475 2.,375 39.5 .73 4.50 3.05 19.2 1.03 4.25 3.60Cl 8 .25 1.33 3.95 3.70 3.27 1.63 3.80 3.825 0.328 f 1.93 3.725 3.85 -0.99 2.23 3.725 3-.i 826'.~ -1.325 (per,cent) TABLE 17c Correlation fo turbulence produced by 1 in. grid. u = 30 ft ./sec. !!: = 99.875 = 22.2 deg. c. P= .1195 T V M B.P. = 746. 5 m...m. y (in.) M+ M_ R .02 21.8 .2 9 8 .25 .04 21.25 .375 96.50 .08 20.7 .95 91.25 .13 19.6 1.95 82.00 .23 18 .05 3.75 65.65 .43 16.00 6.00 45.00 .73 13.725 8.40 24.05 1.03 12.30 9.65 12.06 1.33 1:1.25 10.30 :4~_40 1.63 10.85 10.50 1.64 2.23 10.275 10.35 -0.363 2.53 10.275 10.60 -1.555 (perce nt ) Photo 1 Wind Tunnel Photo 2 Front View of The Entrance Photo 3 Working Section Photo 4 Diffuser and Propeller with Motor Pb oto 5 Potentiometer,Hot-Wire Ampl i f i er, and Galvanomet e r Photo 6 Calibrating Tunnel Photo 7 Hot Wire Behind The Turbulence Producing For The Measurements Of The Decay. Photo 9. 1 in. Grid Photo 10. Grid No. 1 Photo 11 Photo 12. Grid No. 3 Grid No. 4 Photo 13. Grid No . 2