ENGINEERING RESEARCH INSTITUTE P wi''"? _____ ___________ UNIVERSITY OF MICHIGAN __g EMV- _ December 15, 1948 - / ~^ - 4 kit e A A' C k ^ *-M^Q { ((a l:,,.,,,., /?d o ANKAX$ OF T AHNIQUES MPL.OYND IN' 2, E:3ff, "t 4,; A, As, AA STUDY OF - SPR S.ION OF I PHOTOGAPIHC APH:! INUES P -: ED IKeeve M. Siegel D.. B. Cooper D, M1. Brown A^ONAUICAx- aEBACHS CEJWL'ER WIf)W W 1IU PCS- A RYPSIIANTIMICHIGA

ENGINEERING RESEARCH INSTITUTE Page IV-_5/ |UNIVERSITY OF MICHIGAN In E.V-53 the author spoke about taking certain points from photographs. Since these reports might come into readers' hands who are not familiar with the great care taken in the photographic techniques employed, it becomes necessary to explain the photographic work of Mr. Cooper. In the application of EMV 3 certain revisions in the original report seemed to add clarity in the application of this technique by the combustion engineer. These are discussed, A discussion, giving the physical difficulties involved in the application of EMV 2, and an experimental method is suggested for making WV 3 more general. A conclusion is then given concerning the value of EMV 2, EMV and EMV 4, Throughout this report the writers have assumed that the reader is familiar with reports iV 2, EMV 3, BV 4.

ENGINEERING RESEARCH INSTITUTE DIZYV __.-5 UNIVERSITY OF MICHIGAN 2 OT2OGBAPHIC EZCHIIQUES The procedures outlined below involved the problem of producing accurate photographs of thin tttanium-tetrschiLofi smoke strems in a moving gas in addition to showing the inverted cone of flame produced and held in the gas stream. The area. photographed enclosed a vertically moving stream of gas, a V-flame of low visual intensity and blue color held in the stream, and two thin streamers of TT smoke produced in a vertical plane coincident with the tip of the flame cone. The pertlient portion of the photograph included the flame cone, the smoke, and the point of Junction of the cone and smoke streamers. Since accurate measurements were to be taken from enlargements of the record negatives, it was necessary to keep the suoaiation of photographic errors <1%. The photographic equipment was simple. The caoera was a 4 X 5 Speed G:raphic with a 6-3/8" Anastigmet lens in a-Supermatic shutter. This was fastened on a sturdy stand made of 1" pipe. Placement of the camera was such that the lens and film planes were parallel to the plane of the titanium-tetrachloride smoke streams. The source of light was a 500 W. Bardwell and McAllister spotlight, set to maximum brilliance. Its position was at 120~ from the camera in the horizontal plane and 30~ above horizontal in the vertical plane, This gave sufficient illumination so that ~ sec. exposure at F-5.6, through a Written A filter was found to be adequate. The film used was Eastman Super-pancho-press filmType B. The A filter was used, incidentallybecause it decreased the haze around the flame which tended to obscure detail. The blue flame was of sufficient intensity to record itself in spite of the use of the filters, Development of the film was extended to produce maximum contrast without chemical fog being produced. Six minutes in D-72 diluted 1 to 1 at 68 F. was found to give satisfactory results. Fixation was 5 minutes in fresh F-5,followed by a minimum satisfactory wash of 15 minutes in 68~ F water. The film was then hung in a 75~ F stream of clean air until dry. This procedure in handling insured minimum distortion of the film. These negatives were found to have the necessary accuracy for the data desired. It is axiomatic, however, that errors will occur in recorclng photographically. Possible sources of error came from several points. It was

Di4f EM5 ENGINEERING RESEARCH INSTITUTE Pae.....I______________ UNIVERSITY OF MICHIlGAN necessary'to investigate all in order to be sure that the sin.mation of the maximum possible errors were less than 1%, Both information from Eastman Kodak Co. and. our tests showed that with our methods of handling tIhe film that distortion in- eit her t he film | base or emulsion was negligable. Differential distortion was <.1%. It is possible to have a slight shift of the image relative to the base, but it was too slight, if present, to be measured. Non-parallility of film, lens, and object was fould to Introduce the greatest error, but accuracy of aligient within 1c gave results still within limits when added to the other maximum errors in other stages. Printing of these negatives required care to eliminate inaccuracies. The equipment and the paper both were called upon to work to tolerances much beyond the normal range of photographic accuracy. The enlarger was an Omega D-2 4 x 5 enlarger with a Baush and Lomba 51" enlarging Tessar lens. The regular dustless carrier was di.scaxded a a glass sandwich type carrier substituted in order to keep the f1tn flbat. Before any work was started, the enlarger was checkel4 itW the base boardlensand carrier with a machinists.-evel to instre that thly were parallel. An additional check was made frcmthe easel se.rTace to the carrier surface with a nachiniste height gage to both dou:le..eC the original alignment and to check the easel for flatness eai pa.ia.iie ism with the carrier. The next step was to check the paper for differentfia distortion. It was single weight, Type XII, semis-mattee romide paper, Air Cotps Specifications 75-157B, which is plastic impregnated The testing was accomplished by punching fine holes I,8" apart om 20" x 24" paper both across and with the grain of the paper. Ten sheets were marked in this way with a beam compass and then processed. After drying, the compass was again placed over the holes and the shift from original placement was measured. In no case was differential distortion over.35. This is in contrast to standard papers which have an inherent distortion which can reach 2.5% Tests also showed that the paper was held sufficiently flat in t-e easel so that no error was introduced through buckling of the paper. As an added precaution, the paper was allowed to take a"set" in the easel before exposure to eliminate alight springing of the paper during the

ENGINEERING RESEARCH INSTITUTE ~MEIvW ____-5l _ YUNIVERSITY OF MICHIGAN..I.ae 4 exposure. This may not have accomplished anything toward greater accuracy, but at least it was an added precaution. The exposed paper was developed in D-72,diluted 2 parts water to one of developer, for 1I minutes. It was then rinsed in 14 Acetic acid. Fixation was carried out in fresh F-5 for 10 minutes. After fixation, -the paper was washed for 20 minutes in a drum washer with water at 68~ F. All times in liquids were kept at a minimrmaconpatible with proper processing. The prints were then blotted between photographic blotters and allowed to dry between fresh blotters laid on a table and weighted. The use of this procedure and a paper designed for map mosiacs i.nsued prints with accuracy of recording well within the limit of error of 1%.

[ ^ 5 ~~~ENGINEERING RESEARCH INSTITUTE p UNIVERSITY OF MICHIGAN Pae 5 In application of EV one piresum.e s s n ude tanii c the physi caS coordinat system a s used by Durard in his "Aexrcdyinamic Theory" on page 197, Vol. 1. The fact that the sign changes on the velocity vectcr if flow is from left to right instead of right to left seesms te play havoc with some readers. In.order to change this system, all one has to do is to consider at all times that his flow is from right to left. Then the velccIty vector at the jet is always in this direction. Refer back to the regular signs of polar coordinates and cartesian coordinates as far as signas of u and v, U, r,, x and y are concerned..rtos needs to make the velocity at the jet - U n order to make it cornistent with polar coordinates. That is.the velci'ty of the.et is the vector U, but U looks like 3 U which in polar. coordinates is'U = IUl e in -. {F in other words the minus sign oonnotes direction of the vector U which has the mrinitude (UJ. In this system vectors will be signless until related to the coordinate system used. o,o The only changes this makes in V 3 are on Pages 5 and 4 Page 3 (r,n). 0 line 1 u(r,e ) sw as r -+ o line 2 v(r,8 ) x as r c line u(r,O ) t U + Cline 12 The last condition applies far from the origin and clcse to 0'.87 t -92 "- e9 e.tGc. line 31

Evi~~ 6. ErENGINEERING RESEARCH INSTITUTE -___; _ _ __, _ UNIVERSITY OF MICHIGAN PLC Page 4 Repleae (-1.652), wherever it occurs, by (+.5705), It might be helpful to. point out that the infinite boundary conditions are employed to insist on conservation of energy, and are not to be used by the engineer as physical reality, because these foroed boundaary conludtione are Just to make it possible for the product of P V A o' V'A' Ln our case we forced OVA to be an indeterminate., s8 a consta-nt (j =') since the fluid is incompressible. Aios in our case A wwas equal to zero at r = s so V mst be infinite in order that there be a chance that flow exist. It naturally is required that there be no violaticxn of the equation of continuity or, ie tvs sometimes called~ the law of constulnu —lty. (Ref.l). This is exactly what Dt'iand said in his quotationr, but pe-haps a change of words might convey the thought more easily, EKV 5 might be made- completely general for wedge-lite flhaes if oSne were to plot a family of curves C., verau-s fX.d.. for Cdifferent e' In this manner the gecmetry of the bead would determjt the wedge and tbhe angle of the wedge 0'. Given 0' one would then have Cl detemr.ni.ned for3 a. particular gas. Given C1 one then could determine U, kn4ow ing the given Jet output velocity. Thus'by knowing the geometry of the bead and n.crng the o t eloi outpt velocity of the Jet ad the type gas used, the physics of the effect of a wedge-like flase on a Faas fl'ao v,,t to the 1.fiam froni See. to be completely determined. Perhaps it should be pointed out that even thouigh this ap,-,roxia, ti t1-ont] appears almost perfect, in tieory it cannot be exact except ftor a,'f.lm.i at te the e teerature as that of the gas; otherwise the flow is w:'n4t Isentropic. However, we know that mmainy inrctational flow ass miptio'ns seem tn give good approximations for the n on-Isentropic cases*, except.'hen act'tual me6surement of direction o-f rotatU:'.ns' becomes important, In ot:. casle we are only interested in the velocities at the flane front. As a result this asssmption s -probably as valid as the re at cf th.u aasuiX +ons especially to within the precision measure of the voxerit.rnt, _D 2 was an attempted solution of the- cone problem e te to 5e lack of sufficient bourdayry conditions th;e solution had two arblt.ry cronstamnts present. *For'exampile Sauer's approximations for Yaving Cones see Lotkin's;arti.cf-e P 656 Nov.1948 Jouinal of Aeronautical Sciences.

Enr c ENGINEERING RESEARCH INSTITUTE * = C6g in9 e +kx Jo (kr) - U x - C6 sin e = - Cg6 sine' r e+X J (kr) -U-r 2. t - Cg eihe'k ek Jo(kr) + U v = C6 sine k Je+ o (kr) where Jo (kr) = - J1 (kr) However in this problem we assumed that the flow was irrotational. This implies that there a8- no maximnv or mni:a i.'.- thin the flow. Thus, fQr our solution to be physically correct as it now stands,_ J, and J1 cannot have a maxium or a minium with-in the flow. Let us zbake a very rough estimate -of krr by trying to set up a rough approximation on kir. For a typical exasmle.5< r< 1.8. (1) But exoept for calcuJlating the smallest zero of Jo for which n - 1 kr (n i r ic.b+ 1 - 5 3779 " (' ) " ( - ) 384'(n )3 + -.54(i 2-) S' ), thie expansion (Ref.2) is adequate for coiputing all the zeros of Jo up to 5 decimal places. Now let us examine the tfiv P. ~ expressed by the inequality (1) Now assume we are between two zeros of Jo as we'-ave to be,' for irtotational flow. Let the smaller zero be (p = krn) Let the next zero be (q = krn+l) qg kr~ p (3) In other words p is equal to tthe sum of expansion (2) when n s a and q is equal tothe sum of the expansion (2) when n= a + 1. n = 1, 2, 3, 4, etc. Fraa (3) - k x p

T5 5 ENGINEERING RESEARCH INSTITUTE..... UNIVERSITY OF MICHIGAN P ge 8 but this must hold for all possible physical values In the given experiment. thus from (1) and (3) k(5) p (4) k>2 (5) q>l,.8 (k) (6).555 q k (7) Thus from (5) and (7).555 q > 2 p > 3.6 p (8) now supplying the one zero of Jo not given by (2) to witlin 5 decimal places Jo} means n-thf zero of Jo sJ 1= 2.240482 ol Jo, 2 5.52008 Jo, = 8.05573 etc. Thus from examining expansion (2) we see that the greatest ratio of' successive~ zeros of Jo occurs for the ratio of Jo 2 5.52008 2.294 () Jo,l 2,40482 2 2954 (9) but if the physical assumptions are to be correct. >53.6 (8);thus,there are no zeros of Jo whioh meet the physical requirements for the given experiment. In like manner it can be shown that the only possibility for an equation like (1) to be set up o< r<d would be if c and d are very close to the same value. This can only occur physically when the cone angle. is very large, (' - 0 ) or for the cone angle to be very small 0t 5 0. Perhaps one can see this better when one realizes that we have at most only ~ the interval q-p available, since a maximum occurs in the middle between p and q. Even after this ais set up there is a further shortening of the interval when the oesne requirements are put on J1 that have just been put on Jd,

ENGINEERING RESEARCH INSTITUTE Page ______ MVi-_ _ UNIVERSITY OF MICHIGAN This analysis shows the futility of the use of Bessel functions for solving the conical flame problem. Possibly the physics is such that the flow is rotational before a conical flame front. EVY 4 further convinces the writer that this is the case. Thus EMV 5 and EMV 4 ask for experimental evidence of the irrotationality of subsonic flow before a conical flame; and they predict the flow will be rotational.

ENGINEERING RESEARCH INSTITUTE Page EM 5 UNIVERSITY OF MICHIGAN. 10 1. Iemke, "Elementary Applied Aerodynamics" P. 21 2, "Theory of Bessel Functions" Watson P. 505