Article信州大学工学部紀要 33: 1-7 (1972)departmental bulletin pape

IKEDA,  Toshihiko

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Shinshu University Institutional Repository

Swirling Cavity Flow of Water through     a Straight Circular Pipe. III   Toshihiko IKEDA "(Received October 31, 1972)                             1. grkrodiuctiem   WheR a liquid fiow through a pipe has a large swirling component, a hollowcore or cavity is generated at the axis. In the first paperi) of this series (refe-rred to as I hereafter) it was reported that two different types of cavieyfiow were observed and that the nature ef these fiows was infiuenced by theupstream conditions such as the area parameter ao and the swirl ratio r. Inthe second paper2) (referred to as II) some theoretical predictions were madeon a simplified model system to show possible dependences of a swirling cavityflow on the upstream conditions.    However, since the fiow measurements in I were limited to a single cross-section (at z==7'Ocm) oRly, k is natural to extend those measttrements to findaxial variations of the fiow structure. Especially, actual upstream conditiopsjust behind the swirl generator and subsequent changes associated with thecollapes of cavity are of .crreat interest. This is the motivation of the presentreport where the results of some measurementsmade at several different cross-sections will bedisplayed.   Symbols in I and II are used here as before.                2. Apparatus   The experimental apparatus is shown iR Fig.1. It is almost similar to that used in I. A maiRdifference is that the nose of the swirl generatorhas been stretched like Fig. 1 for the purpose ofsimplifying the upstr.eam geometry as far as pos-sible. This modification was found to have littleinfiuence on the structure of cavity fiows. Foradditional details the reader is referred to I.               'El           Isw  yrm.or ･ ･mmnstze 7. :=" O  cm"ii}s'r7'5, cmig)i.isol cmllislt¥ tIll ,IR..islts r7'ocavity?Fig. 1 Apparatus   (in a schematic form)* Research Associate, Department of Mechanical Engineering    Flow measurements were made by a two-hole pitot-tube traversed trans-versely at the sectioR z==Ocm, 75 cm, 135 cm and 180 cm, respectively. In tkepresent experiment the area parameter ae was kept constant (ao == O. 75 or a=O. 5>, while the previous measurements in I were concerned with three values ofthe parameter ae = O. 51, O. 75 and O. 91. As is understood from Fig. 1, measure-ments at z==Ocm correspond to the flow just bekind the swirl generator, andthose at z= 75cm and 135 cm correspond to the flow around the cavity. Thepitot-hole at z=:180cm was drilled in order to get informations on the flowbehind the cavity. Further, the wall pressure distribution in the z-directionwas measured by thirteen pressure taps newly installed at intervals of every15 cm.                         3. Experimental results   Measurements were carried out for several values of tke swirl ratio r bychanging the set angle 8 of tke guide vanes. The experimental conditions aretabulatecl in Table 1 together with some typical quantities. ee Under these condi-tions the cavity, if present, was always of stationary type.-"   The experimental relation between 8 and r is plotted in Fig. 2, whereas                 Table 1 The experimental conclitions and other                    typical quantities for aemO.75 (or cr=O.5).So,I 2oIli40 lcm o 75135 o 75135180  Qm3/secO. 0709O. 0605     i Ol'i     i'1 6o 1 75 o.osesi 1 13s i     j i80 I     11racmo.oo.oO.9O.9o.o1.61.6o.o ilxm/sec6. 344. 734. 735. 404. 124. 124. 034.513.563. 563. 37 r=2vol/v-.O.2O.6O.51.11.21.21.1  Pwkg/cm2O. 8671.0291. 063O. 8591.0261. 0611. 0881.8iO. 8932.02.01.91.0101. 0471. 062  Pakg/cm2Il11   1   1   i   irm 1   1   1   /1O. 423:JIl1O. 635lliIi1i'* We are concerned with the mean values                                ' to boundary perturbations and turbulance.** See I; section 3, p. 3 and Fig. 3.averaglng spatial and temporal fluctuations dueNo. 33 Swirling Cavity Flow of Water through a Straight Circular Pipe III 3                                      1.0          O Zr- Ocm e"          O =4' 75cm          A =･ =-- 135c m          x =180cm                   aits O.5                   diK   1.0            o            A            e     O 20 40 608 O,O 1.0 2.0 7' 3.0   Fig. 2 The swirl ratiorvs. the set Fig. 3 The cavity radius B vs. the        angle of the guide vanes -9. swirl ratio r.Fig. 3 shows the dependence of the non-dimensional cavity radius P on r. It isseen that both relationships are in good agreement with those obtained in I.   The results of the fiow measurements are reproduced in Figs. 4 to 14.   At the section z == Ocm (Figs. 4, 7, 11), the total pressure P, (or k, in non-dimensional form) and the axial velocity v. are nearly constant, and the swirlcomponent ve is slightly decreasing with rp. In comparison with the assumedupstream velocity compoRents in IIee, it was thus found that the upstreamcondition of a rigjd body rotation was not established in reality.   At the section z == 75 cm and 135 cm (Figs. 5, 6 for 8= 200, Figs. 8, 9 forS = 400 and Figs. 12, 13 for 8 = 60e), the pressure and velocity profiles for eachvalues of r are coincident each other with the similar nature to that d£scribed   -ti-i-i-A x--oc.･･oltt .S･;' '-"' Okt ･ISEi 2..=13sc. okt   Lt.'rm,A 8=･:- 2-o ee ks u.o 8xx' 20 elCs vo s..-.2o' re k,   Vz                        Vz                        vz                     2.0                                                       2.0              2.0          aoOooOO ooooo ooooOOo                     G,O 3.0 o"O+3'O easeeee o.o 3･Orv e-e-e-e o.o   a,=,o.52.0 --2.0 2.0 -2.o 2.0 --2.01.o AAAAAA-r4.o l.O AAA A A-A .-,i,o l.OA A-A-A-A-A A-4.0                                                          I                             AA al AA AA ta th th A "ts     AAAthAas                        o.o                                  o.oe,o  O O,5 rp LO O O.5 )7 1,o O O.5 rp LO          Fig.4 Fig.5 Fig.6* That is       ,v-. -- const. and ve= tor.43.02.01,Oo.oo3.02.01,ee,oU'Avzu4t.l.AVzh,ti>esv t IIleetr A-A-AO.5Fig. 7-' t,-75ein l oo e lA  AO,5Fig. 10g,?A vzvfimurm,..N A   2.0   o.o 3.e  --2.o 2.e  --4,O 1.0    o,orp 1.0 Ookteks   2.0oo e o.o 3.0  -2.o 2.eA ft -4.o 1.e    o.o rp 1.02 u'' 135em ' O kt.g=･=- 6o' e ks 6ooo   T. IKEDA No. 33  1,{.Cv,-'-iii".s'i.z'gcmo.h,1 -Es..llli':i:.i.,O,cmgk                      2.0                  oooooo  1  to OOg Ow Oe e.o 3.0                    e-e O.O                  o e as ee     e cr ==- o ,5 .g':Lob -2.o 2.o- -2.o  z･                  AAA  LArmA-.A-A-. -4.o l･O         -4.0       Aa ft AAthAAA  '            o.e     O.5 )] LO O O,5 OLO    Fig.8 Fig.9 -tli/il-lg2 f,:i'8,fm gl', ,., X':,t:,fk-:1,:gci'ig221,,          "2,o 2･O ee --2.e              g      ggAzaSfigde -4,o 1,o A A-AA AA AmA L4,e              A AA      A            O,o A o o.s rp 1.o O O･5 rp 1.e    Fig. 11 Fig. 12  --2.o 2.e -2,o-A -4,o l.O -4.0 A        o.orp LO O O.5 rp LO            Fig. 14o3,O2.01.0o,oVz lh't>aoeIe[iAAArALww A-AL;,･?ttz2==isocmok･tv"tPr--60] eh,s'VzIooooleeeOeeoeA AA AA-ftAAo  O.5Fig. 13No. 33 Swirling Cavity FIow of Water through a Straight Circular Pipe III sin I. The flow in this region is, therefore, practically uRiform in the z-direc-tion.   From the measurements at z== l80cm (Figs. 10, 14), it is seen that theflow behind the cavity is composed of a forced vortex core and a quasi-potentialflow surroudiRg it. As an interesting observation in this connection, v. has avery small value within the "shadow" of the cavity. This suggests that thecavity is followed by a "dead-water" wake rotating like a rigid body. Fig. 15summarizes the circulation profiles.   Lastly, the measured results of the wall pressure P., mean axial velocityv. and swirl velocity voi (at the wall) are shown in Figs. 16, 17. A slight linearincrease in the wall pressure P. (except in the inlet region z :f{ 30 cm) is roughly                                    '                                       I p･[･ kEl!(;m2                                                            ge 2 a9                                     i･o 2 w $ rt gt gy 8g tw   i･OI-"-vli':ll't'krm ".v",,,,.8sfx:-Ogf.illx- o,s- : ･9:,/,:O,1   o･oo" z=-:ocm 1://1";lyxrl[iklioll/1･I o･6o 6tso ="60' 12o ZC"iso   1'O z..,,7s,. .ke-K.-90;'tX" Fig･ 16 The wall pressure                      ..trlo:--"x/-Xs[./l'iili:!i-.;i/'ii.i, i･i2/i.tt"rv-i,1op2l:ii,lkil                                     LL,, .,                                               AA                                                               l                40x/;itt'c/li;:i1s.;:;,.i,J                  /t)'O z .., lso,. . I /xtgO---X"･s ,!/Xle-x.-f'9J""x-      /    .s nOs O O.5 1Fig. 15 The circulation      distributiorns.o4321otootI  O 6e 120 180Fig. 17 The rnean axial velocity and swirl     velocity at wall consistent with the increase in hydrostatic pressure. Accordingly we may suppose that processes governing these types of flow are esseRtially eRergy-conserving. However, the infiuences of the collapse of cavity are seen in the velocity pro- files.                           4. Concludkng reuaarks    The previous measurements in I of swirling cavity flow of water was ex- tended to find axial variations of the fiow structure. The stat'ionary cavity wasobserved to collapse downstream, being followed by a spinning dead-waterwake. Further experimental findin.ffs are recapitulated as follows : (i) The upstream condition of a rigid body rotation was not established iR   reality.(ii) Tke flow around the cavity is practically uiiiform in the z-direction.(iii) The fiow behind the cavity is composed of a forced vortex core and a   quasi potential fiow surrounding it.(iv) The wall pressure is slightly increasing with z hydrostatically, and very   little infiuenced by the collapse of cavity.    Deviation from the upstream condition of a rigid body rotation makes thetheoretical approach difficult, because the governiRg equation in II : (1) becomesthen nonline･ ar. An alternative idea will probably be to replace the nose of swirlgenerator with a cylindrical vortex sheet surrounded by a potential motion.Further poin£-s of interst are the collapse of cavity and a finite transition processknown as the vortex breakdown.3)4)3')6)    The Iatter problem has been considered by Binnie7) and Hashimotog) in thepresence of a cavity, and some preiiminary computations are now in progressin the present context.    The author wishes to express his hearty thanks to Professor M. 0hji, forhis help and guidance in this study and to Assistant Professor H. Takada forhis interest in tkis problem. Thanks are also due to Mr. T. Nishihara and K.Nakamizo for their cooperatio･n in experimental work.                               Referemces1) T. Ikeda and M. Ohji, "Swirling cavity fiow of water through a straight circular pipe I" f. Fkecttliy of En.aineering Shinshu Ubeiversity, IZipan, No. 32 (1972), pp. 1-9.2) T. Ikeda and M. Ohji, "Swirling cavity flow of water through a straight circular pipe II" 1. FkecitUy of Engineering Shiitshu Ub7iversity, 1mpan, No. 32 (1972), pp. 11-22.3) O. M. Philiips, "Centrifugel waves" f. .Eluid Mbch., Vol. 7 (1960), pp. 340-352.4) J. K. Harvey, "Some observations of the vortex breal<down phenomenon" 1 JF7uid Mbch. ,                                                                          'No. 33 Swirling Cavity Flow of Water through a Straight Circular Pipe III 7 Vol. 14 (1962), pp. 585-592.5) T. B. Benjamin, "Theory of the vortex breakdown phenomenon" L ]F7uid Mech., Vol. 14 (1962), pp. 593-629.6) T. Sarpkaya, "On stationary and travelling vortex breakdowns" L 1;lluid Mech., Vol. 45 (1971), pp. 545-559.7) A. M. Binnie, "Annular hydraulic jumps" Proc. Iiloy. Soc. Lond., Ser. A, Vol. 282  (1964), pp. 155-165.8) H. Hashimoto, "Breakdown of swirling cavity flow in a circular pipe `11L Basic Ebigng., 7}rans. ASME., Ser. D, Vol. 93 (1971), pp. 92-95.                                  ERRATAFrom Fig.4 to Fig. 14, for ` ijtO" before the symbol ,Abe , read`3t".                        Vx Vx

Swirling Cavity Flow of Water through a Straight Circular Pipe. Ⅲ

IKEDA  Toshihiko

Swirling Cavity Flow of Water through a Straight Circular Pipe. III

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Swirling Cavity Flow of Water through a Straight Circular Pipe. III

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