1、. . L1 NATIQNAL ADVISORY COMMITTEE roximately equal, for equal Reynolds numbers, to the coefficient of friction for incom.Jressible flow with completely developed bcundary layer. Mach numbers greater than 1 are rarely maintained for lengths of 50 diameters, For attainable lengths the ccefficient of
2、friction is a function of the ratio of length tc diameter and the Reynolds number, with the aach number at entrance determining the maximum attainable length. * . INTRODUCTION The effect of friction on the flow of compressible fluids in ?iges of uniform cross-sectional area was investi- gated analyt
3、ically by Grashof (reference I) and Zeuner (ref- _ erence 2) who arrived at a relationshi.? between velocity and friction coefficient for perfect gases. Stodcla (refer- ence 3) showed that the curves of Fanno ;?ermit a general RESTRICTED Provided by IHSNot for ResaleNo reproduction or networking per
4、mitted without license from IHS-,-,-T NACA TN No. 963 2 graphical treatment for any law of friotion. Frassel (ref- erence 4) presented the first extensive measurements of friction coefficients for the flow of air through a smooth* tube with velocities above and below the velocity of soundr His measu
5、red coefficients for both subsonic and supersonic compressible flow appear to be in excellent agreement at corresponding Reynolds numbers with coefficignts measured for incompressible flow. Keenan (reference 5) presented ex- perimental data on commercial pipe for the flow of water and -for th.e flow
6、 of steam at subsoniu velocities. Those indi- cated that the friction coefficient is the same-for the same Reynolds number for an incompressible fluid and for subsonic flow of a compressible fluid. In the subsonic region the measurements of Frt)ssel and of Keenan were in accord in that they revealed
7、 no variation of the friction coefficient that was peculiar to compressible fluids. In the supersonic region the measurements of Frbssel pointed to a similar conclusion. FrBssels data for this + region were published as a chart (fig, 7 of reference 4) which, despite its small scale, seemed to reveal
8、 great ir- regularities in the data. The friction coefficients, which :- * were computed from the derivatives of the curves through the experimental points, must have been subject to great uncer- tainty This investigation, conducted at Massachusetts Institute of Technology .was sponsored .by and con
9、ducted with the finan- cial assistance of the National Advisory Committee for Aero- nautics. SYMBOLS a D a F . Q Q l h cross-sectional area of test Fipe (sq ft) diameter of test section (ft) throat diameter of nozzle wall-friction force (lb) mass rate of flow per unit area (lb/sq ft set) acceleratio
10、n given to unit mass by unit force (ft/sec2 enthalpy (ft-lb/lb) c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 963 3 . c 4 . t 1 1, , I k L M P Re T rn Ti P V W X A AC Ai P 7 0 ratio of specific heats length of test section (ft) Mach n
11、umber pressure (lb/so_ ft abs.) Reynolds number temperature (p abs.) mean stream temperature at a given cross section of the test pipe (F .abs.) mean stream temperature at the initial state o,fth,_e fluid stream,. that is, where V = 0 (F abs.) mean velocity of the fluid stream at a given cross sec-
12、tion of the test pipe (ft/secj specific volume (cu ft/lb) mass rate of flow (lb/set) distance along test section (ft) friction coefficient 7 $ PV2 friction coefficient calculated from +-= f- -0.8 + 2 log Rem 4% with Re based on T, friction coefficient calculated from above-mentioned oquation with Be
13、 based on Ti mass density 0 L I . vg friction force per unit of wall surface (lb/sq ft) angle between walls of entrance nozzLe Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-r . t . i;. -a NACA TT MO. 963 4 Subscripts I refers to the initial state o
14、f the fluid stream where the velocity is zero 1 and a refer to arbitrary datum sections along the test Pipe Constants used in calculations k ratio of specific heats (1.400) cP specific heat at constant pressure (0.240 Btu/F lb) A number of foot-pounds in 1 Btu (778.3) OBJECT Some preliminary investi
15、gations (reference 6) into supersonic flow of air which were made in the Laboratory Of Mechanical Engineering at the Massachusetts Institute of 1 Technology indicated friction coefficients appreciably dif- ferent from those reported by FrGssel. The present invosti- gation was undertaken in an attemp
16、t to resolve this disa- greement. and to obtain some dependable experimental data on supersonic flow with friction. In order to tie the invdsti- 1 gation into previous studies of the flow of incompressible fluids some measurements of subsonic flow were included. . TEST APPARATUS . The arrangement of
17、 the test apparatus is shown in fig- ure 1. Air is supplied.by either a two-stage, steam-driven compressor or a rotary, electric-driven compressor. At the discharge from the compressor is a receiver to smooth out fluctuations in flow. Eor some tests a dehumidifying system was used to remove moisture
18、 from the air Leaving the compres- sor. This dehumidifying system consists of a cooling coil followed by a heating coil. It is connected into the system as shown in figure 1. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-t NACA TN No. 963 5 c . The
19、 air stream is introduced into the test pipe through a rounded-entrance nozzleof circular cross section. Details of the nozzles used in different tests are shown in figures 2 to 5. . The test pipe is in each instance a piece of standard drawn brass tubing. For the subsonic tests the inside diam- ete
20、r of the tube was 0.375 inch. For the supersonic tests three tubes were uoed having inside diameters Of 0.4375, 0.498, and 0.945 inch, respectively, . The air stream leaving the test pipe is discharged either to the atmosphere or to an ejeutor which uses steam as the primary fluid. The pre-ssure mea
21、surements, from which the friction co- efficients are calculated, were made at holes of 0.020- lower pressures were measured with a mercury column. . The temperature of the air stream in front of the noz- zle could be measured by either a copper-constantan thermo- couple or a mercury-in-glass thermo
22、meter. Readings usually were made with the thermometer. l The discharge coefficient for the 0.375-inch diameter subsonic nozzle was determined by means of a gasometer. The discharge coefficients for each supersonic nozzle were ob- tained from the A.S.1J.B. data on nozzle coefficients (ref- erenco 7)
23、. . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a ri . FA.CA TN No. 963 6 METHOD OF TlSTING The air compressor was started and sufficient time al- lowed to elapse to obtain steady-state conditions before any readings were taken, Temperature readi
24、ngs were taken at def- inite intervals of time. Pressure differences between a .giTren oair of ta-os were measured on either a mercury manom- etor or a water manometer depending upon the magnitude of . the dLfforanco to be measured. In order to establish a COn- P . * tinusl check against possible le
25、akage from either of the two manifolds, $prossure differences were recorded for each pair of taps, with the higher pressure first in one manifold and thon in the other. To check against possible leekage from the connections between the pressure taps and the manifold, a soap-and-water solution was ap
26、plied at each connection. For the supersonic runs, where the pressures measured were below atmospheric pressure, the manometer system was tested by subjecting it to a pressure higher than atmospheric be- fore starting a test. * RISULTS OF TPESTS . . . The Apparent Friction Coefficient The results of
27、 these tests are shown principally in terms of the apparent friction coefficient h, This term A- is intended to represent for any cross section of the stream the quantity where T denotes the shear stress at the pipe wall, p the mean density, and V the mean velocity. In reality the ap- parent frictio
28、n coefficient is defined in terms of the meas- ured auantlfies, flow por unit area, and pressure, through equation (Sj, tcgsther with equation (7), of appendix A. Equation (8) is identical with the statement . h=a7 PV” if the velocity across each section is so nearly uniform that the mean velocity f
29、ound from the flux of kinetic energy Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A MACA TX No. 963 7 . . is identical with that found from theflux of momentum, or if the flux of momentum and the flux of kinetic energy do not change from section t
30、o section. . The flow of an incompressible fluid in a pipe at a great distance downstream from the entrance satisfies the latter condition, The flew of a compressible fluid satis- fies neither condition, It is probable, hO,WBVBr, that the former is nearly satisfied in compressible flow at a great c1
31、 distance dGwnstr8am from the entrance, provided the longi- * tudinal pressure gradient is not inordinately large. The magnitude of the true friction coefficient (21/p?) can be fo:nit only from a determination Of the magnitude Of the shSar streSs at the pipe wall. If the shear stress is - to be m3aS
32、urad directly, the experimental difficultiss are formidable; if it is to be deduced from prossu.re measurements, either the analytical difficulties or the unaertainties in- troduced by supposition are likely to prove discouraging. The. apparent friction coefficient, on the Other hand, may be rather
33、simply deduced from common types of measure- ment. Moreover, when its value is known it may be readily applied to the design of.passages. The adoption of th8 apparent friction coefficient for reporting th8 results of measurements of the type pr8SWLted here will facilitate comparison betwson data fro
34、m different sourc2se The calculation of the apparent friction coeffi- cre2.t ,nvO.ves te simplest calculation and the minimum ex- trantious hypothesis consistent with reducing the measure- ments to a basis of compariSon. The tests of IrBssel (ref- erenc8 4) and Keenan (reference 5) have been so pres
35、ented. In all SUbSeqUent paragraphs the term facti cient is to be interpreted to mean apparent friction zOdfi;- cient ha defined by equation (8). Subsonic Flow Th8 results for the subsonio tests are presented in tables I to IV, The variation in pressure along the length of the test pip8 is shown in
36、figure 6. For test 1 the pres- sure in the exhaust space aftor the and Of the pip8 was be- ? : low tho sound pressure - that is, the pressure at the stat8 of maximum antropy; consequently, tha flow through the pip8 Provided by IHSNot for ResaleNo reproduction or networking permitted without license
37、from IHS-,-,-L r . XACA TX No. 963 8 was th8 maximum flow corresponding to the initial condition of the air stream. l?or test 2 the air stream was throttled behind the pip8 and for tests 3 and 4 in front of the pipe, to prOdUC8 pressures at th8 pipe 8Xft in exc8ss Of the SOUnd pressure, which result
38、ed, in turn, in a flow less than the maximum flow for the existing initial conditions. The friction coefficients corresponding to the inter- vals of pip? length betwoon pressure taps are given in tables I to I?, In figure 7 the arithmetic mean of these values of the frl: tion coefficient for each te
39、st is plotted against the arithmetic mean of the Reynolds number for that test. The lengkh interval from 0 to 1 foot was omitted from the calculation of the mean b8CaU68 the velocity profile was doubt:.83s changing greatly in this interval. The last 3 inches of lsngth also wore omitted beoa,use of t
40、he effect on - velocity an9 pressure distribution of the abrupt discharge into the exhaust spece. Thus the data of figure 7 correspond to a well-developed boundary layer and as stable a velocity ?; profile as the conditions of compressible flow permit. The Van K terval bstween the two points at ze-,
41、o value of L/D. The ratio of pressures across the joint varies from 1.30 for an angle of i2O to 1.03 for an angle of 2O. The departure from 1 in the latter figure is hardly in excess of the uncertainty in the pressure measurements. For an angle of 6O the ratio is 1.16. The analysis of Meyer (referen
42、ce 10) indicates a- pressure ratio of 1.22 across the oblique shock arising from c a change of direction of 3O at a Mach number of 2.29. This analysis is applicable only to two-dimensional flow which the flow near the tube wall should approximate. The experi- . mental and analytical values appear to
43、 be of the same order of magnitude. It may be seen from figure 12 that as the angle of di- vergence decreases the pressure rise at the junction de- creases and the curve of pressure against distance becomes smoothor. Kith a nozzle designed for shock-free conditions the curve becomes smooth and the r
44、ise in pressure at the junction becomes zero within the precision of the pressure measurements. . Although measurements made under other than shock-free conditions are not considered valid, a study was made of the effect on the apparent frictfon factor of nozzles of the . ordinary type. Such nozzles
45、 were used, presumably, by Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I?AciA TIT MO. 963 11 . t FrBssel who gave no indEcation that he had developed a spe- cial nozzle for the purposes of his tests. The friction CO- efficisnts computed from the
46、curves of figure 12 are plotted in figure 13 against the angle of divergence of the nozzle. These friction ccefficients are the mean coefficients f-or the interval of length bet?ieen values of L/D of 1.59 and 27.0. This interval was chosen because it was approximately the samo as that used by Frdsse
47、l. According to the data of figure 13 the friction coeffi- cient for a given Reynolds number approaches the Ilon R whereas the right-hand group shows in compari- son lower values at the minimum point and higher values at large values of L/D. No analogous trend with Mach number can be discerned. Alth
48、ough the top and middle charts in the left-hand group have Mach numbers at entrance of 2.06 and 3.09, respectively, they differ less than the two middle charts which have Mach numbers of 3.09 and 2.84, respectively. Differences appear to depend upon Reynolds number rather than Mach number. Provided
49、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No, 963 13 To test whether the changes in characteristics were the result merely of accidental differences between test pipes and entrance nozzles, two tests were run with the same test pipo and nozzle at approxi
copyright@ 2008-2019 麦多课文库（www.mydoc123.com）网站版权所有
备案/许可证编号：苏ICP备17064731号-1