NASA-TN-963-1945 Friction in pipes at supersonic and subsonic velocities《在超音速和亚音速下管道的摩擦》.pdf
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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
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