1、NASA TECHNICAL MEMORANDUM I NASA TM 73726 (NASA-TH-73726) IUC PHASE CiiCKE FLCZ IN N77-28431 TUBES UITa VEIjY LARGE L/D (N4SA) 23 p HC BOL/i4F .I I CSCL 20: cv Unclas r- rn G3/34 39299 h E t- a VI Z TWO PHASE CHOKE FLOW IN TUBES WITH VERY LARGE LID by R. C. Hendricks and R. J. Simoneau Lewis Researc
2、h Center Cleveland, Ohio 44135 TECHNICAL PAPER to be presented at the 1977 Cryogenic Engineering Conference sponsored by the National Bureau of Standards Boulder, Colorado, August 2-5, 1977 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TWO PHASE CH
3、OKE FLOW IN TUBES WITH VERY LARGE L/D by R. C. Hendricks and R. J. Simoneau National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44 135 ABSTRACT Two phase and gaseous choked flow data for fluid nitrogen were obtained for a test section which was a long constant area du
4、ct of 16 200 L/D with a diverging diffuser attached to the exit. Flow rate data were taken along five isotherms (re- duced temperature of 0. 81, 0.96, 1.06, 1.12, and 2.34) for reduced pressures to 3. The flow rate data were mapped in the usual manner using stagnation condi- tions at the inlet mixin
5、g chamber upstream of the entrance length. The results are predictable by a two-phase homogeneous equilibrium choking flow model which in- L7 L- hl m cludes wall friction. A simplified theory which in essence decouples the long tube I w region from the high acceleration choking region also appears t
6、o predict the data reasonably well, but about 15 percent low. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TWO PHASE CHOKED FLOW IN TUBES WITH VERY LARGE L/D by R. C. Hendricks and R. J. Simoneau National Aeronautics and Space Administration Lewis
7、 Research Center Cleveland, Ohio 44 135 INTRODUCTION Currently, the shuttle engine turbopump is required to boost propellant pres- sures to 30 MPa with proposed second generation engines requiring propellants to be delivered at pressures to 50 MPa. The problem of fluid leaking past the sealing surfa
8、ces in rotating machinery is compounded with cryogenics, high pressure, large temperature gradients, very high speeds of rotation, and static seal requirements. At lower pressure and rotation speeds, self energizing pumping seals with very close clearances have been successfully employed in a variet
9、y of sealing applications (Zuk et al. I ). These seals frequently have very large length to hydraulic diameter ratio (L/D) passages. At the proposed operating pressures, design innovations to minimize losses are required, but choked flow data and models to make such calcu- lations are lacking. A sim
10、ilar problem occurs in very long cryogenic transmission lines. Most two phase choked flow data reported in the literature are from experimen- tal devices with low L/D sections with little attention given to large L/D lines. The literature has been well surveyed in references 2 to 4. In previous expe
11、ri- ments, the authors have studied two phase choked flows in a variety of geometries 5- 1 including the orifice as a limiting case. References 12 to 16 have considered short tubes; in general for L/D 3 short tubes behave much like the orifice and thc effects of friction may be neglected. For larger
12、 L/D the effects of friction bccomc increasingly important in determining the limiting mass flow rate and pressure drop. The question of two phase chokcd flows in large L/D tubes has, to the authors know- ledge, never becn resolved. Toward this elid, experimental two phase chokcd flow data for fluid
13、 nitrogen in a tube of 16 200 L/D are presented hercin, STAR Category 34 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-f These results should have several applications including aerospace, aeronau- P 0 t tical and stationary engines where higher pr
14、essure components will be used to ;. achieve higher efficiencies; high operating pressure evaporators, liquifiers and con- 1 densers associated with the cryogenic and petrochemical industries and geothermal power production pipe lines for transmission of energy/power. In addition the re- sults shoul
15、d be an aid in defining the ultimate cooling capacity of a fluid in a heat ex- change device; and an aid in defining the nature of metastability and reasonable boundaries for metastable operation. DESCRIPTION OF THE APPARATUS AND PROCEDURE The flow system (fig. 1) is essentially that of reference 17
16、 but modified for the present test. The test section was a coil which normally served as a heat shield for other test sections. By a fairly easy rearrangement of the plumbing the flow could be diverted through the coil. The 16 200 L/D test apparatus was made by winding a coil of 54 turns of 0.64 cm
17、(0.25 in. ) o. d. by 0.48 cm (0. 19 in. ) i. d. copper tubing on a 45.7 cm (18 in. ) diameter drum, yielding a 78.3 meter tube length. Coil spacing is main- tained at 0.64 cm by three bakelite strips which also support the coil. The exterior of the coil was covered with 1i cm of multilayer insulatio
18、n and as shown in figure 1, the entire apparatus was located in an evacuated environment. The pressure taps were fabricated from 0.32 cm (1/8 in. ) diameter tubing silver soldered to the tube along the inner surface of the coil at 10 coil intervals cx- cept for the last tap. The axial distance betwe
19、en static pressure measurements are given in Table I in terms of L/D with the first location on the tube taken as zero. 18 In the manner suggested by the work of Henry two diffusers were fabricated and attached to the end of the long tube, one with a 7 half angle divergence section and the other a 3
20、$ O half angle divergence section, see figure 2. It has been ob 18 served that exit pressure measurement can be made more accurately if the exit is not abrupt. To access the effect of static tap diameter OP the flow, two static taps wcrc placed in the 7 half angle diffuser; a 0.04 cm (1/64 in. ) dia
21、meter hole was Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-located 0.64 cm ($ in. ) from the divergewe plane and a 0.08 cm (1/16 in. ) diameter hole located at 0.32 cm (1/8 in. ) from the divergence plane. No adverse effects due to the pressure t
22、aps were noted. The exit Lressure tap, e in Table I, was less than 1 diameter from the divergence plane. A static pressure was measured approximately 8 tube diameters downstream from the choking plane in the 1.6 cm diameter transition tube at the exit of the dif- fuser leading to the back pressure c
23、ontrol valve. This was designated back pressure. Fluid temperatures were monitored at four positions with the following instru- ments: platinum thermometer in the mixing chamber, in the line open ball thermo- couples at approximately 75 L/D from the mixing chamber (inlet), and approxi- mately 50 L/D
24、 from the nozzle (outlet) and an open ball thermocouple located in a well in the diffuser body. The tank was filled with liquid nitrogen and pressurized. The normal exhaust valve was closed in order to divert the flow into the coil. The flow control valve was wide open, and the back pressure valve w
25、as opened; the flow rate through the coil was measured at the venturi and the orifice. Adjustments of the back pressure valve caused changes in the static pressure within the transition tube without changes in the exit plane pressure or pressure profile which assured that the coil was choked. The in
26、let temperature to the coil could be increased using the joule heated tube (central test apparatus) which served as a preheater for these tests. ANALYSIS Consider a tube of length L and diameter D: Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The
27、tube has potentially three flow regions: Entrance (0-1): Since we are dealing with a single phase incompressible, or nearly incompressible, fluid at the entrance, we can simply assign a standard head loss for the entrance configuration. Then using the friction factor we can extend the tube length ap
28、propriately. Single phase (1-2): This region is normally dominated by friction but as the fluid gets closer to the thermodynamic critical point the flow will become more com- pressible. In some cases points 2 and e will coincide. Two-phase (2-e): This region is normally dominated by the momentum of
29、the expanding two-phase fluid, however, if vaporization occurs early enough in a long tube, wall friction may also be important in this region. The basic equation for one-dimensional flow with friction can be written where sat for a given path (e. g., isenthalpic) The friction factor f is the standa
30、rd Fanning friction factor and is computed based on Reynolds number for a smooth tube. Since G is constant the friction factor is dependent only on the fluid viscosity and thus becomes a thermodynamic variable. In the two-phase region the question becomes one of what fluid is in contact with the wal
31、l. At least initially it is expected that there will be a vapor 3 annulus and liquid core 1. Later the flow becomes thoroughly dispersed and the overwhelming majority of the wall area will be in contact with vapor. Thus in this Provided by IHSNot for ResaleNo reproduction or networking permitted wit
32、hout license from IHS-,-,-analysis the two-phase wall friction factor will be based on the vapor viscosity. The flow is assumed to be homogeneous (k =: 1) and in thermodynamic equilibrium. Reference 3 suggests that this assumption becomes more valid aR tube length in- creases, which is the case here
33、in. The thermodynamic path is assumed to be isen- thalpic. Since G is constant, equation (1) can be integrated and rearranged in the form To determine choking, the derivative d/dP is examined at the exit plane. Differ- entiating equation (4) yields The choking condition requires d/d), = 0. Thus It i
34、s known that at the exit plane dP/dz becomes very large, approaching infinity in the ideal case. Thus at the exit dz/d can be neglected relative to dv/d with the familiar result By substituting L for z in equation (4) and iterating between equations (4) and (7) the exit pressure, Pe, and the choked
35、maximum flow rate, G,=, can be obtained. While in the present report thc point of vaporization is taken as the equilibrium Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-r i b i: saturation pressure, a nonequilibrium vaporization point could be defi
36、ned. Once the maximum mass flux is determined, equation (4) can be used to solve , , for the pressure distribution along the tube. f Special Case In many cases, especially in very long tubes and when the initial conditions are well away from saturation, some simplifying assumptions can be applied, w
37、hich allow simple estimates of the maximum flow rates. 1. The two-phase region, dominated by momentum, is very short and friction can be neglected. ! 2. The single-phase region, dominated by friction, is very long and relatively incompressible. Thus specific volume and friction factor can be taken a
38、s constant and the length Lo-2 can be taken as L. Thus equation (4) can be simplified to Clearly equation (8) is the standard single phase friction flow equation found in any fluid mechanics text and it is not necessary to use the above analysis to arrive at it. It is recommended herein that the pro
39、per approach is the simultaneous solution of equations (4) and (7) with real fluid properties, such as available in reference 19. On the other hand it is reassuring that equations (4) and (7) reduce tr a well-known form and that equation (8) can be used to compute flow rate in a fair number of cases
40、. The exercise in obtaining the simplification also shows regimes where it might be applicable. RESULTS Data for fluid nitrogen were acquired and are presented in Table 11. Thc five isotherms are presented as figure 3. In figure 3, the mass flux G and the reduced mass flux (G, = G/G*) are given as a
41、 function of reduced pressure Pr -:- P0/P, where Po is the pressure measured at thc mixing chamber. The five isotherms (0.81, 0.96, 1.06, 1. 12, and 2.34) are also based on the mixing chamber tcmpcra- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-t
42、ure Tr = T/T, The data appear to be repre mted quite well using these mixing chamber parameters even though the choked interface is over 16 200 L/D from the mixing chamber. The mass flux-pressure map of figure 3 resembles the shape and trends of the same map for a nozzle without an entry length at t
43、he same reduced pressure; how- ever, the value of Gmax, is approximately 0. 1 that for the nozzle without the 16 200 L/D entry section. The analysis tends to underpredict the flow at the high pressure end by about 12 percent, while at the lower pressures the data and analysis are quite close. The pr
44、ogram was designed for computing isenthalpic below the critical enthalpy; how- ever, some of the data at higher temperatures and lower pressures are above criti- cd enthalpy, thus only a partial check can be made. The difference in the trend is somewhat disturbing. It could be in the data. The data
45、plotted were metered with the orifice downstream of the test section. The upstream venturi was about 8 per- cent lower at high pressure but at low pressure was unreliable. Since the orifice showed a consistent trend throughout the authors stuck with it. It should be pointed out, however, that in the
46、se long tubes the flows were about one-tenth the normal flow for the test rig and thus the usual high level of flow accuracy was not present. It also should be pointed out that even though there exists a 10 to 15 percent discrepancy in measured versus calculated flow the one-dimensional homogeneous
47、equilibrium analysis with friction is closely predicting flows that are an order of magnitude below nozzle flows. Such a reduction is borne out by the pressure - L/D profiles of figure 4, where the pressure at 100 L/D ahead of the nozzle is approximately 0.1 Po. For the sake of clarity only six prof
48、iles were plotted; however, these are typical of thc data pre- sented in figure 3. They are tabulated in Table 111. Curiously the analysis does an excellent job of predicting the pressure profiles over the whole rmge of the cxperi- men t. Provided by IHSNot for ResaleNo reproduction or networking pe
49、rmitted without license from IHS-,-,-Another interesting trend appears in the slope of the pressure profiles depending on whether or not To is above or below Tc, (Tc = 126.3 K). Such is associated with the friction-momentum pressure losses in the coil as Tr w 1. Actually a closer examination shows the profile
