HYDRODYNAMIC PRESSURE DROP IN SMALL SCALE HIGH-PRESSURE SYSTEMS J A M E S
E.
K N A P , H A R O L D E.
K Y L E , A N D J A M E S
Chemicals Division, C'nion Carbide Corp., South Charleston, TI.'.
H. B R I C K E R
Va.
Pressure drop due to water flowing at Reynolds numbers up t o 60,000 was measured in continuous-flow, small scale (g/16-inch0.d. tubing) high-pressure equipment of various configurations, including: straight pipe, single and double helices, and standard collar-and-gland fittings. Equivalent lengths of the high-pressure fittings were from 30 to several hundred per cent higher than those for similar screwed pipe fittings; the values are tabulated. Pressure had the effect of extending the transition flow region and delaying the onset of turbulence. In a double helix used at 5000 p.s.i. and 350" C., turbulence did not begin until N1te was about 20,000 and pressure-drop measurements were low b y as much as 100% when compared with values predicted b y standard correlations. Test equipment and procedures are presented, and the significance of the data to high-pressure pilot plant operation i s discussed.
T IS
often desirable or necessary to estimate the pressure drop
I to be expected during the design of an experimental highpressure system or to know the flobv regime in an existing system. At present, such information must be estimated from the hydrodynamic performance of standard pipe and fittings, because the appropriate phenomena have not been measured in high-pressure piping of the type used in experimental work. Although other aspects of high-pressure pilot plant design (2) and practice ( 7 , 8)have been discussed, no one has tested the standard hydrodynamic correlations for applicability to small scale high-pressure piping. Such tests are reported in this paper. Systems for continuous-flow experiments are generally relatively complicated. They frequently involve numerous high-pressure fittings (27) and valves which are standard for such operation but different from t h e usual screwed or flanged pipe fittings. Such fittings can be numerous in the case of tubular reactors, which frequently involve several parallel passes ( 7 ) or a series of differential sections (72). For space economy or convenience of fabrication, helical coils are often used for heaters or coolers (4,74, 78, 25) and for tubular reactors (77-73, 22). Each of these design features which offers convenience or experimental expendiency also offers some flow resistance and complicates the hydrodynamic evaluation. T o test the applicability of standard correlations, pressuredrop measurements were made in 9/,&-inch o.d. tubing and fittings. Two sizes of standard tubing Lvere used, with internal diameters of 3!'16 and 5 / 1 , inch. Pressure drop due to typical high-pressure fittings of the gland-and-collar type, designed for use with that tubing, was also measured. T h e head losses in helical coils of two different configurations were also evaluated. T h e experimental conditions included pressures u p to 6000 p.s.i., temperatures to 350' C., and Reynolds numbers to 60,000. T h e pressure-drop data were calculated in terms of the friction factor:
T h e results \yere correlated using the Poiseuille relation for streamline flow f
=
64/.YR,
(2)
and the Blasius equation (76) in the turbulent region
f
= 0.3164
(3)
(.VHe)--0.26
\2:ater was the experimental fluid ; its physical properties were obtained from Keenan and Keyes ( 7 0 j in the case of density and by extrapolation of the d a t a of Sigwart ( 7 7 ) for viscosity. Head l o s s e s in Straight Tubing and Fittings
Pressure drop in straight tubing and in the various fittings was measured by pumping water a t ambient condirions and a t 6000 p.s.i. through a test section, \vhich was so arranged that a t least t\vo of any type of fitting could be inserted to measure the differential pressure drop attributable to the fittings. Test Section. A schematic d r a ~ v i n g or the test section appears as Figure 1. I t Lvould accommodate about 1 5 feet of straight tubing. T h e pressure taps were standard. highpressure tees using ',,-inch gland-and-collar screjved connections (27) just like the fittings tested in this study. These pressure taps presented flow restrictions and acted as turbulence-inducing devices and undoubtedly interfered \vith formation of the boundary layer. Ho\\.ever. their use {vas justified by the convenience they afforded in making changes in the test section. T h e pressure leads \\ere connected to a differential-pressure cell designed for operaiion at 6000p.5.i. g. '1'0 achieve flo\vs \vel1 into the turbulent range it \vas necessary 10 use three high-pressure pumps in parallel. For this purpose n v o electrically driven duplex piston pumps and a simplex air-driven pump \\ere used. ' l o dampen the lxilsdrions that exist in systems fed by piston pumps. a 12-foot long. flanged high-pressure tube v i t h an inside diametrr of 2 inches \vas filled ivith cylinder nitrogen. valved in and opened to the test section. T h e pressure in the test section \vas controlled by a pneumatic high-pressure motor valve and the elfluent water \vas collected in a 55-gallon d r u m and Lveighed. All measurements in the test section \yere made \\bile pumping watrr a t ambient temperature. The d i ~ ~ r e n t i a l - p ~ r s . ; n r e VOL. 4
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3/16 IN I D
0
5/16 IN I D
0
0
Figure 1. Test section for measurement of pressure drop through high-pressure fittings 400
cell was calibrated with a mercury manometer a t atmospheric pressure, and the loss through several of the fittings \vas measured a t both atmospheric pressure and 6000 p.s.i.g. to check the calibration. For a given system, pressure drop \vas first measiired a t the maximum stable flo\v rate, and then the flo\v \vas successively lolvered to obtain the pressure drop values well down into the laminar flo\v regime. Pressure drop was converted to friction factor using Equation 1 and the friction factors bvere correlated by Equations 2 and 3 in the laminar and turbulent ranges, respectively.
600
800 1000
zoo0
woo
REYNOLDS NUMBER, NR.
Figure 2.
5000
m
lop00
20,m
' Dvp P
Pressure drop through high-pressure tubing
Results with Straight Tubing. Reynolds numbers u p to about 9000 were used in the pressure-drop experiments with straight tubes. T h e results are sho\vn in Figure 2 for tubing having inside diameters of 3 / 1 6 and 6 / 1 6 inch. T h e data were displaced from the smooth-pipe correlations because of the end effects due to the use of high-pressure tees as pressure taps, but they could be correlated by parallel lines whose equations were similar in form. 400
I n the laminar region
600
1000
2000
4000
moo
Dpoo 24300
REYNOLDS NUMBER, Drp
Figure 3. Pressure drop through highpressure valves
I n the turbulent region
f
=
0.577
(i\rRe)-".296
(5)
This increased pressure drop did not distort the equivalent lengths of the fittings because the same pressure taps Lvere used in those measurements and the end effects cancelled when the pressure-drop values were subtracted. T h e data taken a t high pressure indicate a spreading of the transition region between laminar and turbulent flow. A t atmospheric pressure turbulence appeared as expected, a t Reynolds numbers of 3000. However, at 6000 p.s.i. turbulent flow \vas not established in either diameter tube below a . V R ~ of about 5000 to 6000. This tendency to spread the transition region disappeared when rurbulence-inducing fittings were in the test section. Because this apparent spreading of the transition zone occurred only when straight tubing was in the test section, the roughness of the tube walls \vas measured. T h e use of roughness comparison specimens revealed surface roughnesses in the range of 18 to 25 microinches. These values \\-hen doubled and ratioed to tube diameter gave roughness ratios varying from 1.1 >: l o p 4 to 2.7 >: for the two diameters of tubing. These ratios revealed the high pressitre titbing to be considerably smoother than standard pipe, and this factor, when coupled with the kinematic nature of the compressed fliiid, appears to caiise the broader transition region. Equivalent Lengths of High Pressure Fittings. Couplings, tees, valves. and three-\-stenis. 'l'his has been done using the pumping auxiliaries available. coupled \vith dif-ferential-pressure devices arranged
Table I.
Pressure Drop through High-pressure Fittings
(Expressed as e q u i v a l e n t length of tubing h a v i n g same inside d i a m e t e r , turbulent flow o n l y )
Eguzaalent
Port Throat or Diameter, T y j e of Filting
Inch 8 ,
Valve
i
16 5/16
3-\2:ay valve Straight through . i s angle v a l \ e Tee
djpro.wnute Eguiwlent
Same LPri,yth Diam fo, t r r Tubing. .Yo. of Dianirtrrs
Siniila, Lrngth SirPrepd o,f P i p I;itting,u
365 410
270 --298
Diairiptprs
5/16
390 333
I35
3/16
Run of tee Branch of tee Branch of tee
18 5. 8 58 1.8
83 108 5/16
244
Coupling 3/ls 42 \r 3th edition of Perry's Handbook ( 7 5 ) lists ,+?ttin,gs in leiiris o,f E;; Delocity hfads. These ualurs =ere o6tazned 6y usins conwrsiori /actor / a i water given in that rpference.
similarly to those sho\vn in Figure 1. Data from t\vo such systems are presented. T h e t\vo systems for which data are presented \\'ere different. T h e first involved four separate coils of , R - by 16-inch high pressure tubing each having a coil diameter of 6 inches. T h e total length of tubing \vas 354 feet and the pump capacity limited the d a t a to the streamline flow range. T h e pressure drop \vas measured by pumping water a t 6000 p.s.i.g. a t room temperature. T h e second system involved a series of dliplex helices. These double coils comprised a 4-inch diameter inner coil with a 6-inch coil around it; both were of j R - bl- 9, inch tubing. Each duplex unit contained 200 feet of tubing! 120 in the 6-inch coil and 80 in the 4-inch. In this case sufficient pumping capacity \vas available to reach Reynolds numbers of about 60,000. Measurements were made at room temperature a t atmospheric pressure and a t 3iOo C. a t 1500 and 5000 p.s.i. Again the fluid pumped \vas Lvater. .4s u i t h the previous data, the pressure drop values were converted to friction factors using Equation 1 . and plotted against Reynolds number to show the exrenuion of laminar flow known to occur in curved-pipe flow. In the case of the double helices laminar flow clearly persisted u p to a Reynolds number of about 10,000 (Figure i). in spite of the fact thst the coils of smooth tubing were connected by turbulence-inducing I
d
P c
REYNOLDS NUMBER, NR, =
Figure
5.
9
Pressure drop in helical coils VOL. 4
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223
high-pressure fittings. I t was of interest to know whether this extension of streamline flow would have been predicted by standard methods and whether the observed head losses could have been estimated. The existence of secondary flow in a helix which leads to this laminar prolongation was treated by Dean (5, 6) and empirical correlations were reported by White (24) and Taylor (20) for the streamline region. White (24) related the friction factor for curved pipe, fc, to the factor for straight pipe, f8, using the Dean number:
He developed the following empirical correlation : 1 11.6
I’C---
1-[1-(\6)
f8
0.45
2.22
]
(7)
Tables of this function and of White’s and Taylor’s values for the critical Reynolds number for turbulent flow are presented by Cremer ( 3 ) along with an empirical correlation for turbulent flow data originally revealed by Spiers (79). This latter correlation is simply a table of values of fc/fs a t vzrious values of 2D/Dc. In a recent paper (Q), Ito contributed some new data for turbulent flow in curved pipe and correlated all of the known data. He found excellent agreement with White’s correlation (24) in the laminar range, but in general used different correlating groups in the turbulent range. Excellent correlation of all available data was given by:
fc
(g!)0’5
= 0.029
being off over 100% a t many measurements. These deviations indicate that fittings a t 90- or 200-foot intervals in smooth, coiled tubing did not adequately induce turbulent flow at high pressure conditions. Signiflcance
The standard procedures for predicting head loss in piping will give very crude approximations of the actual loss in laminar or in fully developed turbulent flow in high-pressure experimental systems. The amount and direction of the error in the estimates will depend on the number of fittings. the amount of curvature. and perhaps roughness in the piping. Prediction of the critical Reynolds number and of the transition region by classical methods may be in error up to 30%. Head losses in this region cannot be predicted with reasonable accuracy. T h e most significant finding of this study is the tendency of high pressure to extend streamline flow or broaden the transition region. Most experimental units are built for measuring heat, mass, or momentum transfer, or quantities bvhich depend on these. This work makes it clear that those quantities cannot be measured accurately in any region below that of fully developed turbulent flow. In the double helices used here that would not be below a Reynolds number of about 20,000. Because the factors involved in this spreading of the transition zone are not fully defined by this work. it would seem advisable for experimenters to determine the critical Reynolds number of their systems and to establish the Reynolds number a t which turbulent flow is fully developed. Fortunately, the procedure used here of measuring pressure drop is a simple and sensitive way to detect this transition.
(321”‘””
+ 0.304 [ATRe
(8)
Nomenclature
Ito ( 9 ) also correlated the existing measurements of the transition point from streamline to turbulent flow. His own work agreed very well with that of Taylor and White; the equation which correlates those results is:
pipe diameter, ft. coil or helix diameter, ft. friction factor, dimensionless friction factor for coiled pipe, dimensionless friction factor for straight pipe, dimensionless dimensional constant, 32.17 (lb.) (ft.)/(lb. force) (sec2) length of pipe, ft. T ~ , Dean number = , V R ~ ~ Ddimensionless Reynolds number D v p , ‘ ~dimensionless , critical Reynolds number, dimensionless pressure drop, lb.,/sq. ft. fluid velocity, ft./sec. fluid density, lb./cu. ft. fluid viscosity, lb.;‘(ft.) (sec.)
(9) In order to use these correlations on the data obtained in the was obtained by duplex coils, an average value of (DID,) multiplying the diameter ratios for each coil by its fraction of the total tubing length in the coil, thus:
0.60 (0.03125) = 0037498 =
+ 0.40 (0.04687)
L-sing this average ratio for the duplex coils and the true ratio for the single coils, pressure drop was predicted. Those curves are presented along with the actual data in Figure 5. Because the calculated pressure loss in the 6-inch single helices was less than 5% different from that in the duplex coils, only a single line is shown for the prediction by the White correlation. It can be seen from Figure 5 that the standard correlations agree well with the experimental data in the laminar flow region and a t Reynolds numbers above 20,000. In fact, in the streamline range these data were closer to the prediction than were the data of \’ernon and Sliepcevich (23) taken a t atmospheric pressure in a helix of noncircular cross section. The prediction of transition from laminar to turbulent flow was 30?4 low, In the actual transition region, which is broadened a t high pressure. the predicted pressure drop is much too high, 224
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
literature Cited
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(1 956). (15) Perry, J. H., ed., “Chemical Engineer’s Handbook.” 4th ed.: pp. 5-33, McGraw-Hill, New York, 1963.
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