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Water-only performance of proportioning jet pumps for hydraulic transportation of solids
POWDER TECHNOLOGY ELSEVIER
Powder Technology 84 (1995) 57--64
Water-only performance of proportioning jet pumps for hydraulic transportation of solids D. Wang, P.W. Wypych Department of Mechanical Engineedn& University of Wollongong Wollongon~ NSW 2522 Australia Received 12 July 1994; revised 5 December 1994
Abstract
Experimental observations of water-only performance and pressure losses have been made for a proportioning jet pump feeder with eighteen different configurations and designs. Based on these results, the influence of structure and configuration on the performance of jet pump feeder has been investigated. Optimal configuration and geometrical parameters have been recommended for design practice. Formulae for performance prediction have been proposed and verified. Keywords: Water-only performance; Pressure loss; Proportioning jet pumpfeeder; Design practice
1. Introduction Jet pumps, particularly those with all the wearing surfaces made of alloy cast iron, ceramics, or other wear-resistant alloys for abrasive applications, are probably the most desirable type of pump to be used as a feeder in the hydraulic transportation of solids. The reasons are simplicity in structure, absence of moving parts, reliability and low capital cost, convenience of operation and maintenance and wear-resistant. These features more than compensate for the relatively poor efficiency of this type of feeder. Furthermore, it possesses the ability to be self-regulating, that is, if it is overloaded, it will reject water and material back through the suction port until the overload is eliminated. A conventional jet pump comprises a central convergent driving nozzle and an annular suction passage. The difference in structure between a conventional jet pump and a proportioning jet pump shown in Fig. 1, is that the pro-
It
~
portioning jet pump consists of a spindle nozzle, the necessary sealing and an adjusting device. Apart from all the advantages of the conventional jet pump, the proportioning jet pump possesses the additional capability of being able to optimize performance characteristics by moving the spindle back and forth manually or mechanically to suit the operating conditions of the hydraulic transportation system. Unfortunately, this type of pump has not received extensive investigation and application in engineering practice, and no design procedure and performance prediction method as yet have been published [1-4]. There also is a shortage of experimental data reported in the literature regarding the influence of configurations on performance characteristics. Therefore, it is of great importance to monitor the water-only performance of this type of jet pump and investigate the effect of geometrical parameters so that performance prediction models can be formulated and strategies to improve performance characteristics can be determined.
q
2. Test rig and experimental procedure 2.1. Test rig
Fig. 1. General configuration of a proportioning jet pump. 1, spindle nozzle; 2, suction chamber; 3, throat tube; 4, diffuser. 0032-5910/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0032-5910(94)02965-Q
Fig. 2 shows the layout of the test rig employed to monitor the performance characteristics of the proportioning jet pump with different configurations. This rig consists of various proportioning jet pumps, centrifugal pumps to supply primary jet flow and secondary
D. Wanget al. / PowerTechnology84 (1995)57--64
58
of nozzle are 40°, 60°, 75° and 90°. The external convergent angles of spindle are 13.5°, 40° and 54°, while the convergent angles of throat entry are 45 ° and 60°. The distances between the nozzle outlet and the throat entry are le = 0.8 dn, 1.2 d, and 1.6 dn.
o orf Jl
2.2.
Fig. 2. General layout of test rig. 1, proportioning jet pump; 2, centrifugal pump; 3, pressure gauges; 4, flowmeter; 5, regulating valve. 2
~ / / / / / / / ~ 1
~'////////////Z
~-~
Fig. 3. Cross-sectional view of proportioning nozzle. 1, spindle; 2, nozzle.
flow, flowmeters to measure primary and secondary flow rates, pressure gauges and the necessary equipment to monitor noise levels of the jet pumps. Bourdon type YD-150 precision pressure gauges with a maximum error of 0.4% full scale and calibrated before and after each group of experiments were used to monitor the pressure at the nozzle inlet, suction port and discharge port. MAGFLO-380 electro-magnetic flowmeters with a nominal diameter of 100 mm and 150 mm and calibrated before the experimental work were used to measure the primary and suction flow rates. The maximum error for this type of flowmeter was 1% for the measuring range 10-100% of full-scale. These maximum measuring errors met the requirements of the standard of pump performance tests [5]. Steadystate conditions were maintained for each set of measurements. The test ranges were 24 to 70 m3 h-1 for primary water flow rate, 30 to 50 m 3 h-1 for secondary flow rate and 600 to 2400 kPa g for primary pressure. Fig. 3 provides a cross-sectional view of the spindle nozzle. The proportioning jet pumps are made from carbon steel and have a throat diameter of 40 mm and a diffuser outlet diameter of 80 mm. The nozzle and spindle are interchangeable and the outlet diameter of the nozzle is 25 mm. The internal convergent angles
Experimentalprocedure
The experimental work was divided into two stages. Firstly, four spindles with different convergent angles were combined with four different nozzles to comprise sixteen configurations of proportioning jet pump. Pump performance was monitored for different throat entry angles and different nozzle-throat gaps. Secondly, by keeping the convergent angle of the spindle nozzle constant, the configurations and geometrical parameters of the nozzle and spindle were modified and tested to investigate their effect on pump performance. The actual test procedure that was adopted to monitor the performance of these pumps with different configurations is detailed below. (1) Measure water temperature and atmospheric pressure. (2) Run both centrifugal pumps, keeping Po and p, as close as possible to the set value by regulating the corresponding valves. Allow Q, to reach a maximum value by opening completely the valve on the discharge pipeline. Then observe and record values of po, Ps, Pc, Qo and Qs. (3) Increase Pc gradually, keeping Po and p, constant and reducing Q, by regulating the valves on the section and discharge pipelines. (4) Repeat step (3) for different Q, until a minimum number of seven readings have been obtained. (5) Adjust p, and repeat steps (1)-(4) to investigate the influence of sunction pressure on performance. (6) Adjust and repeat steps (1)-(5) to investigate the influence of primary pressure on performance.
Po
3. Analysis of experimental results According to Stepanoff [2], the characteristics of conventional jet pumps can be described by the three dimensionless parameters listed below. R=
At
T= O___z~
(1) (2)
Qo N=
(P°+½p°vJ + t'azc)-(P" +½mv'2 (po + ½poVJ + pogzo) - (po + ½povJ + p zo)
(3)
R is the ratio of nozzle area to throat area, T is the ratio of suction volumetric flow rate to primary vol-
59
D. Wang et al. / Power Technology 84 (1995) 57-64
umetric flow rate and N is the ratio of net jet pump head to net primary head. For the proportioning jet pumps considered in this paper, the following nondimensional parameters, viz. Eqs. (4) to (8), are used instead of R, T and N. The effective cross-section of the spindle nozzle can be expressed by the open-ratio of the spindle nozzle. Open-ratio is defined as S, = x,..x-x
0.6 0.5 ~ 0 0 %
h 0.0.3 20"4
(4)
Xrnax If x = 0, from Eq. (4) it can be seen that the effective cross-section of the spindle nozzle will be equal to that of a common convergent nozzle outlet, that is S, becomes unity. If the area ratio of the proportioning jet pump, m is defined as the ratio of throat tube cross-section to the effective cross-section of the spindle nozzle, then m can be expressed by
me
m=
(s,>0)
(5)
1 4(X'a×(1-S~)~ 2 Using the geometrical relationship of the spindle, dn= 2 xm~ tan(~/2), Eq. (5) can be rewritten as
m
me (0
(6)
where mo-- \ d J
(pc + ½pcvo2 + p gzc) - (ps + ½psvs2 + psgzs)
h= O o+½poVJ+pogZo)_Cvs+½psv +p
)
Ms q = Moo
(7) (8)
Note N can be determined easily from h using h N = 1----'h
(9)
The influence of geometrical parameters and configurations as well as operating conditions on pump performance are analyzed from experimental observations, as detailed later on.
3.1. Open-ratio of spindle nozzle From Eqs. (4)-(6), it can be seen that the variation of Sr is equivalent to the variation of nozzle outlet area, and is equal to the variation of area ratio m for a given cross-section of throat. Therefore, the trend of the fundamental dimensionless characteristic of a proportioning jet pump, as shown in Fig. 4, where h and q are defined by Eqs. (7) and (8) respectively,
°A'S=r 1969 0.1
1
2 q Fig. 4. Influence of Sr on fundamental dimensionlesscharacteristics, a=450; 0=60*. Points: experimental data; lines: calculated by performance prediction model, F-qs. (12)-(16). approaches that of a conventional jet pump by varying the area ratio from a small to large value [2]. Note for reasons of clarity, cavitation data and limits have been omitted from Fig. 4. Cavitation effects are considered and discussed later in Sections 3.2 and 3.4. Figs. 5 and 6 also show that the variation of Sr changes the efficiency defined by Eq. (11). The peak point of efficiency decreases as S, is reduced. The slope of h-q lines is dependent on S,. It can be seen from Fig. 4 that the lines become flatter as S, is decreased and steeper as S, is increased. This means that by varying S, for a given h, q may increase or decrease and for a given q, h may increase or decrease. From Eq. (7), increasing h will increase Pc if Po and Ps are kept constant. This suggests that a small S, suits the application of low back pressure and large mass flow rate, and vice versa. It also indicates that the ratio of secondary to primary mass flow rate can be regulated by varying Sr to suit the requirements of the transportation system for given pressures at the nozzle inlet and outlet of the proportioning jet jump. For example, when the back pressure of the jet pump is reduced, reducing S, will shift the characteristics to a flatter h--q line, an increased suction flow rate and better efficiency. This is the advantage of proportioning jet pumps. Open-ratio S~ has a significant influence on cavitation (see also Section 3.4). Proportioning jet pumps are subject to cavitation in the same way as conventional jet pumps. Cavitation limits the maximum flow rate possible for a given suction pressure, irrespective of the back pressure (see Fig. 10). From Figs. 8 and 9, it can be seen that varying Sr can change the flow rate ratio at cavitation qk. If Sr is increased, qk will decrease and vice versa. The discharge coefficient ~p defined in Eq. (10) is also dependent on St. Generally,/Zp will increase with
60
D. Wang et al. / Power Technology 84 (1995) 57-64
S~. For example, refer to the correlation between /xp and Sr given in Eq. (16) which is based on data calculated by Eq. (10) from observed values of Qo, po and psOo
/~p =
~/~
(10)
55 T [ 1
~
45 I / d /
O
t;t=54°, 0=75*
r--466% "
a=45°' 0=9°*
,,/-
-',~
0.5
1.0 q
u o~lsr.~0°
3.2. Convergent angles of spindle and nozzle Experimental results show that the frictional losses and flow characteristics are quite different for the spindle nozzle with different combinations of spindle convergent angle and nozzle convergent angle. For a constant spindle convergent angle and nozzle convergent angle. For a constant spindle convergent angle, the performance characteristics and efficiency curves of the pump are varied with the nozzle convergent angle. The comparison of experimental results as illustrated in Figs. 5 and 6 for different combinations of a and 0, shows that higher efficiency can be obtained for the combinations of a = 54° with 0= 75°, and a = 45 ° with 0 = 60°. Note the efficiency expressed in Figs. 5 and 6 has been calculated using the following expression given in literature [1]. ~7= (1 + q)h
30
25 0.0
2.0
Fig. 6. Variation of efficiency with the combination of a and 0, Sr =46.6%, Sr = 26.2%. 0.6'
0.5 '
00%
0.4' h 0.3 ' "'"
(11)
These combinations influence the flow rate ratio at cavitation qk (see Section 3.4), as well as the dimensionless characteristics and efficiency, as shown in Fig. 7. The reasons are: the spindle nozzles with different combinations of ot and O have different discharge coefficients even for the same open-ratio; also, the flow rate through the spindle nozzle, which influence the distributions of velocity and pressure loss along the jet
1.5
Sr=46.6%
""/5..~,. • 0.2 '
~
0.1
'
"'"o
:' 26.6% !
Ii
A~
Sr=19.6%
0.0
(1
I
q
2
Fig. 7. The influence of the combination of ct with 0 on performance. ( - - ) : a = 13.5", 0=45*; ( - - - ) : a = 4 5 °, 0=60*; ( - . . ) : experimental data.
65
0 60 ~
Sr=l(~)%
55 . ~ ) ~ Y ' - - ~
,of
pump, can be different for the same primary and secondary pressure. Therefore, it is of great importance to select rationally the combination of convergent angles of nozzle and spindle for improving efficiency and cavitation characteristics.
ct=54o, 0=75°
•
a'--45°' 0=90°
•
¢e'---45°, 0=60°
s.,.,,
3.3. Nozzle-throat gap and angle of throat entry
40
,
311
2
5 0.0
0.5
~ 1.0
q
1.5
2.13
2.5
Fig. 5. Variation of efficiency with the combination of a and 0. S, = 100%, Sr = 33.1%, S, = 19.6%.
Nozzle-throat gap and angle of throat entry are related to open-ratio, as shown in Figs. 8 and 9. If the openratio Sr is greater than or equal to 46.6%, then there is little influence of nozzle-throat gap and angle of throat entry on performance. The influence of these parameters on performance becomes more apparent as the open-ratio decreases (that is, as the spindle moves forward to the throat section). This is probably due to the flow boundary condition in the throat entry being changed by moving the spindle closer to the
D. Wang et aL / Power Technology 84 (1995) 57--64 0.6, -
0.5.
, ~ X St= 100%
0.4.
~
= • = • •
% ~41~'~
h
-
13=soo
-
--
The characteristic curves of back pressure with respect to secondary flow rate are illustrated in Fig. 10. For a given S,, primary and secondary pressure, the suction flow rate will increase as the back pressure decreases within a certain range. Beyond this range, the suction flow rate will remain constant. The same results would have been obtained by varying the primary pressure. This means that the ratio of suction flow rate to primary flow rate will remain constant for a given suction pressure and primary pressure. This constant flow rate ratio is defined as the cavitation flow rate ratio [8].
t3=45o
Sr=lO0% * Sr--lO0% Sr=46.6% • S~-46.6% Sr=33.1% • Sr=33.1% Sr=26.2% =' Sr=26.2% St= 19.6% 0 Sr=19.6%
"~".a. 0.2,
~.
• """ " ~ S r;ll =- - ' ~1' , ~9' ~ r.- m6 ~ a
°
0.0
.
,
0.0
.
1 !
0.5
~
,
1.0
1.5
q
llt .... , •
,
.
I=
2.0
4. Performance prediction
2.5
Fig. 8. I n f l u e n c e o f t h r o a t e n t r y a n g l e /~ o n p e r f o r m a n c e . fl=450; ( - - - ) : /3=60°; ot=450, O=6(Y'.
(--):
0.6 - 0.5
Sr=-100% " ~ 0.4 ~
I~,~
.,IL~'~..~I~V~ h
0.3
(I.Sdn
•
;r= |(X)C~
O • .
Sr=46.6% Sr=33.1% Sr=26.2%
1.6dn St=1(10% a Sr=46,6% D Sr=33.1% . Sr=26.2%
II
o.,
.....
Sr=19.6%
,
A
Sr=19.6%
I
0.0
A
0.5
The experimental results show that the fundamental characteristic curves are a series of curves with Sr as a parameter. The performance prediction model is developed by using a one-dimensional momentum and energy approach and then simplified as follows:
.2% ~_ ~
,~
[]
1.0
1.5
I1..Sc=19.6%
2.0
Performance prediction involves the determination of fundamental dimensionless characteristic curves and cavitation flow rate ratios at different S, for a particular configuration. As a fundamental dimensionless characteristic curve is determined, the transformation to dimensional form can be performed from the expressions of/z, ~7, h and q given in Eqs. (10), (11), (7) and (8), respectively. 4.1. Determination of fundamental dimensionless characteristic curve
~Sr--46,6% I~
.~
61
2.5
q
Fig. 9. I n f l u e n c e o f n o z z l e - t h r o a t g a p o n p u m p p e r f o r m a n c e . 0.8 d.; ( . . . . ) 1.6 d.; a = 4 5 * , 0 = 6 0 °, f l = 6 0 °.
(--)
Ch h = ~z ~ ( q _ Cq)
(12) 2
throat section. The experimental results in Fig. 9 also show that higher efficiency can be obtained for larger values of nozzle-throat gap. This suggests the jet pump should be designed with adjustable nozzle-throat gap.
C h = 2 . 6 6 7 - 0 . 0 0 2 5 3 ( ~ +26.07)
1.5< m/zr¢ 3
(13a,
600
3.4. O p e r a t i n g c o n d i t i o n s
500
The operating conditions are expressed by the primary pressure in the nozzle inlet, the secondary pressure at the inlet of the suction chamber and the back pressure at the outlet of the diffuser. All these parameters are determined by the requirements of the transportation system and the particular application. Although the dimensionless characteristic curves are identical for different primary pressures, the maximum flow rate ratio for different Sr will decrease under constant secondary pressure as the primary pressure increases. The maximum flow rate ratio will increase as secondary pressure increases for given Sr and Po, and vice versa.
400
~,~ 300
2OO
100
~.~ m 10
po= 17(IOkPa po=14(X}kPa po= 17(•1 kPa 20
30
T
40
50
60
Qs (m3/h) Fig. 10. O b s e r v e d b a c k p r e s s u r e v i a s u c t i o n f l o w r a t e , a = 4 5 °, 0 = 6 0 °, S~ = 33.11/b.
D. Wang et al. / Power Technology 84 (1995) 57-64
62
-- 0.892
/xr
<10
(13b)
C q = ( 5m/-~r -0.9445)
-1.75
/xe /zp = 0.781 + 0.223S~- 0.158S~2
(15)
P.e + (1 + ~s)½p~v,2-pv hk = (po+pogZo+½Povo2)_(ps+p~gz~+½p~v2)
where the velocity coefficient of conventional nozzle ~ois defined in Eq. (17). (17)
Note that ~ is obtained from [8,9] and q~ is found to be ~ 0.975, which agrees closely with the value of 0.978 found by Aggarwal et al. [10]; Ch and C n are correlated using a least-squares approach based on the results from the numerical solution of the one-dimensional analytical model equations; the discharge coefficient of conventional nozzle /~---0.95 to 0.975; the expression of /z~ in Eq. (16) is correlated using a least-squares approach based on the observed values of pressure at the spindle nozzle inlet and outlet and for water discharged from the nozzle with a = 45° and 0= 60°. For other convergent angles of spindle and nozzle, the expressions can be found elsewhere [6-7]. The nondimensional performance characteristic curves for different S~ and a particular configuration can be determined by solving Eqs. (12)-(16). The prediction results with experimental data have been shown on Figs. 4 and 11. These graphs show good agreement between the experimental data and predictions.
The pressure ratio of the proportioning jet pump at cavitation is defined by Eq. (18).
m
0.1
Sr
°°
;
~
q Fig. 11. Demonstration of performance prediction model• a = 5 4 °, 0=75"; solid lines: calculated by performance prediction model; points: experimental data.
hk
qk o b s
qk cal
(%) 100
Relative
error (%) 0.156 0.201
0.623 0.696
0.598 0.668
4.01 4.02
0.094 0.132 0.112 0.145 0.129
0.72 0.835
0.172
0.912 0.856 0.995
0.762 0.862 0.826 0.930 0.883 1.002
5.83 3.23 3.64 1.97 3.15 0.7
33.4
0.075 0.104 0.092 0.121 0.112 0.147 0.130
1,045 1,205 1.134 1.303 1.242 1.438 1.337
0.991 1.127 1.069 1.210 1.169 1.320 1.248
5.17 6.47 5.73 7.14 5.88 8.21 6.66
26.1
0.078 0.103 0.092 0.122 0.112 0.131 0.173 0.147
1.204 1.376 1.305 1.500 1.444 1.551 1.789 1.643
1.284 1.460 1.388 1.576 1.518 1.628 1.841 1.715
6.64 6.10 6.36 5.07 5.12 4.96 2.91 4.38
21.5
0.078 0.103 0.093 0.121 0.147 0.173 0.131 0.112
1.518 1.715 1.645 1.868 2.063 2.236 1.944 1.803
1.579 1.791 1.707 1.933 2.108 2.263 2.001 1.866
4.02 4.43 3.77 6.93 2.18 1.21 2.93 3.49
46.6
Sr=26.2% 8r=19.6%
1/2
Table I Comparison and verification of flow rate ratio at cavitation
h ~
hk
The results obtained from these calculations are summarized in Table 1. The experimental observations are included for comparison and verification.
0.6 0.s - ~1~ Sr= 1(X)%
(19)
Note that 5~ is obtained from [8,9]. In most cases, it is assumed that ~ = 0 due to the short distance between the sunction port and the nozzle exit section. Assuming cavitation occurs at the throat entry section and modifying the formula obtained from Bernoulli's equation applied between the suction port and throat entry section of a conventional jet pump [8], results in Eq. (20) which is used to calculate the flow rate ratio at cavitation in proportioning jet pumps.
4.2. Flow rate ratio at cavitation
~
(Po + PogZo + ½PoVo 2) -- (Ps + Psg'zs½Psv z )
(14)
(16)
q~=(1 _~e)-la
hk =
Eq. (18) can be rearranged using an energy balance analysis between the suction port and the cross-section of suction passage at the nozzle exit as
0.5
0.2-
(18)
P, +Ps + o~gzs + ½p2v~2-pv -
0.797
D. Wang et al. / Power Technology 84 (1995) 57-64
5. Conclusions
The following conclusions are based on the results and analyses presented in this paper. The structure of the spindle nozzle has a significant influence on the performance of proportioning jet pumps. Efficiency can be improved by a selecting a configuration and the combinations of convergent angle of the spindle and nozzle. On the basis of experimental observations from eighteen different configurations and combinations of different convergent angles, it is recommended for design that the convergent angle of the spindle be 45 ° to 54 ° and the convergent angle of the nozzle 60° to 75 °. Proportioning jet pumps can be regulated easily to suit say, the performance of a hydraulic transportation system. The variation of Sr will change the flow rate through the nozzle and result in the required variation in performance. Mass flow rate can be adjusted conveniently by selecting a given primary pressure, secondary pressure and back pressure. The performance prediction model presented in this paper represents well the water-only experimental resuits. Although its suitability in predicting water-solid performance requires further investigation, which will form the basis of another paper, preliminary results have shown that the water-only model can be used directly in certain water-solid applications.
6. List of symbols
A Cq Ch d g h le It l~ M m mc N q Q p p~ p,c Pv Sr R T v
cross-sectional area (m 2) correlation coefficient in Eq. (14) correlation coefficient in Eq. (13) diameter (m) acceleration due to gravity (m s -2) pressure ratio of proportioning jet pump Eq. (7) nozzle-throat gap (m) length of throat tube (m) length of diffuser, m mass flow rate (kg s -1) area ratio of proportioning jet pump area ratio for Sr = 1 pressure ratio defined by Eq. (3) flow rate ratio of proportioning jet pump, Eq. (8) volumetric flow rate (m 3 s -1) pressure (Pa g) atmospheric pressure (Pa abs) absolute pressure at nozzle exit section (Pa abs) vapour pressure (Pa abs) open-ratio of spindle nozzle area ratio defined by Eq. (1) volumetric flow rate ratio defined by Eq. (2) velocity (m s -1)
63
displacement of spindle (m) elevation above datum (m)
X Z
Greek letters a /3 r/ 0 /x~ /% /~r ~s
~:~ # 9
convergent angle of spindle (o) throat entry angle (°) efficiency of proportioning jet pump defined by Eq. (11) internal convergent angle of conical nozzle (o) discharge coefficient of conventional nozzle discharge coefficient of spindle nozzle defined by Eq. (10) ratio of discharge coefficient of spindle nozzle to conventional nozzle coefficient of pressure loss between suction port and annular cross-section of suction chamber at nozzle exit section coefficient of pressure loss between nozzle inlet and exit section density of fluid (kg m -3) velocity coefficient of conventional nozzle
Subscripts c k n o max s t
outlet of diffuser value at cavitation outlet 6f nozzle inlet of nozzle maximum value suction port throat tube
Acknowledgements
The work described here is based on a research project funded by the National Science Foundation of the People's Republic of China and conducted at the Pumps and Pumping Stations Laboratory, Department of Hydraulic Engineering, Wuhan University of Hydraulic and Electric Engineering, People's Republic of China. This work is supported also by The North-West Investigation and Design Institute of Hydro-Electric Power, People's Republic of China. Special thanks go out to T.L. Wang (Senior Engineer) and Professor H.Q. Lu. The assistance and support provided by all concerned are acknowledged gratefully.
References [1] S.T. Bonnington, Jet Pumps and Ejectors, a State-of-the-Art, Review and Bibliography, BHRA Fluid Engineering, Cranfield, Bedford, UK, 2nd edn., 1976. [2] A.J. Stepanoff, Centrifugal and Axial Flow Pumps, Wiley, New York, 1957, pp. 410--413.
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D. Wang et al. / Power Technology 84 (1995) 57-64
[3] R.D. Blevins, Applied Fluid Dynamics Handbook, Section 9.5, Jet pumps and confined jets, Van Nostrand Reinhold, New York, 1984, pp. 257-262. [4] A.M. Jumpeter, in J.K. Igor (ed.), Pump Handbook, McGrawHill, New York, 1976, Section 4, Jet pumps, pp. 13-20. [5] Centrifugal, mixed flow and axial pumps -- Code for acceptance tests -- Class B, ISO 3555; 1977 B. [6] D. Wang, Irrig. Drainage Hydro-power, 25, (1989) 35 (in Chinese). [7] D. Wang and P.W. Wypych, Investigation into the discharge coefficient of adjustable nozzle, Intern. Res. Rep. 93-06-DW-2,
Department of Mechanical Engineering, University of Wollongong, June 1993. [8] H.Q. Lu, Theory andApplications of Jet Pumps Technology, Water Resources and Electric Power Press, Beijing, China, 1987 pp. 105-106 (in Chinese). [9] N.L. Sanger, Non-cavitating performance of two low-area-ratio water jet pumps having throat lengths of 7.25 diameters, NASA TN D-4445, 1968. [10] D.K. Aggarwal, R.S. Gupta and V.P. Vasandani, Z Inst. Eng. (India), 66 (1986) 139.
Powder Technology 84 (1995) 57--64
Water-only performance of proportioning jet pumps for hydraulic transportation of solids D. Wang, P.W. Wypych Department of Mechanical Engineedn& University of Wollongong Wollongon~ NSW 2522 Australia Received 12 July 1994; revised 5 December 1994
Abstract
Experimental observations of water-only performance and pressure losses have been made for a proportioning jet pump feeder with eighteen different configurations and designs. Based on these results, the influence of structure and configuration on the performance of jet pump feeder has been investigated. Optimal configuration and geometrical parameters have been recommended for design practice. Formulae for performance prediction have been proposed and verified. Keywords: Water-only performance; Pressure loss; Proportioning jet pumpfeeder; Design practice
1. Introduction Jet pumps, particularly those with all the wearing surfaces made of alloy cast iron, ceramics, or other wear-resistant alloys for abrasive applications, are probably the most desirable type of pump to be used as a feeder in the hydraulic transportation of solids. The reasons are simplicity in structure, absence of moving parts, reliability and low capital cost, convenience of operation and maintenance and wear-resistant. These features more than compensate for the relatively poor efficiency of this type of feeder. Furthermore, it possesses the ability to be self-regulating, that is, if it is overloaded, it will reject water and material back through the suction port until the overload is eliminated. A conventional jet pump comprises a central convergent driving nozzle and an annular suction passage. The difference in structure between a conventional jet pump and a proportioning jet pump shown in Fig. 1, is that the pro-
It
~
portioning jet pump consists of a spindle nozzle, the necessary sealing and an adjusting device. Apart from all the advantages of the conventional jet pump, the proportioning jet pump possesses the additional capability of being able to optimize performance characteristics by moving the spindle back and forth manually or mechanically to suit the operating conditions of the hydraulic transportation system. Unfortunately, this type of pump has not received extensive investigation and application in engineering practice, and no design procedure and performance prediction method as yet have been published [1-4]. There also is a shortage of experimental data reported in the literature regarding the influence of configurations on performance characteristics. Therefore, it is of great importance to monitor the water-only performance of this type of jet pump and investigate the effect of geometrical parameters so that performance prediction models can be formulated and strategies to improve performance characteristics can be determined.
q
2. Test rig and experimental procedure 2.1. Test rig
Fig. 1. General configuration of a proportioning jet pump. 1, spindle nozzle; 2, suction chamber; 3, throat tube; 4, diffuser. 0032-5910/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0032-5910(94)02965-Q
Fig. 2 shows the layout of the test rig employed to monitor the performance characteristics of the proportioning jet pump with different configurations. This rig consists of various proportioning jet pumps, centrifugal pumps to supply primary jet flow and secondary
D. Wanget al. / PowerTechnology84 (1995)57--64
58
of nozzle are 40°, 60°, 75° and 90°. The external convergent angles of spindle are 13.5°, 40° and 54°, while the convergent angles of throat entry are 45 ° and 60°. The distances between the nozzle outlet and the throat entry are le = 0.8 dn, 1.2 d, and 1.6 dn.
o orf Jl
2.2.
Fig. 2. General layout of test rig. 1, proportioning jet pump; 2, centrifugal pump; 3, pressure gauges; 4, flowmeter; 5, regulating valve. 2
~ / / / / / / / ~ 1
~'////////////Z
~-~
Fig. 3. Cross-sectional view of proportioning nozzle. 1, spindle; 2, nozzle.
flow, flowmeters to measure primary and secondary flow rates, pressure gauges and the necessary equipment to monitor noise levels of the jet pumps. Bourdon type YD-150 precision pressure gauges with a maximum error of 0.4% full scale and calibrated before and after each group of experiments were used to monitor the pressure at the nozzle inlet, suction port and discharge port. MAGFLO-380 electro-magnetic flowmeters with a nominal diameter of 100 mm and 150 mm and calibrated before the experimental work were used to measure the primary and suction flow rates. The maximum error for this type of flowmeter was 1% for the measuring range 10-100% of full-scale. These maximum measuring errors met the requirements of the standard of pump performance tests [5]. Steadystate conditions were maintained for each set of measurements. The test ranges were 24 to 70 m3 h-1 for primary water flow rate, 30 to 50 m 3 h-1 for secondary flow rate and 600 to 2400 kPa g for primary pressure. Fig. 3 provides a cross-sectional view of the spindle nozzle. The proportioning jet pumps are made from carbon steel and have a throat diameter of 40 mm and a diffuser outlet diameter of 80 mm. The nozzle and spindle are interchangeable and the outlet diameter of the nozzle is 25 mm. The internal convergent angles
Experimentalprocedure
The experimental work was divided into two stages. Firstly, four spindles with different convergent angles were combined with four different nozzles to comprise sixteen configurations of proportioning jet pump. Pump performance was monitored for different throat entry angles and different nozzle-throat gaps. Secondly, by keeping the convergent angle of the spindle nozzle constant, the configurations and geometrical parameters of the nozzle and spindle were modified and tested to investigate their effect on pump performance. The actual test procedure that was adopted to monitor the performance of these pumps with different configurations is detailed below. (1) Measure water temperature and atmospheric pressure. (2) Run both centrifugal pumps, keeping Po and p, as close as possible to the set value by regulating the corresponding valves. Allow Q, to reach a maximum value by opening completely the valve on the discharge pipeline. Then observe and record values of po, Ps, Pc, Qo and Qs. (3) Increase Pc gradually, keeping Po and p, constant and reducing Q, by regulating the valves on the section and discharge pipelines. (4) Repeat step (3) for different Q, until a minimum number of seven readings have been obtained. (5) Adjust p, and repeat steps (1)-(4) to investigate the influence of sunction pressure on performance. (6) Adjust and repeat steps (1)-(5) to investigate the influence of primary pressure on performance.
Po
3. Analysis of experimental results According to Stepanoff [2], the characteristics of conventional jet pumps can be described by the three dimensionless parameters listed below. R=
At
T= O___z~
(1) (2)
Qo N=
(P°+½p°vJ + t'azc)-(P" +½mv'2 (po + ½poVJ + pogzo) - (po + ½povJ + p zo)
(3)
R is the ratio of nozzle area to throat area, T is the ratio of suction volumetric flow rate to primary vol-
59
D. Wang et al. / Power Technology 84 (1995) 57-64
umetric flow rate and N is the ratio of net jet pump head to net primary head. For the proportioning jet pumps considered in this paper, the following nondimensional parameters, viz. Eqs. (4) to (8), are used instead of R, T and N. The effective cross-section of the spindle nozzle can be expressed by the open-ratio of the spindle nozzle. Open-ratio is defined as S, = x,..x-x
0.6 0.5 ~ 0 0 %
h 0.0.3 20"4
(4)
Xrnax If x = 0, from Eq. (4) it can be seen that the effective cross-section of the spindle nozzle will be equal to that of a common convergent nozzle outlet, that is S, becomes unity. If the area ratio of the proportioning jet pump, m is defined as the ratio of throat tube cross-section to the effective cross-section of the spindle nozzle, then m can be expressed by
me
m=
(s,>0)
(5)
1 4(X'a×(1-S~)~ 2 Using the geometrical relationship of the spindle, dn= 2 xm~ tan(~/2), Eq. (5) can be rewritten as
m
me (0
(6)
where mo-- \ d J
(pc + ½pcvo2 + p gzc) - (ps + ½psvs2 + psgzs)
h= O o+½poVJ+pogZo)_Cvs+½psv +p
)
Ms q = Moo
(7) (8)
Note N can be determined easily from h using h N = 1----'h
(9)
The influence of geometrical parameters and configurations as well as operating conditions on pump performance are analyzed from experimental observations, as detailed later on.
3.1. Open-ratio of spindle nozzle From Eqs. (4)-(6), it can be seen that the variation of Sr is equivalent to the variation of nozzle outlet area, and is equal to the variation of area ratio m for a given cross-section of throat. Therefore, the trend of the fundamental dimensionless characteristic of a proportioning jet pump, as shown in Fig. 4, where h and q are defined by Eqs. (7) and (8) respectively,
°A'S=r 1969 0.1
1
2 q Fig. 4. Influence of Sr on fundamental dimensionlesscharacteristics, a=450; 0=60*. Points: experimental data; lines: calculated by performance prediction model, F-qs. (12)-(16). approaches that of a conventional jet pump by varying the area ratio from a small to large value [2]. Note for reasons of clarity, cavitation data and limits have been omitted from Fig. 4. Cavitation effects are considered and discussed later in Sections 3.2 and 3.4. Figs. 5 and 6 also show that the variation of Sr changes the efficiency defined by Eq. (11). The peak point of efficiency decreases as S, is reduced. The slope of h-q lines is dependent on S,. It can be seen from Fig. 4 that the lines become flatter as S, is decreased and steeper as S, is increased. This means that by varying S, for a given h, q may increase or decrease and for a given q, h may increase or decrease. From Eq. (7), increasing h will increase Pc if Po and Ps are kept constant. This suggests that a small S, suits the application of low back pressure and large mass flow rate, and vice versa. It also indicates that the ratio of secondary to primary mass flow rate can be regulated by varying Sr to suit the requirements of the transportation system for given pressures at the nozzle inlet and outlet of the proportioning jet jump. For example, when the back pressure of the jet pump is reduced, reducing S, will shift the characteristics to a flatter h--q line, an increased suction flow rate and better efficiency. This is the advantage of proportioning jet pumps. Open-ratio S~ has a significant influence on cavitation (see also Section 3.4). Proportioning jet pumps are subject to cavitation in the same way as conventional jet pumps. Cavitation limits the maximum flow rate possible for a given suction pressure, irrespective of the back pressure (see Fig. 10). From Figs. 8 and 9, it can be seen that varying Sr can change the flow rate ratio at cavitation qk. If Sr is increased, qk will decrease and vice versa. The discharge coefficient ~p defined in Eq. (10) is also dependent on St. Generally,/Zp will increase with
60
D. Wang et al. / Power Technology 84 (1995) 57-64
S~. For example, refer to the correlation between /xp and Sr given in Eq. (16) which is based on data calculated by Eq. (10) from observed values of Qo, po and psOo
/~p =
~/~
(10)
55 T [ 1
~
45 I / d /
O
t;t=54°, 0=75*
r--466% "
a=45°' 0=9°*
,,/-
-',~
0.5
1.0 q
u o~lsr.~0°
3.2. Convergent angles of spindle and nozzle Experimental results show that the frictional losses and flow characteristics are quite different for the spindle nozzle with different combinations of spindle convergent angle and nozzle convergent angle. For a constant spindle convergent angle and nozzle convergent angle. For a constant spindle convergent angle, the performance characteristics and efficiency curves of the pump are varied with the nozzle convergent angle. The comparison of experimental results as illustrated in Figs. 5 and 6 for different combinations of a and 0, shows that higher efficiency can be obtained for the combinations of a = 54° with 0= 75°, and a = 45 ° with 0 = 60°. Note the efficiency expressed in Figs. 5 and 6 has been calculated using the following expression given in literature [1]. ~7= (1 + q)h
30
25 0.0
2.0
Fig. 6. Variation of efficiency with the combination of a and 0, Sr =46.6%, Sr = 26.2%. 0.6'
0.5 '
00%
0.4' h 0.3 ' "'"
(11)
These combinations influence the flow rate ratio at cavitation qk (see Section 3.4), as well as the dimensionless characteristics and efficiency, as shown in Fig. 7. The reasons are: the spindle nozzles with different combinations of ot and O have different discharge coefficients even for the same open-ratio; also, the flow rate through the spindle nozzle, which influence the distributions of velocity and pressure loss along the jet
1.5
Sr=46.6%
""/5..~,. • 0.2 '
~
0.1
'
"'"o
:' 26.6% !
Ii
A~
Sr=19.6%
0.0
(1
I
q
2
Fig. 7. The influence of the combination of ct with 0 on performance. ( - - ) : a = 13.5", 0=45*; ( - - - ) : a = 4 5 °, 0=60*; ( - . . ) : experimental data.
65
0 60 ~
Sr=l(~)%
55 . ~ ) ~ Y ' - - ~
,of
pump, can be different for the same primary and secondary pressure. Therefore, it is of great importance to select rationally the combination of convergent angles of nozzle and spindle for improving efficiency and cavitation characteristics.
ct=54o, 0=75°
•
a'--45°' 0=90°
•
¢e'---45°, 0=60°
s.,.,,
3.3. Nozzle-throat gap and angle of throat entry
40
,
311
2
5 0.0
0.5
~ 1.0
q
1.5
2.13
2.5
Fig. 5. Variation of efficiency with the combination of a and 0. S, = 100%, Sr = 33.1%, S, = 19.6%.
Nozzle-throat gap and angle of throat entry are related to open-ratio, as shown in Figs. 8 and 9. If the openratio Sr is greater than or equal to 46.6%, then there is little influence of nozzle-throat gap and angle of throat entry on performance. The influence of these parameters on performance becomes more apparent as the open-ratio decreases (that is, as the spindle moves forward to the throat section). This is probably due to the flow boundary condition in the throat entry being changed by moving the spindle closer to the
D. Wang et aL / Power Technology 84 (1995) 57--64 0.6, -
0.5.
, ~ X St= 100%
0.4.
~
= • = • •
% ~41~'~
h
-
13=soo
-
--
The characteristic curves of back pressure with respect to secondary flow rate are illustrated in Fig. 10. For a given S,, primary and secondary pressure, the suction flow rate will increase as the back pressure decreases within a certain range. Beyond this range, the suction flow rate will remain constant. The same results would have been obtained by varying the primary pressure. This means that the ratio of suction flow rate to primary flow rate will remain constant for a given suction pressure and primary pressure. This constant flow rate ratio is defined as the cavitation flow rate ratio [8].
t3=45o
Sr=lO0% * Sr--lO0% Sr=46.6% • S~-46.6% Sr=33.1% • Sr=33.1% Sr=26.2% =' Sr=26.2% St= 19.6% 0 Sr=19.6%
"~".a. 0.2,
~.
• """ " ~ S r;ll =- - ' ~1' , ~9' ~ r.- m6 ~ a
°
0.0
.
,
0.0
.
1 !
0.5
~
,
1.0
1.5
q
llt .... , •
,
.
I=
2.0
4. Performance prediction
2.5
Fig. 8. I n f l u e n c e o f t h r o a t e n t r y a n g l e /~ o n p e r f o r m a n c e . fl=450; ( - - - ) : /3=60°; ot=450, O=6(Y'.
(--):
0.6 - 0.5
Sr=-100% " ~ 0.4 ~
I~,~
.,IL~'~..~I~V~ h
0.3
(I.Sdn
•
;r= |(X)C~
O • .
Sr=46.6% Sr=33.1% Sr=26.2%
1.6dn St=1(10% a Sr=46,6% D Sr=33.1% . Sr=26.2%
II
o.,
.....
Sr=19.6%
,
A
Sr=19.6%
I
0.0
A
0.5
The experimental results show that the fundamental characteristic curves are a series of curves with Sr as a parameter. The performance prediction model is developed by using a one-dimensional momentum and energy approach and then simplified as follows:
.2% ~_ ~
,~
[]
1.0
1.5
I1..Sc=19.6%
2.0
Performance prediction involves the determination of fundamental dimensionless characteristic curves and cavitation flow rate ratios at different S, for a particular configuration. As a fundamental dimensionless characteristic curve is determined, the transformation to dimensional form can be performed from the expressions of/z, ~7, h and q given in Eqs. (10), (11), (7) and (8), respectively. 4.1. Determination of fundamental dimensionless characteristic curve
~Sr--46,6% I~
.~
61
2.5
q
Fig. 9. I n f l u e n c e o f n o z z l e - t h r o a t g a p o n p u m p p e r f o r m a n c e . 0.8 d.; ( . . . . ) 1.6 d.; a = 4 5 * , 0 = 6 0 °, f l = 6 0 °.
(--)
Ch h = ~z ~ ( q _ Cq)
(12) 2
throat section. The experimental results in Fig. 9 also show that higher efficiency can be obtained for larger values of nozzle-throat gap. This suggests the jet pump should be designed with adjustable nozzle-throat gap.
C h = 2 . 6 6 7 - 0 . 0 0 2 5 3 ( ~ +26.07)
1.5< m/zr¢ 3
(13a,
600
3.4. O p e r a t i n g c o n d i t i o n s
500
The operating conditions are expressed by the primary pressure in the nozzle inlet, the secondary pressure at the inlet of the suction chamber and the back pressure at the outlet of the diffuser. All these parameters are determined by the requirements of the transportation system and the particular application. Although the dimensionless characteristic curves are identical for different primary pressures, the maximum flow rate ratio for different Sr will decrease under constant secondary pressure as the primary pressure increases. The maximum flow rate ratio will increase as secondary pressure increases for given Sr and Po, and vice versa.
400
~,~ 300
2OO
100
~.~ m 10
po= 17(IOkPa po=14(X}kPa po= 17(•1 kPa 20
30
T
40
50
60
Qs (m3/h) Fig. 10. O b s e r v e d b a c k p r e s s u r e v i a s u c t i o n f l o w r a t e , a = 4 5 °, 0 = 6 0 °, S~ = 33.11/b.
D. Wang et al. / Power Technology 84 (1995) 57-64
62
-- 0.892
/xr
<10
(13b)
C q = ( 5m/-~r -0.9445)
-1.75
/xe /zp = 0.781 + 0.223S~- 0.158S~2
(15)
P.e + (1 + ~s)½p~v,2-pv hk = (po+pogZo+½Povo2)_(ps+p~gz~+½p~v2)
where the velocity coefficient of conventional nozzle ~ois defined in Eq. (17). (17)
Note that ~ is obtained from [8,9] and q~ is found to be ~ 0.975, which agrees closely with the value of 0.978 found by Aggarwal et al. [10]; Ch and C n are correlated using a least-squares approach based on the results from the numerical solution of the one-dimensional analytical model equations; the discharge coefficient of conventional nozzle /~---0.95 to 0.975; the expression of /z~ in Eq. (16) is correlated using a least-squares approach based on the observed values of pressure at the spindle nozzle inlet and outlet and for water discharged from the nozzle with a = 45° and 0= 60°. For other convergent angles of spindle and nozzle, the expressions can be found elsewhere [6-7]. The nondimensional performance characteristic curves for different S~ and a particular configuration can be determined by solving Eqs. (12)-(16). The prediction results with experimental data have been shown on Figs. 4 and 11. These graphs show good agreement between the experimental data and predictions.
The pressure ratio of the proportioning jet pump at cavitation is defined by Eq. (18).
m
0.1
Sr
°°
;
~
q Fig. 11. Demonstration of performance prediction model• a = 5 4 °, 0=75"; solid lines: calculated by performance prediction model; points: experimental data.
hk
qk o b s
qk cal
(%) 100
Relative
error (%) 0.156 0.201
0.623 0.696
0.598 0.668
4.01 4.02
0.094 0.132 0.112 0.145 0.129
0.72 0.835
0.172
0.912 0.856 0.995
0.762 0.862 0.826 0.930 0.883 1.002
5.83 3.23 3.64 1.97 3.15 0.7
33.4
0.075 0.104 0.092 0.121 0.112 0.147 0.130
1,045 1,205 1.134 1.303 1.242 1.438 1.337
0.991 1.127 1.069 1.210 1.169 1.320 1.248
5.17 6.47 5.73 7.14 5.88 8.21 6.66
26.1
0.078 0.103 0.092 0.122 0.112 0.131 0.173 0.147
1.204 1.376 1.305 1.500 1.444 1.551 1.789 1.643
1.284 1.460 1.388 1.576 1.518 1.628 1.841 1.715
6.64 6.10 6.36 5.07 5.12 4.96 2.91 4.38
21.5
0.078 0.103 0.093 0.121 0.147 0.173 0.131 0.112
1.518 1.715 1.645 1.868 2.063 2.236 1.944 1.803
1.579 1.791 1.707 1.933 2.108 2.263 2.001 1.866
4.02 4.43 3.77 6.93 2.18 1.21 2.93 3.49
46.6
Sr=26.2% 8r=19.6%
1/2
Table I Comparison and verification of flow rate ratio at cavitation
h ~
hk
The results obtained from these calculations are summarized in Table 1. The experimental observations are included for comparison and verification.
0.6 0.s - ~1~ Sr= 1(X)%
(19)
Note that 5~ is obtained from [8,9]. In most cases, it is assumed that ~ = 0 due to the short distance between the sunction port and the nozzle exit section. Assuming cavitation occurs at the throat entry section and modifying the formula obtained from Bernoulli's equation applied between the suction port and throat entry section of a conventional jet pump [8], results in Eq. (20) which is used to calculate the flow rate ratio at cavitation in proportioning jet pumps.
4.2. Flow rate ratio at cavitation
~
(Po + PogZo + ½PoVo 2) -- (Ps + Psg'zs½Psv z )
(14)
(16)
q~=(1 _~e)-la
hk =
Eq. (18) can be rearranged using an energy balance analysis between the suction port and the cross-section of suction passage at the nozzle exit as
0.5
0.2-
(18)
P, +Ps + o~gzs + ½p2v~2-pv -
0.797
D. Wang et al. / Power Technology 84 (1995) 57-64
5. Conclusions
The following conclusions are based on the results and analyses presented in this paper. The structure of the spindle nozzle has a significant influence on the performance of proportioning jet pumps. Efficiency can be improved by a selecting a configuration and the combinations of convergent angle of the spindle and nozzle. On the basis of experimental observations from eighteen different configurations and combinations of different convergent angles, it is recommended for design that the convergent angle of the spindle be 45 ° to 54 ° and the convergent angle of the nozzle 60° to 75 °. Proportioning jet pumps can be regulated easily to suit say, the performance of a hydraulic transportation system. The variation of Sr will change the flow rate through the nozzle and result in the required variation in performance. Mass flow rate can be adjusted conveniently by selecting a given primary pressure, secondary pressure and back pressure. The performance prediction model presented in this paper represents well the water-only experimental resuits. Although its suitability in predicting water-solid performance requires further investigation, which will form the basis of another paper, preliminary results have shown that the water-only model can be used directly in certain water-solid applications.
6. List of symbols
A Cq Ch d g h le It l~ M m mc N q Q p p~ p,c Pv Sr R T v
cross-sectional area (m 2) correlation coefficient in Eq. (14) correlation coefficient in Eq. (13) diameter (m) acceleration due to gravity (m s -2) pressure ratio of proportioning jet pump Eq. (7) nozzle-throat gap (m) length of throat tube (m) length of diffuser, m mass flow rate (kg s -1) area ratio of proportioning jet pump area ratio for Sr = 1 pressure ratio defined by Eq. (3) flow rate ratio of proportioning jet pump, Eq. (8) volumetric flow rate (m 3 s -1) pressure (Pa g) atmospheric pressure (Pa abs) absolute pressure at nozzle exit section (Pa abs) vapour pressure (Pa abs) open-ratio of spindle nozzle area ratio defined by Eq. (1) volumetric flow rate ratio defined by Eq. (2) velocity (m s -1)
63
displacement of spindle (m) elevation above datum (m)
X Z
Greek letters a /3 r/ 0 /x~ /% /~r ~s
~:~ # 9
convergent angle of spindle (o) throat entry angle (°) efficiency of proportioning jet pump defined by Eq. (11) internal convergent angle of conical nozzle (o) discharge coefficient of conventional nozzle discharge coefficient of spindle nozzle defined by Eq. (10) ratio of discharge coefficient of spindle nozzle to conventional nozzle coefficient of pressure loss between suction port and annular cross-section of suction chamber at nozzle exit section coefficient of pressure loss between nozzle inlet and exit section density of fluid (kg m -3) velocity coefficient of conventional nozzle
Subscripts c k n o max s t
outlet of diffuser value at cavitation outlet 6f nozzle inlet of nozzle maximum value suction port throat tube
Acknowledgements
The work described here is based on a research project funded by the National Science Foundation of the People's Republic of China and conducted at the Pumps and Pumping Stations Laboratory, Department of Hydraulic Engineering, Wuhan University of Hydraulic and Electric Engineering, People's Republic of China. This work is supported also by The North-West Investigation and Design Institute of Hydro-Electric Power, People's Republic of China. Special thanks go out to T.L. Wang (Senior Engineer) and Professor H.Q. Lu. The assistance and support provided by all concerned are acknowledged gratefully.
References [1] S.T. Bonnington, Jet Pumps and Ejectors, a State-of-the-Art, Review and Bibliography, BHRA Fluid Engineering, Cranfield, Bedford, UK, 2nd edn., 1976. [2] A.J. Stepanoff, Centrifugal and Axial Flow Pumps, Wiley, New York, 1957, pp. 410--413.
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D. Wang et al. / Power Technology 84 (1995) 57-64
[3] R.D. Blevins, Applied Fluid Dynamics Handbook, Section 9.5, Jet pumps and confined jets, Van Nostrand Reinhold, New York, 1984, pp. 257-262. [4] A.M. Jumpeter, in J.K. Igor (ed.), Pump Handbook, McGrawHill, New York, 1976, Section 4, Jet pumps, pp. 13-20. [5] Centrifugal, mixed flow and axial pumps -- Code for acceptance tests -- Class B, ISO 3555; 1977 B. [6] D. Wang, Irrig. Drainage Hydro-power, 25, (1989) 35 (in Chinese). [7] D. Wang and P.W. Wypych, Investigation into the discharge coefficient of adjustable nozzle, Intern. Res. Rep. 93-06-DW-2,
Department of Mechanical Engineering, University of Wollongong, June 1993. [8] H.Q. Lu, Theory andApplications of Jet Pumps Technology, Water Resources and Electric Power Press, Beijing, China, 1987 pp. 105-106 (in Chinese). [9] N.L. Sanger, Non-cavitating performance of two low-area-ratio water jet pumps having throat lengths of 7.25 diameters, NASA TN D-4445, 1968. [10] D.K. Aggarwal, R.S. Gupta and V.P. Vasandani, Z Inst. Eng. (India), 66 (1986) 139.