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Performance evaluation of a commercial positive displacement pump for wind-water pumping
ARTICLE IN PRESS
Renewable Energy 32 (2007) 1790–1804 www.elsevier.com/locate/renene
Technical Note
Performance evaluation of a commercial positive displacement pump for wind-water pumping Juan La Rotta, Alvaro Pinilla a
Mechanical Engineering Department, Universidad de Los Andes, Cra 1a Este # 18a – 10, Bogota´, Colombia % % Received 28 June 2006; accepted 4 October 2006 Available online 21 November 2006
Abstract This paper presents the experimental performance test evaluation of a commercial wind-driven positive displacement pump type JOBER of 3 in diameter. Results of the behaviour of pump lift rod peak force, in relation with the lift rod elasticity and the piston valve closure delay are presented. The pump performance is analysed in terms of its volumetric and overall efficiencies. Evidence about a possible effect of the piston valve closure delay over the pump overall efficiency is also discussed. r 2006 Elsevier Ltd. All rights reserved. Keywords: Wind-water pumping; Reciprocating pumps; Pumps; Windpumps; Hydraulic testing
1. Introduction With the purpose of providing essential elements for evaluation of wind-water pump equipment, this paper presents laboratory performance evaluation results on the commercial JOBER pump (Fig. 1). Industrias JOBER located in Duitama-Colombia is a small enterprise started in 1984 and currently has more than 800 of its faster running wind pumps operating in the zone of Eastern Prairies in Colombia [1]. Some wind pumps have been exported to neighbouring countries within the Andean Region. The pump and its riser pipe were evaluated in terms of volumetric efficiency; overall input efficiency and peak maximum lift rod forces. Theoretical validation of measured data was carried out using the dynamic model as proposed by Burton and Davis [2]. Corresponding author. Tel.: +571 332 4322; fax: +571 332 4323.
E-mail address: [email protected] (A. Pinilla). 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.10.001
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Nomenclature A Ap cf cd D Fr kr H L m0 N Ns PH Q r R t V Vp
riser pipe cross-sectional flow area effective pumping area (piston area minus lift rod area) dry friction coefficient viscous damping coefficient theoretical volume displaced per piston cycle [ ¼ 2RAp] lift rod force elastic Constant for lift rod (force/unitary extension) static head length of discharge including riser and suction pipe mass of lift rod and piston minus floating effects pump operational speed (r/min) Sommerfeld number ¼ mO/rgH Hydraulic power water flow rate per piston stroke frequency ratio O/Oor crank throw ( ¼ half of the stroke length) time water speed flow in riser pipe maximum effective flow speed in riser pipe for a system with infinitely rigid lift rod ¼ OR(Ap/A)
Greek symbols a g Gr DP Z m r C O Oor
piston valve angular delay closure after Upper Dead Center piston valve angular delay closure after Lower Dead Center dimensionless lift rod force¼ ðF r m0 gÞ=ðrgHAp Þ piston pump differential pressure overall efficiency water viscosity water density dimensionless head¼ ðH=LÞðg=O2 RÞðA=Ap Þ crank Angular velocity natural frequency of oscillation of the system lift rod/riser pipe
Results of this research and the procedure followed are a useful tool for designers of wind-driven pumping systems.
2. Theoretical model The theoretical dynamic model as proposed by Burton and Davis [2] is an excellent guide for structural dimensioning of the reciprocating pump test rig, as well as for the design, execution and interpretation of experiments.
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Fig. 1. Details of the JOBER 3 in reciprocating pump.
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Burton and Davies’ model provides essential elements for the analysis of the behaviour of pump lift rod forces, volumetric and overall efficiencies. 2.1. Pump lift rod force The understanding of the behaviour of the pump lift rod force is important, given that, during the pumping cycle, the lift rod force may reach peak values quite above the corresponding static piston force (rgHAP). Forces in the pump lift rod are due to: (1) weight of lift rod and piston, (2) forces of dry and viscous friction as a consequence of piston displacement inside the pump cylinder and (3) the force due to differential pressure on the piston pump. Eq. (1), taken from [2], represents the dimensionless lift rod force, during discharge stroke, for a system without friction with elasticity in the lift rod and angular delay in closure of piston valve. Gr ¼ 1 þ
1 dðV =V p Þ , C dðOtÞ
where C the dimensionless static head is expressed as follows: H g A C¼ 2 L O R Ap
(1)
(2)
and Gr is defined as the ratio of lift rod force to the static piston force (rgHAP). Peak values of Gr are of great interest. The peak occurs when acceleration of the fluid in the riser pipe reaches its maximum. Depending upon flexibility of the lift rod and the angular delay closure of piston valve, the maximum acceleration in Eq. (1) reaches values, such that the lift rod force may be up to 8 times the force imposed by the static head (GrE8) [1]. Term Cr2 in Eq. (3) provides a clear idea of mechanical elasticity of the lift rod. rgHAp 1 Cr2 ¼ (3) R kr Cr2 relates the static lift rod elongation, due to static head force, on the piston and the length R of the crank throw of the wind pump transmission. It may be interpreted as the fraction of the length R equivalent to the lift rod elongation. 2.2. Volumetric efficiency In a wind-driven reciprocating pump, the theoretical water volume displaced at every pumping cycle is defined as D ¼ 2RAP. Volumetric efficiency is defined as the ratio between the actual amount of water delivered in the pumping cycle to the theoretical water delivered. Water volume delivered in each cycle is usually less than the theoretical volume. This is mainly due to leakage around the piston seals and to the delay in the operation of the valves. For this particular case, the JOBER pump is provided with leather seals, sucking type which guarantees an adequate sealing. Burton et al. [3] propose that lift rod flexibility
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and angular delay closure of the piston valve affect the volumetric efficiency and are related by means of Eq. (4), as follows: 1 1 Zv ¼ ðcos a þ cos gÞ ¼ cos a ðCr2 Þ. 2 2
(4)
2.3. Overall pump efficiency Overall pump efficiency (Eq. (6)) is defined as the ratio of hydraulic power delivered by the system to the input mechanical power absorbed by the system. Hydraulic power is the water pumped to a determined static head (Eq. (5)). PH ¼ rgHQ, Z¼
(5)
Hydraulic Power . Mechanical Input Power
(6)
3. Experimental setup A hydraulic test rig was specially constructed for the 3 in JOBER pump. This assembly allows simulating typical JOBER wind pump operation conditions. (i.e., 8–40 m hydraulic static head; (see Table 1). The hydraulic test rig (Fig. 2) is installed at the laboratory of Mechanical Engineering of the Universidad de Los Andes. Given space limitations, the pumping static head is simulated with a pressurized air tank connected to the pump discharge. By setting the internal tank pressure it is possible to simulate the required hydraulic static heads. Table 2 contains pump dimensions. The pump is powered by an electric motor excited via a variable frequency converter to reach operation speeds up to 80 r/min. The riser pipe of 38 mm (1.5 in nom. dia.) in a typical JOBER wind pump installation is replaced by a galvanized steel tubing of 12 mm (0.5 in nom. dia.). This pipe is connected between pump discharge and the entrance of pressurized air tank. Length of the pipe installed in the rig is varied between 1 and 8 m, which corresponds to equivalent lengths from 8 to 40 m of riser pipe in the real wind pump. Dynamic similitude between real installation and the rig is preserved by means of this hydraulic inductance. For each set of experiments, the riser pipe length coincides with the hydraulic static head; that is, values of hydraulic static head are determined to correspond to 8, 14, 30 and 40 m as described in [4]. The assembly is instrumented with a displacement sensor and a load cell installed in the pump lift rod. This setting allows measurement of the lift rod force and the piston
Table 1 JOBER 3 in pump operational range according to JOBER INDUSTRIES Static lifting head, H Speed of operation Water pumped range
¼ 25–50 m ¼ 60–80 r/min (120 max) ¼ 800–1000 L/h
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Crank Transmission
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Input motor Variable Speed 25-75 r/min
Lift rod
Pressurized Tank Variable pressure 80-400 kPa Pipe arrangement Variable length 1-8 m Pump
Recirculation tank
Fig. 2. Layout of the hydraulic rig for reciprocating pump testing. Table 2 JOBER 3 in pump geometrical characteristics Piston area, Ap Lift rod area, Av Effective pumping area, ApAv Pipe sectional area, A
5418 mm2 127 mm2 5291 mm2 214 mm2
displacement simultaneously. Additionally, pressure transducers are fitted on the pump cylinder, one located on the suction side of pump (below the piston) and the other one above the piston. This setting facilitates measurement of the differential pressure on the piston pump; consequently the force on the piston pump might be deduced. Data acquisition is carried out using a data acquisition board with a sampling frequency of 250 Hz. All data are fed into a computer for processing. This assembly provides the necessary set up for performance evaluation of the pump including its riser pipe, permitting establishing the effect of dynamic behaviour of the water column in the riser pipe, and its influence upon the overall pump performance. 3.1. Operation of test rig 3.1.1. Pumping closed circuit The pump draws water from the suction tank through the foot valve. The water goes through the pump and enters into the pipe arrangement connected between pump
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discharge and pressurized tank inlet. Water enters the pressurized tank and it is maintained inside it until the tank pressure rises above a prefixed value. In this way, water goes out through a relief valve installed at the bottom of pressurized tank and returns to the suction tank. 3.1.2. Configuration of a test scenario Before carrying out any test, it is necessary to correctly configure each one of the parameters of the rig in accordance with conditions of operation to be simulated. The following steps have to be followed to set the rig for evaluating the pump: (1) length of conduction pipe is determined, this one must coincide with static head being simulated; (2) pumping speed is set up via the excitation frequency of the electric motor; (3) the tank is pressurized to a pressure equivalent to the simulated static head; (4) relief valve discharge pressure is set, while the pump starts working. 4. Experimental results Through factorial analysis, the operational range of the pump variables is made discrete as presented in Table 3. A total of 12 experiments were executed in the strict order as in the experimental matrix contained in Table 4. Needless to say every experiment was repeated several times. 4.1. Type of results 4.1.1. Graphs of force vs. time Fig. 3 presents the lift rod force and the force in the piston pump, registered for a pumping cycle under different conditions of operations. Cases illustrated in Fig. 3 correspond to extreme conditions within the range of tests run. In part (a) of Fig. 3 (slowest speed and lowest static head) it can observe that the lift rod force is two-times greater than the force on the piston. Table 3 Discrete values of pump variables for testing Variable
Range
Discrete values
Speed (r/min) Static head (m) Riser pipe length
25–75 8–40 8–40
25, 50, 75 8, 14, 30, 40 8, 14, 30, 40
Table 4 Experimental matrix Number of experiment Variable Speed (r/min) Static head (m)
1 25 8
2 25 14
3 25 30
4 25 40
5 50 8
6 50 14
7 50 30
8 50 40
9 75 8
10 75 14
11 75 30
12 75 40
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a Force on the piston
Lift rod force
Piston displacement
1.0 0.8 Force, kN
0.6 0.4 0.2 0.0 −0.2 −0.4 0
0.5
1
1.5
2
2.5
Time, s Force due to static head
b Lift rod force
Force on the piston Piston displacement
4.5
Force, kN
3.5 2.5 1.5 0.5 −0.5
0
0.2
0.4
0.6 Time, s
0.8
1
1.2
Force due to static head Fig. 3. (a) Lift rod and piston forces, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) lift rod and piston forces, N ¼ 50 r/ min, H ¼ 40 m, L ¼ 8 m.
On the contrary in Fig. 3(b) (fastest speed and largest static head) the difference between the forces on the lift rod and on the piston is just a 10%. The excess in the lift rod force is attributed to dissipative phenomena, what suggests that under low speeds of operation and static heads, the frictional force plays a dominant role in the consumption of energy introduced into the system.
4.1.2. Pressure indicator diagrams Fig. 4 presents the pressure indicator diagrams for the same conditions of operation as in Fig. 3. These diagrams were used for determining the value of angular closure delay of the piston valve for each of the experiments carried out. This procedure yielded evidence of
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a Presure, kPa
90 70 50 30 10 −10
0
14
28
42
56
Piston displacement, mm Pressure above the piston
Pressure below the piston
Pressure due to static head
b Pressure, kPa
800 600 400 200 0 −200
0
14
28
42
56
Piston displacement, mm Pressure above the piston
Pressure below the piston
Pressure due to static head
Fig. 4. (a) Pressure indicator diagrams, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) pressure indicator diagrams, (b) N ¼ 50 r/min, H ¼ 40 m, L ¼ 8 m.
Table 5 Piston valve angular delay closure determined experimentally Pump speed (r/min)
a (degrees)
25 50 75
0 15 30
the strong dependency between valve closure delay and pump operating speed. Table 5 presents average values of a for each of speeds studied.
4.1.3. Force indicator diagrams Fig. 5 presents the force indicator diagrams for the same conditions of operation illustrated above. Area enclosed by curve line of lift rod force is proportional to energy
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a 1.0 0.8 Force, kN
0.6 0.4 0.2 0.0 −0.2 −0.4
0
14
28
42
56
Piston displacement, mm Lift rod force
Force on the piston
Static force
b 5 Force, kN
4 3 2 1 0 −1 0
14
28
42
56
Piston displacement, mm Lift rod force
Force on the piston
Static force
Fig. 5. (a) Force indicator diagram, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) force indicator diagram, N ¼ 50 r/ min, H ¼ 40 m, L ¼ 8 m.
introduced to the system during a pumping cycle. With these diagrams, it is possible to calculate the overall efficiency for each one of experiments carried out. 4.2. Force on the lift rod From the lift rod force vs. time measurements, peak values of lift rod force are determined for each set of the experiments during any pumping cycle. Each of these values was non-dimensionalized when divided by static force on the piston rgHAp, these are contained in Fig. 6. Flexibility for each one of the pumping heads is determined by measuring the displacement registered by the displacement sensor when loading the pump with the transmission system locked. Fig. 6 shows the attenuation effect of lift rod flexibility upon maximum dimensionless lift rod force values. Comparison of values experimentally determined with values calculated via Eq. (1), suggest that in the pump tested, there exist damping forces, not being considered in the theoretical model.
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8
46
84
23
7
14
6
Γr
5 4 3
1+1/ψ
2 1 0 0
0.5
1
1.5 1/ψ 84
46
2
2.5
3
23 14
Fig. 6. Experimental and theoretical peak dimensionless lift rod force (Gr) against the reciprocal of the dimensionless head (1/c) with various lift rod elasticities (1/cr2).
It should be mentioned that the theoretical model is solved for a frictionless system. For the case of the JOBER pump, this is a condition far from true, since it is a new pump, meaning it did not work a number of cycles enough to reach an adequate seals wear condition corresponding to an optimum operating condition of this equipment. Value of 1/Cr2 corresponding to curves of Gr vs. 1/C calculated from Eq. (1), must vary in each test in accordance with simulated static head. It should be assured that it corresponds to the lift rod flexibility with equal length to the static head. Due to the flexibility of transmission system and its anchorages of the test rig, the evaluation of the system was carried out without varying the lift rod flexibility. In spite of this situation, it produces a slight additional difference in the magnitude of measures data; nonetheless it does not interfere in the determination of the effect of flexibility upon maximum lift rod forces. The tendency observed from experimental data in Fig. 6, corroborates the hypothesis from theoretical model, in the sense that peak lift rod force is progressively reduced, with increases in lift rod flexibility. 4.3. Volumetric efficiency Volumetric efficiency of the pump was determined for each experiment comparing the theoretical volume D, with volume of water delivered at the outlet of the pressurized air tank. The procedure was carried out by weighing the mass of water collected during six cycles, to determine the real volume delivered per cycle. Values of volumetric efficiency measured are presented in Fig. 7(a). Additionally, the volumetric efficiency was calculated from Eq. (4) with known values of angular delay in piston valve closure and the lift rod flexibility for each static head and each speed evaluated (Fig. 7(b)). When comparing the results of both procedures, it is possible to observe they follow the same tendency.
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a measured 100% 90%
30m
80%
14m 40m
70%
ηv
60% 50% 40% 30% 20% 10% 0% 0
25
50
75
N, r/min
b calculated 100%
8m 14m 30m
90% 80%
40m
70%
ηv
60% 50% 40% 30% 20% 10% 0% 0
25
50
75
N, r/min Fig. 7. Effect of pump speed variation on the pump volumetric efficiency.
At high speeds of operation, the volumetric efficiency is reduced due to a late closure of the piston valve. Nevertheless, the volumetric efficiency diminishes also as a consequence of increase in static head due to leakage. For values measured, this reduction is not only attributable to the effect of lift rod flexibility; it is also due to a deficient valve piston closure, condition which explains the over-estimation of efficiency by the theoretical model.
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4.4. Overall pump efficiency Overall pump efficiency defined as the ratio of the hydraulic power to mechanical power introduced into the system is the prime indicator, combining in a unique parameter, the effectiveness of the equipment in volumetric terms and hydraulic energy yield. Before talking about overall efficiency of the equipment it is useful to know, the energy consumption of the pumping arrangement under the different conditions of operation. Fig. 8 illustrates the mechanical power consumed by the system with changes in speed of operation and static head. As it is expected the power consumption increases proportionally with increase in the speed of operation and static head. Nevertheless, it is necessary to bear in mind that under less demanding operating conditions, the energy dissipation plays a dominant role on the global power consumption of the system. Fig. 9 synthesizes the pump performance, in terms of the global efficiency determined experimentally with changes in speed of operation of the pump for different static heads.
Power, W
300 250
40m
200
30m
150 100
14m
50
8m
0 0
25
50
75
N, r/min Fig. 8. Mechanical power as function of speed and static head.
100% 80%
40 m 30 m 14m 8m
η
60% 40% 20% 0% 0
25
50
75
N, r/min Fig. 9. Pump overall efficiency as function of speed and static head.
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4 3.5 3
Γr
2.5 8m 14m 30m 40m
2 1.5 1 0.5 0 0
25
50
75
N, r/min Fig. 10. Effect of pump speed on the dimensionless lift rod force at various static heads.
Tendency of the values in the overall efficiency coincide with the one expected accordingly with analysis made up to now, with regards to volumetric yield and pump power consumption. For a fixed static pumping head, the overall efficiency increases inversely proportional to the speed of operation. Likewise for a fixed speed of operation, the overall efficiency increases with larger static heads. 4.5. Practical results Figs. 9 and 10 show the test results of this experimental research in a practical and useful way, both for the manufacturer and the user of this commercial wind pump. Fig. 10 illustrates the behaviour of maximum peak dimensionless lift rod force for different conditions of pumping static heads and speeds of operation. These results are quite useful for the manufacturer at the time of designing and dimensioning the mechanical elements of the system. They also provide an efficient tool for estimating the magnitude of forces involved in the operation of the wind pump drive for an installation with known conditions of operations. Fig. 9 is an excellent guide for selection and performance evaluation of equipment previous to the installation. Use of these results for each one of the equipments produced by Industrias JOBER would stand as an invaluable design and selection tool. 5. Conclusions The results of this research represent an experimental corroboration of theoretical model studied, provided that it is taken into account that conditions of wear and performance of the equipment were not like those of the typical functioning wind pump system. Results presented in this report correspond to a pump powered at a uniform speed of operation. In a real installation, especially a large static head, high speed of operation and long water piping installation, the inertia of water in the pipes predominates upon inertia of rotor and the transmission system. Certain conditions reproduced in these tests, imply that the pump performance could be over estimated when compared to the performance of the equipment in a real installation.
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In spite that the pump arrangement under test represents a damping system, that is to say with non-worthless friction forces, the determined values of Gr might become enough evidence as to corroborate the hypothesis that for reducing the of maximum peak lift rod forces requires more flexibility into it. Choosing a less rigid material for the lift rod will have favourable effects in terms of durability on the long run of mechanical elements of this equipment. The most important deficiency found, in terms of performance, is the functioning of the piston valve. This is no doubt a focus for attention for the designer in terms of redesigning or substitution. Care has to be taken, when deciding to make a change of the piston valve or sealing system because of repercussions in terms of infrastructure and manufacturing costs. Any modification must be carried out with the certainty that both the valve and seals fulfil their function in an adequate way considering they are practical changes and a cheap alternative. This pump has a good performance in the range evaluated. Possibly the typical performance of the JOBER wind pump is not the best, when compared to more traditional more robust wind pumps systems; bearing in mind that this is a direct-driven, low solidity, faster running wind pump. Nevertheless for evaluating the overall wind pump performance it has to be consider the type of necessity covered with this equipment and the low-cost type of water supply solution offered by Industrias JOBER in a less-developed country such Colombia and neighbouring countries. Acknowledgements The authors wish to thank Dr. John Burton for his ever pertinent and appropriate comments during the final stage of this work. In addition they wish to thank Industrias JOBER in collaborating with this project. References [1] Pinilla AE. Lectures noteswind energy course. Bogota´, Colombia: Department of Mechanical Engineering, Universidad de Los Andes; 2005 (in Spanish). [2] Burton JD, Davies DG. Dynamic model of a wind-driven lift pump. Proc Inst Mech Eng 1996;210:279–93. [3] Burton JD, Hijazin M, Rizvi S. Wind and solar driven reciprocating lift pumps. Wind Eng 1991;15(2):95–108. [4] La Rotta JM. Strengthening of wind water pumping drive System. M.Sc. thesis in Mechanical Engineering, Universidad de Los Andes, Bogota´, Colombia. 2005 (in Spanish).
Renewable Energy 32 (2007) 1790–1804 www.elsevier.com/locate/renene
Technical Note
Performance evaluation of a commercial positive displacement pump for wind-water pumping Juan La Rotta, Alvaro Pinilla a
Mechanical Engineering Department, Universidad de Los Andes, Cra 1a Este # 18a – 10, Bogota´, Colombia % % Received 28 June 2006; accepted 4 October 2006 Available online 21 November 2006
Abstract This paper presents the experimental performance test evaluation of a commercial wind-driven positive displacement pump type JOBER of 3 in diameter. Results of the behaviour of pump lift rod peak force, in relation with the lift rod elasticity and the piston valve closure delay are presented. The pump performance is analysed in terms of its volumetric and overall efficiencies. Evidence about a possible effect of the piston valve closure delay over the pump overall efficiency is also discussed. r 2006 Elsevier Ltd. All rights reserved. Keywords: Wind-water pumping; Reciprocating pumps; Pumps; Windpumps; Hydraulic testing
1. Introduction With the purpose of providing essential elements for evaluation of wind-water pump equipment, this paper presents laboratory performance evaluation results on the commercial JOBER pump (Fig. 1). Industrias JOBER located in Duitama-Colombia is a small enterprise started in 1984 and currently has more than 800 of its faster running wind pumps operating in the zone of Eastern Prairies in Colombia [1]. Some wind pumps have been exported to neighbouring countries within the Andean Region. The pump and its riser pipe were evaluated in terms of volumetric efficiency; overall input efficiency and peak maximum lift rod forces. Theoretical validation of measured data was carried out using the dynamic model as proposed by Burton and Davis [2]. Corresponding author. Tel.: +571 332 4322; fax: +571 332 4323.
E-mail address: [email protected] (A. Pinilla). 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.10.001
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Nomenclature A Ap cf cd D Fr kr H L m0 N Ns PH Q r R t V Vp
riser pipe cross-sectional flow area effective pumping area (piston area minus lift rod area) dry friction coefficient viscous damping coefficient theoretical volume displaced per piston cycle [ ¼ 2RAp] lift rod force elastic Constant for lift rod (force/unitary extension) static head length of discharge including riser and suction pipe mass of lift rod and piston minus floating effects pump operational speed (r/min) Sommerfeld number ¼ mO/rgH Hydraulic power water flow rate per piston stroke frequency ratio O/Oor crank throw ( ¼ half of the stroke length) time water speed flow in riser pipe maximum effective flow speed in riser pipe for a system with infinitely rigid lift rod ¼ OR(Ap/A)
Greek symbols a g Gr DP Z m r C O Oor
piston valve angular delay closure after Upper Dead Center piston valve angular delay closure after Lower Dead Center dimensionless lift rod force¼ ðF r m0 gÞ=ðrgHAp Þ piston pump differential pressure overall efficiency water viscosity water density dimensionless head¼ ðH=LÞðg=O2 RÞðA=Ap Þ crank Angular velocity natural frequency of oscillation of the system lift rod/riser pipe
Results of this research and the procedure followed are a useful tool for designers of wind-driven pumping systems.
2. Theoretical model The theoretical dynamic model as proposed by Burton and Davis [2] is an excellent guide for structural dimensioning of the reciprocating pump test rig, as well as for the design, execution and interpretation of experiments.
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Fig. 1. Details of the JOBER 3 in reciprocating pump.
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Burton and Davies’ model provides essential elements for the analysis of the behaviour of pump lift rod forces, volumetric and overall efficiencies. 2.1. Pump lift rod force The understanding of the behaviour of the pump lift rod force is important, given that, during the pumping cycle, the lift rod force may reach peak values quite above the corresponding static piston force (rgHAP). Forces in the pump lift rod are due to: (1) weight of lift rod and piston, (2) forces of dry and viscous friction as a consequence of piston displacement inside the pump cylinder and (3) the force due to differential pressure on the piston pump. Eq. (1), taken from [2], represents the dimensionless lift rod force, during discharge stroke, for a system without friction with elasticity in the lift rod and angular delay in closure of piston valve. Gr ¼ 1 þ
1 dðV =V p Þ , C dðOtÞ
where C the dimensionless static head is expressed as follows: H g A C¼ 2 L O R Ap
(1)
(2)
and Gr is defined as the ratio of lift rod force to the static piston force (rgHAP). Peak values of Gr are of great interest. The peak occurs when acceleration of the fluid in the riser pipe reaches its maximum. Depending upon flexibility of the lift rod and the angular delay closure of piston valve, the maximum acceleration in Eq. (1) reaches values, such that the lift rod force may be up to 8 times the force imposed by the static head (GrE8) [1]. Term Cr2 in Eq. (3) provides a clear idea of mechanical elasticity of the lift rod. rgHAp 1 Cr2 ¼ (3) R kr Cr2 relates the static lift rod elongation, due to static head force, on the piston and the length R of the crank throw of the wind pump transmission. It may be interpreted as the fraction of the length R equivalent to the lift rod elongation. 2.2. Volumetric efficiency In a wind-driven reciprocating pump, the theoretical water volume displaced at every pumping cycle is defined as D ¼ 2RAP. Volumetric efficiency is defined as the ratio between the actual amount of water delivered in the pumping cycle to the theoretical water delivered. Water volume delivered in each cycle is usually less than the theoretical volume. This is mainly due to leakage around the piston seals and to the delay in the operation of the valves. For this particular case, the JOBER pump is provided with leather seals, sucking type which guarantees an adequate sealing. Burton et al. [3] propose that lift rod flexibility
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and angular delay closure of the piston valve affect the volumetric efficiency and are related by means of Eq. (4), as follows: 1 1 Zv ¼ ðcos a þ cos gÞ ¼ cos a ðCr2 Þ. 2 2
(4)
2.3. Overall pump efficiency Overall pump efficiency (Eq. (6)) is defined as the ratio of hydraulic power delivered by the system to the input mechanical power absorbed by the system. Hydraulic power is the water pumped to a determined static head (Eq. (5)). PH ¼ rgHQ, Z¼
(5)
Hydraulic Power . Mechanical Input Power
(6)
3. Experimental setup A hydraulic test rig was specially constructed for the 3 in JOBER pump. This assembly allows simulating typical JOBER wind pump operation conditions. (i.e., 8–40 m hydraulic static head; (see Table 1). The hydraulic test rig (Fig. 2) is installed at the laboratory of Mechanical Engineering of the Universidad de Los Andes. Given space limitations, the pumping static head is simulated with a pressurized air tank connected to the pump discharge. By setting the internal tank pressure it is possible to simulate the required hydraulic static heads. Table 2 contains pump dimensions. The pump is powered by an electric motor excited via a variable frequency converter to reach operation speeds up to 80 r/min. The riser pipe of 38 mm (1.5 in nom. dia.) in a typical JOBER wind pump installation is replaced by a galvanized steel tubing of 12 mm (0.5 in nom. dia.). This pipe is connected between pump discharge and the entrance of pressurized air tank. Length of the pipe installed in the rig is varied between 1 and 8 m, which corresponds to equivalent lengths from 8 to 40 m of riser pipe in the real wind pump. Dynamic similitude between real installation and the rig is preserved by means of this hydraulic inductance. For each set of experiments, the riser pipe length coincides with the hydraulic static head; that is, values of hydraulic static head are determined to correspond to 8, 14, 30 and 40 m as described in [4]. The assembly is instrumented with a displacement sensor and a load cell installed in the pump lift rod. This setting allows measurement of the lift rod force and the piston
Table 1 JOBER 3 in pump operational range according to JOBER INDUSTRIES Static lifting head, H Speed of operation Water pumped range
¼ 25–50 m ¼ 60–80 r/min (120 max) ¼ 800–1000 L/h
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Crank Transmission
1795
Input motor Variable Speed 25-75 r/min
Lift rod
Pressurized Tank Variable pressure 80-400 kPa Pipe arrangement Variable length 1-8 m Pump
Recirculation tank
Fig. 2. Layout of the hydraulic rig for reciprocating pump testing. Table 2 JOBER 3 in pump geometrical characteristics Piston area, Ap Lift rod area, Av Effective pumping area, ApAv Pipe sectional area, A
5418 mm2 127 mm2 5291 mm2 214 mm2
displacement simultaneously. Additionally, pressure transducers are fitted on the pump cylinder, one located on the suction side of pump (below the piston) and the other one above the piston. This setting facilitates measurement of the differential pressure on the piston pump; consequently the force on the piston pump might be deduced. Data acquisition is carried out using a data acquisition board with a sampling frequency of 250 Hz. All data are fed into a computer for processing. This assembly provides the necessary set up for performance evaluation of the pump including its riser pipe, permitting establishing the effect of dynamic behaviour of the water column in the riser pipe, and its influence upon the overall pump performance. 3.1. Operation of test rig 3.1.1. Pumping closed circuit The pump draws water from the suction tank through the foot valve. The water goes through the pump and enters into the pipe arrangement connected between pump
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discharge and pressurized tank inlet. Water enters the pressurized tank and it is maintained inside it until the tank pressure rises above a prefixed value. In this way, water goes out through a relief valve installed at the bottom of pressurized tank and returns to the suction tank. 3.1.2. Configuration of a test scenario Before carrying out any test, it is necessary to correctly configure each one of the parameters of the rig in accordance with conditions of operation to be simulated. The following steps have to be followed to set the rig for evaluating the pump: (1) length of conduction pipe is determined, this one must coincide with static head being simulated; (2) pumping speed is set up via the excitation frequency of the electric motor; (3) the tank is pressurized to a pressure equivalent to the simulated static head; (4) relief valve discharge pressure is set, while the pump starts working. 4. Experimental results Through factorial analysis, the operational range of the pump variables is made discrete as presented in Table 3. A total of 12 experiments were executed in the strict order as in the experimental matrix contained in Table 4. Needless to say every experiment was repeated several times. 4.1. Type of results 4.1.1. Graphs of force vs. time Fig. 3 presents the lift rod force and the force in the piston pump, registered for a pumping cycle under different conditions of operations. Cases illustrated in Fig. 3 correspond to extreme conditions within the range of tests run. In part (a) of Fig. 3 (slowest speed and lowest static head) it can observe that the lift rod force is two-times greater than the force on the piston. Table 3 Discrete values of pump variables for testing Variable
Range
Discrete values
Speed (r/min) Static head (m) Riser pipe length
25–75 8–40 8–40
25, 50, 75 8, 14, 30, 40 8, 14, 30, 40
Table 4 Experimental matrix Number of experiment Variable Speed (r/min) Static head (m)
1 25 8
2 25 14
3 25 30
4 25 40
5 50 8
6 50 14
7 50 30
8 50 40
9 75 8
10 75 14
11 75 30
12 75 40
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a Force on the piston
Lift rod force
Piston displacement
1.0 0.8 Force, kN
0.6 0.4 0.2 0.0 −0.2 −0.4 0
0.5
1
1.5
2
2.5
Time, s Force due to static head
b Lift rod force
Force on the piston Piston displacement
4.5
Force, kN
3.5 2.5 1.5 0.5 −0.5
0
0.2
0.4
0.6 Time, s
0.8
1
1.2
Force due to static head Fig. 3. (a) Lift rod and piston forces, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) lift rod and piston forces, N ¼ 50 r/ min, H ¼ 40 m, L ¼ 8 m.
On the contrary in Fig. 3(b) (fastest speed and largest static head) the difference between the forces on the lift rod and on the piston is just a 10%. The excess in the lift rod force is attributed to dissipative phenomena, what suggests that under low speeds of operation and static heads, the frictional force plays a dominant role in the consumption of energy introduced into the system.
4.1.2. Pressure indicator diagrams Fig. 4 presents the pressure indicator diagrams for the same conditions of operation as in Fig. 3. These diagrams were used for determining the value of angular closure delay of the piston valve for each of the experiments carried out. This procedure yielded evidence of
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a Presure, kPa
90 70 50 30 10 −10
0
14
28
42
56
Piston displacement, mm Pressure above the piston
Pressure below the piston
Pressure due to static head
b Pressure, kPa
800 600 400 200 0 −200
0
14
28
42
56
Piston displacement, mm Pressure above the piston
Pressure below the piston
Pressure due to static head
Fig. 4. (a) Pressure indicator diagrams, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) pressure indicator diagrams, (b) N ¼ 50 r/min, H ¼ 40 m, L ¼ 8 m.
Table 5 Piston valve angular delay closure determined experimentally Pump speed (r/min)
a (degrees)
25 50 75
0 15 30
the strong dependency between valve closure delay and pump operating speed. Table 5 presents average values of a for each of speeds studied.
4.1.3. Force indicator diagrams Fig. 5 presents the force indicator diagrams for the same conditions of operation illustrated above. Area enclosed by curve line of lift rod force is proportional to energy
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a 1.0 0.8 Force, kN
0.6 0.4 0.2 0.0 −0.2 −0.4
0
14
28
42
56
Piston displacement, mm Lift rod force
Force on the piston
Static force
b 5 Force, kN
4 3 2 1 0 −1 0
14
28
42
56
Piston displacement, mm Lift rod force
Force on the piston
Static force
Fig. 5. (a) Force indicator diagram, N ¼ 25 r/min, H ¼ 8 m, L ¼ 1.1 m; (b) force indicator diagram, N ¼ 50 r/ min, H ¼ 40 m, L ¼ 8 m.
introduced to the system during a pumping cycle. With these diagrams, it is possible to calculate the overall efficiency for each one of experiments carried out. 4.2. Force on the lift rod From the lift rod force vs. time measurements, peak values of lift rod force are determined for each set of the experiments during any pumping cycle. Each of these values was non-dimensionalized when divided by static force on the piston rgHAp, these are contained in Fig. 6. Flexibility for each one of the pumping heads is determined by measuring the displacement registered by the displacement sensor when loading the pump with the transmission system locked. Fig. 6 shows the attenuation effect of lift rod flexibility upon maximum dimensionless lift rod force values. Comparison of values experimentally determined with values calculated via Eq. (1), suggest that in the pump tested, there exist damping forces, not being considered in the theoretical model.
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8
46
84
23
7
14
6
Γr
5 4 3
1+1/ψ
2 1 0 0
0.5
1
1.5 1/ψ 84
46
2
2.5
3
23 14
Fig. 6. Experimental and theoretical peak dimensionless lift rod force (Gr) against the reciprocal of the dimensionless head (1/c) with various lift rod elasticities (1/cr2).
It should be mentioned that the theoretical model is solved for a frictionless system. For the case of the JOBER pump, this is a condition far from true, since it is a new pump, meaning it did not work a number of cycles enough to reach an adequate seals wear condition corresponding to an optimum operating condition of this equipment. Value of 1/Cr2 corresponding to curves of Gr vs. 1/C calculated from Eq. (1), must vary in each test in accordance with simulated static head. It should be assured that it corresponds to the lift rod flexibility with equal length to the static head. Due to the flexibility of transmission system and its anchorages of the test rig, the evaluation of the system was carried out without varying the lift rod flexibility. In spite of this situation, it produces a slight additional difference in the magnitude of measures data; nonetheless it does not interfere in the determination of the effect of flexibility upon maximum lift rod forces. The tendency observed from experimental data in Fig. 6, corroborates the hypothesis from theoretical model, in the sense that peak lift rod force is progressively reduced, with increases in lift rod flexibility. 4.3. Volumetric efficiency Volumetric efficiency of the pump was determined for each experiment comparing the theoretical volume D, with volume of water delivered at the outlet of the pressurized air tank. The procedure was carried out by weighing the mass of water collected during six cycles, to determine the real volume delivered per cycle. Values of volumetric efficiency measured are presented in Fig. 7(a). Additionally, the volumetric efficiency was calculated from Eq. (4) with known values of angular delay in piston valve closure and the lift rod flexibility for each static head and each speed evaluated (Fig. 7(b)). When comparing the results of both procedures, it is possible to observe they follow the same tendency.
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a measured 100% 90%
30m
80%
14m 40m
70%
ηv
60% 50% 40% 30% 20% 10% 0% 0
25
50
75
N, r/min
b calculated 100%
8m 14m 30m
90% 80%
40m
70%
ηv
60% 50% 40% 30% 20% 10% 0% 0
25
50
75
N, r/min Fig. 7. Effect of pump speed variation on the pump volumetric efficiency.
At high speeds of operation, the volumetric efficiency is reduced due to a late closure of the piston valve. Nevertheless, the volumetric efficiency diminishes also as a consequence of increase in static head due to leakage. For values measured, this reduction is not only attributable to the effect of lift rod flexibility; it is also due to a deficient valve piston closure, condition which explains the over-estimation of efficiency by the theoretical model.
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4.4. Overall pump efficiency Overall pump efficiency defined as the ratio of the hydraulic power to mechanical power introduced into the system is the prime indicator, combining in a unique parameter, the effectiveness of the equipment in volumetric terms and hydraulic energy yield. Before talking about overall efficiency of the equipment it is useful to know, the energy consumption of the pumping arrangement under the different conditions of operation. Fig. 8 illustrates the mechanical power consumed by the system with changes in speed of operation and static head. As it is expected the power consumption increases proportionally with increase in the speed of operation and static head. Nevertheless, it is necessary to bear in mind that under less demanding operating conditions, the energy dissipation plays a dominant role on the global power consumption of the system. Fig. 9 synthesizes the pump performance, in terms of the global efficiency determined experimentally with changes in speed of operation of the pump for different static heads.
Power, W
300 250
40m
200
30m
150 100
14m
50
8m
0 0
25
50
75
N, r/min Fig. 8. Mechanical power as function of speed and static head.
100% 80%
40 m 30 m 14m 8m
η
60% 40% 20% 0% 0
25
50
75
N, r/min Fig. 9. Pump overall efficiency as function of speed and static head.
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4 3.5 3
Γr
2.5 8m 14m 30m 40m
2 1.5 1 0.5 0 0
25
50
75
N, r/min Fig. 10. Effect of pump speed on the dimensionless lift rod force at various static heads.
Tendency of the values in the overall efficiency coincide with the one expected accordingly with analysis made up to now, with regards to volumetric yield and pump power consumption. For a fixed static pumping head, the overall efficiency increases inversely proportional to the speed of operation. Likewise for a fixed speed of operation, the overall efficiency increases with larger static heads. 4.5. Practical results Figs. 9 and 10 show the test results of this experimental research in a practical and useful way, both for the manufacturer and the user of this commercial wind pump. Fig. 10 illustrates the behaviour of maximum peak dimensionless lift rod force for different conditions of pumping static heads and speeds of operation. These results are quite useful for the manufacturer at the time of designing and dimensioning the mechanical elements of the system. They also provide an efficient tool for estimating the magnitude of forces involved in the operation of the wind pump drive for an installation with known conditions of operations. Fig. 9 is an excellent guide for selection and performance evaluation of equipment previous to the installation. Use of these results for each one of the equipments produced by Industrias JOBER would stand as an invaluable design and selection tool. 5. Conclusions The results of this research represent an experimental corroboration of theoretical model studied, provided that it is taken into account that conditions of wear and performance of the equipment were not like those of the typical functioning wind pump system. Results presented in this report correspond to a pump powered at a uniform speed of operation. In a real installation, especially a large static head, high speed of operation and long water piping installation, the inertia of water in the pipes predominates upon inertia of rotor and the transmission system. Certain conditions reproduced in these tests, imply that the pump performance could be over estimated when compared to the performance of the equipment in a real installation.
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In spite that the pump arrangement under test represents a damping system, that is to say with non-worthless friction forces, the determined values of Gr might become enough evidence as to corroborate the hypothesis that for reducing the of maximum peak lift rod forces requires more flexibility into it. Choosing a less rigid material for the lift rod will have favourable effects in terms of durability on the long run of mechanical elements of this equipment. The most important deficiency found, in terms of performance, is the functioning of the piston valve. This is no doubt a focus for attention for the designer in terms of redesigning or substitution. Care has to be taken, when deciding to make a change of the piston valve or sealing system because of repercussions in terms of infrastructure and manufacturing costs. Any modification must be carried out with the certainty that both the valve and seals fulfil their function in an adequate way considering they are practical changes and a cheap alternative. This pump has a good performance in the range evaluated. Possibly the typical performance of the JOBER wind pump is not the best, when compared to more traditional more robust wind pumps systems; bearing in mind that this is a direct-driven, low solidity, faster running wind pump. Nevertheless for evaluating the overall wind pump performance it has to be consider the type of necessity covered with this equipment and the low-cost type of water supply solution offered by Industrias JOBER in a less-developed country such Colombia and neighbouring countries. Acknowledgements The authors wish to thank Dr. John Burton for his ever pertinent and appropriate comments during the final stage of this work. In addition they wish to thank Industrias JOBER in collaborating with this project. References [1] Pinilla AE. Lectures noteswind energy course. Bogota´, Colombia: Department of Mechanical Engineering, Universidad de Los Andes; 2005 (in Spanish). [2] Burton JD, Davies DG. Dynamic model of a wind-driven lift pump. Proc Inst Mech Eng 1996;210:279–93. [3] Burton JD, Hijazin M, Rizvi S. Wind and solar driven reciprocating lift pumps. Wind Eng 1991;15(2):95–108. [4] La Rotta JM. Strengthening of wind water pumping drive System. M.Sc. thesis in Mechanical Engineering, Universidad de Los Andes, Bogota´, Colombia. 2005 (in Spanish).