Tests of a centrifugal pump operating as a water turbine

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(1)Tests of a Centrifugal Pump Operating as a Water Turbine. Author: Julián Eduardo González Martínez. Supervisor: Álvaro Enrique Pinilla Sepúlveda, Ph.D, M.Sc. School of Engineering Department of Mechanical Engineering Universidad de los Andes. Bogotá, Colombia. First Semester 2011. 1.

(2) Table of Contents 1. Introduction to Pumps as Turbines (PAT’s) ................................................... 4 2. Objectives and Motivation ............................................................................. 7 2.1. General Objective ...................................................................................... 7 2.2. Specific Objectives..................................................................................... 7 3. Theory of Turbomachinery ............................................................................ 9 3.1. Fluid Mechanics Principles applied to Pumps and Turbines ...................... 9 3.2. Characteristic Curves of Pumps and Turbines ......................................... 10 3.3.. Characterization of a Rotary Machine ................................................... 14. 3.4.. Predicting a Pump’s Behavior as a Turbine .......................................... 15. 3.4.1.. Proposed relationships by KR Sharma of Kiloskar Company, India. 16. 3.4.2.. Hancock’s Approach (1963) ........................................................... 17. 3.4.3.. Rojas’ experimental relationships ................................................... 17. 3.4.4. Determination of constants by other methods (Ortíz Flórez & Abella Jiménez, 2008) ............................................................................................... 18 4. Equipment and Instrumentation ................................................................... 21 4.1. The Pump as Turbine .............................................................................. 21 4.2. The Feed Pump ....................................................................................... 22 4.3.. Intake and Discharge Systems ............................................................. 23. 4.4.. Flow Measurement ............................................................................... 23. 4.5.. Torque Measurement ............................................................................ 24. 4.6.. Head Measurement .............................................................................. 25. 4.7.. Electrical Power Measurement ............................................................. 26. 5. The Test Bench/Test Results ...................................................................... 27 5.1. Hydraulic Connections Diagram .............................................................. 27 5.2. Final Assembly .......................................................................................... 27 5.3.. Testing of the Pump under Normal Operating Conditions ..................... 29. 5.4.. Testing as a reversible machine (turbine operation) ............................. 32. 5.5.. Characteristic curves of the PAT ........................................................... 32. 5.6. Determination of the numerical relationships between pump and turbine modes 39 2.

(3) 5.6.1.. Application of KR Sharma’s Theory ................................................ 41. 5.6.2.. Application of Hancock’s Theory .................................................... 42. 5.6.3.. Application of Rojas’ Experimental Relationships ........................... 43. 5.6.4. Application of other Methods to Determine Characteristic Constants (Ortíz Flórez & Abella Jiménez, 2008) ............................................................ 44 6. Conclusions and Recommendations for Future Developments ................... 46 7. References .................................................................................................. 48 8. List of Figures .............................................................................................. 49 9. List of Equations .......................................................................................... 51 10.. Annexes ................................................................................................... 53. 10.1. Annex A – IHM 1A-3/4W (120mm) Manufacturer Curve ........................ 53 10.2. Annex B- APV 6V2 (feed pump) Manufacturer Curve ............................ 54 10.3.. Annex C- Propagation of Uncertainty Analysis .................................. 55. 10.3.1.. Uncertainty in angular velocity measurement.............................. 55. 10.3.2.. Uncertainty in head measurement .............................................. 55. 10.3.3.. Uncertainty in torque measurement ............................................ 55. 10.3.4.. Uncertainty in output power measurement .................................. 56. 10.3.5.. Uncertainty in flow rate measurement ......................................... 56. 10.3.6.. Uncertainty in turbine efficiency .................................................. 57. 3.

(4) 1. Introduction to Pumps as Turbines (PAT’s) Hydro power is one of the world’s most important renewable energy sources. Large-scale generation has been developed and implemented in virtually every country on earth, based mainly in facilities that use a site´s particular characteristic to generateusing traditional water turbines (Pelton and Francis turbines are the preferred choice in large hydroelectricity facilities). Hydrogeneration (Worldwide) 25000,0. 19 18,5 18 17,5. 15000,0. 17 10000,0. 16,5. Ratio (%). Energy (TWh). 20000,0. Hydropower Consumption Electricity Generation. 16. 5000,0. 15,5 0,0. 15 1985. 1990. 1995. 2000. 2005. Hydro Consumption to Total Generated Elecricity (%). 2010. Year. Figure 1.Total en erg y consu m ed by hydropower schem es worldwi de. Also shown is the total electric energy g ene rate d wo rld wi de by all a vailable sourc es. Data from BP Statistical Revie w of W orld Energy 2010 (British Petroleum (BP), 2010) .. Figure 1shows the increase of electricity generation worldwide and the share of that total that comes from hydropower. Electric generation has grown at an accelerated rate in the past two decades; interestingly, hydropower generation has not increased at the same rate. This is mainly due to the rapid development of other renewable technologies that are nowadays making important contributions to the world’s total electric generation. However, this trend does not apply for thirdworld countries where developments and investment in alternative energy generation is still small.Figure 2shows total hydropower consumption and total electric generation in Central and South America only. Wind, solar, geothermal, and nuclear energies remain virtually unexploited in these regions.. 4.

(5) 1200. 76. 1000. 74 Hydropower Consumption. 72. 800. 70 600 68 400. Ratio (%). Energy (TWh). Hydrogeneration (Central & South America). Electricity Generation. 66. 200. 64. 0. 62 1985. 1990. 1995. 2000. 2005. Hydro Consumption to Total Generated Electricity (%). 2010. Year. Figure 2. Total ene rg y consum ed by hydropower schem es in Central and S out h. Also shown is the total electric energy g ene rat ed in these regions by all availabl e sources. Data from BP Statistical Revi e w of W orld Energy 2010 (British Petroleum (BP), 2010) .. Figure 2clearly shows the importance that hydropower still has in the LatinAmerican region. In 2009 about 64% of the total electricity produced in the region came from hydro sources, as opposed to the 16% worldwide ratio for the same year. Hydropower must be researched and implemented in Central and South America not only because of its accessibility, but also because the region is extremely rich in hydraulic resources with generation potential. While the use of regular turbines for large-scale generation is ideal, there is an unexplored potential to use pumps as turbines (PAT) for micro-generation schemes. The main advantages of using a PAT for small-scale generation are the following: A pump is much cheaper than a turbine, mainly because of their widespread use in many hydraulic installations. Turbines have a much more limited use. They can be purchased almost in every town and city in the world. Because they are a commonplace machine pumps are relatively well understood, their maintenance is low-cost and easy and replacement parts are available in the local market. They can be installed as low cost alternatives for electric generation in remote areas where grid electricity in inaccessible (many regions in developing countries are included in this description). Pumps are available in many different sizes and are designed to operate in a wide range of head/flow conditions, which means that for a site´s 5.

(6) particular characteristic an appropriate pump to operate as turbine may be chosen. While it is expected for a PAT to work less efficiently than a regular turbine, this loss is outweighed by the advantages (mainly cost oriented) of using a pump for micro-generation. However, with proper research and investigation in the subject this type of schemes may be improved in order to provide an excellent alternative to traditional hydropower and electrify regions where grid electricity in inaccessible. This is why understanding the operation of pumps as turbines may prove beneficial, and it is one of the goals of developing a test bench for this type of reversible machine.. 6.

(7) 2. Objectives and Motivation Generation of electric power by using centrifugal pumps as turbines is an old engineering practice that has been implemented in some occasions to various degrees of success. It has been stated that a reversible pump-turbine system can be a good option for microgeneration, especially in developing countries. In Colombia some hydrogeneration facilities exist that use this type of approach (also called reversible hydro centrals) which means that the project may have some relevance for the local energy industry. The study of such systems can be interesting for applications in which the available resources are not broad enough (i.e inadequate funding) to operate a fully fledged turbine only facility. This is the main reason why developing a test bench for small scale experimentation and benchmarking of pump-turbine systems can further improve knowledge in the field. Such test bench can be used as a base model to design larger prototypes of reversible turbomachinery, using the similarity relationships further described in fluid mechanics theory.. 2.1.General Objective To design and build a test bench to operate a commercial centrifugal pump that can be bought in the Colombian local market as a hydro powered turbine for energy generation.. 2.2.Specific Objectives Conduct a throughout search of the availability of centrifugal pumps and instrumentation to measure the relevant variables (flow rate, head, torque and rotational speed) in the local market. Select the appropriate equipment for the construction of the test bench. Design a bench that is capable of subjecting the chosen pump to different operating conditions of head and flow rate in order to evaluate its performance as a turbine. Develop a testing and measurement method of relevant variables on the assembly, using the appropriate instruments in order to typify the behavior of the system. Generate the characteristic curves of the chosen turbomachine operating both as a pump and as a turbine. Determine the relationships that exist between the two operating conditions of the same machine. Compare the obtained experimental data with previous theoretical approaches to the problem, in order to evaluate this particular bench’s potential against previous efforts. Create an experimentation standard on the bench in order to be used for academic purposes. One of the main intentions of the construction of the 7.

(8) bench is to be used by future mechanical engineering students to broaden their knowledge in pump-turbine systems and make laboratory practices on said equipment. Apply all the knowledge attained in fluid mechanics, energy conversion systems and basic engineering skills in general to solve an open-ended problem.. 8.

(9) 3. Theory of Turbomachinery 3.1.Fluid Mechanics Principles applied to Pumps and Turbines Water pumps and impulse turbines are rotational machines designed to increase or decrease the energy of a moving fluid. The total energy of a moving fluid (also called head) is described by Bernoulli’s principle, which is stated by the following equation:. Equation 1. Bernoull i’s princ iple.. The first two terms of the equation comprise what is commonly known as the static head, which is simply the pressure head plus the position head (energy of a static fluid, hence its name). The last term of the equation is the dynamic head, that is, the energy stored in the fluid in the as it moves with a certain velocity (hence also called velocity head). A pump receives mechanical work through the input shaft and delivers it to the fluid by increasing its velocity and pressure heads. The impeller is the pump’s main component, and directly transfers the motor’s energy to the moving fluid (by direct contact between the rotor and the fluid itself). The impeller’s rotational movement generates a negative pressure in the pump’s inlet (also called suction) which causes the fluid to enter the pump. The vanes in the impeller push the fluid radially further away from the center of rotation and towards the pump’s volute, thus increasing its pressure significantly. The pumped fluid is then evacuated through the outlet, which is generally placed in the outer part of the volute. The fluid’s tangential velocity guides it smoothly towards the outlet, thus reducing friction losses as it exits the pump. Pump efficiency is defined as the ratio of energy transferred to the fluid to the electric energy consumed by the motor rotating the shaft. In terms of power, the efficiency can be calculated by the following equation:. Equation 2. Pum p efficiency.. Where ρ is the pumped fluid density, g the acceleration of gravity, Q the flow rate, H the head increase in the fluid and Pe the electric power consumed by the motor.. 9.

(10) As opposed to pumps, turbines are designed to operate in the opposite way. If a pump’s purpose is to transfer energy to a fluid, a turbine is designed to convert the fluid’s available energy (or a fraction of it) into mechanical work in the turbine’s output shaft.Water turbines are similar to pumps because they also work by allowing an impeller to come in contact with the moving fluid. However, in the case of a turbine the fluid exerts force on the turbine’s vanes thus making the rotor move around its center of rotation and producing work at the shaft. The shaft then may be coupled to an electric generator to produce electricity. There are several kinds of water turbines that are generally classified in three groups: radial flow turbines, axial flow turbines and mixed flow turbines. Turbines may also be classified by their principle of operation. Under this classification there are two types of water turbines: impulse and reaction turbines. Impulse turbines extract energy from the incoming water jet by reducing its velocity head; reaction turbines reduce the fluid’s pressure head in order to extract energy. A PAT may work as an impulse or a reaction turbine, depending on the type of pump chosen. Centrifugal pumps, which are the most common type of pump will operate as reaction turbines in reversible mode since they bear a striking resemblance to the mixed-flow Francis turbine. As in the case of a pump an efficiency may also be defined for a water turbine as the ratio between the energy delivered to the shaft (or electric energy produced by the generator if the system is complete) to the energy extracted from the fluid. It is easily calculated in terms of the ratio of power delivered to power extracted by using the following equation:. Equation 3. Turbine efficiency .. Where the terms in the denominator represent the same variables as defined for pump efficiency, and Ps is the power delivered to the shaft of the turbine. It is due to the geometric and principle of operation similarities between both operation modes that most pumps can be operated as reversible machines. It should be noted that only rotary pumps are able to work as PAT’s, reciprocating pumps aren´t suitable as turbines due to the evident differences between both machines.. 3.2. Characteristic Curves of Pumps and Turbines In order to typify and characterize a rotary machine it is recommendable to develop a series of curves that show how the machine behaves under different 10.

(11) operating conditions (head, flow rate and speed are the base variables upon which curves are developed). Most turbomachine manufacturers develop the curves for their own equipment and include it in the manual or datasheet of the pump/turbine. However, normally only the “nominal” values of the relevant variables are reported and included in the machine’s plate. For example, a pump’s manufacturer places only one value of head, flow rate and operational speed in the plate; these values correspond to the pump’s best efficiency point (bep). In both cases of pumps and turbines the machine has a fixed point of operating conditions in which it behaves most efficiently, this is the best efficiency point. While it desirable to always operate the machine in this point this is not always possible depending on the characteristics of the site, which is why the performance curves of the machine help understand under which conditions is the equipment capable of working properly. In the case of a pump there are two important curves that typify the machine: the head-flow rate curve and the efficiency curve. The head-flow curve typically looks like the generic example shown inFigure 3; it is evident that as the flow rate increases the available head that the pump can transfer to the fluid is reduced. The head-flow curve is constructed for a single operation speed, which is generally the nominal speed of the machine. This curve is in most cases available from the manufacturer.. Head. Typical Head-Flow Curve. Flow Rate. Figure 3. Typical head -flow curve for a pum p.. The other relevant curve for a pump is the efficiency graph, which relates the pumping efficiency with the flow rate. The typical efficiency curve for a pump is shown inFigure 4. There is a peak value for the efficiency (represented by the star inFigure 4) which corresponds to the flow rate at the best efficiency point Q bep).. 11.

(12) The head at the best efficiency point (Hbep) may then be found from the head-flow curve point.. Efficiency. Typical Efficiency Curve. Flow Rate. Qbep. Figure 4. Typical efficiency curve for a pum p.. It is also possible to plot both curves together, in order to show head, flow rate and efficiency in a single diagram. Some manufacturers provide the characteristic curves of their machines in this form. Figure 5shows such curves for a particular machine.. Figure 5. Hea d-flo w cu rve for a particul ar m achine and di fferent im peller diam eters. Efficiency plots are supe rim posed. Im age taken from “S electing an Irrigation Pum p”, NSW Departm ent of Prim ary Industries. [Availabl e onli ne at: http://www.dpi.ns w.g ov.a u/a griculture/resources/ water/irrigatio n/system s/pum ps/selecting ].. Characteristic curves for turbines are important for the same reason as to why pump performance curves are important: in order to choose a turbine for a certain site the behavior of the machine at different operating conditions must be known. There are three relevant characteristic curves for a water turbine: mechanical 12.

(13) power (or shaft power), torque and efficiency curves. The variables are not plotted against flow rate as is the case for pumps, the turbines angular velocity is used as the base variable instead.. Power. Typical Output Power (Shaft) Curve. Angular Velocity. Figure 6.Typical output power curve for a water turbine.. Torque. Typical Torque Curve. Angular Velocity. Figure 7.Typical torque curve for a water turbine.. From the power curve it is evident that turbines have a best efficiency point as well, which is the point in which the output power is maximum (this is also the point where peak efficiency is attained). As is the case with most rotating machines (including motors and engines) the torque delivered to the shaft by the turbine decreases as the speed increases; torque is maximum when the turbine is fully braked and it is minimum (virtually zero) at the turbine’s runaway speed. Operation at runaway speed is undesirable since it can lead to high loads on the turbine’s structure, generating the risk of structural damage.. 13.

(14) Efficiency. Typical Efficiency Curve. Angular Velocity. Figure 8.Typical efficiency c urve for a water turbine.. The efficiency curve bears a huge resemblance with the output power curve, which is why the best efficiency point for a turbine may be found from either the efficiency curve or the output power curve. The curves also imply that there is an optimal operation speed, which corresponds to the best efficiency point. Determining the bep for a turbine is as important as determining it for a pump and, as it will be shown in further sections, the head/flow/efficiency conditions at this pointare used to construct the numerical relationships between operation modes.. 3.3.. Characterization of a Rotary Machine. In order to evaluate the performance of either a pump or a turbine a series of dimensionless coefficients can be used for comparison between different machines and scaling of geometrically similar models. There are five important coefficients that typify rotary machines (all of them derived from the Pi-Buckingham theorem). These numbers (simply called Pi’s) can be calculated by applying the following equations:. Equation 4. Flow num ber.. Equation 5. Head num ber.. Equation 6. Power num ber.. 14.

(15) Equation 7. Specific Speed (pum p).. Equation 8. Specific Diam eter (pum p).. Equation 9. Specific Speed (turbine).. In equations (4) through (9) Q is the flow rate, H the total head, n the angular velocity, D the impeller diameter and P the input power for a pump or output power for a turbine. The specific speed is obtained by eliminating the machine’s diameter and combining π1 and π2 (for a pump) or π2 and π3 (for a turbine); in a similar fashion, if the angular velocity is eliminated and both numbers are combined the specific diameter is obtained. It should be noted that the head and flow rate used to calculate the dimensionless parameters are their values at the bep of the machine. The dimensionless parameters can be used to: Predict the behavior of the machine under different operating conditions, without actually doing physical testing. Find geometrically similar machines. Apply some empirical relationships to predict the behavior of a pump as a turbine, as will be described in the following section.. 3.4.. Predicting a Pump’s Behavior as a Turbine. Experimental research on PAT’s has yielded different approaches to predict the behavior of a pump as a turbine. The relationship between modes is generally expressed in the form of four constants that relate flow rate, head, efficiency and power between pump and turbine operation. These constants can be calculated with the following three equations:. Equation 1 0. Head constant.. 15.

(16) Equation 1 1. Flow constant.. Equation 1 2. Efficiency constant.. Equation 1 3. Power constant .. Some authors set a fixed value for each of the constants based on experimental data taken from several machines while other provide methods for calculation of their values based on the nominal or bep conditions of the pump. Several methods for the calculation of these constants as well as prediction of turbine operation based on pump characteristics will be further discussed. 3.4.1. Proposed relationships by KR Sharma of Kiloskar Company, India. It relates flow rate in turbine and pump modes through the pump efficiency to a certain power. The relation for head in both operating modes follows the same pattern. The equations proposed by KR Sharma (Williams, 2003) are as follows:. Equation 1 4. Turbi ne flow (KR Sharm a).. Equation 1 5. Turbi ne head (KR S harm a).. These equations can be rewritten in terms of the constants presented in Equation 10 and Equation 11 yielding the following result:. Equation 1 6. Flow coefficient (KR Shar m a).. Equation 1 7. Head coefficient (KR S harm a).. 16.

(17) 3.4.2. Hancock’s Approach (1963) Hancock`s equations have a similar form to Sharma’s proposed relationships, but they use turbine efficiency instead of pump efficiency to relate flow and head in between operation modes. Hancock´s relationships (Hancock, 1963) are as described inEquation 18and Equation 19:. Equation 1 8. Turbi ne head (Hanc ock).. Equation 1 9. Flow head (Hancock).. Both equations can be rewritten in terms of the constants presented in Equation 10 and Equation 11, yielding:. Equation 2 0. Head coefficient (Hancock).. Equation 2 1. Flow coefficient (Hancock).. These relationships imply that the head and flow coefficients are equal; however, in reality this is not the case (the head ratio is usually greater). This is why Hancock’s method is considered a gross estimate, but more accurate methods should be applied if possible. 3.4.3. Rojas’ experimental relationships Andrés Rojas (Rojas Gil, 1989) proposes two different approaches to predict turbine operating conditions based on experimental results. The first approach proposed by Rojas is the determination of the head and flow coefficients based on the pump’s specific speed. Table 1resumes these results.. 17.

(18) Ns < 20 30 - 60 70 - 290. CH 2.2 - 2.5 1.2 - 2.1 1 - 1.2. CQ 2.1 - 2.4 1.1 - 1.8 1. Table 1. He ad a nd flo w coef ficients as a function of pum p specific speed. Taken from (Rojas Gil, 1989).. In order to apply the results shown in Table 1 the specific speed must be calculated using Equation 7. Specific Speed (pump).; all parameters must be in SI units except for the angular velocity (n) with must be expressed in revolutions per minute (rpm). Rojas also presents two equations that can be used to find turbine efficiency and operating conditions if the pump’s best efficiency point is known and some turbine parameters have also been measured or determined by a different method.. Equation 2 2. Pum p efficiency at BEP in terms of power (Rojas).. Equation 2 3. Pum p efficiency at BEP in terms of head and flow (Rojas).. Equation 22 and Equation 23may be rewritten in terms of the power, head and flow coefficients yielding the following results:. Equation 2 4. Power coefficient (Rojas).. Equation 2 5. Pum p efficiency at BEP i n terms of flow and head coefficient (Rojas ).. 3.4.4. Determination of constantsby other methods (Ortíz Flórez & Abella Jiménez, 2008) In the article “Máquinas Hidráulicas Reversibles Aplicadas a Micro Centrales Hidroeléctricas” (Ortíz Flórez & Abella Jiménez, 2008) various 18.

(19) methods used to determine the values of CQ, CH and Cηdeveloped by different scholars working on the subject are summarized. Table 2synthesizes the equations proposed to determine the three coefficients based solely on pump efficiency, by four different authors. Reference Stepanoff1. CQ. CH. Cη. Mc. Claskey2 BUTU3 Sharma Williams4 MICI5 Table 2. Equati ons pro posed by different authors to determ ine head, flow and efficiency coefficients. Rep rod uced from (Ortíz Flórez & Abella Jim énez, 2008) .. In the same article authors Ortíz and Abella cxalso present a table with equations to determine the same coefficients based on the pump’s specific speed rather than calculation based on pump efficiency (as in Table 2). Table 3 resumes these alternative methods for coefficient calculations:. 1. nd. A.J Stephanoff. “Centrifugal and axial flow pumps”. 2 Edition. John Wiley and Sons Inc. , New York, 1957. 2 Ibid. 3 Ibid. 4 Previously presented as KR Sharma’s theory, included in “Pumps as turbines: a user´s guide” by A. Williams [2]. 5 G.I Krivchenko; V.V Berlin; O.A Muraviob; E.M Natarius. “Recomendaciones para la utilización de bombas como turbinas (in Russian)”. Infoenergo, Moscow, 1990.. 19.

(20) Reference Mijailov6. Coefficient. O. Audicio7. Carvalho8. Table 3. Equati ons pro posed by different authors to determ ine head, flow and efficiency coefficients based on p um p specific speed. Reproduced from (Ort íz F lórez & Abella Jim énez, 2008) .. In order to apply the equations presented in Table 3the specific speed must be calculated using different definitions according to the author. These definitions are variations of Equation 9; they are presented in Equations (26) through (28).. Equation 2 6. Pum p specific speed (Mijai lov).. Equation 2 7. Pum p specific speed (Audicio) .. Equation 2 8.Pum p specific speed (Carvalho).. 6. L.P Mijailov, “Pequeña Hidroenergía (in Russian)”. Energoatomizdat, Moscow, 1989. O. Audisio, “Bombas Utilizadas como Turbinas”. Universidad Nacional del Comahue. Available online at: [http://fain.uncoma.edu.ar/centraleshidraulicas/archivos /PCH-BOMBAS%20COMO%20TURBINAS.PDF]. 8 N. Carvalho. “Bombas de flujo operando como turbina. ¿Por qué usarlas? (In Portugese)”. PCH Noticias and SPH News. Available online at: [http://www.cerpch.unifei.edu.br/Adm/artigos/d3339f7f1411fd1867899fa1822ad20b.pdf]. 7. 20.

(21) 4. Equipment and Instrumentation The following section describes the physical resources used to build and operate the test bench, including the instruments used to measure all relevant variables and the PAT itself.. 4.1. The Pump as Turbine In order to select an appropriate pump to be operated as a turbine the following criteria must be met by the machine: Operate at 110/220 V and 60Hz (Colombian standard). It must be a centrifugal pump. According to various references this type of pump has higher efficiencies in turbine mode. The pump shouldn´t have a monoblock construction. This allows the motor to be separated from the pump itself (volute, casing, impeller and seals) in order to measure torque directly on the shaft. The input/discharge diameters must be equal or similar to 1’’. This is because the system will be designed to be coupled to an Armfield F1 Hydraulics Bench, which has 1’’ connections for external equipment. The pump’s nominal power must not exceed 1.5 hp. This is due to the fact that the feed pump for the test bench must have at least four times the power rating of the PAT [2] in order to test it in a wide range of flow/head conditions. The chosen pump is an IHM 1A-3/4 W, produced in Colombia and widely available in the local market as a multipurpose centrifugal pump.The pump’s characteristics are the following: Weg single-phase motor, rated 0.75hp at 3500rpm. Impeller diameter: 120mm. 11/4’’ suction, 1’’ discharge. Rated for a flow range from 0 to 50GPM and from 7 to 27 meters of head. Single spring mechanical pump seal. The characteristic head-flow curve is available from the manufacturer (Annex A), however, the efficiency curve is not supplied which is why the pump must be tested in order to find the conditions at its best efficiency point.. 21.

(22) Figure 9.IHM 1A -3/4W centrifugal pum p at the fluid dynam ics laboratory. The pum p’s m ain body is joined to th e m otor by scre ws, which allows a sim ple disassem bly of both com ponent s.. In order to convert the centrifugal pump to a turbine the motor was removed and replaced with a brake drum. A new axle was also manufactured and installed; finally the pump was coupled to a vertical steel plate using regular ¾’’ screws. F shows this new configuration as a turbine:. Figure 10. IHM 1A -3/4W m ounted as a turbine (prony brake also shown) .. 4.2. The Feed Pump In order to create different head and flow rate conditions at the PAT’s inlet a second pump must be used to “feed” it. As mentioned before the recommendation states that the feed pump must have at least four times the power rating of the PAT in order to test it in a wide range of conditions; in order to test the 1A-3/4W as a turbine the feed pump must be rated at 3hp minimum. The fluid dynamics laboratory has a wide array of centrifugal pumps in storage, which is why a used pump was selected to feed the PAT. The chosen pump is an 22.

(23) APV (SPX Brand) 6V2 clean pump, used in the food and beverage industries. The pumps characteristics are: Casing and impeller made entirely of 316 stainless steel. Baldor motor, rated 5hp at 3450 rpm and efficiency of 87.5%. 2’’ inlet and 1 ½’’ outlet. Conditions of head and flow must be included. The pump’s manufacturer also provides the 6V2 characteristic curves (including efficiency plots), which are included as Annex B.. Figure 11. APV 6V2 centrifugal pum p in the fluid m echanic s laboratory.. 4.3.. Intake and Discharge Systems. To operate the system as a closed hydraulic circuit the feed pump’s inlet and PAT’s discharge must be connected to a water reservoir. The fluid mechanics laboratory has a piped circuit running through the entire workspace, with 2’’ and 5’’ intake and discharge access points. The feed pump´s inlet was connected to the 2’’ circuit discharge using flexible tubing(this is the same as the nominal suction diameter of the feed pump, which guarantees optimal performance). The PAT´s outlet (which has a 1’’ diameter) discharges water to a 1000 liter water tank, using flexible tubing as well. Water can be pumped from this tank to the circuit in order to be recycled, using another pump.. 4.4.. Flow Measurement. A rather simple method is used to measure flow rate in the system. The 1m3 water tank acts as a water reservoir, which is calibrated with a visual scale that measures volume contained. Flow rate can be determined using a chronometer to measure the time t consumed to fill a partial volume V of the reservoir tank, using Equation 29:. 23.

(24) Equation 2 9. Flow rate.. 4.5.. Torque Measurement. The device used to measure torque on the pump´s shaft is a prony brake, which determines the forces acting on a rotating pulley coupled directly to the shaft. ¡Error! No se encuentra el origen de la referencia.shows the basic configuration of a prony brake.. Figure 12.Typical configu rati on of a prony brake depicted m easuring the torque of a m otor. Elem ents (a) a re o ne-a xis d ynam om eters m ounted on a fi xed structure ( b ). The dynam om eters are raised and lo we red to chan ge the fo rce e xe rted b y the braking belt (f) on the pull ey (e) by m eans of the sliding m echanism (c) which is locked into position by the screw (d). Im age from Edibon Technical Teaching Equipm ent, availa ble onl ine at: [ http://www.edibon.com /products/?area=electricity&subarea=m achines ].. For the prony brake used to measure torque on the PAT two Ohaus 50N dynamometers were used, the rest of the structure was manufactured with L-cross section steel beams.. 24.

(25) Figure 13.Pro ny b rake used to m easure torque on the PAT’s s haft.. Torque and brake power are determined using Equations 30 and 31respectively.. Equation 3 0. Torque calculation.. Equation 3 1. Shaft power.. Where F1 and F2are the forces registered by each of the dynamometers, rp is the radius of the pulley or brake drum, T is the torque applied on the shaft, n is the rotational speed in Hz and Ps is the power transmitted by the shaft. The rotational speed is measured by a laser digital tachometer (AMETEK 1726). It is a non-contact measuring method in order to avoid applying other forces on the shaft besides the braking force and the force exerted by the turbine itself.. 4.6.. Head Measurement. Total head is measured using two manometers connected at the intake and discharge of the PAT. The discharge manometer can measure only positive pressure up to 60psi, with a 5psi resolution. The intake manometer can measure both positive and negative pressure (60 psi positive, 30 psi negative, 5 psi. 25.

(26) resolution) in order to measure suction head in pump mode and discharge head in turbine mode.. Figure 14. Intake and discharge m anom eters coupled to the IHM PAT.. Total head can be calculated using the following equation:. Equation 3 2. Total turbi ne head.. Where P2 is the pressure at the discharge (converted to meters of water, mH 20) and P1 is the intake pressure (in mH2O as well).. 4.7.. Electrical Power Measurement. In order to determine pump efficiency accurately consumed electrical power was measured using a Fluke 43B Power Analyzer.. 26.

(27) 5. The Test Bench/Test Results 5.1. Hydraulic Connections Diagram The test bench must be assembled according to the following schematic diagram: 1'’ Flexible Tubing 1'’ Flexible Tubing. 2'’ PVC Tubing 2'’ Circuit Intake Valve. 1'’ to 2'’ PVC expansion. Auxilary Recirculation Pump 1'’ Flexible Tubing. P. E-5. 60psi manometer. Laboratory Reservoir Tank. 1'’ Flexible Tubing. 1'’ Flexible Tubing P. 2'’ PVC Tubing. 2'’ Flexible Tubing. 1'’ Gate Valve. Prony Brake. 60psi Manometer Pump as Turbine. 2'’ Main Circuit Discharge Valve Feed Pump. Figure 15. Test bench schem atic diagram .. 5.2. Final Assembly The test bench was assembled according to the hydraulic schematic diagram depicted inFigure 15. The feed pump, pump as turbine and prony brake were mounted on a single base made from an AISI-1040 steel plate. The auxiliary pump and main body of the bench are supported by a stainless steel cart to move the system freely around the laboratory. The test bench must be operated near the main circuit’s access points and a three-phase electric connection. The main reservoir tank must also be located near the main body of the bench. The following pictures depict the final assembly:. 27.

(28) Figure 16. Test bench for pum ps as turbines (A).. Figure 17. Test bench for pum ps as turbines (B).. 28.

(29) Figure 18. Test bench for pum ps as turbines (C).. 5.3.. Testing of the Pump under Normal Operating Conditions. The IHM 1A-3/4W pump to be used as a turbine was tested using an Armfield F1 Hydraulics Bench. The F1 bench acted as both a water reservoir and flow meter (the instrument has a calibrated scale to measure volume contained; flow rate was determined by following the procedure described in section 4.4. The pump’s suction was connected to the drain of the F1 test bench and the discharge to the calibrated tank of the same instrument by using a manifold specially designed for testing of pumps and turbines. 1’’ flexible tubing was used to connect all of the components described above. 1'’ Flexible Tubing Discharge Manifold. P. Gate Valve 60psi Manometer. P. -30inHg Manometer Armfield F1 Hydraulics Bench. IHM 1A-3/4W Pump. 29.

(30) Figure 19. Schem atic diagram of the setup used for pum p testing.. The characteristic curves for the pump were generated by measuring head, flow rate, speed and consumed power over a broad range of operating conditions (which are changed by opening/closing the gate valve located at the pump’s discharge). The test was repeated ten times, and average curves were plotted from the data array obtained.. Head-Flow Curves for IHM Pumps (3450 rpm) 35. Head (m). 30 25. Experimental 1A-3/4W. 20. Manufacturer 1A-3/4W. 15. Experimental 127mm. 10. Manufacturer 127mm. 5 0 -0,5. 0. 0,5. 1. 1,5. 2. 2,5. 3. 3,5. Flow Rate (Lps) Figure 20. He ad-flo w curves for IHM 1A -3/4W (to be used as turbine) and another IHM pum p (with a 127m m diam eter im peller).. Figure 20 shows the head-flow curve for two IHM pumps (both were tested under the same conditions). The curves supplied by the manufacturer are also shown in the figure. However, the manufacturer doesn’t supply the efficiency or hydraulic power curves, which means that both of them must be determined experimentally.. 30.

(31) IHM Pump Efficiency (3450 rpm) 60. 50. 1A-3/4W Efficiency. Efficiency (%). 40. 30 127mm Efficiency. 20. 10. 0 -0,5. 0. 0,5. 1. 1,5. 2. 2,5. 3. Flow Rate (Lps) Figure 21. Pum p efficiency for IHM 1A-3/4W (to be uses as turbine) and another IHM pum p (with a 127m m diam eter im peller).. Hydraulic Power (3450 rpm) 600 500. Power(W). 400 1A-3/4W Power. 300 200. 127mm Power. 100 0 -0,500. 0,000 -100. 0,500. 1,000. 1,500. Flow Rate (Lps). 31. 2,000. 2,500. 3,000.

(32) Figure 22. Hydraulic po wer curves for IHM 1A -3/4W (to be used as turbi ne) and another IHM pum p (with a 127mm diam eter im peller).. The characteristic pump curves clearly show a problem related to the testing of both pumps. At a flow rate of approximately 1.7 Lps pump efficiency, total head and hydraulic power are greatly diminished, which is not the typical behavior for any centrifugal pump. This loss of head and efficiency is due to a problem regarding the test method used: the Armfield F1 has an insufficient inlet head, thus at a high flow rate cavitation occurs at the suction of the pump. Figure 20 shows that the 1A-3/4W pump behaves in a very similar fashion as to the one depicted in the manufacturer´s supplied curve up until the point where the cavitation problem arises. Thus, it is a good approximation to use the manufacturer´s curve for calculations.. 5.4.. Testing as a reversible machine (turbine operation). In order to test the IHM 1A-3/4W pump as a turbine the configuration depicted on ¡Error! No se encuentra el origen de la referencia.was used, using a secondary pump for water recirculation. Figures 20, 21 and 22 show the final bench assembly with all the components in plain view. Testing procedure was as follows: a. Open the circuit discharge valve completely. b. Turn the feed pump on and set the operation point on a fixed flow rate by opening/closing the gate valve located between the feed pump and the PAT. Flow rate must be measured using the procedure described previously. c. For different braking forces excerpted on the drum by means of the prony brake measure speed, head and torque. d. Once several points have been obtained for a single flow rate, change the condition by opening/closing the 1’’ gate valve. Repeat measurements. Each test was repeated ten times (which means that for each flow rate ten different characteristic curves were obtained). An “average” set of points was then obtained to plot the final characteristic curves.. 5.5.. Characteristic curves of the PAT. The characteristic curves of the IHM 1A-3/4W in reverse operation are reported in this section.. 32.

(33) Shaft Torque 1,2. 1. 0,8. Torque (Nm). 0.9 Lps 1.07 Lps 0,6. 1.15 Lps 1.33 Lps 1.39 Lps 1.89 Lps 2.04 Lps. 0,4. 0,2. 0 0. 500. 1000. 1500. 2000. 2500. 3000. 3500. Angular Velocity (rpm). Figure 23. Shaft torque versus angular velocity plot.. 33. 4000.

(34) Shaft Power 250. 200. 150 Power (W). 0.9 Lps 1.07 Lps 1.15 Lps 1.33 Lps 1.39 Lps 100. 1.89 Lps 2.04 Lps. 50. 0 0. 500. 1000. 1500. 2000. 2500. 3000. 3500. Angular Velocity (rpm). Figure 24. Shaft power vers us angular velocity plot.. 34. 4000.

(35) Turbine Efficiency 60. 50. 40. Efficiency (%). 0.9 Lps 1.07 Lps 30. 1.15 Lps 1.33 Lps 1.39 Lps 1.89 Lps 2.04 Lps. 20. 10. 0 0. 500. 1000. 1500. 2000. 2500. 3000. 3500. Angular Velocity (rpm). Figure 25. Turbine efficiency versus angular vel ocity plot .. 35. 4000.

(36) Turbine Head 30. 25. Turbine Head (m). 20. 0.9 Lps 1.07 Lps 15. 1.15 Lps 1.33 Lps 1.39 Lps 1.89 Lps 2.04 Lps. 10. 5. 0 0. 500. 1000. 1500. 2000. 2500. 3000. 3500. Angular Velocity (rpm). Figure 26. Turbine total head versus angular velocity pl ot.. 36. 4000.

(37) The characteristic curves show typical behavior for a turbine. However, some observations must be done regarding this results: The shaft torque curve has a slightly different shape than a typical torque curve for a water turbine (Figure 7). Torque does not decrease linearly with speed as expected in the case of the PAT, which is an interesting behavior since this trend is repeated for all the flow rates tested. Shaft power increases with flow rate, as expected. It has a maximum value of 210W at 2515rpm for a flow rate of 2.04Lps. The efficiency plot shows that, regardless of the flow rate, the shape and maximum value of the curve tends to be the same (although best efficiency point occurs at different operating conditions depending on the flow rate). However, it is important to notice that the uncertainty in the calculation of turbine efficiency is higher than the one involved in shaft power calculation (more variables are involved, thus error increases), which is why Figure 24 should be used to obtain turbine bep. Although the turbine head plot (Figure 26) is not typically reported, it is included in order to determine head for any other point shown in the characteristic curves. A second set of characteristic curves is presented, which plots unitary flow rate, unitary power and unitary torque versus unitary speed of the turbine. If the experimental data is correct, all of the curves for different flow rates for a single variable should superimpose one another, resulting in a single curve that characterizes the machine. The “unitary variables” are calculated as follows:. Figure 27. Unitary speed.. Figure 28. Unitary flow rate.. Figure 29. Unitary power.. Figure 30. Unitary torque.. 37.

(38) Unitary Flow Rate 0,0006. Unitary Flow Rate [Q/√H]. 0,0005 0,0004. 0.9 Lps 1.07 Lps. 0,0003. 1.15 Lps 1.33 Lps. 0,0002. 1.39 Lps 1.89 Lps. 0,0001. 2.04 Lps. 0 0. 2. 4. 6. 8. 10. 12. 14. Unitary Speed [n/√H]. Figure 31. Unitary flow rate versus unitary speed pl ot.. Unitary Power 2,5. Unitary Power [P/(H1.5)]. 2 0.9 Lps 1,5. 1.07 Lps 1.15 Lps. 1. 1.33 Lps 1.39 Lps 1.89 Lps. 0,5. 2.04 Lps 0 0. 2. 4. 6. 8. 10. 12. Unitary Speed [n/√H]. Figure 32. Unitary power versus unitary speed plot.. 38. 14.

(39) Unitary Torque 0,06. Unitary Torque [T/H]. 0,05. 0,04. 0.9 Lps 1.07 Lps. 0,03. 1.15 Lps 1.33 Lps. 0,02. 1.39 Lps 1.89 Lps. 0,01. 2.04 Lps. 0 0. 2. 4. 6. 8. 10. 12. 14. Unitary speed [n/√H]. Figure 33. Unitary torque versus unitary speed pl ot.. As can be seen from this second set of characteristic curves most of them superimpose correctly, although for the lower flow rates (0.9 and 1.07 Lps) this is not entirely true. A possible solution to this problem will be further discussed in the conclusions section. For the rest of the flow rate conditions Figures 31 through 33 validate the experimental data obtained.. 5.6.. Determination of the numerical relationships between pump and turbine modes. In order to apply the theory presented in section 3.4 the best efficiency point for both pump and turbine must be known at the same operating speed. From the pump characteristic curves presented in section 5.3 the best efficiency point is determined: Pump Best Efficiency Point at 3450 rpm H (m) 20 Q (Lps) 1.74 P (W) 323 η (%) 37.2 Table 4. Ch aracteristics of the pum p bep at 3450 rpm .. 39.

(40) In a similar way, the operating conditions at the turbine bep may be obtained from its characteristic curves (section 5.5) taking into account that the bep is defined by the point where the maximum output (shaft) power is attained. The reason to use this criteria instead of using the efficiency plot were discussed in the previous section. Turbine Best Efficiency Point ω (rpm) 2515.6 P (W) 210.75 T (Nm) 0.8 η (%) 41.5 Q (Lps) 2.04 H (m) 25.32. Table 5. Turbine best efficiency point at 2515rpm .. The best efficiency point operating conditions are given at different speeds for pump and turbine modes, which is why the bep conditions for pump operation must be scaled down from operation at 3450rpm to operation at 2515rpm using the dimensionless numbers described in section 3.3. Using the flow number (Equation 4):. Equation 3 3. Pum p flow rate at 2515rpm , scaled down using the flow num ber.. Using the head number (Equation 5):. Equation 3 4. Pum p head at 2515rpm , scaled down using the head num ber.. Using the power number (Equation 6):. Equation 3 5. Pum p output (h ydraulic) power at 2515rpm , scaled down using the power num ber.. Table 6 summarizes the “new” pump bep at the same speed as the turbine bep. Pump Best Efficiency Point at 2515rpm Q (Lps) 1.27 H (m) 10.63 P (W) 125.13. 40.

(41) Table 6. Pum p best efficiency point at 2515rpm .. Flow, head, power and efficiency constants may now be determined using the equations presented in section 3.4.. Equation 3 6. Calculation of the head constant.. Equation 3 7. Calculation of the flow constant.. Equation 3 8. Calculation of the power constant.. Equation 3 9. Calculation of the efficiency constant.. Flow, head and power constants seem to be in the range of what is normally expected from a reversible machine; however, the efficiency constant presents a rather interesting behavior. Its value of 1.1 suggests that turbine efficiency is superior to pump efficiency, which is not what would be expected from a machine originally designed to operate as a pump. This is an unexpected and interesting behavior, however it is highly likely that pump efficiency is too low since it had a cavitation problem as described before. 5.6.1. Application of KR Sharma’s Theory Using Sharma’s proposed relationships (3.4.1) pump efficiency may be calculated by using both head and flow rate conditions, using Equation 16 and Equation 17. This estimated pump efficiency may then be compared to the measured efficiency. Using Equation 16:. Equation 4 0. Predicted p ump efficiency at bep using Sharm a’ s approach through flow constant (2515 rpm ).. Using Equation 17:. 41.

(42) Equation 4 1. Predicted p ump efficiency at bep using Sharm a’s approach through head constant (2515 rpm ).. Both calculations predict a maximum pump efficiency that is much higher than the 37.2% efficiency determined experimentally. As was mentioned before, the cavitation problems generated when the IHM 1A-3/4W was coupled to the Armfield F1 Hydraulics Bench may be the reason why such a low efficiency was registered. If Sharma’s approach is considered valid, then a new approximation to pump efficiency may be generated by taking the mean value between both calculated efficiencies, which is 52%. This number seems much closer to the actual efficiency of a regular centrifugal pump. This “adjusted” efficiency may then be used to calculate a second efficiency constant:. Equation 4 2. Adjusted efficiency constant using Sharm a’s approach.. This adjusted efficiency constant shows that pump efficiency is higher than turbine efficiency, which is what is normally expected from reversible machine testing. 5.6.2. Application of Hancock’s Theory As was described in section 3.4.2 Hancock’s approach is a gross estimate to turbine efficiency since it implies that CQ=CH, which is not true. Using a similar procedure as the one used in the previous section to verify pump efficiency, Hancock’s approach will be used to compare estimated values of turbine efficiency with its maximum measured value. Using Equation 20:. Equation 4 3. Predicted turbi ne efficiency at bep using Hancock’s approach through head constant (2515 rpm ).. This is an excellent estimation of turbine efficiency, since its measured value at bep was 41.5%. Using Equation 21:. Equation 4 4. Predicted turbi ne efficiency at bep using Hancock’s approach through flow constant (2515 rpm ).. Estimation of turbine efficiency by using the flow constant yields a value of 62.5%, which is much higher than measured efficiency and even pump efficiency itself. It should be noted however that the uncertainty in head measurement (ΔH) is 42.

(43) significantly lower than uncertainty in flow rate measurement (ΔQ), which is why the head constant is a more reliable parameter to work with. Hancock’s approach might be slightly outdated (1963) and thus using it is not recommended except for initial, gross calculations. 5.6.3. Application of Rojas’ Experimental Relationships In order to apply the approximation to head and flow constants proposed by Rojas (Table 1) pump specific speed at bep must be calculated using Equation 7; all variables must be in SI system units except pump speed which must be in rpm.. Equation 4 5. Calculation of 1A -3/4W specific speed.. According to the theory contained in Table 1 the flow constant (CQ) must have a value between 2.1 and 2.4 and the head coefficient (CH) must be between 2.2 and 2.5. This statement is only true for the flow constant (which is almost in the upper limit of 2.4); the head constant is far from being contained within Rojas’ proposed range. Rojas also proposed two equations to calculate the power constant and pump efficiency in terms of other know parameters (Equation 24 and Equation 25, respectively). However, a supposition made by his model is that pump efficiency is about the same as turbine efficiency, which is not entirely true, especially if the adjusted efficiency is used. Using Equation 24 (with turbine efficiency, adjusted pump efficiency and measured pump efficiency):. Equation 4 6. Appro xim ation of the power constant using Rojas’ approach.. None of the approximations used in the previous equation to predict the power constant seems to yield a result similar to the calculated constant (Equation 38). Moreover, there is a significant difference between the three approximated values to such number as predicted by Rojas’ equation. Aside from the fact that finding a machine whose turbine and pump efficiencies are the same is highly unlikely (thus making the model invalid) the other reason for such an error might be that turbine output power might be higher than measured, thus making C P approach to a value 43.

(44) near 2, as predicted. However, it is more likely that pump output power is actually higher than measured (due to the cavitation issue mentioned before). If this assumption is correct then CP would only get smaller, making Rojas’ approach even less accurate. Pump efficiency at bep can be calculated using Equation 25:. Equation 4 7. Pum p efficieny at bep using Rojas’ approac h.. This predicted value differs greatly from adjusted pump efficiency (even more from measured pump efficiency). The conclusion that can be reached is that Rojas’ experimental relationships (which he obtained by testing one particular PAT) cannot be generalized for all reversible machines. 5.6.4. Application of other Methods to Determine Characteristic Constants (Ortíz Flórez & Abella Jiménez, 2008) The theory contained in Table 2 will now be applied to determine CQ, CH and Cη. For the following calculations only adjusted pump efficiency and adjusted efficiency coefficient will be used. Author Stepanoff Mc.Claskey BUTU Sharma-Williams. CQ 1,387 1,923 1,997 2,206. MICI. 0,9 to 1. CH 1,923 1,923 2,396 2,192 1,56 to 1,78. Cη 1 1 0,942 1 0,75 to 0,8. % Error CQ % Error CH 15,378 23,760 16,800 23,760 19,866 0,678 27,464 8,588 (-). (-). % Error Cη 14,5 14,5 9,265 14,5 (-). Table 7. Applicatio n of the theory e xposed in Tabl e 2. Percent error was calculated wit h respect to the val ue of the constants calculated in Equation 3 6 (head), Equati on 37 (flow), and Equation 4 2 (adj usted efficiency).. These methods seem to yield acceptable results for the approximation of the characteristic reversible machine constants; the BUTU approach seems to offer the best results overall. Table 8 shows the application of the theory exposed in Table 3, calculating pump specific speed for each case according to Equation 26 (Mijailov), Equation 27 (Audisio) and Equation 28 (Carvalo).. 44.

(45) Author Mijailov Audicio. Ns 15,224 0,288. CQ 2,104 1,425. CH 1,924 2,267. Carvalo. 253,740 -729,533 1377,297. Cη % Error CQ 0,939 23,972 0,538 12,289 (-). (-). % Error CH 23,669 5,003. % Error Cη 8,915 58,868. (-). (-). Table 8. Applicatio n of the theory e xposed in Tabl e 3 to determ ine characteristic constants based on pum p specific speed.. What can be immediately noticed from Table 8 is that Carvalo’s method (or the way it is reported in (Ortíz Flórez & Abella Jiménez, 2008)) is incorrect and doesn´t yield logical results. The original article by Carvalo doesn´t provide much guidance either since the proposed equations to determine the PAT constants (presented in Table 3) are nowhere to be found in the original publication. However, Mijailov’s and Audicio’s approximations yield acceptable errors in the determination of the constants, which is why they may be considered as a good method to calculate them.. 45.

(46) 6. Conclusions Developments. and. Recommendations. for. Future. Pumps as turbines offer an excellent low cost solution to micro-hydro power, especially in scenarios where financial constraints play a major role in project development. A great deal of investigation needs to be done in order to develop an appropriate theory for general design of PAT schemes, since most available theories are based upon empirical equations obtained from testing of individual machines and there is still no consensus regarding which set of equations better describes the behavior of most reversible machines. However, there are multiple examples of actual PAT installations around the world that operate appropriately, which points to the fact that current theory does not perfectly predict the behavior of the reversible machine but can be used in real design cases. Although actual electric power generation was not carried out in the course of this project, it would be interesting to test the PAT coupled to a generator and evaluate the whole set as an energy conversion system. If total system efficiency evaluation (defined as the ratio of electric output power to hydraulic power) were to yield excellent results for a wide range of head/flow conditions then it would be possible to provide an excellent alternative to micro generation at an extremely low cost. Another interesting approach to future PAT investigation would be to design low-cost modifications for the pump that improve its performance as a turbine (for example a volute especially designed for reverse operation, or coupling to a generator that offers a superior power output than the one offered by the standard motor). Regarding the test bench developed in this particular project, the following improvements can be made. This can also be taken into account for future construction of similar schemes: Use a set of dynamometers in the prony brake with higher resolution and a narrower range. The largest registered force in a dynamometer was about 30N, which means that the maximum of 50N the instrument can measure is far from being reached. However, for low flow rates an instrument with a better resolution would be useful since more points could be taken before the turbine gets to fully braked condition (for 0.9 Lps only three or four points can be taken using the current prony brake). Eliminate the small leak that currently exists between the turbine shaft and the casing. This might involve manufacturing a new shaft or placing a seal in between the two components. Currently, the feed pump has the capacity to move higher flow rates than the recirculation pump. If the recirculation pump were to be replaced with 46.

(47) a pump that could move a similar flow rate to the feed pump then continuous testing could be done. Currently tests can be carried out for about seven minutes at maximum flow rate until the water tank overflows. To improve the lifespan of the PAT a small overhaul in the way the impeller is connected to the shaft should be considered. The impeller is coupled to the shaft by means of a right-hand screw, designed for normal pump operation (clockwise). However, in turbine operation the impeller rotates counterclockwise, which means that the force excerpted by the water plus the force excerpted by the brake on the drum will try to unscrew the impeller from the shaft, thus damaging the PAT. The mechanical seal may also suffer from the reverse operation condition (especially the spring, which is also coiled in a particular direction). Considerations should be made in order to avoid future problems associated with these two components. Carry a series of tests measuring electrical output power provided by a generator. If the PAT were to be tested under these conditions then it would be interesting to develop a configuration for the test bench in which the transition between pump and turbine operation could be achieved by opening/closing a set of valves. This would provide an excellent opportunity to test different machines in normal and reverse operation using a simple configuration (although all machines tested must be coupled to their respective motor, thus the prony brake should be eliminated). In general, the improvements aim to improve the robustness and versatility of the test bench, making it possible to test a wide range of machines with minimal or no structural changes to the bench itself.. 47.

(48) 7. References Amaya Rodríguez, J. O. (1990). Operación de Bombas Centrífugas como Turbinas. Bogotá: Tésis de Mágister, Universidad de los Andes. Audisio, O. (2009). Bombas utilizadas como turbinas. Neuquén: Laboratorio de Máquinas Hidráuilcas, Departamento de Mecánica Aplicada, Universidad Nacional del Comahue. British Petroleum (BP). (2010). Statistical Review of World Energy. Derakhshan, S., & Nourbakhsh, A. (2007). Experimental study of characteristic curves of centrifugal pumps working as turbines in different specific speeds. Tehran: Department of Mechanical Engineering, University of Tehran. Hancock, J. W. (1963). Centrifugal pump or water turbine. Pipeline News, 25-27. Ortíz Flórez, R., & Abella Jiménez, J. (2008). Máquinas hidráulicas reversibles aplicadas a micro centrales hidroeléctricas. IEEE Latin America Transactions, Vol.6, No.2, June, 170-175. Pinilla Sepúlveda, Á., & Amaya Rodríguez, J. O. (1990). Microcentrales y Minicentrales basadas en Bombas Operando como Turbinas. Bogotá: Primer Simposio Colombiano sobre Investigaciones y Desarrollos Tecnológicos en Energía. Ramos, H., & Borga, A. (1999). Pumps as Turbines: An Unconventional Solution to Energy Production. Lisboa: Civil Engineering Department, University of Lisbon. Rojas Gil, A. (1989). Pruebas a una Bomba Centrífuga Utilizada como Turbina Francis. Bogotá: Tésis de Pregrado, Universidad de los Andes. Stepanoff, A. J. (1963). Centrifugal and Axial Flow Pumps: Theory, Design and Application. New York: John Wiley & Sons. Williams, A. (2003). Pumps as Turbines: A User's Guide.London: ITDG Publishing.. 48.

(49) 8. List of Figures Figure 1. Total energy consumed by hydropower schemes worldwide. Also shown is the total electric energy generated worldwide by all available sources. Data from BP Statistical Review of World Energy 2010 (British Petroleum (BP), 2010). ...................................................................................................................... 4 Figure 2. Total energy consumed by hydropower schemes in Central and South. Also shown is the total electric energy generated in these regions by all available sources. Data from BP Statistical Review of World Energy 2010 (British Petroleum (BP), 2010). ............................................................................................................. 5 Figure 3. Typical head-flow curve for a pump. .................................................. 11 Figure 4. Typical efficiency curve for a pump. .................................................... 12 Figure 5. Head-flow curve for a particular machine and different impeller diameters. Efficiency plots are superimposed. Image taken from “Selecting an Irrigation Pump”, NSW Department of Primary Industries. [Available online at: http://www.dpi.nsw.gov.au/agriculture/resources/water/irrigation/systems/pumps/se lecting]. .................................................................................................................. 12 Figure 6. Typical output power curve for a water turbine. .................................. 13 Figure 7. Typical torque curve for a water turbine. ............................................. 13 Figure 8. Typical efficiency curve for a water turbine. ........................................ 14 Figure 9. IHM 1A-3/4W centrifugal pump at the fluid dynamics laboratory. The pump’s main body is joined to the motor by screws, which allows a simple disassembly of both components. ......................................................................... 22 Figure 10. IHM 1A-3/4W mounted as a turbine (prony brake also shown). ........ 22 Figure 11. APV 6V2 centrifugal pump in the fluid mechanics laboratory. ........... 23 Figure 12. Typical configuration of a prony brake depicted measuring the torque of a motor. Elements (a) are one-axis dynamometers mounted on a fixed structure (b). The dynamometers are raised and lowered to change the force exerted by the braking belt (f) on the pulley (e) by means of the sliding mechanism (c) which is locked into position by the screw (d). Image from Edibon Technical Teaching Equipment, available online at: [http://www.edibon.com/products/?area=electricity&subarea=machines]. ............. 24 Figure 13. Prony brake used to measure torque on the PAT’s shaft. ................. 25 Figure 14. Intake and discharge manometers coupled to the IHM PAT. ............ 26 Figure 15. Test bench schematic diagram. ........................................................ 27 Figure 16. Test bench for pumps as turbines (A). .............................................. 28 Figure 17. Test bench for pumps as turbines (B). .............................................. 28 Figure 18. Test bench for pumps as turbines (C). .............................................. 29 Figure 19. Schematic diagram of the setup used for pump testing. ................... 30 Figure 20. Head-flow curves for IHM 1A-3/4W (to be used as turbine) and another IHM pump (with a 127mm diameter impeller). .......................................... 30 49.

(50) Figure 21. Pump efficiency for IHM 1A-3/4W (to be uses as turbine) and another IHM pump (with a 127mm diameter impeller). ....................................................... 31 Figure 22. Hydraulic power curves for IHM 1A-3/4W (to be used as turbine) and another IHM pump (with a 127mm diameter impeller). .......................................... 32 Figure 23. Shaft torque versus angular velocity plot. ......................................... 33 Figure 24. Shaft power versus angular velocity plot. .......................................... 34 Figure 25. Turbine efficiency versus angular velocity plot. ................................. 35 Figure 26. Turbine total head versus angular velocity plot. ................................ 36 Figure 27. Unitary speed. ................................................................................... 37 Figure 28. Unitary flow rate. ............................................................................... 37 Figure 29. Unitary power. ................................................................................... 37 Figure 30. Unitary torque. .................................................................................. 37 Figure 31. Unitary flow rate versus unitary speed plot. ...................................... 38 Figure 32. Unitary power versus unitary speed plot. .......................................... 38 Figure 33. Unitary torque versus unitary speed plot. .......................................... 39. 50.

(51) 9. List of Equations Equation 1. Bernoulli’s principle. .......................................................................... 9 Equation 2. Pump efficiency. ................................................................................ 9 Equation 3. Turbine efficiency. ........................................................................... 10 Equation 4. Flow number. .................................................................................. 14 Equation 5. Head number. ................................................................................. 14 Equation 6. Power number. ................................................................................ 14 Equation 7. Specific Speed (pump). ................................................................... 15 Equation 8. Specific Diameter (pump)................................................................ 15 Equation 9. Specific Speed (turbine). ................................................................. 15 Equation 10. Head constant. .............................................................................. 15 Equation 11. Flow constant. ............................................................................... 16 Equation 12. Efficiency constant. ....................................................................... 16 Equation 13. Power constant. ............................................................................ 16 Equation 14. Turbine flow (KR Sharma)............................................................. 16 Equation 15. Turbine head (KR Sharma). .......................................................... 16 Equation 16. Flow coefficient (KR Sharma). ...................................................... 16 Equation 17. Head coefficient (KR Sharma). ..................................................... 16 Equation 18. Turbine head (Hancock)................................................................ 17 Equation 19. Flow head (Hancock). ................................................................... 17 Equation 20. Head coefficient (Hancock). .......................................................... 17 Equation 21. Flow coefficient (Hancock). ........................................................... 17 Equation 22. Pump efficiency at BEP in terms of power (Rojas). ....................... 18 Equation 23. Pump efficiency at BEP in terms of head and flow (Rojas). .......... 18 Equation 24. Power coefficient (Rojas). ............................................................. 18 Equation 25. Pump efficiency at BEP in terms of flow and head coefficient (Rojas). .................................................................................................................. 18 Equation 26. Pump specific speed (Mijailov). ..................................................... 20 Equation 27. Pump specific speed (Audicio). ..................................................... 20 Equation 28.Pump specific speed (Carvalho). ................................................... 20 Equation 29. Flow rate. ...................................................................................... 24 Equation 30. Torque calculation. ........................................................................ 25 Equation 31. Shaft power. .................................................................................. 25 Equation 32. Total turbine head. ........................................................................ 26 Equation 33. Pump flow rate at 2515rpm, scaled down using the flow number. 40 Equation 34. Pump head at 2515rpm, scaled down using the head number. .... 40 Equation 35. Pump output (hydraulic) power at 2515rpm, scaled down using the power number. ...................................................................................................... 40 Equation 36. Calculation of the head constant. .................................................. 41 Equation 37. Calculation of the flow constant. ................................................... 41 51.

(52) Equation 38. Calculation of the power constant. ................................................ 41 Equation 39. Calculation of the efficiency constant. ........................................... 41 Equation 40. Predicted pump efficiency at bep using Sharma’s approach through flow constant (2515 rpm). ...................................................................................... 41 Equation 41. Predicted pump efficiency at bep using Sharma’s approach through head constant (2515 rpm). .................................................................................... 42 Equation 42. Adjusted efficiency constant using Sharma’s approach. ............... 42 Equation 43. Predicted turbine efficiency at bep using Hancock’s approach through head constant (2515 rpm). ....................................................................... 42 Equation 44. Predicted turbine efficiency at bep using Hancock’s approach through flow constant (2515 rpm). ......................................................................... 42 Equation 45. Calculation of 1A-3/4W specific speed. ......................................... 43 Equation 46. Approximation of the power constant using Rojas’ approach. ....... 43 Equation 47. Pump efficieny at bep using Rojas’ approach. .............................. 44. 52.

(53) 10.. Annexes. 10.1. Annex A – IHM 1A-3/4W (120mm) Manufacturer Curve. 53.

(54) 10.2. Annex B- APV 6V2 (feed pump) Manufacturer Curve. 54.

(55) 10.3. Annex C- Propagation of Uncertainty Analysis 10.3.1. Uncertainty in angular velocity measurement Angular velocity was measured directly using a single instrument (non-contact tachometer). Thus the uncertainty in its measurement is defined as half the instrument’s resolution:. Thus,. 10.3.2. Uncertainty in head measurement Head was measured using two manometers, each with a resolution of 0.5psi. Thus, each instrument induces an error of:. Head is calculated using the following equation:. Absolut error in head measurement is given by the following equation:. Where:. And:. 10.3.3. Uncertainty in torque measurement Torque is measured indirectly and calculated using the following equation:. The radius of the brake drum was measured using a standard vernier caliper, which yields: 55.

(56) Forces in the brake drum were measured using two 50N dynamometers, with a 1N resolution. Thus:. Torque error is calculated using the following equation:. Where:. 10.3.4. Uncertainty in output power measurement Output (or shaft) power is calculated using the following equation:. Absolut error in the indirect measurement of power is given by:. Where the partial derivatives are given by:. 10.3.5. Uncertainty in flow rate measurement Flow rate is calculated as:. 56.

(57) Volume was measured using the main reservoir tank, which is calibrated every 50L. Thus:. Time was measured using a regular chronometer which can measure to the centisecond (0.01s).. Absolut error in flow rate is given by:. Where:. 10.3.6. Uncertainty in turbine efficiency Turbine efficiency is calculated by:. Under the assumption that water density (ρ) and the standard acceleration of gravity (g) are determined without any error; absolute error in efficiency is given by:. The partial derivatives involved in the equation are:. 57.

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