Investigation of Pump As Turbine Performance in Small Hydropower Stations

Prediction of Pump as Turbine's (PAT) Best Efficiency Point (BEP) by Theoretical Method

A.Nourbakhsh1 , Sh.Derakhshan2 1. Professor, Department of Mechanical Engineering, University of Tehran, Tehran 14147, Iran 2. M.S. Student, Department of Mechanical Engineering, University of Tehran, Tehran, Iran

Abstract: Because the behavior of pump when rotates as turbine is change, the prediction of performance of PAT is difficult. Up to now all efforts to perdition of BEP of PAT are done with test and experimental. And any empirical relations give the BEP of PAT with any errors. But there is not existed a certain theoretical method to calculation and prediction of BEP of PAT. Therefore a great interest for research in this field is to investigate a theoretical way for predicting a pump's behavior operating as a turbine. In this present paper, we have predicted the BEP of PAT by calculation of PAT hydraulic characteristics and then we have given the BEP point of the PAT. Finally our result has compared with the other methods and test results.

Keywords: turbine-pump-volute-efficiency-head-discharge

1 Nomenclature b'2: pump impeller outlet angle Ht: turbine actual head D1: pump impeller inlet diameter Hp: pump actual head D2: pump impeller outlet diameter H"t: turbine Euler head z: quantity of pump impeller blade Q"nt: turbine shock less discharge e: pump impeller blade thickness Qt: turbine actual discharge b1: pump impeller inlet passage width Qlt: turbine leakage discharge b2 : pump impeller outlet passage width Qlp: pump leakage discharge b3: pump volute inlet passage width Pmt: pump mechanical losses av:pump volute angle Pdp: pump disk friction losses a2 : pump impeller outlet absolute velocity angle Plt: turbine leakage losses b3 : turbine impeller outlet relative velocity angle Pelt: turbine exit losses a1: pump impeller inlet area Pvt: turbine volute hydraulic losses a2 pump impeller outlet area Pit: turbine impeller hydraulic losses U2: pump impeller outlet peripheral velocity Pmt: turbine mechanical losses U3: turbine impeller outlet peripheral velocity Pdt: turbine disk friction losses Vu2 : pump impeller outlet absolute tangential Pnt: turbine exit power velocity Np: pump rotational speed Vu3 :turbine impeller outlet absolute tangential Nt: pump rotational speed velocity hp: pump total efficiency hmp: pump mechanical efficiency 2 Introduction hdp: pump disk friction efficiency Small hydroelectric power stations became hqp: pump leakage efficiency attractive for generating electrical energy after the hvp: pump volute efficiency oil price crisis of the seventies. However cost per hvt: turbine volute efficiency KW energy produced by these stations is higher hip: pump impeller efficiency than the hydroelectric power plants with large capacity. Numerous publications in recent years ht: turbine total efficiency emphasize the importance of using simple turbine hit: turbine impeller efficiency in order to reduce the cost of produced electrical e: turbine utilization factor energy. b'1: pump impeller inlet angle There is need for installation small hydroelectric power stations many developing countries. We considered the idea of using pumps as hydraulic turbines an attractive and important alternative. Pumps are relatively simple machine, are easy to maintain and are readily available in most developing countries. From the economical point of view, it is often stated that pumps working as turbines in the range of 5 to 500 KW allow capital payback periods of tow years or less which is considerably less than that of a conventional turbine. Because the behavior of pump when rotates as turbine is change, the prediction of performance of Figure.2. turbine impeller inlet and outlet velocity triangles PAT is difficult. Up to now all efforts to perdition of BEP of PAT are done with test and experimental. And any empirical relations give the 3 Calculations BEP of PAT with any errors. The many researchers For doing of calculations, primary we must define such as Stepanof[2], Wong[5], Sharma[6], the important geometrical and Hydraulic Williams[7], gantar[4], Ramos, H., Borga[9], characteristics of pump. In following the important Alatorre-Frenk[8], Nourbakhsh-Derakhshan[6] turbine parameters shall be calculated. In the next have presented relations that predicate some of section the method of parameters calculations have pumps with special characteristics. And they are been presented. not suitable for all of pumps. But there is not existed a certain theoretical method to calculation 3.1 The pump important parameters and prediction of BEP of PAT. For calculation of the BEP of turbine, from pump In this present paper, we have predicted the BEP of geometrical and hydraulic characteristics, these PAT by calculation of PAT hydraulic parameters shall be defined. That is divided two characteristics and then we have given the BEP sections: point of the PAT. Finally our result has compared - Hydraulic characteristics: with the other methods and test results. The hydraulic characteristics consists three parameters: head (H), discharge (Q) and efficiency (h). Be noted that the obtaining of these parameters is very easy. - Geometrical characteristics: Geometrical parameters consist the impeller inlet and outlet angels (b'1,b'2), the impeller inlet and outlet diameters (D1,D2), the impeller blade numbers (z), the impeller blade thickness (e), the impeller inlet and outlet passage widths (b1,b2), the volute outlet width (b3) or volute angle(av). With tow ways we can define these parameters: from pump manufactures or with sizing.

3.2 The turbine important parameters Figure.1. pump impeller outlet velocity triangle In the following the important parameters of turbine shall be defined. For obtaining the BEP of turbine, the bellow parameters shall be calculated: head (H), discharge (Q) and efficiency (h). For calculation of these parameters the following characteristics must be obtained: 1. Hydraulic losses in volute and impeller. in turbine mode the volute is converging, so the 2. Mechanical losses and disc friction losses. hydraulic losses are less than them in pump mode. 3. Leakage losses. So:

4. Utilization factor. 1 vt  0.8(1 vp ) (5) 5. Euler head. Then volute hydraulic losses are calculated. 6. Shock less discharge. The other losses that shall be gotten together with In the following these parameters have been Euler head are losses that are missed in outlet of calculated and finally the BEP of turbine mode has turbine in form of kinetic energy. Then the been obtained. Utilization factor is defined: H 3.3 Analyzing and calculating of turbine mode   t V 2 (6) parameters H  u3 In this section the inlet and outlet velocity triangles t 2g shall be obtained. The pump inlet and outlet Finally the head in BEP of turbine operation is velocity triangles have been shown in figure 1. calculated: And for turbine mode the inlet and outlet velocity H t  .vt .Ht (7) triangles have been shown in figure 2. For calculation of turbine BEP discharge, it is Considerations show that the water inlet angle to assumed that shock less discharge is BEP impeller in turbine mode ( ) is equal with volute a2 discharge. So we shall calculate the leakage angle. In fact the volute performance is same as discharge. With calculate pump leakage discharge guide channel. The water outlet angle (b3) from [2], the turbine leakage discharge is obtained [7]: impeller in turbine operation is equal with impeller H inlet angle ( ' ) too (no whirl at exit). So the Euler t b 1 Qlt  Qlp . (8) H Head is: p t H  U V  U V Then the BEP discharge of turbine is calculated: t 2 u2 3 u3 (1) Then: 2 Q  Q  Q U Q m.cot  cot U t nt lt (9) H  3 nt [ v  3 ]  3 (2) t g a a g For calculation of efficiency shall be the total 2 1 losses in turbine mode calculated. With available That Q"n is shock less discharge and obtained with mechanical and disk friction losses of pump the relation: mechanical and disk friction in turbine are U .a Q  2 2 (3) calculated: nt cot   cot v 2 N t Pmt  Pmp  (10) In the following with hydraulic losses, the actual N head of turbine operation has been obtained. p 3 The head reaches to impeller after reduction in N t Pdt  Pdp  3 (11) volute. So the hydraulic losses in volute shall be N p added to the Euler head. But the calculation of And the leakage losses and the volute hydraulic these losses is difficult. So shall be tried to losses of turbine are: calculation of them from pump hydraulic and P  .Q .H   (12) geometrical characteristics. lt lt t vt The leakage losses for pump operation are obtained Pvt  (1 vt )..Qlt .H t (13) from [1], mechanical losses and disc friction losses The kinetic energy losses in turbine exit are: from [2]. Finally with upper efficiencies, the pump Pelt  (1 ).(.Qlt .H t  Pvt  Plt ) (14) hydraulic efficiency is obtained: In following the hydraulic losses of impeller in p turbine mode has been calculated: hp  (4) qp.mp.dp P  (1  ).(.Q .H  P  P  P ) And with assuming the equal hydraulic losses for it it lt t vt lt elt (15) impeller and volute in pump operation, the pump Shall be noted that with defining of impeller volute hydraulic efficiency is obtained [7]. Because hydraulic efficiency of pump, the impeller hydraulic efficiency of turbine are obtained (the References: impeller in turbine mode is converge): [1] Nourbakhsh, A, and Jahangiri, G.(1992).

1 it  0.8(1 ip ) (16) Inexpressive small hydropower stations for small And the turbine exit power is: areas of developing countries, pp.313-319. conference on Advances in Planning, Design and P  .Q .H  P  P  P  P  P  P (17) nt t t vt lt elt it mt dt Management of Irrigation Systems as Related to And the turbine maximum efficiency is equal to: Sustainable Land use, Louvain, Belgium. .Q t .H t  Pvt  Plt  Pelt  Pit  Pmt  Pdt [2] Stepanoff, A.J. (1957). Centrifugal and axial t  (18) .Q t .H t flow pumps, John Wiley and Sons, New York. [3] Williams, A. (1995). Pumps as turbines a user's 4 Example guide, pp.34, intermediate Technology The Worthington-Simpson 25WB125 pump has publications, London. been used as an example of applying the [4] Gantar, M. (1988). Propeller pumps running as theoretical method to predict the turbine turbines, pp 237-248, conference on Hydraulic performance. The hydraulic characteristics of Machinery, Ljubljana, Slovenia. pump are: [5] Wong, W. (1987). Application of centrifugal That this method gives the BEP of turbine pumps for power generation, pp. 381-348, World Pumps. operation in rotational speed Nt=3100 rpm The results of theoretical method have been [6] Nourbakhsh, A., Derakhshan, S.,(2004). Prediction of pump as turbine performance in small ht (Ht (m (Qt (l/s hydropower stations, pp. 31, Conference of Iran (%) Society of Mechanical Engineering, Tarbiat [Stepanof [2 44.7 3.53 46 Modares University, Tehran, Iran. [Sharma[6 52.3 4.47 46 [7] Williams, A., (1992). Pumps as turbines used [Alatorre-Fre-1nk[8 51.2 4.68 46 with induction generations of stand-alone micro- [Alatorre-Frenk-2[8 67.9 4.63 263 hydroelectric power plants, Nathingham [Area Ratio[7 56.5 4.00 45 Polytechnic, Doctor of philosophy mechanical Theoretical 59.45 4.03 47 engineering project thesis. Method [8] Richard Allan, R.A. (2001). Modeling of [Test[7 59.3 3.93 48 pumped storage and hydropower potential within compared with the other methods results in table 1. water supply networks, Notingham University [9] Ramos, H., Borga, A., (1999). Pump as Table1. Comparison of theoretical method result with turbines: an unconventional solution to energy the other results. production, Urban Water pp 261-263.

5 Conclusions The theoretical method calculates the BEP of turbine mode of pump with considering the hydraulic and geometrical characteristics of pump and pump behavior in turbine mode. Primary with standard relations of pump and using of the other researcher results, the pump hydraulic parameter are obtained. Then the hydraulic parameters in turbine mode are calculated. This method has a little error and predicts the BEP of turbine mode of pump well. Table1 show that the theoretical method gives the good result. The other matter is that the most of methods assume that the efficiency of pump and turbine is equal. But in fact these efficiencies are not equal.