Optimal Design and Experimental Validation of a ...

Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis ESDA2012 July 2-4, 2012, Nantes, France

ESDA2012-82565 OPTIMAL DESIGN AND EXPERIMENTAL VALIDATION OF A TURGO MODEL HYDRO TURBINE John S. Anagnostopoulos School of Mechanical Engineering, National Technical University of Athens, Greece

Phoevos K. Koukouvinis Fotis G. Stamatelos Dimitris E. Papantonis School of Mechanical Engineering, National Technical University of Athens, Greece

ABSTRACT This work presents the development and application of a new optimal design methodology for Turgo impulse hydro turbines. The numerical modelling of the complex, unsteady, free surface flow evolved during the jet-runner interaction is carried out by a new Lagrangian particle method, which tracks a number of representative flow elements and accounts for the various hydraulic losses and pressure effects through special adjustable terms introduced in the particle motion equations. In this way, the simulation of a full periodic interval of the flow field in the runner is completed in negligible computer time compared to the corresponding needs of modern CFD software. Consequently, the numerical design optimization of runner geometry becomes feasible even in a personal computer and affordable by small and local manufacturers. The bucket shape of a 70 kW Turgo model is properly parameterized and numerically optimized using a stochastic optimization software to maximize the hydraulic efficiency of the runner. The optimal runner and the rest turbine parts are then manufactured and installed in the Lab for testing. Detailed performance measurements are conducted and the results show satisfactory agreement with the numerical predictions, thus validating the reliability and effectiveness of the new methodology. Keywords: Turgo impulse turbine; Particle simulation method; Bucket parameterization; Design optimization; Performance measurements

1. INTRODUCTION The Turgo impulse hydroturbine can be used in medium to high heads, from 15 to 300 m, and it was first patented in 1920. Its design and efficiency are remarkably improved during the next decades, rendering it capable of competing with the low-

head multi-jet Pelton or the high head Francis turbines [1]. Like Pelton, Turgo turbine has a flat efficiency curve and provides excellent part-load efficiencies hence it constitutes the best solution for large flow rate variations. An additional advantage of Turgo turbine is that it can operate for long periods and minimum wear when the water is laden with slit and other entrained matter. Also, larger jet and flow rates can be treated compared to a Pelton runner of same diameter. As a result, a Turgo turbine has higher specific speed and smaller size than a Pelton turbine for the same power. Finally, since the water jet enters one side of the runner and exits through the other, the interference of the outflow with the incoming jet can be minimal. In spite of the above advantages, Turgo turbines are much less spread than Pelton, mainly because the runner is more difficult to fabricate by local manufacturers: The buckets are complex in shape and more fragile than Pelton buckets [2]. Moreover, the hydraulic efficiency is more sensitive on the exact shape of the buckets surface than in Pelton. Therefore, implementation of computational fluid dynamics in the design of modern Turgo turbines appears to be necessary in order to improve their efficiency and cost-effective construction beyond the traditional design practices. Very few scientific articles can be found in the literature dealing with the design of Turgo runner, and only few companies manufacture this turbine type worldwide. An extended description is first given in Gibson [3], but without any information about dimensioning and design of the runner. Some details on the latter can be found in [4]. All published works on impulse hydroturbines concern the most common Pelton type turbine. However, the distribution system, the spear valve injector, and the impacting jet flow are common to both types. The importance of jet quality and its relationship with turbine efficiency has been thoroughly investigated in [5-7], and the results can be applied also to Turgo

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turbines. On the other hand, detailed measurements of the freesurface flow properties in the buckets are very difficult because of the contaminating effects of the water outflow. Thanks to the continuous increase of computing power and to the development of advanced simulation methods, complete analysis of the complex unsteady, free-surface flow developed during the jet-runner interaction in impulse turbines is possible, though several complex secondary flow mechanisms are still not modelled, and some inaccuracies associated with the turbulence modeling or the boundary conditions, cannot be avoided. Several such studies have been published, but only for Pelton runners. The volume-of-fluid method and the two-phase homogeneous or inhomogeneous models are implemented in various Eulerian solvers [8-11]. The traditional mesh-based Eulerian approaches face significant numerical diffusion problems due to the complex evolution of the free surface flow pattern. Mesh-less particle simulation approaches can be advantageous in such flows, due to the inherent free surface modelling. The Smoothed Particle Hydrodynamic appears to be the most promising such method, and a recent hybrid SPH-ALE approach [12] can help to overcome the main drawbacks of standard SPH related to stability and accuracy. The SPH method has also applied by the present authors in a first attempt for a CFD simulation of flow field in a Turgo runner [13, 14]. These computations can simulate the entire working cycle of the bucket, but the accuracy of the torque predictions is still not adequate, mainly due to the development of complex secondary flow mechanisms during the jet impingement and cut. Also, due to the unsteady nature of the flow field, the above solvers require large computational effort for a single solution. Hence, a complete design optimization of an impulse turbine runner, which may need thousands of flow evaluations, requires huge computing power and remains non-feasible for industrial design. This paper presents the formulation and application results of a new Fast Lagrangian Simulation (FLS) method, which is developed for the numerical design optimization of impulse turbine runners at minimal computer cost. The method has been recently used to study both Pelton and Turgo runners design [15, 16], and in the present work it is applied in order to design and manufacture a prototype Turgo model, which is then tested in the Lab.

angular location of the bucket (θo, Fig. 1). Calculations are then continued for the particles of oncoming frames, until all particles of a frame are blocked by the next coming buckets (jet cut).

Fig. 1. Initial distribution of representative flow particles.

The equations of motion of the fluid particles are solved in a rotating orthogonal system of reference, and are expressed as follows: d 2x  f x x, y  dt 2 d2y dz  f y  x, y    2 y  2  dt dt 2 2 d z dy  f z x, y    2 z  2  2 dt dt

(1)

where x, y and z are the Cartesian coordinates as defined in Fig. 1, ω is the angular rotation speed of the runner and fx, fy, and fz are functions of the local surface geometrical characteristics.

2. FLS MODEL FORMULATION 2.1. Flow modeling The numerical simulation of the fluid flow on the bucket surface is based on the Lagrangian approach, and the trajectories of an adequate number of representative fluid particles are tracked in order to produce statistically accurate results. The jet volume is divided into several consecutive segments or frames, and a number of particles are uniformly distributed over the circular area of each frame, as shown in Fig. 1. The jet-bucket interaction starts when at least one particle of a frame impinges on the inner bucket surface, at a certain

Fig. 2. Indicative fluid particle trajectories

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Calculation of a particle trajectory is divided into two parts (Fig. 2). At first, the standard particle equations without the ffunctions above are solved to reproduce the particles path in the free jet, and the algorithm checks only if the particle impinges on the next coming bucket in order to stop the integration. Otherwise, the tracking process continues until the particle encounters the inner bucket surface or passes by the bucket without impinging. A third option is also possible in some offdesign operating conditions, when a particle may hit on the hub or the shroud of the runner. The particle tracking after impacting on the bucket is performed by numerical integration of Eqs. (1), assuming that the particle slides along the inner 3-dimensional surface (Fig. 2) of known geometric characteristics (local depth and slopes). A second-order predictor-corrector scheme is adopted for the stepby-step calculation of the trajectory and the procedure is repeated until the particle flows out from the bucket. The above equations do not contain particle interaction or mechanical losses terms and hence they cannot reproduce the real flow picture in the bucket. For this reason, the FLS model introduces a number of additional terms in order to account for the hydraulic losses along the particle’s pathway, and for the free surface flow spreading rate in the bucket.

Flow spreading: In order to model the pressure effects on the surface flow evolution, each particle acquire at the impact point an artificial “spreading” velocity component perpendicular



to its impacting plane ( VS , Fig. 3), while its main velocity component is correspondingly reduced to preserve kinetic energy. The finally adopted scheme involves two more adjustable coefficients to compute the magnitude of the “spreading” velocity. The first quantifies the influence of the relative position of a particle in the jet (radial and angular location in respect to the jet axis). The second is introduced to account for a possible effect of the initial jet diameter (or the spear valve opening) on its spreading rate after the impact.

Friction losses: Assuming a constant mean friction coefficient, the kinetic energy of a particle reduces by a factor analogous to the square of particle velocity and to the sliding distance, hence the new particle velocity magnitude after a time step Δt becomes:



V p'  V p  1  C f  V p   t



(2) Fig. 3. Modeling of the flow spreading on the bucket surface

where Cf is a friction-loss adjustable coefficient. Impact losses: Additional kinetic energy losses take place due to abrupt change of particle momentum at its impact point. The kinetic energy losses are taken analogous to the square of the normal, to the surface, particle velocity component, and this gives:



V p '  V p  1  C i  cos 2  i



(3)

where Ci is the impact-loss adjustable coefficient and φi the angle between the particle impingement velocity and the unit vector normal to the surface at the impact point. Change direction: The progressive change of particle’s path direction (and momentum) as it slides along the curved bucket surface also causes minor energy losses, which can be modeled using a similar to the impact losses term:



V p '  V p  1  C p  cos 2 



The performance and reliability of the FLS model depend on the appropriate tuning of the values of the above coefficients and this task can be accomplished with the aid of experimental data or based on numerical results obtained by a more accurate CFD solver. A sufficiently small time step (2·10–5 sec) is used for the numerical integration of the particle motion equations in order to eliminate numerical error. A total number of the order of 103 trajectories was found adequate to produce independent results for the hydraulic efficiency of the runner, whereas for the reproduction of the surface flow pattern more than 104 trajectories were computed. Even in the latter case, the CPU time requirements are very small, just a few seconds in a modern personal computer.

2.2. Runner geometry and parameterization (4)

where Cp is the adjustable coefficient and Δφ the angular change in direction of the sliding particle during the time step Δt.

The mean velocity of the free jet emerging from the nozzle of the turbine is determined from the net head, by the equation:

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V jet    2 g H  0,97  2 g H

(5)

where the velocity coefficient  stands for the hydraulic losses in the spear valve, and it is usually between 0.95 and 0.99 [17]. The value of  =0.97 is taken for the present study. The corresponding jet diameter, Djet, can be obtained from the nominal flow rate: QK 

 4

 D 2jet  V jet

(6)

At the best efficiency point in impulse turbines the circumferential speed, u, of the runner is about half of the jet velocity. Hence the pitch diameter of the runner is (Fig. 4a): Ds 

60 u n

(7)

where n is the rotation speed in rpm. The runner has a conical shape in the meridian plane (Fig. 4a). The inlet bucket edge is a straight line and the inlet width is larger than the jet diameter (b1 ≈ 1,2Djet [4]), in order to secure the entrance of the entire jet even for the highest flow rate. The outlet edge of the bucket is drawn here with the aid of a Bezier curve. The bucket traces on the hub and the shroud, as well as an intermediate streamline are also generated using corresponding Bezier polynomials. Hence a number of Bezier control points are introduced as design parameters.

The average bucket inlet and outlet angles, β1 and β2, can be computed from the corresponding velocity triangles (Fig. 4b). At the best efficiency point the flow exits with almost zero circumferential velocity, hence the outlet velocity triangle is orthogonal and can also be constructed (Fig. 4b). However, due to rotation, the jet reaches a bucket at different locations: Initially closer to the hub and then progressively towards the shroud. Consequently, the velocity triangles defined in Fig. 4b are not representative of the whole jet-bucket interaction. For this reason, additional design parameters are introduced to allow for differentiation of the inlet and outlet bucket angles along the leading and trailing edges of the bucket. Also, the curvature of these lines can be varied. The above make a total of 12 geometric control variables for parametric description of the bucket geometry. The mean 3-dimensional surface of the bucket is then generated using the conformal mapping methodology and interpolation techniques. An example of the resulting shape is shown in Fig. 5. The above parameterization method ensures always a smooth curvature variation of the surface. The inner and outer surfaces of the bucket can be constructed considering a given bucket thickness distribution. Finally, the hub and the shroud are easily introduced as axisymmetric surfaces, and the entire runner can be reproduced as shown in Fig. 6.

ω Ds

(a) b1

Fig. 5. Indicative view of mean bucket surface.

B

70-80 o

c1=c β1

w1 β1

u1

u

(b)

β2

w2 β2

c2 u2

.

Fig. 4. Turgo runner configuration: a) Meridian plane; (b) Velocity triangles.

Fig. 6. Turgo runner drawn by the present method.

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2.3. Monitoring and post processing the results The FLS model includes post-processing of the results in order to compute the turbine performance variables, such as the developed torque on the buckets and the hydraulic efficiency of the runner. Also, it can calculate the local forces exerted on the bucket due to the change of fluid particles momentum, and hence to assess the local contributions to the energy conversion. Snapshots of the flow pattern at any time instant can be easily obtained, and can be used to produce animation in graphics software at very low computer cost. Indicative such flow pictures are illustrated in Fig. 7. The free-surface flow on a bucket starts, evolves and terminates within about 110-120 degrees of runner rotation. Soon after its impact on the reference bucket (Fig. 7a), the jet starts to interact with the next coming bucket too (not shown in Fig. 7), which eventually cuts the jet (Fig. 7c). A noteworthy behavior that can be observed is that the flow leaves the bucket from quite different regions during the interaction period (Figs. 7b,c,d), because of the bucket displacement due to rotation. Therefore, the correct design of the entire trailing edge line is decisive in order to minimize the kinetic energy of the outflow and thus to achieve high hydraulic efficiency.

(b) (a)

The mechanical torque developed on the runner is computed from the following equation of conservation of angular momentum:



M run   Qu rin win  rout wout

(c)

(8)

where Qu is the cumulative flow rate that enters each bucket and w the absolute tangential velocity component at corresponding radial distance r. Subscripts in and out denote the time instants when a particle impinges on or leaves the bucket, respectively (Fig. 2). The mean angular momentum at the inlet, assuming a uniform jet velocity Vjet, becomes:

rin win  Rrun V jet  cos 

(9)

where Rrun is the runner pitch radius and θ the jet angle relative to the runner disk (Fig. 4b). The mean angular momentum at the bucket outlet is computed by averaging the local fluid particle properties monitored there:

rout wout 

1 N

 ri wi

(10)

i

where ri and wi are the radial distance and the absolute tangential velocity component of a particle i at the moment it flows out from the bucket, and N is the total number of fluid particles that interact with a single bucket. The hydraulic efficiency of the runner can then be obtained as the ratio of the developed mechanical power divided by the corresponding net hydraulic power at the inlet:

h 

(d)



 run   run    g Q H jet  g Q  2 H

 

(11)

where Hjet and H are the hydraulic head of the discharged jet and the net head of the flow at the injector inlet, respectively, and Q is the nozzle flow rate. It must be noted that the runner flow rate Qu in Eq. (8) may be less than Q in Eq. (11) for certain offdesign operating conditions, when some particles do not impinge in the buckets.

2.4. Adjustment of model coefficients

Fig. 7. Selected flow pictures: a) start of jet-bucket interaction; b) full jet impingement; c) jet cut and end of impingement; d) evacuation phase.

The values of the FLS model coefficients included in Eqs. (1) have been previously regulated with the aid of experimental data taken from an 80 kW laboratory Pelton turbine model [15]. In order to check their validity for the Turgo runner geometry, the FLS solution is compared with the results of a more accurate but much more expensive CFD simulation software, which is based on the Smoothed Particle Hydrodynamic method [13, 14] (Fig. 8).

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The comparison showed certain differences, mainly concerning the spreading rate of the surface flow in the bucket. Hence, after several comparative flow evaluations the FLS model coefficients are properly re-adjusted to achieve the best possible agreement. The final results are substantially improved, as shown in the indicative views of Fig. 9, at two bucket angular positions after start of jet-bucket interaction (Δθ, in Fig. 1)

with the aid of literature data [3, 4] and by present calculations, and are given in Fig. 10. The main design and operation data are tabulated in Table 1.

Fig. 10. Dimensions of the model runner.

Table 1. Main Turgo model characteristics.

Net head Number of injectors Nominal flow (per nozzle) Nominal Power (per nozzle) Rotation speed Jet diameter (nominal) Jet angle Pitch diameter

Fig. 8. Indicative picture of the jet-runner interaction simulated by the SPH model.

48 mWG 2 0,09 m3/sec ~35,4 kW 1000 rpm 62 mm 25 deg 285 mm

+36o

3.2. Runner geometry and design optimization FLS

SPH

+72o

Fig. 9. Comparison of free surface flow evolution results of the FLS and the SPH models.

3. MODEL APPLICATION AND VALIDATION 3.1. Turgo model specifications In order to validate the developed simulation methodology and assess its capability to be used for Turgo turbines design, a 70 kW model turbine is designed, manufactured and tested in the Laboratory. The main dimensions of the runner are obtained

A general stochastic optimization software, developed and brought to market by the Lab of Thermal Turbomachinery NTUA [18], is used in the present work to find the runner design that achieves maximum hydraulic efficiency. The optimizer is based on evolutionary algorithms and it is suitable for complex non-linear and multi-parametric problems, as the shape optimization of complex 3D surfaces. The algorithm selects values of the free design parameters within the prescribed ranges and looks automatically for the set that maximizes the cost function (here the hydraulic efficiency of the runner) using populations of candidate solutions. The passage from a population to the next one that contains improved solutions mimics the biological evolution of species generations [19]. The fast flow evaluation achieved by the FLS model allows for using wide variation limits for all design variables. As a result, much different shapes are created and numerically solved during the optimization procedure, as the examples of Fig. 11. Due to the stochastic nature of the operation there is no strict convergence criterion; the procedure is terminated when the efficiency does not increase further within a predetermined number of consecutive evaluations.

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Fig. 11. Various bucket shapes tested during optimization.

A typical convergence curve is given in Fig. 12. The multiparametric optimization requires several hundred evaluations (flow field simulations) for convergence, but with the FLS solver the whole procedure can be completed in only a couple of hours in a modern PC.

and nozzles are increased by about 30%, in order to be able to measure the effect of larger jet diameters on the same runner. A plexiglass window is opened at the front cover of the casing to permit visual observation of the runner outflow (Fig. 15). The new model is installed in one of the test rigs of the Laboratory of Hydraulic Turbomachines, NTUA, after proper adjustments. A simplified sketch of the rig is given in Fig. 16. The characteristics of the main devices used for testing are the following: — Three-stage centrifugal pump, driven by a 220 kW AC motor. The pump’s rotational speed can be adjusted through the hydraulic transmission. At the BEP the pump rotates at 1800 rpm, providing 320 m3/h flow rate and 117 mWG net head. — 110kW DC generator, controlled by either rotational speed or torque. The turbine net head is adjusted by regulating the pump speed, while the water flow rate is manually regulated from the spear valves by precision screw. The turbine rotational speed can be adjusted through the DC generator, so it is possible to test the turbine for a wide range of operating conditions.

3.3. Model construction and installation The optimally designed runner of the Turgo model is constructed by separate fabrication of its parts. The hub and shroud are made by precision machining, and proper slots are opened on the hub surface to accommodate the buckets (Fig. 13a). A prototype bucket of composite material is constructed at first by 3D-printing, and it is then used to produce aluminium prototype. The runner buckets are fabricated by bronze casting and finally assembled with bronze welding (Fig. 13b). This procedure enhances the axial symmetry of the runner and ensures that all buckets are identical.

Fig. 13. Turgo model runner: a) buckets assembly; b) finished.

Overall efficiency, η (%)

0.9 0.88 0.86

Fig. 14. Indicative spear valve drawing.

0.84 0.82 0.8 1

10 100 Number of evaluations

1000

Fig. 12. Convergence history of the design optimization procedure.

Detailed engineering drawings of all turbine model parts are created in CAD environment (Fig. 14). The spear valve and nozzle angles are optimally selected based on the results of CFD simulations in the injector. The final dimensions of the injectors

The performance data of the turbine model are obtained in the form of characteristic operation curves of net head, shaft power and overall efficiency, as function of the flow rate and rotation speed. The corresponding physical quantities were measured with the following instrumentation: 1) The Rotational Speed of the turbine by an electronic pulse meter with measurement error ±0.25 %. 2) The Flow Rate, Q, by an electromagnetic flow-meter, which was calibrated by the volumetric tank (100 m3) of the test stand, with relative uncertainty ±0.5%.

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3) The Relative Static Pressure of the water right before the injectors, using a differential pressure transducer (0-20 bar), with relative uncertainty ±0.25%. 4) The Torque, M, developed at the shaft between the turbine and the brake, by a torque transducer with strain gage sensing and maximum experimental error ±0.5%. The Laboratory test rig and the measuring procedure comply with the IEC model test standards. Prior to the experiments all measuring instruments were calibrated according to their manuals.

Fig. 15. Completed Turgo model installed in the Laboratory.

where M, Q, H and ω are the four quantities measured. Complete sets of experiments are performed in almost the entire turbine operating range that is feasible in this test rig, and with the upper, the lower or both injectors in operation.

3.5. Results and comparison The operation of the Turgo model with the upper or the lower nozzle is generally similar, verifying the good quality and precision of the model manufacturing. The characteristic operation curves of the overall efficiency are obtained for 15 consecutive opening positions of the nozzles (Fig. 17). Each such curve is constructed by varying the rotation speed of the feeding pump and/or the turbine runner. The flow rate results are presented as function of the dimensionless flow rate parameter Φ, defined as: Q (13)  3  Rrun  and they are converted for comparison to the design speed of the runner. The spear valve opening fraction, α, is defined as the distance Δx of the needle from the close valve position, divided by the nozzle exit diameter. The pattern of the efficiency characteristic curves for both injectors (Fig. 17) is in agreement with the theoretical performance of impulse hydro turbines: For a given injector opening there is an optimum flow rate that maximizes the efficiency. At that point, the remaining angular momentum of the runner outflow becomes minimum, as confirmed by visual observation. The efficiency results like the ones given in Fig. 17 show that the new Turgo turbine model is capable to attain high efficiencies for this size, up to 86%, and at a wide range of load conditions either with a single or with both injectors. In all cases the envelope curve is quite flat, and the maximum efficiency is attained for an intermediate spear valve opening. 1.0

Fig. 16. Sketch of the laboratory test rig of Turgo model.

0.9 0.8

 exp 

  gQH

Turbine Overall Efficiency

The LabView 8.6® graphical programming software is implemented for the data acquisition of the analog signals and their conversion into digital. The developed graphical environment allows for continuous monitoring of the pump and turbine operating conditions, and for real time evaluation of a measured value, in respect to the turbine performance characteristic curves. The experimental data for the overall turbine efficiency are obtained from the relation:

0.7 0.6 0.5 0.4 Spear Opening,  0.246 0.369 0.492 0.738 0.923

0.3 0.2 0.1 0.0 0.04

(12)

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Flow Rate Parameter

Fig. 17. Measurements of overall turbine efficiency with the lower (red) and the upper (blue) injector in operation.

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Using the developed data base of the experimental results, complete hill charts of the turbine performance can be constructed, as shown in Fig. 18. These charts confirm that the best efficiency region of the turbine includes the design point for which it is numerically optimized (324 m3/h, 48 mWG). Also, the efficiency remains high for large flow rate variations, while it is much more sensitive in head variations, like in a typical impulse turbine.

Fig. 18. Efficiency hillchart of the Turgo model operating with the upper injector.

The hydraulic and mechanical losses of the runner cannot be directly measured. Consequently, in order to compare the FLS model output with the measurements, the hydraulic efficiency, ηh, of Eq. (11) is converted to overall efficiency by the relation:





  h  2 m

(14)

where ηm is the mechanical efficiency of the runner (shaft bearings and ventilation losses), estimated to 97% for all operating points. 90

Total efficiency (%)

80 70 60 Lines = Numerical Symbols = Measur.

50

α = 0.125 α = 0.246 α = 0.431 α = 0.615 α = 0.923

40 30 0

0.04

0.08

0.12

0.16

Flow rate parameter, Φ

0.2

Fig. 19. Comparison between measured and predicted turbine model performance.

The numerical results are compared with the measurements of lower and of upper injectors for various nozzle openings in Fig. 19. The agreement is quite good almost in the entire loading range of the turbine, and in most operating points the observed discrepancies are up to 2-3%. The differences become more significant for the smallest opening (α=0.12, Fig. 11), which corresponds to load about 50% of the nominal. This deviation can be attributed to the assumption of constant mechanical efficiency degree (97%), instead of constant absolute value of mechanical losses, which would be more correct for the same rotation speed. In that case, the percentage portion of mechanical losses in respect of the shaft power will be double at 50% load hence the predicted total efficiency would be lower and closer to the measurements. On the other hand, the maximum attainable efficiency reduces as the nozzle opening and the jet diameter increase significantly above the nominal values (Fig. 19). In this case, part of the oversized jet flow start to impinge on the hub and shroud of the runner, and this is also reproduced in the numerical simulation results.

4. CONCLUSIONS The formulation and capabilities of a numerical methodology developed for flow analysis and design improvement of impulse hydraulic turbines are presented and demonstrated in this work. The major advantage of the new Fast Lagrangian Simulation (FLS) algorithm is its fast performance and minimal computer requirements. This permits its application for multi-parametric and multi-objective design optimization of the runner geometry, which requires numerous evaluations of the complex, unsteady flow filed developed during the jet-buckets interaction. Parametric and sensitivity analysis of turbine operation or design parameters can be also easily performed. Moreover, the FLS model provides the capability to take into account in an inclusive way the effects of various instabilities and other complex secondary mechanisms evolved during the jet-bucket interaction, which are difficult or even impossible to be modeled by other simulation approaches. The main drawback is that the model contains a number of adjustable coefficients, which must be tuned with the aid of more accurate data, experimental or numerical. However, the present application showed that the appropriate values of those coefficients are similar for different impulse turbines (Pelton and Turgo), as also that after their regulation the model can predict with remarkable reliability the turbine performance in a broad operation range. The application of the new model for the optimal design of the runner of a new Turgo model turbine was successful, and the achieved performance and efficiency of the prototype in the Laboratory is found to be quite close to the predictions. A more elaborate design would require more detailed and accurate modeling, and for this reason further development of

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the FLS model aiming to improve the expressions of the additional terms is currently under way.

ACKNOWLEDGMENTS This work was carried out in the frame of HYDROACTION Project funded by the European Union (FP7-ENERGY-007-1RTD, Project number 211983).

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