This paper addresses the design, modeling, and performance analysis of a Pelton turbine using CFD for one of the selected micro hydro potential sites in Ethiopia to meet the requirements of the energy demands. The site has a net head of 47.5 m and flow rate of 0.14 m^{3}/s. The design process starts with the design of initial dimensions for the runner based on different literatures and directed towards the modeling of bucket using CATIA V5. The performance of the runner has been analyzed in ANSYS CFX (CFD) under given loading conditions of the turbine. Consequently, the present study has also the ambition to reduce the size of the runner to have a cost effective runner design. The case study described in this paper provides an example of how the size of turbine can affect the efficiency of the turbine. These were discussed in detail which helps in understanding of the underlying fluid dynamic design problem as an aid for improving the efficiency and lowering the manufacturing cost for future study. The result showed that the model is highly dependent on the size and this was verified and discussed properly using flow visualization of the computed flow field and published result.
Despite the fact that many rural communities have good access to plenty of water resources, the most serious problem faced by a country like Ethiopia is that of rural electrification. One of the most important and achievable methods to produce electricity is to introduce a standalone electric power generation, using renewable resources. Rural Electrification Fund (REF), which is operating under the Ministry of Water, Irrigation and Energy (MWIE), is working to control the energy crisis in the country [
Figure
Distribution of MHP potential sites in Ethiopia [
Depending on water flow and design, Pelton wheels operate best with heads from 15 meters to 1,800 meters, although there is no theoretical limit. In this turbine, water is brought down through the penstock pipe to a nozzle, and it comes out into the turbine casing. The jet is then directed at a wheel, or runner, which has a number of buckets around its edge. The force of the jet on this wheel makes it turn and gives the output power [
More precisely, in the new context where harvesting small hydro potentials can become economically viable, there is also a need to provide solutions to reduce the design cycle time and cost for Pelton runners. It is known that, with increasing demand, the performance analysis of turbine such as efficiency and dynamic behavior is also an important aspect to analyze its suitability under different operating conditions [
The main topic of investigations by the CFD method has focused on the interactions between the jet and the rotating buckets as well as the relative flows within the buckets. These are flows that are so far not easily accessible by experimental measurements [
As explained by Zhang [
So far, few investigators have only reported diverse values of maximum efficiencies as shown in Table
Some Pelton turbine studies and maximum efficiency levels attained.
Investigators  Net head (m)  Flow rate (m^{3}/sec)  Runner speed (rpm)  PCD (mm)  Maximum efficiency, % 

Panthee et al. [ 
53.9  0.05  600  400  82.5 
Panagiotopoulos et al. [ 
100  135% of BEP  1000  400  86.7 
Solemslie and Dahlhaug [ 
70  —  —  513  77.75 
Pudasaini et al. [ 
80.85  0.09218  600  490  87.71 
Due to the natural limitations concerning publication of results concerning turbines from commercial companies, one of the goals of this research paper has been to design and simulate using a Pelton turbine and compare the obtained result with the reference from Table
After surveying different villages in the SouthWest District of Ethiopia, we narrowed our choices down to one: Melkey Herra Village. It is a rural community, Keble, roughly 149 kilometers from Addis Ababa, and is well renowned for tourism. Its geographical coordinates are 08° 51′ 40′′ North and 37° 45′ 10′′ East which does not have the access to electricity. The selected water resource for hydroelectric generation is “Indris River” for the communities living in the village called “Melkey Herra” [
Proposed site data for MHP development [
Region  Zone  Wereda  Kebel  River name  Head (m)  Flow rate (L/s) 

Oromia  W/showa  Tokikutay  Melkey Hera  Indris  >50  140 
To start the initial design, calculations will be conducted to size turbine parts. The theory behind these is mainly taken from the “Micro Hydro Pelton Turbine Manual, by Thake [
The net head at the nozzle exits can be expressed by the following formula [
For the proposed site data head, 50 m, and flow rate, 140 liter/sec combination (from Table
Application ranges for different types of turbine [
The pressure at the bottom of the penstock creates a jet of water with velocity,
Combining (
Figure
Diagram of a Pelton runner showing PCD [
Beginning with the derived formula to determine the turbine speed which can be expressed as
A spreadsheet is prepared as shown in Table
Calculation summary to determine the turbine speed
Name  Symbol  Unit  Value  

Number of jets 

—  1 

3  4 
Jet diameter 

mm 


44.4  38.5 
Runner PCD  PCD  m 


403.953  349.834 
Available PCD  PCD  mm 


425  350 
Turbine speed 

rpm 


611  742 
Gear ratio 

— 


2.45  2.02 
From Table
Pelton turbine parts’ assumed efficiency [
Part  Symbol  Assumed efficiency 

Penstock 

0.95 
Manifold 

0.98 
Nozzle 

0.94 
Runner 

0.8 
Drive 

1 
Generator 

0.8 


Overall efficiency 


The equations used to determine the different design parameters of wheel are collected in Table
Basic design calculation summary of Pelton turbine.
Descriptions  Data  Unit  Design guidelines Thake 2000 [ 


46.5  mm 


0.97  —  Ranges (between 0.95–0.99). 

29.6  m/s  Velocity of the jet (for 

54.4  mm  Diameter of the jet (for 

0.46  —  For maximum power output (blade speed/ 
Bucket speed  13.6  m/s 


1500  Rpm  Standard generator RPM 

1170  Rpm  Runaway speed = 1.8, turbine optimum speed 

0.56  Total system efficiency  

36.57  kW  Estimated electrical power = 

51.2  kW  Turbine mechanical power = 
Figure
Physical baseline bucket dimensions result for the selected site data.
Parameters, formula [ 
Calculation  Dimensions/result  Unit 

Height of bucket, 

170  mm 
Cavity length: 

28  mm 
Length to impact point: 

57  mm 
Width of bucket opening, 

56  mm 
Bucket thickness: 

1  mm 
Approximate number of buckets, 

18  
Depth of the bucket, 

60.5  mm 
Width of the bucket, 

190  mm 
A scalable Pelton bucket. All dimensions are in % of PCD [
A basic stem for machining, used for bolting or clamping the buckets to the hub, is shown in Figure
A basic bucket stem design for bolted fixing. All dimensions are in % PCD [
From all the above calculated parameters in Table
Solid model of Pelton turbine for the selected site data, (a) bucket and (b) 3D view of the runner right.
The basic bucket model was adapted to form an entire bucket by the use of patterning. Twodisc plate was used to mount the buckets circularly as shown in Figure
For the selected Melkey Herra’s micro hydro power site, Pelton turbine was the most suitable hence chosen for our numerical performance analysis. The main dimensions of the turbine examined here correspond to this ideal plant. The numerical techniques created during this section included many numerical and physical assumptions to simplify the problem. This was necessary because accurate modeling of impulse turbines (Pelton in this case) that include complex phenomena like free surface flow, multifluid interaction, rotating frame of reference, and unsteady time dependent flow is a challenge from a computational cost point of view [
The computational domain was created removing the features that were assumed to have no or minor effect when comparing the runner designs as follows. The following are some of the simplifying assumptions made in the analysis.
Table
Turbine geometry and setup values for prototype and model.
Parameters  Symbol  Unit  Prototypes’ values  Selected model operating condition 

Flow rate 

Lts/s  140  20.84278 
Head 

m  47.5  13.34275 
PCD 

mm  500  265 
Bucket width 

mm  190 

Power 

KW  51.2  2.14 
Number of buckets 



Figure
Domain geometries: stationary (a) and assembly of the rotating and stationary domain (b).
Imagine that the rotating domain in Figure
Figure
Meshed rotating (a) and stationary domain (b) sizing and inflations were applied.
In this section, the essentials of the ANSYS Pre setup are presented.
Boundaries applied on the domains.
Expressions defined in ANSYS Pre for the baseline design [
Name  Expression  Description 

Gravity  9.82 [ms^{−2}]  Acceleration due to gravity 
Head  13.34 [m]  Model head based on scaling 
Turbine radius  132.5 [mm]  Model turbine radius based on scaling 
Inlet velocity  (2 × gravity × head)^{0.5} [m/s]  Water velocity at the nozzle inlet 
Omega  Inlet velocity/(2 × turbine radius) [rad/s]  Angular velocity: rotation in the negative direction is selected 
Torque middle bucket wall 

The entire middle bucket is selected 
Total time 

Total simulation running time 
In general rule, a small runner is cheaper to manufacture than the larger one. It takes less material to cast it and the housing and associated components also can be smaller. For this reason, consequences of reducing PCD (=400 mm) from the baseline design (PCD = 500 mm) are evaluated and results are compared with those published by Panthee et al. [
Next, a visualization of the flow in the turbine buckets for this study can be seen in Figure
Flow visualization of the baseline design, side views, and face views (PCD = 500 mm).
As seen in Figures
Flow distribution of the runner: water velocity in Stn frame, side views, and face views (PCD = 500 mm).
It can be observed on Figure
Pressure contours on the bucket (PCD = 500 mm).
As seen in Figure
Flow distribution of the runner: water velocity in Stn frame, side views, and face views (PCD = 400 mm).
The water is unevenly distributed across the buckets and there are several local accumulations of cells with a high volume fraction of water, most visible in the bottom bucket in Figure
Volume fraction of water for reference bucket design at a particular time step (PCD = 400 mm).
Looking at Figures
The pressure distribution in the bucket was due to impact of high jet. This pressure distribution applied on the bucket again varies with the time due to the rotation of the runner. It was found that the pressure peaks are obtained at bucket tip and PCD of the runner. The pressure peak in bucket tip is due to flow disturbance when jet strikes bucket tip. It is obvious to obtain the pressure peak at the runner PCD since the Pelton runners are designed such that it would convert most of the hydraulic energy to mechanical energy when the jet strikes the runner PCD. Result showed high pressure with the value of 3.559 × 10^{4} Pa for the first top and the second middle bucket at some degree of rotation of the runner as shown in Figure
Pressure distribution at some degree of rotation of reference bucket design (PCD = 400 mm).
The images in Figure
The hydrodynamic torque and the hydraulic efficiency of the runner are computed after completing the evaluation of a jetbucket interaction flow, starting from the moment of impingement (jet cut in) until the evacuation of the bucket (jet cutout) [
Torque generated by middle bucket versus time.
At the start (cut in) a countertorque can also be observed caused by the interaction of the jet with the back surface of the bucket; this value is larger for PCD = 400 mm comparing to the baseline design (Figure
Next, the total curves of the complex unsteady flow in the bucket for the seven buckets analyzed can be acquired with the aid of time history views like the ones in Figures
Dynamic runner and bucket torque over time for (PCD = 500 mm).
Dynamic runner and bucket torque over time for (PCD = 400 mm).
To calculate the efficiency, power input has to be calculated as well which for a complete turbine is calculated using two variables describing the flow conditions: the net pressure head and the flow rate [
The next validation phase is to compare efficiency of this model to the published results by Panthee et al. [
Mesh or grid independent study is done in order to get a solution that does not vary significantly even when we refine our mesh further. Eight different mesh sizes were tested with an effective head of 47.5 m for two different cases. The mesh size on the rotating domain is controlled by element size. The relevance was increased for finer mesh. Afterwards, the orthogonal quality of the mesh has been checked and it was in an acceptable range (0.15–1.00) for each mesh developed. Each mesh was also created with the same physical setup and boundary conditions. During the simulations, results obtained were directly dependent on the accuracy in quality of mesh. And it was performed while analyzing the torque variation by developing the SST turbulence model.
Tables
Mesh dependent test analyzed for PCD = 500 mm.
Mesh type  M1  M2  M3  M4  M5  M6  M7  M8 

Total number, elements  294952  520687  2011665  2239650  2398044  2861243  3955723  5050204 
Calculated total torque (Nm)  −30.93  −32.20  −34.32  −34.50  −34.69  −34.92  −35.02  −35.25 
Standard torque (Nm)  −35.06  −35.06  −35.06  −35.06  −35.06  −35.06  −35.06  −35.06 
Torque error percent (%)  11.8  8.2  2.1  1.6  1.1  0.4  0.1  0.5 
Mesh dependent test analyzed for PCD = 400 mm.
Mesh type  M1  M2  M3  M4  M5  M6  M7  M8 

Total number, Elements 








Calculated total torque (Nm) 








Standard torque (Nm) 








Torque error percent (%) 








The standard torque was calculated with the power obtained from power coefficient and the angular velocity of runner for comparison. One can observe that, from the result in Tables
Total torque variations for different mesh sizes for PCD = 500 mm.
Total torque variations for different mesh sizes for PCD = 400 mm.
Table
Validation and performance prediction of Pelton runner.
Parameters  Unit  Baseline design test cases  Off design test cases  Published result by Panthee et al. [ 
Published result by Panagiotopoulos et al. [  

Head  m  47.5  53.9  100  47.5  53.9  100  53.9  100 
Flow rate  m^{3}/s  0.14  0.05  135% BEP  0.14  0.05  135% BEP  0.05  135% BEP 
PCD  mm  500  500  500  400  400  400  400  400 
Runner speed  Rpm  520  520  520  650  600  1000  600  1000 
Number of buckets  —  18  18  18  18  22  22  22  22 
Model efficiency  %  78.8  83.5  84.6  62.6  66.1  71.6  82.5  86.7 
The computational analysis results presented in Table
The nextgeneration turbine designs for smallscale hydropower systems seek higher efficiency and low manufacturing costs. The (size of Pelton turbine) PCD is an important parameter to lower the manufacturing cost of a Pelton turbine runner. However, no consistent guidance based on numerical research data is available in the public domain. This study provides a guideline for selecting, designing, modeling, and performance analysis of a micro hydro Pelton turbine and provides an example of how the size of turbine (PCD) can affect the efficiency of the turbine.
The paper describes also the methods used for CFD analysis of scaled model Pelton turbine which is ideally designed for Melkey Herra Village hydropower plant using ANSYS CFX software. The bucket model was designed according to the baseline design or calculated parameters. The time and cost in CFD analysis of Pelton turbine are also reduced by selecting 3 buckets to predict the flow behavior of complete turbine. One of the objectives was to understand how the turbine performance will change when the flow field is perturbed by reducing the size of turbine for a given operating condition (i.e., flow rate and head). Results obtained from the baseline design (PCD = 500 mm) have been successfully compared to that of the reduced size (PCD = 400 mm) of the turbine. The results of the two turbine designs at the design flow rate and head of turbine are as follows: one turbine (PCD = 400 mm) has a maximum efficiency of 62.6% and the baseline design turbine (PCD = 500 mm) has a maximum efficiency of 78.8%. The flow visualization study of this research provides insights into the reasons for efficiency as well as guidance for improving the efficiency. The low efficiency in the reduced size of the turbine is mainly caused by a large amount of water leaving the bucket through the lip and hence transferring close to zero of its energy to the shaft. The problem was therefore the choice of the runner PCD that could give the best advantages in terms of efficiency on the whole plant’s operational field. For the purpose of validation and performance characterization, two Pelton turbines reported in the literature were considered. The first turbine has PCD = 400 mm, a maximum efficiency of 82.5%, which was studied by Panthee et al., 2014, for Khimti Hydropower in Nepal [
The design optimization, production, and experimental testing of a model runner based on this design may also be realized in the next part of this paper. Based on the result obtained, this study planned a modification on the baseline design and will consist of the following new designs being tested:
Changing the length, depth, angular position (Jetbucket interaction), and number of the buckets while keeping all other parameters constant
Altering the surface close to the lip and redefining the shape of the lip curve to reduce the leakage
Based on the results presented in this study, there are opportunities for improving the maximum efficiency as well as reducing manufacturing cost of Pelton turbines, if the design is prescribed using the above criteria, followed by highfidelity computational simulations. It would then no longer be necessary to start the design and numerical simulation each time from scratch.
A natural extension of this paper would be also to validate the model for other selected sites. Achieving such a goal would be a great step towards improving the understanding of the micro hydro power development and making tools for validating CFD results, so that the benefits of this technology can be brought to rural populations.
Computational fluid dynamics
CFD code by ANSYS
Shear stress transport
Volume of fluid
Micro hydro power
Micro hydro turbine
Ministry of Water, Irrigation and Energy
Best efficiency point.
The authors declare that they have no conflicts of interest.
This paper was funded by Ministry of Water, Irrigation and Energy. The authors would like to thank Ministry of Water, Irrigation and Energy Office for the fund and for all information and data provided to accomplish the research work.