Deliverable D.6.5: Final Public Report€¦ · 3 Water turbines Water (hydro) turbines transform...

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ACCUSIM_Final_Public_Report_D.6.5_v01.doc of 39

This project has received funding from the European

Union’s Seventh Framework Programme for research,

technological development and demonstration under

grant agreement no 612279

Accurate Simulations in Hydro-Machinery

and Marine Propellers (ACCUSIM)

Deliverable D.6.5: Final Public Report

Document identifier: ACCUSIM_Final_Public_Report_D.6.5_v01.doc Preparation date: 30/01/2018

Version: 01 State: Final

Distribution: Public Issued : Dragica Jošt

Verified : Aljaž Škerlavaj Approved : Enrico Nobile

Call Identifier: FP7-PEOPLE-2013-IAPP Call Theme: Industry-Academia Partnerships and Pathways (IAPP)

Contract start date: 01/02/2014 Duration: 48 months

Project coordinator: Kolektor Turboinštitut Participating partner: University of Trieste

Project website: www.accusim.eu

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Document History Version Date Amended by Changes

01 30/01/2018 Dragica Jošt Document creation

Contributors

Both partners contributed and agreed with the content of this deliverable, which is the property of

the ACCUSIM consortium.

This document may be copied and reproduced. It may not be modified neither whole nor partially for

any purpose without written permission from the ACCUSIM project coordinator with acceptance of

the Project Consortium.

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Executive Summary

The report consists of two parts. Part 1 is a general purpose report, meant for general public interested in renewable energy sources and in particular in water turbines and numerical (computer) simulations. It comprises some basics about numerical simulations of flow in different types of water turbines. Part 2 is meant for a more professional public. It comprises a short overview of results achieved

during the ACCUSIM project. In this part the improvement of efficiency prediction with advanced

(scale resolving) turbulence models, the prediction of different forms of cavitation and finally design

optimization are presented in more detail. A comparison of results obtained with commercial code

ANSYS CFX and the open-source code OpenFOAM is also presented. At the end the references are

provided, where the reader can find more information about numerical simulations and accuracy of

results.

Note

In the email correspondence (13/03/2017) with Project Officer Olivier Delaunoy it was accepted that this deliverable can be created in month 48 instead of in month 40 of the project.

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Table of Contents

Part 1: Numerical Simulations of Flow in Different Types of Water Turbines

1 Introduction ..................................................................................................................................... 7

2 Numerical flow simulations ............................................................................................................. 8

3 Water turbines .............................................................................................................................. 10

3.1 Francis turbines ..................................................................................................................... 10

3.2 Axial Turbines ........................................................................................................................ 13

3.3 Pelton turbines ...................................................................................................................... 16

Part 2: Some of the Results Achieved during the ACCUSIM Project

1 Introduction ................................................................................................................................... 21

2 Scale resolving turbulence modelling ........................................................................................... 22

3 Cavitation ...................................................................................................................................... 26

3.1 Calibration of mass transfer models for the numerical prediction of sheet cavitation around

a hydrofoil ......................................................................................................................................... 26

3.2 Cavitation in water turbines .................................................................................................. 26

3.2.1. Cavitation in Francis turbines ........................................................................................ 27

3.2.2. Cavitation in Kaplan turbines ........................................................................................ 28

3.2.3. Cavitation in a prototype of a bulb turbine ................................................................... 29

3.2.4. Cavitation in Pelton turbines ......................................................................................... 29

3.3 Sheet and cloud cavitation prediction in double suction centrifugal pump ......................... 30

3.4 Numerical predictions of the cavitating flow around model scale propellers working in

uniform and non-uniform inflow ...................................................................................................... 32

4 Comparison of results obtained with OpenFOAM and ANSYS-CFX .............................................. 33

5 Optimization .................................................................................................................................. 34

5.1 Optimization of a double-sided centrifugal pump ................................................................ 34

5.2 Multi-objective optimization of the Francis turbine runner cone ........................................ 36

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Abbreviations

CFD Computational Fluid Dynamics

mF modeFRONTIER© (optimization software)

KTI Kolektor Turboinštitut

UniTS University of Trieste

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Part 1

Numerical Simulations of Flow in Different Types of Water Turbines

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1 Introduction

A growing world population, striving for a better quality of life, is demanding access to reliable, low-

cost electricity supply. Global demand for electricity is increasing from 3% to 6% annually on average

in different parts of the world. Around 20% of the world’s electricity is produced by hydropower. In

Europe and around the world, the present development of intermittent renewable energy sources,

such as wind and solar energies, nowadays increases the need for energy storage. Pump Storage

Power plants are the cheapest solution for large scale energy storage, and have, at present, a global

efficiency much higher than other solutions for energy storage. Therefore development of hydro

machines with high efficiency and good cavitation and dynamic characteristics is of paramount

significance.

CFD (Computational Fluid Dynamics) has been a useful tool in design of all turbine parts for thirty

years. Numerical analysis of flow in water turbines and pumps is not only important because it

enables to reduce expensive and time consuming model tests, but also because it gives the insight

into the flow details in all turbine parts. On the basis of numerical results it is easier to find the

reasons for low efficiency or for cavitation and to improve the hydraulic shapes of all turbine parts.

Furthermore, for small projects the model tests are too expensive and CFD analysis is the only way to

foresee whether the required efficiency and cavitation characteristics on the prototype will be

obtained.

In the last fifteen years a large progress in numerical simulation of flow in water turbines has been

achieved. Nowadays the possibility of simultaneous calculation of flow in rotating and non-rotating

turbine parts and development of more powerful computing platforms, enable coupled analysis of

the whole turbine in a reasonable time. By performing unsteady simulations, using more advanced

turbulent models, the accuracy of numerical results became similar to the experimental ones.

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2 Numerical flow simulations

Fluid flow is defined by flow equations (Navier–Stokes equations and continuity equation). Numerical

flow simulation means that we discretize, approximating a continuous mathematical problem with

an algebraic one, the region of interest where the equations will be solved. In the process of domain

discretization the region of interest is divided into small elements (cells). At the nodes of the

elements the values of velocity components and pressure are calculated during the numerical

simulations.

The main steps of each flow simulation are:

Defining a computational domain

Mesh generation

Setting up boundary conditions

Defining flow and solver parameters

Setting initial conditions

Solution of the problem

Post-processing.

The definition of the computational domain is very important for the accuracy of results and for

computational time (CPU). With reduction of computational domain to the region of interest, we can

significantly reduce CPU but in some cases we lose some information which might influence the flow

in the region of interest.

Quality and density of computational mesh significantly influence the results. The meshes should be

as orthogonal as possible. Density and mesh refinement near the walls depend on flow conditions

and turbulence models used in the simulations. Computational domain can be reduced by exploiting

symmetry or periodic boundary conditions.

Fluid properties are fluid density and dynamic viscosity. Solver parameters are number of iterations,

convergence criterion, etc. Discretization schemes have to be defined as well.

Good initial conditions can significantly improve the convergence and reduce CPU. If we numerically

analyze several similar cases, the results of a previous one can be used as initial condition for the

next case.

When all the conditions and parameters are defined, the solver starts to solve discretized equations.

The computing time of numerical simulations depends on many parameters, such as number of

elements in the mesh, steady or transient simulation, turbulence model, performances of the chosen

computing platform etc.

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In the post-processing phase, when flow simulation is completed, the flow can be visualized with

streamlines, velocity vectors, pressure contours etc. From velocity and pressure some additional

information can be calculated, such as flow energy losses in the flow, forces on surfaces, torque

acting on some parts, etc. For water turbines and pumps the most important results are flow energy

losses and torque on the shaft from which the efficiency of the machine can be predicted.

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3 Water turbines

Water (hydro) turbines transform energy of water into electrical energy via rotation of the turbine

runner, which in turn runs the electric generator through rotation of the turbine shaft. Such turbines

can be classified as high head (Pelton), medium head (Francis) or low head (propeller, Kaplan and

bulb) turbines. The specific speed nq , defined by the expression below, is a measure of the operating

condition (head and flow rate) of a turbine:

4/3

H

Qnn

q , (1)

where Q is discharge (m3/s), H is water head (m) and n is rotor speed (rpm).

Fig. 1 visually represents the choice of turbine type according to available head and flow rate.

Figure 1: Types of water turbines, according to head H and flow rate Q.

3.1 Francis turbines

Francis turbines are the most widely used water turbines. More than 60% of installed hydropower is

produced by Francis turbines. They operate at a wide range of head, from 6 to 600 m. Specific speed

nq is between 12 and 120.

Typical Francis turbine consists of a spiral casing with stay vanes, a guide vane cascade, a runner and

a draft tube. The amount of water which flows through the turbine is regulated by opening or closing

the guide vanes (see Fig. 2). Shape and number of runner blades depend on design conditions.

Turbines for higher head values have more blades than those which operate at moderate head. In

Q [-]

H [m]

Pelton

Francis

Kaplan Bulb

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Fig. 3 a Francis turbine for extremely high head is presented. Its runner consists of 15 full length

blades and 15 splitters.

Figure 2: Definition of guide vane opening. Angles of guide vanes are adjusted to the flow conditions.

Figure 3: Francis turbine (Workshop Francis 99). Spiral casing with 14 stay vanes – blue, wicket gate cascade with 28 vanes – orange, runner – red, draft tube – green.

Results of numerical simulation are: velocity components, pressure and turbulence quantities in a

complete computational domain. In post processing we can visualize the flow with vectors or

streamlines and check pressure distribution on guide vanes and runner blades (see Fig. 4). From the

results of numerical simulation torque on the shaft, losses in all turbine parts and turbine efficiency

can be calculated.

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Figure 4: Results of numerical flow analysis at the BEP (Best Efficiency Point): pressure contours on guide vanes and runner blades and streamlines in distributor (spiral casing, stay and guide vane cascades) and in the draft

tube.

From measured or calculated efficiency values at several guide vane openings and several values of

head the efficiency hill chart diagram is obtained in such a way, that iso-lines with constant efficiency

values are drawn. From the hill chart diagram efficiency for all operating conditions can be seen. In

Fig. 5 an efficiency diagram for a middle head Francis turbine is presented. Iso-lines of efficiency are

in black while blue lines present constant guide vane openings. Efficiency values are divided by the

efficiency value at the Best Efficiency Point (BEP).

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H/HBEP

Q/QBEP Figure 5: Efficiency hill chart diagram. Efficiency values are divided by the efficiency value at BEP. Isolines of

constant efficieny curves –black, iso-lines of constant guide vane opening – blue.

3.2 Axial Turbines

Low-head turbines are axial-type (with axial entry and axial discharge) reaction turbines, with 3 to 7

runner blades. Kaplan turbines are used for head H up to 80 m, whereas bulb turbines are used for

head up to 15 m. Specific speed nq of Kaplan turbines is between 95 and 250. For bulb turbines nq is

higher than 170. Different types of axial turbines are presented in Fig. 6.

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Kaplan turbine

Saxo turbine

Bulb turbine

Figure 6: Different types of axial, double regulated turbines.

Kaplan and bulb turbines are double-regulated turbines, which means that the inclination of guide

vanes, as well as of runner blades can be adjusted. The angle of guide vanes and runner blades for

small and large values of flow rate is presented in Fig. 7. A typical mesh for a Kaplan turbine is

illustrated in Fig. 8, and its corresponding flow path in Fig. 9.

a) b)

Figure 7: Adjustment of guide vane opening and angle of runner blades to flow conditions: (a) Small guide vane opening and small angle of runner blades (for a small flow rate value); (b) Wide guide vane opening and large angle of runner blades (for a large flow rate value)

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Figure 8: Typical grid for a Kaplan turbine. Unstructured mesh in the semi-spiral casing with stay vanes and

structured mesh in the other turbine parts. Total number of nodes is around 8.3 million, total number of

elements is around 11.5 million.

Figure 9: Flow in a Kaplan turbine

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In Fig. 10 an efficiency diagram at constant head for an axial turbine is presented. For each angle of

runner blades a partial efficiency curve (in blue) has to be obtained with measurements or

numerically. The envelope of partial efficiency curves presents the efficiency of the turbine at

constant head. From efficiency curves for several values of head a hill chart diagram can be obtained.

With double regulation, high efficiency for a wide range of operating conditions can be achieved.

Q

Figure 10: Efficiency diagram for a double regulated axial turbine at constant head – model test.

3.3 Pelton turbines

Pelton turbines operate at high head and small flow rate values. For Pelton turbines nq is less than

20.

Two-phase flow (water, air) in Pelton turbines is turbulent and unsteady. While reasonable results for

Francis and Kaplan turbines can be obtained by steady state analysis, runner flow simulations for

Pelton turbines have to be time dependent (transient). Besides, we have two fluids, water and air.

The shape and thickness of water jets and evacuating water sheets are not known in advance, and

they have to be calculated during the simulation. Numerical analysis of flow in a Pelton turbine is

therefore much more complex and time consuming.

Optimization of distributors with injectors is extremely important for the efficiency of Pelton

turbines. Discharge should be distributed equally between all injectors. Losses in the distributor have

to be as small as possible, but the quality of the jets is even more important. Jets should be compact

and velocity within the jet should be as uniform as possible. Secondary velocities caused by bends in

the distributor are most undesirable as they cause jet dispersion and deviation.

Numerical simulation is usually divided into two parts. At first, steady state simulation in distributor

is performed. Calculated thickness and velocity of the jets are then used as inlet conditions for

transient simulation of flow in the runner.

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Figure 11: Model of a two-jet Pelton turbine. Test rig – left, numerical model – right. In numerical simulations

the casing is not included.

For Pelton turbines efficiency prediction is a bit less accurate than for the Francis and axial turbines,

but the results are nevertheless very helpful. Numerical results help to improve the shape of the

distributor with injectors in order to get smaller losses and good quality of the jets. Numerically we

can verify whether the evacuating water sheets impact the previous buckets and if there is any

interaction between the evacuating sheets and the incoming jets.

Some results for a 2-jet Pelton turbine with horizontal axis and for a 6-jet turbine with vertical axis

can be seen in Fig. 12 and Fig. 13, respectively. As well, a comparison of calculated and measured

efficiency is presented.

a)

b)

c) Figure 12: Results for a 2-jet Pelton turbine.

a) Jets and evacuating water sheets b) Pressure distribution on runner buckets c) Measured and numerically obtained efficiency values

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a)

b)

c)

d)

Figure 13: Numerical simulation of flow in distributor and runner of a 6-jet Pelton turbine.

a) Computational domain and grid for distributor with injectors. In the cones behind the injectors the jets are forming during the simulations.

b) Streamlines in distributor and jets c) Jets and evacuating water sheets and pressure on runner buckets. d) Comparison of measured and calculated values. Flow rate was input data, head, torque and efficiency

were calculated from the numerical results.

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Part 2

Some of the Results Achieved during the ACCUSIM Project

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1 Introduction

The ACCUSIM project aims to identify, develop and apply accurate, high-fidelity CFD approaches for

the numerical predictions of the unsteady, turbulent and possibly cavitating flow in hydraulic

turbines, pumps and marine propellers, and to develop advanced shape and functional optimization

strategies for the best design of these systems.

In accordance with these aims, the main activities during the projects were related to the topics:

Advanced (scale resolving) turbulence modelling of flow in water turbines, pumps and

marine propellers

Use of the OpenFOAM CFD open source libraries

Cavitation in water turbines, pumps and marine propellers

Design optimization

In this 2nd part of the report some of the results are presented with particular reference to the papers

where more details about numerical simulations and accuracy of results can be found.

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2 Scale resolving turbulence modelling

Flow in water turbines, pumps and marine propellers is turbulent, with Reynolds number ranging

between 105 and 107. Direct numerical simulation (DNS) of the turbulent flow for complex

geometries and high Reynolds number is not possible nowadays, so one of the turbulence models

has to be used. Flow in water turbines, pumps and marine propellers is unsteady because of runner

rotation and also because of turbulent structures which are forming and disappearing in the flow.

Unfortunately, transient simulations are very time consuming. Therefore often steady state

simulations are used, especially in the design process, where a lot of different geometries have to be

analysed.

Francis turbines

For Francis turbines efficiency and cavitation are usually quite accurately predicted by steady state

simulations, while unsteady phenomena, like rotating vortex rope in a draft tube, can be predicted

only by transient simulations with more advanced turbulence models.

The ACCUSIM group participated in the first Workshop Francis 99, organized by the Norwegian

University of Science and Technology (NTNU), Norway, and Luleå University of Technology (LTU),

Sweden. The goal of the first workshop was to determine the state-of-the-art of numerical

predictions for steady operating conditions. The ACCUSIM group performed several numerical

simulations by two CFD (Computational Fluid Dynamics) codes, ANSYS CFX and OpenFOAM. Steady-

state simulations were performed by k-ɛ and SST (Shear Stress Transport) turbulence models, while

for transient simulations the SAS (Scale Adaptive Simulation) and SST ZLES (Zonal Large Eddy

simulation) models were used. With proper grid refinement in distributor and runner, and taking into

account losses in labyrinth seals, very accurate prediction of torque on the shaft, head and efficiency

was obtained. Calculated axial and circumferential velocity components on two planes in the draft

tube matched well with experimental results [1].

Figure 1: Flow in the draft tube at Part Load (bottom), BEP (middle) and High Load (top)

a) streamlines;

b) vortex structures. Results obtained with the ZLES turbulence model.

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Axial turbines

For axial turbines the efficiency prediction at large flow rate values is very poor mostly because of

overrated flow losses in the draft tube. During the ACCUSIM project a comparison between

numerical results and measurements for a six-blade Kaplan turbine for middle head and for a three-

blade bulb turbine for extremely low head was done in order to determine an appropriate numerical

setup for accurate and reliable simulations of flow in axial turbines. Values of discharge, torque and

losses obtained by different turbulence models were compared to each other and to the

measurements. Steady state simulations were performed with various turbulence models. The effect

of curvature correction (CC) and Kato-Launder (KL) limiter of turbulence production was tested.

Transient simulations were performed with shear-stress-transport (SST) turbulence model, the scale-

adaptive-simulation (SAS SST) model, and with zonal large-eddy-simulation (ZLES). Details about

turbulent structures in the draft tube were illustrated in order to explain the reasons for differences

in flow energy losses obtained by different turbulence models. Also the effects of different advection

schemes (high resolution scheme – HRS and bounded central differential scheme – BCDS) and mesh

refinement were tested.

On the basis of a detailed analysis of flow in a Kaplan turbine and in a bulb turbine with different

turbulence models and at different operating regimes it can be concluded:

• Results of steady state simulations in the Kaplan turbine were improved by using the Kato Launder

limiter of production term (KL) and the curvature correction (CC), therefore KL and CC were used also

in simulations of flow in the bulb turbine.

• For Kaplan and bulb turbines it was found out that steady state analysis is not suitable for all

operating regimes. While for the Kaplan turbine the prediction of efficiency by RANS two-equation

models and by SSG RSM was quite accurate for small and optimal runner blade angles, and

significantly failed only at full rate, for the bulb turbine steady-state simulations failed entirely. In

both cases the main reasons for discrepancy between measured and calculated efficiency were

underestimated torque on the shaft and overestimated flow energy losses in the draft tube.

• Transient simulations by the SST, SAS SST and SAS SST ZLES were performed at one operating point

for maximal runner blade angle. Compared to the steady-state simulations, results improved

significantly. The largest improvement was achieved by SAS SST ZLES.

• Comparing transient results of SST HRS, SAS HRS and SAS BCDS, it can be concluded that the

improvement due to the usage of BCDS instead of HRS was even larger than the improvement due to

the usage of SAS instead of pure SST. With BCDS, the agreement with measurements was improved

mostly because of smaller losses in the runner and better prediction of torque on the shaft.

• For bulb turbine, meshes of different density were used. The results of the SAS SST ZLES model

were better than the results of the SAS SST model on all meshes. Positive effect of mesh refinement

in the draft tube was clearly seen. While with mesh refinement only of the runner no improvement

was obtained, the best results were obtained when both meshes, the runner and the draft tube were

refined.

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Steady-state simulation, SST model, basic grid

Transient simulation, SAS SST with zonal LES in the draft tube, basic grid

Figure 2: Flow in the draft tube (stream lines and velocity distribution on several sections) and contours of viscosity ratio on mid cross-section for a low head bulb turbine.

• Finally, in both cases the simulations by SAS SST ZLES were performed at several operating points

for three runner blade angles. Comparing the results of the steady state analysis to the results of the

SAS SST ZLES the agreement of the former ones with measurements was improved at all operating

regimes. For Kaplan turbine the discrepancy was everywhere smaller than 0.8 %. For bulb turbine, in

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spite of large improvement, the discrepancy with measurements was even on the finest mesh still

about 2.1 %.

• Too long CPU time is the main disadvantage of transient simulations and the reason for their

limited use in design process. It can be expected that with future development of hardware and

software the problem will be overcome.

More about an improvement of results for axial turbines can be found in [2], [3], [4] and [5].

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3 Cavitation

Cavitation refers to the process by which vapour forms in low pressure regions of a liquid flow. In

water turbines, pumps and marine propellers the consequences of cavitation are flow instabilities,

excessive vibrations, damage of material surfaces, and reduced performance of the machines.

3.1 Calibration of mass transfer models for the numerical prediction of sheet

cavitation around a hydrofoil

Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of

methods/models [6]. Here, a so-called homogeneous model [7, 8] is applied to the numerical

predictions of sheet cavity flow around a hydrofoil. In the considered model the working fluid is

treated as a homogeneous mixture of two fluids, i.e. water and vapour, behaving as a single one, and

the mass transfer rate due to cavitation is modelled by the mass transfer model. Here, three

widespread mass transfer models are alternatively used. The considered mass transfer models share

the common feature of employing empirical coefficients to tune the condensation and evaporation

processes, whose values affect the accuracy and the stability of the numerical predictions. Thus, in

order to ensure stable and accurate predictions, the empirical coefficients of the considered mass

transfer models are properly and congruently tuned using a calibration strategy driven by the

modeFRONTIER [9] optimization platform. The numerical predictions based on the three different

well-tuned mass transfer models are very close to each other and in line with the available

experimental data.

Figure 3: Distribution of water and water vapour along a hydrofoil NACA66 obtained with Zwart model with standard (a) and calibrated (b) evaporation and condensation constants.

3.2 Cavitation in water turbines

Accurate prediction of cavitation in water turbines is more and more important because nowadays

due to commercial reasons turbines often operate at regimes far from their best efficiency point.

Besides, to reduce manufacturing costs, the dimensions of turbines are reduced; to get the same

power, rotating speed has to increase. The consequence of higher speed is smaller cavitation

(Thoma) coefficient.

During the ACCUSIM project different forms of cavitation in different types of water turbines were

simulated. Cavitation predictions were done for models of Francis and Kaplan turbines and for

prototypes of bulb and Pelton turbines. For all cases the homogeneous multiphase model was used.

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Mass transfer due to cavitation was modelled by the Zwart model with standard constants. In cases

of Kaplan and Francis turbines, cavitation was also modelled by Zwart model with evaporation and

condensation constants that were previously calibrated on a hydrofoil. For Kaplan and Francis

turbines the extent and shape of cavitation were compared to the experimental observation on the

test rig. The effect of cavitation on turbine efficiency was also investigated.

3.2.1. Cavitation in Francis turbines

For a Francis turbine we simulated leading edge cavitation, travelling bubble cavitation on suction

side near the trailing edge and vortex rope at part and high load.

Overload operating regime

Steady-state simulations of flow in a medium-head Francis turbine were performed at overload

operating regime with high flow rate. SST turbulence model with curvature correction and with the

Kato-Launder limiter of production term in equation for turbulence kinetic energy was used.

Simulations were done for different values of cavitation coefficient, which means from non-cavitating

to strongly cavitating regimes.

a) b)

Figure 4: Cavitation in the Francis turbine at full load. a) vapour at suction side of runner blades, left - standard, right - calibrated coefficients. b) Cavitation on suction side of runner blades near the trailing edges and rotating

vortex rope, left - test rig, right - CFD.

Numerical results showed three types of cavitation: inlet cavitation, cavitation at the suction side

near the blade trailing edge and vortex core cavitation behind the hub. Blades' inlets are not visible

on photos, because they are hidden behind the runner band, therefore the extent of inlet cavitation

cannot be compared to the observation on the test rig. Shape and extent of numerically predicted

cavitation at the suction side of the blades near the trailing edges, and shape and size of the

cavitating vortex core behind the hub are in good agreement with observation on the test rig. Results

were presented in [10].

Part load operating regime

Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure

pulsation frequencies and amplitudes caused by rotating vortex rope at part load operating regime.

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Simulations were done with the SAS SST turbulence model with curvature correction on basic and

refined computational meshes. Without cavitation modelling too small values of frequency and

amplitudes were obtained. With mesh refinement the calculated amplitudes were a bit closer to the

measured values, while the accuracy of predicted frequency did not improve at all. Agreement

between measured and numerical values was significantly improved when cavitation was included in

simulations. In addition, the predicted value of the dominant frequency was slightly more accurate

when, in the Zwart et al. cavitation model, the default condensation and evaporation model

constants were replaced with previously calibrated ones. Results were presented in [10] and [11].

a)

b)

c)

d)

Figure 5: Vortex rope a) on the test rig; b) without cavitation modelling, iso-surface of evaporation pressure,

basic mesh; c) default cavitation constants, iso-surface of Vapour Volume Fraction = 0.1 d) calibrated cavitation constants, iso-surface of Vapour Volume Fraction = 0.1.

Figure 6: Comparison of numerical and experimental results at part load operating regime

Exp. - experimental values, 1 - no cavitation modelling, basic mesh, 2 - no cavitation modelling, fine mesh, 3 -

cavitation modelling, default parameters, basic mesh, 4 - cavitation modelling, calibrated parameters, basic

mesh

3.2.2. Cavitation in Kaplan turbines

For a Kaplan turbine numerical simulations were done at one operating point for maximal runner

blade angle and nominal head. Steady-state results obtained with the SST (Shear Stress Transport)

turbulence model were improved by transient simulations, where the SAS (Scale Adaptive

Simulation) SST model was used. Cavitating flow was simulated using the homogeneous model. Mass

transfer rate due to cavitation was regulated by the Zwart et al. model with default model constants

used in ANSYS CFX commercial code and also with the evaporation and condensation parameters

previously calibrated considering the sheet cavity flow around a hydrofoil. The numerical results

were compared with the observation of cavity size on the test rig and with the measured sigma break

curve. Steady-state simulations predicted significantly too small efficiency level and too small extent

of cavitation on the runner blades. With transient simulations, the shape and size of the predicted

sheet cavitation agreed well with the cavitation observed on the test rig. In addition, also the

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predicted efficiency was more accurate, although the value of σ (cavitation or Thoma number) where

the efficiency dropped for 1% was a bit too large. The difference between the results obtained with

standard and calibrated model parameters of the Zwart mass transfer model was small. Details about

the simulations and the accuracy of results can be found in [12].

Figure 7: Comparison of shape and size of cavity, a) experiment, b) steady state simulation, calibrated

coefficients, c) time dependent simulation, calibrated coefficients.

3.2.3. Cavitation in a prototype of a bulb turbine

For a prototype of a bulb turbine numerical flow

simulation was performed with a purpose to obtain

pressure distribution for the stress analysis. To get

accurate pressure on runner blades the cavitation

modelling has to be included. The prototype diameter of

the turbine was very large (Dp = 7.5 m.) therefore

hydrostatic pressure has to be included in the simulation.

Due to hydrostatic pressure a cavity at upper blades is

much larger than at the bottom ones. During transient

simulation a size of a cavity at each blade increases when

the blade rotates up and decreases when it rotates down.

Figure 8: Pressure distribution and

attached cavity at suction side of bulb turbine runner blades

3.2.4. Cavitation in Pelton turbines

Cavitating flow in Pelton turbines consists of three components: water, air and water vapour.

Transient simulations include modelling of free surfaces and mass transfer between water and

vapour due to cavitation and condensation processes.

The presence of water vapour does not necessary cause material erosion. The conditions for

cavitation pitting on Pelton buckets are [13]:

• Vapour cavity is sticking to the bucket surface.

• Water vapour is condensed in a very short time.

• The condensation of water vapour is developed in absence of air.

In Fig. 9 regions with water vapour on the inner and on the back side of the bucket are presented. At

the inner side the vapour is condensing very slowly. At the back side the condensation is also slow

and the vapour is in contact with air. So no cavitation damages are expected in this case.

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Figure 9: Detail of computational grid (left), water vapour on the inner side of the bucket (middle), water

vapour at the back side of the bucket (right). Water vapour is coloured by wall distance.

3.3 Sheet and cloud cavitation prediction in double suction centrifugal pump

Cavitation at the leading edges of the impeller blades in a pump is quite a usual phenomenon, due to

the limitations in the available suction head (or, in simple words, due to too low "submergence" of

the pump). Usually the sheet-type cavitation (also called blade cavitation) is of small size and occurs

on the suction side of the blade, so the pump performance is only negligibly affected. At specific

conditions, the so-called cloud cavitation can appear (Fig. 10), when large clouds of vapour are torn-

off of the sheet cavity, and are carried along with the stream.

Two types of numerical approaches for the prediction of cloud cavitation in a centrifugal pump were

used: a single-blade simulation and a (symmetrical) half-geometry simulation. For both approaches,

simulations were performed with the default and with the modified [8, 14] parameters of the mass

transfer model. Simulations, performed with the modified parameters, were found to be less stable

than the ones with the default parameters.

The single-blade simulation with the modified parameters of the mass transfer model produced

cloud cavities of dubious origin (Fig. 12). The results obtained on a single-blade mesh are of limited

use due to the negligence of the suction chamber effect on the inlet velocity distribution.

It is possible to conclude that simulations performed on the geometry of a half-pump, using the

default and the optimized parameters, can predict the pinch-off of vapour clouds (Fig. 13).

Figure 10: Cloud cavitation, observed on the double-suction pump at HPP Fuhren [15].

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Figure 11: Geometry of the double-suction pump. Left: numerical model (in green: inlet pipe with suction

chambers; in blue: impeller; in red: volute with outlet pipe). Right: experimental setup with visible observation window.

Figure 12: Prediction of cavity (isosurface of 10% water vapour) with single-blade passage simulation

Figure 13: Half-geometry simulation with default constants (isosurface of 10% water vapour).

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3.4 Numerical predictions of the cavitating flow around model scale propellers

working in uniform and non-uniform inflow

The numerical predictions of the turbulent cavitating flow around two model scale propellers,

recognized as international benchmarks, were performed. In particular, cavitating flow around PPTC

propeller working in uniform inflow [16] and cavitating flow around the E779A propeller working in

uniform as well as non-uniform inflow [17] were simulated.

The simulations were performed using commercial and open source CFD (Computational Fluid

Dynamics) codes. The cavitating flow was modelled using the homogeneous model along with three

different widespread mass transfer models, previously calibrated considering the sheet cavity flow

around a two-dimensional hydrofoil [8]. The turbulence effect was modelled using the RANS

(Reynolds Averaged Navier Stokes) approach.

The numerical results were compared with the available experimental data. The simulations

performed with the three different calibrated mass transfer models were very similar to each other

and in line with the experimental data, even though the numerical cavitation patterns were generally

slightly overestimated [14, 18].

Ex

per

imen

t

Zw

art

Figure 14: PPTC propeller; RANS simulation performed with Zwart mass transfer model;

cavitation patterns depicted using isosurfaces of vapour volume fraction equal to 0.2

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4 Comparison of results obtained with OpenFOAM and ANSYS-CFX

Comparison of results obtained with OpenFOAM and ANSYS-CFX was done for 6 cases:

• High head Francis turbine (Tokke model from Workshop Francis99)

• Middle head Francis turbine

• Kaplan turbine

• Bulb turbine

• Cavitation prediction: Attached cavity flow around a hydrofoil

• Cavitation prediction: Attached cavity flow around E779A model scale marine propeler

Approximately the same level of accuracy of numerical results was achieved with both codes. CPU

time was significantly longer in case of simulations with OpenFOAM.

Figure 15: High-head Francis turbine, computational domain and mesh with a detail of mesh in stay and guide vane cascade (left), and comparison of predicted efficiency to the measured values (right).

Figure 16: Prediction of the attached cavity for a hydrofoil, results of CFX and OpenFOAM, both with the Kunz

mass transfer model.

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5 Optimization

The results of two design optimization cases are presented: an optimization of a runner of a double-

sided centrifugal pump and an optimization of a Francis turbine runner cone.

5.1 Optimization of a double-sided centrifugal pump

Centrifugal pumps are widely used in industrial applications. Compared to single-entry centrifugal

pumps, double-sided pumps allow transportation of greater flow rates due to smaller proneness to

cavitation, and offer counter-balancing of axial hydraulic forces due to double-entry design [19].

In the modern world of rapidly-improving technologies it is important to design excellent products in

short time. The optimization techniques bring many benefits over the traditional "trial-and-error"

design process: shorter design phase, exploration of design space in a more systematic way,

development with less hard-to-spot human-based errors, etc. In turbomachines, usually multiple

objectives have to be optimized. One of the first multi-objective optimization studies was performed

by Lipej and Poloni [20].

The optimization study of a double-sided centrifugal pump with specific speed nq=62 (per impeller

side), presented in Fig. 17, was performed within modeFRONTIER® optimization platform [21]. During

the optimization only the impeller geometry was allowed to be modified, while the rest of the

geometry was fixed. The objective of the study was twofold:

To compare different Response Surface Methods (RSMs), also called metamodels or surrogates,

for their ability to predict pump efficiency [22],

To propose and validate an economical decoupled simulation method for the optimization of a

pump [23].

Figure 17: Geometry of the double-sided centrifugal pump.

In the first phase, during the study of RSMs, a simplified pump geometry comprised of (symmetrical)

half of volute and of one impeller channel (Fig. 18). Since the impeller channel and volute were

simulated simultaneously, we call this model coupled model. An example of successful modification

is presented in Fig. 19.

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In the second phase of the study, based on flow simulations of the volute, flow losses in the volute

were estimated with a simple function ΔHvolute=(f(α2,hub)+ f(α2,midspan)+ f(α2,shroud))/3, where α2 is angle

between circumferential and absolute velocity at the impeller outlet. Afterwards, geometry

optimization was performed only on one impeller channel (Fig. 20). We call this model decoupled

model. Two optimization objectives were used, namely pump efficiency and reluctance to cavitation.

For the latter, a simple procedure for its estimation was proposed. Results for forty most promising

candidates for high pump efficiency were validated with full-geometry CFD numerical simulations.

The following conclusions were drawn:

The presented method with estimation of flow losses in the volute represents a good

approach for quick optimization;

Angle α2 at hub and at shroud needs small adjustments;

Low value of angle α2, when compared to the average α2 value, acted beneficially on

reducing the volute flow losses.

Figure 18: Geometry and mesh for the coupled model.

Figure 19: Blade geometry before (left) and after (right) the optimization. Relative efficiency increased

for 0.9 %. Green surface: inlet surface. Yellow: outlet surface.

Figure 20: Geometry and mesh for the decoupled model. Blue arrows represent inlet and outlet boundary

conditions.

Volute

mesh

Single-channel impeller

mesh

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5.2 Multi-objective optimization of the Francis turbine runner cone

A multi-objective optimization with the genetic algorithm MOGA-II in modeFRONTIER was used to

optimize the shape of a simplified runner-cone extension (RCE) for a Francis turbine of higher specific

speed nq. The objective of the optimization was the minimization of the draft tube pressure losses for

two operating regimes. To evaluate the progress, a baseline case without the extension was

calculated first. Six geometric design variables, defining the shape of RCE, were being modified

during the optimization. Finite-volume based commercial software ANSYS CFX was employed to

calculate the flow field on a structured mesh. Shapes of RCE on Pareto front were long and thin. At

the best-efficiency point (BEP) the draft tube pressure losses were larger than without the RCE. At

the maximal discharge point (MAX) the draft tube pressure losses were smaller than without the

RCE; turbine efficiency increases for 0.15% at full size computation grid.

Figure 21: Case 0, total pressure contours at meridional section, QBEP at left, Qmax at right

Figure 22: Design ID_54, total pressure contours at meridional section, QBEP at left, Qmax at right

Details about the optimization of the runner cone and the results of optimization can be found in

[24].

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Conclusions

Scale resolved SAS SST model in combination with zonal LES was successfully used for flow simulation

in Francis, Kaplan and bulb turbines. In comparison to the steady-state results with the SST

turbulence model, significant improvement was achieved, especially for a Kaplan and a low head

bulb turbine.

Cavitation prediction with standard or/and calibrated cavitation models was done for several cases:

initial and travelling bubble cavitation as well as cavitating vortex rope at overload operating

regime for Francis turbine,

cavitating vortex rope at part load in a Francis turbine with analysis of pressure pulsations,

cavitation in a Kaplan turbine at high load and its effect on efficiency,

cavitation on a prototype size of a bulb turbine,

three-phase flow in a Pelton turbine with detailed analysis of results to verify occurrence of

pitting cavitation,

sheet and cloud cavitation in a double-suction centrifugal pump,

cavitating flow around model-scale propellers working in uniform and non-uniform inflow.

For all cases, except for the prototypes of bulb and Pelton turbines, numerical results were validated

with observations on test rigs and with measured values, and good agreement was obtained.

For design optimization two cases are presented: optimization of a double-sided centrifugal pump

and multi-objective optimization of a Francis turbine runner cone.

A comparison of results obtained with the commercial code ANSYS CFX and with the open-source

code OpenFOAM shows that approximately the same level of accuracy was achieved, although CPU

time was significantly higher in case of simulations with OpenFOAM.

Overall the results achieved during the ACCUSIM project are very good, as demonstrated by the large

number of technical papers and conference presentations, or even better by the exceptional results,

in comparison with other teams and research centers, obtained by ACCUSIM researchers in blind and

non-blind benchmarks.

IAPP 2013 – 612279


References:

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http://dx.doi.org/10.1088/1755-1315/22/2/022007

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