Numerical Methods for Fluid Dynamical Simulation of Hydro …wseas.us/e-library/conferences/2009/lalaguna/EPREWA/... · 2009-09-07 · Numerical Methods for Fluid Dynamical Simulation

Numerical Methods for Fluid Dynamical Simulation of Hydro Power Plants

HELMUT JABERG, PROF. DR.

Institute for Hydraulic Fluid Machinery University of Technology Graz

Kopernikusgasse 24, A 8010 Graz AUSTRIA

[email protected] http://www.hfm.tugraz.at Abstract: Hydro power plants of any size – be it large or small hydro - are always quite complicated arrange-ments as they cannot be designed for a definite duty point of operation but in fact the duty point varies strongly with the flow rate and in many cases also with the pressure head available. The optimization of these plants has always been a challenge to the design engineers from all faculties involved, in the course of this presentation mechanical or civil engineering are concerned.

Due to the more or less - and sometimes extremely – variable duty points the dimensioning and the set-up in detail are remarkably different from on plant to another – and so is the stationary and transient operation. Both the specific arrangement as well as the varying duty points often cause a number of problems as any hydro power plant exist exactly once and in so far is always a prototype thus often causing unforeseeable difficulties.

On the example of a number of components fluid dynamical optimizations by means of numerical methods are outlined for intakes, valves and different turbine designs. Specific problems as they can frequently occur in hydro power and remedy to solve the problems are described. On the example of a cavitating Francis runner a new way for cavitation simulation will be presented.

Key words: Hydro power, Francis turbines, Kaplan turbines, bulb turbine, draft tube, valves, numerical methods

1 Introduction Hydro power is the largest source of the renewable energy and is furthermore the only possibility of large scale energy storage. On a world wide scale around fifteen percent all the energy consumption is covered by hydro power, though in some coun-tries with favourable geography it can reach much higher values like Norway, Switzerland and Aus-tria.

Hydro power plants resemble each other as the basic set up is always similar: Water flows from the upper reservoir to a lower reservoir through intake buildings, shut-off valves of different kind and in different places, headraces, surge chamber, pen-stocks, turbines, suction pipe and outlet buildings. In many cases – especially if pumped storage hydro power plants are taken into consideration - the plant and the machinery equipment must be de-signed for extremely variable duty points defining remarkable challenges for the design, the optimisa-tion and the stationary and transient operation.

On the example of a number of components this paper will outline the application of fluid dynami-

cal optimisations by means of numerical methods for intakes, valves and different turbine designs.

Specific problems as they can frequently occur in hydro power plant design and operation are de-scribed taking care of cavitating flow, detached and recirculating flow and also the unsteady conditions in strongly branched hydro power plants as a whole.

2 Double decker shut-off valve Shut-off valves are important components in hydro power plants as they must be capable of reliably blocking the headrace, the penstock and the suction pipe and also the machinery contained in the differ-ent sections of the hydro power plant. Shut-off valves are not used to control the flow through the plant but stay always open in normal plant opera-tion while the flow rate is controlled by the position of guide vanes and runner blades for Francis or Kaplan turbines, respectively, or the needle posi-tion in case of Pelton turbines. In normal operation the flow resistance of shut-off valves shall be as close to zero as possible whereas shutting-off re-quires an infinitely high flow resistance. To cope

Proceedings of the 3rd WSEAS Int. Conf. on RENEWABLE ENERGY SOURCES

ISSN: 1790-5095 399 ISBN: 978-960-474-093-2

with these two contradicting fluid dynamical re-quirements in one and the same component defines the challenge for the hydro dynamical design engi-neer. Further requirements come from the fact, that

in case of emergency shut-off valves must be able to close reliably for all flow rates, also extremely high flows exceeding the nominal value by the factor of roughly 2.5.

Figure 1 gives an impression of the geometry of such shut-off valves and the internal flap with its lower and upper belt and the two support struts in between. In most cases two of such valves are in-stalled behind each other for reasons of redundancy and inspection. The reliable shut-off mentioned above requires that in any position of one of the two the other one can still be closed. So the coeffi-cient for through flow, torque and force kQ, kM or kF, respectively, are of outstanding importance for the safety of the power plant as a whole and also the unsteady behaviour and the magnitude of the water hammer in the system. Therefore designers

usually rely on data concerning these coefficients which are found experimentally by model tests, the set up of which is shown in fig. 2. Recent progress in the development of numerical methods even rendered possible the simulation of extremely com-plicated flows like the one shown in fig. 1 with important recirculation areas and detached zones and to find in this way these coefficients mentioned above.

The Institute for Hydraulic Machinery performed in parallel the experimental (fig. 2) and comprehen-sive numerical investigations using software pack-

Fig. 1: Flow distribution in double decker valve, result of numerical simulation

Fig. 2: Model test of shut-off valve


ISSN: 1790-5095 400 ISBN: 978-960-474-093-2

ages consisting of pro-engineer, CFX 5, CFX built and TASC grid. The computational grid consisted of about four million knots and structured meshes in the upper and lower pipe connections and un-structured grids around the two flaps (fig. 3).

The turbulence was modelled using the SST shear stress transport model by Menter [1].

In fig. 1 examples of the flow around the two valves is shown. As had to be expected separated flow can be seen throughout the arrangement if one or both of the flaps are partially closed. It was also expected that in case of a blockage of either of the two flaps the other one might be exposed to strong

forces and moments acting against the closing ten-dency. The numerically found flow patterns (fig. 1) were not compared to experimental results but measurement and experiment were only compared to each other on the basis of the above mentioned coefficients for flow rate (fig. 4) and torque (fig.5). From the surprisingly good coincidence of numeri-cally and experimentally gained results it was con-cluded that also the flow patterns will at least satis-factorily agree but it must be considered that this comparison is still open to be done. But the coeffi-cients which are the crucial values for the designers are shown to be found numerically and can be used for further design purposes.

Fig. 3: Shut-off valve, grid for numerical simulation

Total number of grid points (ca. 4 mio. nodes): - Up stream pipe, length = 2m, ø = 0.2 m (structured) - Flap 1, length = 0.209m, ø = 0.2 m (un-structured) - Flap 2, length = 0.209m, ø = 0.2 m (un-structured) - Down stream pipe, length = 2m, ø = 0.2 m (structured)

Fig. 4: Shut-off valve, comparison experiment-simulation for flow coef-ficient kQ

Turbine-mode: tandem-configuration

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Valve1=Revision-valve | Valve2=Operation-valve


ISSN: 1790-5095 401 ISBN: 978-960-474-093-2

Despite the extremely complicated flow regimes the experimental and numerical results exhibit sur-prisingly good coincidence and this statement holds for both flaps ad for any combination of opening

angles of either valve. These findings underline the applicability of numerical methods even for this complicated configuration [2].

3 Simulation of Ball Valve The further example for valves in hydro power are ball valves, which are used in high pressure appli-cation and combine best of all valves the two con-tradictory requirements of extremely low resis-tances in the open position and being very tight when closed. The capability of resisting extremely-

high pressure differences and also very high system pressures together with manufacturing require-ments renders these components very expensive so that the application in practise is limited due to economic reasons. Also for this component the numerical and experimental investigations were performed in parallel [3].

In the open position (fig. 6) the ball valve is very much the same as a straight pipe and is no chal-lenge neither for numerical simulation nor for ex-perimental investigation. Again the different coef-

ficients for through flow, forces and moments must be known for different opening angles of the valve in order to define the proper size of the drive servos as well as to calculate the unsteady behaviour and

Fig. 5: Shut-off valve, comparison experiment-simulation for torque coefficient kM

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)Valve1=00°-KM2-Num.Sim.Test-plate Valve1=05°-KM2-Num.Sim.Test-plateValve1=10°-KM2-Num.Sim.Test-plate Valve1=15°-KM2-Num.Sim.Test-plateValve1=20°-KM2-Num.Sim.Test-plate Valve1=25°-KM2-Num.Sim.Test-plateValve1=30°-KM2-Num.Sim.Test-plate Valve1=35°-KM2-Num.Sim.Test-plateValve1=40°-KM2-Num.Sim.Test-plate Valve1=50°-KM2-Num.Sim.Test-plateValve1=60°-KM2-Num.Sim.Test-plate Valve1=70°-KM2-Num.Sim.Test-plateValve1=80°-KM2-Num.Sim.Test-plate Valve1=85°-KM2-Num.Sim.Test-plateValve1=00°-KM2-Test-plate Valve1=10°-KM2-Test-plateValve1=15°-KM2-Test-plate Valve1=20°-KM2-Test-plateValve1=25°-KM2-Test-plate Valve1=30°-KM2-Test-plateValve1=40°-KM2-Test-plate Valve1=50°-KM2-Test-plateValve1=60°-KM2-Test-plate Valve1=70°-KM2-Test-plateValve1=80°-KM2-Test-plate SingleValveConfiguration

Turbine-mode: tandem-configuration Valve1=Revision-valve | Valve2=Operation-valve

Fig. 6: Flow field in Ball valve

0° l iti 30° l i

50° l i 80° l i


ISSN: 1790-5095 402 ISBN: 978-960-474-093-2

the sizes of the water hammer of the hydro power plant as a whole. As can be seen in fig. 6 and also in fig. 7 the flow regime inside the ball valve and also in the gap between the ball and the valve hous-ing becomes enormously complicated. The simula-tion was again performed by use of pro-engineer to design the ball valves, by CFXbuilt and TASCgrid to model the computational domain and CFX 5 to perform the numerical simulation. The turbulence model is again the Menter shear stress transport model SST [1]. The computational grid comprises 2.6 million knots and is unstructured inside the valve with structured meshes in the connecting pipelines. Again, the coincidence between numeri-

cal simulation and the experimental results is quite good, see fig. 8 where the coefficients kF, kQ, kM for force, flow and torque are shown both for the numerical and experimental results. Again both methods agree well with each other with the excep-tion of the torque coefficient kM between 15° and 40° which is somewhat overestimated by the nu-merical method asking for further investigation in order to improve the numerical results. But it should be noted that this is rather of scientific im-portance whereas the coincidence of numerically and experimentally gained results is quite satisfying for the practitioner and design engineer.

Pressure

Velocity

Streamlines

80°

Fig. 7: Flow field in Ball valve,numerical simulation

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Fig. 8: Ball valve, comparison experiment-simulation for flow, force and torque coefficient kQ, kF, kM


ISSN: 1790-5095 403 ISBN: 978-960-474-093-2

In case of the ball valve the numerical simulation even has an advantage over the experimental inves-tigation with a scaled model: Because of the gap between the central ball body and the housing also in the closed position (90°) the ball valve still al-lows a small but considerable leakage and only once the seal rings are inserted the ball valve is perfectly tight as is usual for this type of seal. In general the downscaled model does not allow for seal rings so that the 90° position will yield zero flow rate on the model test whereas the numerical simulation can easily provide for the seal ring leak-age also in the 90° position and insofar yields even better results than the experiment which is quite important for water hammer calculations though not so much for the dimensioning of the piston servos.

4 Cavitation in a Bulb Turbine The numerical simulation of bulb turbines looks back at a comparatively long history as their ge-ometry is comparatively simple with dominating axial flow [4]. What still is a challenge for numeri-cal bulb turbine simulation are reliable statements on cavitation and also to find a very good suction pipe. The mesh arrangement generally yielding good results for axial flow turbines is exhibited in fig. 9. In general it is sufficient to model the gate and the runner with only one blade in each compo-nent thus profiting from a very limited number of nodes in the mesh. Our example (fig. 9) uses just 1.26 mio nodes which comprises also the vertical half of the suction pipe, all this for reasons of symmetry.

As for the suction pipe it is important to mention that the exit condition of the suction pipe can seri-ously influence the simulation results a condition which would be fully unacceptable in practice. To avoid this inconvenience the turbine tail water after the suction pipe outlet is also modelled with ex-trapolation boundary conditions for the velocity and a fixed pressure.

The challenge for bulb turbine simulation is the cavitation. Incipient cavitation is simple to calcu-late as one just has to find the lowest pressure which indicates the onset of the cavitation once this lowest pressure reaches the vapour pressure. But in practice it is much more important to simulate par-tial or full cavitating flow which in most cases re-quires the full simulation of two-phase flow includ-ing phase change from water to vapour and back-wards. Gehrer and Egger [5] have developed a re-markably simple so-called histogram-analysis to simulate the incipient as well as developed cavita-

tion. Based on the practical observation that cavita-tion is the stronger the larger the area is which is covered by cavitation they define a certain pressure threshold for which a certain percentage of the blade surface has lower pressures than this thresh-old. With this pressure the Thoma coefficient sigma is calculated.

For example 5% of the plate surface shall lie below a certain pressure. Then the pressure distribution around the plate is calculated in a standard way and the final result is evaluated in such a way that the pressure is found for which the required 5% of the plate surface has pressure lower than this bench-mark pressure. As has been mentioned above with this pressure the Thoma coefficient is calculated in a standard way. Certainly this method is only then reliable when we know which area portion is typi-cal for a certain sigma value. But once one has scaled typical turbine geometry by evaluating measurement data and recalculating them to find

Fig. 9: Bulb turbine: Simulation mesh

• Full machine simulation (360°): 8.02 Mio. nodes

• Model with one guide vane (22.5°), one runner passage (90°), half suction pipe (180°): 1.26 Mio. nodes


ISSN: 1790-5095 404 ISBN: 978-960-474-093-2

the area portion and the appropriate pressure threshold, experience tells that the same area por-tion is also representative for other turbines of the same type. By this method the results for the sigma value can be found (fig 10) where also the effi-ciency for the different propeller curves and the Kaplan envelope are shown.

The σ value is shown in fig. 10 as a function of the

turbine pressure head. It can be seen how σ in-creases with relative head – strongly for increasing head which is coupled with increasing velocities through the Torricelli formula and weakly for de-creasing head ratios below design point. If the plant designer calculates the σavailable in the plant it is very easy to find the limiting turbine operation range with the restriction σavailable > σ.

In fig. 11 for the same turbine the sigma values are shown in form of a hill chart and again the surpris-ingly good agreement between numerical simula-tion and experiment can be seen. Here head and flow are non-dimensionalised using the transforma-tions

5 Calculation Method It is well known that numerical simulations depend on grid size and grid density which results from the truncation errors when replacing the differentials in the Navier-Stokes-equations by differences. When a numerical simulation is started we therefore pro-ceed in two directions: By changing the grid den-sity (i.e. the number of nodes) the minimum neces-

MM

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LR16.5_sigma_(pHisto_0.002)



Experimental data

Highest measured efficiency

Fig. 10: Bulb turbine simulation results

Fig. 11: Bulb turbine cavitation results


ISSN: 1790-5095 405 ISBN: 978-960-474-093-2

sary number of nodes is elaborated above which the numerical results do no longer show a grid effect. And secondly the validity of these simulations w.r.t. grid size and turbulence model is verified by comparing the numerical results with experiments both of which should be found with a geometry as similar as possible to the geometry to be investi-gated or designed. Only once the researcher is sure to have found satisfying accordance between theory and experiment a practical problem should be tack-led. In so far it is no additional effort to find the area percentage and the appropriate critical pres-sure value necessary to simulate the hydraulic ge-ometry under fully developed cavitation as outlined before

6 Bulb Turbine Results The efficiency for the propeller curves are depicted in fig. 10 together with the Thoma coefficient σ and the Kaplan envelope as found by experiments is shown for comparison. As for the efficiency some discrepancy between measurement and experiment can be observed as the experiments show a slightly better turbine performance than anticipated by the simulation. To our experience it is typical for tur-bine simulations that the theoretical efficiency is exceeded in reality. In fact all our turbine simula-tions show this phenomenon and it is worthwhile mentioning that exactly the opposite happens with

pumps where the effective efficiency is slightly overestimated by theory.

7 Francis Turbine Trouble Shooting The same method was applied to solve cavitation problems in a Francis turbine plant. Fig. 12 shows a perspective view of a Francis turbine blade where the cavitation zones are marked. The plant owner complained about the noise emitted by the turbine above a certain flow rate or pressure head, respec-tively. When the turbine was opened and inspected cavitation could clearly be detected as the normally shining blade surface becomes opaque under cavi-tation influence: A well known effect to detect early cavitation. Surprisingly enough cavitation appeared at the blade leading edge and not – as is normally observed in turbines – on the trailing edge where the pressure is lower. The σ curve as func-tion of the flow rate (fig. 13) nicely exhibits the flow rates where σ exceeds the σavailable as provided by the plant. That these values are reliable is made plausible by the fact that exactly at this flow rate the turbine in the plant started to become noisy. As can also be seen the turbine noise is only indirectly related to incipient cavitation (the pmin curve in fig. 12) but rather to developed cavitation. Also inter-esting is the observation that the critical operation range starts as early as at the optimal flow rate and increases for even larger flows.

A redesign of the impeller for the same geometry of the wicket gate (fig. 14) allows for much larger flow rates and still has a safety margin against the maximum allowable flow rate for the turbine plant.

Without further model tests a new impeller with an optimised geometry was casted and installed: The plant operates for roughly two years and the tur-bines have been accepted by the plant user.

Fig. 12: Francis turbine cavitation detection and numerical simula-tion


ISSN: 1790-5095 406 ISBN: 978-960-474-093-2

8 Draft Tube As mentioned before draft tubes gain increasing importance especially for low head hydro. The flow deceleration in the draft tube shall reduce the veloc-ity to minimise turbine exit losses and to adjust the pressure to the ambient pressure at the outlet. The usual challenges in any diffuser design are to minimise diffuser losses and also to minimise con-struction efforts i.e. it shall build as short as possi-ble. As all decelerated flows are related to increas-ing pressure gradients all draft tubes in general work close to separation which must be avoided by any means as it would increase losses seriously. Already the difference between stationary and un-steady calculations leads to very different interpre-tations for one and the same draft tube geometry as stationary calculations indicate stable flow whereas the unsteady simulation signals detached flow (fig. 15) asking for a redesign. Also the jet wake behind the runner hub is by far overestimated by the sta-

tionary simulation whereas unsteady simulation indicates a region of lower energy behind the hub but no distinct wake. The transient calculation agrees with experiment not the stationary one.

Draft tube simulation and design is a strong chal-lenge and seems to remain one for the next future as the decelerated flow tends to separate. And to find the point of separation still is the real problem for CFD codes or more exact the real problem of quite often unsatisfying turbulence models – inspite of all the progress that has been made and has al-lowed the results which are outlined in this report. The point of separation is of special interest as the than vertical velocity wall gradient means a practi-cally frictionless suction pipe

0=∂∂

=wy

uητ if 0=∂∂

wyu

Thus a turbulence model that allows finding the point of separation will allow at the same time to

Fig. 13: Thoma coefficient σ for Francis turbine

SYLVENSTEIN, SIGMA, LA 1, H=23m

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cavitation

From this point: risk of cavitation according tosimulation

from this point:operatinglimit due to noise emission

Fig. 14: Cavitation characteristics for Francis turbine


ISSN: 1790-5095 407 ISBN: 978-960-474-093-2

develop superb suction pipes. It is exactly there where fluid dynamical simulations reaches one of its nowadays limits and where future research has

to focus. It is also somewhat astonishing that this limit is reached in case of such a simple geometry as a suction pipe be it an elbow or straight.

9 Turbine Inlet and Turbine Outlet It is an old question dating back into early times of hydraulic engineering whether turbine inlet and outlet regions belong to mechanical engineering or civil engineering. Though there is no doubt that the suction pipe as treated above belongs to the turbine itself and thus to mechanical engineering already its outlet geometry is an interface between these two

sciences. And although a headrace intake will doubtlessly fall under civil engineering but the intake area of Kaplan or bulb turbines should be treated by the mechanical engineer because of its extremely direct relation to turbine performance. In any case it is absolutely obvious that hydro power plants can only reach their utmost possible per-formance when mechanical and civil engineers cooperate.

Fig. 15: Bulb turbine: Transient simulation

Stationary

Transient

4-blade runner at optimum Flow separation

Fig. 16: Power plant entrance

Multiphase simulation with air water con-tact surface

Airbreathing vortices

Swirl breaker did not yield desired solution


ISSN: 1790-5095 408 ISBN: 978-960-474-093-2

In fig. 16 the entrance region of three vertical Kap-lan turbines is shown. Evidently the oncoming flow will be swallowed up by the first turbine without any problems but the suction side of the second and third one will form problems due to their arrange-ment which was required on geographical reasons. As can be seen in the upper part of fig. 16 the sepa-rated flow upstream of the lower two turbines starts to rotate forming air-breathing vortices. Both ef-fects (i.e. prerotation as well as the two phase air water flow) will considerably reduce the turbine efficiency. The geometrical modifications of the building construction which assured an evenly dis-tributed flow into all three turbines without air loading was an rounded contour behind the turbines (opposite the oncoming flow) and the new form of separation walls. Here it is quite evident that only the common treatment of the flow upstream of the turbine together with the flow through wicket gates and the runner will yield these reliable results. In-compressible flow always induces flow effects upstream of any components, the effects of which are of special importance for turbo machinery like turbines and pumps.

The plant entered service in 2009, air breathing vortices are not observed.

As for the suction pipe it was outlined in the last chapter that the outlet conditions behind the exit i.e. in the tail water more or less far downstream have a strong influence on the flow conditions inside and that it is indispensable to extend the simulation

Zufluss Mur

Abfluss Mur

Zufluss Pöls

2 x Saugrohr inkl. Kraftwerksauslauf

Schotter-bank

Zufluss Mur

Abfluss Mur

Zufluss Pöls

2 x Saugrohr inkl. Kraftwerksauslauf

Schotter-bank

Fig. 17: Power plant suction pipe exit and river mouth

Fig. 18: Power plant suction pipe exit and river mouth

Water jump

Velocity profile through exit region (detail)

Velocity profile through exit region

Velocity profile through exit region


ISSN: 1790-5095 409 ISBN: 978-960-474-093-2

mesh far into the tail water. A comparatively com-plex example of a twin turbine which leads its tail water into a river which has exactly there its mouth into another one is shown in fig. 17. Although only the power plant outlet directly behind the turbine suction pipe is of special interest it cannot be treated without the two rivers and their interaction. And as the main criterion is the turbine and plant efficiency it is the interrelationship between the flow of the two rivers, the flow in the turbine outlet region and the flow inside the suction pipe which must be studied. In the present case it is most inter-esting to see that even small modifications of the outlet region reduce the pressure loss coefficient from 39.4 to 37.2.

And also the flow area extending into the rivers (fig.18) reacts to small geometrical variations. A horizontal river bottom will yield a water jump because of the comparatively steep surface in the remaining distance down into the river whereas already a slight inclination of only 2° (not shown) avoids this flow phenomenon (fig. 18). This power plant will enter service in 2010 and we are quite sure that reality will proof the simulation results as true. Experience will tell.

10 Unsteady Operation, Water Ham-mer and Surge Chambers Apart from all these 3D calculations outlined so far also 1D calculations play an important role in the design of hydropower plants namely if the unsteady behaviour of the plant as a whole is concerned and how strong the water hammers are which form when the flow rate and or the pressure head (i.e the point of operation) is changed which can happen within very short time spans. In Austria in 2009 a pumped hydro power plant has been put into ser-vice which can switch its 500 MW power within such a short period of only 20 seconds from turbine into pump operation and as fast backwards. Of course these extreme operational conditions require a thorough under-standing of the unsteady effects in the plant which are of special importance as this plant is equipped with three Pelton turbines in counter pressure operation. This is (together with the extremely short reaction time) also the reason why besides the surge chamber at the connection between headrace and pressure pipe a second surge chamber is located in the tail race. And also the pressurised chamber for the Pelton turbines may be regarded a surge chamber.

One dimensional flow is treated by integrating the 1D Navier-Stokes equation

from 1 to 2 (fig. 19)

As the elevation z1 and z2 and also pressure p1 and velocity v1 are generally known the two unknowns pressure p2 and velocity v2 can be found if addi-tionally the continuity equation is taken into ac-count

Generally the flow can be treated either compressi-bly or incompressibly where the compressibility mainly results from the wall elasticity of the piping system and to a smaller extend from the water elas-ticity. As the 1D Navier-Stokes equation together with the equation of continuity are differential equations of the Cauchy-Riemann type their nu-merical solution is generally performed by the well known method of characteristics which is outlined in well known text books [e.g. 6]. It is also remark-able that another application of the same type of fluid dynamical equations is gas dynamics and in fact the development of shock waves is in some aspects related to water hammer.

As 1D systems and also the method of characteris-tics are both well known and established the real problem of unsteady hydro power plants lies in the treatment of unsteady effects such as opening and closing of ball or shut-off valves (see above), the opening and closing of variable guide vanes and

sp

gsz

sv

gv

tv

g ∂∂

−∂∂

−=∂∂

+∂∂

ρ11

( ) ( ) 012

11212

21

22

2

1

=−+−+−

+∂∂∫ pp

gzz

gvvds

tv

g ρ

210)( QQorsvA

tA

==∂

∂+

∂∂ ρρ

Fig. 19: Suction chamber principle with node positions


ISSN: 1790-5095 410 ISBN: 978-960-474-093-2

runner blades (or needles) and the modelling of surge chambers which become quite complicated for such power plants (fig.20, fig. 22).

Generally also complex branched systems are dealt with by splitting up the whole system into an even-tually large number of pipe elements - each of them with a beginning and an end - and writing the equa-

tions of momentum and continuity for each of these pipe elements and its two nodes beginning at a position with known pressure and velocity as boundary conditions. Thus a large linear equation system is found which can be inverted by conven-tional means.

In fig. 20 the upper surge chamber connected to the system at the interface between head race and pres-sure pipe for the power plant mentioned above is shown, and in fig. 21 the surge chamber in the tail race. Both surge chambers are designed as multi-chamber differential castles having multiple throt-

tles some of which with bi-directional throttling effects [7] to increase the dampening effect of the surge chambers. The left part in fig. 20 exhibits the flow field in throttle 3 in the mode when the rise shaft is emptying and when the throttle has very large resistance thus dosing back the water from the

Fig. 20: Throttled differential suction chamber with 2 chambers and three throttles and three free surfaces

Throttle 3 (detail)

upper chamber

Rise shaft andaeration pipe

Lower chamber

throttle 1

throttle 2

throttle 3

towards power house

towards reservoir

Fig. 21: Throttled differential suction chamber with 2 chambers and three throttles and three free surfaces, water levels as function of time

OverlayDiff.-WS: Spiegelhöhe v.Time [KWKopsII : KWKops_Voith_1 : res_13: Voith BLF_1c]Diff.-WS: Spiegelhöhe im Schacht v.Time [KWKopsII : KWKops_Voith_1 : res_13: Voith BLF_1c]Diff.-WS: Spiegelhöhe Oberkammer v.Time [KWKopsII : KWKops_Voith_1 : res_13: Voith BLF_1c]Diff.-WS: Q Drossel 3 (pos. Abschwingen) v.Time [KWKopsII : KWKops_Voith_1 : res_13: Voith BLF_1c]Diff.-WS: Q Belüftung (pos. Abschwingen) v.Time [KWKopsII : KWKops_Voith_1 : res_13: Voith BLF_1c]

150 200 250 300 350 400 450 500Time <s>

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egel

höhe

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>

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. Abs

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inge

n) <

m3/

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Water level in lower chamber

Separation of water levels in shaft and upper chamber

Water level in aeration pipe at connection to upper chamber

Different levels in shaft (red) and aeration (blue)


ISSN: 1790-5095 411 ISBN: 978-960-474-093-2

surge chamber into the system in a very slow flow. The filling mode with opposite flow direction and low throttle resistance would allow rapid filling of the rise shaft and the upper chamber absorbing rapidly the water from the system and thus damp-ing out the excess pressure that may be formed. An example for simulations of these unsteady effects is shown in fig. 21 where the water levels at the point where the upper end of the rise shaft and the paral-lel aeration pipe are connected to the upper cham-ber. The operation mode is the cyclical switch from pumping mode into turbine mode and backwards. One can see how the rise shaft is emptied faster than the upper chamber due to the chosen concept to outbalance the decreasing pressure in the head

race and the pressure pipe. Consequently the water levels in the chamber and the shaft separate. The aeration line always has a lower level than the par-allel shaft and it also reaches a lower level. Where the level in the aeration line is horizontal the lower chamber (not shown) is no longer ful to its top though the rise shaft still feeds the lower chamber. When the pressure in head race and pressure pipe rise again the lower chamber fills again which can be concluded from the time dependent shape of the aeration level which is then oscillatory. When the lower chamber is full the rise shaft fills again (as does the aeration pipe), reaches the upper chamber and fills it (together with the aeration pipe).

Results for a double chamber shaft surge chamber are shown in fig. 22 where the upper left depicts the filling and emptying characteristics of both cham-bers as a function of the water level at their begin-ning. The lower left shows the water level in the upper and the lower chamber and also the water level in the connection shaft between them. It can be seen that during this period of time the oscilla-tions of system pressure and chamber level never leads to empty chambers, neither the upper nor the lower one. But whereas the lower chamber is fre-quently fully filled the upper is never full to its top this way indicating that the size of the surge cham-

ber has been sufficiently dimensioned. It is also interesting to see that the shaft water level sinks and rises much faster than both chamber levels (which must be the case due to very different cross sections) and how the levels separate when the chambers are emptied and how the join again in the filling mode. Then we see that the shaft level is remarkably higher for a while than the upper chamber level which results in its rapid filling. This is why the flow characteristics in the upper left of fig. 22 are needed.

Fig. 22: Throttled double suction chamber

Abflussmengen, obere und untere Kammer, Schacht-WS

-30

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-10

0

10

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-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Überfallhöhe [m]

Abf

luss

men

ge [m

³/s]

Abflusscharakteristik Oberkammer (pos. Aufschwingen)

Abflusscharakteristik Unterkammer (pos. Aufschwingen)

OverlaySchacht-WS: Spiegelhöhe im Schacht v.Time [KW_Bodendorf : KW_Bodendorf_Anlage : res_Schacht-WS: Spiegelhöhe Unterkammer v.Time [KW_Bodendorf : KW_Bodendorf_Anlage : resSchacht-WS: Spiegelhöhe Oberkammer v.Time [KW_Bodendorf : KW_Bodendorf_Anlage : res

500 550 600 650 700 750 800 850Time <s>

0

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Spi

egel

höhe

im S

chac

ht <

m>

S

Separation of water level between shaft and upper chamber

Separation of water level between shaft and lower chamber


ISSN: 1790-5095 412 ISBN: 978-960-474-093-2

11 Conclusion and Outlook Hydro power is for now and for the foreseeable future the most important source for renewable energy. On a number of examples it was tried to show how complicated the flow regimes in the different components and parts of hydro power plants can be and what information the designer, maker or user of these plants may need. But fortu-nately modern CFD techniques yield possible nu-merical simulations that could not be performed until recently. It is remarkable how exact and reli-able recirculating flows can be treated and also the big problem of hydraulic liquids – cavitation – can now be dealt with in straight forward manner and with reasonable or low efforts.

Experimental work will certainly still keep its im-portant role that it has always had in hydraulic en-gineering both as for civil as for mechanical engi-neering. But due to the enormous improvements that have been made in recent years and that were tried to outline in this paper the role of experiments will certainly change in the time coming. If the experiment served as a tool to develop, improve and optimise hydro power plants and machinery by way of trial and error it will serve to control and check the results and designs that were found nu-merically. For now it is hard to believe that a de-signer would renounce to perform this experimental check of numerical results. The big advantage is that not a number of models of prototype are to be built and modified in a extremely time and money con summing way until the final result is found but all modifications are made by way of fast and cheap simulations – and experiment “only” tells that all variations are reasonable and plausible.

As has also been outlined the only inconvenience of fluid dynamical simulations is the shortfall of turbulence. Though also extremely complicated flows can now be calculated reliably – as has been shown – the estimation of the onset of flow separa-tion as well as reattachment points is still an unre-solved question but it is important especially for suction pipes. This turbulent problem is now be-lieved to be solved by applying the direct numerical simulation DNS where one treats all flows laminar and “just” resolves the flow field in such a detailed way and on such a small geometry scale that also the smallest turbulent eddies can be calculated. Certainly the present computer storage capacity is by far not yet sufficient for fluid dynamical prob-lems in an industrial frame. We shall see how this

approach will also help to solve the problem of separating and reattaching flow.

The future development and application of numeri-cal methods is expected to concentrate on fluid-structure interference which has a strong effect on the design of runner blades and guide vanes.

The still unsatisfactory treatment of suction pipes was addressed a few times. Another open question is the widely controllable Francis turbine. Francis turbines represent roughly two thirds of all turbines world wide, are the largest and most powerful turbo machinery that exists and yield the best efficiency of all turbines. But they are normally not operable outside the design point where unsteady operation with strong vibrations and cavitation commences and though some methods have been tried a general solution to this problem is presently not available. So it is expected that future research will concen-trate on part load behaviour of Francis turbines and on suction pipes.

References: [1] Menter, F.R., Two-equation eddy-viscosity turbulence models for engineering applications, AIAA-Journal, Vol. 32, No. 8, 1994, pp. 1598 - 1605 [2] G. Penninger, H.Benigni, H.Jaberg, New design of butterfly valves for modern pump-storage power plants, Hydro2005 Conference and exhibition, Vil-lach, 2005 [3] Penninger, G., Benigni, H., Numerical simula-tion and design of spherical valves for modern pump storage power plants, 14th International Seminar on Hydropower Plants, Vienna, 2006. [4] Keck, H., Goede, E., Pestalozzi, J., Experience with 3-D-Euler-Flow-analysis as a practical design tool, proceedings from the 15th symposium on hy-draulic machinery and cavitation: modern technol-ogy in hydraulic energy production, Belgrade, 1990. [5] Gehrer, A., Egger A., Riener J., Numerical and Experimental Investigation of the draft tube flow downstream of a bulb turbine, proceedings of the 21st IAHR Symposium on Hydraulic Machines and Systems, Lausanne, 2002. [6] Wylie, E.B., Streeter, V.L., Fluid Transinets in Systems, Englewodd Cliffs, Prentice Hall, 1993. [7] Meusburger, P., Die 1D transiente numerische Simulation von modernen Hochdruck-Wasserkraftanlagen. Doctoral Thesis, University of Technology Graz, 2009.


ISSN: 1790-5095 413 ISBN: 978-960-474-093-2

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