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Scientific Bulletin of the Politehnica University of Timisoara

Transactions on Mechanics Special issue

The 6th International Conference on Hydraulic Machinery and Hydrodynamics Timisoara, Romania, October 21 - 22, 2004

ANALYSIS OF THE GAMM FRANCIS TURBINE DISTRIBUTOR 3D FLOW FOR THE WHOLE OPERATING RANGE AND OPTIMIZATION OF THE GUIDE VANE AXIS

LOCATION

Sebastian MUNTEAN, PhD, Senior Researcher* Center of Advanced Research in Engineering

Sciences Romanian Academy - Timisoara Branch

Romeo F. SUSAN-RESIGA, PhD, Professor Department of Hydraulic Machinery “Politehnica” University of Timisoara

Sandor BERNAD, PhD, Senior Researcher Center of Advanced Research in Engineering

Sciences Romanian Academy - Timisoara Branch

Ioan ANTON, PhD, Professor, Member of the Romanian Academy

Department of Hydraulic Machinery “Politehnica” University of Timisoara

*Corresponding author: Bv Mihai Viteazu 24, 300223, Timisoara, Romania Tel.: (+40) 256 403692, Fax: (+40) 256 403700, Email: seby@acad-tim.tm.edu.ro

ABSTRACT The paper presents a numerical investigation of the 3D flow in the distributor (stay vanes and guide vanes) of the GAMM Francis turbine. The domain corresponds to the distributor (stay vane and guide vane) interblade channel. The distributor computational domain is bounded upstream and downstream by cylindrical and conical patches, respectively. The first one corresponds to the spiral casing outflow section, while the second one is conventionally considered to be a conical patch upstream the runner. On the distributor inlet section a constant radial and circumferential velocity compo-nents corresponding to an ideal spiral case, with zero axial velocity. Since we assume a perfect spiral casing, the distributor inlet velocity field has no circumfer-ential variation. On the outlet section a measured pressure profile is considered. The distributor domain is discretized using an unstructured mesh. There are three main issues addressed in this paper: first, using the numerical methodology presented above, the distributor flow for several guide vane angle values is computed. As a result, the guide vane torque versus guide vane opening angle is computed for the actual position of the guide vane axis; second, we investigate the flow for the whole range of the guide vane posi-tions, at four different locations of the guide vane axis.

KEYWORDS Francis turbine distributor, guide vane axis optimization.

NOMENCLATURE

ref

rr

EVc

2= [-] radial velocity coefficient

ref

uu

EVc

2= [-] tangential velocity coefficient

ref

za

EVc

2= [-] axial velocity coefficient

( ) ( )22zrm ccc += [-] meridian velocity coefficient

M [Nm] torque g [m/s2] gravity

Subscripts and Superscripts r radial direction u tangential direction z axial direction

ABBREVIATIONS ref reference section (draft tube inlet section) gv guide vane in, out inlet section, outlet section min, max minimum and maximum opening

1. INTRODUCTION The Francis turbine distributor, which includes two radial cascades in tandem, is an essential component of the turbine. The stay vanes are fixed and unloaded, while the guide vanes have adjustable position in correlation with the turbine discharge. The guide

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vanes open synchronously modified by an appropriate rotation around axes parallel to the machine axis. The corresponding guide vane loading is transmitted to the vane axis as a force and torque. The position of the force vector support with respect to the guide vane axis influences the torque magnitude. The maximum torque magnitude influences the mechanical design of the turbine regulating system, and it is preferable to minimize this value. The present paper addresses this issue, by examining the variation of the torque in the guide vane axis at variable guide vane opening. As a result, an optimization criterion is proposed and used in order to minimize the loading of the turbine regulating system.

Figure 1. The three-dimensional cut through the GAMM Francis turbine.

Figure 1 shows a three-dimensional view of the GAMM Francis turbine considered in the present study, [7,8]. One can easily observe the typical configu-ration of a Francis turbine distributor, and the regulating mechanism. Although the stay vane and guide vane radial cascades can be analysed using a simplified 2D inviscid flow model, in the present study we are employing a full 3D flow computation to obtain an accurate evaluation of the guide vane loading and torque. This choice is motivated by observing that 3D flow affects are significant in the neighbourhood of the guide vane trailing edge, as one can infer from the meridional cut shown in Figure 2. This is generally the case for medium/large specific speed Francis turbines. Since the flow in the turbine distributor is acceler-ated, there are practically no flow detachments on the guide vanes for the whole operating range. As a result, as far as the blade loading is concerned, viscous effects can be neglected for the present analysis and optimization procedure. Moreover, the flow can be considered steady, since no sources of unsteadiness are present in the spiral case or further upstream. In conclusion, in this paper we consider a 3D steady Euler flow in the Francis turbine distributor.

Figure 2. Meridional cross section through the

GAMM Francis turbine model [7,8]

Section 2 presents the 3D computational domain and the boundary conditions. The parametric study performed in this paper requires the modification of the domain geometry according to variable guide vane opening angle. In Section 3 we first compute a least squares approximation of the discharge versus guide vane opening correlation, at constant head, from the turbine hillchart. Then, the variation of the torque in the guide vane axis is computed versus the guide vane opening angle, considering the original guide vane axis location. Moreover, the distributor discharge-pressure drop characteristic curve is computed, and later used to define equivalent guide vane openings as the guide vane axis location is modified. Section 4 presents a parametric study of the turbine distributor, by modifying the guide vane axis location. For each axis position considered, a momentum versus opening angle curve is computed, and the extremum torque values are obtained. We define the optimum axis position by imposing the equality of the magnitudes of torque extremum values. As a result, a new location of the guide vane axis is identified, with a minimum torque value and a minimum loading of the regulating mechanism. This result is particularly important for large hydraulic turbines, where the torque magnitude reaches very large values. The paper conclusions are summarized in the last section

2. COMPUTATIONAL DOMAIN AND BOUNDARY CONDITIONS Figure 3 presents a top view of the GAMM Francis turbine distributor, with the actual stay vane and guide vane geometry [7].

The guide vane is shown for several positions, rang-ing from completely closed ( 0=gvα ) to maximum opening ( o35=gvα ). The computational domain is bounded by two angular periodic lateral surfaces that

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are able to include the guide vane for all opening angle values, as shown in Fig. 3 bottom. This choice allows the minimum change in the computational domain geometry, as well as a rapid re-meshing for each guide vane position under consideration.

Stay vane

Adjusting guide vane

(24 blades)

(24 blades)

Distributorinlet section

Distributoroutlet section

Maximum opening

Nominal opening

Minimum opening

Displacement of the guide vane blade at:=35αgv

=25αgv

=0αgv

Figure 3. Top view of the GAMM Francis distributor

and computational domain.

Figure 4 shows the full 3D computational domain for the distributor flow computation. It corresponds to a 3D channel which includes one stay vane and one guide vane. Besides the periodic lateral surfaces, the channel is bounded by the upper and lower distributor rings. The inlet section corresponds to the spiral case outlet. The velocity field here has a negligible com-ponent parallel to the machine axis ( 0=ac ). The radial and tangential inlet velocity components are computed for each discharge value, while keeping the inlet angle constant (corresponding to the spiral case geometry).

The outlet section for the distributor domain in Figure 4 corresponds to a conical patch upstream the runner (see BB’ in Figure 2). On this section pressure conditions must be imposed. Since the present study does not deal with a coupled flow distributor-runner, an experimental pressure profile, measured on the survey axis BB’ form Fig. 2, is considered in the present investigation. This is not a rigorous boundary condition, since the pressure profile is changing with variable

discharge. However, the influence on the guide vane torque is unlikely to be significantly affected by the details of the outlet condition.

Figure 4. Three-dimensional computational domain

for the GAMM Francis turbine distributor.

3. DISTRIBUTOR FLOW ANALYSIS Using the above computational domain and boundary conditions, we compute the steady 3D Euler flow in the Francis turbine distributor.

First, we compute the correlation between the dis-charge and the guide vane opening angle, )(f αQ = . In doing so, we are considering the experimental data from the turbine hillchart, for constant nominal head, as shown in Figure 5. Two hillcharts were available for the GAMM turbine, one of them being the conventional one, and the second one being computed without taking into consideration the draft tube. The differences are quite small, as one can see from Fig. 5. An analytical representation for the experimental data is obtained using a polynomial least squares fit. It has been concluded, see Fig. 5, that a parabolic representation of the )(f αQ = dependence is accurate enough, and can be further used for the parametric study.

Once the discharge known at each guide vane opening, the 3D flow simulation is performed, and the torque in the guide vane axis is computed using the pressure distribution on the guide vane.

Figure 6 shows the variation of the torque for twelve guide vane openings, including the completely closed position. A polynomial least squares fit (solid line) is used to interpolate the numerical values, and to deter-mine the extremum values. It can be seen that there are two extrema: the minimum (negative) value cor-responds to the completely closed position, while the maximum (positive) torque corresponds to an opening smaller than the value at best efficiency point ( o25=α ). Of course, when designing the turbine regulating system, the maximum absolute value of the torque is to

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be considered for the structural analysis. An optimum design will first minimize the loading, and this can be accomplished by an appropriate choice of the axis location.

Figure 5. The correlation between the turbine discharge and the guide vane opening angle.

Figure 6. Guide vane torque versus guide vane angle

for the GAMM distributor at n0 = 0.07208 (e = 0, i.e. actual GAMM Francis turbine design).

The results shown in Fig. 6 correspond to the actual GAMM Francis turbine design, i.e. the original guide vane axis location. Figure 7 presents the geometrical parameters used to define the axis position with respect to the symmetrical guide vane chordline.

The eccentricity e is the distance from the axis position to the guide vane mid-chord point. The original design considers 0=e . The dimensionless eccentricity 0n is defined as,

0

02010 2 l

lln⋅−

= ,

where the segments 0l , 01l , and 02l are defined in Figure 7.

b

Ogv

1l

Rgv

01l

l0

02l

gv

a e0

ll2

a

c

Figure 7. Guide vane geometrical parameters.

One can easily see that by changing the guide vane axis position, practically the whole radial cascade geometry is modified. As a result, one question to be answered is how can one define equivalent guide vane openings, since the

)(f αQ = dependence shown in Fig. 5 is no longer valid for other eccentricity values. Traditionally, this equivalence can be established using various geometrical considerations, without any reference to the actual flow field. However, we are proposing here a new approach, based on the results of the numerical simulation. When computing the flow field at variable guide vane opening, one obtains the distributor pressure drop ( )α1f∆p = . Such a curve is shown in Fig. 8, where the numerical data were approximated quite well by a third degree polynomial least squares fit. This curve is computed for the original guide vane axis position.

Figure 8. Pressure drop versus guide vane angle for

the GAMM distributor.

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After eliminating the guide vane opening angle between ( )αQ f= (from Fig. 5) and ( )α1f∆p = (from Fig. 8), one obtains the hydraulic character-istic curve for the distributor, ( )Qf∆p 2= shown in Fig. 9.

Figure 9. Pressure drop versus discharge for the

GAMM distributor at n0=0.07208 (e=0). Using the distributor characteristic curve above, we

can introduce a hydraulic equivalence criterion as follows: two guide vane radial cascade configurations are said to be equivalent if for the same discharge values the corresponding pressure drop values are equal. In other words, two hydraulically equivalent cascade regimes should coincide on the characteristic curve from Fig. 9. Obviously, at different eccentricity values, the corresponding opening angles will be different, and the constant opening lines on the turbine hillchart will be slightly shifted. However, the above criterion will insure the same runner inlet flow con-ditions at a give discharge, no matter the guide vane eccentricity.

4. OPTIMIZATION OF THE GUIDE VANE AXIS LOCATION Using the methodology described in Section 3, we are performing a parametric study of the guide vane torque for several axis eccentricity values. The torque variation is shown in Figure 10, for three additional guide vane axis position (besides the original one, which corresponds to the solid curve):

♦ for n0 = -0.00247 (e = -5 mm), • for n0 = 0.07208 (e = 0), ■ for n0 = 0.14508 (e = +5 mm), ▲ for n0 = 0.21656 (e = +10 mm).

The dashed curves correspond to the third order polynomial least squares fits. It is easy to see from Fig. 10 that the torque extremum values are largely influenced by the axis position. These extrema are plotted versus the eccentricity in Figure 11.

Figure 10. Guide vane torque variation versus the guide vane opening, for several values of the axis

eccentricity.

We are now in position to state an optimization criterion, as follows: the optimum guide vane axis location is the one that gives equal magnitudes of the torque extrema. It is easy to see that in this case, the torque extrema has also a minimum value in comparison to other configurations, thus answering to the original requirement of minimizing the turbine regulating system loading.

Figure 11. Guide vane torque extrema versus the

guide vane shaft axis eccentricity.

The optimum shaft position corresponds to the intersection of the torque extreme value lines, i.e. the maximum value ( )gv

maxM and the value at the closing

position of the guide vane - ( )gvoM . According to the

criterion defined above the optimum eccentricity for GAMM distributor is 6972.eopt −= mm. In other words, the minimum guide vane torque ( ) Nm.81650M gv

min = is obtained by moving the guide vane shaft by

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2.697 mm toward the trailing edge of the guide vane blade from its actual position.

Figure 12. The original (solid line) and optimum (dashed line) torque variation versus guide vane

angle for the GAMM turbine.

Figure 12 presents the original (solid line) and optimum (dashed line) torque distribution for the whole range of the GAMM guide vane opening. It can be seen that the optimized location leads to a more rational loading of the regulating mechanism. According to the dimensionless eccentricity defini-tion n0, the optimum position of the guide vane shaft is obtained at n0 = 0.032. The literature recommends for the guide vane that contains 24 blades and sym-metric profile n0 = 0.040, [6, p324]. One can see that the value found through the present analysis is 20% smaller, but has a robust justification.

5. CONCLUSIONS The paper addresses a design optimization problem for the location of the guide vane rotation axis position. Although the particular example presented in detail corresponds to the GAMM Francis turbine model, it is quite obvious that both the methodology, as well as the optimization criterion, are valid for any Francis or Kaplan turbines. The optimization criterion considered in this paper is the minimization of the mechanical loading of the turbine regulating system. This means that the extre-mum value of the torque appplied to the guide vane shaft has to be minimized. The designed parameter to be optimized is the location of the guide vane shaft axis along the guide vane chordline. Our methodology employs rigorous hydrodynamic considerations, rather than geometric arguments. Al-though the methodology seems to be quite laborious, since it involves a series of 3D flow simulation, the result clearly shows an improvement over the original design.

ACKNOWLEDGMENTS The present work has been supported from the

National University Research Council Grant (CNCSIS) 109/2002-2004 and 220/2003-2004. Numerical com-putations have been performed at the Numerical Simulation and Parallel Computing Laboratory from the “Politehnica” University of Timisoara, National Center for Engineering of Systems with Complex Fluids.

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