DEVELOPMENT OF A SWIRLING FLOW APPARATUS FOR...

DEVELOPMENT OF A SWIRLING FLOW APPARATUS FOR ANALYSIS AND

DEVELOPMENT OF SWIRLING FLOW CONTROL Sebastian Muntean1, Albert Ruprecht 2, Romeo Susan-Resiga 3

Introduction For Francis turbines operated at partial load a high level of residual swirl

ingested by the draft tube results from a mismatch between the swirl generated by the wicket gates (guidevanes) and the angular momentum extracted by the turbine runner [11]. In the turbine draft tube the flow exiting the runner is decel-erated, thereby converting the excess of the kinetic energy into static pressure. The decelerated swirling flow often results in vortex breakdown above a certain level of swirl number, and this is now recognized as the main cause of the severe pressure fluctuations experienced by hydraulic turbines at part load. The pressure fluctuations are caused by the transformation of an axisymmetrical swirling flow into one or more precessing helical vortices as the operation condition shifts toward part load. This self-induced precessing motion of the helical vortex results in a fluctuating pressure on any stationary point of the draft tube cone.

The draft tube design is aimed at maximizing the conversion of kinetic energy downstream the hydraulic tubine runner into potential pressure energy with minimum hydraulic losses. Thicke [21] reviews some optimum design rules for draft tubes, as well as some practical solutions for draft tube instability problems. Since most of the kinetic-to-potential energy conversion occurs in the draft tube cone, particular attention should be devoted to conical diffuser optimization. McDonald et al. [18] provide basic design information for diffusers with incompressible swirling inlet flow. They show that swirling inlet flow does not affect the performance of diffusers which were unseparated or only slightly separated with axial inlet flow. For diffusers which were moderately or badly separated for axial inlet flow, swirling inlet flow caused large performance increases. Clausen et al. [8] have measured the swirling boundary layer devel-opment in a conical diffuser with a 20° included angle and an area ratio of 2.84. The inlet swirl was close to solid-body rotation and was strong enough to prevent boundary layer separation without producing recirculation in the core flow. The mean velocity measurements of the swirling flow in the conical diffuser emphasize 1 PhD, Romanian Academy – Timişoara Branch, Romania 2 PhD, Institute for Fluid Mechanics and Hydraulic Machinery, Universität Stuttgart, Germany 3 PhD, “Politehnica” University of Timişoara, Romania

42 3rd GERMAN-ROMANIAN WORKSHOP on TURBOMACHINERY HYDRODYNAMICS, May 10-12, 2007

the subtle interaction between the tendency of the boundary layer to separate, which increases the mean velocity near the center line, and the tendency of the swirling flow to recirculate near the axis, which increases the velocity near the boundary layer edge. Both must be avoided if the diffuser is to perform efficiently. In their experiments, Clausen et al. [8] found a ratio of maximum circumferential velocity (for solid-body rotation inlet swirl) to the axial velocity (practically constant at diffuser inlet) of 0.59, which is quite close to the value of 0.6 for swirling flow downstream the Francis turbine runner at best efficiency point, with 17° draft tube cone, investigated in the FLINDT project [4][20]. It is clear that at design operating point the hydraulic turbine runner blades can be shaped such that the swirl at the draft tube inlet can insure the best efficiency of the kinetic-to-potential energy conversion in the draft tube cone, and as well as overall best turbine efficiency. However, when a Francis turbine, which has a fixed pitch runner, is operated at partial discharge the swirl number at the inlet of the draft tube cone increases and the decelerated swirling flow evolves in vortex breakdown with associated self-induced instabilities.

The purpose of the present investigation is to develop and test a novel flow control method aimed at mitigating the vortex breakdown using an axially injected water jet.

The test case corresponds to a straight conical diffuser, with inlet swirling flow generated by an adjustable axial guide vane apparatus. The swirling flow at the diffuser inlet should mimic the actual swirl downstream the Francis turbine runners operated at partial discharge. In order to achieve this swirl configuration, in addition to suitable axial guide vane design we use a central body (hub) which ends with a nozzle for control jet injection.

Experimental studies for swirling flow in conical diffusers McDonald et al. [18] performed an experimental investigation to determine

the effect of swirling inlet flow on the performance and outlet profile of conical diffusers. Twenty four different diffusers were tested, with total divergence angles ranging from 4.0° to 31.2°, and with area ratios from 1.30 to 8.28. Swirling inlet flow does not affect performance of diffusers which were unseparated or only slightly separated with axial inlet flow. For diffusers which were moderately or badly separated for axial inlet flow, swirling inlet flow caused large performance increases.

Clausen et al. [8] investigated experimentally the swirling flow in a 20 included angle conical diffuser, Fig. 1, with a solid body rotation inlet swirl generated with a honeycomb. They found that generally there is a small range of swirl number values (defined as the ratio of maximum circumferential to average axial velocity) that avoids both recirculation and separation. Their results highlight the interaction between the tendency toward boundary layer separation and the advent of recirculation in the core flow.

Kurokawa et al. [16] use the swirl generator from Fig. 2 to investigate the so-called “J-groove” technique for suppressing the swirl in a 20 conical diffuser.


The aim of their investigations was to suppress the draft tube surge for Francis turbines. The main difference with respect to the swirl generator used by Clausen et al., Fig. 1, is the upstream central body , with a shroud diameter twice the throat diameter, and an end cone of 60 . The convergent swirling flow upstream the diffuser throat is closer to the Francis turbine configuration, and could produce a swirling flow similar to the one downstream the Francis runner.

Fig. 1. Swirl generator used by Clausen et al. [8].

Fig. 2. Swirl generator used by Kurokawa et al. [16].

Flow control in diffusers with swirl The analysis of decelerated swirling flow in the turbine draft tube cone

shows that the flow is abruptly decelerated near the centerline as the turbine discharge decreases, resulting in a central quasi-stagnant region. This vortex


breakdown phenomenon leads to an increase in hydraulic losses, and as the turbine discharge is further decreased an unsteady helical vortex breakdown develops. It is obvious that flow deceleration near centerline is further enhanced by the presence of the runner crown wake. The radial extent of the velocity deficit region in the crown wake rapidly grows as discharge decreases as a result of the fixed pitch runner behaviour at part load. All these observations suggests that mitigating the vortex breakdown in the draft tube cone is the main approach for improving the Francis turbine operation at discharge significantly smaller than the one corresponding to the best efficiency operating point.

There are two main approaches for reducing or eliminating the vortex breakdown downstream the Francis turbine runners. First, one can reduce the swirl intensity in the cone. Thicke [21] reviews the development and performances of stabilizer fins installed on the cone wall, and Nishi et al. [19] performed extensive experimental investigations on various configurations of fins. The idea is to hinder the circumferential flow mainly in the neighbourhood of the cone wall. The fin shape, size and location are mainly subject to trial-and-error approaches. The main drawback of this solution is that it introduces additional losses and it cannot be adjusted with the operating point. Recently, Kurokawa et al. [16] proposed and examined the so-called “J-groove” for controlling and suppressing the swirl component of the flow in the draft tube cone of Francis turbines. The “J-groove” is a very simple passive device composed of shallow grooves mounted on the diffuser wall, parallel to the pressure gradient. The reduction in swirl intensity obtained with such devices decreases the pressure fluctuations caused by the rotation of vortex core around the dead water region near the diffuser inlet. Along the same lines, other technical solutions propose the introduction of various structures (e.g. splitter plates) in the draft tube cone, aimed at reducing the swirl intensity or destroying the coherent helical structures at part load. Kjelsen et al. [15] develop a technology for mitigation or reduction of pressure pulsations in Francis draft tube by injecting high speed water jets from distributed positions at the draft tube walls. The jets are injected tangentially and angled downstream with respect to the machine axis. This injection system would presumably have the following effects: i) by injecting water in opposite direction of the swirl down-stream the runner one can reduce the large scale swirls, ii) by filling the boundary layers with high impulse water jets separation at the wall can be delayed. Injecting multiple water jets at the wall has the drawback of large water consumption, thus significantly reducing the overall turbine efficiency. The second approach for mitigating the vortex breakdown in the cone is to act on the axial momentum of the flow instead of reducing the circumferential momentum. Runner cone extensions attached to the crown have been shown to play an important role in controlling the velocity distribution in the draft tube below the runner. Falvey [12] presents this solution starting from the idea that reducing the draft tube surges can be achieved by filling the stagnant of reverse flow region with a solid body of rotation. Obviously, such large runner cone extensions would be subject to large lateral forces in addition to a significant decrease in kinetic energy recovery within the cone. Practical solutions shown by Thicke [21] use rather


small conical or cylindrical extensions of the runner crown. Vekve [22] investigates several configurations of runner cone – attached semi-tapered cones, and concludes that the necessary size required to avoid the vortex breakdown vary with the part-load operating point. He suggests that an ideal solution would be to attach an arrangement to the runner cone which can vary the diameter and length according to the operating point. Unfortunately, this is not practical. Karashima [14] investigates numerically the interaction between a swirling flow and a coaxial jet in order to clarify the feasibility of vortex breakdown control by means of a small blowing. He found that applying the blowing to a broken vortex flow having a bubble induces an amount of leeward movement and bubble shrinking, and concluded that this technique can offer a significant improvement in breakdown characteristics of the swirling flow.

The above analysis of various solutions for mitigating the vortex breakdown in conical diffusers with inlet swirling flow led us to the conclusion that a successful technology should address the axial momentum deficit near the axis rather than reducing the circumferential momentum near the wall.

Swirl Generator Design and Analysis The present study is aimed at developing a technical solution for an axial

swirl generator which mimics the swirl downstream the Francis turbine runner at partial discharge. In the conical diffuser downstream the swirl generator a helical vortex breakdown (precessing vortex rope) should occur, with associated pressure fluctuations.

Fig. 3. Meridian cross-section of the IHS swirl generator domain.

Fig. 3 shows the IHS swirl geometry in a meridian cross-section. The upstream part corresponds to an annular section with Ø 35 mm hub and Ø 80 mm shroud. In this annular section axial blades are used to add a tangential velocity component to the axial incoming flow. The present study is concerned with the design and analysis of this bladed region.

If the flow upstream the cone has no swirl, the flow detaches from the wall and the pressure recovery is poor, with large hydraulic losses generated by the recirculation region near the wall. When a tangential velocity component is added, the diffuser performances improve significantly because the flow remains attached to the wall. However, pushing the flow in the radial direction produces a severe deceleration near the axis, resulting in a quasi-stagnant or reverse


flow region. This phenomenon is known as vortex breakdown. For moderate swirl, the recirculation bubble remains quasi-stable and axial symmetric. At the boundary between the central stagnnat region and the main annular stream there in a vortex sheet. The vorticity magnitude in this vortex sheet increases as the swirl increases, until a certain value where the axi-symmetrical vortex sheet becomes unstable and rolls-up in a helical vortex, with precessing motion. This self-induced swirling flow instability is known as helical vortex breakdown, and leads to an unsteady flow with associated pressure fluctuations. The aim of the present numerical and experimental investigations is to restore the steady character of the flow, using various flow control techniques, thus improving the pressure recovery in the diffuser, reducing the hydraulic losses, and restoring the axial symmetry of the flow.

In order to achieve a helical vortex breakdown similar to the one encoun-tered in the discharge cone of Francis turbines operated at partial discharge, a large enough swirl intensity must be provided upstream the conical diffuser. One technical solution is to use adjustable cambered guide vanes. However, in order to avoid flow detachment on the blades sucction side, a rather small pitch-to-chord ratio should be used. This is implies a Kaplan-like blade configu-ration, which is more complicated from technological viewpoint. Particular attention should be paid to the tip/hub clearance, in order to avoid spurious leakage jets that may alter the swirling flow behaviour in the diffuser. Numerical studies, as well as measurements of velocity profiles downstream Francis runner at partial discharge (e.g. FLINDT project) have shown that an average swirl angle (angle between the velocity vector and the axial direction) that produces a strong vortex rope should be around 35°. This level of flow deflection is difficult to achieve with guide vanes that have a pitch-to-chord ratio larger than unity, because of the severe flow detachment on the blade suction side. As a result, we have investigated a solution that uses stay vanes to provide a 35° swirl flow angle, followed by symmetric guide vanes that can further increase/decrease the swirl angle within ±10°.

0 10 20 30 40 50axial coordinate [mm]

−5

0

5

10

15

20

25

tang

entia

l coo

rdin

ate

[mm

]

hub blade sectionshroud blade section

Fig. 4. Thin foil cascades designed for hub and shroud of stay vanes.


Fig. 4 shows the thin blade designed for 2D cascades at hub and shroud, with corresponding streamlines in Fig. 5 and Fig. 6. One can see that there is no shock at the leading edge, while the blade camber line is not aligned with the incoming axial flow.

Fig. 5. Streamlines for the stay vanes hub cascade, pitch-to-chord ratio

0.25512 (8 blades with 50 mm axial extent on a 35 mm diameter).

Fig. 6. Streamlines for the stay vanes hub cascade, pitch-to-chord ratio

0.58177 (8 blades with 50 mm axial extent on a 80 mm diameter).

Fig. 7 shows the thin stay vanes designed for a constant downstream swirl angle of 35°. The 3D blade geometry results from several 2D cascade design, for a given flow deflection distribution from leading edge to the trailing edge and zero angle of attack at leading edge. Obviously, the swirl presence at outlet alters the uniform axial velocity profile, according to the radial equilibrium condition (radial component of the momentum equation), as shown in Fig. 8.


Fig. 7. Pressure coefficient distribution on the stay vanes,

for an average swirl angle 35°.

0.015 0.02 0.025 0.03 0.035 0.04radius [m]

0

2

4

6

8

10

axia

l vel

ocity

[m/s

]

upstream statordownstream stator

0.015 0.02 0.025 0.03 0.035 0.04radius [m]

0

2

4

6

8ta

ngen

tial v

eloc

ity [m

/s]

upstream statordownstream stator

Fig. 8. Axial and circumferential velocity profiles upstream/downstream

the stay vanes.

Fig. 9. Pressure coefficient distribution on the guide vanes at 35°,

i.e. aligned with the swirl downstream the stay vanes.


Fig. 10. Pressure coefficient distribution on the guide vanes at 35°+5°,

swirl increase.

Fig. 11. Pressure coefficient distribution on the guide vanes at 35°-5°,

swirl decrease.

Fig. 12. Pressure coefficient distribution on the guide vanes at 35°-10°,

swirl decrease.


Average flow angle versus adjustable blade angle.

Velocity components for adjustable blade angle 25°.

Velocity components for adjustable blade angle 30°.

Velocity components for adjustable blade angle 35° (aligned with incoming

swirl).

Velocity components for adjustable

blade angle 40°. Velocity components for adjustable

blade angle 45°. Fig. 13. Average flow angle and velocity components downstream the swirl

generator for variable angle of adjustable blades (guide vanes).


25° 30° 35° 40° 45°

Fig. 14. Streamlines in the diffuser, for variable adjustable blade angle.


25° 30° 35° 40° 45° Fig. 15. Vorticity in the diffuser, for variable adjustable blade angle.


The swirling flow generated by the stay vanes enters in the adjustable guide vanes, considered here as symmetric constant-thickness blades, with rounded leading edge and sharpened trailing edge. The guide vanes only adjusts the tangential velocity in a certain range centered on the swirl produced by the stay vanes. Note that the stay vanes can have a relatively small pitch-to-chord ratio, while the guide vanes have a larger that unity pitch-to-chord ratio. Fig. 9 shows the guide vanes aligned with the incoming swirl, resulting in an unchanged swirl further downstream.

When the guide vane is rotated with respect to this position, it increases or decreases the swirl. This can be clearly seen in Fig. 13. The five swirl profiles from Fig. 13 are further used for a 2D axi-symmetric flow analysis in the domain from Fig. 3. Fig. 14 shows the streamlins in the meridian half-plane, with a clear recirculation bubble corresponding to vertex breakdown. Moreover, Fig. 15 shows the increase in the vortex sheet strenght, which ultimately leads to the helical vortex breakdown.

Acknowledgements

The present work has been supported by the Romanian Government – Ministry of Education and Research, National Authority for Scientific Research through CEEX-M1-C2-1185 contract No. 64/2006-2008 “iSMART-flow” project.

References [1] Armfield, S.W., Cho, N.-H., Clive, A., Fletcher, J., 1990, Prediction of Turbulence

Quantities for Swirling Flow in Conical Diffusers, AIAA Journal, Vol. 28, No. 3, pp. 453-460.

[2] Armfield, S.W., Fletcher, C.A.J., 1986, Numerical Simulation of Swirling Flow in Diffusers, International Journal for Numerical Methods in Fluids, Vol. 6, pp. 541-556.

[3] Armfield, S.W., Fletcher, C.A.J., 1989, Comparison of k-ε and Algebraic Reynolds Stress Models for Swirling Diffuser Flow, International Journal for Numerical Methods in Fluids, Vol. 9, pp. 987-1009.

[4] Avellan, F., 2000, Flow Investigation in a Francis Draft Tube: the FLINDT Project, 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, U.S.A.

[5] Benim, A.C., 1990, Finite Element Analysis of Confined Turbulent Swirling Flows, International Journal for Numerical Methods in Fluids, Vol. 11, pp. 697-717.

[6] Cervantes, M.J., and Engström, T.F., 2004, Factorial Design Applied to CFD, Journal of Fluids Engineering, Vol. 126, pp. 791-798.

[7] Chang, K.-C., Chen, C.-S., 1993, Development of a Hybrid k-ε Turbulence Model for Swirling Recirculating Flows Under Moderate to Strong Swirl Intensities, International Journal for Numerical Methods in Fluids, Vol. 16, pp. 421-443.

[8] Clausen, P.D., Koh, S.G., Wood, D.H., 1993, Measurements of a Swirling Turbulent Boundary Layer Developing in a Conical Diffuser, Experimental Thermal and Fluid Science, Vol. 6, pp. 39-48.


[9] Durst, F., Wennerberg, D., 1991, Numerical Aspects of Calculation of Confined Swirling Flows with Internal Recirculation, International Journal for Numerical Methods in Fluids, Vol. 12, pp. 203-224.

[10] Elkaim, D., McKenty, F., Reggio, M., Camarero, R., 1994, Control Volume Finite Element Solution of Confined Turbulent Swirling Flows, International Journal for Numerical Methods in Fluids, Vol. 19, pp. 135-152.

[11] Escudier, M., 1987, Confined Vortices in Flow Machinery, Ann. Rev. Fluid Mech., Vol. 19, pp. 27-52.

[12] Falvey, H.T., 1971, Draft tube surges – A Review of Present Knowledge and an Adnotated Bibliography, U.S. Bureau of Reclamation, REC-ERC-71-42.

[13] Fletcher, C.A.J., 1985, Application of the Dorodnitsyn Finite Element Method to Swirling Boundary Layer Flow, International Journal for Numerical Methods in Fluids, Vol. 5, pp. 443-462.

[14] Karashima, K., 1984, Effect of a Small Blowing on Vortex Breakdown of a Swirling Flow, Computational Techniques and Applications CTAC-83, North-Holland, pp. 553-564.

[15] Kjeldsen, M., Olsen, K.-M., Nielsen, T., and Dahlhaug, O.G., 2006, Water Injection for the Mitigation of Draft-Tube Pressure Pulsations, IAHR Int. Meeting of W.G. on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Barcelona.

[16] Kurokawa, J., Kajigaya, A., Matusi, J., and Imamura, H., 2000, Suppression of Swirl in a Conical Diffuser by Use of J-groove, Proc. 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North Carolina, U.S.A., paper DY-01.

[17] Launder, B.E., Reece, G.J., Rodi, W., 1975, Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mechanics, Vol. 68, Part 3, pp. 537-566.

[18] McDonald, A.T., Fox, R.W., and Van Dewoestine, R.V., 1971, Effects of Swirling Inlet Flow on Pressure Recovery in Conical Diffusers, AIAA Journal, Vol. 9, No. 10, pp. 2014-2018.

[19] Nishi, M., Yoshida, K., and Morimitsu, K., 1998, Control of Separation in a Conical Diffuser by Vortex Generator Jets, JSME International Journal, Series B., Vol. 41, No. 1, pp. 233-238.

[20] Susan-Resiga, R., Ciocan, G.D., Anton I., and Avellan, F., 2006, Analysis of the Swirling Flow Downstream a Francis Turbine Runner, Journal of Fluids Engi-neering, Vol. 128, pp. 177-189

[21] Thicke, R.H., 1981, Practical Solutions for Draft Tube Instability, Water Power & Dam Construction, Vol. 33, No. 2, pp. 31-37.

[22] Vevke, T., 2004, An Experimental Investigation of Draft Tube Flow, PhD Thesis, Norwegian University of Science and Technology, 2004:36.

[23] Wegner, B., Maltsev, A., Schneider, C., Sadiki, A., Dreizler, A., Janicka, J., 2004, Assessment of unsteady RANS in predicting swirl flow instability based on LES and experiments, International Journal of Heat and Fluid Flow, pp. 1-9.

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