Numerical Investigations for Jet Flow ... - Semantic Scholar

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012)

Numerical Investigations for Jet Flow Characteristics on Pelton Turbine Bucket Vishal Gupta 1, Dr. Vishnu Prasad2 1

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PhD Scholar, Department of Energy, MANIT, Bhopal, MP Professor, Department of Civil Engineering, MANIT, Bhopal, MP Earlier model testing was the only method available for assessing performance of impulse turbines for different nozzle and bucket shapes. But this approach is time consuming, costly and did not provide detailed flow behavior. With the improvements in the field of computers and advancement in numerical techniques, detailed flow analysis in given flow domain can be obtained for its design optimization in the least time. The geometry can be altered till the best performance is obtained. The flow of water jet on Pelton bucket is free surface flow and requires flow simulation for multiphase flow taking water and air as fluid medium. In the present paper, numerical flow simulation of circular and rectangular shapes of jets for two jet velocities has been carried out using Ansys CFX for study of jet shape on flow characteristics on bucket. As Pelton bucket is symmetrical, geometry of half of the Pelton bucket has only been considered and thus the shapes of jets: semicircle and square of same cross section area are considered. The numerical and theoretical forces have been compared. Pressure distribution, velocity stream lines, water volume fraction on stationary half bucket have been shown.

Abstract— In Pelton turbines, the jet of circular cross section is issued from nozzle and moves in air before striking the bucket. The bucket is divided into two symmetrical semiellipsoidal cups by sharp edge splitter. The jet strikes the bucket on the splitter. The splitter divides the jet into two equal sheets of water having free surface which moves on the curved path of bucket. The profile of curved path of bucket affects the force and also pressure and velocity distribution over bucket. Many investigators have worked for improvement of bucket profile for circular jet. The jet shape may also affect force, pressure and velocity distribution on bucket. Earlier, experimental techniques were used to predict the forces on bucket but it was difficult to get pressure and velocity distributions. Secondly, the experimental approach is time consuming as well as costly and needs special laboratory facilities. The development of CFD for multi phase free surface flow made it possible to investigate the fluid flow on Pelton turbine and also to visualize the flow pattern. The objective of this paper is compare the flow characteristics on Pelton bucket with circular and rectangular jet using numerical multi phase flow simulation. Numerical and theoretical results have been compared for typical bucket profile and bears closed comparison. Keywords— computational fluid dynamics, free surface flow, Impulse turbine, multi-phase fluid flow.

II. GEOMETRIC MODELING AND BOUNDARY CONDITIONS Depending on the nature of problem, the numerical flow simulation needs input of 2D or 3D geometry of flow domain. The flow domain is divided into small elements forming mesh. The numerical method is used for discretisation of governing equations over an element.

I. INTRODUCTION In hilly areas, high head hydro power plants are common and the turbines used for such plants are impulse turbines. Among impulse turbines, Pelton turbine is commonly used. In an impulse turbine, all the available energy of water is converted into kinetic energy or velocity head by passing it through a contracting nozzle provided at the end of penstock. The water coming out of the nozzle is circular in cross-section. The water jet moves freely in air and impinges on a series of buckets of the runner thus causing it to revolve. The performance of the turbine depends upon many factors and one of them is the shape of jet striking the turbine bucket which depends upon the shape of the nozzle.

A. Geometry The geometry of two nozzles shapes namely semi-circular and rectangular with same cross sectional area has been modeled. The flow domain consists of jet and half of the bucket. The modeling has been done in ANSYS ICEM CFD-13.0.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012) The 3D views of half bucket [5] and complete domain for semi-circular jet are shown in figure 1 and figure 2 respectively.

Fig 3: Mesh for semi-circular jet

Fig 1: 3D View of half Bucket

Fig 2: 3D View of complete domain for semi-circular jet Fig 4: Mesh for square jet

B. Mesh Generation The tetrahedral elements have been used for 3D flow domain and triangular elements for 2D surfaces. The meshing of domains for semi-circular and square jets has been shown in fig.3 and fig.4 respectively. The summery of mesh data for two cases is given in Table 1.

TABLE 1 MESH DATA

Part Name Inlet Jet Back Jet Half Opening Bucket Fluid Flow Region

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Number of Elements Circular Rectangular 689 643 10487 10123 5205 3125 51756 52981 28766 28774 7351929 7368493

Element Type Triangular Triangular Triangular Triangular Triangular Tetrahedral

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 7, July 2012) C. Common Input Data The fluid properties and some common input data used in the two variants are mentioned in Table 2.

III. COMPUTATION OF THEORETICAL FORCE The bucket placed in front of jet deflects the jet from its direction at an angle of 170°. As per Newton’s second law of motion, the theoretical impulse force exerted by the jet on plate is calculated by neglecting losses as:

TABLE 2 COMMON INPUT DATA

Domain type Fluid type Reference pressure Buoyancy Domain motion Mesh deformation Interphase transfer Free surface model Surface tension coeff Density of water

FT  AV1 (V1  V2 cos )

Fluid Domain Air and Water 1 atm -9.81 m/sec2 Stationary None Free Surface Standard 0.072 N/m 997 kg/m3

(1)

Hence actual force experienced by bucket will be less than theoretical force given by equation (1). The ratio of computed and theoretical force is expressed as force coefficient as:

 

FC FT

(2) The deviation between theoretical and computed force is expressed in percentage as

FT  FC x100 FT

D. Boundary Conditions The flow parameters like pressure and velocity or mass flow rate are to be specified in the form of inlet and outlet boundary conditions to obtain numerical simulation and the solution of the problem depends on the values given at boundary conditions.



Inlet boundary condition: This condition has been defined at inlet in the form of water velocity as 50 m/s and 68 m/s normal to surface and uniform distribution. The value of water volume fraction was given as 1 and 0 for air.

The flow simulation has been carried out for two different shapes of jet of same cross-sectional area (307 mm2) with jet velocity of 50 m/s and 68 m/s. The distance between jet and bucket (80mm) is also kept same in all cases. The root mean square (RMS) residual is set to 10 -6 for the termination of iterations. The simulation has provided water velocity stream lines, pressure distribution etc. within the flow domain and also on bucket. The theoretical impulse force by jet on the bucket depends upon the cross-sectional area of the jet, density of liquid, velocity of the jet striking the bucket, angle at which the water is leaving the bucket. The shape of jet is not considered in theoretical computation but surrounding air and surface tension will affect the force due to different surface areas of jets.

(3)

IV. RESULTS AND DISCUSSIONS

Wall conditions: The bucket half is defined as smooth wall and wall contact angle is taken as 0°. Symmetry: The section dividing jet into two equal parts was given as symmetry type boundary condition. Outlet boundary conditions: As the jet flow is free surface, hence all boundaries except bucket are defined as opening type with relative pressure as 0 atmospheric.

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Fig 5: Velocity streamlines for semi-circular jet (50 m/s) Fig 8: Velocity streamlines for square jet (68 m/s)

Fig 6: Velocity streamlines for rectangular jet (50 m/s)

Fig 9: Pressure contour for semi-circular jet (50 m/s)

Fig 7: Velocity streamlines for semi-circular jet (68 m/s)

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Fig 10: Pressure contour for semi-circular Jet (68 m/s) Fig 12: Pressure contour for square jet (68 m/s)

Fig 11: Pressure contour for square jet (50 m/s) Fig13: Water volume fraction for semi-circular jet (50 m/s)

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Fig16: Water volume fraction for square jet (68 m/s)

Fig14: Water volume fraction for semi-circular jet (68 m/s)

It is seen from streamline pattern that jet has parallel stream lines before striking the plate. The stream lines diverse near the bucket due to deflection of jet at 170°. The jet spreads after striking the bucket. It is observed that more water leaves through the cut-out which leads to wastage without contribution to impulse force. It is also observed that more area of bucket surface experiences high pressure in case of circular jet. The pressure distributions on the bucket due to jet strike in the figures 9, 10, 11, 12 indicate that the pressure is maximum in the sharp curvature zone of the bucket due to stagnation of jet velocity. It is observed from figures 13, 14, 15, 16 that water spreads uniformly over bucket in case of circular jet TABLE 3 COMPARISON OF THEORETICAL AND COMPUTED FORCES

Jet Circular- 50 (m/s) Square- 50 (m/s) Circular- 68 (m/s) Square- 68 (m/s)

Fig15: Water volume fraction for square jet (50 m/s)

FT (N) 1518.8 1518.8 2809.1 2809.1

FC (N) 1462.55 1454.25 2640.06 2614.64

ζ 0.963 0.957 0.939 0.931

ϕ 3.70 4.25 6.01 6.92

The theoretical and numerical values of forces are given in Table 3. The theoretical force in all cases is more than computed as the losses are neglected in theoretical force. It is seen that the jet force on bucket is more for circular jet than the force by the square jet. This is due to the less surface area of circular jet in contact with air

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V. CONCLUSIONS The force coefficient for circular and rectangular jet are found to be nearly same for a given jet velocity. As the jet velocity is increased, force coefficient decreases and deviation increases indicating more losses. The pressure distribution over bucket surface is more uniform for circular jet as compared to rectangular jet. The deviation between the theoretical and computed within acceptable limit, CFD can be use to access the flow pattern for optimization of bucket shape.

REFERENCES [1] Alexandre Perrig, François Avellan, Jean-Louis Kueny, Mohamed Farhat. 2006. Flow in a Pelton Turbine Bucket: Numerical and Experimental Investigations. Transaction of ASME. Journal of Fluid Engineering. Vol. 128. pp. 350-358

[2] B. Zoppe, C Pellore, T. Maitre, P. Leroy. 2006. Flow Analysis Inside a Pelton Turbine Bucket. Transaction of ASME. Journal of Turbomachinery. Vol. 128. pp. 500-511.

[3] M.S. Konnur, Kiran Patel. 2006. Numerical Analysis of Water Jet on Flat Plate. 33rd National Conference on Fluid Mechanics and Fluid Power. Raipur. India.

[4] K Patel, B Patel, M Yadav, and T Foggia. 2010. Development of Pelton turbine using numerical simulation. IOP Conf. Series: Earth and Environmental Science 12.

[5] V V Barlit. 1974. Fundamentals of the theory of hydraulic turbines. [6] Parkinson Etienne. 2003. New Developments in CFD Extend Application to Pelton Turbines. CFX Update.

[7] ANSYS CFX-13 software manuals.

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