hydraulic turbine design 1

8/6/2019 Hydraulic Turbine Design 1

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ESSENTIALS OF HYDRAULIC TURBINE ANALYSIS AND DESIGN

Hydraulic turbines extract energy from the gravitational potential of water sourcesor from the kinetic energy of flowing water or from a combination of the two.These turbines are generally classified as either impulse or reaction . Reaction

turbines are further classified as radial and mixed-flow (Francis) turbines or asaxial-flow or propeller turbines.

Efficiency generally governs which turbine type is selected. Figure 16.14 1 plotsefficiency against specific speed ( N s) for the three turbine types.

3

4

e s

n gpm N

h

=

Where h is in feet and ne is that rpm corresponding to optimum operating

efficiency.

1 Finnemore, E.J. and Franzini, J.B., Fluid Mechanics with Engineering Applications , 10 ed., p. 707,McGraw Hill, 2002.

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IMPULSE TURBINES (See Figure 16.1 and 16.3, Finnemore) 2

Impulse turbines operate under relatively high heads and low flow rates. One or more nozzles convert available energy into kinetic energy, most of which istransferred to buckets attached to a rotating wheel (runner). The resulting shaft

torque drives a generator or other machinery. Windage, fluid friction, turbulence,separation and leakage cause the principal losses.

• Nozzle Design

V0 V i1

Figure 1

2 Id., p. 686.

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The ideal exit velocity, V i1, is calculated from the Bernoulli equation:

2 20 0 11

0 12 2i P V V P

z z g g γ λ

+ + = + +

The ideal velocity is multiplied by a velocity coefficient, C v , to account for friction and turbulence. C v varies from about 0.95 (needle valve partly closed) to0.99 (needle valve fully opened) .3

1 1v iV C V =

The actual quantity rate is obtained by multiplying the ideal rate by a dischargecoefficient, C d . The discharge coefficient is the product of the velocity coefficientand the contraction coefficient, C c, (ratio of area of emerging jet to the area of thenozzle at the discharge point). The value of C c is about 0.94. 4

Conservation of mass leads to:

1 1d Q C AV =

Where : d c vC C C =

• Nozzle Dimensions

The nozzle diameter at discharge is made about 20% greater than the calculateddiameter of the jet. The nozzle should terminate in a cone of 30-45 °.5

• Rotational Velocity

Calculate rpm from the specific speed that results in reasonable efficiency.Guidelines follow:

Head (ft) Specific Speed (n s)1000 5.0 – 5.52000 4.0 – 5.0

5/ 4

shaft s

n W n

H =

&

Where: n = rpm; shaft W & = shaft horsepower; H = turbine head, ft. If the turbinedrives a generator select a rotational velocity equal to the nearest synchronousspeed calculated from:

3 Id., p. 695.4 Id., Figure 11.13, p. 506.5 Marks’ Standard Handbook for Mechanical Engineers, 8 ed,, p. 9-145, McGraw-Hill, 1978.

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120 f n

p=

Where: f = frequency (60 cycles per second in U.S.) p = number of poles

• Runner Diameter ( D p). The runner diameter is determined from a formulasimilar to that for the centrifugal pump .6

•1840

p

H D

nφ =

Enter Figure 13 7 with n s to obtain an estimate of φ , a factor based uponexperience.

• Absolute Bucket Entering Velocity

1, 2ideal V U =

Where: U = peripheral velocity of a point on the pitch diameter of the bucket.Because V 2 must be greater than zero, however, U is decreased somewhat.

Let 2β be the angle through which the water is turned relative to the bucket. For

maximum work, 02 180β = ; however, to prevent water from striking the

succeeding bucket, it must be somewhat less, say, 150-1600

.

6 See class notes, “Centrifugal Pump Design,” equation (13), p. 5.7 Marks’ p. 9-144.

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• Bucket Shape and Dimensions 8

The bucket shape on either side of the vertical centerline is semi-ellipsoidal. Asharp-edged “splitter” divides the flow, one-half going to either side.

Approximations for bucket dimensions follow:

Width - B = 3dDepth - D = 0.85dLength -L = 2.6d

Where: d = jet diameter at rated capacity.

• Power Analysis (See Figure 16.4, Finnemore) 9

1 1 1V V U W θ = = + 2 2 cosV U W θ β = + 2 1V V V θ θ θ

∆ = −

W mU V θ = ∆& &

Where: V θ = tangential velocity

U = peripheral velocity m =& mass flow rate W =& power

8 Id., Figure 14, p. 9-145.9 Finnemore, p. 688.

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REACTION (FRANCIS) TURBINES(See Figures 16.8 and 16.11, Finnemore)

The Francis turbine consists of a runner with shrouded buckets, somewhatanalogous to a centrifugal pump. Wicket gates that direct the flow and control the

power and speed surround the runner. The water enters the turbine through aspiral scroll casing with a changing area to keep the entering velocity constant.The usual range for available head is 75-1600 feet; for specific speed, 15-100.

• Design

The turbine buckets are tangent to the entering relative velocity at the tip. Theyare designed to leave without appreciable tangential velocity (whirl). Thus, theexit term in Euler’s equation can be neglected, and the angle between the exitingabsolute velocity and the tangent, 2α , can be set at 90 °. Refer to Figure 2 for thevelocity triangles. The power equation becomes:

• 1W mUV θ =& &

• Selection of Speed

Economics calls for high rotational speeds resulting in small units.Considerations of efficiency, cavitation and structural strength, however, place anupper practical limit on speed.

Figure 16.14 (see page 1) plots efficiency against specific speed ( N s) for the three

principal turbine types. Figure 16.16 (following page) plots specific speed againstmaximum effective head ( h). To select a practical speed, enter Figure 16.16 withmaximum effective head and draft head and select the highest specific speedoutside of the cavitation region. Then calculate the resulting rpm. Enter Figure16.14 to estimate efficiency. Select the nearest synchronous speed correspondingto the value calculated from specific speed.

Figure 2

U U

V1

W2

W1V

r1V

2=V

r2

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• Selection of Runner Diameter

The runner diameter is determined from a formula similar to that for thecentrifugal pump. 10

1840 e

e

h D

nφ

=

Where D is in inches and the peripheral-velocity factor, eφ , is found fromFigure 16.14.

The number of buckets can be estimated from: 11

1/ 3

55

s

z n

=

The usual range is 21 for low and 12 for high specific speed. Refer to Marks’ for

other runner dimensions.

• Draft Tubes10 See class notes, “Centrifugal Pump Design,” equation (13), p. 5.11 Marks’ , p. 9-141.

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After passing through the turbine, the water enters a draft tube, Figure 16.11,(page 6). The purpose of this tube, which is an integral part of the turbine design ,is threefold:

1) To permit the turbine to be set above the tailwater level without loss of head.2) To recover a reasonable amount of the kinetic energy leaving the runner by

diffuser action.3) To facilitate inspection and maintenance.

Note that the pressure at the upper end of the draft tube is below atmospheric thuslimiting the height above the tailwater because of cavitation considerations. Thevelocity at the upstream end of the tube ranges from 24 to 30 ft/s; at the lower end, 5-7 ft/s. The included angle of the diffuser tube should be kept reasonablysmall, say 8-12 °, to limit losses due to separation. Typical loss coefficients are: 12

Cone Angle Loss Coefficient8° 0.23

12 ° 0.33

( )21 2

2 L

V V h K

g

−=

Where: K = Loss Coefficient and numerals 1 and 2 refer to entering and leaving stations.

12 Finnemore, Figure 8.20, p. 310.

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hydraulic turbine design 1

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