preliminary design of some hydraulic structures, hydraulic circuit … · preliminary design of...

Preliminary design of some hydraulic structures, hydraulic circuit and

powerhouse of a hydropower case study

Teacher: Helena M. Ramos

Professor at IST

2013

Preliminary design of hydraulic structures, hydraulic circuit and powerhouse of a hydroelectric scheme

2

Abstract

This support document deals with the optimization study on the discharge design of the

turbine/generator units are established inquiry of the developed adaptation mechanism for optimum

cash flow, design of the hydraulic circuit, verification of the powerhouse including the analysis of

the hydraulic transients. In this report students will find further material than the one for the work to

be developed under the hydropower course.

Key words: Hydropower systems, optimization, hydraulic structures, hydraulic transient


3

Table of Contents 1. Introduction........................................................................................................................................... 5

1.1 Remarks………………………………………………………………………………………………………………………………………….5

1.2. Small Scale Hydropower (SHP)........................................................................................................ 5

1.3. Objectives ...................................................................................................................................... 6

2. Main Components of Small Hydropower Scheme ................................................................................... 7

2.1. Water ways .................................................................................................................................... 8

2.2. Power house and Tailrace ............................................................................................................ 35

2.3. Forces applied to a solid anchor ................................................................................................... 42

3. Transient and safety analysis (system dynamics) .................................................................................. 48

3.1. The Method of Characteristics...................................................................................................... 48

3.2. Hydraulic transient analysis: Preventing water hammer ............................................................... 50

3.3. Transient flow due to fast/ slow manoeuvre................................................................................. 65

3.4. Transient flow due to valve closure operations............................................................................. 66

3.5. Recommendations ....................................................................................................................... 69

4. References ........................................................................................................................................... 70


4

LIST OF FIGURES FIGURE 1: SHP OVERVIEW ................................................................................................................................................... 6

FIGURE 2: RESERVOIR OPERATING RULE .................................................................................................................................. 9

FIGURE 3: MONTHLY VOLUME FLOW RATE .............................................................................................................................10

FIGURE 4: MONTHLY VOLUME VARIATION 1 ............................................................................................................................14






FIGURE 10: MONTHLY VOLUME VARIATION 7 ..........................................................................................................................20



FIGURE 13: MONTHLY VOLUME VARIATION 10 ........................................................................................................................23

FIGURE 14: CASH FLOW AND TURBINE DISCHARGE ....................................................................................................................24

FIGURE 15: CASH FLOW AND OPTIMUM TURBINE DISCHARGE ......................................................................................................25

FIGURE 16: MONTHLY OPTIMUM VOLUME VARIATION ...............................................................................................................26

FIGURE 17 INTAKE SCHEME WITH SUBMERGENCE .....................................................................................................................29

FIGURE 17: PENSTOCK ......................................................................................................................................................29

FIGURE 18: HYDRAULIC GRADIENT ........................................................................................................................................34

FIGURE 19: HEAD LOSS WITH DISCHARGE ...............................................................................................................................35

FIGURE 20: OPERATIONAL ENVELOPES OF TURBINES ..................................................................................................................37

FIGURE 21: SPECIFIC SPEED VS NET HEAD...............................................................................................................................39

FIGURE: 22 GROUP G FRANCIS TURBINES OPERATIONAL PARAMETERS ...........................................................................................41

FIGURE 23: SUCTION HEAD ................................................................................................................................................42

FIGURE 24: RESULTANT FORCES PRODUCED BY WEIGHT, PRESSURE AND CHANGE IN MOMENTUM .........................................................43

FIGURE 25: SCHEMATIC VIEW OF THE MODEL POWERHOUSE .......................................................................................................44

FIGURE 26: POWER HOUSE LAYOUT.......................................................................................................................................45

FIGURE 27: POWERHOUSE FLOOR AREA REQUIRED ....................................................................................................................45

FIGURE 28: TAIL RACE SHAPE ..............................................................................................................................................46

FIGURE 29: POWER HOUSE DISCHARGE CURVE .........................................................................................................................46

FIGURE 30: TAIL RACE LAYOUT .............................................................................................................................................47

FIGURE 31: NOMENCLATURE FOR THE INTEGRATED EQUATIONS ...................................................................................................50

FIGURE 32: SUMMARY OF DIFFERENT CLOSURE TYPES AND TIMES..................................................................................................52

FIGURE 33: HYDRAULIC HEAD IN THE SHUTTER (VALVE) - TIME VARIATION ......................................................................................59

FIGURE 34: MAXIMUM AND MINIMUM HEAD ENVELOPE AND PIPE LINE PROFILE ..............................................................................64

FIGURE 35: VARIATION OF HYDRAULIC HEAD IN THE SHUTTER WITH CLOSURE TIME ...........................................................................68


5

1. Introduction

1.1. Remarks

Flowing water, either falling directly upon paddles or filling buckets attached to a wheel, was

humankind’s first source of mechanical power. The origin of waterwheels can be traced to ancient

Egypt, China, and Persia where these devices took over many tasks such as raising water for

irrigation purposes and water supply as well as grinding grain for flour. As demands for power

increased, large water wheels were built.

Water is, thus, one of the most important renewable energy sources already exploited by man on a

large scale with a well-developed technological base to support its continued exploitation.

Hydropower is, in fact, a form of none depleting, self-replenishing energy. It is usually the cheapest

form of bulk energy; and, in most cases, it is also the most efficient and least pollution form of

power. To date, it is the only practical means to store electrical power through pumped storage for

use at a later time.

1.2. Small Scale Hydropower (SHP)

There is no consensus in the definition of small hydropower: Some countries like Portugal, Spain,

Ireland and now, Greece and Belgium, accept 10 MW as the upper limit for installed capacity. In

Italy the limit is fixed at 3 MW and in Sweden 1.5 MW. In France the limit has been recently

established at 12 MW, not as an explicit limit of SHP, but as the maximum value of installed power

for which the grid has the obligation to buy electricity from renewable energy sources. In the UK

20MW is generally accepted as the threshold for small hydro. For the purposes of this text any

scheme with an installed capacity of 20 MW or less will be considered as small.

Small hydropower plants offer several advantages for today’s energy aesthetically acceptable.

Effects upon stream ecology are minor compared to those caused by large hydropower facilities.

Small dams may, in fact, enhance the stream by maintaining water depths sufficient to support

aquatic life. Ideally, a small hydro system should serve several purposes in addition to power, such

as water supply, flood control, irrigation, and recreation.


6

Figure 1: SHP overview

1.3. Objectives

This Project work is one part of a small scale hydropower carried out by the group of students listed

in the front page, Recognizing that the small scale hydro can be a Viable and appropriate renewable

energy technology, our project effort is to Optimize discharge to the turbine and verify a given

hydraulic structures of a small scale hydro power system and so that it could solve major problems

by providing adequate domestic electricity.

The main aims of this project work are:

To Optimize Design flow

To check the minimum submergence in water intake design provided

Calculation of losses, analysis of equipment, calculation of forces applied to a solid anchor

To determine the flow curve in the area of powerhouse, verify the general layout and preliminary

design of the building of the powerhouse

To carry out an analysis of hydraulic transients adaptive for a given small hydroelectric power

scheme.


7

2. Main Components of Small Hydropower Scheme

This stage and the next section are the most critical stages in this project work as it determines the

feasibility and achievability of the proposed small hydropower system. There are many factors that

determine the feasibility and achievability of the system. This includes:

i. The capacity of the reservoir to supply water for the small hydro system

ii. The cost of developing the project and the net profit

iii. The amount of power available from the water flow

iv. The turbine selection and availability of required power house, suction head and transient

condition.

Table1: List of Givens

No. Description Value

1 Purpose

1.1 Small hydro electric power plant

2 Working range

2.1 Discharge To be Determined

2.2 Gross Head 63 m

2.3 Head Loss 5% of gross head

4 Efficiency 82%

5 Power and cost

5.1 1 MW 2100 €/kW

5.2 20 MW 1530 €/kW

6 Discount rate 5%-10% (10%)

7 Life 20 years

8 Energy cost 0.08 €/kWh

9 Reservoir capacity

9.1 Vmax given

9.2 Vmin calculate

10 Velocity

10.1 Intake 1 m/s


8

No. Description Value

10.2 Pipe 3 m/s - 4 m/s

11 Opening

11.1 Intake 2.4 m

11.2 Pipe 1.5 m

12 Penstock length 486.47 m

13 Height

13.1 Intake 94.4 m

13.2 Pipe 93.5 m

13.3 Limit 97.5 m

14 Bends

14.1 Number of Bends 5

15 Butterfly Valve Fully opened

16 Discharge range

16.1 Maximum 110%

16.2 Minimum 40%

2.1. Water ways

A hydropower development includes a number of structures, the design of which will be dependant

upon the type of scheme, local conditions, access to construction material and also local building

traditions in the country or region. The following structures are common in a hydro scheme:

• Diversion structure

o Dam

o Spillway

o Energy dissipation arrangement

o Residual flow arrangements

• Water conveyance system

o Intake

o Canals and Tunnels

o Penstocks

o Power house


9

2.1.1. Optimization of flow design

Way of organizing discharge data and reservoir capacity is by plotting a reservoir operating rule

volumetric curve, that shows for a particular point on a reservoir the proportion of time during which

the discharge there equals or exceeds certain limit values. This can be obtained from the hydrograph

by organizing the data by monthly volume flow rate. If the individual daily flows for one year are

organized in categories as shown in Figure 3 the reservoir volumetric curve can be determined by

arranging the data in the range of the boundary conditions and calculating the relative values via

excel as shown in Figure 2.

Figure 2: Reservoir operating rule

The requirements of the discharge at the given head and the site where the power plant can be

founded was also computed parallel with the cash flow to choose the optimum discharge in both

safety and net profit as shown in the next tables and figures.


10

Given Data

Figure 3: Monthly Volume flow rate

Values of discharge converted to volume within a month using excel are depicted in the table below:

Table 2: monthly volumetric flow

Month Qm (m3/s) No. of day Vin(hm

3)

Jan 80 31 214.27

Feb 40 28 96.77

Apr 30.2 31 80.89

Mar 20.3 30 52.62

May 15.1 31 40.44

Jun 10 30 25.92

Jul 3 31 8.04

Aug 0 31 0

Sep 1 30 2.59

Oct 5.6 31 14.99

Nov 10.9 30 28.25

Dec 30 31 80.35

Total 365 645.14

Month Qm

(m3/s)

Jan 80

Feb 40

Apr 30,2

Mar 20,3

May 15,1

Jun 10

Jul 3

Aug 0

Sep 1

Oct 5,6

Nov 10,9

Dec 30


11

Summary of values required for the optimization is also presented in the table below:

Table 3: summary of given Data

QT(m

3/s) η Hb (m)

HL (m)

Hu (m)

P (MW) Cost(€/kW) Discount rate (a)

Life(n) (yrs)

s (€/kWh)

arbitrated 0.82 63 3.15 59.85 1 2100 0.10 20 0.08

Vfull (hm3) Vmin (hm

3) 20 1530

50 20

Using the data summarized above we first tried to determine the cash flow at a low discharge value

knowing the net profit increases with increasing flow rate of the turbine to some optimum value.

Trial 1: when the discharge to the turbine (QT =2.9 m3/s)

Given formulas

Power to be installed

[1]

=9.8KN/m3*2.9m

3/s*59.85m*0.82

= 1394.77 kW

Since the calculated power is between the given limits for a small hydro scheme then by linear

interpolation the cost per kW (C/kW) will be:

C/kW=2088.16 €/kW

Global cost (C)

C = P*C/kW [2]

= 1394.77kW*2088.16 €/kW

= 2912495.20 €

Turbine volume (VT)

VT = Q*number of seconds of turbining [3]

= Q*days*24hr/day*3600sec/hr

= 2.9*31*24*3600/1000000 (January - 31 days)

= 7.77 hm3

This is for January and the procedure is similar for the other months.


12

Energy production (E)

E = (9.8ηHuVT total)/3600 [4]

= 9.8*0.82*59.85*91.45*106/3600

=12218170.66 kWh

Gross profit (Bb) [5]

Bb =E*0.08 €/kWh

=12218170.66 KWh*0.08 €/kWh

=977453. 65 €

Net profit (Bl)

Bl =0.9*Bb [6]

=0.9*977453. 65 €

=879708.29 €

Discount factor (actualization factor)

[7]

Where: n - life of the power plant

a - discount rate

= 10.96

Updated new profit (Bla) = Bl*F [8]

= 879708.29 €*10.96

= 9640791.92 €

Cash flow (VAL) = Bla – C [9]


13

= 9640791.92€-2912495.20 €

= 6728296.72 €

This result is obtained only for a small discharge value of 2.9 m3/s using excel. The calculation of

the various characteristics is rather bulky; thus all the established values were calculated via Excel as

shown in the tables below:

Where:

Qm-mean monthly flow rate

Vin-mean monthly volume to the reservoir

VT-mean monthly volume to the turbine

∆V = Vin-VT+VR

VR-mean monthly reservoir volume

HR-monthly reservoir height

Table 4: Summary of trial 1 (QT =2.9 m3/s)

Description Value Month Qm

(m3/s) No. of

day Vin(hm

3) VT(hm3) ∆V (hm3) VR(hm

3) HR(m)

Global cost ( € ) 2912495.20 Jan 80 31

214.27

7.77 256.50

50.00

5.00

Power (kW) 1394.77 Feb 40 28

96.77

7.02 139.75

50.00

5.00

C/kW 2088.16 Apr 30.2 31

80.89

7.77 123.12

50.00

5.00

Energy production (kWh) 12218170.66 Mar 20.3 30

52.62

7.52 95.10

50.00

5.00

Gross profit (€) - Bb 977453.65 May 15.1 31

40.44

7.77 82.68

50.00

5.00

Net profit (€) - BL 879708.29 Jun 10 30

25.92

7.52 68.40

50.00

5.00

Discount factor - f 10.96 Jul 3 31

8.04

7.77 50.27

50.00

5.00

Updated net profit (€)- Bla 9640791.92 Aug 0 31 -

7.77 42.23

42.23

4.22

Cash flow (€) - VAL 6728296.72 Sep 1 30

2.59

7.52 37.31

37.31

3.73

Oct 5.6 31

15.00

7.77

44.54

44.54

4.45

Nov 10.9 30

28.25

7.52

65.28

50.00

5.00

Dec 30 31

80.35

7.77

122.58

50.00

5.00

Total 365

645.14

91.45


14

Figure 4: monthly volume variation 1

From table 4 and figure 4 we can understand that the volume flow to the turbine is almost constant

only due to the small variation in number of days for different months and our reservoir is full for

the first seven months and starts to decrease from July to November but it can deliver the calculated

power the whole year. Since our concern is to maximize profit this is not sufficient enough then we

have to search other options. Hence, all the other results were calculated with the same procedure

like the first trial via excel we present the outcomes only in a tables and figures.

Table 5: Trial 2- when the discharge to the turbine (QT = 7m3/s)


(m3/s)

No. of day

Vin(hm3) VT(hm

3) ∆V (hm3) VR(hm3) HR(m)

Global cost ( € ) 6830996.61 Jan 80.00 31.00 214.27 18.75 245.52 50.00 5.00

Power (kW) 3366.68 Feb 40.00 28.00 96.77 16.93 129.83 50.00 5.00

C/kW 2029.00 Apr 30.20 31.00 80.89 18.75 112.14 50.00 5.00

Energy production (kWh) 24563313.33 Mar 20.30 30.00 52.62 18.14 84.47 50.00 5.00

Gross profit (€) - Bb 1965065.07 May 15.10 31.00 40.44 18.75 71.70 50.00 5.00

Net profit (€) - BL 1768558.56 Jun 10.00 30.00 25.92 18.14 57.78 50.00 5.00

Discount factor - f 10.96 Jul 3.00 31.00 8.04 18.75 39.29 39.29 3.93

Updated net profit (€)- Bla 19381771.58 Aug 0.00 31.00 0.00 18.75 20.54 20.54 2.05

Cash flow (€) - VAL 12550774.96 Sep 1.00 30.00 2.59 0.00 23.13 23.13 2.31

Oct 5.60 31.00 15.00 0.00 38.13 38.13 3.81

Nov 10.90 30.00 28.25 18.14 48.24 48.24 4.82

Dec 30.00 31.00 80.35 18.75 109.84 50.00 5.00

Total 365.00 645.14 183.86


15


Table 5 and figure 5 are evidence for the volume flow to the turbine is almost constant until august

and decreases to zero on September and October with no energy production and our reservoir is full

until May, decreases to the minimum value and it returns back to its full state on November. But

since our concern is to get maximum net profit and comparably trial 2 is better than trial1 in cash

flow we have to search for other trials which have a maximum cash flow by increasing the flow to

the turbine.

With similar reasoning only the values of trials 3, 4, and 5 are presented in the next three tables and

figures.


16

Table 6: Trial 3- when the discharge to the turbine (QT =11m3/s)


(m3/s) No. of

day Vin(hm

3) VT(hm

3) ∆V (hm

3) VR(hm

3) HR(m)

Global cost ( € ) 10429084.38 Jan 80 31.00 214.27 29.46 234.81 50.00 5.00

Power (kW) 5290.50 Feb 40 28.00 96.77 26.61 120.16 50.00 5.00

C/kW 1971.28 Apr 30.2 31.00 80.89 29.46 101.43 50.00 5.00

Energy production (kWh) 34663359.93 Mar 20.3 30.00 52.62 28.51 74.11 50.00 5.00

Gross profit (€) - Bb 2773068.79 May 15.1 31.00 40.44 29.46 60.98 50.00 5.00

Net profit (€) - BL 2495761.92 Jun 10 30.00 25.92 28.51 47.41 47.41 4.74

Discount factor - f 10.96 Jul 3 31.00 8.04 29.46 25.98 25,98 2.60

Updated net profit (€)- Bla 27351250.02 Aug 0 31.00 0.00 0.00 25.98 25.98 2.60

Cash flow (€) - VAL 16922165.64 Sep 1 30.00 2.59 0.00 28.57 28.57 2.86

Oct 5.6 31.00 15.00 0.00 43.57 43.57 4.36

Nov 10.9 30.00 28.25 28.51 43.31 43.31 4.33

Dec 30 31.00 80.35 29.46 94.20 50.00 5.00

Total 365.00 645.14 259.46



17




(m3/s)

No. of

day Vin(hm


3) HR(m)

Global cost ( € ) 13805107.51 Jan 80 31 214.27 40.18 224.10 50.00 5.00

Power (kW) 7214.32 Feb 40 28 96.77 36.29 110.48 50.00 5.00

C/kW 1913.57 Apr 30.2 31 80.89 40.18 90.71 50.00 5.00

Energy production (kWh) 42073908.41 Mar 20.3 30 52.62 38.88 63.74 50.00 5.00

Gross profit (€) - Bb 3365912.67 May 15.1 31 40.44 40.18 50.27 50.00 5.00

Net profit (€) - BL 3029321.41 Jun 10 30 25.92 38.88 37.04 37.04 3.70

Discount factor - f 10.96 Jul 3 31 8.04 0.00 45.08 45.08 4.51

Updated net profit (€)- Bla 33198570.21 Aug 0 31 0.00 0.00 45.08 45.08 4.51

Cash flow (€) - VAL 19393462.7 Sep 1 30 2.59 0.00 47.67 47.67 4.77

Oct 5.6 31 15.00 40.18 22.49 22.49 2.25

Nov 10.9 30 28.25 0.00 50.74 50.00 5.00

Dec 30 31 80.35 40.18 90.18 50.00 5.00

Total 365 645.14 314.93


18



(m3/s) No. of days

Vin(hm3) VT(hm

3) ∆V (hm

3) VR(hm

3) HR(m)

Global cost ( € ) 16959066.01 Jan 80 30 207.36 49.25 208.11 50.00 5.00

Power (kW) 9138.14 Feb 40 28 96.77 45.96 100.80 50.00 5.00

C/kW 1855.86 Apr 30.2 31 80.89 50.89 80.00 50.00 5.00



Net profit (€) - BL 3331838.00 Jun 10 30 25.92 0.00 65.47 50.00 5.00



Cash flow (€) - VAL 19554807.23 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Now 10.9 30 28.25 49.25 29.00 29.00 2.90

Dec 30 31 80.35 50.89 58.47 50.00 5.00

Total 364 638.23 346.38



19



(m3/s) No. of

day Vin(hm

3) VT(hm

3) ∆V (hm

3) VR(hm

3) HR(m)

Global cost ( € ) 19890959.87 Jan 80 31 214.27 61.60 202.67 50.00 5.00

Power (kW) 11061.96 Feb 40 28 96.77 55.64 91.13 50.00 5.00

C/kW 1798.14 Apr 30.2 31 80.89 61.60 69.28 50.00 5.00



Net profit (€) - BL 3478940.85 Jun 10 30 25.92 0.00 47.76 47.76 4.78



Cash flow (€) - VAL 18235025.01 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Nov 10.9 30 28.25 0.00 78.25 50.00 5.00

Dec 30 31 80.35 61.60 68.75 50.00 5.00

Total 365 645.14 361.67


Now, as table 9 and figure 9 indicates the volume of the reservoir is within the reservoir operating rule

but the water flow to the turbine is very high for the first five months with no flow to the turbine in the

next five months the cash flow also starts to drop down therefore we have to do another trial to prove

whether the cash flow continues to decrease or not as shown in the next tables and figures.


20




(m3/s)

No. of day

Vin(hm3) VT(hm

3) ∆V (hm

3) VR(hm

3) HR(m)

Global cost ( € ) 22600789.10 Jan 80 31 214.27 72.32 191.96 50.00 5.00

Power (kW) 12985.77 Feb 40 28 96.77 65.32 81.45 50.00 5.00

C/kW 1740.43 Apr 30.2 31 80.89 72.32 58.57 50.00 5.00



Net profit (€) - BL 3388352.09 Jun 10 30 25.92 0.00 75.92 50.00 5.00



Cash flow (€) - VAL 14532426.47 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Now 10.9 30 28.25 0.00 78.25 50.00 5.00

Dec 30 31 80.35 72.32 58.04 50.00 5.00

Total 365 645.14 352.25


21



(m3/s) No. of

day Vin(hm

3) VT(hm

3) ∆V (hm

3) VR(hm

3) HR(m)

Global cost ( € ) 25088553.69 Jan 80 31 214.27 83.03 181.24 50.00 5.00

Power (kW) 14909.59 Feb 40 28 96.77 75.00 71.77 50.00 5.00

C/kW 1682.71 Apr 30.2 31 80.89 83.03 47.86 47.86 4.79

Energy production (kwh) 54032363.58 Mar 20.3 30 52.62 80.35 20.12 20.12 2.01


Net profit (€) - BL 3890330.18 Jun 10 30 25.92 0.00 75.92 50.00 5.00



Cash flow (€) - VAL 17545878.99 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Nov 10.9 30 28.25 0.00 78.25 50.00 5.00

Dec 30 31 80.35 83.03 47.32 47.32 4.73

Total 365 645.14 404.44



22



(m3/s)

No. of day

Vin(hm3) VT(hm


Global cost ( € ) 27354253.65 Jan 80 31 214.27 93.74 170.53 50.00 5.00

Power (kW) 16833.41 Feb 40 28 96.77 84.67 62.10 50.00 5.00

C/kW 1624.99 Apr 30.2 31 80.89 93.74 37.14 37.14 3.71



Net profit (€) - BL 3519664.24 Jun 10 30 25.92 0.00 75.92 50.00 5.00



Cash flow (€) - VAL 11218022.02 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Nov 10.9 30 28.25 0.00 78.25 50.00 5.00

Dec 30 31 80.35 93.74 36.61 36.61 3.66

Total 365 645.14 365.90



23



(m3/s)

No. of day

Vin(hm3) VT(hm


Global cost ( € ) 29397888.98 Jan 80 31 214.27 104.46 159.81 50.00 5.00

Power (kW) 18757.23 Feb 40 28 96.77 94.35 52.42 50.00 5.00

C/kW 1567.28 Apr 30.2 31 80.89 104.46 26.43 26.43 2.64



Net profit (€) - BL 3921911.58 Jun 10 30 25.92 0.00 75.92 50.00 5.00



Cash flow (€) - VAL 13582646.77 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Nov 10.9 30 28.25 0.00 78.25 50.00 5.00

Dec 30 31 80.35 104.46 25.89 25.89 2.59

Total 365 645.14 407.72


At this stage from the figures and tables of trials seven to ten though the cash flow is flactuating it is

with a pick value of lower than the trials perior to seven as shown in the summary of all values,

table 14 and figure 14 below thus from trial 5 and 6 we can estimate that the optimum discharge

value is between 19 and 23 m3/s .


24

Table 14: Summary

Tri

al

Q (

m3/s

)

VA

L (

€)

Glo

bal

cost

( €

)

Po

wer

(k

W)

C/k

W

En

erg

y p

rod

uct

ion

(k

Wh

)

Gro

ss p

rofi

t (€

) -

Bb

Net

pro

fit

(€)

- B

L

Dis

cou

nt

fact

or

- f

Up

da

ted

net

pro

fit

(€)-

Bla

Ca

sh f

low

(€

) -

VA

L

1 2,9 6728296.7 2912495.20 1394.77 2088.16 12218170.66 977453.65 879708.29 10.96 9640791.92 6728296.72

2 7 12550775 6830996.61 3366.68 2029.00 24563313.33 1965065.07 1768558.56 10.96 19381771.58 12550774.96

3 11 16922166 10429084.38 5290.50 1971.28 34663359.93 2773068.79 2495761.92 10.96 27351250.02 16922165.64

4 15 19393463 13805107.51 7214.32 1913.57 42073908.41 3365912.67 3029321.41 10.96 33198570.21 19393462.70

5 19 19554807 16959066.01 9138.14 1855.86 46275527.79 3702042.22 3331838.00 10.96 36513873.24 19554807.23

6 23 18235025 19890959.87 9138.14 1798.14 48318622.93 3865489.83 3478940.85 10.96 38125984.88 18235025.01

7 27 14532426 22600789.10 12985.77 1740.43 47060445.70 3764835.66 3388352.09 10.96 37133215.57 14532426.47

8 31 17545879 25088553.69 14909.59 1682.71 54032363.58 4322589.09 3890330.18 10.96 42634432.69 17545878.99

9 35 11218022 27354253.65 16833.41 1625.00 48884225.54 3910738.04 3519664.24 10.96 38572275.67 11218022.02

10 39 13582647 29397888.98 18757.23 1567.28 54470994.18 4357679.53 3921911.58 10.96 42980535.75 13582646.77

Figure 14: cash flow and turbine discharge


25

There fore, with similar analysis for the range 19 – 23 m3/s using excel a value of 22.45 m

3/s is found to

be the optimum discharge in both ecnomic and safety considerations with a cash flow of 23847505.75€

as shown in figure 15 with the other details in table 15 and figure 16.

Figure 15: cash flow and Optimum turbine discharge

Table 15: maximum cash flow with optimum discharge (QT = 22.45m3/s)


(m3/s) No. of

day Vin(hm


3) HR(m)

Global cost ( € ) 19500992.20 Jan 80 31 214.27 60.13 204.14 50.00 5.00

Power (kW) 10797.43 Feb 40 28 96.77 54.31 92.46 50.00 5.00

C/kW 1806.08 Apr 30.2 31 80.89 60.13 70.76 50.00 5.00



Net profit (€) - BL 3955487.60 Jun 10 30 25.92 0.00 50.66 50.00 5.00



Cash flow (€) - VAL 23847505.75 Sep 1 30 2.59 0.00 52.59 50.00 5.00

Oct 5.6 31 15.00 0.00 65.00 50.00 5.00

Nov 10.9 30 28.25 58.19 20.06 20.06 2.01

Dec 30 31 80.35 60.13 40.28 40.28 4.03

Total 365 645.14 411.21


26

Figure 16: monthly optimum volume variation

2.1.2. Intake structures

A water intake must be able to divert the required amount of water into the power canal or into the

penstock without producing a negative impact on the local environment and with the minimum

possible head loss. The intake serves as a transition between a stream that can vary from a trickle to

a raging torrent, and a controlled flow of water both in quality and quantity. Its design, based on

geological, hydraulic, structural and economic considerations, requires special care to avoid

unnecessary maintenance and operational problems that cannot be easily remedied and would have

to be tolerated for the life of the project.

Intake location

The location of the intake depends on a number of factors, such as submergence, geotechnical

conditions, and environmental considerations especially those related to fish life, sediment exclusion

and ice formation-where necessary.

Power intake

The power intake is an alternative of the conventional intake, usually located at the end of a power

canal, although sometimes it can replace it. Hence it has to supply water to a pressure conduit

(penstock) where its hydraulic requirements are more inflexible than those of a conveyance intake.


27

In this particular project we are only considering the minimum submergence and it is calculated

using the given data and is verified with the available model via excel as presented in the analysis

below.

Minimum submergence is based on the fact that if the intake does not have sufficient submergence it

is going to be prone to vortex formation. The vortex formation by insufficient intake submergence

can induce air dragging or even solid material to the intake, reducing the turbine efficiency.

Therefore, the design of intake is based on the minimum submergence which will enable the power

house not to suffer from entrance of foreign materials like air and solid materials which will reduce

the performance of the power house and reduce the life of the turbine.

The following model equation (developed by Gordon) is the most widely used to estimate the

minimum submergence of the intake to avoid vortex formation. The equation can equally be used for

the intake opening and the pipe given by:

[10]

Where: -

S - is the submergence [m]

d -is the intake opening [m]

V -is the mean flow velocity at the inlet [m/s]

g -is the gravity acceleration [m/s2]

Given parameters and assumptions:

1. The intake line is assumed to be symmetric ( C = 1.7 for symmetric and 2.3 for asymmetric

intakes, for this case we took 1.7)

2. The gravitational acceleration, g is equal to [9.81 m/s2]

3. The mean velocity in the pipe intake opening should be between 3m/s and 4m/s. for this case

we took 3.5m/s and that of intake opening should be 1m/s.

4. The Pipe is given to be 1.5 m in diameter on the model and the Intake opening is 2.5m (need

adaptation and verification based on the velocity criteria).

Pipe

Now, by rearranging and substituting the above values on equation 10 it results


28

S=

However, this value of minimum submergence should comply with the parameters given on the

model i.e. the sum of the pipe opening, the minimum submergence and the piezometric head of the

penstock inlet should not exceed 97.5m. The total piezometric head of the pipe is given to be 93.5m

and the pipe opening is 1.5 m. Now the sum of these three parameters is given by:

Since the value is below 97.5m the given model is verified for minimum submergence at the pipe

section.

Intake

With similar approach the minimum submergence of the intake opening is given by equation 10 as:

S=

Once again the sum of the height of the intake opening, the intake opening diameter and

submergence should not exceed 97.5 m. The intake opening is 2.5 m; the height of the penstock from

the intake opening is 94.4 m. Now their sum is:

But this value is a bit higher than the limit 97.5 m thus we decide to decrease the opening of the

intake to 2.25 m in order to verify the minimum submergence at the intake opening and we found a

value as shown below:

S =

Now the sum < 97.5

The Minimum submergence values of both the pipe and the intake opening via excel is summarized

in the table below:

Table 16: Minimum submergence

Component S [m] Htotal [m] Hlimit [m] d [m] dmodified [m] Smodified [m]

Pipe 2.33 97.33 97.5 1.5 1.5 2.33

Intake 0.86 97.46 97.5 2.5 2.25 0.81


29

Figure 17 Intake scheme with submergence

2.1.3. Hydraulic circuit

Penstocks

Conveying water from the intake to the powerhouse (this is the purpose of a penstock) may not

appear a difficult task. However deciding the most economical arrangement for a penstock is not so

simple. Penstocks can be installed over or under the ground, depending on factors such as the nature

of the ground itself, the penstock material, the ambient temperatures and the environmental

requirements.

Figure 17: penstock

Economic Diameter

The economic diameter is given by the following correlation developed by JIANDONG et al., 1997

[11]

Where:

CEC - coefficient of energy cost (zones where the energy cost is low = 1.2, medium = 1.4 and high or

no alternative source = 1.6)

CMP = coefficient for the pipe materials (for steel = 1 to 1.2; or plastic = 0.9)


30

Ho = net head [m]

Q = design discharge [m3/s].

Given parameters and assumptions

1. The penstock is made of steel (CMP =1.2 )

2. The coefficient of energy is given to be 1.6

3. The net head is taken to be 95% of the gross height assuming 5% loss ( = 59.85m )

4. Another criteria based on the maximum velocity of flow in the penstock can give a first

estimation for the diameter: 2-3 m/s low head plants; 3-4 m/s for medium head and 4-5 m/s

for high head plants. These are typical values based on real cases. For our case the power

plant is medium head, the velocity in the penstock should be between 3 and 4 m/s.

The design flow rate is the optimum discharge from the previous section with a value of 22.45 m3/s

and as a general rule; the number of turbines should be kept as low as possible i.e between 1 and 3

for SHP. The need to install more than one turbine arises with a variable stream flow. Hence it is

given small hydropower plants with long hydraulic conveyance circuit work effectively at a flow

rate of less than 10 m3/s we decide to have three turbines with three penstocks for each working at a

flow rate of 7.48 m3/s where the maximum flow rate is 110% of the optimum discharge and the

minimum flow rate is 40% of the optimum discharge.

Now substituting these values:

= = 1.708 m

However, being economic diameter could not be a guarantee to fulfill the criterion imposed by

velocity. Based on this the velocity of the water inside the penstock is going to be

= [12]

This velocity is within the range but we can still modify the diameter (reduce) to optimize it as long

as the velocity is within the range of 3 – 4 m/s because a penstock with large diameter is more

costly.

For this reason we changed the economic diameter to1.65 m and see if the velocity is in the range.


31

=

As a result this is enough because reducing more will drive the velocity to be out of range and we

took the diameter of the penstock as 1.65 m

Thickness of the pipe

The thickness of the pipe is given by the following correlation

t’ = 0.0084*D = 0.014 m, including 1mm for corrosion, [13]

t = t’+0.001 = 0.015m [14]

Thus, considering the empirical formulas to calculate the economic diameter and arranging the

calculated value to the allowable values using excel is presented in the table below.

Table 17: Penstock Dimensions

Penstock

Do (m) 1.65

t (m) 0.015

Head losses

In any real moving fluid, energy is dissipated due to friction (major losses) proportional to the length

associated and singular losses (minor losses) associated with bends, fittings, valves, etc. here, with

respect to the given data we calculated the head losses for friction and singularities as follows for

design, maximum and minimum discharge by the well known empirical formulas.

[15]

[16]

The mean velocity is given by the ratio of the flow rate and the cross sectional area of the penstock

with economic diameter of 1.65 m.


32

[17]

where:

D – is the economic diameter of the pipe [m]

Reynolds Number, Re is given by the equation

= [18]

where:

V – is the mean velocity [m/s]

d – is the economic diameter of the pipe [m]

[ kg/m3]

[kg/sm]

[m2/s]

Friction Loss through a pipe is proportional to the length of the pipe and given by the product of

hydraulic gradient and length of the pipe.

[19]

Where:

J- is the hydraulic gradient

L- is the total length of the penstock.

The hydraulic gradient is proportional to the square of the velocity and friction factor f.

[20]

For bends, valves, expansions and contractions the same equation can be used by replacing f by ᶓ

(singularity factor) whose value is given for different bend angles and valves.


33

[21]

Friction factor f, is a factor given by the following correlation

[22]

Where: -

k – is the absolute roughness of the pipe [0.00025m for steel]

Using the above equations the friction factor, f, the hydraulic gradient, J and Reynolds number Re for

the optimum, maximum and minimum flow rates via excel are summarized in the following table:

Table 18: Summary

Q (m3/s) Mean velocity

(m/s) Re f J (H-gradient ) Bend αb (0) ξ

Optimum 3.50 5956214.49 0.010667286 0.003897291 1 29 0.2

Maximum 3.85 6551835.94 0.010618327 0.004694079 2 10 0.2

Minimum 1.40 2382485.80 0.011349384 0.000663439 3 26 0.2

4 47 0.55

5 28 0.2

The head loss for the bends and valves is a function of ξ that its value depends on the respective

angles indicated in the following table.

Table 19: singularity factor

α [o] 30 40 60 80 90

ξ 0.2 0.3 0.55 0.99 1.10

The modeled penstock has five bends and a butterfly valve at the entrance to the turbine. The

butterfly valve is considered to be fully opened that there will be no loss associated with it. The

actual bend angles are tabulated in table 18 and the tabulated values are not the exact values at that

angle rather the next higher angle from table 19.


34

The table below also shows the sum of all the head losses and their percentage share with respect to

the gross head for the optimum, minimum and maximum discharge.

Table 20: Head losses

Head Losses

Component Type of head loss

Qopt(m3/s) % Qmax(m3/s) % Qmin(m3/s) %

Penstock Friction 1.92 3.01 2.32 3.62 0.33 0.51

Bend 1 singular 0.12 0.2 0.15 0.24 0.02 0.03

Bend 2 singular 0.12 0.2 0.15 0.24 0.02 0.03

Bend 3 singular 0.12 0.2 0.15 0.24 0.02 0.03

Bend 4 singular 0.34 0.55 0.42 0.66 0.05 0.09

Bend 5 singular 0.12 0.2 0.15 0.24 0.02 0.03

Butterfly valve

singular 0 0 0 0 0 0

Total 2.77 4.35 3.34 5.24 0.46 0.73

From table 20 the percentage of the head losses is a bit less than 5% for the optimum discharge and a

bit higher than 5% for the maximum flow with a very small head loss for the minimum flow. Thus

the 5% loss given for the model is verified.

There fore, the hydraulic grade line is verified using the next figure:

Figure 18: Hydraulic grade line


35

Generally figure 19 from the excel analysis dipicts the variation of head loss with discharge

(minimum to maximum) in which the Head loss increases exponentially.

Figure 19: Head loss with discharge

2.2. Power house and Tailrace This subtopic gives the main description of the electromechanical equipment, some preliminary

design rules and some selection criterion which is helpful to size our power house.

2.2.1. Hydraulic turbines

The purpose of a hydraulic turbine is to transform the water potential energy to mechanical

rotational energy. It is appropriate to provide a few criteria to guide the choice of the right turbine

for a particular application and even to provide appropriate formulae to determine its main

dimensions.

Turbine selection criteria

The type, geometry and dimensions of a turbine will be fundamentally conditioned by the following

criteria:

• Net head

• Range of discharges through the turbine

• Rotational speed

• Cavitations problems


36

• Cost

Net head

The gross head is well defined, as the vertical distance between the upstream water surface level at

the intake and the downstream water level for reaction turbines or the nozzle axis level for impulse

turbines.

The first criterion to take into account in the turbine's selection is the net head. Table 21 specifies the

range of operating heads for each type of the most known turbines. The table shows some

overlapping, as for a certain head several types of turbines can be used.

Table 21: Range of heads

Turbine type Head range in meter

Kaplan and propeller 2 < Hn < 40

Francis 25 < Hn < 450

Pelton 50 < Hn < 1000

Discharge

It is necessary to know the flow regime, commonly represented by the Flow Duration Curve (FDC)

or the Reservoir Storage Capacity for Regulation schemes. The rated flow and net head determine

the set of turbine types applicable to the site and the flow environment. Suitable turbines are those

for which the given rated flow and net head plot within the operational envelopes of the graph

below. A point defined as above by the flow and the head will usually plot within several of these

envelopes. All of those turbines are appropriate for the job, and it will be necessary to compute

installed power and electricity output against costs before taking a decision. It should be


37

remembered that the envelopes vary from manufacturer to manufacturer and they should be

considered only as a guide.

Figure 20: Operational range of application

Using the above graph it is clear that for an optimum discharge of 7.48 m3/s and a net head of 59.85

m Francis turbine is selected and the selection is verified for the model given to be installed at the

small hydro power plant.

Francis turbines

Francis turbines are reaction turbines, with fixed runner blades and adjustable guide vanes (or wicket

gates), used for medium heads. In this turbine the admission is always radial but the outlet is axial.


38

Francis turbines can have vertical or horizontal axis, this configuration being really common in small

hydro.

Photo1: Horizontal axis Francis turbine

The water enters the turbine by the spiral case that is designed to keep its tangential velocity constant

along the consecutive sections and to distribute it peripherally to the distributor.

The draft tube of a reaction turbine aims to recover the kinetic energy still remaining in the water

leaving the runner. As this energy is proportional to the square of the velocity one of the draft tube

objectives is to reduce the turbine outlet velocity.

Specific speed

The specific speed constitutes a reliable criterion for the selection of the type and dimensions of

turbine, given by:

ns= N 4

5

H

P [23]

ns- is known as specific speed [rpm]


39

N- is rotational speed of the generator [rpm]

P- is power developed by the turbine in Horse power [HP]

H- is net head [m]

The specific speed can be chosen from the graph of specific speed and net head for different turbines

as shown below:

Figure 21: Specific speed Vs net Head

Using the given net head of 59.85 m and the selected Francis turbine an average specific speed

between the two curves for Francis turbine is taken by:

ns= [24]

=250.77 rpm

For the hydraulic power

when

where the maximum efficiency is 0.90.

Therefore rearranging the above equation for specific speed the rotational speed N will be 401.74

rpm.


40

Generators

Generators transform mechanical energy into electrical energy. Depending on

characteristics of the network supplied, the generator can be chosen between:

Synchronous generators

Asynchronous generators

Below 1 MW, synchronous generators are more expensive and are used in power systems where the

output of the generator represents a substantial proportion of the power system load. But here since

the power produced from each turbine is 3.6 MW we choose synchronous generator.

The number of poles for the chosen synchronous generator with the selected specific speed of the

Francis turbine from the graph at a 50 Hz grid is given by:

[25]

where:

nPP- number of pair of poles

N- Rotational speed [rpm]

Using equation 23 the number of pair poles is found to be 7.5 but this is not synchronous we have to

re-arrange the nPP to the nearest integer (npp=8) and calculate the modified values of N (375 rpm)

and ns (234.08 rpm) using the above equations and this is done in excel in a similar way as

presented in the Table 22.

Table 22: summary of specific speed

N (rpm) npp nppnew Nnew (rpm) nsnew(rpm)

401.74 7.46 8 375 234.08


41

Now, using the net head, optimum discharge, power output (for Q/Qmax=1) and the rotational speed

from the standard manufacturer’s graphs we select a group G Francis turbine which suits our

parameters as shown in the Figure 22.

Figure: 22 Group G Francis turbines operational parameters

The value of the suction head for the selected turbine can also be established from the same given

standard manufacturer’s graphs as shown below based on the net head and group of turbine (G).


42

Figure 23: Suction Head

Therefore, the summary of all the calculated and selected values of the Francis turbine are presented

in Table 23.

Table 23: Summary of scheme parameters

Scheme Parameters

Turbine Type G

Turbine size (m2) 13.5

Q (m3/s) 7.48

P(KW) 3599.14

N (rpm) 375

Ho (m) 59.89

Hs (m) 5

2.3. Forces applied to a solid anchor Net forces due to pressure and momentum change are computed as follows:


43

Figure 24: Resultant forces produced by weight, pressure and change in momentum

[26]

[27]

[28]

[29]

where:

P- maximum pressure in penstock ( from the transient analysis - next section Hmax = 133 m)

A-Cross-section area of penstock (2.14m2)

Q-Discharge (7.48m3/sec)

θ1 and θ2 – angles as shown in figure above

At each pipe change direction, the penstock and its supporting structures must be designed to resist

the forces resulting from changes in direction calculated by equation 26 to 29 via excel and are

presented in Table 24.

Table 24: Forces due to pressure and momentum

Forces Value (kN) Resultant – R (kN)

Fpx -107.2830242 393.63913

Fpy 374.1403682

Fmx -1.218625807

Fmy 4.249853241


44

2.2.3 Powerhouse

Due to the presence of large and heavy equipment units the powerhouse stability must be completely

secured. In a small hydropower scheme the role of the powerhouse is to protect the

electromechanical equipment that convert the potential energy of water into electricity from the

weather hardships. The number, type and power of the turbo-generators, their configuration, the

scheme head and the geomorphology of the site determine the shape and size of the building.

In order to mitigate the environmental impact the powerhouse can be entirely submerged. In this way

the level of sound is sensibly reduced and the visual impact is nil.

Figure 25: Schematic view of the model powerhouse


45

Area of power house

The layout of the given model power house is shown below and from the figure the area of the

power house can be approximated to be (150 m2).

Figure 26: power house layout

Here to verify the general lay out we chose the area of the power house from a given standard graph

presented below and we found a value of 152 m2

for each turbine and since we select three turbines

to handle the available discharge the total area must be three times greater and it results to 150 m2

with a very small deviation the area of the power house is verified for the given model.

Figure 27: powerhouse floor area required

Flow discharge curve in the area of powerhouse

The flow curve in the power house area is determined assuming a rectangular shape tail race shown

below schematically and using the relation:


46

Q = K s RH 2/3 i1/2 [30]

where:

K=30 m1/3

s-1

RH = s/p is the hydraulic radius

S = 6*h is the area

P- is the perimeter

Figure 28: tail race shape

Thus, the values of h at the tail race for different values of Q are established in excel and presented

as shown in the table and graph below.

Figure 29: Power house discharge curve


47

Maximum suction head

Based on the tail race layout given in the model the allowable head for flood prevention and the

maximum height for the given maximum discharge which is 34.29 m from equation 31 as shown in

the table below calculated via excel.

Figure 30: Suction head and tail race layout

Hmax=hsmax+Ht [31]

where: Ht-tail race piezometric head (FSWL(NPA) -Hgross)[m] (Figure 30)

hsmax- maximum suction head [m]

Hmax-the level of the characteristic point of the turbine runner [m]

Table 25: Summary of tail race head

Ht (m) hmax (m) Hmax (m)

32.8 2 34.29


48

3. Transient and safety analysis (system dynamics)

3.1. The Method of Characteristics Turbines are designed for a certain net head and discharge. Any deviation from these parameters

must be compensated for by opening or closing the control devices, such as the wicket-gates, vanes,

spear nozzles or valves, to keep either the outlet power, the level of the water surface in the intake,

or the turbine discharge constant and more over huge load variation at for instance start-up and close

down. This will give huge pressure fluctuation caused by the retardation of the water masses.

The Method of Characteristics (MOC) is a numerical method for solving so called hyperbolical

differential equations, the wave equations. For all kinds of pipe net work analysis, the method is very

common and is described in several text books.

In order to use MOC, one thing is to set up a system of the equation of motion and the continuity

equations for all the pipe or conduit elements, another thing is to describe the boundary conditions

like valves, turbines, shafts etc.

Nomenclature for the integrated equations

[32]

C ~1000 m/s

where:

C - the celerity of the elastic waves in circular pipelines.

- is the fluid bulk modulus of elasticity (2×10³ MPa for water),

- is the fluid specific mass (10³ kg/m³ for water),

E- is Young’s modulus of elasticity of the pipe wall ( steel = 2,5 Gpa)

D- is the diameter of the pipeline and e is thickness (1.65 m, 0.15 m)

e

D

E

ε1ρ

εc


49

2

CCH 21P

[33]

2B

CCQ 21P

[34]

ΔtcΔx [35]

2Q

ΔxJR

[36]

AAA1 QQRBHC [37]

BBB2 QQRBHC [38]

gA

cB

[39]

where:

Hp- is the hydraulic head of internal point p

Qp - The discharge of internal point p

C - The elastic waves celerity

g - The acceleration of gravity

A - The section of the pipeline

J- The hydraulic gradient and

x,t- the space and time variables


50

Figure 31: Nomenclature for the integrated equations

Numerical procedure

The numerical procedure for calculating the pressure propagation in a pipe line will be:

1. The pipe line is made discrete and each part is Δx = cΔt. In order to fit in the border

conditions, the total length of the pipe line must be n Δx where n is an integer

2. Qp and Hp for all the internal points of the pipeline at time to is found

3. Equation 33 and 34 are solved with respect to the P-points, i.e. the condition at time to+Δt is

found

4. When the condition at time to+Δt is known, the procedure is repeated in order to find the

condition at to+2Δt etc

Boundary Conditions

At the ending points of the pipe line, there is only one characteristic equation, C+ or C-.

Another equation is needed. This equation is the relation between the flow and head defined by the

border condition. For instance a reservoir will keep a constant head and will give the following

equation:

RP ZH [40]

Where:

ZR- is the hydraulic head in the reservoir.

If in the boundary there is a shutter (valve) the following equation:

PPVRP QQCHH [41]

Where:

HR- is the hydraulic head of the other side of the shutter, CV - the flow coefficient that can be time-

function. The signal + or – depends on the position of the valve and the pipeline.

3.2. Hydraulic transient analysis: Preventing water hammer Water hammer is a type of hydraulic transient that refers to rapid changes of pressure in a pipe

system that can have devastating consequences, such as collapsing pipes and ruptured valves. It is

therefore important to understand the phenomena that contribute to transient formation and be able


51

to accurately calculate and analyze changes as well as maximum and minimum pressures occurring

in a pipe system for different conditions knowing that closure time for fast manoeuvre is less than

2L/c and that of slow manoeuvre is greater than 2L/c as follows:

Table 26: summary of data and trial times

Data

Q (m³/s) 7.483

L (m) 486.47

D (m) 1.65

c (m/s) 981.8

Zm (m) 103

Zj (m) 100

tf (s) 16

i) Linear

ii) Bi-linear

Trial 1 2 3 4

Time (s) L/c 3L/c 20L/c 50L/c

Value 0.5 1.5 10 25


52

iii) Upward parabolic

iv) Down ward parabolic

Figure 32: summary of different closure types and times

Table 27: Maximum and minimum pressure of penstock for different closure types and times

i) Linear

Section 0 1 2 3 4 5 6 7 8 9 10

L/c

H Máx (m) 103 172,6 242 311,3 380,3 449 452,1 452,2 452,4 452,5 452,7

H mín (m) 103 33,95 -35,03 -103,9 -172,4 -240,6 -243,6 -243,7 -243,9 -244 -244,2

3L/c

H Máx (m) 103 126,2 149,4 172,6 195,7 218,8 241,8 264,7 287,6 310,3 333

H mín (m) 103 79,82 56,67 33,56 10,49 -9,635 -10,06 -10,42 -10,71 -10,94 -11,11

20L/c

H Máx (m) 103 106,4 109,7 113,1 116,4 119,7 123,1 126,4 129,7 133 136,3

H mín (m) 103 100,3 100,2 100,1 99,93 99,8 99,66 99,51 99,35 99,19 99,02

50L/c

H Máx (m) 103 104,3 105,5 106,8 108 109,3 110,6 111,8 113,1 114,3 115,5

H mín (m) 103 102,7 102,4 102,1 101,8 101,5 101,2 100,9 100,6 100,3 100


53

ii) Bi-linear

Section 0 1 2 3 4 5 6 7 8 9 10

L/c

H Max (m) 103 241.2 346.1 380.9 415.8 450.7 452.3 452.4 452.6 452.7 452.9

H mín (m) 103 -34.3 -138.4 -173 -207.6 -242.1 -243.7 -243.9 -244 -244.2 -244.3

3L/c

H Max (m) 103 149.3 195.5 241.5 287.4 333.1 346.2 357.9 369.6 381.3 393

H mín (m) 103 68.43 33.94 -0.422 -34.6 -68.54 -80.16 -91.8 -103.5 -115.1 -126.8

20L/c

H Max (m) 103 109.9 116.7 123.5 130.3 137.1 143.9 150.6 157.3 164 170.7

H mín(m) 103 97.86 92.73 87.61 82.51 77.43 72.36 70.48 70.63 70.79 70.49

50L/c

H Max (m) 103 105.6 108.3 110.9 113.5 116.1 118.7 121.3 123.9 126.5 129

H mín (m) 103 101 99.07 97.12 95.17 95.22 95.32 95.41 95.5 95.59 95.67

iii) Upward parabolic

Section 0 1 2 3 4 5 6 7 8 9 10

L/c

H Máx (m) 103 227.1 324.4 394.4 437 452.1 452.2 452.4 452.5 452.7 452.8

H mín (m) 103 -20.16 -116.7 -186.3 -228.5 -243.5 -243.7 -243.8 -244 -244.1 -244.3

3L/c

H Máx (m) 103 147.2 188.5 226.9 262.3 294.8 324.3 350.8 374.3 394.7 412

H mín (m) 103 72.52 42.15 11.9 -18.21 -48.15 -77.33 -103.7 -127.1 -147.4 -164.6

20L/c

H Máx (m) 103 109.6 116.1 122.6 129 135.4 141.7 148 154.2 160.4 166.5

H mín (m) 103 99.68 96.38 93.09 89.81 86.55 83.31 80.08 76.87 73.68 70.5

50L/c

H Máx (m) 103 105.5 107.9 110.4 112.8 115.2 117.7 120.1 122.6 125 127.4

H mín (m) 103 101.8 100.7 99.53 98.38 97.24 96.11 94.98 93.86 92.75 91.64


54

iv) Downward parabolic

Section 0 1 2 3 4 5 6 7 8 9 10

L/c

H Máx [m] 103 227 323.1 391.5 432.4 448.4 451.8 451.9 452.1 452.2 452.4

H mín [m] 103 -20.07 -115.5 -183.5 -224 -239.8 -243.2 -243.3 -243.5 -243.6 -243.8

3L/c

H Máx [m] 103 133.9 164.8 195.6 226.3 256.9 285.9 311.8 334.5 354.2 370.8

H mín [m] 103 72.28 41.57 10.88 -19.72 -50.23 -79.12 -104.9 -127.6 -147.1 -157.9

20L/c

H Máx [m] 103 106.5 109.9 113.4 116.9 120.3 123.8 127.2 130.7 134.1 137.5

H mín [m] 103 99.53 96.07 92.61 89.15 85.7 82.25 78.8 75.36 71.93 69.65

50L/c

H Máx [m] 103 104.4 105.8 107.2 108.6 110 111.4 112.8 114.2 115.6 117

H mín [m] 103 102.7 102.4 102.1 101.8 101.5 101.2 100.9 100.6 100.3 100

i. Linear

a) L/c

b) 3L/c


55

c) 20L/c

d) 50L/c

ii. Bi-linear

a. L/c


56

b. 3L/c

c. 20L/c

d. 50L/c


57

iii. Upward parabolic

a. L/c

b. 3L/c

c. 20L/c


58

d. 50L/c

iv. Down ward parabolic

a. L/c

b. 3L/c


59

c. 20L/c

d. 50L/c

Figure 33: Hydraulic head in the shutter (valve) - time variation

i. Linear

a) L/c


60

b) 3L/c

c) 20L/c

d) 50L/c


61

ii. Bi-linear

a. L/c

b. 3L/c

c. 20L/c


62

d. 50L/c


a. L/c

b. 3L/c


63

c. 20L/c

d. 50L/c


a. L/c


64

b. 3L/c

c. 20L/c

d. 50L/c

Figure 34: Maximum and Minimum head envelope and pipe line profile


65

3.3. Transient flow due to fast/ slow manoeuvre

3.3.1 Fast manoeuvre: Causes and effects of water hammer

Rapid pressure changes are a result of rapid changes in flow, which generally occur in a pipe system

at valve opening or closing as shown in figure 33 (L/c). Because of the compressibility of water and

the elasticity of pipes, pressure waves will then propagate in the pipe until they are attenuated at a

velocity, which is dependent upon pipe material and wall thickness. The effects of the water hammer

vary, ranging from slight changes in pressure and velocity to sufficiently high pressure or vacuum

through to failure of fittings, burst pipes and turbine damage.

Due to liquid inertia in the pipe sections downstream of the valve the pressure decreases, and vapour

bubbles are formed near the valve. As a result of fast re-condensation of vapour bubbles, the liquid

being transported is stopped rapidly at the closed valve. This pressure surge is referred to as

cavitational hammer.

While it is difficult to determine when the risk of water hammer exists and calculations are required,

there are several factors that generally indicate when taking precautions against water hammer are

advisable.

Pipeline profile

The minimum pressure line (red profiles in figure 34) depends upon various factors such as the wave

speed. Therefore the minimum pressure line will retain the same shape regardless of the pipeline

profile (pink profiles in figure 34) as long as no vaporization occurs. The magnitude of the sub

pressure that the pipe will experience will therefore depend on the pipeline profile, i.e., the distance

between the minimum pressure line and the pipeline profile (see figures 34 above).

Pipeline length

Pipe length will influence the reflection time and the inertia of water inside the pipe. The longer the

pipe is, the longer the reflection time, that is, the time it takes for the wave to reflect at the outlet and

return to the starting point. In addition, the longer the pipe the larger the mass of water that will

affect the moment of inertia of the water column. Generally speaking, whenever the pipe length is


66

greater than 300 m in length, the risk of sub pressures exists and water hammer calculations should

be conducted.

3.3.2 Slow manoeuvre: means for reducing the transient pressure, Prevention of Water Hammer

and Cavitation

A simple and often the best method to prevent water hammer are to close or open the valves slowly.

The question whether a valve closes slowly enough can be easily calculated by the use of Excel. The

minimum closing time depends on the pipe length and profile upstream the valve to the next point

where pressure is fixed (i.e. minimum). Furthermore one has to take into account that there are

different valve characteristics (figure 32) so that pressure increase due to closing process occurs at

different times. In practice, 3 - 10 times the minimum closing time is needed to avoid high water

hammer pressure peaks. Another possibility is to use air vessels, surge shafts or bladder

accumulators, which are installed upstream the shut-off valve.

3.4. Transient flow due to valve closure operations

The results of closing the valve in different times shown in table 26 and figure 32 can be seen in

Figure 33 and 35 for comparison. The maximum and minimum pressure varies from T = L/c to T =

50L/c. The details of the maximum and minimum pressures of the valve closure operations for

different types and times of closure are tabulated and are summarized in Table 28 below to show

how the system responds to the different closure types and times.

Table 28: Summary of shutter valve head variation for different closure types and times

L/C Linear Bi-Linear Upward parabolic Downward parabolic

Hmax[m] 452.7 452.9 452.8 452.4

Hmin [m] -244.2 -244.3 -244.3 243.8

3L/C Linear Bi-Linear Upward parabolic Downward parabolic

Hmax[m] 333 393 412 370.8

Hmin [m] -11.1 -126.8 -164.6 -157.9


67


Hmax[m] 136.3 170.7 166.5 137.5

Hmin [m] 99.02 70.49 70.5 69.65


Hmax[m] 115.5 129 127.4 117

Hmin [m] 100 98.67 91.64 100

i. Linear

ii. Bi-linear


68



Figure 35: Variation of Hydraulic head in the shutter with closure time

Therefore, the closure type with higher positive minimum pressure from the higher penstock profile

level and low maximum pressure for the chosen time of closure (which is Linear at T = 20L/C = 10

sec) is selected from tables 28 above . The maximum pressure ( at Hmax =133 m) of the bend

positioned at a distance of 473.52 m at this closure time from tables 27 is also used to calculate the

occurring forces in section two of this report.


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3.5. Recommendations

Slow-closing valves: as a solution for waterhammer

To prevent the occurrence of high and low pressures, slow-closing valves gradually decrease the

flow before the power to the turbine is shut off. It can be a time-consuming procedure, especially for

long pipe systems, so for cases such as these, the use of valves with multi-stage motors is

recommended. This enables the speed at which the valve is closed to occur at a slightly faster rate

during the first stage of the valve closure and then at an extremely slow rate during the last stage of

the valve closure.

Advantages: these can be an economical alternative to other protection methods.

Disadvantages: slow-closing valves are not suitable for the protection of the pipeline in the event of

power failure.

For a total pressurised circuit with pipes followin

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