5.lecture on changing top-altitude tail tunnel

Changing Top-altitude Tail Tunnel A.1

Jianxu ZhouMay, 2015

Hydraulic Characteristic of the Governor-Turbine-Hydraulic System with a Changing Top-A

ltitude Tail Tunnel


Introduction

Special Tail Tunnel in Hydropower Stations

Case analysis

Discussion and Conclusion

Mathematical Model

How to cancel the downstream surge tank

Brief presentation on surge tank


Introduction

For the governor-turbine-hydraulic system of a

hydropower station, the traditional hydraulic transients

computation and analysis mainly include:

(1) Water hammer and surge analysis

(2) Hydraulic disturb analysis

(3) Stability analysis under small disturbances

which all depend on units’ parameters, governors’ parameters and layout design of hydraulic system etc..


Brief presentation on surge tank


Functions of surge tank

(1) The free surface of the surge tank effectively reflect water

hammer waves from the turbine, preventing the waves entering

the tunnel;

(2) The introduction of the surge tank shortens the length of the

penstock, and thereby greatly reduces the intensity of the water

hammer waves;

(3) The surge tank improves the operating condition of the turbine

units during load variation by accommodating surplus water

from the tunnel or supplying additional water to the turbine

quickly to fit the new load demand.


Criteria for provision of the surge tank

For upstream surge tank:

For downstream surge tank:

02015 H)~(LV

s4~2

gH

LVTw

s

dsW H

g

V

V

TL

29008

5 2


Requirement to surge tanks

(1) Be as close to the powerhouse as possible;

(2) Reflect the water hammer wave as effectively as possible;

(3) The surge should be stable and be damped rapidly;

(4) Max. surge will not cause overtopping and min. surge

should not allow air to be drawn into the tunnel, and the

range of surges must not be great enough;

(5) Low head loss of flow passing the base of the surge tanks;

(6) Be of structural safety and reliability.


Fundamental flow equations

dt

dZFfVQ

dt

dv

g

LhzhZf

dt

dv

gfL ww )(

))(()( 0000 wmwowmowo hxhHqQhhHQ


Surge analysis (Upstream surge tank) Load rejection

调压井水位

2360

2370

2380

2390

2400

2410

0 80 160 240 320 400

t (s)

Z(m

), H

d(m

)

Load acceptance

调压井水位

2360

2370

2380

2390

2400

2410

0 80 160 240 320 400

t (s)

Z(m

), H

d(m

)


阻抗连接管直径1.8m

2362

2372

2382

2392

2402

2412

0 80 160 240 320 400

t (s)

Hd

(m),

Z(m

)

Combined conditions.

阻抗连接管直径1.8m

2355

2365

2375

2385

2395

2405

0 80 160 240 320 400

t (s)

Hd(m

), Z

(m)


Stability analysis (Upstream surge tank)

Assumption of the critical stability criteria ：(1) The surge oscillation is very small, so the l

inearization is used for further derivation.

(2)The unit’s output keeps a constant.

(3) The unit is in isolated operation.

The obtained critical stability area is not a comprehe

nsive conception, but it ensures the safety and reliabil

ity, and it is conservative.


Based on the above assumption and the fundamental equations, the Thoma area for surge tank was derived.

kFgH

LfF

12

03

1Hhh wmowo gF

LfT 2

0001 3 wmw hhHH


Factors that influence the stability:

(1) Head of the power station;

(2) Roughness coefficient of the tunnel;

(3) Location the surge tank;

(4) Velocity head at the bottom of the surge tank;

(5) Efficiency of the turbine;

(6) Governor;

(7) Power network.


How to cancel the downstream surge tank


In the underground powerhouse, there are lots of

chambers in different sizes with centralized layout,

mainly including main power house, auxiliary power

house, transformer chamber and downstream surge

tank etc. We must pay more attention on the stability

of surrounding rock and the effect of tank’s surge on

units’ reliable operation.


How to cancel the downstream surge tank?

(1) Reduce the length of tail tunnel;

(2) Move the power house towards downstream reasonably;

(3) Enlarge the area of the tail tunnel; or

(4) Other substitutions.

In order to ensure the safe and reliable operation of

the underground power house, if possible, to cancel

the downstream surge tank is a reasonable choice

with other alternatives.


Downstream surge tank was

cancelled

Jinping II power station:


A pumped-storage power station: Its original

downstream surge tank was cancelled by the

enlargement of the approximate 800m-long tail tunnel.

A hydropower station: A special tail tunnel is

designed and put into normal operation successfully

instead of its original large scale downstream surge

tank. The special tail tunnel is relatively short, with

larger top-slope to the tail water, enlarged sectional

area and special flow patterns inside.


Generally, during the daily operation of the hydropower stations, both in the steady and transient conditions, the designed hydraulic system are always

Special Tail Tunnel in Hydropower Stations

Meanwhile, There are some special tail tunnel designed for some hydropower stations, in which the flow patterns are relatively complex with possible unsteady free-surface pressurized flow.

(1) Pressurized flow or

(2) Channel flow


Hydropower station with flat-ceiling tail tunnel

If tail water level is slightly lower than the top altitude of tail tunnel, in steady states, a separation point for pressurized flow and channel flow exists at a specified section; in transient states, unsteady free-surface pressurized flow appears along the flat-ceiling tail tunnel with several separated air masses.


Hydropower station with changing top-altitude tail tunnel

If tail water level is lower than the top altitude of the outlet of tail tunnel, both in steady states and transient states, a separation point for pressurized flow and channel flow exists. In transient states, this point is traveling along the tail tunnel and tends to be a steady state.


Mathematical Model

The basic equations of transient flow in open channels are

0

x

Q

t

hB

)(2

2

2

fJigAx

A

A

Q

x

hgA

x

Q

A

Q

t

Q

Because the classical slot model (PCW model) may result in divergent computation, two coefficients are introduced

BgAA

Ql / BgA

A

Qc /

Improved slot model


The continuity equation multiplies these two coefficients, and pluses with the momentum equation, and then at node (m, n),

(1) forward difference for /t items,

(2) different difference methods for /x items based on n+1 time step,

(3) gravity item, friction item, A/x item calculated at n+1 time step, and

(4) the others calculated at n time step,


111

1111

111 1

eQdhcQbha nm

nm

nm

nm

2112

112

12

12 eQdhcQbha n

mnm

nm

nm

where ai, bi, ci, di and ei (i=1,2) are coefficients calculated from relative variables on n time step.

Finally, two basic difference equations can be gotten

For the flow rate and water depth at all the sections along the changing top-altitude tail tunnel, an overall band matrix can originally be formed.


This is named as the improved slot model, which is basically a characteristic implicit formats.

The improved slot model is suitable for the hydraulic transients computation in the changing top-altitude tail tunnel, but it has less accuracy for the flat-ceiling tail tunnel with complex unsteady free-surface pressurized flow inside like other mathematical models.

This means it is also a key problem how to accurately analyze the complex hydraulic transients in the flat-ceiling tail tunnel. Below focuses on the hydraulic transients computation in the changing top-altitude tail tunnel.


Boundary conditions

(1) Separation point

With the known variables at i and i+1 sections, the variables at f section are easy to be computed out, and water depth at f section should approximately be equal to the height of corresponding section of tail tunnel.


(2) Bifurcation of tail tunnel

The C+ equation for 2# pressurized tail branch tunnel is

: PlPPPl QBCHC

Then, combined with the flow and head balance conditions at the bifurcation point, we obtain

0 12 PjjPjPj CQBQBhF

01113 PjjPjjP CQBhQBF

The elements of rows 2j and 2j+1 and the corresponding right items in the overall band matrix are modified.


(3) Other boundary conditions

Starting point and outlet of changing top-altitude tail

tunnel are exited inevitably.

For the starting point boundary condition, the first

line and corresponding right item in the overall band

matrix are modified.

For the outlet boundary condition, the elements of

row 2n and the corresponding right items in the

overall band matrix are modified.


Built of the unified model

Combined with the above-mentioned boundary

conditions, the final unified equations are easily

formed. Combined with the method of characteristics

in the pressurized pipelines, mathematical model of

governor and the motion equations of units, the

unified algorithm is further built for hydraulic

transient computation and stability analysis.


Case analysis Layout design of two cases for a hydropower station

tail water

2# unitsurge tank

pressurized tail tunnel

1# unitreservoir

2 4

3

5

1

65

1 3

42

tail waterreservoir

1# unit

2# unit pipe 5：top slope 0.04, bottom slope 0.099pipe 6：top slope 0.04, bottom slope 0.03

changing top-altitude

tail tunnel

tail water

2# unitsurge tank

pressurized tail tunnel

1# unitreservoir

2 4

3

5

1

65

1 3

42

tail waterreservoir

1# unit

2# unit pipe 5：top slope 0.04, bottom slope 0.099pipe 6：top slope 0.04, bottom slope 0.03

changing top-altitude

tail tunnel

(1) Tail surge tank case

(2) Changing tail-tunnel tail tunnel case


Water hammer control

Some controlling values including max. speed of units nmax, max. pressure of spiral case Hcmax and min. pressure of draft tube Hwmin are obtained below.

Optional cases nmax (r/min) Hcmax (m) Hwmin (m)

Changing top-altitude tail tunnel

112.82 151.28 -2.88

Tail surge tank 113.00 151.92 -5.57

It is known that the designed changing top-altitude tail tunnel are satisfied with the requirement of hydraulic transient control, and some items are better than that of tail surge tank case.


Stability analysis

The stability of operating unit under hydraulic disturb is analyzed while one unit rejects full load. In the following figures, the thick line is for the changing top-altitude tail tunnel case.

Hydraulic disturb

71

73

75

77

79

0 50 100 150 200

Time (s)

Spe

ed (

r/m

in)

74

76

78

80

82

0 50 100 150 200


Meanwhile, the stability of operating unit under small disturb is analyzed while one unit rejects 10% load .

71

73

75

77

79

0 50 100 150 200

Small fluctuation

74

76

78

80

82

0 50 100 150 200

Time (s)

Sp

eed

(r/m

in)

From the viewpoint of operating unit’s stability and regulation performance, the changing top-altitude tail tunnel case is superior to the tail surge tank case, including obvious shorter regulating time, less oscillation number, larger attenuation degree.


Discussion and Conclusion

(1) Based on the improved slot model and the method

of characteristics, an unified algorithm can be built for

hydraulic transient computation and stability analysis,

which is suitable for the hydropower stations with the

changing top-altitude tail tunnel.


(2) The designed changing top-altitude tail tunnel is

easily satisfied with the requirement of hydraulic

transient control, and has better stability and

regulation performance than the tail surge tank case,

(3) The changing top-altitude tail tunnel is a new type

of tail tunnel and it is a reasonable and optional case as

tail tunnel is 150 to 600m length and tailrace water

level has greater variation.


Thank you!

5.lecture on changing top-altitude tail tunnel

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