proponiona] relationship with the rpm. It is at the stage of the measurement of the maximum torque, that the rpm is measured and recorded as the rpm at stall condition.
40
- - P1
... -...
- - P2
30
- - P3
t··· ... . ---P4
• . . . . PS 20
10
kP a
o ..
,.
·10 • •••••• _. _. _ •••• ~ ••.•.•• _. _. _. _. _.~ .•••• 1 •••••••.
• . ~ , ... -... -~ . -. -... . , •
-20 _ _ _ • • • • • • • • • • • • , • • • • _ • • • _ . _ • • • • • • , ~ • • _ • • • • • _ . _ . _ • • • • , "
..
; . ... . . 4· _ ", • • • • • _ . _ : _ • • • • • _ . _ . _ • • • _ . ::
. . .
~ .. -o
100 200 300 400 500rpm
Figure 5.4.1 Pressure vs Stall rpm Test 1
The period between the first and second test included heavy rainfall and some settling of the draft tube piping occurred. marginally offsetting the aJignment of the flanges joining the turbine diffuser and the draft tube pipe. The resultant air leak in the draft tube therefore caused a regulating effect on the vacuum pressure. resulting in the pressure leveling off as seen in Figure 5.4.2.
Table 5.2: Test results· Test 2 on the 14/1212000
Shaft Dower Stall Soeed Pl P2 P3 P4 P5 Pressure Hnett
kW rpm kPa kPa kPa kPa kPa Coefficient m
@ stall rpm Load
0.13C 4 ..<: -1.59 4.30
0.609 6 C C C -1.45 4.431
2.382 13 C C -1.09 4.59
5.114 18 C C -0.78-< 4.801
9.55 24 lC 2 1 -2C 0.61 6.12
11.47 27 11 2 1 -2C 0.57 6.361
13.36 30 1 2 lE 10 -2C 0.53 6.76
14.50C 31 lE 2 H 1 -2C 0.50 6.91
16.34 32 2C 3 21 1 -2C 0.46 7.141
17.97 33 2 3 2E 2 -2C 0.401 7.79
22.23E 41 2E 3 3C 20 -2C 0.40 8.01
44. 75 6 5 4 25 -2E 0.89 9.89
Figure 5.4.2 shows the plots of the pressure distribUlion curves generated by the turbine during loading for the second test carried out on the turbine. The pressure distribution curves are similar to those for the first test except for the leveling off of the pressure values around 400rpm, which is expected to be a result of the air leak affecting the vacuum pressure on the downstream side of the turbine.
The general trend of the increase in pressure PI-P4 in Figure 5.4.1 and Figure 5.4.2 indicates the increase in the static pressure, which corresponds lO an increase in mass flow rate. This is also refJected in the lower negative pressure Ps, which measures the vacuum pressure of the draft tube. The larger volume of water, as the turbine piping fil1s to capacity, has a larger mass, which in turn increases the vacuum pressure through (he draft tube. The increasing gradient of P1-P4 shows (he increase in the static pressure caused by increasing the load on the turbine.
40
30
20
10
kPa
o
· .... _ -
-IT···
:- - P1 - - P 2
- - P3 · , ' :
---P4
· ~;L,---~ · ····
- - - --PS '
.1f' :
... , ... . .. · ~J'~t/' ··· ... .
: '/
' .. _.-' :
. .
.. _. -... " .. ~ --
-
-... _ .. -_.: ... _ ..._.
_.-'
-10 ... , ... , ... , ... .
-20 .
_.
_ ... .... .
:. _ ... _ ... _ .•. _ ... _. _-
. _. _. .-
_.-
_ .. ; . ... _. _. _. _ .. --~.
_. -_ ... -_. --..
_.o
100 200 300 400 500rpm
Figure 5.4.2 Pressure vs Slalll"pm - Test 2
Figure 5.4.3 and Figure 5.4.4 showing the torque and power versus rpm curves were taken in real time, using a strain gauge attached to the shaft linking the dynamometer to the turbine. The plots show the points that were measured as well as the best-fit trend lines, which are typically a 2nd or 3rd order polynomials. The torque curves show a typically linear relationship to the rpm and are spaced by setting the no-load rpm condition by adjusting the gate valve opening.
600
--- 400 500
400
Nm
300
200
100
---- 600
.... 't\ ... ... .
: < , ._. -
800~,
'\
·
...
~ , ~',' ...•.. " .... ~ ... " ·r····
:
'., , : ,
: .
.
: ...,, : '
·
...
~, , :- .', : ,',
· ~ , . ~ .
:
:.. " .. : , :
......
,
..., ... •
;.~~ ....... , .~.;..:.: t " . "
': , ! ' :'.', ~ , .
~ ',
! ' ! .... .. ! ' \ : !
... j ...
~.~.-~... t· . " . : .
~.~ r~"" ~\~- + \ " . _ .. --_. -
~_. -_ ... .
, :
:
;,..
: '....
..
' ;: ' : ''\. '
:" ...
~. ,
. :~'.
.
: :" , : '
:.,
. ",,
.\
: :··· ~···f···~,·~ j · ···r, · ···f···"! ·;~ .. ~·-· \ _,"\ -· : ... .
'
.... ....
: ;.:,
: ,, : . ..
:" ..
\ : ...
' "-. ... .' , ' . "'" , .: : \ !". , ,", : .. :
- - 1000 -- " ' 1050 ---1100 - - 1200 - - 1250 - - 1300
o
o
200 400 600 800 1000 1200 1400rpm
Figure 5.4.3 Torque Curves Test 2: Range 400 - 1300rpm
The power curves shown in Figure 5.4.4 expose an excellent progression of the maximum power output with an increase in the rpm up to the max.imum power output, which tapers off with increasing rpm. The decrease in the power output after the peak
shows the limitations induced on the performance of (he turbine due to the limit on mass flow rate by the initial setting of the gate valve. Further restrictions are incurred by cavitation in the boundary layers on the blades and in the draft tube. This phenomenon is observed again in Figure 5.4.11 showing power versus efficiency.
30
25
20
kW
15
10
5
--- 400 ---- 600 ---- BOO - - 1000 ---1050 ---1100 - - 1200 - - 1250 - -1300
!,--
-~... " ... c .... / ... : .. \ ... j ...•...
• ,'/-< , : •
,
" " : : , \
... i ...
/c .. /. ... ; ... .... , ... " .... " ... ... ..
: ' I: .--- , , :\
· ,. . ..., . .
: : , : , : :
: I : ' : " : \: \
:
-,
--:-. \. :\
: (,." : ~ ~
·
,- .
. . :" .
... ... ·i· ", ...
~;::~...
~ T~...
~ ';~.-'\
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, ,. y , ,, : . . ,
; ' :
:: " : "
: -; . : 'X ... ,'
...
~- .--_···j···1···( - \ ··· _ · · · : . .. \ · .. ··· \ --· + , i· ... .
: : :
.
" \ :-~'-.... ' : .:, \ 1
,
- :-
, :\ ' .
::.\• ;- : I \
'/
.
:, .
:.,
···l····.·~~~·
..
l···~···A,:.... j ... " \JA; \ .... \ j., ... .
•• ,:- : -..... : ' . : : ' j
: : ', :
\:••• ---;-----~ ". "I.:
o
o
200 400 600 BOO 1000 1200 1400rpm
Figure 5.4.4 Power Curves Test 2: Range 400 - 1300rpm
The first equation that is required to analyse the above results is that of Bernoulli, governing the summation of the static and dynamic pressure heads. Since it may be assumed that PI - P6 are all set at the same height, the respective component of Bemoulli's equation. typically the potential energy, may be excluded. However, the losses for a section of tapered pipe and those for a gate valve should not be neglected.
The various areas of losses are mentioned as follows:
I) Pressure losses through the gate valve, as the flow is converted from potential energy into kinetic energy at narrow gate valve openings. This is typically a function of the measure of the gate valve opening. Characteristic results are available from which the curve of the loss coefficient may be extracted.
2) Turbulent losses through the nozzle and following into the turbine. These can simply be measured by the frictional losses within a pipe.
3) It has been well researched that the ideal flow condition through the turbine is laminar and flow that is turbulent tends to cause losses due to early separation from the blade surface, negatively affecting the pressure distribution. This tends to be more of a problem for airfoil blading, used in the design of the turbine under examination, when compared to momentum blading.
4) At smaller gate valve openings, the turbine will not be "flooded" and neither will the diffuser. The net result is very low draft tube efficiencies, since it is not possible to utilise the negative pressure of the draft tube due to the air cavity.
Furthermore, the turbine itself will not be flooded, where only the lower half of the blades would receive water. This makes measurement of any results literally impossible until such time as the draft tube is flooded. It is therefore determined that the results which show that the draft tube is not completely flooded, typically when there pressure readings are zero, will be ignored.
5) Losses from blade tip clearance. This would occur in both the stator and the rotor and is caused by excessive clearances between the blade tips and the outer wall.
In these areas, the flow does not conform to the designed free vortex pattern and therefore does not produce any work.
6) Losses caused by the shaft of the turbine restricting the flow on the outlet, resulting in turbulence in the draft tube and thus reducing its efficiency. However, these losses may be sufficiently small to neglect.
7) Losses caused by the draft tube are expected to account for the first or second highest value of loss compared to that of the gate valve losses. The reason for this is that the draft tube efficiency affects the overall head of the turbine, which is directly proportional to the power. The design of the draft tube shape. cross- section and setting has a large bearing on the cavitation coefficient. This is
typically what is used to define the efficiency of the draft tube, which is then cross-checked against the Bernoulli equation.
8) Losses caused by the friction of the bearings~ namely the two radial bearings, the single thrust bearing and the rubber bush supporting the shaft overhang and additional friction losses due to the stuffing box packing running on the surface of the shaft
9) Furthermore, when taking measurements, the PTO shaft and dynamometer incur their own losses, but these do not form part of the losses of the system since the voltage gain on the strain gauge is adjusted during calibration to read the exact measurements to within INm of torque. It is further assumed that drift is negligible and the measurements are repeatable.