Älvkarleby, Sweden, June 18-20 2001 The second ERCOFTAC Workshop
on Draft Tube Flow
Proceedings of
Turbine-99 - Workshop 2
T.F. Engström, L.H. Gustavsson and R.I. Karlsson
Proceedings of
Turbine-99 – Workshop 2 on draft tube flow in Älvkarleby, Sweden, 18-20 June, 2001
by
T. Fredrik Engström*, L. Håkan Gustavsson* and Rolf I. Karlsson†+
*: Division of Fluid Mechanics, Luleå University of Technology, S-97187 Luleå, Sweden
†: Vattenfall Utveckling AB, 81071 Älvkarleby, Sweden
+: and Dept of Thermo and Fluid Dynamics, Chalmers University of Technology, S-41296 Göteborg, Sweden
Contents
1. INTRODUCTION
2. EXPERIMENTAL SETUP, PROVIDED DATA AND REQUESTED INFORMATION
3. EXPERIMENTAL AND SIMULATION RESULTS (CASE T) 3.1 Engineering quantities
3.2 Pressure distributions
3.3 Mean velocity distributions (axial and secondary) 3.4 k-distribution
3.5 Near-wall results 3.6 Flow structures 3.7 Comparison with case R 4. DISCUSSION
4.1 Scatter in engineering quantities (Cp and ζ)
4.2 Influence of changed experimental conditions 4.3 Simulation protocol
5. CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK
6. REFERENCES ACKNOWLEDGEMENTS
APPENDICES
A. Experimental and simulation results (Articles in separate pdf-document) B. Background data
Task and boundary conditions
Requested information
C. Evaluation of simulation data
C1 Engineering quantities (Recalculated) C2 Velocity difference plots
C3 Clauser plots at CS II
C4 Sample of simulation protocol D. Participants
1.INTRODUCTION
The first Turbine-99 workshop on draft tube flow [1], held in Porjus 1999, attempted to assess the state of art of flow simulations in a complex flow typical to a hydro power system. The flow, chosen for its technical significance rather than for its generic qualities, was shown to offer challenges well outside the original intentions of the workshop. The case showed that still too many flow parameters were unspecified by the organizers which made impossible a serious discussion about eg turbulence models. Rather, the issues of grid topology and inlet conditions (one velocity component was not given by the experiments) became central to the discussions. Therefore, it was decided that a follow-up workshop would eliminate these questions in at least one case by stipulating more data to be used by all participants. Thus, the following items were considered:
i) Specify all boundary conditions, even if there are no experimental data. This applies in particular to the radial velocity component at the inlet, and the turbulent length scale.
ii) Supply one high quality grid to be used by all participants for a reference simulation.
This would make it easier to evaluate differences between different codes and models.
iii) Make additional experimental data available, particularly time dependent results.
To meet these demands, it was decided to make available a grid which had proven to generate a reasonable value of the pressure recovery coefficient and the flow contour at test section III (See figure 1). By courtesy of Professor Lai at IIHR-Hydroscience and Engineering, a grid with 700k elements was chosen and supplied to the participants.
Here, we summarize the main findings of the workshop by comparing the simulations with available experimental results. Even with the use of the same grid, individual adjustments have been made in some contributions, both in the pre and the post processing of data.
Therefore, the pressure recovery coefficient has been calculated using the same spatial positions at the inlet cross section. Also, since most contributions use wall functions, Clauser plots have been made to assess the validity of the near-wall treatment.
2.EXPERIMENTAL SETUP, PROVIDED DATA AND REQUESTED INFORMATION
The experimental setup used for the flow measurements is the same as that for the first workshop. The draft tube model (scale 1:11) was mounted in VUAB's turbine rig at the Älvkarleby laboratory, Sweden, and the detailed geometry and dimensions of the model are found in [1]. A detailed account of the experimental procedures and accuracy of data is given in the paper by Andersson and Karlsson [2]. The overall geometry of the draft tube, with the
various cross sections, is shown in figure 1. The input data for the workshop calculations comprised of i) axial and tangential velocity components along two different radii at cross section Ia, together with associated RMS values and one component of the Reynolds’ stress tensor and ii) pressure distributions around the periphery of cross sections IVa and IVb. The data were given for two flow cases, at the top (T) and on the right leg (R) of the propeller curve. In a previous report [3] the velocity distribution at section Ib has been published, a fact used by some participants to get an extra calibration of the simulations.
Figure 1: Cross sections for LDV (Ia, II and III) and pressure (IV) measurements.
In addition to the experimental input, the grid of Lai, the radial velocity and the turbulent length scale at section Ia were also given, to be used in a ‘calibration’ calculation on flow case T (Case 1). Also, the standard k-ε model was requested to use. The other cases addressed the following items:
Case 2: Same conditions as in 1, arbitrary turbulence model; case R.
Case 3: ‘Free’ method on case R.
The requested information comprised a number of ‘engineering quantities’ defined in the following manner:
Pressure recovery factor,
2 _
_ _
2 1
inlet mean
inlet wall outlet wall p
U p C p
ρ
= − (1)
Energy loss coefficient,
∫∫
∫∫ ∫∫
⋅ ρ
⋅
+ρ +
⋅
+ρ
= ζ
Ain 2
Ain Aout
2 2
dA nˆ 2 u u
dA nˆ 2 u p u dA
nˆ 2 u p u
(2)
Kinetic energy correction factors, αaxial and αswirl:
∫
= α
A 3 3
mean
axial U dA
AU
1 α =
∫
A 2 3
mean
swirl V UdA
AU
1 (3)&(4)
Momentum correction factor: β=
∫
A 2 2
mean
dA AU U
1 . (5)
Swirl intensity:
∫
∫
= +
+
0
0 0
r R
r 2 r R
r0
2
rdr U
dr UVr
R
Sw 1 , (6)
Here, the α:s, β and Sw are evalutaed at cross sections Ia and III, whereas Cp and ζ use values at both sections Ia and IVb. Also, the pressure profiles along the centerline (upper and lower wall) and the velocity contours at sections II and III were requested. In addition to these quantities, Cp,average,based on the average pressures at inlet and outlet i.e.
2
1
A 1 A
2 average , p
A Q 2 1
dA A p
dA 1 A p
1
C 2 1
ρ
−
=
∫ ∫
(7)
has been determined from the experiments. Still another pressure coefficient can be defined as
A Q Q 2 1
dA pu dA pu '
C 2
1
A A
ax ax
p 2 1
ρ
−
=
∫ ∫
(8)
in terms of which the loss coefficient, ζ, can be written as
1 p 2
2 1 1
2 C '
A 1 A
− α
α
−α
=
ζ (9)
where α1 and α2 are the sum of the swirl components at inlet and outlet, respectively.
Since the last term in this expression is close to unity, the evaluation of ζ is ill-conditioned, a fact that will be discussed in some detail when assessing the accuracy of ζ.
3.EXPERIMENTAL AND SIMULATION RESULTS (CASE T)
The simulation results were collected and made available in printed form at the workshop.
They can be also be accessed through the website:
http://www.sirius.luth.se/strl/research.asp
The simulations produced many quantities not available from the experiments. Therefore, we present those data that can be directly compared to the experiments and some quantities that are of direct engineering importance for characterizing the draft tube flow.
3.1 Engineering quantities
The engineering quantities are defined in the section 2 and a summary of the experimentally obtained values are found in Table 1. The simulation data is collected in figure 2.
T(n) C.S. Ia (1) C.S. Ib C.S. II C.S. III
Umean [m/s] 3.33 2.22 1.01
Vmean [m/s] 1.06 0.87# 0.08
Q_int/Q [ ] 0.94 0.97 1.00
α_ax 1.06 1.09 1.04 1.09
α_sw 0.11 0.18 0.06 * 0.04 *
β 1.15 1.17 1.12 * 1.02 *
Sw 0.31 0.42 -
# Tangential component
* Only the horizontal component.
Table 1. Engineering quantities from LDA-measurements; Case T; Cp,wall = 1.12 (+0.017/-0.003) T(n) indicates data taken after resetting of the equipment (cf § 4.3).
0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000
Cp wall Cp average Loss factor Alpha ax III Alpha sw III Beta III -Swirl III AEAT NUT TEV HTC VUAB CKD HQ-FIDAP HQ-FINE HQ-TASC LTU Iowa
Figure 2: Engineering quantities
It is observed that some of the quantities in figure 2 show a considerable scatter. However, the original data showed an even larger scatter partly due to the preparation and evaluation of the data. This was obvious when the parameters which used the input data were calculated (eg.
the flow rate). In order to eliminate spurious effects of data evaluation, the data have been recalculated in a common form, illustrated in Appendix C1.
The experimental value for Cp,wall was determined to 1.12. Despite the recalculation of this parameter, the values show a considerable scatter indicating that the actual wall pressure is a sensitive quantity to calculate. Cp based on the average pressure over the cross sections is seen to be more evenly calculated. Both αax and β show less scatter which may be expected since these quantities involve only the axial velocity component. The loss factor, although small, has a relatively large scatter, an observation that will be elaborated upon in the discussion.
3.2 Pressure distributions
The radial pressure distribution at the inlet was measured using a three-hole Pitot tube and the result is shown in figure 3a. Of interest to note is that the pressure makes a sharp increase approaching the outer wall followed by a sudden decrease, as illustrated by the point at r*=1.
Since the value at this point is the basis for the calculation of Cp,wall, the result suggests that simulations must be quite accurate in this region to catch the strong radial gradients. The large scatter in the simulated Cp,wall values suggests that the resolution in this region is not accurate enough and detailed plots show that the pressure development is not well simulated at the outer wall as seen in figure 3b.
0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2
−0.15
−0.1
−0.05 0 0.05 0.1 0.15
r* [ ]
Cp [ ]
Cpstat Ia T(n)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
−0.3
−0.25
−0.2
−0.15
−0.1
−0.05 0 0.05 0.1
Radius (m)
Pressure
Experiments CFD
Figure 8. Pressure coefficients along the centerline,
a) b)
Figure 3: a) Experimentally determined radial pressure distribution at cross section Ia.
Case T. b) Simulation results (Cervantes & Engström)
The pressure distribution on the upper and lower centerlines are better covered by the simulations, as is illustrated in figure 4. Most of the pressure recovery is seen to occur within the draft tube cone well before the elbow.
-0.20 0.00 0.20 0.40 0.60 0.80 1.00
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Distance [m]
elbow corner
CFX-TASCflow
FINE/Turbo experiments [7]
-0.20 0.00 0.20 0.40 0.60 0.80 1.00
0 0.5 1 1.5 2 2.5 3 3.5 4
Distance [m]
elbow
CFX-TASCflow
FINE/Turbo experiments [7]
upper centerline wall
lower centerline wall
Figure 4: Pressure distribution along upper and lower centerlines (From Page & Giroux)
FIDAP FIDAP
3.3 Mean velocity distributions (axial and secondary)
The experimental results for the axial and the horizontal velocity components at cross section II are shown in figure 5. Despite the lack of the vertical component, the complexity of the secondary flow is evident.
1.7 0.9 1.5
1.4
1.9 2.1
0.842
1.2
2.2
1.4
y [ m ]
z [ m ]
Mean axial flow T−II
−5000 0 500
100 200 300
Figure 5: The axial (contours) and horizontal (vectors) at CS II (view from downstream).
−0.3 −0.2 −0.1 0 0.1 0.2 0.3
−0.4 −0.2 0 0.2 0.4
−1
−0.8
y
z
LTU kepsilon T C.s II diff. in U−vel.
0 0 0 0
An illustrative way of showing the accuracy of the simulations relative to the measured veloctiy values is shown in figure 6 where the difference between the simulations and the experiments are shown. The difference is defined as Uexp/Uexp, average – Usim/Usim,average.
Figure 6: Deviation between simulation and experimental values of the axial velocity at cross section II. From Cervantes & Engström.
In Appendix C2 are collected the difference plots for some selected simulations. It is seen that the general feature of two minima are similarly determined among the contributions, and that the maximum deviations are large (30%).
An integral measure of the accuracy of these calculations can be assessed by studying the standard deviation of the data integrated over the cross section. The result is collected in figure 7.
Unit standard deviation, U-vel Case T
0,00 0,05 0,10 0,15 0,20 0,25
AEAT keps NUT keps TEV keps HTC keps VUAB keps CKD keps HQ-FIDAP keps HQ-FINE keps HQ-TASC keps Iowa keps LTU keps
Standard dev./Mean vel. [-]
CS II CS III
Figure 7: Standard deviation of velocity difference integrated over cross sections II and III.
3.4 k-distribution
Of interest when assessing turbulence models is to compare the predictions of the turbulent kinetic energy (k) with the experimental data. These are shown for cross section II in figure 8.
For the corresponding simulation results, see
“Results from experiments and simulations”
on the web site.
Figure 8: Experimental values of turbulent kinetic energy at CSII.
−5000 0 500
100 200 300
0.06
0.08 0.1
0.12
0.13
0.14
0.15
0.16
0.17 0.18
0.2 0.19
0.2
0.1 0.11
0.110.12
0.04
0.140.16
0.180.19
0.11
0.1 0.2
0.04 0.06
0.15 0.17 0.1
0.08 0.02
0.09
0.07
0.14 0.19
0.2 0.08
0.180.0121
0.08 0.17 0.17
0.0121
y [ m ]
z [ m ]
RMS values T−II
3.5 Clauser plots
The large scatter in the loss coefficient indicates that the near-wall region has been non- uniformly treated. All contributions use wall-functions for which the ERCOFTAC Best Practice Guidelines [4] recommend that the y+-value of the most wall-near point to be down to 30. Also the value should not exceed ~100, still being in the logarithmic region. To check this value in the simulations, a Clauser plot was made at two vertical sections off the centerline (y=± 250 mm) at CS II. A typical result is shown in figure 9 and the data for
selected contributions are found in appendix C3. In these plots, the straight lines represent values from the log-law using different values of the friction coefficient ( Cf /2= 0.06, 0.05, 0.04 and 0.03 from top, respectively). For details of the procedure, see Appendix C3.
Figure 9: Example of Clauser plot (Data from Cervantes & Engström).
1e3 1e4 1e5
0 0.5 1 1.5
Urefy
wall/ν
U/U ref
LTU kepsilon T
It is observed that with some exceptions, the closest point to the wall does generally not satisfy the BPG recommendation. This may contibute to some of the scatter in loss-data and is a serious challenge for the simulations since losses are directly associated with efficiency.
3.6 Flow structures
The simulations produce a considerable amount of graphical data and the reader is recommended the individual papers for details. The experimental observations are by necessity not so detailed but we show here surface streamlines obtained by dye injections at the wall. The reader is recommended the individual papers for comparisons.
C. Right view D. Down stream view (c.s. III)
Figure 10: Streamlines close to the surface at the elbow and outlet diffuser, obtained by dye injection.
3.7 Comparison with the R-case
The velocity contours at section II for the T- and the R-cases are shown in figures 11a and 11b, respectively. It is observed that the axial flow distribution is drastically changed between the two cases. Also, the secondary flow is reduced and it may be inferred that the vortex rope from the runner cone is shifted to the right. This seems to be well captured by many simulations illustrated in figures 12 a) and b).
Figure 11a: Mean axial flow and secondary flow in cross section II. T-case. View from downstream position.
−5000 0 500
100 200 300
1.1
1.2
0.8 1
1.2 0.7
0.9
0.9 1
1.3
1.1 0.6
1
y [ m ]
z [ m ]
Mean axial flow R−II
Figure 11b: Mean axial flow and secondary flow in cross section II. R-case.
−5000 0 500
100 200 300
0.80.9 1
0.6
1.3
0.9
1.4
0.8 1.3
1.2
0.567
y [ m ]
z [ m ]
Mean axial flow T−II
Figure 12: Distribution of axial velocity and vortex rope for a) T-case and b) R-case (From Cervantes & Engström)
4.DISCUSSION
4.1 Scatter in engineering quantities (Cp and ζ)
In the results collected, it is noticed that the two key engineering quantities, Cp and ζ, are subject to considerable scatter among the contributions. Part of the scatter is due to the post- processing of data, but other factors also contribute, as will be discussed here.
From the figures of the radial pressure distribution at section Ia (Figure 3) the reason for the large values of Cp,wall, and also its large scatter, is explained by the observation that the computed radial pressure distributions generally fall off sharply near the outer wall, whereas the experimental distribution show a sharp rise in this region, followed by a small decrease as the wall is approached. The computed wall pressure levels at CS Ia are therefore much lower than the average pressure over the same cross-section. Using the average pressure over the inlet cross-section therefore gives a more representative (and lower) value of Cp. (Cp,wall is in the range 1.14 -1.66 and Cp,average in the range 0.89-0.99).
An explanation for the scatter in the radial pressure distribution at CS Ia may be that the grid in this region is not fine enough to resolve the rapid evolution of the pressure and that it does not represent the surface geometry accurately enough. From the (inviscid) equation for the radial pressure,
r u u z u u r u r p
1 r
r r ax 2
∂
− ∂
∂
− ∂
∂ =
∂ ρ
θ
it is noticed that a large contribution to the radial pressure gradient comes from the second term even in regions where the streamwise gradient is moderate because of the magnitude of uax. A finer resolution of this region may result in a 10% reduction of the Cp,wall- value as demonstrated by Jonzén et al.
The scatter in the loss coefficient may be due to at least two reasons. In the expression for ζ, (9), the last term is close to unity, and the second is small (the area ratio is small) which means that the evaluation of ζ is ill-conditioned despite the accuracy in Cp'. This indicates that the use of ζ as a key parameter to evaluate gains in efficiency from e.g. a geometry optimisation may be risky unless a reconditioning of the calculations can be done. To validate such a gain experimentally, may be even more difficult since not all of the α-values are available experimentally. From the experimental results it has been deduced that ζ = 0.09
(+0.06/-0.07) which illustrates the difficulty encountered in this evaluation.
A second source of uncertainty in ζ emanates from the use of wall-functions for the near-wall calculations. Since it is expected that most flow losses occur in this region, and in fact will be reflected in the pressure results, a more careful evaluation based on the energetics associated with the wall functions could be recommended as a separate method to determine ζ. A further factor adding to the losses is also the periodic character of the flow, most notable at the impeller.
4.2 Influence of changed experimental conditions
During the long experimental period the turbine testing facility experienced a breakdown which damaged parts of the model. All measurements at the inlet cross section CS Ia were made before the breakdown, and all measurements at CS II and CS III were made after the breakdown. At the end of the measurement program the measurements at CS Ia were repeated again. Then it was noted a difference between the measurements and the previous measurements, particularly for the tangential velocity component, in spite of the fact that the settings of the test parameters of the rig were the same. This issue is discussed by Andersson (2003 b) (see appendix A). The previously measured data, called T(r) and R(r), for test case T and R, respectively, were used as inlet boundary conditions in both the first and the second workshop, since it was not realised until later that there was a difference.
The new inlet boundary data are called T(n) and R(n). In order to see if this difference in inlet boundary conditions had an influence on the engineering parameters and the flow field, some computations with the new boundary conditions were performed. Results indicated that the change in e.g. the pressure recovery factors Cp,wall and Cp,average were about 0.02, thus smaller than the difference between different computations with the same inlet boundary conditions and also smaller than the difference between experiment and computations. Thus, our conclusion is that the difference in results between experiments and computations is not caused by the small changes in inlet boundary conditions due to the breakdown of the rig. For further computations, however, we recommend the use of inlet data T(n) and R(n), since together with the data from CS II and III they then constitute a consistent set of data, all taken after the rig breakdown.
4.3 Simulation protocol
From the first Turbine-99 workshop it was concluded that simulations with too many arbitrary conditions give results which conceals attempts to assess the qualities of the flow models.
Therefore, as much common data as possible was prescribed to the second workshop.
Despite this, the treatment of data still varies among the participants and leads to scatter in the simulations. In order to be able to repeat an individual calculation, the idea was therefore raised to attach to the simulations a protocol where the details of the calculations were listed.
The idea, proposed by Page & Giroux, has resulted in a protocol of which a sample is attached in Appendix C4.
5.CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK
The most important results and suggestions of the workshop are summarised below.
• The 700k computational grid suggested by the organisers turns out to be too coarse, particularly near the inlet section, where it has a large effect on computed pressure recovery Cp,wall . This is caused by the fact that the pressure gradients in both the axial and radial directions are large and must be resolved properly.
• The uncertainty in the experimentally determined energy-loss factor is large because it is an ill-conditioned quantity, to a large extent determined by Cp.
• It was found that the y+ criterion for wall functions was violated also in other regions.
• The importance of complete and well-defined inlet boundary conditions is highlighted in many of the workshop contributions.
• The pressure recovery coefficient Cp,average , based on the average pressure over the inlet cross-section, is a suitable assessment parameter, which for Case T is calculated with a scatter of about + 5%. The difference between computed and experimentally determined Cp,average, is statistically significant.
• Computations of Case T by different groups but with the same mesh, inlet- and outlet boundary conditions, and turbulence model, generally give very similar results. Thus, the “Quality” in the concept of “Quality and Trust”, is not too far away.
• Because of the abovementioned weaknesses, it has, so far, not been possible to draw conclusions about the influence of turbulence model on the solution.
Suggestions for further computational and experimental work are given below:
• For further computational work, as a first step, a much finer grid must be constructed, particularly near the inlet. This is necessary also when using wall functions.
• As step 2, it is recommended that the wall functions should be replaced by suitable near-wall models.
• Since more than 80 % of the pressure recovery takes place in the first 10 % or so of the draft tube length (the draft tube cone), more detailed (axial and radial) pressure and velocity measurements are required.
• Also, complete 3-component velocity measurements in some cross sections are highly desirable.
These suggestions are directed towards increasing the quality of the computed solutions and increasing the accuracy of the experimentally determined engineering parameters, thus increasing the value and usefulness of the draft tube test case.
6. REFERENCES
[1] Gebart, B.R., Gustavsson, L.H. and Karlsson, R.I. (2000), Proceedings of Turbine-99 – Workshop on draft tube flow in Porjus, Sweden, 20-23 June 1999, Technical report 2000:11, Luleå University of Technology, Luleå, Sweden.
[2] Andersson, U. and Karlsson, R., "Quality aspects of the Turbine-99 experiments", in Proceedings of Turbine-99 – Workshop on draft tube flow in Porjus, Sweden, 20-23 June 1999.
[3] Andersson, U. and Dahlbäck, N.: "Experimental evaluation of draft tube flow – a test case for CFD simulations", in Proceedings of XIX IAHR Symposium, Section on Hydraulic Machinery and Cavitation, Singapore, 9-11 September 1998.
[4] Casey, M.V., "ERCOFTAC Best Practice Guidelines for Industrial CFD". ERCOFTAC 2000.
ACKNOWLEDGEMENTS
The organizers are indepted to Prof. Patel, IIHR-Hydroscience and Engineering Research, for suggesting some of the evaluations of the simulation data and also for giving opportunity for Fredrik Engström to spend time at IIHR.
The Swedish research agency ELFORSK has supported the workshop through its research program on Turbine Technology.
Appendix A Experimental and simulation results Experiments
Andersson U (Vattenfall Utveckling AB, Sweden): Test case T – some new results and updates since workshop I.
Simulations
Bélanger A. (EXA Corporation, USA): Simulation of the ERCOFTAC draft tube using PowerFlow.
Cervantes M.J. and Engström T.F. (Luleå University of Technology, Sweden): Influence of boundary conditions using factorial design.
Grotjans H. (AEA Technology GmbH, Germany): Simulation of draft tube flow with CFX.
Hanjalic K. (Delft University of Technology, The Netherlands): Turbulence modelling of complex flows; some recent developments.
Hutton A.G. (DERA) and Casey M.V. (Sultzer Innotec): Quality and trust in industrial CFD-a European initiative. (Presented by R.I. Karlsson)
Jonzén S., Hemström B. and Andersson U. (Vattenfall Utveckling AB, Sweden): Turbine 99 – Accuracy in CFD simulations on draft tube flow.
Kurosawa S., Nagafuji T., Biswas D. (Toshiba, Nagoya U. and Toshiba, Japan): Turbulent flow simulations in the draft tube of a Kaplan turbine.
Lai, Y.G. and Patel, V.C. (IOWA Institute of Hydraulic Research, USA): Effect of boundary conditions on simulation of flow in the T99 draft tube.
Nilsson H. and Davidson L. (Chalmers Institute of Technology, Sweden): A numerical
investigation of the flow in the wicket gate and runner of the Hölleforsen (Turbine 99) Kaplan turbine model.
Page M. and Giroux A-M. (IREQ- Hydro-Quebec, Canada): Turbulent flow computations in Turbine 99 draft tube with CFX-TASCflow, FIDAP and FINE/Turbo.
Shimmei K., Ishii T. And Niikura K. (Hitachi, Japan): Numerical simulations of flow in Kaplan draft tube Turbine 99 ERCOFTAC workshop on draft tube flows.
Skotak A. (CKD Blansko Engineering a.s., Czech Republic): Simulation of the vortex flow in the sharp heel draft tube.
Skåre P.E. and Dalhaug O.G. (SINTEF Energy Research AS and Norwegian University of Science and Technology, Norway): CFD Calculations of the flow in Kaplan draft tube.
Appendix B Background data
Turbine-99 - Workshop 2
Task and boundary conditions
The task
The participants are asked to study at least cases 1 and 2:
Cases
1. Simulation of Operational mode T (see below) with the following specifications:
Grid – the distributed grid of Dr. Yong Lai, IIHR, with about 700k cells should be used.
Turbulence model – the standard k-epsilon model with wall functions should be used.
Inlet boundary conditions – Use velocity data from profile Ia(1) only.
In addition to the experimental data, use a. Mean radial velocity defined below b. w′2 =v′2
c. a dissipation length scale of 0.1m d. u′w′=v′w′=u′v′
This is a calibration case to resolve numerical issues.
2. Simulation of Operational mode R (see below) with the following specifications:
Grid – the distributed grid of Dr. Yong Lai, IIHR, with about 700k cells should be used.
Turbulence model – free choice.
Inlet boundary conditions – Use velocity data from profile Ia(1) only.
In addition to the experimental data, use a. Mean radial velocity defined below b. w′2 =v′2
c. a dissipation length scale of 0.1m d. u′w′=v′w′=u′v′
This is the main case for the investigation of turbulence models.
3. There will be additional experimental data available such as angular resolved velocity data. Also at the workshop, new visualizations will be presented. It is therefore encouraged that simulations are done with alternative methods (LES, Unsteady-
RANS, ...). This case also allows for the use of different grids and modifications to the grid above, such as refinement in the near-wall region. The simulations should be at the right leg of the propeller curve.
This is the 'free' case.
Radial velocity for Case 1 and 2.
The radial velocity at the inlet is not known from experiments. It seems useful to assign a nonzero radial velocity distribution, in order to keep the flow attached. Therefore the following radial velocity should be used at the inlet for cases 1 and 2:
wall cone
cone cone
wall cone wall cone
axial radial
R r R R
R r R U U
≤
≤
− − + −
=
=
), (
where ,
tan θ θ θ
θ
θ
whereθcone =−12.8 and θwall =2.8. θ is the flow angle in a vertical plane and is zero at the z-axis. Uaxial is the measured axial velocity; see below.
Operational mode
Data are supplied for two operational modes, T and R, both conducted at 60 % load, which is close to the best efficiency for the system, and at the same test head (H = 4.5 m).
The first mode is on-cam i.e. the top-point (T) on the propeller curve (single runner blade angle curve). The second mode is off-cam i.e. the right-leg (R) on the propeller curve, see Figure 1. The exact settings of the runner speed (N) and the flow (Q) are shown in Table 1.
Figure 1. Sketch of the propeller curve and location of the test modes.
Table 1. The settings for the two modes
H=4.5 m N Q Unit runner speed (DN/√H) Unit flow (Q/D2√H)
T(r) 595 rpm 0.522 m3/s 140 1.00
R(r) 595 rpm 0.542 m3/s 140 1.04
The experiments where conducted at approximately 15 °C.
Geometric specification
LDV-measurementsFigure 2. Side and top view of the inlet cone of the test draft tube.
The measurements are done at z=0, (i.e. 127 mm below the runner hub centre) and at α1=-10° for Ia(1) / α2=-180° for Ia(2). The coordinate system and the exact geometry are defined by the CAD-file (an overview of the design is found in the appendix). The location of a single measurement is specified by the radius, r = x2+ y2 .
The two measured mean velocityƒ1 components are:
U: the axial velocity (in the negative z-direction; cf. Figure 2, side view), V: the tangential velocity (in the negative α-direction; cf. Figure 2, top view).
(A positive tangential velocity co-rotates with the runner.)
Corresponding to these mean values, RMS-valuesƒ2 and the cross correlation between the two components have been determined.
u’: the RMS(root mean square) valueƒ3 of U v’: the RMS valueƒ3 of V
uv’: the cross correlationƒ3 of U and V
ƒ1The mean velocity (X) is defined as
∑ ∑
=
i i
xi
X τ
τ , where xi is an individual sample ant τi is the
corresponding weight constant. For these data τi=1.
ƒ2The RMS-values (x’)is defined as 2
2
' x X
x
i i
i −
=
∑ ∑
τ
τ , see above.
ƒ3Note that these values include the periodic behaviour of the components and do not only relate to the turbulence intensity.
Pressure measurements
Figure 3. Upstream view of the pressure tap locations at the outlet of the test draft tube.
Together with the geometry downstream the draft tube (see appendix, Figure 3) the wall pressure at the outlet is supplied to help the setting of a suitable outlet condition in the calculations.
The wall pressure measurements are located at IVa and IVb (see appendix). The approximate locations of the pressure taps along the circumference of the cross sections are shown in Figure 3. The exact coordinates (in mm) in the data tables are given in the local coordinate system, [yl zl], defined in the same figure.
y y
z z
1
1 4212
=
= − +
.
The mean value and the standard deviation of the measurements are given.
Pw mean value of the wall pressure
pw’ standard deviationƒ of the wall pressure
ƒNote that this value includes the periodic behaviour of the component and the cross correlation with the reference point.
Surface roughness
Although the surface roughness varies in the geometry, it is appropriate to use an equivalent sand-roughness of 10µm everywhere.
err_X X
X
s C err_X
meas real
x x
±
=
=
Experimental data
The measured series are named according to the following nomenclature
where ‘Measured quantity’ and ‘Location of measurements’ are specified under the section
‘Geometric specification’ and ‘Operational mode’ under the same section.
Error margins (err) are supplied, with the measured value (Xmeas) and the specific location, to help the reader evaluate the quality of the data. err is defined as
with sx as the standard deviation for independent measurements of Xmeas, Cx as a constant depending on the number of independent measurements and Xreal is the real value that is found within the error margin with 95% certainty.
See the full data report for details on the measurements and analysis of the results. The discussion of error margins and the interpretation of RMS-values might also be of interest.
Boundary layers (calculated)
The measurements do not resolve the boundary layers, so to ensure that the same boundary conditions are used at the entire cross-section, especially between the runner hub and the last measurement point some additional points are given in these regions.
These points are marked calc in the data tables and should be used in Case1 and 2.
Construction of the boundary layers
The constructed boundary layers consist of two parts:
• logarithmic region
• wake region
The wake region is constructed to give a smooth connection between the logarithmic region and the measurement point closest to the wall (and should not be confused with wake functions used in studies of boundary layers).
The logarithmic region starts close to the wall ( ν yu*
> 8) and is described by:
2 . 5 ln
44 .
2 *
*
+
=
ν yu u
ul
,
with u as the velocity component, l y as the distance to the wall, u as the friction velocity * and ν as the kinematic viscosity.
Measured quantity
Location of measurements
Operational mode
At the chamber wall:
The friction velocity u has to be 0.207 m/s for case 1(T) and 0.206 m/s for case 2(R), if one * assumes that the last measurement point um
( )
y2 (with u as the measured total velocity at m y 2 the actual location of the measurement point closest to the wall) lies at the logarithmicboundary layer. This corresponds to ν yu*
= 116 for case 1(T) and 115 m/s for case 2(R).
To calculate the profile, for the individual velocity components (axial and tangential), through the boundary layer, the angle between the components is assumed to be constant from the chamber wall to y . 2
At the runner hub:
The distance between the runner hub and the closest measured point is larger than the corresponding distance at the wall and there is also an indication of a small leakage between the runner blade and the hub, therefore a different approach in the determination of the friction velocity is used.
The friction velocity, u , is determined as *
( )
25 y2
Kum and K is a constant ( = 1.4 at the hub;
the corresponding constant at the chamber wall would be 1.49).
The wake region is constructed to give a smooth connection between the measured values and the logarithmic region. For simplicity this region has been chosen as:
0 1 2 2 3
3y a y a y a
a
uw = + + + ,
with u as the velocity component and w y as the distance to the wall. The coefficients a are i given by the relation:
= ′
′
=
= ′
′
=
) ( ) (
) ( ) (
) ( ) (
) ( ) (
2 2
2 2
1 1
1 1
y u y u
y u y u
y u y u
y u y u
m w
m w
l w
l w
,
with y as the connection point between 1 u and w u chosen as l ν yu*
= 200 for the boundary layer at the hub and 100 for the chamber.
Some of these assumptions are quite arbitrary so the participants are encouraged to make their own assumptions for Case 3.
Operational mode T Velocity data
Section Ia(1) X Ia(1) T(r)
R [mm]
U [m/s]
err U [100⋅⋅⋅⋅
m/s]
V [m/s]
err V [100⋅⋅⋅⋅
m/s]
u' [m/s]
err u' [100⋅⋅⋅⋅
m/s]
v' [m/s]
err v' [100⋅⋅⋅⋅
m/s]
uv' [m2/s2]
err uv' [100⋅⋅⋅⋅m2 /s2]
98,1 -0.04 0.1 5.98 0.1 0.05 0.1 0.06 0.1 98.14 2.08 calc 2.31 calc
99.14 3.69 calc -0.28 calc 100.14 3.98 calc -0.72 calc 101.14 3.99 calc -0.55 calc 102.14 3.84 calc -0.14 calc 103.14 3.66 calc 0.20 calc
103,5 3.61 20.0 0.24 20.0 0.39 20.0 0.44 20.0 106,3 3.39 20.0 0.29 20.0 0.47 20.0 0.47 20.0 109,0 3.32 20.0 0.35 20.0 0.45 20.0 0.51 20.0
115,8 3.18 5.0 0.34 7.5 0.48 6.0 0.46 3.5 -0.06 0.4 122,6 3.18 5.0 0.28 7.5 0.41 6.0 0.41 3.5 -0.05 0.4 129,4 3.22 5.0 0.25 7.5 0.33 6.0 0.34 3.5 -0.03 0.4 136,2 3.27 2.5 0.28 5.0 0.28 2.0 0.32 1.5 -0.02 0.2 143,1 3.32 2.5 0.32 5.0 0.26 2.0 0.31 1.5 -0.02 0.2 149,8 3.36 2.5 0.39 5.0 0.26 2.0 0.33 1.5 -0.03 0.2 156,7 3.41 2.5 0.45 5.0 0.26 2.0 0.33 1.5 -0.03 0.2 163,4 3.47 2.5 0.52 5.0 0.26 2.0 0.35 1.5 -0.04 0.2 170,3 3.53 2.0 0.59 3.5 0.26 0.7 0.36 1.0 -0.04 0.2 177,0 3.60 2.0 0.66 3.5 0.26 0.7 0.39 1.0 -0.04 0.2 183,9 3.64 2.0 0.74 3.5 0.27 0.7 0.42 1.0 -0.05 0.2 190,6 3.68 2.0 0.88 3.5 0.32 0.7 0.56 1.0 -0.09 0.2 197,5 3.73 3.0 1.04 6.0 0.36 0.8 0.72 3.0 -0.13 0.7 204,2 3.81 3.0 1.10 6.0 0.34 0.8 0.74 3.0 -0.09 0.7 211,1 3.83 3.0 1.06 6.0 0.30 0.8 0.58 3.0 -0.03 0.7 217,8 3.74 3.0 1.08 6.0 0.30 0.8 0.51 3.0 -0.02 0.7 225,0 3.64 1.5 1.32 4.5 0.42 0.8 0.67 2.0 0.01 0.1 229,1 3.62 1.5 1.40 4.5 0.48 0.8 0.76 2.0
231,8 3.62 1.5 1.38 4.5 0.49 0.8 0.75 2.0 0.04 0.1 234,5 3.50 1.5 1.28 4.5 0.47 0.8 0.64 2.0 0.03 0.1 235,9 3.26 1.5 1.18 4.5 0.51 0.8 0.66 2.0 0.02 0.1 236.02 3.15 calc 1.14 calc
236.22 2.86 calc 1.03 calc 236.42 2.00 calc 0.72 calc 236.46 0.00 wall 0.00 wall
Pressure data
Section IV X IV T(r)
Section Position (Fig. 2)
yl [mm] zl
[mm] Pw [mBar]
err Pw [mBar]
pw'
[mBar] err pw' [mBar]
b b1 -250 1063 -1.604 0.30 1.63 0.10
b b2 0 1063 0.000 0.30 1.56 0.10
b b3 250 1063 -0.039 0.30 1.62 0.10
b l1 500 925 -0.711 0.30 1.92 0.10
b l2 500 660 -0.693 0.30 1.85 0.10
b l3 500 395 -1.210 0.30
b l4 500 130 -0.516 0.30 1.74 0.10
b r1 -500 130 -2.309 0.30 1.77 0.10
b r2 -500 395 -1.807 0.30 1.66 0.10
b r3 -500 660 -1.208 0.30 1.68 0.10
b r4 -500 925 -1.708 0.30 1.71 0.10
a l1 500 925 -0.330 0.30 1.76 0.10
a l2 500 660 0.085 0.30 1.78 0.10
a l3 500 395 -0.800 0.30 1.68 0.10
a l4 500 130 -2.489 0.30 1.62 0.10
a r1 -500 130 -2.986 0.30 1.89 0.10
a r2 -500 395 -2.174 0.30 1.83 0.10
a r3 -500 660 -1.829 0.30 1.66 0.10
a r4 -500 925 -1.726 0.30 1.60 0.10
Plots of velocity data from section Ia(1), operational mode T.
Axial and tangential velocity
-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
95.0 145.0 195.0 245.0
r [mm]
velocity [m/s]
U Ia(1) T(r) U Ia(1) T(r) calc V Ia(1) T(r) V Ia(1) T(r) calc
RMS-values
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
90.0 140.0 190.0 240.0
r [mm]
RMS-value [m/s]
u' Ia(1) T(r) v' Ia(1) T(r)
Operational mode R Velocity data
Section Ia(1) X Ia(1) R(r)
r [mm]
U [m/s]
err U [100⋅⋅⋅⋅
m/s]
V [m/s]
err V [100⋅⋅⋅⋅
m/s]
u' [m/s]
err u' [100⋅⋅⋅⋅
m/s]
v' [m/s]
err v' [100⋅⋅⋅⋅
m/s]
uv' [m2/s2]
err uv' [100⋅⋅⋅⋅m2 /s2]
98.1 -0.05 0.1 6.00 0.1 0.06 0.1 0.07 0.1 98.14 2.12 calc 1.92 calc
99.14 3.78 calc -0.96 calc 100.14 4.09 calc -1.45 calc 101.14 4.10 calc -1.25 calc 102.14 3.95 calc -0.76 calc 103.14 3.75 calc -0.34 calc
103.5 3.69 20.0 -0.29 20.0 0.04 20.0 0.60 20.0 106.3 3.46 20.0 -0.20 20.0 0.64 20.0 0.61 20.0 109.0 3.46 20.0 -0.17 20.0 0.46 20.0 0.60 20.0
115.9 3.28 5.0 -0.17 7.5 0.50 6.0 0.58 3.5 -0.11 0.4 122.7 3.36 5.0 -0.30 7.5 0.39 6.0 0.46 3.5 -0.07 0.4 129.5 3.41 5.0 -0.30 7.5 0.30 6.0 0.37 3.5 -0.04 0.4 136.3 3.43 2.5 -0.25 5.0 0.27 2.0 0.35 1.5 -0.04 0.2 143.2 3.46 2.5 -0.19 5.0 0.27 2.0 0.35 1.5 -0.04 0.2 149.9 3.49 2.5 -0.11 5.0 0.25 2.0 0.33 1.5 -0.04 0.2 156.9 3.55 2.5 -0.03 5.0 0.26 2.0 0.32 1.5 -0.03 0.2 163.7 3.60 2.5 0.08 5.0 0.26 2.0 0.33 1.5 -0.04 0.2 170.5 3.64 2.0 0.16 3.5 0.26 0.7 0.34 1.0 -0.04 0.2 177.2 3.70 2.0 0.24 3.5 0.26 0.7 0.37 1.0 -0.05 0.2 184.0 3.75 2.0 0.34 3.5 0.28 0.7 0.40 1.0 -0.06 0.2 190.8 3.78 2.0 0.52 3.5 0.33 0.7 0.56 1.0 -0.10 0.2 197.7 3.85 3.0 0.72 6.0 0.35 0.8 0.76 3.0 -0.13 0.7 204.4 3.89 3.0 0.77 6.0 0.33 0.8 0.74 3.0 -0.10 0.7 211.3 3.88 3.0 0.76 6.0 0.31 0.8 0.58 3.0 -0.06 0.7 218.0 3.81 3.0 0.78 6.0 0.31 0.8 0.51 3.0 -0.04 0.7 225.0 3.84 1.5 1.15 4.5 0.44 0.8 0.80 2.0 0.04 0.1 229.1 3.90 1.5 1.23 4.5 0.49 0.8 0.85 2.0 0.10 0.1 231.8 3.87 1.5 1.15 4.5 0.50 0.8 0.78 2.0 0.08 0.1 234.5 3.67 1.5 1.04 4.5 0.46 0.8 0.68 2.0 0.04 0.1 235.9 3.33 1.5 0.93 4.5 0.46 0.8 0.64 2.0 0.01 0.1 236.02 3.22 calc 0.90 calc
236.22 2.92 calc 0.81 calc 236.42 2.04 calc 0.57 calc 236.46 0.00 wall 0.00 wall
Pressure data
Section IV X IV R(r)
Section Position (Fig. 2)
yl [mm] zl
[mm] Pw [mBar]
err Pw [mBar]
pw'
[mBar] err pw' [mBar]
b b1 -250 1063 -0.101 0.30
b b2 0 1063 0.000 0.30
b b3 250 1063
b l1 500 925 -0.234 0.30
b l2 500 660 -0.158 0.30
b l3 500 395 -0.379 0.30
b l4 500 130
b r1 -500 130 -0.757 0.30
b r2 -500 395 0.041 0.30
b r3 -500 660 -0.190 0.30
b r4 -500 925 -0.240 0.30
a l1 500 925
a l2 500 660
a l3 500 395 -1.367 0.30 2.63 0.10
a l4 500 130 -2.473 0.30 2.58 0.10
a r1 -500 130 -0.702 0.30 2.62 0.10
a r2 -500 395 -0.250 0.30 2.53 0.10
a r3 -500 660 -0.519 0.30 2.64 0.10
a r4 -500 925 -0.350 0.30 2.63 0.10
Plots of some velocity data from section Ia(1), operational mode R.
Axial and tangential velocity
-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
95.0 145.0 195.0 245.0
r [mm]
velocity [m/s]
U Ia(1) R(r) U Ia(1) R(r) calc V Ia(1) R(r) V Ia(1) R(r) calc
RMS-values
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
95.0 145.0 195.0 245.0
r [mm]
RMS-value
u' Ia(1) R(r) v' Ia(1) R(r)
