AC 607 Evaluation
Contents
Draft tube
Application Challenge 607 © copyright ERCOFTAC 2004
Evaluation
Comparison of CFD Results and Test data
Both workshops used (r) as BC but (n) is currently the most complete test case. It is therefore recommended that future calculations use the (n)set of data for each case for comparisons with the experiments. However, if the purpose is e.g. to validate a new code or for some other reason compare with other computations the (r)set of data is still recommended.
Thus, data presented here are all based on computations using the (r) inlet boundary condition for both the T test case and the R test case. Comparison of CFD with test data may be qualitative (e.g. scatter plots, contour plot comparison) or quantitative (statistical measures, e.g. mean bias and variance). Particular focus is given to comparisons between measured and calculated [../../help/glossary.htm DOAP]s. All data discussed here are available in the ProcW2.
Engineering Quantities and DOAP:s
The results on engineering quantities, calculated by the contributors themselves, for both the T and the R test cases, are presented in Table 4.1.
In Table 4.2. is presented the engineering quantities for all computations, evaluated in a uniform way as described in ProcW2, Appendix C1. Table 4.3 shows the major design and assessment parameters DOAPs from experiment and simulations. Figure 4.1 present the results in graphical form.</nowiki>
Discussion
A comparison between results in Tables 4.1 and 4.2 shows immediately, in some cases, large difference in computed results, depending on how the engineering parameters are estimated (how extrapolation to the wall is carried out, etc.), and the code used. This is particularly important for Cp_{r,wall} and ζ.
It is also clear that there is a large difference between computed Cp_{r,wall} and Cp_{r,average}. The reason for this latter discrepancy is the following: Radial pressure distributions, experimentally determined and computedcurves, in CSIa, were shown in Proc.T99W2, Part2, pp.5558. For the experimental profile, see also Andersson (2003b), fig.19.
An analysis of these figures clarifies the main reason for the large values of Cp_{r,wall}, and also for the large scatter in Cp_{r,wall}:
The computed radial pressure distributions generally fall of sharply near the outer wall whereas the experimental distributions exhibit a sharp rise in pressure in this region, followed by a very small decrease just at the wall. The computed wall pressures at CSIa are therefore much lower than the average pressure over the same crosssection. Cp,_{wall} is thus dominated by the wallvalue, which is not representative for the average pressure. Using the average or average pressure over the inlet crosssection therefore gives a much more representative (and lower) Cp_{r}, as shown in Table 4.2. (generally Cp_{r},_{wall} is 1.141.66, and Cp_{r,average} is 0.890.99).
The main reason for this difference in radial pressure distribution is that the grid in this region is not fine enough and that it does not represent the true surface geometry sufficiently accurate. Evidence of this can be found in Proc.T99W2, paper by Jonzén et al. (2003), Table 2, where a much finer grid than the standard grid recommended by the organizers, gave a difference in Cp_{r,wall}of 0.12, that is, a 10 % decease in Cp_{r,wall}. So, in spite of the relatively fine grid that was proposed by the organizer, it is found that this grid is still too coarse, particularly near the inlet.
For the remaining discussion we will focus on the results of Table 4.3 and Figure 4.1, which show the major design or assessment parameters taken from computations (recalculated by the organizers) and the corresponding experimental values.
It is clear that the scatter in computed Cp_{r,average} is much smaller than in Cp_{r,wall}. This fact, together with the discussion above, shows that Cp_{r,average} is a much more suitable DOAP than Cp_{r,wall}. Table 4.3 also shows that the computed values of Cp_{r,average} are lower than the experimentally determined value, the difference being larger that the estimated uncertainty. Thus, the difference is significant. The reason for this discrepancy is discussed further in section 4.2.1.
From Table 4.3 and Figure 4.1 one can also see that the computed energyloss coefficient (ζ) shows a surprisingly large scatter and also that the experimental value has a very large uncertainty, Andersson, (2003a). There are several reasons for the large scatter in (ζ): It is an illconditioned quantity since it comes out as the difference between two (almost equal) large numbers, (see eq. 9) and the uncertainty in Cp thus has a large effect on (ζ). The experimental value also has a large uncertainty, mainly for the same reason. Also, quantities which could not be measured are determined as a best estimate from the computed result. So, in spite of the effort made, it seems to be very difficult to obtain an accurate experimental determination of (ζ).
Table 4.1 Engineering quantities, calculated by the contributors. (from Proc.T99W2, part 2, p.5)
ACRONYM 
Remark  
CASE T 
Cp 










AEAT keps 
1,1300 
0,0830 
1,0180 
1,1700 
0,0690 
0,0640 
1,0760 
1,1250 
0,0460 
0,0430 

CKD keps 
1,1606 
0,1044 
0,9986 
1,1702 
0,0588 
0,0121 
1,0602 
1,1089 
0,1865 
0,0605 

HQFIDAP keps 
1,7460 
0,1050 
1,0300 
1,3150 
0,0560 
0,0270 
1,0800 
1,1470 
0,2920 
0,0870 

HQFINE keps 
1,1040 
0,1590 
1,0300 
1,0900 
0,0560 
0,0500 
1,0800 
1,1360 
0,2930 
0,1290 

HQTASC keps 
1,3940 
0,0910 
1,0300 
1,2220 
0,0560 
0,0490 
1,0800 
1,1400 
0,2920 
0,1320 

HTC keps 
1,2500 
0,1250 
1,0260 
1,4620 
0,0670 
0,0410 
1,0770 
1,2140 
0,2860 
0,1080 

NUT keps 
1,2730 
0,0690 
1,0100 
1,2520 
0,0590 
0,0190 
1,0720 
1,1240 
0,3070 
0,0800 

TEV keps 
1,2330 
0,1410 
1,0040 
1,2180 
0,0570 
0,0740 
1,0540 
1,1110 
0,3020 
0,2570 

VUAB keps 
1,2946 
0,0870 
1,0239 
1,2360 
0,0580 
0,0091 
1,0771 
1,1029 
0,3024 
0,2018 
Values are from recalculation by F. Engström. 
LTU keps 
1,2880 
0,0570 
1,0381 
1,2226 
0,0596 
0,0594 
1,0889 
1,2244 
0,1772 
0,1506 
Corrected value for Cp wall 
Iowa keps 
1,1950 

Experiment T 
1,120 
0,09 
1,040 
1,090 
0,060 
0,040 
1,110 
1,020 
0,310 
αsw III, without vertical comp.  
β III, only axial comp.  
CASE R 











CKD realizablekeps 2 
1,1608 
0,1047 
0,9980 
1,1475 
0,0299 
0,0075 
1,0327 
1,0849 
0,1034 
0,0333 

HQFIDAP keps 2 
1,7980 
0,0920 
1,0280 
1,1940 
0,0290 
0,0190 
1,0520 
1,0920 
0,1570 
0,0680 

HQFINE keps 2 
1,1200 
0,1690 
1,0270 
1,2220 
0,0280 
0,0330 
1,0510 
1,1210 
0,1570 
0,0450 

HQTASC keps 2 
1,4050 
0,0920 
1,0280 
1,2090 
0,0290 
0,0450 
1,0520 
1,1260 
0,1570 
0,0620 

HTC cubickeps 2 
0,9950 
0,2050 
1,0240 
1,4750 
0,0390 
0,0300 
1,0480 
1,2160 
0,2370 
0,0610 

HTC quadratickeps 2 
0,9510 
0,2480 
1,0240 
1,4500 
0,0390 
0,0390 
1,0480 
1,2200 
0,2370 
0,0490 

NUT keps 2 
1,0750 
0,0700 
1,0080 
1,3540 
0,0290 
0,0260 
1,0400 
1,1820 
0,1640 
0,0850 

TEV rsm 2 
1,2080 
0,1250 
1,0030 
1,2930 
0,0280 
0,0130 
1,0300 
1,1230 
0,1630 
0,0250 

VUAB keps 2 
Resimulated after workshop, no data available  
LTU keps 2 
1,3971 
0,0586 
1,0332 
1,1875 
0,0307 
0,0524 
1,0584 
1,1487 
0,0964 
0,0879 

Iowa keps 2 
1,2365 
different ε  
Iowa komega 2 
1,2273 
different ε  
VUAB keps 3 
Resimulated after workshop, no data available  
CKD rsm 3 
1,0420 
0,1230 
0,9854 
1,2531 
0,0291 
0,0074 
1,0195 
1,1332 
0,1024 
0,0009 

EXA vl 3 
1,1880 
0,1480 
1,0100 
1,2360 
0,0280 
0,0450 
1,0000 
1,0840 
0,0950 

HTC LES 3 
0,9370 
0,2170 
1,0850 
1,8000 
0,0470 
0,0900 
1,1080 
1,3700 
0,2600 
0,0700 

NUT LES 3 
1,0900 
1,0080 
1,1630 
0,0290 
1,0400 
1,1210 
0,1640 

Experiment R 
1,09 
1,040 
0,030 
1,080 
0,170 
Table 4.2. Engineering quantities, recalculated by the organizers (from Proc.T99W2, part 2, p. 17)
ACRONYM 
Remark  
CASE T 












AEAT 
1,361 
0,952 
0,150 
1,038 
1,210 
0,059 
0,036 
1,093 
1,140 
0,302 
0,087 

NUT 
1,262 
0,925 
0,043 
1,023 
1,234 
0,059 
0,010 
1,079 
1,104 
0,308 
0,227 

TEV 
1,276 
0,963 
0,050 
1,024 
1,201 
0,058 
0,025 
1,077 
1,119 
0,301 
0,131 

HTC 
1,250 
0,916 
0,172 
1,042 
1,270 
0,056 
0,009 
1,091 
1,117 
0,293 
0,205 

VUAB 
1,295 
0,917 
0,087 
1,024 
1,236 
0,058 
0,009 
1,077 
1,103 
0,302 
0,202 

CKD 
1,185 
0,892 
0,110 
1,019 
1,276 
0,059 
0,009 
1,076 
1,119 
0,305 
0,252 

HQFIDAP 
1,665 
0,921 
0,120 
1,037 
1,325 
0,056 
0,016 
1,089 
1,152 
0,292 
0,105 

HQFINE 
1,144 
0,991 
0,077 
1,037 
1,219 
0,056 
0,034 
1,088 
1,142 
0,293 
0,094 

HQTASC 
1,397 
0,956 
0,152 
1,037 
1,230 
0,056 
0,035 
1,089 
1,145 
0,292 
0,145 

Iowa 
1,195 
0,887 
0,162 
1,037 
1,347 
0,059 
0,011 
1,093 
1,151 
0,302 
0,108 

LTU 
1,537 
0,980 
0,066 
1,034 
1,144 
0,059 
0,030 
1,082 
1,106 
0,302 
0,037 

CASE T 












AEAT 
0,145 
0,520 
1,065 
0,519 
0,513 
0,511 
0,989 
0,984 
1,107 
1,277 
2,308 

NUT 
0,145 
0,518 
1,064 
0,503 
0,509 
0,511 
1,013 
1,017 
1,094 
1,257 
2,888 

TEV 
0,145 
0,520 
1,064 
0,515 
0,517 
0,518 
1,004 
1,006 
1,092 
1,251 
2,516 

HTC 
0,145 
0,520 
1,065 
0,518 
0,515 
0,512 
0,993 
0,988 
1,107 
1,292 
3,022 

VUAB 
0,145 
0,522 
1,064 
0,514 
0,516 
0,517 
1,005 
1,007 
1,092 
1,258 
2,842 

CKD 
0,145 
0,520 
1,064 
0,509 
0,510 
0,510 
1,002 
1,003 
1,089 
1,295 
3,343 

HQFIDAP 
0,145 
0,521 
1,064 
0,522 
0,522 
0,522 
1,000 
0,999 
1,102 
1,366 
3,730 

HQFINE 
0,145 
0,521 
1,064 
0,521 
0,522 
0,517 
1,001 
0,991 
1,102 
1,285 
3,235 

HQTASC 
0,145 
0,521 
1,064 
0,522 
0,516 
0,515 
0,989 
0,986 
1,102 
1,294 
2,487 

Iowa 
0,145 
0,520 
1,064 
0,509 
0,508 
0,506 
0,999 
0,994 
1,106 
1,381 
3,049 

LTU 
0,145 
0,520 
1,065 
0,516 
0,519 
0,518 
1,005 
1,003 
1,103 
1,200 
1,967 
Table 4.3. Major design and assessment parameters (DOAPs).
CASE T 



AEAT 



NUT 



TEV 



HTC 



VUAB 



CKD 



HQFIDAP 



HQFINE 



HQTASC 



Iowa 



LTU 



Experiment T 
1,12 + 0,02  0,01 
1.06 + 0,04  0,02 
0,09 + 0,06 
Figure 4.1 Major design and assessment parameters
Velocity Field
Table 4.4 shows differences in results between calculations and experiments in CS II and III. Briefly, two fields (e.g. Uvelocity), one field obtained from experiments and the other one obtained from computations, are compared on the same grid, and the standard deviation or RMS value and Mean value, Max and Minimum values are computed. By this method, we get a comparison of the whole field and also a quantitative measure of the difference between the fields (the Stdv).
Figure 4.2. Normalised axial velocity at the horizontal midplane of CS II. (Mean value of CFDcalculations T99 W2; : Max /min value from CFD simulations T99 W2; + VUAB CFD simulation; x Experiment)
In Figure 4.2 one can see that there is a rather good agreement between the different CFDcalculations for test case T, comparing the (normalised) axial velocity. The mean variation is ± 0.04 for the CFDcalculations at each point of the midplane of the calculations. However, in the worst regions the differences are as high as ± 0.15. The results from VUAB (+) is also included, to show how a single computation behaves along the profile. Compared with Experiments (x), there is a significant difference in the resulting profile, that cannot be explained by the variation between CFDcalculations or experimental uncertainties.
An illustrative way of showing the accuracy of the simulations relative to the measured veloctiy values is shown in Figure 4.3 where the difference between the simulations and the experiments are shown. The difference is defined as U_{exp}/U_{exp, average} − U_{sim}/U_{sim,average}
Figure 4.3: Difference plot of the axial velocity at cross section II. From Cervantes & Engström 
In ProcW2, 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 quantitative integral measure of the accuracy of these calculations can be defined as the standard deviation of the data integrated over the cross section. The result of such calculations is collected in Figure 4.4 and in Table 4.4.
Figure 4.4: Standard deviation of velocity difference integrated over cross sections II and III.
Table 4.4 Comparisons between computations and experiments at CS II and III
Discussion of Scatter in Design or Assessment Parameters
and ζ)
In the results collected, it is noticed that the two key engineering quantities, C_{p} and ζ, are subject to considerable scatter among the contributions. Part of the scatter is due to the postprocessing 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 in ProcW2) the reason for the large values of C_{p,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 crosssection. Using the average pressure over the inlet crosssection therefore gives a more representative (and lower) value of C_{p}. (C_{p,wall} is in the range 1.14 1.66 and C_{p,average} in the range 0.890.99).
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,
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 u_{ax}. A finer resolution of this region may result in a 10% reduction of the C_{p,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 illconditioned despite the accuracy in C_{p}'. 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 αvalues 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 wallfunctions for the nearwall 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 runner.
Conclusions and Recommendations
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 C_{p,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 energyloss factor is large because it is an illconditioned quantity, to a large extent determined by C_{p}.
• It was found that the y^{+} criterion for wall functions was violated in many regions of the flow.
• The importance of complete and welldefined inlet boundary conditions is highlighted in many of the workshop contributions.
• The pressure recovery coefficient C_{p,average }, based on the average pressure over the inlet crosssection, is a suitable assessment parameter, which for Case T is calculated with a scatter of about + 5%. The difference between computed and experimentally determined C_{p,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 nearwall 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 3component 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.
References
Bergström, J. (2000). “Modeling and Numerical Simulation of Hydro Power Flows”. Doctoral Thesis 200006, Luleå University of Technology, Department of Mechanical Engineering, Division of Fluid Mechanics.
Casey M. & Wintergerste T. (editors). (2000) ERCOFTAC Best Practice Guidelines. ERCOFTAC Special Interest Group on “Quality and Trust in Industrial CFD”.
Gebart B.R., Gustavsson L.H. & Karlsson R.I. (editors) (2000a) “Turbine 99 – Workshop on Draft Tube Flow”. Technical Report 200011, Luleå University of Technology, Department of Mechanical Engineering, Division of Fluid Mechanics. ISSN:14021536
Gebart B.R., Gustavsson L.H. & Karlsson R.I. (2000b) “Report from Turbine 99 – Workshop on Draft Tube Flow in Porjus, Sweden, 2023 June 1999”. Paper presented at the 20^{th} IAHR Symposium Hydraulic Machinery and Systems. Aug. 69, 2000, Charlotte, North Carolina, U.S.A.
Engström T.F., Gustavsson L.H. & Karlsson R.I. (2002) “Report from Turbine 99 – Workshop 2 on Draft Tube Flow”. The second ERCOFTAC Workshop on Draft Tube Flow, held in Älvkarleby, Sweden, June 1820, 2001. Paper presented at the 21^{st} IAHR Symposium Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002
Engström, T.F., Gustavsson, L.H., & Karlsson, R.I. (2003), Proceedings of Turbine99  Workshop 2. The second ERCOFTAC Workshop on Draft Tube Flow. Älvkarleby, Sweden, June 1820 2001. http://epubl.luth.se/14021536/2000/11/indexen.html.
Andersson U. (2003a) Turbine 99 – Experiments On Draft Tube Flow (Test Case R) In: Proceedings from Turbine 99 – Workshop 2, Engström et al. (editors) (2003).
Andersson U. (2003b) Test Case T – some new results and updates since Workshop I. In: Proceedings from Turbine 99 – Workshop 2, Engström et al. (editors) (2003).
Jonzén S, Hemström B, Andersson U (2003) “Turbine 99 Accuracy in CFD simulations on draft tube flow” (2003). In Proceedings from Turbune 99 – Workshop 2, Engström et al. (editors) (2003).
© copyright ERCOFTAC 2004
Contributors: Rolf Karlsson  Vattenfall Utveckling AB
