AC 607 Best Practice Advice
Contents
Draft tube
Application Challenge 607 © copyright ERCOFTAC 2004
Best Practice Advice
Best Practice Advice for the AC
Key Fluid Physics
The draft tube is basically a curved diffuser, which features adverse pressure gradients, flow curvature and the possibility for flow separation. The draft tube is located after a runner of a hydro turbine (for the D30 a Kaplan turbine) causing swirling periodic inlet conditions, which leads to an asymmetric flow pattern after the bend.
The main Design and Assessment Parameters (DOAPs) for this AC are the pressure recovery (Cp) and the loss coefficient (ζ), which describes the performance of the draft tube. Additional DOAPs are used to evaluate the flux of kinetic energy and angular momentum at different cross sections of the draft tube.
The Underlying Flow Regimes (UFRs) related to the draft tube and confined flow are ‘Flow in a curved rectangular duct  non rotating’ (UFR 404) ‘Curved passage flow (accelerating)’ (UFR 405) and ‘Swirling diffuser flow’ (UFR 406). Unfortunately UFR 404 was missing at the time of writing and no references were made to this UFR. UFR 406 is the most significant UFR, but as for the D30 no separation has been observed.
Important UFRs related to the behavior of boundary layers relevant for the AC are ‘2D Boundary layers with pressure gradients’ (UFR 303) and ‘3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation’ (UFR 308). Both give valuable information on turbulence models and separation.
Table 1. A summary of UFRs related to this AC.
Underlying Flow Regimes  
Nr 
Name 
Status 
Importance 
BPA 
303 
2D Boundary layers with pressure gradients 



308 
3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation 



404 
Flow in a curved rectangular duct  non rotating 



405 
Curved passage flow (accelerating) 



406 
Swirling diffuser flow 



Importance: The relevance of the UFR for the specific AC.
BPA:The number of specific BPA:s given (important for the AC).
Application Uncertainties
The main application uncertainty for the AC is missing or incomplete boundary conditions. For the draft tube described in the D30, the axial and tangential velocity component are well documented at the inlet, but it has been shown that different assumptions on the third radial velocity component has a gross impact on the resulting flow field. More comments on the boundary conditions can be found in the next section.
The evaluation of ζ and Cp is illconditioned, so great care has to be taken in the calculation of these values to get comparable results from time to time. This problem is especially valid for the draft tube in D30 due to the high area ratio (outlet/inlet).
After a recomputation of the Cp the variation between different calculations of the same test case resulted in a scatter of about ± 5 %. Flow patterns are generally uniformly determined but show large deviations from the experimental results. 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.
One uncertainty that should be mentioned is that draft tubes are designed to operate at the verge of separation for optimal performance. The ability to predict separation is one crucial factor when evaluating new designs of draft tubes.
Computational Domain and Boundary Conditions
Draft tube geometry can be fairly complicated. There can also be additional modelling complications, as for the geometry of the D30 draft tube, which contains two singular points that are caused by the intersection between three different surfaces. These singular points results in small angles for all types of grids and in skew cells if hexahedral cells are used at the wall.
An extension after the draft tube is recommended to avoid back flow at the outlet boundary.
For the D30 draft tube it was chosen to include the runner cone to avoid starting the calculation with a more undefined vortex rope in the centre of the inlet section.
It is extremely important to specify all relevant boundary conditions, particularly the inlet boundary conditions. For the first workshop, when only the axial and tangential velocities were specified, the different calculations resulted in five groups with different secondary flow patterns after the bend.
When sufficient experimental data is not available, reasonable assumptions and sensitivity tests should be performed. If there are strong axial gradients in the specified mean velocities, turbulence quantities or in the resulting pressure the first few millimetres, some unreasonable assumption could be suspected.
UFR 406 points out that the radial pressure distribution in a swirling flow is nonuniform and therefore recommends that a uniform pressure outlet boundary condition should not be imposed. However, no alternative is given in the UFR.
Discretisation and Grid Resolution
A lot of thought should be employed in the grid design, e.g. to obtain a good cell distribution close to the walls.
The computational grid used in the D30 containing 700000 cells turned out to be too coarse, particularly near the inlet section, where the grid density has a large effect on computed pressure recovery (C_{p,wall}). Here, the pressure gradients in both the axial and radial directions are large and must be resolved properly.
Based on recommendations in different UFR:s that at least 1520 nodes should be used to resolve vortices or boundary layers (e.g. UFR 102) a starting guess would be that around 6080 nodes should be used in the radial direction at the inlet. If symmetric (and nonperiodic) flow is assumed at the inlet, the initial distribution in the tangential (and axial) direction only needs to be large enough to avoid stretching problems. To capture the secondary flow that evolves in the bend a refinement in the tangential direction is needed through and after the bend.
UFR 406 gives the following additional advice:
Use a higher order scheme (second order or above) for momentum equations.
If wall functions are used, ensure that the near wall grid is not refined beyond the limit of their validity based on the y^{+} values. Where possible, hexahedral elements should be used.
Physical Modelling
The general consensus when it comes to turbulence modelling is that kε is insufficient for modelling adverse pressure gradients, separation and swirling flow. According to Menter (2003) the kε model should not be used for flows with adverse pressure gradients and pressureinduced separation. More advanced models like the SpalartAlmaras or the SST model will provide more realistic answers. For flows with a strong swirl component (draft tubes etc.), models with curvature correction, nonlinear stressstrain models, or full Reynolds stress models should be used.
The conclusion from the D30 and UFR 406 is that no major affects on DOAPs can be seen from the choice of turbulence models. Both the cases in the D30 and in UFR 406 are without separation. However, several workshop participants reported important differences in specific details of the flow and according to UFR 308 the non linear kε and the Reynolds stress turbulence models provide a better prediction of the separated zone and the pressure coefficient (at separation) then the linear k ε. Durbin (1995) suggests v2f models for this type of flow.
UFR 303 states that it is known from other studies that all RANS turbulence models seem to have significant problems to properly predict reattachment of the flow and flowrecovery downstream of a separation zone. Models, which predict the correct separation onset, are especially prone to give larger separation zones and slower flow recovery than indicated by the data. Note that this does not mean that the other models are superior in that respect. It is only due to a cancellation of errors that models, which fail to predict the separation onset, have little problems in the downstream region. The user is advised to keep this deficiency in mind when judging CFD simulations of diffuser flows.
The main conclusions seems to be that other factors affect the results more than the choice of turbulence model in the draft tube as long as there is no separation, which would be considered to be a risky assumption for an unknown draft tube.
Due to the large difference in velocities close to the walls the y^{+} criterion for wall functions is often violated. Therefore it is recommended that suitable nearwall models replace the wall functions.
Recommendations for Future Work
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. Complete 3component velocity measurements in some cross sections are also highly desirable. These additions will increase the value of the experimental data bank considerably.
For further computational work, as a first step, a much finer grid must be constructed, particularly near the inlet and along the walls. Recent developments in computer capacity make this a quite feasible option. With cheap PCclusters, grids with 34 million cells are readily handled.
References
Durbin, P. A. (1995) Separated flow computations with the kepsilon v2model.AIAA J, vol 33 (4), pp. 659664.
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. Available on the web, http://www.sirius.luth.se/strl/Turbine99/index.htm (Bad link, DCE 100310).
Menter F. R. (2003) Turbulence Modelling for Turbomachinery, QNETCFD Network Newsletter, Volume 2, No. 3
© copyright ERCOFTAC 2004
Contributors: Rolf Karlsson  Vattenfall Utveckling AB