Draft tube

Application Challenge 6-07 © 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 4-04) Curved passage flow (accelerating) (UFR 4-05) and Swirling diffuser flow (UFR 4-06). Unfortunately UFR 4-04 is missing at this time and no references can be made to this UFR. UFR 4-06 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 3-03) and 3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation (UFR 3-08). Both gives valuable information on turbulence models and separation.

Table 1. A summary of UFR:s related to this AC.

Underlying Flow Regimes
Nr	Name	Status	Importance	BPA
3-03	2D Boundary layers with pressure gradients	No D33	Low	Low
3-08	3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation	Accepted	Medium	Low
4-04	Flow in a curved rectangular duct - non rotating	Missing	Medium	-
4-05	Curved passage flow (accelerating)	Accepted	Medium	High
4-06	Swirling diffuser flow	Accepted	High	High

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 ill-conditioned, 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 4-06 points out that the radial pressure distribution in a swirling flow is non-uniform 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 15-20 nodes should be used to resolve vortices or boundary layers (e.g. UFR 1-02) a starting guess would be that around 60-80 nodes should be used in the radial direction at the inlet. If symmetric (and non-periodic) 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 4-06 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 k-ε is insufficient for modelling adverse pressure gradients, separation and swirling flow. According to Menter (2003) the k-ε model should not be used for flows with adverse pressure gradients and pressure-induced separation. More advanced models like the Spalart-Almaras or the SST model will provide more realistic answers. For flows with a strong swirl component (draft tubes etc.), models with curvature correction, non-linear stress-strain models, or full Reynolds stress models should be used.

The conclusion from the D30 and UFR 4-06 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 4-06 are without separation. However, several workshop participants reported important differences in specific details of the flow and according to UFR 3-08 the non linear k-ε 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 v2-f models for this type of flow.

UFR 3-03 states that it is known from other studies that all RANS turbulence models seem to have significant problems to properly predict re-attachment of the flow and flow-recovery 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 near-wall 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 3-component 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 PC-clusters, grids with 3-4 million cells are readily handled.

References

Durbin, P. A. (1995) Separated flow computations with the k-epsilon v2-model.AIAA J, vol 33 (4), pp. 659-664.

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 18-20, 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 Turbine-99 - Workshop 2. The second ERCOFTAC Workshop on Draft Tube Flow. Älvkarleby, Sweden, June 18-20 2001. Available on the web, http://www.sirius.luth.se/strl/Turbine-99/index.htm

Menter F. R. (2003) Turbulence Modelling for Turbomachinery, QNET-CFD Network Newsletter, Volume 2, No. 3

Contributors: Rolf Karlsson - Vattenfall Utveckling AB