| 1. |
|
|
| 2. |
- Bergström, John, et al.
(författare)
-
Estimation of numerical accuracy for the flow field in a draft tube
- 1999
-
Ingår i: International journal of numerical methods for heat & fluid flow. - : Emerald. - 0961-5539 .- 1758-6585. ; 9:4, s. 472-486
-
Tidskriftsartikel (refereegranskat)abstract
- The potential for overall efficiency improvements of modern hydro power turbines is a few percent. A significant part of the losses occurs in the draft tube. To improve the efficiency by analysing the flow in the draft tube, it is therefore necessary to do this accurately, i.e. one must know how large the iterative and the grid errors are. This was done by comparing three different methods to estimate errors. Four grids (122,976 to 4,592 cells) and two numerical schemes (hybrid differencing and CCCT) were used in the comparison. To assess the iterative error, the convergence history and the final value of the residuals were used. The grid error estimates were based on Richardson extrapolation and least square curve fitting. Using these methods we could, apart from estimate the error, also calculate the apparent order of the numerical schemes. The effects of using double or single precision and changing the under relaxation factors were also investigated. To check the grid error the pressure recovery factor was used. The iterative error based on the pressure recovery factor was very small for all grids (of the order 10-4 percent for the CCCT scheme and 10-10percent for the hybrid scheme). The grid error was about 10 percent for the finest grid and the apparent order of the numerical schemes were 1.6 for CCCT (formally second order) and 1.4 for hybrid differencing (formally first order). The conclusion is that there are several methods available that can be used in practical simulations to estimate numerical errors and that in this particular case, the errors were too large. The methods for estimating the errors also allowed us to compute the necessary grid size for a target value of the grid error. For a target value of 1 percent, the necessary grid size for this case was computed to 2 million cells.
|
|
| 3. |
- Bergström, John, et al.
(författare)
-
Time-phase averaging for the approximate solution of the flow in a hydraulic turbine
- 1999
-
Ingår i: Proceedings of ASME/JSME FEDSM'99. - : American Society of Mechanical Engineers.
-
Konferensbidrag (refereegranskat)abstract
- The refurbishment of old hydropower installations and the continuos development of new installations has increased the interest for better design tools to improve their efficiency. Computational fluid dynamics has been used with great success to improve the design of the runner. However, extensive model testing has been necessary to improve the design of the surrounding waterways. Even after testing, some uncertainty has remained concerning the difference between the model scale and the full scale turbine system. The current trend is therefore to include as much as possible of the water conduits with a simultaneous solution of the flow in the turbine runner in an effort to reduce the need for model testing. However, if high numerical accuracy is required the number of mesh points for a complete model of the turbine system has to be at least 10^7. The mesh size together with the need for a time dependent mesh in the runner makes it unlikely that a full simulation with a rotating runner and advanced turbulence modeling will be possible within the next several years, even if the most optimistic estimate of future computer capacity are taken into account. It is therefore of great interest to find new approximations that will make a more refined analysis of the waterways external to the runner possible.In this paper we present a model for the runner that preserves any flow non-uniformity existing at the inlet of the runner in a realistic way through the runner. This has enabled a complete analysis of the interaction of the flow through the penstock, spiral casing and guide vanes with the flow in the draft tube. The mesh requirement and the computational time is considerably reduced compared to a full simulation with a sliding mesh model for the runner. The main drawback with the new model is believed to be that the blade wakes are averaged out of the problem.The model we propose is based on a time-phase averaging technique. The essence of the model is similar to the time averaging technique used by Adamczyk (Adamczyk, 1985), but with different averaging time and different mathematical notation that makes it possible to use the model in a general case, i.e. both for axial and radial machines. A phase function is central to the technique and is introduced for weighting in the averaging procedure. The phase function makes it possible to time average the flow inside a runner. It is constructed with generalised functions and a geometrical description of the suction and pressure side of a runner blade at a reference position. Exact equations for the time-phase averaged variables are derived by a formal time-phase averaging of the governing equations. Some of the terms are accounted for in an approximate way in the present simulation but it is possible to calculate better approximations with a simulation of an isolated runner in a rotating coordinate system. However, even with the crude approximations that we have used the simulation produces realistic results for the particle paths through the runner.
|
|
| 4. |
- Engström, T. Fredrik, et al.
(författare)
-
Gyroscopic design of swirling flow diffusers
- 1999
-
Ingår i: Proceedings of ASME/JSME FEDSM'99. - : American Society of Mechanical Engineers.
-
Konferensbidrag (refereegranskat)abstract
- The flow in the draft tube of a hydro power plant is often swirling when the turbine is operating outside its best efficiency point. The swirl gives rise to gyroscopic effects when the flow is forced through the bend in the draft tube. The resulting complex flow field causes losses.The idea in this paper is to investigate the possibility of using a simple model to calculate a new geometry of the draft tube that avoids distortion of the vortex core. Simulations are carried out using the CFD code CFX. A Reynolds stress model, with wall functions, is used to model turbulence.A loss factor is calculated and it was found that the new design draft tube shows approximately the same loss as a non-modified draft tube. The explanation to the somewhat surprising result is that the flow through and after the bend is dominated by the centrifugal effects from streamline curvature. It is therefore concluded that the most important loss mechanism appears to be triggered by streamline curvature.
|
|
| 5. |
- Gebart, Rikard, et al.
(författare)
-
Squeeze flow rheology in large tools
- 1999
-
Ingår i: Fifth International Conference on Flow Processes in Composite Materials. - : University of Plymouth Press. - 1870918010 ; , s. 365-372
-
Konferensbidrag (refereegranskat)
|
|
| 6. |
- Lundström, T. Staffan, et al.
(författare)
-
In-plane permeability measurements on fiber reinforcements by the multi-cavity parallel flow technique
- 1999
-
Ingår i: Polymer Composites. - : Wiley. - 0272-8397 .- 1548-0569. ; 20:1, s. 146-154
-
Tidskriftsartikel (refereegranskat)abstract
- This report discusses the advantages and drawbacks of the multi-cavity parallel flow technique for permeability measurements. An experimental series with repeated measurements on material from the same roll shows that the repeatability of the technique is very good considering the manufacturing variability of the fabric. The measured standard deviation in the repeatability study is about 10%. It is, however, shown that the permeability can vary considerably- between reinforcements of similar geometry. Furthermore, computer simulations were used to estimate the errors when highly anisotropic materials are oriented at an angle to the material principal direction in the parallel flow technique. The conclusion based on the simulations is that the length to width ratio of the cavity should be larger than the anisotropy of the reinforcement for an acceptable error.
|
|
| 7. |
|
|
| 8. |
|
|
| 9. |
|
|
| 10. |
|
|
