34th IAHR World Congress - Balance and Uncertainty 33rd Hydrology & Water Resources Symposium 10th Hydraulics Conference
26 June - 1 July 2011, Brisbane, Australia
3D-numerical optimisation of an asymmetric orifice in the surge tank of a high-head power plant R. Gabl1 , S. Achleitner1 , J. Neuner2 , H. Götsch2 and M. Aufleger1 1
Unit of Hydraulic Engineering University of Innsbruck Technikerstraße 13, 6020 Innsbruck AUSTRIA 2 TIWAG-Tiroler Wasserkraft AG Division Engineering Services, Eduard-Wallnoefer-Platz 2, 6010 Innsbruck AUSTRIA E-mail:
[email protected] Abstract: In this presented work, the results of 3D-numerical investigations will be utilized to improve the 1Dnumerical calculation of water hammer and surge tanks of high-head power plants. Usually, tabular values are used to quantify local head losses as a first approach. For existing high head power plants, the coefficients can be calibrated based on measurements. In a planning stage, physical laboratory tests and 3D-numerical simulations provide an alternative to assess loss quantities. In case of the presented work, a 3D simulation using ANSYS-CFX is carried out to calculate the local head loss coefficients. Furthermore, the investigated orifice is optimised for stationary and non-stationary cases. The present investigations on an asymmetric orifice, which is located in an elbow and part of a restricted entry surge tank, have shown that the local loss coefficient for the numerical simulations is higher than the simplified theoretic approach (tabular value). The findings using a 3D numerical approach are in agreement with earlier laboratory experiments. Thus, the numerical method was applied to optimise the orifice geometry with respect to the asymmetric effects of the orifice and to minimise the construction costs. Keywords: 3D-numerical analysis, asymmetric orifice, surge tank, high-head power plant
1. INTRODUCTION In order to offer a non-restricted operation for a high-head power plant, it is essential to reduce the mass oscillation of the water flow and the effects of the water hammer in the hydraulic system (Sharp & Sharp, 1996). The requirements for the dimension of the surge tank are increased for peak-load pumped storage power plants of which there are many examples in Austria. In general, the use of a surge tank is a widely applied and economic way to reduce the construction costs for the headrace power tunnel and the penstock. Orifices are used to introduce additional head loss and consequently to minimise the volume of the chambers in a surge tank. Asymmetric behaviour of the loss quantity allows increased loss during reverse flow situations (Popecu et al, 2003). The ultimate goal is the achievement of a new equilibrium state after a sudden change in the flow regime as fast as possible (Novak et al, 2005 and Jaeger, 1977). Since mass oscillation is required to be stable and nonincreasing, different criterions were developed in the past to identify and avoid unstable configurations. The Thoma criterion (Thoma, 1910) is well known to provide a critical (minimum) area for the surge chamber. As a result, there are hardly two similar constructions of surge tanks, because they are always adjusted to the specific boundary conditions. Steyrer (1999) compared different types of surge tanks which are typical for Austria. Where the general layout is the same, the types are distinguished by the way head losses are introduced at the transition between lower chamber and shaft of the surge tank. Steyrer (1999) compared (a) a symmetric orifice, (b) an asymmetric orifice and (c) a reverse flow throttle focusing on the economic value within a certain case study. A detailed assessment of specific applied losses and their optimisation was not included. The presented case study is therefore focused on an asymmetric orifice and its impact on the overall situation. It is placed in an elbow between the lower chamber of the surge tank and the shaft, which leads up to the upper chamber of the surge tank. The radius of curvature of the 90°-elbow is chosen with 7 m. The diameter of the shaft is 6.3 m and the also circular lower chamber measures 5.0 m in diameter (Figure 1). The wall thickness of the orifice is a constant 3 cm. The flow through the orifice is limited with 140 m³/s.
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2. METHODOLOGY 2.1. Basic equations As a starting point, the energy equation (Eq. (1)) between two sections is used (Bollrich, 2007 and Roberson et al, 1995). The head loss hL comprises of friction and local losses. In general, the friction coefficients are subject to calibration in the 1D-numerical software and the local head losses are input value for these calculations. Depending on the software, the values xi [-] or ZETA [s²/m5] are used, relating to the velocity head or the discharge respectively (Eq. (2)). The reliability of the water hammer calculations depends strongly on the accuracy of the local head loss coefficient. (1) (2) Commonly tabular values are applied for the local head loss coefficients. As a next step, these first assumptions are optimised in physical laboratory tests (Huber, 2010 and Wu et al, 2010). Consequently, any optimisation approach can hardly be made using tabular values. In the following 3D-numerical simulations of the orifice are introduced to assess losses and to allow optimisation of the geometry. The goal is to introduce 3D numerics as appropriate alternative to physical modelling. Benefits would be flexibility in the optimisation procedure and a reduction of cost for the optimisation process. In order to determine the loss coefficient, pressures and velocities on both ends of the orifice have to be known. Combining Eq. (1) and (2) leads to the dimensionless value xi (Eq. (3)). (3) The velocity v in Eq. (2) and (3) refers to the section after the orifice. In most cases, the change in the velocity head is zero when there are equal areas in the in- and outflow section (Wu et al, 2010). Since this is not the case in this example (A1 not equal A2), the change in velocity head is considered.
2.2. Concept of investigation 2.2.1. Modell building The aim of this work is to assess and optimise the losses of an exemplary asymmetric orifice. Therefore, the upward and downward flow through the orifice is investigated locally. The gained results serve as a basis for future integrated assessment of the complete system including shaft and upper chamber in a 3D numerical approach. The presented investigation includes a stepwise increase of model complexity and can be divided into three parts: (i) Comparison of the tabular values with 3D simulation the orifice excluding the elbow (ii) Comparison of the tabular values with 3D simulation the orifice including the elbow (iii) Variation of the geometry to optimise the behaviour of the asymmetric orifice As a first approach the geometry is approximated without the elbow section. The asymmetric orifice is joined to two aligned pipes (Figure 2). To assess the tabular values of the specific orifice, the geometry of the orifice is simplified as shown in Figure 1 (a). The quantification of the local head loss for the upward process can be approximated by a smooth contraction followed by a sudden expansion. In case of the change of a flow direction, a sudden contraction precedes a smooth expansion. The smooth expansion and contraction is divided into two parts due to varying angles of 14.25° and 43.60° for the last frustum.
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Figure 1 Orifice geometry of (a) simplified theoretical model (b) simplified numerical model and (c) complete numerical model including elbow This theoretical geometry can be reproduced with the help of 3D-numerical simulation (not part of this paper) as well as the realistic orifice (Figure 1 (b)). The 3D-numerical model (Figure 2 (b)) is realised as 12°-segment model using the rotational symmetry. Consequently, the local head loss xi covers the effects of the orifice only and can be compared with the respective theoretical tabular values. Last, the full geometry of the orifice including the effect of the elbow is realized as a halved 3D model.
2.2.2. Optimisation of geometry parameters For an efficient optimisation process it is essential to assess the sensitivity of single geometry parameters with regard to the behaviour of the orfice. Starting from an initial set, the geometry parameters are varied separately in a certain range (see Figure 2 and Table 1, those parameters that are not used will be displayed in italics). Table 1 Parameters for optimisation Variable DS 1 DS 2 LS 1 LS 2 RS 1 W1 T DOK
Min 1.5 1.5 0.1 0.5 0.0001 10 0.02 1.6
Initial 1.55 1.75 0.5 1 90 0.03 3.15
Max 1.9 2.1 1.5 6.45 0.03 140 0.05 6.5
minimal diameter of the orifice [m] second smallest diameter of the orifice [m] length of the last segment (between DS 1 and DS 2) [m] length of the outer part of the orifice [m] radius to define an additional filet at the end of the orifice [m] angle at the end of the orifice[°] wall thickness of the orifice [m] diameter of the shaft [m]
(a)
(b) Figure 2 (a) initial value of diameter and length; (b) parameters for optimisation
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The diameter of the shaft (DOK) is in general defined by the building method and criterions for stability of the mass oscillation. Here it was varied in order to compare the numerical results with the tabular values. This investigation was conducted beforehand and is not part of this paper. The parameters RS 1, W 1 and T have very little influence on the local head loss of the orifice. Thus, in the following results for the parameters DS 1, DS 2, LS 1 and LS 2 are presented. Most of the variations are first tested in the segment model (numbers of elements: ~200 000). The convergence criterion can normally be reached in about 6 to 12 hours. In contrast to this, the half model (up to 2.7 million elements) needs one to two weeks to get to and equal state, albeit the use of up to four cores in parallel processing. Thus, it is obvious that the efficient use of a half model needs to be limited to the minimum and concentrated on the elbow. For comparison purpose λDownUp, being the ratio of loss coefficients in the down and upward case is introduced. As λDownUp quantifies the asymmetric effect of the orifice (Eq. (4)), a value of greater than 2.5 [-] is set as target in the optimisation process. (4)
2.2.3. Software For the 3D-numerical simulation the software ANSYS-CFX 12.1 was used. The main advantage was found with respect to the geometry optimisation process, where software provides a full parametric environment with high flexibility. This and an automated meshing procedure allowed the variation of geometry and boundary conditions. The software and it’s tools was used earlier by Huber (2010), who realized an asymmetric orifice in a T-shaped branch in ANSYS and compared the results with a physical laboratory test (scale 1:21). Most valuable were his findings that the numerical simulations could yield reliable results compared to the lab tests. The verification of the results by physical laboratory tests is currently ongoing. By using the ANSYS-Meshing-Tool, the option “First Layer Thickness” is used to define the inflation layers, so that the maximal value of the parameter yPlus is less than 20 (ANSYS, 2010). All simulation processes are conducted with respect to the Best Practice Guidelines for CFD-Modelling (ANSYS, 2010 and Menter, 2007). The calculation of the local loss coefficient xi is implemented by using different expressions in the Pre-Processing (relating to the inflow and outflow boundary) and so it is possible to control the convergence of the target value via monitor points while the solver is still in operation. As turbulence model the Shear-Stress-Transport model (SST-model) was used. To reduce the losses caused by friction (wall option of the connecting pipes are defined as “smooth wall”) between the orifice and the boundaries, the control sections are moved as close to the orifice as possible during the Post-Processing.
3. RESULTS 3.1. Comparison of theory and simplified 3D-numeric The results of the literature research are shown in Table 2 and 3. The results of the 3D-numerical simulation at the segments are added at the end of each table and in Figure 3. Table 2 Local head loss xi [-] for upward flow related to vShaft Author Truckenbrodt (2008) Bollrich (2007) Bohl & Elemendorf (2005) Rössert (1999) Idelchik (1960) 3D-numerical simulation
Contraction Sudden expansion 9.797 1.024 9.797 1.279 9.797 2.468 9.797 3.360 9.797 related to boundaries (solver): minimised wall effects (Post-Processing):
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Summation 9.797 10.821 11.076 12.265 13.157 14.490 14.436
Table 3 Local head loss xi [-] for downward flow related to vLower Chamber Author Rössert (1999) Bollrich (2007) Bohl & Elemendorf (2005) Idelchik (1960) Truckenbrodt (2008) 3D-numerical simulation
(a)
Sudden Contraction expansion 2.842 0.718 2.791 0.876 3.654 0.873 4.514 2.332 3.654 4.100 related to boundaries (solver): minimised wall effects (Post-Processing):
Summation 3.560 3.667 4.527 6.846 7.754 12.313 12.216
(b)
Figure 3 Streamlines and vectors for (a) upward flow and (b) downward flow (segment model) As a first result the maximal velocities are compared. By using the continuity equation, the theoretical velocity at the orifice can be calculated to 18.55 m/s. In reality, the stream – by passing through the orifice – turns into a jet with higher velocities (about 20 m/s for upward flow and 30 m/s for downward flow). With respect to the velocity vectors, a backflow can be observed, which is higher than in the theoretical figures. These effects are not considered in the theoretical approach of contractionexpansion-models and so these values can be seen as a lower bound of the local head loss. Far higher values (up to 30 [-]) can be found in Bollrich (2007) and Idelchik (1960) for sharp orifices. Overall, the 3D-numerical results of the segment are higher than those of the theoretical approach caused by additional effects, which are indicated through the special geometry. This could be proved by modifications of the geometry (sudden variation of the diameter) and also various physical tests.
3.2. Comparison of theory and orifice with elbow Based on the results of the segment simulation, the elbow is added to the model. The 3D-model was realized as half model using a symmetry plane boundary as already applied in the segment-model. Table 4 Local head loss xi [-] for elbow related to vShaft related to vLower Chamber Author Rössert (1999) 0.18 0.45 Bollrich (2007) 0.45 1.13 Bohl & Elemendorf (2005) 0.31 0.78 Idelchik (1960) 0.49 1.24
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(a)
(b) Figure 4 Streamlines for (a) upward flow and (b) downward flow – with elbow
The use of tabular values is only justified for the homogeneous flow conditions in the bend. This is the case for upward flow only. In the case of the downward flow back flow and turbulences occur in the bend. Regardless of the flow direction the local head losses of the bend were found to be small compared to the losses of the orifice (Table 4). These findings based on the 3D-numerical model are confirmed by the tabular values for the case of the upward flow. Thus, the numerical simulation of the elbow is negligible in the assessment of the total losses. When focusing on constriction issues the occurring backflow and the possible cavitation are important.
3.3. Optimisation of the geometry One of the main parameters is the diameter DS 1, which defines the last part of the orifice. The radius of this part is altered between 1.5 m to 1.9 m (Figure 5) with an initial value of 1.55 m. The variation was made independent from DS 2 with an initial diameter of 1.75 m. Thus, cases of DS 1 larger DS 2 occur where the DS 2 section becomes the dominating diameter. Variations of DS 2 between 1.5 m and 2.1 m were made the same way. For the lower limit, DS 2 became again the dominating (smaller) section of the orifice.
(a)
(b) Figure 5 Variation DS 1 – (a) lower and (b) upper limit
In Figure 6 the results for the variation of DS 1 and DS 2 are shown. The local head losses were found to be sensitive for both flow directions when varying DS 1. In contrast, the variation of DS 2 is almost without effects onto the losses in case of the downward flow, but not in the case of upward flow. Consequently, changes in the parameter DS 2 lead to larger changes in the ratio λDownUp..
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(a)
(b) Figure 6 Results for (a) DS 1 and (b) DS 2
Variation of this length of the last segment LS 1 showed a similar sensitivity of the results as found for DS 2. For both flow directions the angle between the axis and the wall is changed. Hence, Figure 6 (b) and Figure 8 (a) show the same characteristics were the parameter LS 1 was varied between 0.1 m and 1.5 m. Finally, the parameter LS 2 is varied in the range of 5.0 m to 6.5 m for the last segment of the orifice (Figure 8). The volume of the dead space around the truncated cone provides room for turbulences and cross flows in case of the downward flow. Thus, the applied variations can be seen as a variation (or even optimisation) of the required size of the dead zone. Changes in the section due to the divergence angles of 14.25° showed no significant effects on the local head loss.
(a)
(b) Figure 7 Variation of LS 2 – (a) lower and (b) upper limit
(a)
(b) Figure 8 Results for variation of (a) LS 1 and (b) LS 2
The local head loss xi for upstream direction is found almost independent from the size of the orifice’s dead zone. For the case of downstream flow, an upper limit of meaningful length of the dead zone can be determined. Starting from the case of sudden contraction (LS 2=6.5 m), the losses increase with a decreasing value of LS 2. When LS 2 becomes less than 6.1 m, no significant change in the loss coefficient is found. Thus, the maximum required dead zone length is found around 0.4 m.
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Still, the parameter DS 1 was found to be the dominating design parameter for the magnitude of the local head loss for both flow directions. The last divergence angle (combination of DS 2 and LS 1) of the orifice can be used for fine tuning in case of upward flow. For the case of downward flow, the parameter LS 2 is found critical, since a certain dead space shall be provided in order limit the development of losses above the case of sudden contraction.
4. CONCLUSION AND OUTLOOK Numerical modelling allows the assumption that local head losses on an asymmetric orifice are higher than the theoretical reference values for extensions and contractions (sudden and smooth depending on the flow direction). After gaining head losses for the orifice the parameter settings were optimized. The variation of the geometry parameters was made at a segment of 12°, were the most sensitive parameters could be specified separate for the two flow directions. These results can be used for the complete orifice simulation including the elbow. The elbow geometry was varied for the radius R (between 5.0 m to 9.0 m), the length, the number and the diameters of the single segments. These further numerical investigations are a main part of the ongoing work on this research project. 3Dnumerical simulations might be a flexible, less costly and reliable alternative to physical model tests. Although the optimisation process is considered as reliable, a physical model test for the optimized structure is in progress in order to verify the obtained results for the 3D-numerical simulations. Findings on the independent parameter sensitivities reveal that an investigation of dependent variation of geometry parameters would be a vital extension of the investigations in the future.
5. REFERENCES ANSYS-CFX (2010), User Manual Version 12.1, digital. Bohl, W. and Elmendorf, W. (2005), Technische Strömungslehre, Vogel Buchverlag, Würzburg. Bollrich, G. (2007), Technische Hydromechanik 1 – Grundlagen, HUSS-MEDIEN, Berlin. Huber, B. (2010), Physikalischer Modellversuch und Cfd-Simulation einer asymmetrischen Drossel in einem T-Abzweigstück, Österreichische Wasser- und Abfallwirtschaft, 3-4, 58-61. Idelchik, I.E., (1960), Handbook of Hydraulic Resistance Coefficients of Local Resistance and of Friction. U.S. Department of Commerce National Technical Information service (NTIS). Jaeger, C. (1977), Fluid Transients in Hydro-Electric Engineering Practice, Blackie, London. Menter, F. (2007), CFD Best Practice Guidelines for CFD Code Validation for Reactor – Safety Applications, European Commision 5th Euratom Framework Programm 1998-2002, CONTRACT N° FIKS-CT-2001-00154. Novak, P., Moffat, A.I.B., Nalluri, C. and Narayanan, R. (2005), Hydraulic Structures, Taylor & Francis, London – New York. Popescu, M., Arsenie, D. and Vlase, P. (2003), Applied Hydraulic Transients for Hydropower Plants and Pumping Stations, A.A.BALKEMA PUPLISHERS, Lisse. Roberson, J.A., Cassidy, J.J. and Chaudhry, (1995), Hydraulic Engineering, John Wiley & Sons, New York – Chichester – Brisbane – Toronto – Singapore. Rössert, R. (1999), Hydraulik im Wasserbau, R. Idenbourg Verlag, München. Sharp, B.B. and Sharp D.B. (1996), Water Hammer – Practical Solutions, Butterworth-Heinemann, Oxford. Steyrer, P. (1999), Economic Surge Tank Design by Sophisticated Hydraulic Throttling, 28th IAHR Congress, Graz, 22. August – 27. August. Thoma, D. (1910), Zur Theorie des Wasserschlosses bei selbständig geregelten Turbinenanlagen, R. Oldenbourg, München – Berlin. Truckenbrodt, E. (2008) Fluidmechanik Band 1 – Grundlagen und elementare Strömungsvorgänge dichtebeständiger Fluide, Springer Verlag, Berlin – Heidelberg – New York.
Wu, J., Ai, W. and Zhou, Q. (2010), Head loss coefficient of orifice plate energy dissipator, Journal of Hydraulic Research, 48:4, 526-530.
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