Comparison of numerical and experimental investigations of trashrack losses

 

Hubert Meusburger, Felix Hermann and Roland Hollenstein

 

Laboratory of Hydraulics, Hydrology and Glaciology (VAW)

ETH Zürich, CH-8092

PHONE: 0041-(0)1-6326601, FAX: 0041-(0)1-6321192

 

 

Abstract

Trashracks, consisting of an array of bars, are typical inlet devices of river power plants which prevent large obstacles from damaging the turbines. They produce energy losses which increase significantly as the spacing of bars decreases. This paper presents a comparison between different numerical methods and experimental investigations to predict these losses for arbitrary inflow conditions to trashracks. First, simulations with high resolution grids using either the Direct Numerical Simulation (DNS) technique or a Large Eddy Simulation (LES) are made, depending of the Reynolds number. These simulations cover only a small part of a trashrack domain, typically 3 or 4 bars, but they allow a precise description of the flow phenomena which occur upstream, between and downstream of the bars. As the bar spacing reduces, substantial changes in the flow structure occur. The results of simulations are then compared with experimental results on such trashracks in laboratory scale. Different inflow angles were examined. The velocity range extended from 0.50 m/s to 1.5 m/s, while the blockage ration lie between 0.18 and 0.54. The numerical and experimental agree.

 

Keywords: Trashrack loss, Direct-Numerical-Simulation (DNS), Large Eddy Simulation (LES) Vortex

 

Introduction

The flow around obstacles is one of the topics in hydrophysics, which is investigated both experimentally and numerically with considerable interest by a large number of researchers. Therefore, it may be used as a test case for numerical modeling and for implementation of large eddy schemes. In applications, however, the flow through an array of obstacles is a common problem of interest. Once a numerical technique is developed, it may be applied to these configurations. The sensitivity to different parameters, such as obstacle dimensions, bar spacing or inflow angle may be studied. The drawback of any DNS or LES is the still high demand on computer resources and simulation time and these simulations are limited to arrays of only a few obstacles. Hence, the steps from LES down to simpler turbulence models such as the Reynolds-Stress-Model (RSM) or even the k-e-model are of major interest. Having a set of high definition simulations on the same object gives the possibility of a quality check for other turbulence models. These offer in turn the ability to simulate a much larger array of obstacles since the grid requirements are less limiting. In the present article, only the flow around an array of bars is studied. It will then be compared with the results of the experimental investigation.

 

Principles and Parameters for experimental investigation

The trashrack loss Dh_R determines itself from the difference of the energy line (EL) up- and downstream of the rack cross-section and is defined as

 

, (1)

 

where z_R is the dimensionless loss coefficient and v_R the mean velocity across rack cross-section. The parameters of the rack geometry and the flow field are represented in figure 1.

 

 

Figure 1. Parameters of trashrack loss.

 

In the hydraulic model tests the relevant parameters were examined and varied as shown in Table 1.

 

Table 1. Selected parameter and their variation.

 

The model scale was 1:3. The hydraulic model involved Froude similarity. The examined racks (Table 2) consisted of a number n of bars and spacing elements. The height of the rack amounted to 700 mm and the width to 500 mm. The blockage ratio p varied with the clear spacing b between the bars.

 

Table 2. Dimensions of the examined model racks.

 

experimental results

Figure 2 shows the relation between blockage ratio p and loss coefficient z_R. The loss coefficient increases strongly with rising blockage ratio p. Further the loss coefficient is practically independent of the mean velocity v_R, and Reynolds effects are absent.

 

 

Figure 2. Relation between loss coefficient z_R and blockage ratio p.

 

Numerical Simulation

The basis of each numerical simulation are Navier-Stokes-Equations (NSE), for example Griebel et al. (1995). It concerns four coupled partial differential equations, whose solution is analytically possible only in special cases. In a turbulent flow, a large range of scales is usually encountered. They range from the dimension of the problem itself down to the Kolmogorov length. The latter may be estimated by the Heisenberg formula (1948):

 

(2)

 

where L₀ is the diameter of the largest eddy, Re₀ their Reynolds number and k @ 1. The resolution of a vortex within a computational grid requires at least two gridpoints in each direction. Therefore, a simulation containing all turbulent structures.

Figure 3. Vortex distribution around two bars for p 0.18. Figure 4. Vortex distribution around three bars for p = 0.31. Figure 5. Vortex distribution around three bars for p = 0.45. Figure 6. Vortex distribution around three bars for p = 0.54.

(DNS) is of practical relevance but far beyond the capabilities of present computers. DNS simulations were used to model the flow between bars in an array to obtain the flow resistance. In figure 3, the blockage ratio p is 0.18, for which each bar behaves roughly like a single bar, and no interaction between the bars is discernable. With a blockage ratio p = 0.31 (fig. 4) the vortices begin to loose their identity. The side eddies are still present, but reduced in their expansion. In contrast, the vortex streets behind the bars are decoupled from each other. With a blockage ratio p = 0.45 (figure 5), the vortex structures along the bar sides are more compressed, but still discernable. The vortex streets behind the bars are no longer independent, they rather intermix and form an irregular pattern of vortices distorted in all directions. This process is enhanced for a blockage ratio p = 0.54 (figure 6). Behind the trailing edge of the bars, only one or two vortices is clearly visible before they "vanish" in the irregular vortex structure further downstream.

 

The single side vortices are still present, but they are reduced to enlargements of the general shear layer along the bar sides.

In terms of flow resistance the following scenario applies: As the blockage ratio p increases, the space where the flow may cross the rack gets narrower. This gap may be defined as the space between the bars occupied by the vortices. Due to the extension of the latter, the flow velocity through the gaps rises more than does the blockage ratio p. Despite the fact that the vortices between the bars are well compressed for large blockage ratio, the remaining gap is only about one third of the possible space with p = 0.54. Both the increased flow velocity and the reduced vortex thicknesses form an intense shear zone along the bar sides to produce the major part of the head loss.

The experiments mentioned were simulated on a coarser grid using the k-e turbulence model. Geometrical and boundary conditions were basically the same as in the DNS runs, but the grid covered the whole channel and contained all the bars. The layout was in 2D, which was sufficient for the determination of pressure losses and allowed a finer resolution in the remaining dimensions. These simulations were performed with the commercial flow code CFX-F3D. Further details may be found in Hermann et al. (1998). For some cases, DNS results, k-e results and experimental results were compared in figure 7.

 

Comparison between experiments and numerical simulations

The results of the numerical and physical models are summarized in figure 7. There is in general a good agreement between the k-e simulations and the experiment. This agreement improves with increasing blockage ratio. Since one of the calibration cases for the k-e model is the grid, this tendency is not a surprise. This implies that if the blockage ratio is large enough to provide a boundary layer along the bar side as it may be observed along the infinite plate, the k-e model behaves better than with blockage ratio, where a fully developed vortex structure is present.

The DNS simulations compare well for low blockage ratio, but result in too large head losses for the higher blockage ratios. This implies that the vortex structures along the bar sides for a blockage ratio lower than 0.45 are well reproduced by the numerical model. A test run for p = 0.45 with the same model, but a significantly larger grid spacing (200 x 200 instead of 600 x 600) resulted in a pressure difference which was 50 % higher than for the fine grid (Hermann et al. 1998). The error for high blockage ratio results from a large grid extent, which is too coarse in the turbulent boundary layer zone. Another possibility is the transition from a 2-D dominated flow to a fully developed 3-D turbulence flow that occurs earlier for high blockage ratio. In this case, the use of a 2-D model would no longer be justified.

 

 

Figure 7 Comparison of numerical and experimental investigation for trash rack loss.

 

Conclusions

This investigation on trashrack loss with numerical and experimental techniques shows substantial agreement. Further, the processes around bars within a rack may be investigated both in a qualitative and quantitative manner. In a practical view, the most important aspect is that simulations with the k-e model provide results accurate enough to be used for planning and prediction of head losses for different inflow conditions. DNS and LES provide also insight to the generation of these processes. The simulations indicate, that the resolution requirements for any Direct Numerical Simulation is considerably larger than for a free flow field. Furthermore, the distribution of 2-D and 3-D dominated processes is not known within whole arrays, particularly if the blockage ratio is large.

 

References

Hermann, F. - Hollenstein R. (1998). Zur Entstehung von Rechenverlusten bei gerader und schräger Anströmung. Beiträge zum Symposium Planung und Realisierung im Wasserbau. Heft 82 Technische Universität: München,. (in German).

 

Griebel, M. - Dornseifer, T. - Neunhoeffer, T. (1995). Numerische Simulation in der Strömungsmechanik. Vieweg, Scientific Computing (in German).

 

Heisenberg, W. (1948). Zur statistischen Theorie der Turbulenz. Zeitung für Physik 124, 249-266 (in German).