Experimental and Numerical Study of the Flow Through a Trifurcation

 

Branislav Basara, Herwig A. Grogger

 

Advanced Simulation Technologies - AVL List GmbH

Hans List-Platz 1, A-8020 Graz, Austria

Tel: ++43-316-787-705, -1697, Fax: -777, basara@avl.com, massimo@avl.com

 

Roman Klasinc, Dominik Mayr

Institute for Hydraulic Engineering and Water Resources Management

Graz University of Technology

Stremayrgasse 10, A-8010 Graz, Austria

Tel: ++43-316-873-8859, Fax: -8357, mayr@kwb.tu-graz.ac.at

 

 

Abstract

A study of the flow through a trifurcation has been performed experimentally and numerically. For the experiments a plexiglas trifurcation was used. The pressure head were measured for several discharges in the three branches. The computations were carried out on a quarter of the real domain since the boundary conditions as well as the geometry were symmetric. It is demonstrated that the mean-flow parameters are predicted well by the k-e turbulence model. More advanced turbulence model, namely Reynolds stress model has been used as a complementary model to describe the flow more accurately. The calculations were assessed for available measurements and later extended to higher discharges, for which experiments could not be done because of incipient cavitation in the model. The agreement of the calculated and measured pressure drop is relatively good and helps to transfer test results from the model to the prototype.

 

Keywords: trifurcation, experiment, numerical simulation, Reynolds stress model

 

Introduction

To operate a hydro power plant under best conditions, energy losses in power conduits and manifolds must be reduced to a minimum. Since tests on prototypes of hydraulic structures are very costly, these tests are usually performed on scale models. Using correlation of discharge and pressure losses, energy loss coefficients can be calculated and transferred to the prototype [1]. In order to advance the reduction of costs involved in those experiments or in the design of hydraulic systems, numerical simulation could be of great help. But before it can relied completely on the results of a simulation different numerical models have to be assessed. In this paper the numerical simulation was compared to experimental results.

 

Model setup

The test setup under study is shown in Figure 1. The trifurcation (Fig. 2) and the adjacent pipes were constructed of plexiglas. The trifurcation itself consists of cone and spherical elements. For static reasons (of the prototype) two sickles were arranged inside the trifurcation. The arrangement of the flow meters is indicated in figure 1. The three outgoing branches pass into straight pipes. Electrically controlled Howell-Bunger valves allowed variation of discharges in the branches.

 

 

Figure 1: Test Setup

 

 

Figure 2: Trifurcation, Layout

 

Data Aquisition

The area to be studied covered the range between the inlet cross section of the trifurcation (measuring cross section B) and the respective outlet cross sections (measuring cross section 3D). As the flow patterns in closed systems are mainly determined by inertia and friction forces, the studies were carried out according to Reynolds' law of similarity.

Flow was measured by means of magnetic-inductive flow meters. In order to take into account the effect of fluctuation of measured data, several hundreds of values were measured by computer-controlled measuring equipment and used for averaging.

Inductive differential pressure transducers were used for the measurements on the model. Each measuring cross section was equipped with eight bores spaced at 45° over the circumference of the pipe wall.

A LABVIEW software package was used for acquisition of instrument data. Control of the measuring sequence was partly automatic.

The pressure signal has a greatly fluctuating character. Using low-pass filters and an observation period of appropriate length, a high level of reproducibility was obtained for a chosen scanning rate.

 

Experimental Results

Pressure head differences between the cross section B and cross section 3D (Fig. 1) were measured for incoming flow which was divided equally to the three outgoing branches (load case XXX). Measurement of pressure head differences which are shown in table 1 were made with total discharges of 107.4 l/s, 180.5 l/s and 263.4 l/s. These data are used for comparison with the calculated values.

 

Total discharge		for B - 3D
107.4 l/s		0,157 m
180,5 l/s		0,402 m
263.4 l l/s		0,818 m

Table 1: Pressure head differences , B - 3D

 

Flow patterns were visualized in the model by injection of air bubbles. Besides the expected separation zones at the edges to the lateral branches, vortices in the top and the bottom of the trifurcation were observed and documented by the means of a high-speed video-camera. The axis of these vortices are orthogonal to the model center line. These vortices extend from the trifurcation into one of the two lateral branches. The shift of the vortex from one lateral branch to the other side has a random characteristic. This phenomenon is also reported in [2].

Calculations

Numerical simulations were performed for the same load case XXX using the flow solver AVL-SWIFT [3]. The flow for five different discharges was calculated. For three cases measurements were available. Two higher discharges were also calculated to check the performance of the numerical model for higher Reynolds numbers, i. e. prototype Reynolds numbers. Table 2 gives an overview of the calculations.

 

Table 2: Overview of the performed calculations

 

In each of the load cases the outlet flow was the same in all three branches. In the calculation, the outlet boundary condition was adopted to ensure a third of the inlet volume leaving each pipe. Since the geometry is symmetric, a quarter of the trifurcation was used for the simulation. The length of the pipes in the calculation model were chosen according to the location of the pressure transducers in the experiment. The inlet tube was modeled even longer to ensure that a regular turbulent velocity profile at the entrance of the upstream measuring section was developed. Therefore, the dimension of the calculation domain was rather large. In Table 3 the lengths for the pressure transducers refer to the midpoint of the junction.

 

 

Table 3: Dimensions of the calculation domain

 

Figure 2 shows a detail of the calculation mesh. To capture the flow characteristics in the junction as good as possible, the mesh density in this region was increased. The whole model consisted of ~110.000 calculation cells. Since this study was intended to investigate the basic predictability of numerical simulation small sickles in the junction of the branches have been neglected in the model. This neglect was based on the results of physical model results, where tests with various sickle designs showed no significant influences on pressure head differences.

 

 

Figure 2: Trifurcation, Calculation mesh

 

The calculations were performed as steady state simulations. Effects of turbulence have been modeled using the k-e model. For comparision purposes a higher order turbulence model, namely the Reynolds stress model was applied in order to investigate the flow pattern in the junction.

 

Mathematical Framework

The mathematical model is based on the Reynolds-averaged Navier-Stokes equations. The governing differential equations are discretized using a fully conservative finite volume approach. The method utilizes a general non-orthogonal coordinate system by transferring the differential equations from Cartesian space coordinates to computational space coordinates using a curvilinear coordinate transformation. All dependent variables such as momentum, pressure, turbulence kinetic energy and dissipation rate are evaluated in the cell centers.

In the k-e model the Reynolds stresses u_iu_j are evaluated from the Boussinesq assumption. In the Reynolds stress transport equations, the Reynolds-stresses are obtained from the solution of their own modeled transport equations. In these six additional equations diffusion has been adopted as simple gradient transport term and the pressure-strain term as proposed in [4]. The standard form of dissipation rate equation was used in both of the models. The discretised equations are solved using a SIMPLE-like algorithm.

 

Results of the Calculations

The recirculation zone in the spherical part of the junction was also found in the presented calculations for all load cases (Fig. 3). As mentioned under 0. the vortex is unstable and propagates into one of the lateral branches randomly. As a quarter of the domain was used in the calculations, any instability of the vortex was suppressed from the beginning (Only averaged values were requested from the calculations).

 

 

Figure 3: k-e velocity distribution in the vertical symmetry plane of the trifurcation

 

It is well known that the k-e model is defective for flows with high amounts of secondary flows. To study the influence of these secondary flows on the simulation model a tentative calculation was performed using the Reynolds stress model (RSM) instead of the k-e model. Figure 4 shows a comparison of the velocity fields in the vertical symmetry plane for 263.4 l/s discharge. It is evident, that in the RSM-calculation a more distinctly vortex is created.

 

 

Figure 4: Velocity distribution in the vertical symmetry plane for (left: k-e right: RSM)

 

Based on the calculated pressure field the head losses are found. Table 4 gives the calculated head losses, evaluated between the locations corresponding to the pressure transducers in the model test.

 

	Discharge		Pressure Head Loss
Case 1	107.4 l/s		0.1494 m
Case 2	180.5 l/s		0.3830 m
Case 3	263.4 l/s		0.7931 m
Case 4	763.4 l/s		5.1494 m
Case 5	1263 l/s		12.9019 m

Table 4: Calculated head losses (k - e model)

 

In Fig. 5 the calculated head losses are compared with those of the experiments. The agreement between the simulation and the measurements is relatively good in all three cases. In order to study the predictive capability of the computational model for higher Reynolds numbers the discharge was increased to values, for which no measurements were available due to the start of cavitation in the physical model. Obviously, the head losses increase according to a polynomal extrapolation curve with increasing discharge.

 

 

Figure 5: Comparison of calculated and measured head losses

 

Conclusion

Pressure head losses of a trifurcation were measured on a physical model. Additionally the flow in the trifurcation has been calculated using the k-e turbulence model. Calculated and measured head losses are in good agreement which was the main goal of the investigations. A next step of the investigations was to present the flow pattern in the trifurcation. A vortex in the spherical part of the junction found in the model tests was also reproduced by the calculations. Shedding of that vortex could not be predicted since the simulation was based on a quarter of the real geometry using symmetrical boundary conditions. Furthermore, the calculation was performed as steady state, which also suppresses a time-dependent detachment of the vortex. Using a higher order turbulence model namely the Reynolds stress model in a calculation gives a stronger recirculation in the junction compared to k-e model. Future investigations will be based on the whole domain and performed as transient calculations where new turbulence models will be tested in order to describe the transient flows and vortex shedding.

 

References

[1] Klasinc R., Knoblauch H.; Dum T.: Power losses in distribution pipes, Fluid flow modeling, Computational Mechanics Publications, Southampton, Boston(1992)

[2] Ruprecht A. et al.: Strömungseffekte in einem Dreifach-Abzweiger. (1998)

[3] AVL-SWIFT: Theoretical Manual, AVL (1998)

[4] Speziale C.G., Sarkar S. and Gatski T.B. (1991): Modeling the pressure-strain correlation of turbulence, an invariant dynamical systems approach, Journal of Fluid Mech., vol.227, pp245-272