Scale Model Test for a Distribution Piping

 

Helmut Knoblauch**, Roman Klasinc**, Guenther Heigerth*, Wolfgang Sattler**

 

Department of Hydraulic Structures and Water Resources Management

Graz Technical University, Stremayrgasse 10, 8010 Graz, Austria

Email:knoblauch@kwb.tu-graz.ac.at

* Professor and Head of the Department

** Associate Professors

 

 

Abstract

The paper deals with model tests for a manifold of a hydropower station with 4 turbines installed, to determine relevant energy losses. Construction of model, monitoring equipment and basic suggestions are discribed. Measurements and evaluations at various load cases are presented and commented on, especially the phenomenon of negative energy losses.

 

Keywords: Model tests, manifold, energy losses

 

Introduction

In the spring of 1997, the Institute of Hydraulic Structures and Water Resources Management was let a contract for carrying out a hydraulic scale model test concerning the Kapichira manifold. The client was VOEST Alpine MCE, designer of the steel structure and at the same time the supplier of the structural steel elements.

 

The task of the Institute as the contractor was to determine the energy losses incurred in the distribution piping (see fig. 1). For this purpose a plexiglass model was constructed to scale 1:26.43 at the Institute's Hermann-Grengg Laboratory, and the appropriate measurements were carried out and evaluated.

 

Design of the Kapichira Manifold

The Kapichira power station will be equipped with four turbines for power generation. Water will be fed to the turbines through a steel-lined power tunnel. The steel lined section covers a straight length of 68m followed by a bend and the 56m long distribution pipe system of the manifold.

 

Water supply to the manifold is through a pipe 7.8m in diameter, which divides into four penstocks of 3.7m diameter each.

 

The first three legs branch off at angles of 42.28° (branch 1), 42.11° (branch 2), and 41.99° (branch 3). The deflection angle of branch 4 is formed by a pipe bend with an angle of 87.00°. (Note: All the above angles are values measured in the horizontal plane.) In the longitudinal profile, the plane of the manifold is inclined at 1.97° to the horizontal.

 

Purpose of the Scale Model Test

The purpose of the hydraulic scale model test was to determine the energy losses incurred in the distribution piping. For this purpose a plexiglass model was constructed to scale 1:26.43. The model included the straight intake line and the distribution pipe. Upstream of the intake cross section as well as downstream of the legs of the manifold appropriate additional lengths were provided in order ensure straight uniform pipe flow for the pressure measurements. The manifold region is exactly defined by the intake cross section and the four outlet cross sections.

 

The scale model test was intended to determine the energy losses incurred in the legs of the manifold for an approach flow to the manifold of Q = 270m³/s (operation of the four turbines at Q = 4 x 67.5m³/s). The region under study extended from the cross section at the intake to the manifold (measuring plane B as shown in fig. 1) to the respective outlet cross sections (measuring planes 1A, 2A, 3A, and 4A, as shown in fig. 1).

 

Test Set - up

 

4.1 Construction of the Model

The manifold model was constructed in plexiglass to scale 1:26.43 so as to reproduce the prototype on the basis of the drawings supplied by the Client (see fig. 1). The selection of the model scale was determined by the dimensions of the plexiglass pipes available (150mm in outside diameter and 140mm in inside diameter) for the outlet legs of the junction. The remaining plexiglass pipe elements were manufactured at the laboratory. The outside diameter of the inlet pipeline is 307.1mm, the inside diameter 295.1mm. The wall thicknesses of the pipes vary between 5mm and 12mm. From measuring planes 1A, 2A, 3A, and 4A, the three legs and the bend continue as straight pipelines with an inside diameter of 140mm.

 

The legs of the pipe dividing system consist of cone and cylinder elements. These were manufactured of plexiglass, which was formed warm over wooden models, cut, and glued or welded.

 

Downstream of the respective branches, plexiglass pipelines of appropriate diameter (D = 140mm), leading to the flow meters, were provided to simulate gates and turbines. Electrically controlled Howell-Bunger valves arranged downstream of the flow meters allowed infinite variation of the respective flows.

 

Water supply to the model was from an overhead tank and through piping systems.

 

 

Fig.1: Plan of model for Kapichira power station (model scale, 1:26.43)

 

4.2 Acquisition of Instrument Data

4.2.1 Measuring Planes

As stipulated in the contract, the purpose of our studies was to determine the energy loss incurred between the inlet cross section (measuring plane B) above the distribution pipe and the respective outlet cross sections (1A, 2A, 3A, and 4A). Each of these five measuring cross sections was equipped with 8 measuring bores (D = 1.5mm) evenly distributed over the circumference of the pipe wall.

 

 

Fig.2: Bores in a measuring cross section as viewed in the direction of flow

 

Apart from the above measuring planes, the measuring system included one upstream cross section and three cross sections downstream of the junctions and four each further downstream in the outlet legs to allow potentially required subsequent measurements.

4.2.2. Measured Values

The data measured comprised the head loss incurred between two measuring cross section as well as flow. Since the two values are functionally connected, particular care had to be exercised in making the measurements.

4.2.2.1 Pressure Measuring

Pressure difference was measured by means of inductive differential-pressuer transducers, which directly measured the pressure difference between two measuring cross sections. The various measuring points and cross sections were connected with the differential-pressure transducer via a special change-over switch. The eight measuring points of a cross section were interconnected by a closed circular pipe so as to balance pressure variations within a cross section. On the basis of previous experience and preliminary tests, a measuring period of 20 seconds for a scanning rate of 30 individual values per second was chosen. The measuring accuracy allowed for in interpreting the pressure differences was 1mm.

4.2.2.2 Discharge Measuring

Flow was measured by means of magneto-inductive precision flow meters which in combination with flow control through the Howell-Bunger valves ensured very accurate flow adjustment. The measuring range per branch was between 25 l/s and 75 l/s for a symmetrical approach flow to the four branches. The differential pressure data was digitally logged on data acquisition boards, stored on a PC, and appropriately processed.

 

Theoretical Basis

 

5.1 Similarity Laws

Similarity between scale model test and nature conditions require geometrical and dynamic similarity.

 

Geometrical similarity exists for a model where all the geometrical lengths (L_N) of the prototype bear a constant ratio to the respective lengths (L_M) on the model. This ratio is termed the scale factor (L_R) of the model (L_R= L_N/L_M). For the model under study L_R= 26.43.

 

Dynamic similarity signifies that the sequence of flow processes on the model corresponds to that on the prototype. The flow processes and, hence, the energy losses are largely governed by inertia and friction forces. That means that the studies and the conversion of measured data had to be based on Reynolds' law of similarity. Therefore, apart from the geometrical similarity criterion, it was necessary to keep the Reynolds' number, Re, equal for model and prototype.

 

Re_N/Re_M = 1

 

Reynolds' number is defined as the ratio of inertia forces to viscosity forces:

 

 

where

 

v...... characteristic velocity [m/s]

D ..... diameter of pipe [m]

n ...... kinematic viscosity of water [m³/s]

(n = 1.01 x 10^-6 m²/s; water temperature T = 20°C).

 

The requirement of equal Reynolds' numbers can be met only where the velocity on the model corresponds to the product of prototype velocity and model scale.

 

 

(This applies to laboratory tests using the same liquid and temperature on the model as on the prototype.)

 

As it is not possible, however, to accomplish on a water-operated model the Reynolds range of the prototype, it is necessary to conduct serial tests trying to operate the model to a point in the vicinity of that Reynolds range from which the zeta value in the square law of loss becomes constant. Where this is not possible, it is necessary to extrapolate the results of the serial tests using a mathematical method.

 

On the model under study, the maximum Reynolds values reached were Re_max = 1.28 . 10⁶ related to intake cross section B. Compared to that, the prototype Reynolds values are Re_Natur = 4.3 . 10⁷, for a flow of Q = 270m³/s.

 

5.2 The Hydraulic Situation

The total head loss (h_v) in a pipe dividing system is composed of the friction loss (h_R) plus the local head losses (h_Form) resulting from the flow deflections.

 

h_v = h_R + h_Form

 

An exact quantitative separation between friction loss and local head loss is not possible due to interaction effects between the two quantities. Instead, for transferring model results, the friction loss is determined for equivalent straight pipe sections on the assumption of a fully developed pipe flow and is then deducted from the total head loss.

 

According to the above definition, the local head losses are

 

h_Form = h_v - h _R

 

The frictional head loss is expressed by the equation:

 

where

l_i ..... dimensionless friction factor according to Prandtl/Colebrook

Li ..... length of sub-section i

Di ..... diameter or equivalent diameter of pipe section i

vi ..... flow velocity in pipe section i

 

The zeta value z, governing local head loss is defined as

 

 

and generally becomes constant from a Reynolds range Re >10⁶ and, hence, independent of the Reynolds number.

 

Both head loss quantities are proportional to the velocity head. Energetic comparision of two cross sections allows the following relationship after Bernoulli to be established:

 

h_V = v_e²/2g + dp - v_a²/2g

 

with the pressure head differences (dp) between two cross sections being obtained by measurement.

Velocities v_e and v_a were determined using the continuity equation (Q_i = V_i . F_i).

 

 

Fig.3: Comparison of energy lines after Bernoulli

 

Test Results

 

6.1 Energy Losses

The purpose of the scale model studies was to determine the energy losses incurred in the manifold for a symmetrical operation of the four turbines at a design flow of 4 times 67.5 m³/s.

 

As to the determination the energy losses on the distribution pipe of the prototype, it should only be mentioned in this context that the local head loss coefficient, z , is equal to the difference of the kinetic share of loss between the two measuring planes and the net pressure difference (after deduction of plexiglass friction) on the model. The absolute value of this difference is so small (a few percent of the measured pressure differences), however, that despite the maximum possible measuring accuracy applied it was severely affected by the natural pressure variations as reflected in the relatively large scattering of the results. For this reason three (branch 1) and four measuring series (branches 2, 3, and 4) were run. Such a series involved the simultaneous measurement of flow and pressure difference between the two measuring cross sections for model flows of between 4 x 20 l/s and 4 x 75 l/s. One flow increment of 4 x 5 l/s yielded 12 points for the flow - pressure difference function. These points were then used to determine - as described above - a curve function using a mathematical balancing method and deducting plexiglass friction. The total losses on the prototype are composed of the local head losses as measured on the model and the calculated friction losses for the steel pipe.

 

The table below is a list of the results of the measurements (local head loss coefficient z with the resulting local head loss h_Form) and the analytical results (frictional head loss h_R, total head loss h_v), with measuring cross section B being used for reference in accordance with the provisions of the Contract.

 

 

6.2 Notes

6.2.1 Results from Branch 1

Branch 1 gives a mean local head loss of 0.249m. The mean total head loss is 0.292m.

6.2.2 Results from Branch 2 and Branch 3

The local head loss coefficients (z) determined from the four measuring series give negative values for branches 2 and 3. Hence, negative quantities also result for the local head losses. This fact, which may at first appear impossible, can be explained as follows:

It is known from the relevant literature [2] and [6] that there is a certain interaction among the branches connected in series in a distribution system: The total loss incurred in the branches connected in series is not equal to the sum of the losses occurring in the individual branches. In fact, the total loss decreases as a function of the distances between the junctions. The shorter the spaces, the lower the losses, and the reduction involved can be substantial. This phenomenon is actually a result of the asymmentry of the velocity profile behind the junction. The "boundary layer material" flowing at a lower velocity is largely "absorbed" by the first branch. This causes the core flow in the continuing pipe to be shifted towards the junction of the second branch. In this way, flow towards the downstream branch is much more favourable. Due to the shape of the velocity profile, the energy content of this core flow is larger than its mean value. If it is mainly this core flow that reaches the junction, then negative loss coefficients are no longer surprising.

 

The mean value of local head loss resulting from the four measuring series for the 2nd branch is -0.055. With allowance being made for the friction losses of the steel pipeline, a mean value of 0.011m is obtained for the total loss.

 

The mean value of local head loss resulting from the four measuring series for the 3rd branch is -0.074m. With allowance being made for the friction losses of the steel pipeline, a mean value of 0.031m is obtained for the total loss.

6.2.3 Results from Branch 4

The mean value of local head loss resulting from the four measuirng series for the 4th branch is 0.085m. With allowance being made for the friction losses in the steel pipeline, a mean value of 0.253m is obtained for the total loss.

 

Summary

The Kapichira power station will be equipped with four turbines for energy generation. Water supply to the turbines is through a steel-lined power tunnel. The steel lining covers a straight section followed by a bend and the 56m long distribution system. Approach to the manifold is through a 7.8m diameter pipe branching to four penstocks of 3.7m diameter each.

 

This Report refers to the calculation of the energy loss incurred in the four outlet legs of the manifold.The studies were conducted on a plexiglass model constructed to scale 1:26.43. The model reproduced the straight supply line and the four outlet legs. Appropriate pipe sections were added upstream of the entrance cross section and downstream of the branches of the manifold in order to accomplish well-developed turbulent flow conditions for the pressure measurements.

 

By way of summary, it can be stated that the distribution pipe upstream of the turbines of Kapichira power station shows favourable magnitudes of energy loss, which allow the conclusion that acceptance of the shape of the manifold by the water current is good. Visual inspection using dye injections gave no perceptible separation phenomena.

 

References

 

[1]    HARB V. Modellversuch und hydraulische Probleme der Verteilrohrleitung; Seminar AK Konstruktiver Wasserbau 1988, TU Graz

[2]    CHRIST A., ALLMEN W.v. Strömungstechnische Erkenntnisse über Abzweigstücke von Verteil-rohrleitungen. Escherwyss Mitteilungen 1/2 1980

[3]    KOBUS H. Wasserbauliches Versuchswesen; Mitteilungsheft Nr. 4; Deutscher Verband für Wasserwirtsch. 1978

[4]    KRESNIK E.: Kunststoffe im wasserbaulichen Versuchswesen und deren rauhig-keitsmäßige Erfassung; TU-Graz, 1965

[5]    MÜLLER W., STRATTMANN H. Rohrreibungsverluste in Druckleitungen von Wasserkraftanlagen. Technische Rundschau Sulzer 3/1964

[6]    MÜLLER W., STRATTMANN H. Druckverluste in Abzweigrohren Verteilleitungen; Technische Rundschau Sulzer 4/-1971

[7]    PETERMANN F. Der Verlust in schiefwinkeligen Rohrverzweigungen; Mitteilungen des hydraulischen Institutes der TU München, 1929