Hydrodynamic efficiency and optimization on the project · PDF fileHydrodynamic efficiency and optimization on the project of hydroelectric power plants ... where the valve is installed,

Hydrodynamic efficiency and optimization on the project of hydroelectric power plants

A. Pereira H. M. Ramos (scientific supervisor)

ABSTRACT

This study includes theoretical research and numerical and experimental analysis in components of

hydroelectric power plants of middle and high heads. The theoretical research focuses on geometric

and on hydraulic behavior characteristics of fittings, hydromechanical equipment, as flow control

valves and reaction turbines, and on the hydraulic structure of a water intake. The numerical analyses

by the use of a CFD numerical model (Computational Fluid Dynamics), intend to analyze the

hydrodynamic phenomena of the flow on those components, and set to the same components the

geometry and the operating conditions, that enable more favorable hydraulic and energy efficiencies.

The purpose of experimental analysis is the collection of results, in order to compare those results with

the numerical results, to assess their accuracy level and validate the CFD model. By means of a CFD

model, flow hydrodynamic analysis are made on different geometric configurations of each

component, for different boundary layer conditions of the flow field on the several components, and

different operating conditions of those components. The results obtained for the different simulated

conditions are compared, that is a sensitivity analysis is made that allows determining the effects of

the variations on the boundary geometry, and on the boundary and operation conditions, on the

resulting flow field. Depending on the numerical description obtained for the flow field on each

simulation, on the sensitivity analysis results, and on the objectives to attain in terms of hydraulic and

energetic efficiency, geometries and operating conditions for their components are set, that conduct to

a performance adjusted to the required efficiency. In laboratory the hydraulic behavior of the flow in a

pump as turbine is analyzed for several volume flow values, and values of head and rotational velocity

of the pump as turbine are collected. Flow velocity profiles are collected with a UDV. The experimental

results are compared with the results of numerical analysis made on a geometric model that

represents the laboratory installation, for the same boundary and operating conditions of the pump as

turbine.

Keywords: hydro power plants, flow hydrodynamic, CFD models, experimental analyses.

1 INTRODUÇÂO

Nowadays, the main objective of European Union member states is to achieve a significant growth in

the development of new capacity and in upgrading capacity of existing hydroelectric power plants

throughout Europe. The growing interest in electrical energy production from hydropower is the

motivation for this study. It’s intended to analyze the flow hydrodynamic on of fittings, hydromechanical

equipment, as flow control valves and reaction turbines, and on the hydraulic structure of a water

intake. With the objective of determining, for the several components to analyze, the optimal geometric

configuration and their optimal operating conditions, analysis of flow hydrodynamic are conducted on

different geometric configurations of each component, for different boundary layer conditions of the

flow field in the several components and different operating conditions, by using a CFD numerical

model. To better understand the hydrodynamic flow phenomenas within each component, sensitivity

analysis are conducted, that allow to determine the effect that the variations on geometric

configuration, boundary layer conditions of the flow field, and on operating conditions, has on the

intensity of those phenomenas, and thus on the hydraulic performance of those components.

With the purpose of determine geometric configurations and their operating conditions that lead to

more favorable hydraulic and energetic efficiencies, optimization processes supported by sensitivity

analyses are made. The analysis to be made should be guided by a set of objectives to achieve, in

relation to the hydraulic and energetic efficiencies, and by the objective of ensure steady flow

conditions, in order to determine the geometric configurations that fulfill those objectives. In order to

assess the accuracy level of the numerical results to obtain, and thereby validate the used CFD

model, experimental results are taken. Accordingly, the hydraulic flow behavior through a pump as

turbine is analyzed at laboratory, for several discharge values, and comparisons are established

between experimental and numerical data. A geometric model that represents the laboratory facility is

built, on which numerical analysis are performed, for the same boundary layer conditions of the flow

field in the laboratory facility, and for the same pump as turbine operating conditions. All the analyses

are done considering steady flow under pressure.

2 STATE OF THE ART

2.1 Tangential stresses, boundary layer and energy dissipation

The viscosity in the flow gives rise to resistance forces that act on the boundary surfaces, thus

tangential stresses which lead to energy dissipation are formed. In a flow of a real fluid in a conduit the

fluid adheres to the conduit wall, thus there is no direct sliding of the fluid on the wall. The boundary

layer is the region adjacent to the wall where the fluid adheres to the wall, because in this region the

viscous effects are more significant. On the boundary layer the relative velocity of the real fluid is null,

which implies the existence of a strong velocity gradient normal to the wall. Considering that the

tangential stress is proportional to the velocity gradient normal to the flow direction, there are

tangential stresses on the wall surface with energy dissipation.

2.1.1 Boundary layer separation

For retarded flows (whose stream lines are divergent due to the geometry) the boundary layer

thickness tends to grow up rapidly to downstream, and the boundary layer separation phenomena can

occur. In this flow type occurs transformation of kinetic energy into pressure energy, thus the velocity

the velocity becomes null at a point where the flow separates from the wall. Further downstream, the

flow direction adjacent to the solid surface is reversed. The boundary layer separation is caused by

the velocity reduction at the boundary layer combined with the positive pressure gradient, which

supports the boundary layer effect of velocity reduction. As a result of reverse flow, large irregular

vortices are formed in which much energy is dissipated and the region of disturbed fluid extends to

downstream.

2.1.2 Local head loss through a abrupt enlargement

The local head loss value ΔH is determined by an expression of type (2.1).

(2.1)

where K is a coefficient which depends on singularity geometry, on Reynolds number, and in some

cases (as the ramifications) on certain flow conditions (-), U is the velocity at a reference flow section

(m/s), and g is the acceleration of gravity (9.8m/s2). In the case of an abrupt enlargement, the head

losses are fundamentally due to separation caused by a positive pressure gradient resulting from

velocity reduction.

By means of a few simplifying assumptions and applying the linear

moment equation to the control volume between sections 1 and 2

(Figure 2.1), the equation (2.2) to estimate the local head loss in this

type of singularity is deduced.

(2.2)

where u1 is the flow velocity at section (1) (m/s) (Figure 2.1), and u2 is the flow velocity at section (2)

(m/s) (Figure 2.1). To obtain ΔH from an expression of type (2.1), the conservation of mass

is considered and applied to equation (2.2), thus the equation (2.3) is obtained.

(2.3)

If the divergent angle is sufficiently small the boundary layer separation may not occur, in divergent

conduits. The boundary layer separation causes disturbances, energy losses and vibrations on liquids

conveyance. Thus, hydrodynamic shapes that reduce the tendency to the occurrence of these

phenomena should be prescribed for boundaries.

2.2 Flow control valves

The flow control valves have the function to regulate the steady flow in an hydraulic installation. These

valves should control the discharge without causing transients, excessive cavitation, or head losses,

and should operate under all expected flow conditions (TULLIS, 1989). During the opening and

closure operations the discharge should be controlled, in order to protect the installation against

transient pressure variations (ALMEIDA E MARTINS, 1999). The flow control valves are classified,

depending on the type of movement of the obturator shaft, on valves with linear movement and on

valves with obturator angular movement.

2.2.1 Effect of the valve in the flow

The valves introduce resistance to the flow and cause local energy dissipation. In general, at the zone

of the valves there is a section of contracted flow, which causes upstream the convergence of the

stream lines and downstream causes their divergence. From the convergence of the streamlines the

result is the velocity increase, which in turn induces an increase of turbulence intensity and head

losses. The divergence can lead to flow separation. The local head losses through a valve depend on

geometric valve characteristics and on the obturator position that is on valve opening degree. The

head loss through valve can be determined by the equation (2.4) and represents the resistance

imposed to the flow for any valve opening degree depending on Kv value.

(2.4)

where ΔHV is the hydraulic head loss caused by the valve (m), KV is the valve head loss coefficient (-),

and U0 is the average velocity at a reference section (m/s).

2.2.2 Valve head loss coefficient

The valve head loss coefficient KV depends on: (1) valve obturator position, (2) valve dimensions and

geometry, (3) characteristics of the hydraulic system where the valve is installed, and (4) flow

Reynolds number. For sufficiently high Re values, that occur in most hydraulic systems, the Kv value

becomes practically independent of Reynolds number. The Kv values vary between a minimum value

that corresponds to the fully opened position, and a very high value, theoretically infinite, that

Figure 2.1: Abrupt enlargement (MASSEY, 2006)

corresponds to the fully closed valve position. The cavitation occurrence in valves may change

significantly the estimated value for Kv.

2.2.3 Discharge coefficient

The discharge Q0 through a valve, expressed by the valve discharge coefficient, may be determined

by the equation (2.5), deduced from the equation (2.4).

(2.5)

where is the valve discharge coefficient (-), and AC is the reference section area or

conduit, where the valve is installed, section area (m2).

The coefficient Cd is function of valve type and their obturator position. The variation of Cd with the

obturator position expresses the hydraulic characteristic of valve. The value of these coefficient is

comprised between zero, for the fully closed valve position, and the value that corresponds

to the fully opened valve position (ALMEIDA E MARTINS, 1999).

2.2.4 Cavitation in valves

The stream lines convergence at upstream of the contracted flow section induces a pressure

reduction. At downstream of the contracted flow section, the velocity reduction and the pressure

increase causes a separated flow zone, where vortices of reduced size are formed. The pressure

reduction at upstream combined with the surrounding pressure reduction, generated at the cores of

vortices, creates favorable conditions for the formation of vapor bubbles, which collapse downstream

in result of pressure increase that occurs there. Extreme cavitation conditions may result in a

considerable reduction of the hydraulic system discharge capacity, and in a limitation or blocking of

the discharge (blocking cavitation). Too intense local stresses resulting from gas bubbles collapse,

may have as effect the erosion of boundaries and of hydraulic devices surfaces, local pressure

fluctuations, noise caused by the acoustic waves associated with gas bubbles collapse, and

transmission of vibrations to the walls and to the conduits supports, leading to unsatisfactory operation

conditions and to partial destruction of hydraulic system components.

2.3 Water intake

In hydroelectric power plants of middle and high heads, the water intakes divert the turbine discharge

in free surface or pressure flow to a circuit of conveyance by gravity structures, in channel, conduit, or

gallery, that is constructed parallel to the water course and ends in a forebay and/or continues to a

penstock where the flow is conducted to the hydroelectric power plant. The racks, installed at the

water intake entrance has the function of avoid the entrance of debris in the hydraulic circuit, which

cause the deterioration of the hydromechanic and electromechanic equipment, as valves and turbines,

performance. The maximum flow velocity value through the rack, has influence in rack clogging, and

therefore on head losses through the rack and it shouldn’t exceed 0,80 a 1,00 m/s, in order to avoid

the drag of floating debris to the rack (ESHA, 2004). The vortex formation depends on submergence,

orientation and geometry of water intake, and on the approach flow velocity. Thus, ensure adequate

water intake submergence and avoid velocity and geometries that may cause flow separation, are the

simpler ways to avoid vorticity (ASCE, 1995). The vortex formation has consequences that leads to

loss of hydraulic efficiency, in particular it originates non uniform flow conditions, drag solid debris to

the water intake, promotes the air entrance which leads to adverse operating conditions for the

hydraulic turbomachines. These conditions are vibration, cavitation and differential pressures that may

induce release of trapped air resulting in bullous flow conditions and high overpressures, which in turn

may lead to penstock collapse.

2.4 Hydraulic turbines

The hydraulic turbines extract total mechanical energy from the flow, and convert this energy on

rotational mechanical energy through the rotor, that transfers it to the axis, which in turn is connected

to a generator which transforms this energy on electric energy. The turbines are classified on action or

impulse turbines, when the rotor is actuated by the flow at atmospheric pressure, and on reaction

turbines when the rotor is actuated by the pressure flow force. The reaction turbines are also classified

on radial, mixed or axial flow turbines depending on the main direction of the flow relatively to the

rotor. In rotodynamic pumps the impeller transfers to the flow total mechanical energy that it receives,

on their axis, from an external electric engine, which allows to move liquids from one place or level to

another. There are reversible pumps, named pump as turbines, in which when the pumped water,

intentionally or not, starts to flow in reverse that is from the exit conduit for the suction conduit, the

impeller also starts to rotate in reverse, and thus the pump operates as a turbine.

2.4.1 Action of the flow on the rotor

In the direction tangential to the reaction turbine rotor, the liquid has a velocity component and

therefore a angular momentum component, whose time rate of change corresponds to the torque

exerted on the rotor by the fluid. The flow angular momentum is reduced, thus the energy is

transferred from the fluid to the rotor and therefore to the axis. The torque available on a turbine axis is

less than the torque value exerted on the rotor by the fluid, as a result of friction losses in bearings and

between the fluid and the rotor, then the power transferred by the flow to the turbine is greater than the

available power on the turbine axis. The turbine efficiency is equal to the relation between the

available power on the turbine axis and the power transferred by the flow to the turbine. The available

torque on the turbine axis and the corresponding

power only depends on velocity conditions at the

rotor entrance and exit, being independent of

blades configuration. The shocks occurrence in the

flow within the rotor depends on the blades

configuration, thus head losses, available head and

efficiency also depends on that configuration. The

rotor blades are designed so that, for the optimal

turbine operating conditions, the relative velocity

has through the rotor the direction given by the

blades. Thus, for ideal conditions the flow occurs

without shocks. In the velocity triangle at entrance (Figure 2.2) the α1 angle, which define the absolute

flow velocity direction is determined by the guide vanes opening. The flow entrance without shocks

may be achieved for a wide range of blades velocities and discharges by the adjustment of guide

vanes and thus of α1 angle. However, for each α1 angle value there is only one configuration of the

velocity triangle at entrance which allows ideal flow conditions. Not all the fluid energy is extracted by

the turbine rotor, the remaining energy is mainly in the form of kinetic energy. Thus to obtain high

efficiencies the turbine rotor should be designed so that the flow kinetic energy at the rotor exit is

reduced. For a particular discharge value, the minimum value of v2 is obtained when v2 is

Figure 2.2: Velocity triangles at entrance and exit of a Francis turbine rotor (MASSEY, 2006).

perpendicular to u2 (Figure 2.2), that is when at the exit the tangential absolute velocity component vw2

becomes zero. A zero value or near zero for the component vw2 is considered as a basic requirement

on the design of turbine rotors, thus their configuration must allow the angle α2 to be equal or near to

90° at the optimal performance point.

2.4.2 Specific rotation number for pumps and turbines

The parameter specific rotation number of a turbine ns is expressed, as the rotation velocity n, in rpm,

and is determined by the equation (2.6).

2.6

To define ns the available head corresponding to the optimal efficiency and the maximum power that is

obtained for this head, are considered (RAMOS, 1995 e 2000 e QUINTELA, 2005). The ns value

obtained for a set of values of n P e H, is associated with the turbomachine geometric shape which

satisfies the operation conditions expressed by this set of values. The rotor shape depends on their

specific velocity, and the turbine runners are classified on: (1) slow, (2) medium, (3) high and (4) very

high speed runners, depending on the value of specific velocity. With the head reduction and the

discharge increase, the ns value increases, and the rotor shape changes from axial to radial taking the

mixed shape for ns intermediate values. The specific rotation number of a pump ns (rpm) with

rotational velocity n, that pumps the discharge Q to a total pump head H, is obtained by the equation

(2.7).

2.7

To specify the specific rotation number of a pump ns the values of Q(m3/s) and H (m) corresponding to

the optimal efficiency point are considered. The ns value obtained for a set of values of n Q e H, that

expresses the pump operating conditions, is associated with the impeller shape which satisfies these

conditions.

2.4.3 Cavitation in turbines

At the rotor exit section, low pressure section, regions where the pressure is reduced to levels

considerably below atmospheric pressure may occur, leading to the cavitation phenomena (MASSEY,

2006 e PEREIRA E RAMOS, 2010). The vapour bubbles colapse causes high local pressures exerted

on the adjacent walls, which are subject to erosion and abrasion. The material suffers a progressive

and local weakening by fatigue and corrosion, thus the surface becomes chequer and pitted. The

cavitation has other undesirable effects as noise, vibrations, efficiency reduction, deviation of flow

conditions in relation to the design conditions, and changes in operating characteristics of

turbomachines in terms of head, power, and efficiency (RAMOS, 2000 e 2003 e MASSEY, 2006). The

higher the value of the flow velocity at the rotor exit section, the lower the pressure value that occurs

there, and thus more likely is the cavitation occurrence at the rotor exit section, which is an additional

reason for this velocity to be the lowest possible.

2.5 Computacional model. Numerical Methods

The fundamental physical principals of mass conservation, linear momentum conservation, and

energy conservation, govern the physical aspects of fluid flows, and maybe expresses by

mathematical equations. The CFD model allows to resolve those equations and distribute the results

on space and/or on time, thus obtaining a complete numerical description of the flow field. The utilized

CFD model solves the Navier-Stokes equations, which are formulations of the conservation laws of

mass, linear momentum, and energy for the fluid flows. For the calculation of turbulent flows the model

uses the transport equations for the turbulent kinetic energy k and its dissipation rate ε, which

constitutes the so-called k-ε model.

2.5.1 Computational mesh, boundary conditions, solution convergence and precision

The utilized CFD model has several parameters which governs their technique to obtain the numerical

solution and allows the user to adjust the values of those parameters, so that it’s important to know

their meaning. The computational mesh of the utilized CFD model, used as a support to resolve the

equations, is rectangular in the whole computational domain, and the sides of the mesh cells are

orthogonal to the axis of cartesian coordinate system. The utilized CFD model includes an automatic

procedure to construct the initial calculation mesh, which can be posteriorly refined during the

calculation, governed by parameters whose values are defined by the user. The initial calculation

mesh is constructed before calculation, therefore it doesn’t allow the correct flow field resolution. Thus,

this mesh can be refined in certain moments during the calculation, in accordance with the solution

spatial gradients. In regions with lower gradients the cells are merged, while in regions of higher

gradients are split. The moments during the calculation to refine the computational mesh are specified

either automatically or manually by the user (MENTOR GRAPHICS, 2008). The boundary conditions

for internal flows, have the objective of specify the values for the physical variables that determine the

flow field, at the boundaries of entrance and exiting of the flow in the geometric models. In simulations,

boundary conditions of type pressure opening, that allows to specify pressure values, and of type flow

opening, that allows to specify discharge values, were assigned to all the boundaries of entrance and

exiting of the flow in the geometric models. The utilized CFD model contains internal criteria to finish

the simulation process and allows the user to specify their own criteria, named goals, and conditions

to finish the calculation. To specify this criterion one or more physical parameters, that are relevant to

the simulation, are selected (each physical parameter corresponds to one criterion), and it is

considered that the solution is only obtained when the convergence of all specified criteria occurs.

Additionally, the dispersion and the analyses interval are determined. The dispersion is the difference

between the maximum and the minimum values of the parameter associated with each criterion, and

the analyses interval is the interval over which that difference is determined. This interval is defined from

the last iteration to previous iterations, and is the same for all the goals criteria specified. Once the

dispersion obtained during the calculation becomes less than the dispersion value specified, by the

user or by the CFD model, it is considered that their goal criterion has converged. The solution

precision depends on the adequacy of the computational mesh to the geometric model regions, where

the flow has nonlinear behavior.

3 COMPUTATIONAL MODELING RESULTS ANALYSIS

3.1 Fittings. Abrupt and soft enlargement

This study analysis the flow hydrodynamics in fittings which connect conduits with straight axis. The

Figure 3.1 shows the velocity and static pressure distribution in planes that intersect the geometric

models and shows flow trajectories along the model.

Figure 3.1: Distribution of velocity (m/s) in longitudinal planes to the, (a) abrupt enlargement, and (d) soft enlargement. Distribution of velocity vectors (m/s) and distribution of static pressure (Pa) in longitudinal planes to the, (b) abrupt

enlargement, and (e) soft enlargement. Flow trajectories (m/s) along the, (c) abrupt enlargement, and (f) soft enlargement.

The Figure 3.1 presents a positive pressure gradient in the flow direction, combined with a velocity

reduction, more significant along the conduit walls downstream the enlargement section. This

pressure and velocity variation is the cause of flow separation, visible on Figures 3.1(c) e (f), resulting

in the energy dissipation in enlargement. In flow separation zone, turbulent vortices are formed, as

observed on Figures 3.1(c) e (f), with strong dissipative effect.

3.2 Valves. Ball Valve

This study also proceeds to the flow hydrodynamic analysis in flow control valves. The H e VK

values, presented in Table 3.1, were obtained for different opening angles and they allow the draw of

Chart 3.1, that expresses the ball valve local head loss coefficient variation, with their opening angle.

Table 3.1: H e VK values, obtained by the CFD model for different opening angles of the ball valve.

Ângulo de abertura da válvula esférica (°)

20 40 45 60 80 90

( )H m “1300,25” 24,28 11,13 2,46 0,48 0,01

( )VK 180,80 13,62 8,16 3,17 0,84 0,02

Chart 3.1: Ball valve local head loss coefficient variation with their opening angle (°).

In Figure 3.2 the contraction of the flow section is shown upstream the obturator and at their exit.

Upstream, this contraction causes within the obturator the flow trajectories divergence and therefore

an increase of turbulence intensity. At downstream of the obturator, the flow trajectories divergence

occurs (Figure 3.2(b)) combined with a pressure increase, which leads to flow separation.

Figure 3.2: Vector velocity distribution (m/s) and static pressure distribution (Pa) in a longitudinal plane to the ball valve for a 40° opening angle. (b) Flow trajectories (m/s) along the ball valve for a 40° opening angle

The Figure 3.3(a) shows in a longitudinal plane to the ball valve for a 20° opening angle the water

vapour volume fraction distribution, which is defined as the quotient between the water and other

(a) (b)

0,01

0,10

1,00

10,00

100,00

1000,00

0 20 40 60 80 100

Co

eficie

nte

de p

erd

a d

e

carg

a, K

v (-)

Ângulo de abertura (⁰)

(a) (b)

(d)

(c)

(e) (f)

dissolved gases vapour volume and the water volume, in the gas – water mixture. The Figure 3.3(b)

presents in the same plane and for the same opening angle the density distribution of the flowing fluid.

At Figure 3.3 water vapor volume fraction values approximate to the unit value and gas – water

mixture density values significantly lower than the water density values, are verified downstream the

obturator, which proves the presence of vapour bubbles formed as a result of low pressure values that

occur there Figure 3.3(a). Thus for the ball valve and for a 20° opening angle, cavitation occurs, once

there are vapour bubbles downstream the obturator. As the opening angle increases, the flow

separation zone downstream the obturator becomes less significant, thus the pressure reduction

decreases and the flow conditions are less propitious to the formation of vapour bubbles, therefore the

cavitation intensity decreases or fails to occur.

Figure 3.3: Water vapour volume fraction distribution (-) in a longitudinal plane to the ball valve for a 20° opening angle. (b) Density or volumic mass distribution (kg/m

3) in a longitudinal plane to the ball valve for a 20° opening angle.

3.3 Water intake

The water intake is one of the hydraulic structures which is part of hydroelectric power plants of middle

and high heads, thus the hydrodynamic flow analysis in water intakes is considered in this study. In

this analysis, an optimization of the geometric shape of the water intake is performed, by means of the

CFD model. Thus, a first geometric model of the water intake is constructed, here designated as

original water intake, on which same changes are made in order to increase their hydraulic efficiency.

The geometric model, here designated as redesigned water intake, is the result from these changes.

Comparing the Figure 3.4(a) with the Figure 3.5(a) it follows that in the case of original water intake

occurs flow separation below their cover (visible near point A of the Figure 3.4(a)), and that in the case

of redesigned water intake the flow separation ceases to occur. Within the flow separation zone

turbulent vortices that lead to energy dissipation and to entrainment of air into the hydraulic circuit of

the hydroelectric power plant are formed, reducing the turbine efficiency.

Figure 3.4: Original water intake. (a) Module velocity distribution (m/s) and vector velocity distribution (m/s) in a longitudinal plane to the geometric model. (b) Flow trajectories (m/s) along the geometric model. (c) Static pressure

distribution (Pa) in a longitudinal plane to the geometric model.

Based on the analysis of Figures 3.4 (a) and (b) and 3.5 (a) and (b), it follows that in the case of the

redesigned water intake the flow velocity through the trash rack is lower, and the flow velocity

distribution along the water intake is more uniform. As can be observed in Figure 3.5(b), the flow along

the redesigned water intake is gradually accelerated, which allows to reduce vorticity, flow turbulence

intensity and head losses, and thus increase the turbine efficiency.

(c) (a) (b)

A

(a) (b)

Figure 3.5: Redesigned water intake. (a) Module velocity distribution (m/s) and vector velocity distribution (m/s) in a longitudinal plane to the geometric model. (b) Flow trajectories (m/s) along the geometric model. (c) Static pressure

distribution (Pa) in a longitudinal plane to the geometric model.

The Figures 3.4(c) e 3.5(c) show the trash rack local head loss and the total head loss along the water

intake. Comparing both figures the conclusion is that the trash rack local head loss is lower in the case

of redesigned water intake, and that, in the same case, the total head decrease along the water intake

is more gradual. The variations, in relation to the original water intake, in the static pressure

distribution, obtained in the case of the redesigned water intake are improvements in the water intake

hydraulic efficiency.

3.4 Hydraulic turbines

This study includes the flow hydrodynamic analysis in radial and mixed flow Francis hydraulic turbines

rotors and in propeller hydraulic turbines rotors. Here only the results related to the mixed flow Francis

hydraulic turbines and to the 4, 5, e 6 simulation scenarios are shown. In relation to the operation

conditions, a 60% guide vane open degree was considered for the three scenarios, and a rotation

velocity of 500, 1000, e 2000 rpm was considered respectively for the scenarios 4, 5, e 6. The Figure

3.6 presents that from the inlet flow section until the spiral case, inclusive, the flow is irrotational, which

is confirmed taking into account that in this model region occurs a velocity increase, to which

corresponds a static pressure decrease, as observed in Figures 3.6 and 3.9.

Figure 3.6: Module velocity distribution (m/s) and vector velocity distribution (m/s) in

longitudinal planes to the geometric model. (a) Scenario 4, (b) scenario 6, and (c)

scenario 5.

Figure 3.7: Module velocity distribution (m/s) and vector velocity distribution (m/s) in transversal planes to the diffuser. (a) Scenario

4, (b) scenario 5, and (c) scenario 6.

The flow force actuates the rotor, and in turn the rotor rotation velocity and the shape of their blades

confer to the flow a rotational behavior. In the diffuser the axial flow velocity is low while the tangential

velocity is high, resulting in a velocity distribution with reduced values near the diffuser axis, which

increase towards their walls, as observed in Figures 3.6 and 3.7.

(a) (b)

(c) (c) (a) (b)

(a) (b) (c)

Figure 3.8: Flow trajectories (m/s) along the geometric model. (a) Scenario 4, (b) scenario 6, and (c) scenario 5.

Figure 3.9: Static pressure distribution (Pa) in longitudinal planes to the geometric model. (a) Scenário

4, (b) scenario 6, and (c) scenario 5.

The turbulent vortex which is formed at the rotor exit is visible in Figure 3.8. In result of the rotational

behavior of this vortex the flow reaches the diffuser walls with high tangential velocity, as the flow

trajectories show, which near the diffuser walls have higher velocity values than the flow trajectories

near their axis. The Figure 3.8 also presents the region in the passage of the diffuser to the tailrace

where the flow turbulence is high. The Figure 3.9 shows the net head related to the mixed flow Francis

hydraulic turbine. The lower values of the static pressure are verified in the core of the vortex, which is

formed downstream the rotor exit, as observed in Figure 3.9, indicating the occurrence of cavitation at

the diffuser initial stretch. In scenario 6, to which corresponds the greater rotational velocity of the

rotor, the vortex develops along a greater length of the diffuser, as observed in Figures 3.6 and 3.8,

and the pressure values that are verified in the core of scenario 6 vortex are even more reduced.

Thus, the tendency for cavitation occurrence inside the diffuser is greater in the case of scenario 6.

4 EXPERIMENTAL AND COMPUTATIONAL MODELING. ANALYSIS AND COMPARISON

OF RESULTS

At the end of this study the laboratory analysis of the flow hydrodynamic in a pump as turbine is made

for several operation conditions. The Figure 4.1 presents the hydraulic system mounted in the

laboratory.

Figure 4.1: Pump as turbine and hydraulic system mounted in the laboratory.

Figure 4.2: Hydraulic system sections to register velocity diagrams with Doppler.

For each experimental analysis a certain discharge value is regulated and the rotational velocity is

measured by means of a digital tachometer, the pressure values are registered in the transducers

located upstream and downstream the pump as turbine, respectively in the points A and B, indicated

in Figure 4.1, and velocity diagrams are collected in different flow sections (Figure 4.2) by means of a

Doppler equipment. With the support of the used CFD model the experimental analysis were

simulated computationally, under the same operating conditions in which the experimental analysis

were made. From the computational analysis the velocity variation is obtained in the stretch that

belongs to the section in which, for the corresponding experimental analysis, the velocity diagrams

were registered, and the flow field descriptive physical parameters distributions are obtained in planes

A

B

S4 S1

S2

S6

S3

S7

S4

(b)

S5

(a)

(a) (b)

(c)

(a) (b)

(c)

that intersect the pump as turbine geometric model. Therefore the comparison between the velocity

diagrams experimentally and computationally obtained is made. Here are compared the velocity

diagrams, concerning to only one experimental analysis, in which the velocity diagrams were collected

in section 5 (Figure 4.2). The physical parameters distributions are also only analyzed for that

experimental analysis, to which corresponds a discharge value of 2.8 l/s, rotational velocity of 850

rpm, pressure value in point A of 6.11 m, and in point B of 2.77m, that is a net head of 3,34m. The

comparison is represented on Chart 4.1. The S5 section of the diffuser conduit is crossed by a

turbulent vortex, whose core, where the lower values of the flow velocity through this section are

verified, is located in S5 section center zone. The Chart 4.1 shows that the both obtained velocity

diagrams represent this rotational flow behavior that is verified in section S5. The Charts 4.1(a) and

4.1(b) present the minimum velocity values approximately near the conduit axis, that are crescent from

the axis to their periphery, in accordance with the flow vorticity reduction in the same direction.

Chart 4.1: Experimental analysis 13. (a) Experimental and (b) computational velocity profiles (mm/s).

The velocity distribution is represented on Figure 4.3. The vortex formed in the diffuser conduit (Figure

4.3(b)) leads to a velocity differential between the axis and the periphery of the diffuser conduit. This

vortex may cause the blockage of the flow axial velocity, depending on the area of the diffuser conduit

transversal section that is occupied by the vortex core, where the lower velocity values are verified.

Figure 4.3: Experimental analysis 13. Module velocity distribution (m/s) and vector velocity distribution (m/s), (a) in a longitudinal plane to the geometric model, (b) in a transversal plane to the diffuser conduit, and (c) in a longitudinal

plane to the rotor.

The Figure 4.4(a) shows near the rotor periphery the maximum values of the tangential flow velocity

that are an effect of the rotational velocity of the rotor. The maximum values of the turbulent intensity

(Figure 4.4(b)) are also verified near the rotor periphery and are a result from the maximum values of

the tangential flow velocity that occurs there.

Figure 4.4: Experimental analysis 13. (a) Flow trajectories (m/s) along the geometric model. (b) Turbulent intensity distribution (%) in a longitudinal plane to the rotor. Static pressure distribution (Pa), (c) in a longitudinal plane to the

geometric model, (d) in a longitudinal plane to the rotor, and (e) in a transversal plane to the rotor.

Comparing the physical parameters distributions obtained computationally for the different

experimental analysis, the conclusion is that the net head (Figure 4.4(c)) for the pump as turbine

(a) (b) (c) (d) (e)

(a)

(b)

(c)

0

10

20

30

40

50

0 500 1000 1500 2000 2500 3000

L(m

m)

V(mm/s)

Perfil de velocidades - Experimental

(a)

0

10

20

30

40

50

0 500 1000 1500 2000 2500

L(m

m)

V(mm/s)

Perfil de Velocidades - CFD

(b)

decreases with the decreasing of the rotational velocity, thus the susceptibility to the cavitation

occurrence increases with the rotor rotational velocity.

5 CONCLUSIONS AND RECOMMENDATIONS

The flow hydrodynamic analysis supported by the used CFD model allows to obtain a numerical

description of the flow field, that is flow field descriptive physical parameters distributions by means of

multiple resources for processing results. The flow field numerical description allows to determine

pressure, velocity and discharge averaged values in different flow sections, to obtain those

parameters variation along linear stretches, and determine head losses, net head, pressure and other

flow characteristic parameters variation. Additionally, allows concluding about hydrodynamic

phenomena relative to the flow within each geometric model, for different configurations, namely

boundary layer separation, cavitation, vorticity, with recirculation and inversion of the flow, and

turbulence. The conclusions about each one of the analyzed phenomena may be obtained for different

flow boundary conditions, and different operating conditions of the geometric models. Therefore, it is

possible to perform sensitivity analysis that allow to establish comparisons, and thus conclude about

which are the operating conditions that allow for each boundary layer conditions set, the approach to

undisturbed flow conditions, and identify the best hydraulic and energetic efficiencies. The integration

between the theoretical investigation and the numerical analysis allowed to understand and conclude

about flow hydrodynamic phenomena within some components of hydroelectric power plants of middle

and high heads, about the effects of the geometric boundaries characteristics on the flow behavior,

and about the interaction between the flow at one component exit and the flow at the entrance of the

next component, along the geometric model. The flow hydrodynamic analysis is recommended in

others hydroelectric power plants components that were not analyzed in this study. The flow

hydrodynamic analysis for transient conditions is also recommended, in order to obtain a global

characterization of the dynamic flow behavior for hydroelectric power plants.

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ESHA. 2004. Guide on How to Develop a Small Hydropower Plant. ESHA.

KOTHANDARAMAN, C.P. e RUDRAMOORTHY, R. 2007. Fluid Mechanics and Machinery, 2ªedição.

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LENCASTRE, A. 1983. Hidráulica Geral. Hidroprojecto, Lisboa.

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RAMOS, H. 2000. Guidelines for Design of Small Hydropower Plants. Book published by WREAN

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