Modeling turbine kaplan in heliciel guide vanes draft tube turbine
Tutorial example small hydropower plant design 3/3:
lChoice sections, design draft tube

Chapter Summary hydroelectric turbines::

 

We have seen that there are two basic rules that justify the choice of sections:" Minimize pressure losses and minimize the cost of parts by concentrating energy" and these 2 rules, respectively lead to an increase and a decrease of the dimensions.

Concentrer l'energie dans la zone technique précieuse permet de diminuer les couts de materiel

We have seen that the energy losses are important if:
  • The fluid velocity is high and the roughness is important
  • Speed ​​variation due to the change of section is important and sudden
  • the change of direction is important and sudden

attention aux vitesses élevées dans les conduitesAttention aux changements de sections brusquesAttention aux changements de directions brusques

and that these energy losses will therefore be minimal if:
  • the speed is low and surfaces are smooth
  • the speed variation due to a change in section is gradual and low
  • the change of direction is low and progressive

vitesse lente = faible pertes de chargesVariation de section progressive = faible pertes de chargesChangement de direction progressif = faibles pertes de charge

 

 

Zone d'adduction de la turbine

The Adduction Area leads the flow to the guide vanes or stator. The sections will be the largest possible, to avoid losses, and surface vortex created by the fluid aceleration. In installations such kaplan, this zone terminates in a volute,which tangentially directs the fluid in the guide vanes, so as to reduce the deflection angle and so the pressure drops caused by the passage of the vanes. The role of this area is to reduce the section as gradually as possible, to the section of the organs "precious" in order to focus energy and reduce manufacturing costs. The losses in the converging cones are less sensitive to the angle of the cone, than divergent, and accept reasonable values ​​to large angles. For example, the coefficient of pressure loss of a converging cone of 30 degrees is about 0.1, whereas a divergent cone of the same angle will have a coefficient of 2.5! This partly explains, why the area of adduction, admits reductions sections, more abrupt than the draft tube part. The calculation of the sections of this area presents no difficulties: We will use mecaflux to assess and validate the sections of this part, with regard the pressure losses:

 

We will evaluate for example, the pressure loss of a convergent cone from 3 meters to 1.9 meters at 30 degrees, for a rate of 8m3/sec:

calcul de perte de charge d'un cone convergent

We get a head loss of 25 mm for the inlet cone.

 

 

We have calculated the loss of the stator vanes or guide in the previous chapter about the calculation of stator vanes or guide: We got 0.7 meter pressure loss in the guide vanes stator. At the beginning of the previous chapter (calculation of stator vanes or guide) we calculated our propeller with Heliciel introducing a tangential flow of 4.4 rad / sec. In the results area, we have access to the pressure difference generated between the upstream and downstream of the propeller. This pressure difference gives us the "pressure loss" generated by the turbine

perte charge turbine

(delta pressure upstream downstream turbine)

What gives with the pressure value measured in Heliciel: 20339 =(we will remember for simplicity that 1 bar = 10 meters of water so 0.2 bars = 2 meters of head losses)
So we will estimate the height of load required for the crossing of the turbine to the operating point calculated: 2 meters
Total pressure loss consumed by the guide vanes and turbine Area = 0.7 2 = 2.7 meters
Gross height available is 4 meters, we could generate more tangential flow with our distributor (This is an information for optimization and adjustment of the vanes of the distributor)
Before defining the vacuum (diffuser, draft tube),we must take into account the relationship between volume, speed and flow rate for an incompressible fluid. We have a volume flow 12 m3/sec that through our system. Due to the compressibility of our fluid,the inlet flow rate is identical to the output flow.We can even establish that the section is related to the speed by law::
  • axial velocity(m/sec) = rate of flow (m3/sec) / section (m²)
To avoid uncontrolled changes speeds which will translate by losses, it is important to check the sections according to the desired speed or estimated in the different parts of the system.

 

In the results area of software HELICIEL, select the tab "fluid velocities". We can see the axial velocity downstream (output propeller). The relation: axial velocity(m/sec) = rate of flow (m3/sec) / section (m²), therefore gives the section that should be our conduct at turbine outlet to accompany speed change caused by the turbine, with no additional disturbance:

Section output turbine:

  • axial velocity(m/sec) = rate of flow (m3/sec) / section (m²)
  • => section (m²) = Débit (m3/sec) /Vitesse axiale(m/sec)

 

We saw in Chapter turbine design, that the kinetic energy can not be fully captured by a propeller as this would completely stop the flow at the output and to have an infinite volume of fluid stokage, at the outlet point of the turbine..it is possible to expand the sections to approach a very low speed. It is 40% of the kinetic energy of axial velocity at the turbine outlet. This speed energy can be recovered and converted into local depression at the outlet of the turbine, with a variation of regular section.

 draft tube

If a vacuum is generated at the turbine outlet, this will result (depending on Bernoulli's Theorem) to increase the rate of passage of turbine and generating a power gain. So we will create a diverging conical vacuum, which will locate a depression, to turbine output by varying its section(Thus the fluid velocity)between its input and outlet. If this speed change is too abrupt, we will create a loss of energy by turbulence and the draft tube will not be very effective. The optimum cone angle generating the speed variation with minimal losses is approximately 6°, but for reasons of economy of material and space, cones of draft tubes are about 12 degrees.
The calculation of the depression created by the draft tube can be done with the application of Bernoulli mecaflux software:

depression aspirateur turbine

Enter Data::

vitesse axiale helice

 

Nous avons estimé ici que le diffuseur pourra réaliser une variation de vitesse de 2 m/sec à 0.5 m/sec.We estimated that ledraft tube can realize speed variation, from 2 m / sec to 0.5 m / sec. This generates a pressure at the inlet of the draft tube, of 98125, so a depression :98125-100000 =1875 pascals:

depression aspirateur turbine

With héliciel we resume our propeller to evaluate the gain in power caused by the depression located downstream of the propeller,we use the parameter menu / simulate depression located downstreamand by enter the value of 1875 Pascals:

depression sortie turbine

We launch a search for Optimum speed to rebuild a propeller at the optimum operating point in these new conditions:

depression helice

 

The Optimum speed and power is increased by the suction parameter:

vitesse aspiration

Depression is used by heliciel to increase the through speed following Bernoulli, this allows to quickly assess and temporarily gain power, but a new study with the modified flow through this depression, should be made ​​to adjust the actual efficiency ...

We conclude this small tutorial here, but it is obvious that we could further optimize our system, including the increase of tangential introduction to our Central are perfectly suited to the site.

 

Chapter Summary hydroelectric turbines::