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Design of stay vanes and spiral casing - IV - NTNU of the stay vanes • The stay vanes have the...

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Design of stay vanes and spiral casing Revelstoke, CANADA
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  • Design of stay vanes and spiral casing

    Revelstoke, CANADA

  • Guri-2, VENEZUELA

  • Aguila, ARGENTINA

  • Sauchelle-Huebra, SPAIN

  • Sauchelle-Huebra, SPAIN

  • Three Gorges Turbine, GE Hydro

  • The spiral casing will distribute the water equally around the stay vanes

    In order to achieve a uniform flow in to the runner, the flow has to be uniform in to the stay vanes.

  • Flow in a curved channel

    Streamline

  • StreamlineStreamline

    The pressure normal to the streamline can be derived as:

    dbdsdnnpdbdsdn

    nppdbdspdFn

    =

    +=

  • Newton 2. Law gives:

    StreamlineStreamline

    Rc

    np

    adbdsdndbdsdnnp

    n

    21=

    =

    Rca

    2

    n =

    1

    m

  • The Bernoulli equation gives:

    .const2cp 2=+

    Derivation of the Bernoulli equation gives:

    0ncc

    np1

    =+

    2

  • Equation 1 and 2 combined gives:

    .constcR

    0)Rc(d

    0dRcdcR

    Rc

    nc

    =

    =

    =+

    =

    Free Vortex

    Rc

    np 21=

    0ncc

    np1

    =+

    2

    1

  • Inlet angle to the stay vanes

    icm

    cu

    =

    u

    mi c

    ctana

  • Plate turbine

  • Find the meridonial velocity from continuity:

    BR2Q

    AQc

    cAQ

    0m

    m

    ==

    =B

    R0

  • Find the tangential velocity:

    =

    ==

    =

    =

    00y

    u

    0y

    R

    Ry

    R

    Ry

    u

    R

    Ry

    RRlnRB

    Qc

    RRln.constB

    rdr.constBQ

    drr

    .constBQ

    drcBQ

    0

    0

    0

    By

    R0 R

  • Example

    By

    Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

    Find: L1, L2, L3 and L4

    L1

    C

    L3

    L2

    L4

    R0R

  • Example

    By

    Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

    L1

    C

    L3

    L2

    L4

    R0R

    sm

    RRRB

    QC

    y

    u 9,12ln

    00

    =

    =

    mBCQL

    y

    5,01 ==

  • Example

    By

    Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

    We assume Cu to be constant along R0.

    At =90o, Q is reduced by 25%

    L1

    C

    L3

    L2

    L4

    R0R

  • Example

    By

    Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m

    L1

    C

    L3

    L2

    L4

    R0R

    00

    00

    0

    ln

    ln.

    RCBQ

    uy

    y

    uyeRR

    RRRCBQ

    RRconstBQ

    =

    =

    =

  • Example

    By

    Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m

    L1

    C

    L3

    L2

    L4

    R0R

    00

    RCBQ

    uyeRR =

    L2 = 0,35 mL3 = 0,22 mL4 = 0,10 m

  • Find the meridonial velocity from continuity:

    10m

    m

    kBR2Q

    AQc

    cAQ

    ==

    =R0B

    k1 is a factor that reduce the inlet area due to the stay vanes

    2yB

  • Find the tangential velocity:

    Rcc

    .constcRc

    Tu

    Tu

    =

    ==

    =

    =+

    drRcrQ

    dRcBQ

    tT

    u

    rR

    Ry

    t

    cossin

    2

    2

    2

    0

    R0B R0B

    drdRrRR

    rB

    T

    y

    ==

    =

    sincos

    sin2

    2yB

  • =

    dcosrR

    sinr2

    Qc

    T

    22

    T

    R0B R0B

    =

    dcosrR

    sinr2R

    Qc

    T

    22

    u

    2yB

  • Spiral casing design procedure1. We know the flow rate, Q. 2. Choose a velocity at the upstream section of the spiral

    casing, C3. Calculate the cross section at the inlet of the spiral casing:

    4. Calculate the velocity Cu at the radius Ro by using the equation:

    =CQr

    =

    dcosrR

    sinr2R

    Qc

    T

    22

    u

  • Spiral casing design procedure5. Move 20o downstream the spiral casing and calculate the

    flow rate:

    6. Calculate the new spiral casing radius, r by iteration with the equation:

    totalo

    o

    new QQ = 36020

    =

    drRcrQ tT cos

    sin2

    2

    2

  • Outlet angle from the stay vanes

    cm

    cu

    =

    u

    m

    cctana

    .constRcu =

    kBR2Q

    AQcm ==

  • Weight of the spiral casing

  • Stay Vanes

  • Number of stay vanes

    16

    18

    20

    22

    24

    26

    28

    30

    0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6

    Speed Number

    Num

    ber o

    f Sta

    y Va

    nes

  • Design of the stay vanes

    The stay vanes have the main purpose of keeping the spiral casing together

    Dimensions have to be given due to the stresses in the stay vane

    The vanes are designed so that the flow is not disturbed by them

  • Flow induced pressure oscillation

    56.09.1

    +=tcBf

    Where f = frequency [Hz]B = relative frequency to the Von Karman oscillationc = velocity of the water [m/s]t = thickness of the stay vane [m]

  • Where A = relative amplitude to the Von Karman oscillationB = relative frequency to the Von Karman oscillation


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