secondary blade paper

8/14/2019 Secondary blade paper

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SECONDARY FLOWS

IN TURBINE BLADING SYSTEMS

THEORY AND COMPUTATION

17-19.09.2008 Gliwice, Poland

22nd TURBOMACHINERY WORKSHOP 2008

Piotr LampartIMP PAN, Gdask

Secondary flows in pipes and channels

pressure-driven

secondary flows

stress-driven

secondary flows

n

p

R

v

=

2

p/n=const, v0

R0


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A - model of Hawthorne (1955), B model of Langstona (1980),

C model of Sharma & Butler (1987), D model of Goldstein & Spores (1988).

Formation of horse-shoe vortex,

Marchal & Sieverding (1984)

Secondary flows in turbine cascades

Secondary flows modify

boundary layers at the endwalls

Endwall boundary layer, Harrison [17]

Secondary flows in cascades

with a tip clearance


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SECONDARY FLOWS IN OTHER FIELDS

Tip vortex behind aircraft

Tip vortex behind marine propeller

TORNADO

River bend flow

Formation of the inlet boundary layer upstream of the blade leading edge;

Formation of the boundary layer downstream of the horse-shoe vortex lift-off lines;

Shear effects along the horse-shoe vortex lift-off lines, separation lines,

between the secondary vortices, main flow and blade surfaces,

especially at the suction surface;

Dissipation of the passage vortex, trailing shed vortex, corner vortices and other vortex flows

in the process of their mixing with the main flow;

Exit non-uniformities may lead to local separations and upstream relocation of the laminar-

turbulent transition at the downstream blade in the secondary flow dominated region.

Endwall / secondary flow losses


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Evolution of vorticity from the endwall boundary layer

( ) ( ) ( )

+

=

p uuu

u - velocity, - vorticity, p pressure, - density, - viscous stress tensor

=ss + nn + b

=

b

p

n

b

n

p

qR

q

sq ns

2

12

( )

+

=

b

p

s

b

s

p

qs

a

a

q

sq

b

b

nbn 2

11

+ viscous terms

+ viscous terms

inviscid incompressible flow

R

q

sq ns

2=

( )000 2 nss =

inviscid perfect gas flow

b

p

qRq

sq

*s

=

2dscos

p

qRq

q

*ss =

2

12

12

2

Lakshminarayana, Horlock

1s =

,.

n

vr

=1r

vn

=1

( )

xdydvhp

xdydvvvhp

nr

sec

+=

1

0

1

0

1311

1

0

1

0

121

2111

cos

cos

Calculation of secondary flow losses

(it is assumed that the secondary kinetic energy of the relative

motion in the exit section is lost during mixing)


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EFFECTS OF SECONDARY FLOWS

(A) INCREASED CASCADE LOSSES,

(B) REDISTRIBUTION OF EXIT VELOCITY,

(C) INCREASED NON-UNIFORMITY AT EXIT,

(D) REDISTRIBUTION OF STEADY AND UNSTEADY LOADS.

Durham cascade distribution of loss coefficient and exit swirl angle at slot 10; experimental,

computed by FlowER with Menterk-SST model and computed by Fluent with RSM LRR model.

Entropy function contours in a rotor cascade

h=20mm, 60mm i 100mm

Span-wise distribution of enthalpy losses and exit angle in a rotor cascade;

1 h=20mm; 2 h=60mm, 3 h=100mm

The effect of blade height


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Velocity vectors at the mid-span section (left) and at the root (right)

in the stator (left) and rotor (right) cascades; blade heighth=60mm.

Pressure distribution at the stator (left)

and rotor (right) profile; blade heighth=60mm

Profile type

Entropy function contours in the stator

and rotor at the trailing edge;h=60mm

Flow turning in the cascade

Static pressure contours at the mid-span of the rotor cascade for three inlet angles

Velocity vectors at the endwalls of the rotor cascade for three inlet angles

Secondary flow vectors at the trailing edge and total pressure contours

15% axial chord downstream of the trailing edge in the rotor cascade for three inlet angles


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Secondary flow vectors and total pressure contours in the HP rotor cascade in selected sections located

15% axial chord upstream of the trailing edge, at the trailing edge and 15% axial chord downstream of

it; tip gap size 2%,Ma=0.2, 0 = 63o, 1 = -63

o.

Secondary flow vectors and total pressure contours in the HP rotor cascade in selected sections located

60% and 15% axial chord upstream of the trailing edge and at the trailing edge;

tip gap size 2%,Ma=0.4, 0 = 75o, 1 = -72

o.

Flow turning in the cascade with tip clearance

Total pressure contours and secondary flow vectors

in exit section experiment, Yamamoto [4]

Total pressure contours in normal sections

Enthalpy losses

UHL cascade of Yamamoto

HIGHLY LOADED CASCADES

Profiles used in gas turbines

for a low weight-to-power ratio

Velocity vectors in sections from hub to tip


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Total pressure contours and secondary flow vectors at the exit experiment, Moustapha et al. [4]

Total pressure contours in normal sectionsEnthalpy losses

HL cascade of NRC

The case of non-nominal inflow onto the suction side of the blade

Secondary flow vectors 85%, 55% and 5% axial chord upstream of the trailing edge of the rotor

cascade for the case of non-nominal inflow onto the suction side of the blade for 0 = 0o and 30o;

Static pressure contours and velocity vectors at the endwall of the rotor cascade

for the case of non-nominal inflow onto the suction side of the blade, 0 = 0o.

Loss contours and distribution


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The effect of span-wise distribution of static pressure and cascade load

Straight and compound

leaned stator blade

Spanwise distribution of static pressure, relative velocity and swirl angle

in the stator and rotor 5% axial chord upstream of the trailing edge;

stage with straight stator blades (1), stage with compound leaned stator blades (2)

Redistribution of loss in the stator and rotor;

straight blades (left, 1), compound leaned blades (right, 2)

Velocity vectors at the rotor suction surface;

stage with straight stator blades (left),

stage with compound leaned stator blades (right)

Computational domain

with source/sink-type boundaries

The effect of leakage flow (the case of shrouded blades)

Velocity vectors in the rotor (upper part) at the suction surface and entropy function contours

at the rotor trailing edge - computed without sources and sinks (left), computed with tip leakage (right)

Static pressure contours and velocity vectors at the suction surface of the second s tator blade

Secondary flow vectors 35% and 75% axial chord downstream of the leading edge (left) and entropy function

contours 15% axial chord downstream of the trailing edge in the second stator (right).

S2

S2

R1


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Total pressure contours in the second stator in subsequent sections located 90%, 75% and 25% axial

chord upstream of the trailing edge and 15% axial chord downstream of the trailing edge

Entropy function contours in the second stator in subsequent sections located 75%, 50% and 25%

axial chord upstream of the trailing edge and 15% axial chord downstream of the trailing edge (L).

Also entropy function contours behind the second stator computed without leakage (NL)

S2

S2

Redistribution of secondary flows due to unsteady effects

Instantaneous entropy function contours in the rotor at the mid-span in unsteady flow

Instantaneous total pressure contours at the rotor trailing edge in unsteady flow

R1

upstream interaction of the moving blade row

downstream transport of 2D and 3D wakesAachen

turbine

S1/R1/S2

R1

unsteady effects =


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Instantaneous total pressure and entropy function contours

at the second stator trailing edge in unsteady flow

Instantaneous secondary flow vectors in the second stator

40% axial chord downstream of the leading edge in unsteady flow

S2

S2

The effect of thickness and skewness of the inlet boundary layer

Durham cascade: Total pressure contours for different skew configurations

of the inlet boundary layer; experiment - Walsh & Gregory-Smith [16]

Skewed inlet boundary layer


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Conclusions

Losses in the endwall boundary layers can be found from an analytical expression.

Secondary flow losses need to be evaluated numerically.

RANS calculations typically overpredict losses in the secondary flow region. The predictions are

improved with the Reynolds Stress Model.

A decrease of the relative blade height and/or increase of flow turning in the cascade increases

the intensity of passage vortices and the level of secondary flow losses.

Spanwise gradients of pressure and profile load cause a redistribution of secondary loss centres

along the blade span and endwall boundary layer losses.

The development of secondary flows for the case of non-nominal incidence angles onto the

suction surface of the blade looks different than for the classical case of nominal incidence.

In front part of the blade the role of the convex and concave surface is reversed.

Two passage vortices appear a reverse (counter-rotating) and a regular passage vortex.

The shroud leakage helps to remove the low-energy endwall boundary layer into the leakage

slots, which retards the development of secondary flows in the current blade row.Local span-wise pressure gradients at the second stator blades induce a strong recirculating

flow in the stator. It rolls up both the low-energy endwall boundary layer fluid and high-energy

mixing layer of the shroud leakage and gives rise to an intensive tip passage vortex in the stator

The transport of two-dimensional stator wakes leads to significant oscillations in size of the

secondary flow zones. Segments of the tip leakage vortex from unshrouded rotors are found

periodically within the recirculating flow in the downstream stator and a strong pulsating

passage vortex is formed.

secondary blade paper

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