15004 Turbine HP Stage - Flow Characteristics

8/9/2019 15004 Turbine HP Stage - Flow Characteristics

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Copyright © 2000 by ASME1

INVESTIGATIONS OF FLOW CHARACTERISTICSOF AN HP TURBINE STAGE INCLUDING

THE EFFECT OF TIP LEAKAGE AND WINDAGE FLOWSUSING A 3D NAVIER-STOKES SOLVER

WITH SOURCE/SINK-TYPE BOUNDARY CONDITIONS

Piotr Lampart and Andrzej GardzilewiczInstitute of Fluid Flow Machinery

Polish Academy of Sciences, Gda!sk, Polande-mail: [email protected]

Sergey Yershov and Andrey RusanovInstitute of Mechanical Engineering Problems

Ukrainian National Academy of Sciences, Kharkov, Ukrainee-mail: [email protected]

ABSTRACTEnergy conversion in turbomachinery flows takes place in

extremely complex three-dimensional geometries. Besides

blade-to-blade channels and axial gaps - the domain of the main

flow - there are places of completely different aspect ratios like

labyrinth seals and passages between the fixed and rotating

parts of the machinery where leakage and windage flows take place and then mix in the blade-to-blade passage with the main

stream. 3D modelling of the entire impulse turbine stage or a

group of stages, that is accounting for all these areas simultane-

ously, only inlet and exit conditions assumed, is an extremely

difficult task.

The approach presented in the paper enables injection of

the medium at arbitrary velocities and angles, determination of

the effect of mixing of injected medium with the main flow -

which is the main source of entropy creation due to tip leakage

and windage flows, as well as interaction of injected streams

with other vortex flows - secondary flows or separations. 3D

viscous, compressible flow in the blade-to-blade passage and

axial gaps is modelled with the help of thin-layer Reynolds-

averaged Navier-Stokes equations with a modified Baldwin-

Lomax algebraic model of turbulence. In addition to boundary

conditions typical for turbomachinery codes - total pressure and

temperature at the inlet to the stage, static pressure assumed at

the exit, no slip and no heat flux at the walls - the source/sink-

type boundary conditions are assumed at some places at the

endwalls referring to design locations of injection of leakage

and windage flows into, or their extraction from the blade-to-

blade passage. Injection and extraction of the streams is accom-

plished thanks to the application of non-reflective boundary

conditions there, giving four values of invariants for injection

and one for extraction. The corresponding mass flow rates of

injected/extracted medium - equivalent to the intensity of

sources/sinks - are calculated from more simple one-

dimensional studies of leakage and windage flows.

Three computational examples of a high pressure turbinestage with short height blading are enclosed in the paper. First,

computations are made without tip leakage and windage flows

with source/sink slots closed. Second, tip leakage slots are

open. Third, both tip leakage and windage flow slots are open,

and the effect of mixing of tip leakage and windage flows with

the main flow, on the performance of the stage is studied.

INTRODUCTION

3D modelling of the entire turbine stage or a group of

stages, only inlet and exit conditions assumed, still remains an

extremely difficult task. The main difficulty lies in the complex-

ity of turbomachinery geometries, and different aspect ratios

and flow scales between the main flow in the blade-to-blade

passages, tip leakage over shrouded rotor blades, leakage

through stator sealing glands, and windage flows in passages

between the fixed and rotating parts of the machinery. A picture

of a group of stages for an impulse turbine with indicated direc-

tions of the above mentioned streams is presented in Fig. 1.

Before full 3D computations of the entire flow geometry of

the impulse turbine shown in Fig. 1 are within easy reach, a

recent paper of Tajc, Polansky 1999, describes their CFD com-

Proceedings of2000 International Joint Power Generation Conference

Miami Beach, Florida, July 23-26, 2000

IJPGC2000-15004


2/8


Fig. 1. Impulse turbine geometry.

putations of tip leakage labyrinth seals using the commercial

software FLUENT with the RNG k-ε turbulence closure. Theauthors consider a number of labyrinth seal configurations

which are then ranked according to the resultant computed

leakage flow rate. A notice on labyrinth seal computations can

also be found in a recent news release from NREC & NU-

MECA Int. Partnership, NREC News, 1999. The notice under-

lines an importance of, first, fine resolution of computational

grids to conform accurately to very small clearance gaps and

large cavities between the seal teeth and, second, choice of turbulence models since the majority of the cavity regions is

dominated by large secondary flows. CFD-based analysis can

minimise the leakage flow rates and improve performance of

labyrinth seals. NS computations also enable the evaluation of

the entropy creation processes in the labyrinth seals. However,

unlike for the leakage flow rate that is inherent to the labyrinth

seal geometry, most of entropy creation due to tip leakage takes

place not in the labyrinth seals but in the blade-to-blade passage

downstream of the tip leakage jet re-entry where the injected

leakage jet mixes with the main stream.

At the highest level of simplification, the relative enthalpy

losses due to tip and root leakages (referred to isentropic en-

thalpy drop across the turbine stage) can be assumed equal to

the relative mass flow rate of the tip and root leakages (referred

to the total mass flow rate of the main flow plus leakages),

Gardzilewicz 1984. Tip leakage losses over both shrouded and

unshrouded blades are discussed in detail in a landmark paper

of Denton 1993, on loss mechanisms in turbomachinery. The

author derived a formula for tip leakage losses making a num-

ber of simplifications, among others assuming a constant swirl

velocity of the leakage jet through the rotor, and neglecting the

axial velocity of the leakage jet at its re-entry, obtaining

T s

V

m

m

L∆

052 1

22

1

2

22

.(

tan

tansin )= −

α

α α

where α 1 and α 2 are the swirl angles upstream and downstreamof the blade row, m L is the tip leakage mass flow rate compared

to the mass flow rate in the blade-to-blade passage m. The for-mula shows the determinant effect of the difference in swirl

velocity across the blade row, or in other words, the difference

in swirl velocity between the main stream and leakage jet at its

re-entry on the tip leakage losses.

However, the swirl velocity of the tip leakage can change in

the labyrinth seals. The tip leakage jet can also have some axial

component of the velocity on its re-entry, and it is expected that

the direction of the tip leakage jet re-entry as well as the angle

at which the windage jet is injected can have a significant influ-

ence on the entropy creation in the downstream mixing process.

Leakage and windage flows as mass injections or extractions

interact also with secondary flows and separations. It is highly

recommended that 3D codes for turbomachinery flow predic-tion should enable modelling of these phenomena.

COMPUTATIONAL METHOD

The computations whose results will be presented in the

paper are carried out with the help of a code FlowER - solver of

viscous compressible multi-stage turbomachinery flows devel-

oped by Yershov & Rusanov 1996ab, see also Rusanov & Yer-

shov 1996, Yershov et al. 1998. The code has been tested on a

number of turbomachinery geometries and flow regimes for real

full-scale and model turbines, including tests held at the ER-

COFTAC Workshops on Turbomachinery Flow Prediction, see

Yershov et al. 1997. The main features of the code will shortly

be described below.

Governing equations

Flow in the blade-to-blade passages and axial gaps is de-

scribed by a set of thin-layer Reynolds-averaged unsteady

Navier-Stokes equations written in a curvilinear body-fitted

coordinate system ( ξ - radial ,η - pitch-wise , ζ - stream-wise ) rotating with an angular speed Ω

∂

∂

∂

∂ξ

∂

∂η

∂

∂ς

∂

∂ξ

∂

∂η

ξ η QJ

t

E F G JH

R R+ + + = + + , (1)

where Q is a conservative variable vector, E, F and G are flux

vectors; H is a source term vector; Rξ and Rη are cross-streamviscous terms (with stream-wise diffusion discarded)

Q

u

v

w

h

=

!

"

#############

$

%

&&&&&&&&&&&&&

ρ

ρ

ρ

ρ

ρ

; H

v r

u r

x

y=

+

− +

!

"

###########

$

%

&&&&&&&&&&&

0

2

2

0

0

2

2

ρ ρΩ

ρ ρΩ

Ω

Ω ;


3/8


E J

U

uU p

vU p

wU p

h p U

x

y

z

=++

+

+

!

"

###########

$

%

&&&&&&&&&&&

ρ

ρ ξ

ρ ξ

ρ ξ

ρ ( )

; F J

V

uV p

vV p

wV p

h p V

x

y

z

=++

+

+

!

"

###########

$

%

&&&&&&&&&&&

ρ

ρ η

ρ η

ρ η

ρ ( )

; G J

W

uW p

vW p

wW p

h p W

x

y

z

=++

+

+

!

"

###########

$

%

&&&&&&&&&&&

ρ

ρ ς

ρ ς

ρ ς

ρ ( )

;

R J

u

v

w

U uu

vv

ww i

x

y

z

ξ

ξ

ξ

ξ

ξ

µ

σ ξ ξ ∂

∂ξ

σ ξ ξ ∂

∂ξ

σ ξ ξ ∂

∂ξ

σ ξ ∂

∂ξ

∂

∂ξ

∂

∂ξ

∂

∂ξ

=

+

+

+

+ + + +!

"

###

$

%

&&&

!

"

#######################

$

%

&&&&&&&&&&&&&&&&&&&&&&&

0

1

3

1

3

1

3

1

3

1

02

02

02

02

Pr

;

R J

u

v

w

V uu

vv

ww i

x

y

z

η

η

η

η

η

µ

σ η η ∂

∂η

σ η η ∂

∂η

σ η η ∂

∂η

σ η ∂

∂η

∂

∂η

∂

∂η

∂

∂η

=

+

+

+

+ + + +!

"

###

$

%

&&&

!

"

#######################

$

%

&&&&&&&&&&&&&&&&&&&&&&&

0

1

3

1

3

1

3

1

3

1

02

02

02

02

Pr

.

where p is the pressure, u,v,w - Cartesian components, U,V,W -

contravariant components of velocity, i - enthalpy, h - rothalpy

U u v w x y z = + +ξ ξ ξ ;V u v w x y z = + +η η η ;W u v w x y z = + +ς ς ς ;

i p

const =−

+γ

γ ρ 1 ; h

p u v w r const =

− +

+ + −+

1

1 2

2 2 2 2 2

γ ρ

Ω ;

ξ ξ ξ ξ 02 2 2= + + x y z ; η η η η 0

2 2 2= + + x y z ;

σ ξ ∂

∂ξ ξ

∂

∂ξ ξ

∂

∂ξ ξ = + + x y z

u v w; σ η

∂

∂η η

∂

∂η η

∂

∂η η = + + x y z

u v w.

J denotes the Jacobian of transformation from the Cartesian to

curvilinear coordinate system and γ is the specific heat ratio, Pr- Prandtl number. The effective (molecular and turbulent) vis-

cosity and conductivity are as in the Bussinesq hypothesis

where the laminar part is found from the formula of Sutherland

whereas in order to determine the turbulent part a modified

Baldwin-Lomax model is used. The original model of Baldwin-

Lomax, 1978, was modified to better calculate turbulent viscos-

ity in the regions of separation and wake.

Boundary conditions

As the boundary conditions at the inlet, span-wise distribu-

tions of total pressure, total temperature, pitch and yaw angles

are assumed, and also a span-wise distribution of static pressure

- as a voluntary condition to help evaluate the initial flow field.

At the exit from the computational domain we use optionallyeither a span-wise distribution of static pressure, or static pres-

sure at the mid-span section, with its span-wise distribution

calculated from the radial equilibrium equation. There is no slip

and no heat flux at the walls, and the static pressure is found

from Eq. (1) written along cross-flow gridlines at blade walls

( ){ ( )∂

∂η

∂

∂η η µ

∂

∂η ξ η ξ η ξ η

p

J x x y y z z

JU = + + ⋅

'

())

*

+,,

+1

02

( ) ( ) ( )

+ + + '

())

*

+,,

+ +! " #

$ %&

'

())

*

+,,

-./

0/ x x y y z z

JW JV η ζ η ζ η ζ

∂

∂η η µ

∂

∂η η µ

∂

∂η

∂

∂η 02

021

3,

and at endwalls

( ){ ( )∂

∂ξ ρΩ

∂

∂ξ ξ µ

∂

∂ξ ξ ξ ξ η ξ η ξ η

pr x r y

J x x y y z z

JV x y= + + + + ⋅

'

())

*

+,,

+2 021( )

( ) ( ) ( )

+ + + '

())

*

+,,

+ +! " #

$ %&

'

())

*

+,,

-./

0/ x x y y z z

JW JU η ξ η ξ η ξ

∂

∂ξ ξ µ

∂

∂ξ ξ µ

∂

∂ξ

∂

∂ξ 02

021

3.

The assumption of complete spatial periodicity at free bounda-

ries upstream of the leading edges and downstream of the trail-

ing edges, combined with the concept of a mixing plane be-

tween the fixed and moving blade rows in the steady-state ap-

proach, or time-space periodicity with a sliding plane in the

unsteady approach are assumed.

Source/sink-type boundary conditionsIn order to account for the effect of leakage over shrouded

blade tips and windage flows the computational domain is

modified at the endwalls where some places are permeable

boundaries of the domain - sources or sinks, see Fig. 2. In addi-

tion to the boundary conditions typical for turbomachinery

codes as presented in the preceding subsection, source/sink-

type boundary conditions are used at places at the endwalls

referring to design locations of injection of leakage and wind-

age flows into, or their extraction from, the blade-to-blade pas-

sage. The injection and extraction are accomplished with the

Fig. 2. Computational domain with source/sink-type permeable

boundaries to simulate the effect of leakage over shrouded rotor

blade tips and windage flows; S - stator, R - rotor.


4/8


application of non-reflective boundary conditions there, giving

four values of invariants for injection ( un > 0 )

I u a const n+ = + − =2 1/ ( )γ ,

u const t 1 = , u const t 2 = , S p const = =/ ργ

and one value for extraction ( un < 0 )

I u a const n− = − − =2 1/ ( )γ

where u u un t t , ,1 2 are velocity components - one normal and

two tangential to the source/sink boundaries, p - pressure, ρ -density, S - entropy function, a - speed of sound, γ - isentropicexponent, I I − +, - left and right Riemann invariant, see also

Yershov et al. 2000. These invariants can be found, first, from

preliminary computations in the basic computational domain

without sources and sinks, giving p and ρ at places referring tothe source/sink locations, with the density at the sink throat of

the tip leakage jet determined from isenthalpic conditions. The

corresponding mass flow rates of the injected/extracted fluid -

equivalent to the intensity of sources/sinks - can be calculated

from more simple 1D studies of leakage and windage flows.

Then, the needed velocity components can be obtained based

on the density and size of source/sink slots.

Stage lossesThe presented approach enables injection of the medium at

arbitrary velocities and angles, determination of the effect of

mixing of injected medium with the main flow, as well as inter-

action of injected streams with other vortex flows - secondaryflows or separations. The approach embodies the message that

most of the entropy creation due to tip leakage is inherent to the

blade-to-blade passages not to the tip clearance or labyrinth seal

itself. Mass averaged kinetic energy losses of the stage can be

found from a formula that takes into account leakage streams

ξ ξ= 1 1+ +

iex s

i iex s

G G. . . .

/

where the summation extends on all streams that carry away the

fluid from the blading system (exit and sinks) and ξ i is the ki-netic energy loss, Gi - mass flow rate in a stream i. In the case

of nominal directions of leakage and windage flows and equal

intensities of respective sources and sinks, the formula reducesto the summation over exit streams only. Exit velocity losses

are found as in non-source/sink computations.

NUMERICAL SCHEME

Explicit stepThe applied scheme draws on cell-centred finite-volume

discretisation

[ ] [ ]

[ ] [ ][ ] [ ]

δ τ τ

ξ ξ

η η

Q Q Q H J

E R E R

F R F R

G G

i j k n

i j k n

i j k n

i j k n

i j k

n

i j k

n

i j k

n

i j k

n

i j k

n

i j k

n

i j k

, , , , , , , ,/

, ,

/ , , / , ,

, / , , / ,

, , / , , /

( )

( ) ( )

( ) ( )

= − = −

− − − +234

− − −

+ − -.0

+ +

+ −

+ −

+ −

1 1 2

1 2 1 2

1 2 1 2

1 2 1 2

∆ξ∆η ∆ς

∆η ∆ς ∆η ∆ς

∆ξ ∆ς ∆ξ ∆ς

∆ξ ∆η ∆ξ ∆η

(2)

where subscripts i,j,k refer to cell centres, i± 1/2, j± 1/2, k ± 1/2 tocell sides, n is a time instant.

ENO reconstructionIn Godunov-type schemes inviscid fluxes are found from the

solution of the Riemann problem, Godunov et al. 1976. In our

method, initial values for the Riemann problem are found from

( ) ( )

( ) ( )

q t qq q

q q

t t t

mm

mm

m

m

m

n

n

( , , , )ξ η ς

∂

∂ξ ξ ξ

∂

∂η η η

∂

∂ς ς ς

∂

∂

= + !

" #

$

%& − +

!

" #

$

%& − +

!

" #

$

%& − +

!

" #

$

%& −

(3)

where q = ( ρ , u, v, w, p) is the primitive variable vector, qm - itsvalue at the cell centre, ξ m , η m , ζ m - cell centre coordinates. Thespatial derivatives that appear in Eq. (3) are found from the

following ENO approximation written for the characteristic

variable vector φ , see Harten & Osher 1987,

( )[

∂φ

∂ψ

ϕ α ϕ ϕ ϕ ϕ

!

" #

$

%& = =

+ − −− +

m

def

m m m m m

1

1 1

∆ψ

∆ ∆ ∆ ∆ ∆

minmod

min mod , ,

(4)

( )]∆ ∆ ∆ ∆ ∆m m m m m+ + + +− − −1 1 2 1ϕ β ϕ ϕ ϕ ϕ min mod ,

where ∆ψ is the cell size, ∆mφ =φ m-φ m-1 and

minmod(a, b) = sign(a) max{0, min[a,bsign(a)]}.

This formulation requires transformation from the primitive to

characteristic variables and the other way round. The choice of

constants α , β determines the order of the numerical scheme.For α =1/2, β =1/2, we have an ENO scheme that is second-order accurate everywhere in time and space. For α =2/3,

β =1/3, the scheme is locally third-order accurate, remaining atleast second-order everywhere, see Yershov 1994, and this

scheme is implemented in the present paper. The time deriva-

tive in Eq. (3) is found from the non-divergent form of Eq. (1)

J q

t D

q D

q D

qT JH

R R∂

∂

∂

∂ξ

∂

∂η

∂

∂ς

∂

∂ξ

∂

∂η ξ η ς

ξ η + + + = + +!

" #

$

%& ,

where matrices Dψ can be found from Eq. (1), and T is the

transformation from primitive to conservative variables.


5/8


Implicit stepOne drawback of the explicit scheme - Eq. (2) - is its insuf-

ficient effectiveness in terms of computational costs. The proc-

ess of convergence to a steady-state can be accelerated with the

aid of an implicit scheme of Beam & Warming, 1978

I x J

A B C Q

x RHS

x

xQ

n n n++

+ +!

" #

$

%&

'

())

*

+,,

=+

++

−θ ∂

∂ξ

∂

∂η

∂

∂ς δ δ

( ),

1

1

1 1

1 (5)

where I = diag {1} is a unit matrix; θ , x are constants; Q - theconservative variable vector. In order to obtain second-order

accuracy it is necessary to put down θ = 2, x = 1, and assure theapproximation of the right-hand side (RHS) term with second-

order accuracy in space. Solving Eq. (5) requires its factorisa-

tion (with regards to space coordinates) and diagonalisation of

matrices A, B, C. The employed factorised implicit scheme

works on the characteristic variable vector

( ) I x J n n+

+ +'

() *

+, =+ − +τθ ∂

∂ξ δϕ δϕ ξ ξ ξ ξ

( );/

1

1 3Λ Λ

( ) I x J

n n++

+'

()

*

+, =

+ − + +τθ ∂

∂η δϕ δϕ η η η η

( );/ /

1

2 3 1 3Λ Λ (6)

( ) I x J

n n++

+'

()

*

+, =

+ − +τθ ∂

∂ς δϕ δϕ ς ς ς ς

( )

/

1

2 3Λ Λ ,

where Λ Λ Λψ ψ ψ ± = ±( ) / 2 , the diagonal matrix Λψ consisting

of eigenvalues of Dψ . This formulation requires transformation between the characteristic, primitive and conservative variables.

Viscous fluxesThe viscous fluxes are calculated based on ENO approxima-

tion and a weighted linear interpolation, for example (sub-

scripts i,k are left out as constant)

µ ∂ ∂η η η µ ∂ ∂η η η µ ∂ ∂η u u u

j

j j

j

j j

j

!

" # $

%& = − !

" # $

%& + − !

" # $

%&++

++ +

1 2

1 2

1

1 1 2

/

/ /( ) ( ) . (7)

COMPUTATIONAL RESULTS

The computed turbine stage is a typical impulse HP stage of

a 200MW steam turbine operating at the pressure drop of about

0.9, inlet temperature - 780K, flow rate - 170 kg/s, average re-

action - 0.15; the aspect ratios are: span/chord - 0.8 (stator) and

2.0 (rotor), pitch/chord - 0.8, span/diameter - 0.08. Prior to

CFD computations, the stage was scrutinised with the aid of a

1D code to evaluate the mass flow rate of the main flow in the

blade-to-blade passage of the stator and rotor G1, G2 as well asflow rates of leakages at the tip and root GT , G R and windage

flows GW , GW’ based on the given pressure drops and geometry

of labyrinth seals and passages. The results obtained from the

1D approach necessary for further 3D computations are as fol-

lows: GT =2.7%G1, GW =GW’ =1.2%G1. Then 3D computations

were made in three variants. First, without tip leakage and

windage flows with source/sink slots closed, second, with only

tip leakage slots open, third, with both tip leakage and windage

flow slots open. In source/sink computations, it was assumed by

way of example that the fluid is extracted and injected through

the sinks and sources in the radial direction (no axial and swirl

velocity), which is far from the real turbine situation. However,

Fig. 3. Axial distribution of mass flow rate in the computational domain of the rotor -

computed without sources and sinks (left), computed with tip leakage (centre), computed with tip leakage and windage flows (right).

Fig. 4. Entropy function contours and velocity vectors in the rotor at 9% blade span from the root -



6/8


Fig. 5. Entropy function contours in meridional view in the computational domain of the rotor

at 3% (left), 12% (centre left), 48% (centre right) and 96% (right) blade-to-blade distance from the suction surface -

computed without sources and sinks (top), computed with tip leakage (centre), computed with tip leakage and windage flows (bottom).

the computational results presented comparatively below in

subsequent Figs. from 3 to 7 can be viewed as an illustration of

the described idea of flow solving, showing interesting effects

of leakage and windage flows on turbomachinery performance.

The axial distribution of mass flow rate in the rotor com-

puted with source/sink slots closed can be considered nothing

more than a measure of convergence of the numerical algo-

rithm. In source/sink computations, sink and source throats be-

long entirely to the rotor computational domain. In this case,

therefore, the axial distribution of mass flow rate in the rotor

illustrates the tip leakage mass flow rate equal to 2.7% of the

total mass flow (as assumed in the boundary conditions for

variant 2), or the summary mass flow rate for tip leakage and

windage flows equal to 3.9% of the total mass flow (variant 3)

by-passing the rotor blade-to-blade passage and not contribut-

ing to the rotor work, see Fig. 3.

Fig. 4 with entropy function contours and velocity vectors in

the rotor at 9% of the blade span from the root computed with-

out sources and sinks, and with tip leakage, or tip leakage plus

windage flow sources and sinks shows an interesting flow fea-

ture - separation from the front part of the suction surface of the

rotor blade at the root. It seems that pitch/chord/stagger angle

optimisation and stator/rotor matching for that stage may not

have been executed with due care. The shape of the separation

zone undergoes changes with the presented computational vari-

ants. The separation zone is the smallest for non-source/sink

computations. It slightly changes with a tendency to increase in

size in computations with tip leakage. However, the changes are

not spectacular as the flow modification takes place at the op-

posite endwall, that is at the tip. The separation zone significan-


7/8


Fig. 6. Entropy function contours in the rotor at 10%, 52%,

96% axial chord from the leading edge, and downstream of the

rotor at 10% and 45% axial chord from the trailing edge -

computed without sources and sinks (top), computed with tip

leakage (centre), with tip leakage and windage flows (bottom).

tly extends when tip leakage and windage flows are taken into

account. No wonder. Extraction of the fluid prior to the rotor

reduces the mass flow rate in the rotor blade-to-blade passage

and changes the angle of attack locally. Especially, extraction

of the fluid into the windage slot at the root acts to extend the

zone of separation at the root section, compared to non-

source/sink computations.Figs. 5 and 6 illustrate contour of the entropy function

S=p/ ρ γ in the rotor at pitch-wise subsequent sections betweenthe suction and pressure surface, and also at axially subsequent

sections beginning from the leading edge to the trailing edge

and downstream into the wake of the rotor for non-source/sink

computations, as well as for source/sink computations with tip

leakage and tip leakage plus windage flow. The pictures exhibit

characteristic features of subsonic flows in axial turbines. Non-

source/sink computations illustrate the development of secon-

dary flows, separation, and wake. The separation and secondary

flow vorticity at the root merge towards the mid-span section,

giving more loss than that due to secondary flows at the oppo-

site endwall. Computations with the tip leakage (pictures in the

centre) show also the effect of mixing of the leakage stream

with the main flow adding to flow losses near the tip endwall.The effect of separation at the root slightly increases. However,

as the high entropy boundary layer fluid is sucked out into the

tip leakage slot prior to the rotor, an interesting feature is ob-

served that the intensity of secondary flows is reduced. The

span-wise extension of the secondary flow zone considerably

shrinks, compared to non-source/sink computations. Results of

source/sink computations with tip leakage and windage flows

(pictures at the bottom) confirm all the previous findings. The

separation zone conspicuously extends, intensity of secondary

flows is reduced. The zone of mixing due to the tip leakage is

seen to extend more significantly in the radial direction, com-

pared to that of the windage flow. The effect of windage flow is

of a lesser consequence for the flow downstream of the rotor blades than that of the tip leakage flow due to the fact that its

flow rate at the source throat was assumed only 1.2%G1, com-

pared to 2.7%G1 for the tip leakage mass flow rate.

Fig. 7 is a quantitative reflection of the phenomena observed

on previous pictures. The figure shows a comparison of span-

wise distribution of kinetic energy losses in the rotor and stage,

computed for three considered variants. In all cases the losses

are calculated at a section located 42% of the axial chord down-

stream of the rotor trailing edge. There will certainly be more

loss further downstream as the mixing processes is not yet ac-

complished at the assumed test section. The shape of graphs

undergoes considerable redistribution over the considered com-

putational variants. For non-source/sink computations, similar

to pictures of entropy function contours, the maximum at the

mid-span is due to the merged root separation and secondary

flow vorticity. The second, lower maximum should be attrib-

uted to secondary flows at the opposite endwall. Source/sink

computations add losses near the endwalls as a result of interac-

tion (mixing) of the injected fluid from the sources with the

main stream in the exit diffuser downstream of the rotor trailing

edge. Although tip leakage and windage flow losses can not be

easily separated from other losses, especially the tip leakage

loss is seen to have a great share of the total stage loss. The loss

maximum due to separation at the root increases with the in-

creasing mass flow rate by-passing the blade-to-blade passage.The maximum due to secondary flows at the tip is hardly dis-

cernible from other sources of loss, giving testimony to the de-

creased rate of secondary flows in source/sink computations.

The presented results are obtained assuming that the me-

dium is extracted and injected through the sinks and sources in

the radial direction (no axial and swirl velocity). The investiga-

tions will be continued extending on extraction and, especially,

injection of tip leakage and windage jets also with axial and

swirl velocities according to the geometry of the tip leakage


8/8


Fig. 7. Span-wise distribution of kinetic energy losses in the rotor (1), stage without the exit velocity (2) and with the exit velocity (3) -


labyrinth seal and windage flow passages. It is expected that the

direction of the tip leakage jet re-entry as well as the angle at

which the windage jet is injected have a significant influence on

the entropy creation in the downstream mixing process.

CONCLUSIONSInvestigations of the effect of tip leakage over shrouded

rotor blades and windage jet on the flow through an HP stage of

an impulse turbine have been carried out using a 3D Navier-

Stokes code with source/sink-type permeable boundary condi-

tions implemented at places at the endwalls referring to design

locations of injection of leakage and windage flows into, or

their extraction from, the blade-to-blade passage. These ap-

proach enables tracing and quantitative evaluation of the proc-

ess of mixing of tip leakage and windage flows with the main

stream, and their interaction with secondary flows and separa-

tions. The investigations have been conducted for the medium

extracted and injected through the sinks and sources in the ra-dial direction with no axial and swirl velocity. More research is

required to find the effect of direction of the tip leakage jet re-

entry, or the effect of angle at which the windage jet is injected

on the entropy creation in the downstream mixing process.

ACKNOWLEDGEMENTS Part of numerical calculations for this paper were carried

out on work stations of the TASK Centre in Gdañsk.

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Documents

15004 Turbine HP Stage - Flow Characteristics