TURBINE MASS FLOW EVALUATION IN A ... Karman Institute for Fluid Dynamics The VKI CT3 Facility - Fully annular cascade facility - Test time below 0.4 s - Variable Reynolds and Mach

von Karman Institute for Fluid Dynamics

TURBINE MASS FLOW EVALUATION IN A COMPRESSION TUBE FACILITY

Luca Porreca and Rémy Dénos

Von Karman Institute for Fluid Dynamics,Turbomachinery Department1640 Rhode Saint Genèse

Belgiumcontact: [email protected]


Table of contents

- The VKI CT3 facility

- The VKI CT3 model

automatic fitting of the experimental data

model validation against experimental data

- Mass flow calculation

- Uncertainty analysis

- Conclusions


The VKI CT3 Facility

- Fully annular cascade facility

- Test time below 0.4 s

- Variable Reynolds and Mach number- RPM equal to 6500


Modelisation of the compression tubeShutter valve closed

Vol 1 Vol 2

inm&

Two logical step

the piston is blocked in its position

( )101

1

110101 1

−− −+

+= iin

ii TTx

xTT γ

+= −

101

10101 1 x

TT

PP iinii γ

- Volume 1: injection of inm∆

iin

mmx

11

∆=

tmmmm inii ∆=−=∆ − &1

111

thmumum ininiiii ∆=− −− &1

11

111

iv

i Tcu =

iiii RTmVP 1111 =

mass conservation

energy balance

perfect gas

the piston is sliding until p2=p1

- No mass is admitted

- Volume 1 and 2: isentropic evolution

γ

=

−

− i

i

i

i

V

V

P

P

1

11

11

1

γ1

11

11

1

1

−

−−

=

y

i

i

i

i

P

P

T

T

Vol 1 Vol 2


Shutter valve opened

the piston is sliding until p2=p1

- No mass is admitted or ejected

- Volume 1 and 2: isentropic evolutionγ

=

−

− i

i

i

i

V

V

P

P

1

11

11

1

γ1

11

11

1

1

−

−−

=

y

i

i

i

i

P

P

T

T

Vol 1 Vol 2Vol 1 Vol 2

inm& outm&

the piston is blocked in its position

- Volume 1: injection of inm∆- Volume 2: ejection of outm∆

( )102,01,

2,1

2,1102,0102,01 1

−− −+

±= ioutin

ii TTx

xTT γ

±= −

2,102,01

,102,0102,01 1 x

T

TPP i

outinii γ

iin

mmx

11

∆=i

out

mmx

22

∆=

Vent hole valve


Modelisation of the test section

dump tank

Vent hole valve

stage

Test section

Sonic throat Leakm&Coolm&

)(

)(

)(

3

03

03

tm

tT

tP

)(

)(

0

0

tT

tP

ex

ex

04,hmS&outout hm ,&

Balance of mass flows and internal energy:

( )11)( 1

0300003 −+−++

+−+=

−

γγ

SLeakCoolout

iLeakLeakCoolCooloutouti

xxxxTTxTxTx

T

3

03303 V

RTmP

iii =

Compression tube


Mass flow evolutionoutm&

- Choked condition

ConstT

tAPm V

out02

02 )(=&

- Unchoked condition

Static pressure pv is artificially coupled to P02

iTSc

iV

i PPPP ∆−∆=−02

difference between P02(t) and P03(t)i

TSP∆

cP∆ difference between P02(t) and pv in steady condition (knowledge of Mach number)

Shutter opening law AV(t) is implemented

Vent hole valve

Settling chamberCompression tube

)()(

02

02

tTtP

)()(

03

03

tTtPVP

outm&stage


Turbine stage

π03

0

PP ex =

−−=

−γγ

πη1

030 11TT ex

- from the stage pressure ratio:

Dump tank closed volume with injection of Sm&

Mass flow evolutionSm&- from the pressure ratio : )()( 40 tptP ex

44

4 RTARTp

m SS γ=& unchoked condition

ConstAtT

tPm S

ex

exS ⋅=

)()(

0

0& choked condition

sonic throat areaSA

dump tank

Sm&04Pstage

Test section

Sonic throat

)()(

0

0

tTtP

ex

ex


Shutter opens

Fitting of the tube pressure evolution

Validation against the experimental data

The model is able to calculate the mass flow for each test

Initial conditions: initial tube pressure and temperature

Two parameters are needed: and ASinm&

inm&same sonic throat area

SA

significant test to test variation of the pressure slope non perfect matching

“Matching conditions”out

out

in

in mmρρ&&

=

Vol 1 Vol 2

inm& outm&


Validation against the experimental datapiston displacement

- piston is decelerating until the shutter opens

- piston velocity is constant during the blowdown

shutter opens

- good agreement between calculated and measured detection signals

isentropic assumption is reasonable

Re Nom

Re High


Pressure and temperature in the test section

Validation against the experimental data

- the steady value of P03 and T03 is set by imposing the losses

- the transient and test time is well predicted

- the peak in the temperature is due to the sudden compression in the settling chamber

Re NomRe High03P Re NomRe High03T


Mass flow evaluation: results

Re Nom

Vent hole outm&

Sonic throat Sm&

Re High

Vent hole outm&

Sonic throat Sm&

- the mass flows are matching after the transient time

- the difference between and is provided by the coolants and the leakage flows

outm& Sm&


Mass flow evaluation: uncertainty analysis- most critical parameter: sonic throat area

1% of area variation 0.62% in the mass flow

- Uncertainty in the slope detection provides an inaccuracy in the sonic throat area computation

- The uncertainty is larger at High Reynolds than at Nom Reynolds

Re Nom Re High


Mass flow calculation from the integration of the

pitchwise averaged data

- Most sensitive parameter Downstream Total pressure

,,, 00 exexex TP α

Total exit temperature

Re nom P/p nom

Re nom P/p nom

Re nom P/p nom

Absolute exit angle

Mass flow evaluation: using P.W.A. Data


Mass flow evaluation: results

-15.352% rotor cooling [kg/s]

+/- 0.21 %Dispersion

+/- 1.6 %Uncertainty

-15.363% rotor cooling [kg/s]

-15.27without rotor cooling [kg/s]

+/- 1.43 %Dispersion

1 and ½ stage

+/- 3.92 %+/- 0.82 %Uncertainty

10.5210.1 P/p Nom Re Low [kg/s]

10.5410.55 P/p Nom Re Nom [kg/s]

P.A.ProfileCt3 Model1 stage


Conclusions

A model of the VKI CT3 facility is developed and validated

- simple approach

- the isentropic compression assumptions is reasonable

- good agreement between calculated and measured values

Better understanding of the flow parameters in the test rig

Easily usable for compression tube facilities

Usable to predict and/or design different test conditions

Stage mass flow calculation is performed

accurate evaluation for each test (uncertainty of +/- 0.82% or +/- 1.6 %)

compared with P.W.A. profile calculation

Documents

TURBINE MASS FLOW EVALUATION IN A ... Karman Institute for Fluid Dynamics The VKI CT3 Facility - Fully annular cascade facility - Test time below 0.4 s - Variable Reynolds and Mach