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]
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
The VKI CT3 Facility
- Fully annular cascade facility
- Test time below 0.4 s
- Variable Reynolds and Mach number- RPM equal to 6500
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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&
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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&
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
von Karman Institute for Fluid Dynamics
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
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