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ORC 2011 First International Seminar on ORC Power Systems,
Delft, NL, 22-23 September 2011
Influence of Molecular Complexity on
Nozzle Design for an Organic Vapor
Wind Tunnel
A. Guardone, Aerospace Eng. Dept., PoliMI
A. Spinelli, V. Dossena, Energy Dept., PoliMI
V. Vandecauter,Aerospace Eng., TUDelft
A. Guardone et al, PoliMi September 23rd 2011 1
Chapter: Expanders for ORC Applications
Motivation & Current Activities
Motivation of the proposed work:
Improvement of the performances of Organic Rankine Cycles(ORC) via better turbine design calls for experimental studieson ORC turbine flows
TROVA@PoliMI
is designed to provide experimental data for flows typical ofORC turbine blade passages
is a blow-down facily; expansion occurs through a test section:straight axis, planar, convergent-divergent nozzle
Working fluid: siloxane MDM
A. Guardone et al, PoliMi September 23rd 2011 2
Chapter: Expanders for ORC Applications
Motivation & Current Activities
Motivation of the proposed work:
Improvement of the performances of Organic Rankine Cycles(ORC) via better turbine design calls for experimental studieson ORC turbine flows
TROVA@PoliMI
is designed to provide experimental data for flows typical ofORC turbine blade passages
is a blow-down facily; expansion occurs through a test section:straight axis, planar, convergent-divergent nozzle
Working fluid: siloxane MDM
A. Guardone et al, PoliMi September 23rd 2011 2
Chapter: Expanders for ORC Applications
TROVA@PoliMI
Presentation at 11.20 Senaatszaal. . .
TMD Cycle
4 - High Pressure Vessel
6 - Nozzle Inlet
7 - Nozzle Outlet
8 - Low Pressure Vessel
Design issue
The understanding of thegasdynamics of supercriticaland close-to-critical flows isincomplete!
A. Guardone et al, PoliMi September 23rd 2011 3
Chapter: Expanders for ORC Applications
TROVA@PoliMI
Presentation at 11.20 Senaatszaal. . .
TMD Cycle
4 - High Pressure Vessel
6 - Nozzle Inlet
7 - Nozzle Outlet
8 - Low Pressure Vessel
Design issue
The understanding of thegasdynamics of supercriticaland close-to-critical flows isincomplete!
A. Guardone et al, PoliMi September 23rd 2011 3
Chapter: Expanders for ORC Applications
Nozzle design for ORC applications
Expansion occurs in highly non-ideal gas conditions
Real-gasthermodynamicmodels
High compressibility
Non-ideal dependenceof the speed of sound con specific volume v atconstant T
Dense gas dynamics
Inlet
Outlet
s [kJ/(kg K)]
T[°
C]
0 0.2 0.4 0.6 0.8
150
200
250
300
35025 bar
10 bar
1 bar
MDM
A. Guardone et al, PoliMi September 23rd 2011 4
Chapter: Expanders for ORC Applications
Nozzle design for ORC applications
Expansion occurs in highly non-ideal gas conditions
Real-gasthermodynamicmodels
High compressibility
Non-ideal dependenceof the speed of sound con specific volume v atconstant T
Dense gas dynamics
Inlet
Outlet
s [kJ/(kg K)]
T[°
C]
0 0.2 0.4 0.6 0.8
150
200
250
300
35025 bar
10 bar
1 bar
MDM
A. Guardone et al, PoliMi September 23rd 2011 4
Chapter: Expanders for ORC Applications
Fundamental derivative of gasdynamics
Phil Thompson, J. Fluids Mech. 1971
Fundamental derivative Γ
Γ = 1 + ρc
(
∂c∂ρ
)
s
c sound speedρ densitys entropy p.u.m.
A. Guardone et al, PoliMi September 23rd 2011 5
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Expanders for ORC Applications
Goal of the research
Goal of the research
To design the divergent section ofsubsonic-supersonic nozzles operatingin the dense gas regime
Assumptions
Flow is two-dimensional, flow is expanding from uniformreservoir conditions into uniform ambient conditions,high-Reynolds number flow, no flow separation, no shock waves,adiabatic walls
A. Guardone et al, PoliMi September 23rd 2011 6
Chapter: Governing equations and design procedure
Mathematical model
Full potential equation
Compressible non-viscous isentropic irrotational flow(
Φ2x − c
2)
Φxx + 2ΦxΦyΦxy +(
Φ2y − c
2)
Φyy = 0
with Φ ∈ R, u = Φx and v = Φ flow velocities, w2 = u2 + v2.
Thermodynamic closure
c = c(s, h) = c(sr, hr − w2/2) ?
StanMix and RefProp libraries in FluidProp:- Stryjek-Vera Peng-Robinson cubic EOS (PRSV)- Span Wagner multiparameter EOS (SW)
A. Guardone et al, PoliMi September 23rd 2011 7
Chapter: Governing equations and design procedure
Mathematical model
Full potential equation
Compressible non-viscous isentropic irrotational flow(
Φ2x − c
2)
Φxx + 2ΦxΦyΦxy +(
Φ2y − c
2)
Φyy = 0
with Φ ∈ R, u = Φx and v = Φ flow velocities, w2 = u2 + v2.
Thermodynamic closure
c = c(s, h) = c(sr, hr − w2/2) ?
StanMix and RefProp libraries in FluidProp:- Stryjek-Vera Peng-Robinson cubic EOS (PRSV)- Span Wagner multiparameter EOS (SW)
A. Guardone et al, PoliMi September 23rd 2011 7
Chapter: Governing equations and design procedure
Mathematical model
Full potential equation
Compressible non-viscous isentropic irrotational flow(
Φ2x − c
2)
Φxx + 2ΦxΦyΦxy +(
Φ2y − c
2)
Φyy = 0
with Φ ∈ R, u = Φx and v = Φ flow velocities, w2 = u2 + v2.
Thermodynamic closure
c = c(s, h) = c(sr, hr − w2/2) ?
StanMix and RefProp libraries in FluidProp:- Stryjek-Vera Peng-Robinson cubic EOS (PRSV)- Span Wagner multiparameter EOS (SW)
A. Guardone et al, PoliMi September 23rd 2011 7
Chapter: Governing equations and design procedure
Design procedure
Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977)
x / Ht
y/H
t
0 5 10 15 20 25 30
0
5
10
D
I
K
B
E
F
Initial data (BD)
Sauer (1947) scheme2Γ∗φxφxx − φyy = 0
Kernel region (BIKD)
Direct MOC frominitial data line BD
Turning region (IKF)
Inverse MOC from exitcharacteristic KF
A. Guardone et al, PoliMi September 23rd 2011 8
Chapter: Governing equations and design procedure
Design procedure
Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977)
x / Ht
y/H
t
0 5 10 15 20 25 30
0
5
10
D
I
K
B
E
F
Initial data (BD)
Sauer (1947) scheme2Γ∗φxφxx − φyy = 0
Kernel region (BIKD)
Direct MOC frominitial data line BD
Turning region (IKF)
Inverse MOC from exitcharacteristic KF
A. Guardone et al, PoliMi September 23rd 2011 8
Chapter: Governing equations and design procedure
Design procedure
Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977)
x / Ht
y/H
t
0 5 10 15 20 25 30
0
5
10
D
I
K
B
E
F
Initial data (BD)
Sauer (1947) scheme2Γ∗φxφxx − φyy = 0
Kernel region (BIKD)
Direct MOC frominitial data line BD
Turning region (IKF)
Inverse MOC from exitcharacteristic KF
A. Guardone et al, PoliMi September 23rd 2011 8
Chapter: Governing equations and design procedure
Design procedure
Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977)
x / Ht
y/H
t
0 5 10 15 20 25 30
0
5
10
D
I
K
B
E
F
Initial data (BD)
Sauer (1947) scheme2Γ∗φxφxx − φyy = 0
Kernel region (BIKD)
Direct MOC frominitial data line BD
Turning region (IKF)
Inverse MOC from exitcharacteristic KF
A. Guardone et al, PoliMi September 23rd 2011 8
Chapter: Governing equations and design procedure
Recovery of perfect gas results
x /Ht
y/H
t
0 1 2 3 4 5 6 7 8
0
1
2
3
4
Ideal gas modelZucrow & Hoffman 1977
x /Ht
y/H
t
0 1 2 3 4 5 6 7 8
0
1
2
3
4
Ideal gas modelvan der Waals model
Perfect gas results
Diatomic nitrogendilute conditions
A. Guardone et al, PoliMi September 23rd 2011 9
Chapter: Design of the test nozzle
Nozzle design for MDM
Reservoir conditions
P0 = 25 barT0 = 310.3 ◦C
Expansion ratio
β = 25
Design conditions
Exit Mach numberMd = 2.25Velocity vector parallelto x axis
A. Guardone et al, PoliMi September 23rd 2011 10
Chapter: Design of the test nozzle
Nozzle design for MDM
Reservoir conditions
P0 = 25 barT0 = 310.3 ◦C
Expansion ratio
β = 25
Design conditions
Exit Mach numberMd = 2.25Velocity vector parallelto x axis x / Ht
y/H
t
0 10 20 30
-10
-5
0
5
10
15
20
M2.221.81.61.41.21
Ideal Gas
MDM
Real gas
A. Guardone et al, PoliMi September 23rd 2011 10
Chapter: Design of the test nozzle
Nozzle design for MDM
x / Ht
y/H
t
0 10 20 30
-10
-5
0
5
10
15
20
M2.221.81.61.41.21
PIG model
SW model
MDM
dMdx = 1+(Γ−1)M2
M2−1
MH
dHdx
x / Ht
M
0 5 10 15 20 25 301
1.2
1.4
1.6
1.8
2
2.2
SW modelPIG model
MDM
x / Ht
y/H
t0 10 20 30
-10
-5
0
5
10
15
20
2218141062
MDM
PIG model
SW model
P (bar)
dPdx = ρu2
P1
M2−1
PH
dHdx
x / Ht
P(b
ar)
0 5 10 15 20 25 300
5
10
15
SW modelPIG model
MDM
x / Ht
y/H
t
0 10 20 30
-10
-5
0
5
10
15
20
2.31.91.51.10.70.3
MDM
PIG model
SW model
Γ
Γ = 1 + ρc
(
∂c∂ρ
)
s
x / HtΓ
0 5 10 15 20 25 300
0.5
1
1.5
2
2.5
3
SW modelPIG model
MDM
A. Guardone et al, PoliMi September 23rd 2011 11
Chapter: Influence of molecular complexity
Nozzle design for different fluids
Fluids
D4, D5, D6,MM, MDM, MD2MR245fa, Toluene,Ammonia
A. Guardone et al, PoliMi September 23rd 2011 12
Chapter: Influence of molecular complexity
Nozzle design for different fluids
Fluids
D4, D5, D6,MM, MDM, MD2MR245fa, Toluene,Ammonia
Warning
Thermal decomposition!!!
A. Guardone et al, PoliMi September 23rd 2011 12
Chapter: Influence of molecular complexity
Nozzle design for different fluids
Fluids
D4, D5, D6,MM, MDM, MD2MR245fa, Toluene,Ammonia
Warning
Thermal decomposition!!!
Design parameters
P0 = 0.78Pc
T0 = 0.975Tc
β = 25 → Pd = 0.031Pc
A. Guardone et al, PoliMi September 23rd 2011 12
Chapter: Influence of molecular complexity
Nozzle design for different fluids
Fluids
D4, D5, D6,MM, MDM, MD2MR245fa, Toluene,Ammonia
Warning
Thermal decomposition!!!
Design parameters
P0 = 0.78Pc
T0 = 0.975Tc
β = 25 → Pd = 0.031Pc
18 20 22
5
6
7
TolueneR245fa
D4, D5,D6
MM, MDM,MD2M
Ammonia
x
y
0 5 10 15 20
-10
-5
0
5
10
Ammonia
R245faToluene
Siloxanes
A. Guardone et al, PoliMi September 23rd 2011 12
Chapter: Influence of molecular complexity
Nozzle design for different fluids
Fluids
D4, D5, D6,MM, MDM, MD2MR245fa, Toluene,Ammonia
Warning
Thermal decomposition!!!
Design parameters
P0 = 0.78Pc
T0 = 0.975Tc
β = 25 → Pd = 0.031Pcx
y
0 5 10 15 20
-10
-5
0
5
10
18 20 22
5
6
7
TolueneR245fa
D4, D5,D6
MM, MDM,MD2M
Ammonia
Zoom area
A. Guardone et al, PoliMi September 23rd 2011 12
Chapter: Conclusions & future work
Conclusions
A nozzle design tool for dense gases was developed andvalidated against ideal gas results using the the cubicPRSV EoS and the multi-parameter Span-Wagner EoS inFluidProp
If the expansion process occurs in region where Γ is lessthan its dilute-gas value, then resulting nozzles are longer,in accordance with the one-dimensional theory.
For increasing molecular complexity of the fluid, Γdecreases and the nozzle length increases.
Caution: normalized mass flow varies dramatically for thediverse operating conditions
A. Guardone et al, PoliMi September 23rd 2011 13
Chapter: Conclusions & future work
Thank you!
A. Guardone et al, PoliMi September 23rd 2011 14