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