Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel

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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

1 ORC 2011 First International Seminar on ORC Power Systems, Delft, NL, 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

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 studies on ORC turbine flows is designed to provide experimental data for flows typical of ORC 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

3 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 studies on ORC turbine flows is designed to provide experimental data for flows typical of ORC 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

Chapter: Expanders for ORC Applications TROVA@PoliMI TMD Cycle 4 - High Pressure Vessel 6 - Nozzle Inlet 7 - Nozzle Outlet 8 - Low Pressure Vessel Presentation at 11.

4 Chapter: Expanders for ORC Applications TMD Cycle 4 - High Pressure Vessel 6 - Nozzle Inlet 7 - Nozzle Outlet 8 - Low Pressure Vessel Presentation at Senaatszaal... Design issue The understanding of the gasdynamics of supercritical and close-to-critical flows is incomplete! A. Guardone et al, PoliMi September 23rd

5 Chapter: Expanders for ORC Applications TMD Cycle 4 - High Pressure Vessel 6 - Nozzle Inlet 7 - Nozzle Outlet 8 - Low Pressure Vessel Presentation at Senaatszaal... Design issue The understanding of the gasdynamics of supercritical and close-to-critical flows is incomplete! A. Guardone et al, PoliMi September 23rd

6 Chapter: Expanders for ORC Applications Nozzle design for ORC applications Expansion occurs in highly non-ideal gas conditions Real-gas thermodynamic models High compressibility Non-ideal dependence of the speed of sound c on specific volume v at constant T T [ C] MDM Inlet 25 bar 10 bar 1 bar Outlet Dense gas dynamics s [kj/(kg K)] A. Guardone et al, PoliMi September 23rd

7 Chapter: Expanders for ORC Applications Nozzle design for ORC applications Expansion occurs in highly non-ideal gas conditions Real-gas thermodynamic models High compressibility Non-ideal dependence of the speed of sound c on specific volume v at constant T T [ C] MDM Inlet 25 bar 10 bar 1 bar Outlet Dense gas dynamics s [kj/(kg K)] A. Guardone et al, PoliMi September 23rd

8 Chapter: Expanders for ORC Applications Fundamental derivative of gasdynamics Phil Thompson, J. Fluids Mech Fundamental derivative Γ Γ = 1+ ρ c ( c ρ c sound speed ρ density s entropy p.u.m. ) s A. Guardone et al, PoliMi September 23rd

Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is

9 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

10 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

11 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

12 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

13 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

14 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

15 Chapter: Expanders for ORC Applications Goal of the research Goal of the research To design the divergent section of subsonic-supersonic nozzles operating in the dense gas regime Assumptions Flow is two-dimensional, flow is expanding from uniform reservoir conditions into uniform ambient conditions, high-reynolds number flow, no flow separation, no shock waves, adiabatic walls A. Guardone et al, PoliMi September 23rd

16 Chapter: Governing equations and design procedure Mathematical model Full potential equation Compressible non-viscous isentropic irrotational flow ( Φ 2 x c 2) Φ xx +2Φ x Φ y Φ xy + ( Φ 2 y c2) Φ yy = 0 with Φ R, u = Φ x and v = Φ flow velocities, w 2 = u 2 +v 2. Thermodynamic closure c = c(s,h) = c(s r,h r w 2 /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

17 Chapter: Governing equations and design procedure Mathematical model Full potential equation Compressible non-viscous isentropic irrotational flow ( Φ 2 x c 2) Φ xx +2Φ x Φ y Φ xy + ( Φ 2 y c2) Φ yy = 0 with Φ R, u = Φ x and v = Φ flow velocities, w 2 = u 2 +v 2. Thermodynamic closure c = c(s,h) = c(s r,h r w 2 /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

18 Chapter: Governing equations and design procedure Mathematical model Full potential equation Compressible non-viscous isentropic irrotational flow ( Φ 2 x c 2) Φ xx +2Φ x Φ y Φ xy + ( Φ 2 y c2) Φ yy = 0 with Φ R, u = Φ x and v = Φ flow velocities, w 2 = u 2 +v 2. Thermodynamic closure c = c(s,h) = c(s r,h r w 2 /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

19 Chapter: Governing equations and design procedure Design procedure Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977) 10 F y / H t 5 I B 0 D E K x / H t Initial data (BD) Sauer (1947) scheme 2Γ φ x φ xx φ yy = 0 Kernel region (BIKD) Direct MOC from initial data line BD Turning region (IKF) Inverse MOC from exit characteristic KF A. Guardone et al, PoliMi September 23rd

20 Chapter: Governing equations and design procedure Design procedure Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977) 10 F y / H t 5 I B 0 D E K x / H t Initial data (BD) Sauer (1947) scheme 2Γ φ x φ xx φ yy = 0 Kernel region (BIKD) Direct MOC from initial data line BD Turning region (IKF) Inverse MOC from exit characteristic KF A. Guardone et al, PoliMi September 23rd

21 Chapter: Governing equations and design procedure Design procedure Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977) 10 F y / H t 5 I B 0 D E K x / H t Initial data (BD) Sauer (1947) scheme 2Γ φ x φ xx φ yy = 0 Kernel region (BIKD) Direct MOC from initial data line BD Turning region (IKF) Inverse MOC from exit characteristic KF A. Guardone et al, PoliMi September 23rd

22 Chapter: Governing equations and design procedure Design procedure Method Of Characteristics (MOC) (Zucrow & Hoffman, 1977) 10 F y / H t 5 I B 0 D E K x / H t Initial data (BD) Sauer (1947) scheme 2Γ φ x φ xx φ yy = 0 Kernel region (BIKD) Direct MOC from initial data line BD Turning region (IKF) Inverse MOC from exit characteristic KF A. Guardone et al, PoliMi September 23rd

23 Chapter: Governing equations and design procedure Recovery of perfect gas results 4 3 Ideal gas model Zucrow & Hoffman 1977 y / H t x /H t Ideal gas model van der Waals model Perfect gas results Diatomic nitrogen dilute conditions y / H t x /H t A. Guardone et al, PoliMi September 23rd

24 Chapter: Design of the test nozzle Nozzle design for MDM Reservoir conditions P 0 = 25 bar T 0 = C Expansion ratio β = 25 Design conditions Exit Mach number M d = 2.25 Velocity vector parallel to x axis A. Guardone et al, PoliMi September 23rd

25 Chapter: Design of the test nozzle Nozzle design for MDM Reservoir conditions P 0 = 25 bar T 0 = C Expansion ratio β = 25 Design conditions Exit Mach number M d = 2.25 Velocity vector parallel to x axis y / H t MDM Real gas Ideal Gas x / H t M A. Guardone et al, PoliMi September 23rd

26 Chapter: Design of the test nozzle Nozzle design for MDM 5 M PIG model x / H t y / H t MDM SW model dm dx = 1+(Γ 1)M2 M dh M 2 1 H dx y / H t MDM SW model P (bar) PIG model x / H t dp dx = ρu2 P 1 P M 2 1 H dh dx y / H t MDM SW model PIG model x / H t Γ = 1+ ρ c ( Γ c ρ ) s MDM MDM M MDM SW model PIG model P (bar) 10 5 SW model PIG model Γ SW model PIG model x / H t x / H t x / H t A. Guardone et al, PoliMi September 23rd

27 Chapter: Influence of molecular complexity Nozzle design for different fluids Fluids D 4, D 5, D 6, MM, MDM, MD 2 M R245fa, Toluene, Ammonia A. Guardone et al, PoliMi September 23rd

28 Chapter: Influence of molecular complexity Nozzle design for different fluids Fluids D 4, D 5, D 6, MM, MDM, MD 2 M R245fa, Toluene, Ammonia Warning Thermal decomposition!!! A. Guardone et al, PoliMi September 23rd

29 Chapter: Influence of molecular complexity Nozzle design for different fluids Fluids D 4, D 5, D 6, MM, MDM, MD 2 M R245fa, Toluene, Ammonia Warning Thermal decomposition!!! Design parameters P 0 = 0.78P c T 0 = 0.975T c β = 25 P d = 0.031P c A. Guardone et al, PoliMi September 23rd

30 Chapter: Influence of molecular complexity Nozzle design for different fluids Fluids D 4, D 5, D 6, MM, MDM, MD 2 M R245fa, Toluene, Ammonia Warning Thermal decomposition!!! Design parameters P 0 = 0.78P c T 0 = 0.975T c β = 25 P d = 0.031P c y Ammonia Siloxanes MM, MDM, MD 2 M D 4, D 5,D 6 R245fa TolueneR245fa Toluene Ammonia x A. Guardone et al, PoliMi September 23rd

31 Chapter: Influence of molecular complexity Nozzle design for different fluids Fluids D 4, D 5, D 6, MM, MDM, MD 2 M R245fa, Toluene, Ammonia 10 5 Zoom area Warning Thermal decomposition!!! Design parameters y MM, MDM, MD 2 M Ammonia D 4, D 5,D 6 R245fa Toluene P 0 = 0.78P c T 0 = 0.975T c β = 25 P d = 0.031P c x A. Guardone et al, PoliMi September 23rd

32 Chapter: Conclusions & future work Conclusions A nozzle design tool for dense gases was developed and validated against ideal gas results using the the cubic PRSV EoS and the multi-parameter Span-Wagner EoS in FluidProp If the expansion process occurs in region where Γ is less than its dilute-gas value, then resulting nozzles are longer, in accordance with the one-dimensional theory. For increasing molecular complexity of the fluid, Γ decreases and the nozzle length increases. Caution: normalized mass flow varies dramatically for the diverse operating conditions A. Guardone et al, PoliMi September 23rd

33 Chapter: Conclusions & future work Thank you! A. Guardone et al, PoliMi September 23rd

Design, Simulation and Construction of a Test Rig for Organic Vapours

1 st International Seminar on ORC Power Systems Sept 22-23, 2011 Delft, NL Design, Simulation and Construction of a Test Rig for Organic Vapours A. Spinelli, M. Pini, V. Dossena, P. Gaetani, F. Casella