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 studies on ORC turbine flows TROVA@PoliMI 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 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 studies on ORC turbine flows TROVA@PoliMI 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 2011 2
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 11.20 Senaatszaal... Design issue The understanding of the gasdynamics of supercritical and close-to-critical flows is incomplete! A. Guardone et al, PoliMi September 23rd 2011 3
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 11.20 Senaatszaal... Design issue The understanding of the gasdynamics of supercritical and close-to-critical flows is incomplete! 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-gas thermodynamic models High compressibility Non-ideal dependence of the speed of sound c on specific volume v at constant T T [ C] 350 300 250 200 MDM Inlet 25 bar 10 bar 1 bar Outlet Dense gas dynamics 150 0 0.2 0.4 0.6 0.8 s [kj/(kg K)] 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-gas thermodynamic models High compressibility Non-ideal dependence of the speed of sound c on specific volume v at constant T T [ C] 350 300 250 200 MDM Inlet 25 bar 10 bar 1 bar Outlet Dense gas dynamics 150 0 0.2 0.4 0.6 0.8 s [kj/(kg K)] 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+ ρ c ( c ρ c sound speed ρ density s entropy p.u.m. ) s 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 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 2011 6
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 2011 6
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 2011 6
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 2011 6
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 2011 6
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 2011 6
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 2011 6
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 2011 7
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 2011 7
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 2011 7
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 0 5 10 15 x / H t 20 25 30 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 2011 8
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 0 5 10 15 x / H t 20 25 30 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 2011 8
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 0 5 10 15 x / H t 20 25 30 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 2011 8
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 0 5 10 15 x / H t 20 25 30 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 2011 8
Chapter: Governing equations and design procedure Recovery of perfect gas results 4 3 Ideal gas model Zucrow & Hoffman 1977 y / H t 2 1 0 4 3 0 1 2 3 4 5 6 7 8 x /H t Ideal gas model van der Waals model Perfect gas results Diatomic nitrogen dilute conditions y / H t 2 1 0 0 1 2 3 4 5 6 7 8 x /H t A. Guardone et al, PoliMi September 23rd 2011 9
Chapter: Design of the test nozzle Nozzle design for MDM Reservoir conditions P 0 = 25 bar T 0 = 310.3 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 2011 10
Chapter: Design of the test nozzle Nozzle design for MDM Reservoir conditions P 0 = 25 bar T 0 = 310.3 C Expansion ratio β = 25 Design conditions Exit Mach number M d = 2.25 Velocity vector parallel to x axis y / H t 20 15 10 5 0-5 -10 MDM Real gas Ideal Gas 0 10 20 30 x / H t M 2.2 2 1.8 1.6 1.4 1.2 1 A. Guardone et al, PoliMi September 23rd 2011 10
Chapter: Design of the test nozzle Nozzle design for MDM 5 M 2.2 2 0 1.8 1.6-5 1.4 PIG model 1.2 1-10 0 10 20 30 x / H t y / H t 20 15 10 MDM SW model dm dx = 1+(Γ 1)M2 M dh M 2 1 H dx y / H t 20 15 10 5 MDM SW model P (bar) 22 0 18 14-5 10 PIG model 6 2-10 0 10 20 30 x / H t dp dx = ρu2 P 1 P M 2 1 H dh dx y / H t 20 15 10 5 0-5 MDM SW model PIG model -10 0 10 20 30 x / H t Γ = 1+ ρ c ( Γ c ρ 2.3 1.9 1.5 1.1 0.7 0.3 ) s 2.2 2 15 MDM 3 2.5 MDM M 1.8 1.6 1.4 1.2 MDM SW model PIG model P (bar) 10 5 SW model PIG model Γ 2 1.5 1 0.5 SW model PIG model 1 0 5 10 15 20 25 30 x / H t 0 0 5 10 15 20 25 30 x / H t 0 0 5 10 15 20 25 30 x / H t A. Guardone et al, PoliMi September 23rd 2011 11
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 2011 12
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 2011 12
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 2011 12
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 10 5 0-5 -10 7 6 5 Ammonia Siloxanes MM, MDM, MD 2 M D 4, D 5,D 6 R245fa TolueneR245fa Toluene Ammonia 18 20 22 0 5 10 15 20 x A. Guardone et al, PoliMi September 23rd 2011 12
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 0-5 7 6 5 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 -10 18 20 22 0 5 10 15 20 x A. Guardone et al, PoliMi September 23rd 2011 12
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 2011 13
Chapter: Conclusions & future work Thank you! A. Guardone et al, PoliMi September 23rd 2011 14