Numerical study of multistage transcritical ORC axial turbines

Transcription

1 Numerical study of multistage transcritical ORC axial turbines L. Sciacovelli, P. Cinnella Laboratoire DynFluid - Arts et Métiers ParisTech 151 Boulevard de l Hôpital, Paris 08 October 2013 L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

2 Table of Contents 1 Context 2 Thermodynamic modelling and numerical method 3 Simulation setup 4 Results 5 Conclusions and perspectives L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

3 uperheating as shown in the diagram would not e realized due to the tremendous heat exchange rea Context needed due to the low heat-exchange oefficient for the gaseous phase. Temperature [ C] For the heat exchange system that transfers the heat from the heat source to the organic fluid, Supercritical ORCs are a promisingthe improvement efficiency is for defined ORCby technology the following equation: Subcritical subcritical ORC Supercritical supercritical ORC ORC Entropy [kj/kg] ,75 1,25 1,75 2,25 Comparison sub- and supercritical ORCs. [Karellas and Schuster, 2010] provides new frontiers in the investigation of ORC applications. Q& Organic fluid η HEx = (4) Q & Heat source Finally, the efficiency of the whole system is defined as follows: Heat source 2.1 Organic Fluids Figure 2. Sub- and supercritical ORC. Example Advantages: of R245fa. The first Problems: step when designing an ORC cycle application is the choice of the appropriate Higher thermal and heat recovery working fluid. The working Higherfluids pressures, which can higher be costs The thermal efficiency of the cycle is efficiencies used are well known mainly from refrigeration efined as follows: Difficulties in modelling the fluid technologies. The selection of the fluid is done Better thermal match in the heat exchanger P according to the process in the parameters critical of region the cycle. mech Simplified η th = (1) Q & cycle architecture According to the critical pressure and Thermal oil temperature, as well as the boiling temperature in various pressures, the appropriate fluid which η System P = Q& mech = η HEx η th (5) The above presented efficiencies will be used for the qualitative analysis of the ORC applications which will be described in this paper. Heating phase for an organic fluid at sub- and supercritical pressure. [Saleh et al., 2007] 2. Cycle design L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

4 Thermodynamic Modelling Candidate working fluids: R134a, R245fa, CO 2 Dense gas behavior modeled through EoS based on Helmholtz free energy Φ Reduced parameters δ = ρ/ρ c and τ = T c/t as indipendent variables EoS composed by ideal and residual part Φ 0 (δ, τ) = ln δ + a 1 ln τ + Φ r (δ, τ) = M 3 m=m 2 +1 M 5 m=m 4 +1 Φ(δ, τ) = Φ 0 (δ, τ) + Φ r (δ, τ) M 1 m=1 a mδ im τ jm + a mτ jm + M 4 m=m 3 +1 M 2 m=m 1 +1 a m ln[1 exp( u mτ)] a mδ im τ jm exp( δ km )+ a mδ im τ jm exp[ α m(δ ɛ m) 2 β m(τ γ m) 2 ] The ideal part requires an ancillary equation for the ideal-gas heat capacity Coefficients, exponents and number of terms calibrated on experimental data by means of an optimization algorithm [Setzmann and Wagner, 1989] L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

5 Thermodynamic Modelling Reference EoS available only for R134a and CO 2. For R245fa, the Span-Wagner short technical multiparameter EoS has been used The ideal part Φ 0 (δ, τ) conserves the same form Less accurate w.r.t. the complete EoS, due to the smaller experimental data bank available Φ r (δ, τ) = n 1δτ n 2δτ n 3δτ n 4δ 3 τ n 5δ 7 τ n 6δτ exp( δ)+ + n 7δ 2 τ 2.0 exp( δ) + n 8δ 5 τ exp( δ)+ + n 9δτ 3.5 exp( δ 2 ) + n 10δτ 6.5 exp( δ 2 )+ + n 11δ 4 τ 4.75 exp( δ 2 ) + n 12δ 2 τ 12.5 exp( δ 3 ) Fluid viscosity µ and thermal conductivity κ evaluated using the relations described in [Chung et al., 1988]: µ = FcM 1/2 w T 1/2 V 2/3 Ω v κm w = 3.75Ψ µc v C v/r L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

6 Numerical method Equations of motion: Ω(t) ω dω+ (f e f v ) n ds = s, ω = Ω(t) with p = p(e(ω), ρ(ω)) or Spatial discretization: Caloric EoS: Structured finite-volume approach Third-order accuracy, centered, conservative scheme with artificial viscosity Extension to curvilinear grid using weighting coefficients that take into account mesh deformations ρ ρv f e = ρe e = e(t (ω), ρ(ω)) Thermal EoS: p = p(t (ω), ρ(ω)) Time integration: ρv ρvv + pi ρvh f v = 0 τ τ v q Four-stage Runge-Kutta method with implicit residual smoothing Turbulence modeling: Algebraic Model: Baldwin-Lomax One-equation Model: Spalart-Allmaras L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

7 Rapport d avancement n.3- Partenaire n 1 ARTS Simulation setup Non conformal joins Stage 1 Stage N Wall Wall Outlet Inlet Wall Wall Mixing plane Wall Mixing plane Wall Mixing plane Mesh composed by C-blocks Inviscid model: 273x33 points Figure 1. Schématisation des domaines deand calcul etdownstream des conditions aux limites Distances upstream the respectively equal andthermodynami 0.2c, Les Fig.2-4 montrent blades l évolution sur le diagramme T-sto des0.15c conditions Viscous model: 389x49 points y+ = 1 being c the axial chord cours de la détente pour le trois fluides considérés. Les triangles indiquent le début et l chaque étage. La position de la courbe de détente par rapport à la courbe de coex Gap between rotor and stator: 0.35c liquide/vapeur révèle trois situations différentes: pour le R134a (Fig.2), dans le premie L. Sciacovelli - P. Cinnella (Dynfluid Lab) on a des conditions supertranscritiques, tandis que le reste 08 deoctober l'expansion ASME ORC et est7sous-c / 15

8 Simulation setup R134a R245fa CO 2 Both sub- and supercritical admission conditions for R134a and R245fa Supercritical admission conditions only for CO 2 (light, wet fluid) Parameters SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO 2 p0 (bar) T0 (K) Stages β β β β β tot L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

9 Results: inviscid model Turbine stage efficiencies for the inviscid model. Stage SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO Different isentropic efficiencies mainly due to different fluid dynamic behaviour Important parameter to evaluate the results: Fundamental derivative of Gas Dynamics [Thompson, 1971]: Γ = 1 + ρ ( ) a a ρ = (Γ 1) a ρ s a ρ L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

10 Results: viscous model Turbine stage efficiencies for the B-L model. Stage SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO Turbine stage efficiencies for the S-A model. Stage SUBR134a SUBR245fa SUPR134a SUPR245fa SUPCO Efficiencies about 10% lower w.r.t inviscid case Baldwin-Lomax predicts an efficiency about 1% higher than Spalart-Allmaras L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

11 Turbulence model comparison - R134a 1 st stage rotor Wall pressure on suction side slightly lower for B-L model Friction Coefficient higher for S-A model Dimensionless wall pressure Friction coefficient Overall S-A efficiency lower Results presented in the following are computed with B-L L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

12 Results: SUPR134a case Relative Mach Number Fundamental Derivative of Gas Dynamics Sound speed Presence of a weak shock at each rotor upper side, decreasing moving downstream I stage: Γ decreases but stays close to 1, thus sound speed nearly constant II-IV stage: Γ < 1, relative sound speed variation positive The higher the sound speed, the weaker the shocks L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

13 Results: SUBR245fa vs SUBR134a R245fa R134a Γ 1 Sound speed nearly constant Stronger shocks Lower efficiencies Relative Mach Number Relative Mach Number Better behavior for R134a Fundamental Derivative of Gas Dynamics Fundamental Derivative of Gas Dynamics L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

14 Results: SUPCO2 case Relative Mach Number Sound speed Supercritical expansion, Γ > 1 always Light fluid: high sound speed Absence of shocks: maximum efficiency in viscous and inviscid cases Higher plant costs due to higher mean pressures of the cycle Fundamental Derivative of Gas Dynamics L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

15 Conclusions and perspectives Conclusions: In all the test cases performed, transcritical and supercritical admission conditions allowed to increase the turbine isentropic efficiency Overall efficiencies are globally about 10% lower than inviscid ones Viscous and inviscid models provide similar flow evolutions, due to the absence of recirculation zones and unsteady effects being neglected The B-L and S-A turbulence models predict similar results in terms of overall efficiency and evolution of thermodynamic variables CO 2 has the best fluid dynamic behavior, but also higher plant costs R134a ensures satisfactory adiabatic efficiencies, despite the presence of weak shocks at the suction sides of the rotor blades R245fa develops stronger shocks for the same configuration, leading to higher losses SUPR134a is the best compromise between fluid dynamic behavior and plant requirements for the ORC. Perspectives: 2D unsteady simulations in order to evaluate wakes and transient effects 3D viscous simulations L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

16 THANKS FOR THE ATTENTION L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

17 References Chen, H., Goswami, D., and Stefanakos, E. (2010). A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renewable and Sustainable Energy Reviews, 14(9): Chung, T. H., Ajlan, M., Lee, L. L., and Starling, K. E. (1988). Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Industrial & engineering chemistry research, 27(4): Karellas, S. and Schuster, A. (2010). Supercritical fluid parameters in Organic Rankine Cycle applications. International Journal of Thermodynamics, 11(3): Saleh, B., Koglbauer, G., Wendland, M., and Fischer, J. (2007). Working fluids for low-temperature Organic Rankine Cycles. Energy, 32(7): Setzmann, U. and Wagner, W. (1989). A new method for optimizing the structure of thermodynamic correlation equations. International Journal of Thermophysics, 10(6): Thompson, P. (1971). A Fundamental Derivative in Gas Dynamics. Physics of Fluids, 14: L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15

18 Isentropic or dry fluids were suggested for organic Rankine cycle to avoid liquid droplet impingent in the turbine blades during Supercritical ORCs [(Fig._4)TD$FIG] the expansion. However, if the fluid is too dry, the expanded Fig. Saturated 4. Three types vapour of curve working slope fluids: for three dry, different isentropic, working and fluids. wet. [Chen et al., 2010] the two-phase region (the dashed lines in Fig. 5(a) an fluids may leave the turbine with substantial amount of which adds to the burden for the condensation pr recovery system is needed. Wet fluids, on the other han higher turbine inlet temperature to avoid two-phase there is less concern about desuperheating after the ex the process is allowed to pass through the two-phase solid Saturated lines in Fig. vapour 5), thecurve dry fluid slope can still leave the superheated state, while wet fluid stays in the Fluid thermodynamic properties region at the turbine exit. Bakhtar et al. [64 68] foun wet fluid, such as, water, fluid first subcools and the Cycle thermodynamic properties: to become a two-phase mixture. The formation and beh liquid enthalpy in thefall, turbine turbine creatework, problems global that would performance efficiency; of the turbine. For dry fluids, Goswami et Demuth [70,71] found that only extremely fine droplets formed Turbine thesize two-phase region and no liquid was actu to damage the turbine before it started drying expansion. Environmental Demuth [70] properties also found that the turbine p should not degrade significantly as a result of t expansion Economic process criteria passing through and leaving th region if condensation occurs. Meanwhile, potential net Knowledge fluid effectiveness of an onaccurate the order ofeos 8% can be achieve Criteria for the working fluid choice: Candidate working fluids: R134a, R245fa, CO 2 Fluid name Molar mass (g/mol) T c (K) p c (kpa) ρ c (mol/l) R134a R245fa CO L. Sciacovelli - P. Cinnella (Dynfluid Lab) ASME ORC October / 15