Organic Rankine Cycles

Giovanni Manente

University of Padova

University of Ljubljana, April 2017 Photograph of a 250-kW ORC prototype. (1) Preheater, (2) evaporator, (3) turbine, (4) generator, (5) condenser, (6) pump, (A) cooling water inlet, (B) cooling water outlet, (C) hot water inlet, (D) hot water outlet.

Outline of the presentation

• Organic Rankine Cycle configuration 3

• Thermodynamic properties of organic fluids 8

• Choice of the optimum evaporation T and working fluid 13

• Supercritical ORC configurations 23

• Mixtures of organic fluids and Kalina cycle 27

• ORC coupled to internal combustion engines 32

• Other evaluation metrics in working fluid selection 36

• Thermodynamic optimization of ORC 39

• Axial and radial turbines in ORC 44 – Traditional efficiency prediction tools 47 – Main features of the developed meanline model 56 – New efficiency prediction maps for axial flow turbines 65 – Inclusion of the new maps in the design optimization of ORC 75

2

A geothermal Organic Rankine Cycle system (ORC)

(DiPippo, Geothermal power plants, 2008) 3

Geofluid in the ORC

• The production wells (PW) are fitted with pumps (P) that are set below the flash depth determined by the reservoir properties and the desired flow rate

• Sand removers (SR) may be needed to prevent scouring and erosion of the piping and heat exchanger tubes

• The geofluid is everywhere kept at a pressure above its flash point and is reinjected in injection wells (IW) still in the liquid phase

• The geofluid temperature is not allowed to drop to the point where silica scaling could become an issue in the preheater and in the piping and injection wells

4

Working fluid in the ORC

• The working fluid, chosen for its appropriate thermodynamic properties, receives heat from the geofluid, evaporates, expands through a turbine, condenses and is returned to the evaporator by means of a feedpump

• There are two steps in the heating-boiling process, conducted in the preheater (PH) where the working fluid is brought to its boiling point and in the evaporator (E) from which it emerges as a saturated vapor

5

Thermodynamics of the conversion process

• The turbine power is the product of the mass flow rate of the working fluid and the enthalpy drop across the turbine

• The power absorbed by the feed pumps is

• The net power output is

21 hhmW wft

45 hhmW wfp

ptnet WWW 6

Heat exchanger analysis: preheater and evaporator

Temperature-heat transfer diagram for preheater and evaporator

• The pinch point temperature difference is generally set to 5°C or 10°C

• State points 5, 6 and 1 are known from the cycle specifications

• The working fluid mass flow rate (mwf) can be calculated by

• The temperature (TC) of the geofluid leaving the plant can be obtained by

61 hhmTTcm wfBAgeogeo

56 hhmTTcm wfCBgeogeo

The place in the heat exchanger where the brine and working fluid experience the minimum temperature difference is called the “pinch-point” 7

Wet, dry and isentropic fluids

(Bao J., Renewable and Sustainable Energy Reviews, 2014)

Wet

Dry

Isentropic

The working fluids can be classified in

three categories according to the saturation vapor curve

8

Saturation vapor curves of organic fluids

(Yang, Renewable Energy, 2016)

9

Saturation curves of organic fluids versus water

(Quoilin et al., Renewable and Sustainable Energy Reviews, 2013)

• Two main differences:

1) Positive slope of the saturated vapor curve for organic fluids → the limitation of the vapor quality at the end of the expansion process disappears → no need to superheat the vapor at turbine inlet

2) Vaporization enthalpy smaller for organic fluids → better coupling with the heat source

10

Effects of vaporization latent heat on the thermal matching heat source – working fluid

(Bao J., Renewable and Sustainable Energy Reviews, 2014)

(Larjola J., International Journal of Production Economics, 1995)

water toluene Lower vaporization heat of the working fluid causes the heat transfer process in the evaporator to occur mostly at variable temperature → the temperature profile of the working fluid in the evaporator better follows the temperature profile of the heat source → lower irreversibility in the heat transfer process

11

Regenerative configuration of ORC

• If the temperature t4 is markedly higher than the temperature t2, it may be rewarding to implement an internal heat exchanger (recuperator) into the cycles

• In the recuperator the vapor leaving the turbine is cooled in the process (4–4a) by transferring heat to the compressed liquid that is heated in the process (2–2a)

• In this way the thermal efficiency of the ORC increases

Recuperator

(Dai et al., Energy Conversion and Management, 2009) 12

Optimum evaporation temperature

(Quoilin S. et al., Applied Thermal Engineering, 2011)

Increasing the evaporation temperature implies two effects: 1) The heat source is cooled down to a higher temperature 2) The expander specific work is increased since the pressure ratio is increased

245fa

13

Performance metrics

• Thermal efficiency:

• Heat recovery efficiency:

• Total heat recovery efficiency (or “system efficiency”):

av

in

Q

Q

in

netTH

Q

W

av

netT

Q

W

th

av

in

in

netT

Q

Q

Q

W

outingeo

netTH

hhm

W

00 TT

TT

hh

hh

in

outin

in

outin

0hhm

W

ingeo

netT

14

Optimum evaporation temperature – the effect of heat source temperature

(Liu B-T et al., Energy, 2004)

• Increasing the evaporation temperature:

1) The heat recovery efficiency ( ) decreases

2) The thermal efficiency (TH) increases

3) The total-heat recovery efficiency (T) initially increases, reaches a maximum and then decreases

TCR = 327°C

Tin,a = 200°C

Tin,b = 300°C

TH

T

TH

a

b

T,a

T,b

15

Optimum evaporation temperature – the effect of critical temperature

(Liu B-T et al., Energy, 2004)

• Variation of total heat recovery efficiency (T) and thermal efficiency (TH) versus evaporation temperature (TH) for toluene and R123

• The critical temperature of toluene is higher than that of R123 → the thermal efficiency using toluene is higher

• However, the total heat recovery efficiency of R123 is higher

TH

T

16

Thermal efficiency versus total heat-recovery efficiency

• Analysis of total heat-recovery efficiency is very different from the conventional analysis of fossil-fueled power plants which focused on thermal efficiency

• When the evaporation temperature (TH) is increased, the outlet temperature of waste heat is also increased

• Therefore, although TH is increased with the increase of TH, the heat availability is decreased, thereby showing a maximum value of T

• It will lead to significant difference between design of the ORC system from the viewpoints of the thermal efficiency and that based on the total heat-recovery efficiency (i.e., power output)

(Liu B-T et al., Energy, 2004) 17

Optimum evaporation temperature – the effect of working fluid

(Schuster A. et al., Energy, 2010)

Tin = 210°C • Variation of total heat recovery efficiency (also called “system efficiency”) versus evaporation temperature (+2°C of superheating) for different working fluids at subcritical state

• Heat source inlet temperature = 210°C

• The highest system efficiency is reached by R245fa and isobutene

18

Optimum working fluid

Tin= 145°C

(Dai Y. et al., Energy Conversion and Management, 2009)

• The maximum power output in the utilization of waste heat at 145°C is achieved by R236ea and isobutane

• These fluids have critical temperatures slightly lower than the heat source inlet T TCR R236ea = 139,3 °C

TCR iC4 = 134,7 °C

19

Optimum working fluid at different heat source temperatures

0

10

20

30

40

50

100 110 120 130 140 150 160 170 180 190 200

Geofluid Temperature, oC

Uti

lizati

on

Eff

icie

ncy, % Isobutane

Isopentane

N-Pentane

Propane

R134A

R245FA

R32

Ammonia

Cyclopentane

Toluene

(MIT, Utilization of low-enthalpy geothermal fluids to produce electric power, Private report, 2008)

Isobutane

geo

netu

E

W

“Utilization efficiency”: ratio between power output and exergy available from the geofluid

20

Optimum working fluid

Tin = 150°C

(He et al., Energy, 2012)

• The maximum power output in the utilization of waste heat at 150°C is achieved by R114, R142b and R600a (isobutane)

• These fluids have critical temperatures slightly

lower than 150°C: TCR R114 = 145,8 °C TCR R142b = 137,2 °C TCR R600a = 134,7 °C

21

Guidelines for the optimum selection of working fluid

(Wang D. et al., Energy, 2013)

47°C 92°C 122°C 147°C 172°C 192°C 227°C

Also in this study isobutane (R600a) is suggested as promising fluid in the utilization of heat source temperatures between 147°C and 172°C

22

Subcritical vs supercritical ORC

(Schuster A. et al., Energy, 2010)

Subcritical maximum pressure Supercritical maximum pressure

Better thermal matching between heat source and working fluid → lower exergy destruction and lower exergy loss

23

Supercritical (or transcritical) ORC

(Baik et al., Applied Energy, 2011)

R125

Optimum parameters

T3 85 °C

p3 44.6 bar

mWF 0.042 kg/s

Wnet 330.8 W

Power output in response to changes in turbine inlet temperature (T3) and max pressure (p3)

24

Supercritical (or transcritical) ORC

(Baik et al., Applied Energy, 2011)

CO2

Optimum parameters

T3 92.5 °C

p3 123.3 bar

mWF 0.030 kg/s

Wnet 289.8 W

Power output versus turbine inlet temperature (T3) and maximum pressure (p3)

(i.e., 12.5% lower than using R125) 25

Subcritical vs supercritical ORC

Subcritical cycles Supercritical cycles

(Shengjun Z. et al., Applied Energy, 2011)

Tin= 90°C

• Supercritical cycles give higher power output compared to subcritical cycles

• The highest system efficiency is obtained by R218, R41 and R125

• Also in this study R125 results in a higher power output compared to CO2

26

Mixtures of organic fluids

1000 1200 1400 1600 1800 20000

50

100

150

200

s [J/kg-K]

T [

°C]

R245fa

R152a TCR = 113,3 °C

R245fa TCR = 154,1 °C

Let’s consider a mixture of R152a (wet fluid, having a lower TCR) and R245fa (dry fluid, having a higher TCR) 27

Mixtures of R245fa/R152a

(Wang X.D. et al., Solar energy, 2009)

Three compositions of R245fa/R152a: Ma: 0.9/0.1 Mb: 0.65/0.35 Mc: 0.45/0.55

The saturated vapor curve and critical temperature of the mixture depend on the composition

Main advantage: evaporation and condensation at variable temperature

28

Mixtures of R245fa and R227ea

(Feng et al., Energy Conversion and Management, 2015)

29

Kalina cycle: mixture H2O/NH3

• The mixture of ammonia and water boils at a variable temperature depending on its composition

• The higher the fraction of ammonia in the mixture, the lower is its boiling temperature

• Comparison between boiling of pure water and different ammonia–water mixtures at 30 bar

• Before the turbine, the ammonia-rich steam is separated from the liquid phase in a separator

• After the turbine, the steam and liquid phases are merged together and condensed in the condenser

• In the Kalina cycle, geothermal heat at a low temperature is transferred to a mixture of ammonia and water

30

Kalina power plant in Husavik (Iceland)

• Geofluid Tin = 124°C • Mass flow rate of

ammonia-water mixture to the evaporator = 16.8 kg/s

• Mass fraction of ammonia in the evaporator and condenser = 82%

• Turbine inlet pressure = 32.3 bar

• Generator power output = 2.2 MW

(Ogriseck, Applied Thermal Engineering, 2009) 31

Two-stage Organic Rankine Cycle coupled to ICE

(Smolen S., Energy Science and Technology, 2011)

Utilization of waste heat from internal combustion engines at two different temperature levels: 1) from the exhaust gases 2) from the cooling system of the combustion engine

20.6°C 19 bar 0.5 kg/s

119.5°C

20.3°C 8 bar 1.1 kg/s

0.6 kg/s

80.6°C

32

Dual loop ORC system combined with a Diesel engine

(Zhang H.G., Applied Energy, 2013)

• The high temperature loop (yellow) recovers the exhausts heat

• The low temperature loop (green) recovers the residual heat of the HT loop, the waste heat of intake air in the intercooler, and the coolant waste heat

• The LT loop is coupled to the HT loop via the pre-heater, which is used as the condenser for the HT loop

33

Dual loop ORC system: T-s diagrams

(Zhang H.G., Applied Energy, 2013)

• The working fluid in the HT loop is R245fa whereas R134a was selected for the low temperature ORC

• The saturation curves of R245fa and R134a are shown in the T–s diagram

• The upper red lines correspond to the HT loop, while the lower blue lines show the LT loop

34

Dual pressure ORC systems for geothermal resources

Tin,geo = 160°C

(Lazzaretto A. et al., Report ENEL-UNIPD, 2012)

Optimum ORC configuration Optimum design parameters

R245fa

35

Other evaluation parameters in the working fluid selection

(UA)tot

(He et al., Energy, 2012)

250

50

.

.

is

out

h

VSP

Total heat transfer capacity when the maximum Pnet is obtained

Expander size parameter when the maximum Pnet is obtained

36

Economic objective functions

(Shengjun Z. et al., Applied Energy, 2011)

net

tot

W

AAPR

Ratio of total heat transfer area to total net power:

Levelized cost of electricity:

EnergyAnnual

M&OCRFCCLEC

37

Specific investment costs of ORC systems

(Quoilin et al., Renewable and Sustainable Energy Reviews, 2013)

• For a given target application, the cost tends to decrease when the output power increases

• Lowest costs are reported for waste heat recovery applications, while geothermal and CHP plants exhibit higher total cost

• “Total cost” differs from “module cost” in that it includes engineering, buildings, boiler (in case of CHP), process integration, etc., and can amount to two to three times the module cost

Module (empty dots) and total (plain dots) costs of ORC systems

38

Optimization of a single pressure ORC

• Independent variables of the model are fixed as parameters: ‒ mgeo = 100 kg/s

‒ Tgeo,in = 130÷180°C at 10°C steps

‒ Tgeo,out ≥ 70°C

‒ Working fluids: R600a (isobutane), R134a

‒ P = 70%, T = 85%, el = 96%

‒ Tamb = 20°C

‒ Tair,out = Tcond - 5°C

‒ PACC = 0.15 kW per kg/s of air

• Decision variables: – condensation pressure (pcond)

– mass flow rate of the organic fluid (mwf)

– cycle maximum pressure (pmax)

– degree of superheating, measured in terms of specific entropy (ssup)

• Objective function:

39

Results for isobutane

• Optimum isobutane cycles are mostly subcritical with saturated vapor at turbine inlet

• At the highest brine temperatures the optimal isobutane cycles are either subcritical with slightly superheated vapor (170°C) or supercritical (180°C)

Optimum values of the decision variables

Optimum values of the objective function zrec

40

Results for R134a

• R134a optimum cycles are supercritical (except at 130°C)

• The exergy recovery efficiency achieved by R134a is always higher compared to that achieved by isobutane

Optimum values of the decision variables

Optimum values of the objective function zrec

41

Isobutane vs R134a

Working fluid Isobutane R134a

Tgeo,in (°C) 150 150

mgeo (kg/s) 100 100

mWF (kg/s) 81.8 159.5

pmax (bar) 18.9 48.0

TT,in (°C) 98.5 129.4

Tcond (°C) 32.8 32.7

pcond (bar) 4.4 8.3

Pgen (kW) 3863 4823

Ppump (kW) 311 757

PACC (kW) 557 568

Pnet (kW) 2995 3498

zrec (%) 38.1 44.5

th (%) 9.1 10.3

Isobutane

R134a

42

Variation of the thermodynamic objective function around the optimum

Isobutane, Tgeo,in=150°C R134a, Tgeo,in=150°C

• The highest values of zrec are obtained at turbine inlet states close to saturated vapor and maximum pressures close to the optimum pressure

• The trend of zrec is quite flat in response to changes of the turbine inlet supercritical pressure whereas it rapidly decreases when the turbine inlet enthalpy is lowered

(Toffolo et al., Applied Energy, 2014) 43

Axial and radial turbines in Organic Rankine Cycles

44

Motivations

• Several studies on Organic Rankine Cycles (ORCs) in the literature search for the optimal cycle parameters and working fluids that maximize the net power output

• Only few studies carry out a preliminary turbine design to calculate an accurate value of turbine efficiency

• This is done only after the cycle thermodynamic optimization is performed assuming a fixed and somewhat arbitrary value of turbine efficiency (e.g., 85%)

• A new design optimization procedure of ORCs is proposed here which embeds correlations for the design efficiency of both axial and radial turbines

45 (Lazzaretto et al., 2014)

Methods

• A one dimensional meanline model of an axial flow turbine is built in Matlab® environment to evaluate efficiency and main geometrical parameters

• Unlike previous models in the literature, real fluid properties taken from NIST REFPROP are considered and the most recent loss correlations proposed by Aungier are used

• The predicted efficiencies are correlated to:

1) Parameters traditionally selected by the turbine designer (i.e., the so called “duty parameters”)

2) Volumetric expansion ratio and size parameter to highlight the influence of working fluid properties, thermodynamic cycle parameters and turbine size on the achievable turbine efficiency

46

Axial and radial turbines in Organic Rankine Cycles

• Axial and radial turbines are both used in practical applications of Organic Rankine Cycle systems

• A radial turbine stage can deliver a greater specific power than an equivalent axial stage, and this may imply smaller and/or fewer stages in a machine

• The enthalpy drop in the expansion processes of Organic Rankine Cycles is lower than the steam enthalpy drop over the same temperature interval owing to the use of heavy substances as working fluids → in many low temperature applications the work transfer can be simply achieved by using a single axial stage

47

Turbine efficiency versus specific speed

• The isentropic efficiency of both axial and radial turbines can be correlated with the specific speed NS

• The figure on the right presents a broad correlation of maximum efficiencies for hydraulic and compressible fluid turbines as functions of specific speed (Ns = Ws) which apply to favorable design conditions

48

• Over a limited range of specific speed (0.4÷0.8) the best radial-flow turbines match the best axial-flow turbine efficiency

The specific diameter

• The use of an appropriate specific speed does not directly imply that a high efficiency design will result → the specific speed vs specific diameter chart clearly shows that the specific diameter ds, defined by:

is an additional variable that strongly affects the turbine efficiency at fixed specific speeds

• A high efficiency turbine design should provide both a specific speed in the optimal range and the corresponding optimum specific diameter

• The best designs lay along the Cordier line

49

Balje diagram (Ns - ds chart) for expanders

5.0

25.0

out

iss

V

hDd

75.0

5.0

is

outS

h

VN

50

A high efficiency turbine design should provide both a specific speed in the optimal range and the corresponding optimal specific diameter

Main limitations in the use of Ns-ds correlations

• The specific speed versus specific diameter correlations are often dated and may not represent modern turbine technology

• Data on which they are based are usually not available and their application is questionable for high pressure ratios and real gases

• Specific speed is a guide to turbine type and overall size but gives no further information

• To progress, it is helpful to use design coefficients such as stage loading coefficient (ψ) and flow coefficient ( )

51

Efficiency (Smith) chart for axial turbines

• The efficiency of both axial and radial turbine stages can be correlated with the flow coefficient ( ) and the stage loading coefficient ( y )

• The Smith chart is a widely used efficiency correlation for axial flow turbines and shows that for best efficiency both the stage loading and the flow coefficients must be low

52

Efficiency chart for radial turbines

• A similar chart linking turbine efficiency with blade loading and flow coefficients was obtained for radial turbines using test data taken from a wide variety of stage designs

• It shows that maximum radial turbine efficiency occurs at loading coefficients between about 0.9 and 1.0 and flow coefficients in the range 0.2÷0.3

53

Dimensional analysis

• The turbine efficiency can be expressed as:

• So the efficiency reduces to:

54

True independent variables that can be selected by the designer

Variables which depend both on the designer choices and the resulting flow regimes

So, YN and YR are known only after a detailed turbine design procedure is carried out, making this equation impractical for a preliminary turbine efficiency estimation

Size parameter and volumetric expansion ratio

• To avoid the need of a detailed turbine design the total pressure loss coefficients (YN and YR) are replaced by SP and VR which somehow keep the effects of Re and Ma separate, and can be directly evaluated from the thermodynamic cycle parameters

where:

55

explicitly takes into account the turbine size

explicitly takes into account compressibility

Flowchart of the model

56

• The turbine design procedure is organized according to the flowchart on the right where: − blue dashed line indicates

stator − red dashed line rotor − green dotted arrows indicate

updates for guess values • Local design optimizations of

stator and rotor are performed in series starting from a guess value of the total-to-total efficiency (tt) which is then calculated by the procedure and used as new guess in the next iteration steps until convergence

(Da Lio et al., 2016)

Flowchart of the model

57

• The “operating duty specifications” (mass flow rate and enthalpy drop) obtained by the thermodynamic analysis of the ORC system represent the turbine boundary conditions

• The “duty parameters” y, , R along with guess values for tt and p2 enable the evaluation of total and static thermodynamic states and velocity triangles at stator and rotor inlet and outlet

Stator design (1)

58

• Stator design: Some geometrical features as sweep angle (gN), pitch-to-chord ratio (s/c)N, and throat-to-pitch ratio (o/s)N are directly derived from relationships and diagrams taken from the literature (Aungier) using outlet flow angles and Mach number as inputs

Stator design (2)

59

• Stator design: The remaining stator geometry (number of blades zN, blade spans h2, mean diameter Dm, chord cN) is obtained by minimizing the stator losses (YN) for a wide set of combinations of stator axial chords (bN) and hub-to-tip radius ratios (l1)

• From the minimum YN a new pressure value at stator outlet (p2) is calculated by solving

Rotor design

60

• Pressure p2 allows all rotor calculations to be performed using a procedure similar to the stator

• YR is simply minimized by selecting an optimum axial chord value (bR) being the meridional channel geometry in the rotor dependent on the choice of l1

• The outcomes of the rotor block are p03 (deriving from minimum YR) and h3

• Accordingly, the rotor outlet state is updated and a new tt is calculated to update the guess

Upper and lower bounds of the free variables in the optimization procedure

61

Loss model

• The general structure of the loss model used here is derived from Aungier's work

• The total pressure loss coefficient ( Y ) through the blade rows

is expressed as the sum of several terms representing specific loss sources: Yp : profile, Ys : secondary, Yte : trailing edge, Ysh : shock, Yex : post expansion, Ycl : clearance 62

• The output of the loss model is the total pressure loss coefficient of the stator (YN) and rotor (YR), respectively defined by:

Calculation of loss sources (from Aungier)

63

where

where

1) Profile losses

2) Secondary losses

3) Trailing edge losses

4) Shock losses

5) Supersonic expansion losses

6) Blade clearance losses

Calculation procedure

• The main outcomes of the design procedure are the geometry and efficiency of an axial flow turbine fulfilling given design specifications (i.e., mass flow rate and specific work)

• Different turbine designs are generated assuming different values of the design parameters y, and R

• The range and step of variation of the design parameters are:

• Accordingly new Smith charts are obtained, which show the efficiency achievable at different y--R values

64

New Smith charts for axial flow turbines operating with organic fluids

• Smith charts showing lines at constant turbine efficiency for m=50 kg/s (i.e., SP ≈ 0.16 m) at two VR values:

– Upper figure: Tevap = 50°C, corresponding to VR ≈ 1.7

– Lower figure: Tevap = 100 °C, which corresponds to VR ≈ 7

• Red dots indicate the best efficiency points:

– Optimum = 0.4

– Optimum y = 1÷1.1

65 (Da Lio et al., 2014)

New Smith charts for axial flow turbines operating with organic fluids

• The volumetric expansion ratio has a strong influence on turbine efficiency: a maximum efficiency of 89.1% is obtained when VR=1.7 whereas a maximum efficiency of 85.5% is obtained when VR=7

• So, the efficiency markedly decreases and the optimum y slightly increases with VR → a single general Smith chart cannot be representative of the wide range of operating conditions experienced by organic fluids 66

Critical remarks

• Thus, the well-established Smith chart is no more sufficient for a reliable design of ORC expanders operating with high molecular weight fluids due to the wider range of operating conditions (e.g., size) and Mach numbers compared to traditional applications using conventional fluids (e.g., air or flue gases)

• The model of the single stage axial flow turbine developed in this work enlarges the range of operating conditions of the above mentioned charts by explicitly accounting for the influence of the volumetric expansion ratio (VR) and size (SP) parameters in addition to either the flow and loading coefficients (i.e., the “duty” parameters)

67

SP-VR efficiency maps (1)

• The simulation model is run at different values of mass flow rate (in the range 10÷100 kg/s) and evaporation temperature (in the range 50÷110°C) to cover a wide spectrum of SP and VR

• The main goal was to study the effects of the operating conditions on the optimum turbine efficiency

68

Find the optimum , y, R

For any couple (SP, VR)

Calculate the corresponding

SP-VR efficiency maps (2)

• The highest efficiencies are located in the region of low VRs and high SPs

• At fixed SP large volume variations cause relevant losses mainly due to high Mach flow regimes (i.e., high velocities)

• At fixed VR small turbines (i.e, having low SP) are disadvantaged because geometric similarity is not fulfilled, resulting in higher clearance losses 69 (Da Lio et al., 2014)

Optimum turbine efficiency versus SP and VR R1234yf, R134a, R1234ze(E) and iC4

70 (Da Lio et al., 2016)

Optimum turbine efficiency versus SP and VR R1234ze(Z), R245fa, iC5 and cyclopentane

71 (Da Lio et al., 2016)

Optimum results for R1234yf at three different VR values (1.6, 4.8 and 8.9) and constant SP=0.14m

72

Meridional sections

Velocity triangles (blue for stator and red for rotor)

Total pressure loss coefficients breakdown

(Da Lio et al., 2016)

Optimum results for R1234yf at three different SP values (0.067, 0.122 and 0.1725) and constant VR=4.8

73 (Da Lio et al., 2016)

The effect of critical temperature on turbine efficiency

74

The selection of working fluids with lower critical temperatures enables the detrimental effects on turbine efficiency deriving from low SP and high VR to be reduced (Da Lio et al., 2016)

Main outcome: use of the turbine efficiency maps in the thermodynamic optimization of ORCs

• The turbine efficiency maps obtained have been included in the thermodynamic optimization procedure of the ORC system to help select the optimum design point, overcoming any arbitrary assumptions on turbine efficiency

• The black contour lines show the maximum efficiencies achievable by single stage axial flow turbines at given turbine inlet conditions (p, h) or (T, s) 75 (Manente et al., 2016)

76

Thank you for your attention