Three-dimensional off-design numerical analysis of an organic Rankine cycle radial-inflow turbine

Applied Energy 135 (2014) 202–211

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Three-dimensional off-design numerical analysis of an organic Rankine cycle radial-inflow turbine Emilie Sauret ⇑, Yuantong Gu Queensland University of Technology, 2 George Street, Brisbane, Qld 4000, Australia

h i g h l i g h t s  This study presents the complete design process of a R143a 400 kW radial-inflow turbine in geothermal conditions.  Three-dimensional viscous simulations are presented and discussed at the nominal and off-design conditions.  The results show that the nominal point is well-suited to handle variations of rotational speed, inlet temperature and pressure ratio while maintaining a

relatively high efficiency.  The results also highlight the sensitivity of the turbine performance against the real gas thermodynamic properties.

a r t i c l e

i n f o

Article history: Received 6 April 2014 Received in revised form 1 August 2014 Accepted 18 August 2014

Keywords: Radial-inflow turbine Organic Rankine cycles Geothermal energy CFD

a b s t r a c t Optimisation of organic Rankine cycles (ORCs) for binary cycle applications could play a major role in determining the competitiveness of low to moderate renewable sources. An important aspect of the optimisation is to maximise the turbine output power for a given resource. This requires careful attention to the turbine design notably through numerical simulations. Challenges in the numerical modelling of radial-inflow turbines using high-density working fluids still need to be addressed in order to improve the turbine design and better optimise ORCs. This paper presents preliminary 3D numerical simulations of a high-density radial-inflow ORC turbine in sensible geothermal conditions. Following extensive investigation of the operating conditions and thermodynamic cycle analysis, the refrigerant R143a is chosen as the high-density working fluid. The 1D design of the candidate radial-inflow turbine is presented in details. Furthermore, commercially-available software Ansys-CFX is used to perform preliminary steady-state 3D CFD simulations of the candidate R143a radial-inflow turbine for a number of operating conditions including off-design conditions. The real-gas properties are obtained using the Peng–Robinson equations of state. The thermodynamic ORC cycle is presented. The preliminary design created using dedicated radial-inflow turbine software Concepts-Rital is discussed and the 3D CFD results are presented and compared against the meanline analysis. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Organic Rankine cycles (ORCs) have been receiving lots of attention for many years [1]. This interest is continuously growing [2] because of the suitability of ORCs to low-to-mid-temperature renewable applications. Two key parameters for the optimization of the ORC performance are the working fluid and the turbine [3]. Extensive literature has been published on the working fluid selection [4–9] and separately on the preliminary one-dimensional turbine design [10–14]. As underlined by Aungier [15], the ⇑ Corresponding author. E-mail addresses: [email protected] (E. Sauret), [email protected] (Y. Gu). http://dx.doi.org/10.1016/j.apenergy.2014.08.076 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

preliminary design of a radial-inflow turbine remains a crucial step in the design process. Indeed, the objective of the design phases (preliminary and detailed) is to create an aerodynamic design that will correctly and completely achieve a design that delivers the desired outputs. However, Pasquale et al. [16] also highlighted the need to use more advanced 3D viscous computational simulations to further investigate the proposed turbine configuration. Computational Fluid Dynamics (CFD) will provide detailed flow analysis which is required to improve the aerodynamic performance of the machine [17]. In order to achieve better cycle performances, the organic working fluid at the inlet of the turbine is in thermodynamic conditions close or above to the critical point. This prevents the numerical simulations to use ideal gas laws and so require the developement

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E. Sauret, Y. Gu / Applied Energy 135 (2014) 202–211

Nomenclature C0 cp0 DRin h M Ns Nr Pc P Q_ m R Re Tc T U yþ w W Wc

spouting velocity ðm s1 Þ 1 zero pressure ideal gas specific heat capacity ðkJ kg KÞ inlet rotor diameter (m) 1 enthalpy ðkJ kg Þ absolute Mach number (–) stator number of blades (–) rotor number of blades (–) absolute pressure at the critical point (kPa) pressure (kPa) mass flow rate ðkg s1 Þ 1 ideal gas constant ðJ mol K1 Þ Reynolds number (–) absolute temperature at the critical point (K) temperature (K) blade velocity ðm s1 Þ non-dimensional grid spacing at the wall (–) power (kW) cycle power (kW)

of codes to calculate the thermodynamic properties of the real gas. For accurate viscous simulations these codes need to be interfaced with the CFD solvers [18]. Table 1 gives a summary of the published numerical simulations of expanders working with organic fluids. Since the end of the 90s, CFD solvers capable to handle real gas have been developed [28,20]. Then, numerical simulations on expanders and turbine nozzles using high-density fluids have been reported in the literature. In 2002, Hoffren et al. [19] are amongst the first to perform two-dimensional numerical simulations of a real gas flow in a supersonic turbine nozzle using toluene as working fluid. Their extension of the Navier–Stokes solver for real gas appears to be robust and accurate. Later, Colonna et al. [22] investigated the influence of three different equations of state (EoS), a simple polytropic ideal gas law, the Peng–Robinson–Stryjek–Vera cubic equation of state (EoS) and the state-of-the-art Span–Wagner EoS, on the aerodynamic performance of a two-dimensional ORC stator blade working with the siloxane MDM. The two more sophisticated models (Peng–Robinson–Stryjek–Vera and Span– Wagner) were shown to produce similar results. Pini et al. [24] recently performed a 2D throughflow simulation on their proposed centrifugal turbine for an ORC application working with the siloxane MDM. Finally, to the best of the authors’ knowledge, Boncinelli

Greek symbols b blade angle (deg) g efficiency (%) x acentric factor (–) X rotational speed (rpm) P pressure ratio (–) l dynamic viscosity ðkg m1 s1 Þ Subscripts in turbine inlet is isentropic out turbine outlet ref reference T total S static T–S total-to-static T–T total-to-total

et al. [21] in 2004 were the first to successfully perform threedimensional viscous simulations of a transonic centrifugal impeller working with R134a using a fitting model from gas databases to get the thermodynamic properties of the fluid. Recently, pseudo3D CFD simulations using equations of state for the real dense gas are produced by Wheeler and Ong [25] on a turbine vanes. Finally, Harinck et al. [18] were the first to perform three-dimensional viscous CFD simulations of a complete radial turbine including the stator, the rotor and the diffuser using toluene as the working fluid. Pasquale et al. [16] looked at the blade optimisation of expanders using real gas. However, only two-dimensional nozzle simulations have been considered. Recent studies [26,27] have looked at the whole process including thermodynamic cycle, 1D design and numerical simulations of the expander. Klonowicz [26] designed and numerically investigated a R227ea impulse turbine at partial admission. However, they only simulate one stator and rotor pitch and so were not able to take numerically into account the partial adnmission. Both cases with and without clearances were run. Cho et al. [27] also numerically studied a partial admission radial impulse turbine with a vaneless nozzle. The ouput power in this case is 30 kW and the working fluid R245fa.

Table 1 Numerical simulations of turbines working with high-density fluids. Author

Working fluid

Simulation

Geometry

Hoffren et al. [19] Cinnella and Congedo [20] Boncinelli et al. [21] Colonna et al. [22] Harinck et al. [2] Harinck et al. [23]

Toluene BZT flows R134a Siloxane MDM Toluene Steam R245fa Toluene Siloxane MDM

2D 2D 3D 2D 2D 2D

Radial turbine nozzle NACA airfoil transonic VKI LS-59 linear turbine cascade Transonic centrifugal impeller Radial turbine nozzle Radial turbine nozzle Radial turbine nozzle

Pini et al. [24] Pasquale et al. [16] Harinck et al. [18] Wheeler and Ong [25] Klonowicz et al. [26] Cho et al. [27]

Not mentioned Toluene Pentane R245fa R227ea R245fa

viscous inviscid viscous inviscid inviscid inviscid

Pseudo-3D Throughflow 2D inviscid 3D viscous Quasi-3D Viscous 3D Viscous 3D viscous

3-Stage and 6-stage Centrifugal turbine Impulse radial turbine nozzle Radial-inflow turbine Radial turbine nozzle Impulse turbine Impulse radial turbine Vaneless nozzle

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E. Sauret, Y. Gu / Applied Energy 135 (2014) 202–211 Table 2 Thermodynamic data required for the turbine design obtained from the R143a ORC cycle analysis. Variables

Fig. 1. Basic organic Rankine cycle (ORC) system.

It is important to note that so far, very few studies including the whole process for sensible geothermal conditions have been presented in the literature. Furthermore, 3D viscous simulations on complete turbines working with organic fluids are at a pioneering stage and all the published numerical studies on expanders coupled with ORCs consider small-scale power cycles with output power less than 50 kW. Most of them are impulse turbines with partial admission. This paper will fill that gap by providing a complete ORC analysis including the thermodynamic cycle, the preliminary meanline design and finally pioneering three-dimensional CFD simulations of a 400 kW-R143a radial-inflow turbine in sensible geothermal brine and cycle conditions. Off-design conditions are also presented and discussed. 2. Organic Rankine cycle A thermodynamic model for a binary power cycle was developed using Engineering Equation Solver (EES, F-Chart Software) based on the basic components of an ORC system: evaporator, turbine, generator, condenser and fluid pump (Fig. 1). Simulations for realistic condensing ORC cycles for geothermal applications were carried out and analysed leading to the promising cycle for a brine temperature of 423 K at a sensible flow rate of 15 kg s1 as encountered during the testings at the Habanero pilot plant in Australia. The condensing temperature was set at 313 K (10 K above ambient, assumed to be 303 K) while the turbine inlet temperature is fixed to 413 K through a temperature difference of 10 K with the brine inlet temperature at 423 K. In this analysis, turbine and pump efficiencies were assumed to be 85% and 65%, respectively. Promising cycles were identified by varying the evaporator pressure in order to optimise the net cycle power. As outlined by Sauret and Rowlands [29] and recently by Toffolo et al. [9] a coupled optimisation between the thermodynamic cycle and the cycle components such as the 1D turbine design is required to maximize the net cycle power. Such a coupled Multi-Objective optimisation has been developed by Persky et al. [30] and applied to the present study. Therefore, the optimum turbine inlet total pressure has been optimised to 5 MPa which lead to a performance factor ðPF ¼ W c =D2Rin Þ of 20.6 compared to PF = 17.2 previoulsy obtained by Sauret and Rowlands [29]. In this study, the refrigerant R143a is chosen as the working fluid for the turbine based on the study of Sauret and Rowlands [29]. This study evaluated 5 different fluids based on the QGECE (Queensland Geothermal Energy Center of Excellence) thermodynamic modelling and published results from others [4,7,31–33]. It showed that R143a at 413 K gave the best performance factor

P T in (kPa)

P Sout (kPa)

T T in (K)

W (kW)

5000

1835

413

400

based on the cycle net power and the size of the turbine. Thus, R134a is a suitable fluid at 413 K capable to generate a relatively large turbine power compared to the compactness of the turbine. The choice of R143a is based not only on its theoretical thermodynamic performance, but a balance of several different desired criteria such as relatively low critical pressure and temperature and low flammability, low toxicity and relative inert behaviour. Striking an acceptable balance between the aforementioned criteria, environmental concerns, cost and thermodynamic performance is not an insignificant challenge for ORC system designers [4]. The selection of the radial-inflow turbine is based on numerous published studies highlighting the suitability of such turbines for ORC cycles [34,29,35,24]. As mentioned by Clemente et al. [36], the selection of the best suited machine requires a detailed analysis of the given case. The thermodynamic data required for the turbine design are summarized Table 2. 3. One-dimensional design of the radial-inflow turbine In this study, the preliminary design of the turbines was performed using the commercial software RITAL following the design procedure established by Moustapha et al. [37]. The general procedure implemented was to determine overall dimensions of the machine for the stator, rotor and diffuser along with blade and flow angles and isentropic efficiency by fixing the mass flow rate, inlet and outlet pressures as calculated by the cycle analysis (Table 2) and by assuming flow and loading coefficients [37]. From the basic design specifications and the performance analysis, a refinement of the results was performed in order to optimise the geometry. The refinements included: rotational speed adjustments in order to get closer to the optimum 0.7 value of the U=C 0 ratio [37]; tip outlet rotor radius modification in order to reduce the swirl as much as possible at the outlet of the rotor; and, blade span (i.e. changes to throat area). 3.1. Assumptions and constraints In the Moustapha et al. procedure [37], the flow and loading coefficients are assumed in order to give the best efficiency. In this current study, these coefficients were set respectively to 0.215 and 0.918 giving around 90% efficiency according to the Flow and Loading Coefficient Correlation Chart proposed by Baines [13]. The rotor clearances were set using an assumed value of 0.3 mm. The wish to

Table 3 Preliminary R143a turbine design data. Global variables

PT—S (–) PT—T (–) Q_ m (kg/s)

gT—S (%) gT—T (%) X (rpm) W (kW) U=C 0 (–)

Geometric parameters 2.72 2.62 17.24 76.8 79.8 24,250 393.6 0.675

N s (–) N r (–) DRin (mm)

19 16 127.17

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on the 3D diffuser geometry. The nozzle hub and shroud contours are defined as straight lines. The nozzle hub and shroud thicknesses, the rotor blade angle and rotor thickness distributions were iteratively adjusted using Bezier curves in order to achieve reasonnable preliminary results with blade-to-blade and throughflow solvers notably in terms of loading and Mach numbers which were maintained in the transonic region. The same thickness distribution was used for the stator hub and shroud while two separate distributions were set for the rotor hub and shroud. The main 3D geometric parameters are presented in Table 4. 5. Three-dimensional numerical simulations Viscous turbulent CFD simulation was carried out on the 3D turbine geometry at the nominal condition using commercially-available software ANSYS-CFX. 5.1. Mesh

The results of the preliminary design are presented Table 3. The power is slightly lower than the expected value from the thermodynamic cycle. However, the total-to-total efficiency almost reached 80% while the total-to-static efficiency is close to 77%. This is in close agreement with the previous study proposed by Sauret and Rowlands [29]. The size of the turbine is also in close agreement with the previous study [29]. One can also note that because of a relatively high power compared to a relatively small size, this turbine achieves a high performance factor ðPF ¼ W c =D2Rin Þ of 20.6 compared to PF = 17.2 obtained by Sauret and Rowlands [29].

The O–H three-dimensional computational mesh for the simulation of one blade passage is shown in Fig. 3 for the nozzle and in Figs. 4 and 5 for the rotor shroud and hub respectively. An initial grid was created with a total grid number is 1359,907 nodes, 678,389 for the stator, 444,341 for the rotor and 237,177 for the diffuser. The average non-dimensional grid spacing at the wall yþ w ¼ 703 is slightly above the recommended range of up to 500. With the scalable wall function used in the simulations, recommended yþ w values lay between 15 and 100 for machine Reynolds number of 105 where the transition is likely to affect significantly the boundary layer formation and skin friction and up to 500 for Reynolds number of 2  106 when the boundary layer is mainly turbulent throughout [40]. However, based on Remachine ¼ ðqref U tip Rin RRin Þ= lref where lref ¼ 1:9  105 kg=ðm sÞÞ is the reference dynamic viscosity of R143a and qref ¼ 163:2 ðkg=m3 Þ the reference density at the inlet of the domain, the present machine Reynolds number at the inlet is 8:8  107 well above 2  106 . This initial mesh was found good enough to run pioneering simulations of the 3D candidate R143a radial-inflow turbine in sensible geothermal brine and cycle conditions and establish the complete methodology (thermodynamic cycle, meanline analysis and preliminary viscous CFD simulations).

4. 3D geometry

5.2. Numerical model

The commercial software Axcent were used to define the 3D geometry of the turbine presented in Fig. 2. The data from the preliminary 1D design were transferred into Axcent, including amongst the most important parameters, radii and blade heights. An annular diffuser at the exit of the rotor is built from the 1D radii values. No optimisation was carried out

The CFD solver ANSYS-CFX has been used to perform steadystate 3D viscous flow simulations. For robustness consideration, the discretization of the Navier–Stokes equations is realized using a first order Upwind advection scheme. For these preliminary 3D simulations, the standard k- turbulence model with scalable wall function was chosen.

Fig. 2. 3D view of the full 3D turbine geometry (stator and rotor blades).

use widely available inverter technology in order to simplify future experimental rigs led to the shaft speed being limited to a maximum of 25,000 rpm. The default RITAL recommended loss models were used: the Rodgers stator loss model [38] and the CETI rotor passage loss model from Concepts [39]. These models were found to provide a reasonable first approximation. 3.2. 1D design results

Table 4 Turbine 3D geometric dimensions. Nozzle Rin (mm) Blade height (mm) TE thickness (mm) Rout (mm)

Rotor 83.45 8 1 66.76

Rin (mm) Inlet blade height (mm) TE thickness (mm) Axial length (mm) (deg) btip in

Diffuser 63.6

Rtip (mm) in

44

8

Rhub in (mm)

18.5

Axial length (mm)

45

1.27 38.15 0

bhub in (deg)

0

btip out (deg)

60.4

(deg) btip in Clearances (mm) Axial Radial

38.9 0.3 0.3

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In order to describe the properties of the refrigerant R143a in the radial-inflow turbine, the cubic equation of state (EoS) of Peng–Robinson [41] (Eq. (1)) is chosen. This choice was motivated by the good balance between simplicity and accuracy of this model to perform preliminary real gas computational simulations. This EoS is also considered as having reasonable accuracy especially near the critical point [42].

p¼

RT aa  V m  b V 2m þ 2bV m  b2

0:457235R2 T 2c pc 0:077796RT c b¼ pc

5.3. Boundary conditions

a¼

ð1Þ 2

a ¼ ð1 þ jð1  T 0:5 r ÞÞ j ¼ 0:37464 þ 1:54226x  0:26992x2 Tr ¼

temperature and pressure of R143a, V m , the molar volume and R is the universal gas constant. To complete the description of the real gas properties, the CFD solver calculates the enthalpy and the entropy using relationships which are detailed in [43]. These relationships depend on the zero pressure ideal gas specific heat capacity cp0 and the derivatives of the Peng–Robinson EoS. cp0 is obtained by a fourth-order polynomial whose coefficients are defined by Poling et al. [44].

T Tc

where x ¼ 0:259 is the acentric factor of refrigerant R143a, T c ¼ 346:3 K and Pc ¼ 3492 kPa are respectively the critical

An extension of the domain was placed in front of the stator blades at a distance equivalent to approximately 25% of the axial stator chord. The nominal rotational speed for this case is defined from the preliminary design and set to 24,250 rpm (Table 3). The mass flow rate, total temperature and inlet velocity obtained from the meanline design analysis were set at the inlet of the domain (Table 2). The static pressure was specified at the exit of the diffuser (Table 2). A mixing plane condition was set at the interface between the stationary (stator) and rotational (rotor) frames and a frozen rotor interface was set between the rotor and the diffuser. Periodic boundary conditions are applied as only one blade passage for both the stator and the rotor is modelled.

Fig. 5. 3D view of the O–H grid around the rotor blade at the hub.

Fig. 3. 3D view of the O–H grid around the stator blades.

Table 5 Comparison of the meanline analysis and the present 3D CFD simulations. Variables

Preliminary design

Present CFD

Global variables PT—S (–) PT—T (–) gT—S (%) gT—T (%) W (kW)

2.72 2.62 76.8 79.8 393.6

2.64 2.54 83.5 87.6 421.5

499.2

501

4989.6

4849.85

0.88 4886.5 412.2

0.94 4717 411.9

0.363 1961.4 370.2 476.4

0.364 1933.1 367.1 476.3

Stator inlet 1

hT ðkJ kg P T (kPa)

Þ

Rotor inlet M (–) P T (kPa) T T (K) Rotor outlet M (–) P T (kPa) T T (K) 1

Fig. 4. 3D view of the O–H grid around the rotor blade at the shroud.

hT ðkJ kg

Þ

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E. Sauret, Y. Gu / Applied Energy 135 (2014) 202–211

6. Results and discussion

3.2

6.1. Comparisons of the 3D CFD results against the meanline analysis at the nominal condition

gT—T ¼

hT in  hT out hT in  hT is out

gT—S ¼

hT in  hT out hT in  hSis out

ð2Þ

Thus, any small variations of temperatures can lead to big discrepancy in efficencies. Several studies [46,42] have shown that the Peng–Robinson EoS was comparing fairly well against the highaccuracy models implemented in REFPROP [47] and especially near the critical point. Thus, it is not assured that a more accurate EoS will dramatically improve the CFD efficiencies. Instead, it is highly recommended here to investigate the sensitivity of the efficiency to the EoS using non-statistical state-of-the-art uncertainty quantification methods such as Stochatic Collocation using Adaptive Sparse Grid. Furthermore, compared to the meanline design, the Mach number at the inlet of the rotor (Table 5) is also higher. The Mach number at mid-span is presented Fig. 6.

2.8

P [Mpa]

Due to the lack of experimental data in radial-inflow turbines working with high-density fluids, the validation of the present 3D viscous simulation was firstly made against the meanline analysis results. Table 5 compares the results from both the preliminary 1D design and the numerical 3D turbulent simulations. It is observed that the CFD results are in relatively good agreement with the 1D analysis, especially in terms of temperatures, pressures and enthalpy. However, the slight difference (less than 0.5%) on the total enthalpy at the inlet of the nozzle and outlet of the rotor between the viscous simulation and the 1D analysis leads to approximately 8% difference in terms of DhT ¼ hT in  hT out explaining the difference of power as W ¼ Q_ m ðhT in  hT out Þ. The CFD results are in fairly good agreements with the meanline analysis except for efficiencies for which a maximum difference of nearly 9.8% is obtained. The overestimation of the efficiency has already been highlighted in a less extent by Sauret [45] on the simulations of an ideal gas high pressure ratio radial-inflow turbine. The present result can be attributed to the use of real gases which are extremely sensitive to small temperature variations. As shown in Table 5, a slight variation of the total temperatures and enthalpies can lead to large variation of the enthalpy and temperature drops in the turbine. The isentropic efficiencies defined below in Eq. (2) are function of the enthalpy drop:

25% Span 50% Span 75% Span

3

2.6 2.4 2.2 2 1.8 1.6 0

0.2

0.4

0.6

0.8

1

Meridional Axis Fig. 7. Blade loading at three different rotor blade heights for the nominal condition.

One can note that the exit of the stator is slightly chocked with a maximum Mach number of approximately 1.05. This, in return, leads to the higher Mach number at the inlet of the rotor. As a consequence, further 3D shape optimisation is required in order to improve the blade loading profile shown in Fig. 7 and thus reduce the Mach number in order to remain in the transonic region. Also the relatively high loading at the leading edge of the rotor presented Fig. 7 associated with relatively low loading from the mid-blade to the trailing edge may cause structural issues for the blade integrity. This will require in the future to also run a structural blade analysis which would need to be linked to the blade optimisation. Thus, it is very likely that the CFD simulations on a fully-optimized 3D geometry with a more accurate modelling of the real gas properties will provide much better agreement with the meanline design in terms of efficiencies. 6.2. Results at off-design conditions The 3D numerical simulations have also been performed at offdesign conditions for different rotational speeds, inlet total temperatures and pressure ratios. The evolution of the total-to-total efficiency with the total inlet temperature and rotational speed are presented in Figs. 8 and 9 respectively. As one can note in Fig. 8, at the nominal rotational speed, the turbine can effectively handle temperature variations with a maximum efficiency difference of 3.3% over the range of tested

Fig. 6. Mach number at mid-span for the nominal condition.

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E. Sauret, Y. Gu / Applied Energy 135 (2014) 202–211

0.9

600

TT =380K TTin=413K TTin=450K

550

0.85

in

Power [kW]

500

ηT-T [-]

0.8 0.75 0.7

450 400 350 300

80% RPM Nominal RPM 120% RPM

0.65 0.6 380

400

420

440

250 200 460

70

80

90

100

110

120

130

Ω/ΩNominal [%]

TT [K] in

Fig. 8. Evolution of the total-to-total efficiency with the total inlet temperature at three different rotational speeds.

Fig. 11. Variation of the turbine power with the rotational speed at three different inlet temperatures.

0.9

0.9

0.88 0.85 0.86

ηT-T [-]

ηT-T [-]

0.8 0.75 0.7

0.84 0.82 0.8

TT =380K TTin=413K TTin=450K

0.65

0.76 1.8

in

0.6 70

80

TT =380K TT in=413K TTon=450K

0.78

90

100

110

120

130

in

2

2.2

2.4

temperatures. The maximum efficiency is reached at T T in = 405 K, slightly lower than the nominal temperature of 413 K. At 80% rpm, the total-to-total efficiency continually decreases with the inlet temperature while at the highest rotational speed, the efficiency increases with the temperature and reaches a plateau from T T in = 430 K. The total-to-total efficiency dramatically drops at high rotational speed with low temperatures. Fig. 9 shows that at low temperature, the maximum efficiency is reached at a low rotational speed. After that point, the total-tototal efficiency rapidly drops with an increase of the rotational speed. At the nominal temperature (413 K), the turbine can better

550

0.88

500

0.86

ηT-T [-]

Power [kW]

3.2

3.4

3.6

handle the variation of rotational speed. In that case, the maximum efficiency is reached at 105% of the nominal rotational speed (25463.5 rpm), slightly above the nominal rotational speed of 24,250 rpm. At higher temperature, the efficiency keeps increasing with the rotational speed. Figs. 10 and 11 presents the variation of power with the inlet temperature and the rotational speed respectively. For all rotational speeds, the power increases with the inlet turbine temperature as shown in Fig. 10. However, this increase is more pronounced at the highest rotational speed. It is also

0.9

400

3

Fig. 12. Variation of the total-to-total efficiency with the total-to-static pressure ratio at three different inlet temperatures for the nominal rotational speed.

600

450

2.8

ΠT-S [-]

Ω/ΩNominal [%] Fig. 9. Evolution of the total-to-total efficiency with the rotational speed at three different inlet temperatures.

2.6

80% RPM Nominal RPM 120% RPM

0.84 0.82

350 0.8

300

80% RPM Nominal RPM 120% RPM

250 200

380

400

420

440

0.78 460

TT [K] in

Fig. 10. Variation of the turbine power with the total inlet temperature at three different rotational speeds.

0.76 1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

ΠT-S [-] Fig. 13. Variation of the total-to-total efficiency with the total-to-static pressure ratio at three different rotational speeds for the nominal inlet temperature.

E. Sauret, Y. Gu / Applied Energy 135 (2014) 202–211

3.5e4

-1

dhT [kJ.kg ]

3.0e4 2.5e4 2.0e4

TT =380K TTin=413K TTin=450K

1.5e4

in

1.0e4 70

80

90

100

110

120

130

Ω/ΩNominal [%] Fig. 14. Evolution of the enthalpy drop with the rotational speed at 3 different inlet temperatures.

3.5e4

-1

dhT [kJ.kg ]

3.0e4 2.5e4 2.0e4

A variation of the pressure ratio was also performed and the results at three different inlet temperatures for the nominal rotational speed are presented in Fig. 12. At the lowest temperature, the maximum efficiency is reached at PT—S = 2.3. The efficiency rapidly drops on each side of the best efficiency point such that no numerical results were obtained for pressure ratios above 2.9 at 80% of the nominal rotational speed. For the nominal temperature ðT T in ¼ 413 KÞ, the maximum efficiency is reached at PT—S ¼ 2:1 well below the nominal pressure ratio of 2.65. After this point, the efficiency gradually decreases with an increase of the pressure ratio. Similar trends are observed at the highest temperature with a faster drop compared to the nominal temperature. The evolution of the efficiency with the pressure ratio was also plotted at three different rotational speeds as shown in Fig. 13 at the nominal inlet temperature. At low rotational speed, the efficiency continually decreases with the total-to-static pressure ratio while at the nominal rotational speed, the maximum efficiency is reached at PT—S ¼ 2:1 and then decreases. At the highest rotational speed, the maximum efficiency is shifted towards higher total-to-static pressure ratio (2.9). At low total-to-static pressure ratio, the highest rotational speed gives the lowest efficiency while at higher pressure ratios, it is the lowest rotational speed that provides with the lowest efficiency. The highest efficiencies are obtained over the range of pressure ratios at the nominal rotational speed. 6.3. Discussion

1.5e4 1.0e4

209

80% RPM Nominal RPM 120% RPM 380

400

420

440

460

TT [K] in

Fig. 15. Evolution of the enthalpy drop with the inlet temperature at 3 rotational speeds.

observed in Fig. 11 that, as the temperature increases, the maximum power tends to move towards higher rotational speeds. Furthermore, the power increases with the temperature for a constant rotational speed.

We can note that the effects of rotational speed, inlet temperature and pressure ratio are less pronounced at the nominal conditions. Therefore, the nominal point is the most capable of handling a variation of rotational speed, temperature or pressure ratio while maintaining a relatively high efficiency over the range of variation. The effect of the rotational speed is also more important at T T in ¼ 380 K than at T T in ¼ 450 K. This is explained by the variation of enthalpy drop through the turbine as shown in Figs. 14 and 15. We can note that at T T in ¼ 380 K, the enthalpy drop dhT at 120% rpm is 32.1% smaller than at 80% rpm. Thus the efficiency at T T in ¼ 380 K is largely higher for the lowest rotational speed. On the contrary, at T T in ¼ 450 K, dhT at 120% rpm is 17.1% larger than

(a) TTin =380K, 80% nominal rpm

(b) TTin =450K, 80% nominal rpm

(c) TTin =380K, 120% nominal rpm

(d) TTin =450K, 120% nominal rpm

Fig. 16. Mach number at mid-span for T T in ¼ 380 K and T T in ¼ 450 K at 80% and 120% nominal rpm.

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0.9 0.8

ηT-T [-]

0.7 0.6 0.5 0.4 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

U/C0 [-] Fig. 17. Variation of the total-to-total efficiency with the blade-to-jet speed ratio.

0.9 0.89 0.88

ηT-T [-]

0.87 0.86 0.85 0.84 0.83 0.82 0.81 0.8 0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

U/C0 [-] Fig. 18. Variation of the total-to-total efficiency with the blade-to-jet speed ratio at nominal turbine power W ¼ 400 kW.

dhT at 80% rpm explaining the lower efficiency at T T in ¼ 450 K for the lowest rotational speed. In addition, as shown in Fig. 16, increasing the rotational speed at the lowest temperature dramatically damage the flow with large separation areas in the rotor associated with large density values at the exit of the stator. The effect of the rotational speed at the highest temperature is different as the flow pattern improves with the increase of rotational speed. At T T in ¼ 450 K and 120% rpm no separation is visible at mid-span. Furthermore, the flow at these conditions is really similar to the flow at T T in ¼ 380 K, 80% rpm explaining the similar efficiencies obtained for these 2 conditions (Figs. 8 and 9). All these effects are related to the high-density fluid properties associated with opposite flow behaviours when increasing the temperature at 80% rpm and 120% rpm or when increasing the rotational speed at T T in ¼ 380 K and T T in ¼ 450 K. Thus accurate advanced uncertainty quantification would benefit the understanding of the sensitivity of the numerical simulations to the fluid properties. The variation of the power presented in Figs. 10 and 11 is also linked to the fluid properties, enthalpy drop as seen in Figs. 14 Table 6 Comparison of the nominal best efficiency points. Variables

Nominal point

Best efficiency point

Best efficiency point at W = 400 kW

gT—T (%) T T in (K) X (rpm) Q_ m ðkg s1 Þ

87.6 2.64 413 24,250 17.24

88.8 2.1 413 24,250 12.56

88.45 2.46 413 24,250 17.24

W (kW) U/C 0 (–)

421.5 0.681

257.2 0.748

390.8 0.711

PT—S (–)

and 15 and flow modifications in the turbine (Fig. 16). The variation of enthalpy drop through the turbine is different according to the temperature. While dhT keeps increasing with the rotational speed at 450 K, it starts decreasing for 380 K after 95% rpm due to the increased separation regions in the rotor with the rotational speed at the lowest temperature. This low temperature high rotational speed case also corresponds to a very high density bringing back the question of the sensitivity of the Peng–Robinson EoS. Thus further detailed uncertainty quantification is required to accurately quantify this sensitivity. The nominal point and all the off-design conditions numerically simulated are gathered in Fig. 17 which shows the variation of efficiency with the blade-to-jet speed ratio U/C 0 . One can note that the maximum efficiency of 88.8% is reached at a blade-to-jet speed ratio of 0.748 well above the optimum value of 0.7 [11,13]. However, this point corresponds to a turbine output power of only 257 kW well below the nominal power of around 400 kW. For that reason, the efficiency versus the blade-to-jet speed ratio was plotted only considereing the points with an output power of approximately 400 kW. The resulting graph is shown in Fig. 18. While only considering the conditions leading to the nominal turbine power of 400 kW, one can note that the maximum efficiency is now 88.45% and is reached at U/C 0 = 0.711, slightly above the optimum value of 0.7. The nominal point is then compared to the best efficiency points in Table 6. The best efficiency point is almost the efficiency obtained at a fixed turbine power of approximately 400 kW. Furthermore, the nominal efficiency is extremely close to the best efficiency with a 1.4% difference. We can also note that the best efficiencies are obtained at the nominal inlet temperature and nominal rotational speed. However, the best efficiency is obtained at a lower pressure ratio due to a lower mass flow rate, In return, the power is lower. At the nominal turbine power, the best efficiency is obtained at the nominal flow rate but also with a reduced pressure ratio, achieved by varying the outlet static pressure. A coupled optimisation of the thermodynamic cycle and 1D turbine design would be then beneficial. It would provide the best outlet pressure for the turbine in order to achieve the the best efficiency at the required turbine power output.

7. Conclusion This paper is the first to present the full design process of a radial-inflow turbine working with R143a in sensible geothermal brine and cycle conditions. The thermodynamic cycle, the preliminary 1D design, the meanline analysis of the turbine and eventually the steady-state 3D viscous simulations of the turbine both at nominal and off-design conditions are produced. The CFD simulations provided satisfactory results compared to the meanline analysis except for the efficiencies due to the sensitivity of real gas properties to the temperature variations. Parametric studies were carried out highlighting the relative robustness of the design point over the variations of temperature, rotational speed and pressure ratio. The CFD results also confirmed the need for a coupled optimisation of the thermodynamic cycle and 1D turbine design. Optimising the system parameters will positively impact the turbine and thus cycle efficiencies. These pioneering 3D CFD simulations confirmed previouslypublished studies for the need of more detailed optimization in order to improve the blade loading profiles of the turbine and lower the maximum Mach number at the exit of the nozzle. As a perspective to the presented work, the direct use of the RefProp database for the real gas properties in the CFD solver instead of the Peng–Robinson EoS will be performed in order to improve

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the prediction of the thermodynamic properties and so the power and turbine efficiency. In addition, it is recommended that the sensitivity of the efficiency to the EoS will be studied using non-statistical state-of-the-art uncertainty quantification methods such as Stochatic Collocation using Adaptive Sparse Grid. Finally, a 3D shape optimization tool coupled with a structural analysis will be developed and applied to this candidate R143a radial-inflow turbine in sensible geothermal conditions. Acknowledgements Dr. E. Sauret would like to thank the Australian Research Council for its financial support (DE130101183). References [1] Angelino G, Gaia M, Macchi E. A review of italian activity in the field of organic rankine cycles. In: International VDI-seminar (ORC-HP-technology, working fluid problems). Zurich, Switzerland; 1984. p. 465–82. [2] Harinck J, Turunen-Saaresti T, Colonna P, Rebay S, van Buijtenen J. Computational study of a high-expansion ratio radial organic rankine cycle turbine stator. J Eng Gas Turb Power 2010;132:1–6. [3] Badr O, Naik S, O’Callaghan PW. Expansion machine for low power-output steam rankine-cycle engine. Appl Energy 1991;39:93–116. [4] Madhawa-Hettiarachchi H, Golubovic M, Worek W, Ikegami Y. Optimum design criteria for an organic rankine cycle using low-temperature geothermal heat sources. Energy J 2007;32:1698–706. [5] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic rankine cycles. Energy 2007;32:1210–21. [6] Facao J, Oliveira A. Analysis of energetic, design and operational criteria when choosing an adequate working fluid for small ORC systems. In: Proceedings of the ASME 2009 international mechanical engineering congress & exposition, IMEC2009-12420, November 13–19, Lake Buena Vista, Florida, USA; 2009. [7] Guo T, Wang H, Zhang S. Fluid selection for a low-temperature geothermal organic rankine cycle by energy and exergy. In: Power and engineering conference (APPEEC); 2010. [8] Chen H, Goswami Y, Stefanakos E. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew Sustain Energy Rev 2010;14:3059–67. [9] Toffolo A, Lazzaretto A, Manente G, Paci M. A multi-criteria approach for the optimal selection of working fluid and design parameters in organic rankine cycle systems. Appl Energy 2014;121:219–32. [10] Glassman AJ. Computer program for design analysis of radial-inflow turbines. Tech. rep., NASA; 1976. [11] Whitfield A. The preliminary design of radial inflow turbines. J Turbomach, ASME 1990;112:50–7. [12] Ebaid MSY, Bhinder FS, Khdairi GH. A unified approach for designing a radial flow gas turbine. J Turbomach 2003;125(3):598–606. http://dx.doi.org/ 10.1115/1.1574824. [13] Baines NC. Radial turbines: an integrated design approach, concepts NREC. In: 6th European turbomachinery conference – fluid dynamics and thermodynamics. Lille, France; 2005. [14] Ventura CAM, Jacobs PA, Rowlands AS, Petrie-Repar P, Sauret E. Preliminary design and performance estimation of radial inlflow turbines: an automated approach. Trans ASME J Fluids Eng 2012;134:031102-1–031102-13. [15] Aungier RH. Turbine aerodynamics. Axial-flow and radial-inflow turbine design and analysis. New York, USA: ASME; 2006. [16] Pasquale D, Ghidoni A, Rebay S. Shape optimization of an organic rankine cycle radial turbine nozzle. J Eng Gas Turb Power 2013;135:042308-1–042308-13. [17] Mueller L, Alsalihi Z, Verstraete T. Multidisciplinary optimization of a turbocharger radial turbine. J Turbomach 2013;135:021022-1–2-9. [18] Harinck J, Pasquale D, Pecnik R, van Buijtenen J, Colonna P. Performance improvement of a radial organic rankine cycle turbine by means of automated computational fluid dynamic design. Proc Inst Mech Eng, Part A: J Power Energy 2013;227:637–45. [19] Hoffren J, Talonpoika T, Larjola J, Siikonen T. Numerical simulation of real-gas flow in a supersonic turbine nozzle ring. J Eng Gas Turb Power 2002;124:395–403.

211

[20] Cinnella P, Congedo P. A numerical solver for dense gas flows. In: 34th AIAA fluid dynamics conference and exhibit. Portland, OR, paper no. AIAA 20042137; 2004. p. 1–12. [21] Boncinelli P, Rubechini F, Arnone A, Cecconi M, Cortese C. Real gas effects in turbomachinery: a computational fluid dynamics model for fast computations. J Turbomach 2004;126:268–76. [22] Colonna P, Rebay S, Harinck J, Guardone A. Real-gas effects in orc turbine flow simulations: influence of thermodynamic models on flow fields and performance parameters. In: European conference on computational fluid dynamics – ECCOMAS CFD 2006; 2006. [23] Harinck J, Colonna P, Guardone A, Rebay S. Influence of thermodynamic models in two-dimensional flow simulations of turboexpanders. J Turbomach 2010;32:1–17. [24] Pini M, Persico G, Casati E, Dossena V. Preliminary design of a centrifugal turbine for organic rankine cycle applications. J Eng Gas Turb Power 2013;135:042312-1–2-9. [25] Wheeler APS, Ong J. The role of dense gas dynamics on organic rankine cycle turbine performance. J Eng Gas Turb Powereng 2013;135:102603-1–3-9. [26] Klonowicz P, Borsukiewicz-Gozdur A, Hanausek P, Kryllowicz W, Bruggemann D. Design and performance measurements of an organic vapour turbine. Appl Therm Eng 2014;63:297–303. [27] Cho S-Y, Cho C-H, Ahn K-Y, Lee YD. A study of the optimal operating conditions in the organic rankine cycle using a turbo-expander for fluctuations of the available thermal energy. Energy 2014;64:900–11. [28] Hoffren J. Adaption of FINFLO for real gases. Tech. rep., Helsinki University of Technology, Laboratory of Applied Thermodynamics; 1997. [29] Sauret E, Rowlands SA. Candidate radial-inflow turbines and high-density working fluids for geothermal power systems. Energy 2011;36:4460–7. [30] Persky R, Sauret E, Ma L. Optimisation methods for coupled thermodynamic and 1D design of radial-inflow turbines. In: Proceedings of the ASME 2014 Joint US-European fluids engineering, division summer meeting and 11th international conference on nanochannels, microchannels, and minichannels, FEDSM 2014, August 3–7, 2014, Chicago, Illinois, USA; 2014. [31] Marcuccilli F, Thiolet D. Optimizing binary cycles thanks to radial inflow turbines. In: Proceedings world geothermal congress 2010, Bali, Indonesia, 25– 29 April; 2010. [32] Hung T, Wang SK, Kuo C, Pei B, Tsai K. A study of organic working 495 fluids on system efficiency of an orc using low-grade energy sources. Energy 2010;35(3):1403–11. [33] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic rankine cycles. Energy 2010;35(3):1033–9. [34] Marcuccilli F. Advantages of using radial inflow turbines for Kalina and organic rankine cycles. In: GRC transactions; 2008, vol. 32, p. 413–8. [35] Fiaschi D, Manfrida G, Maraschiello F. Thermo-fluid dynamics preliminary design of turbo-expanders for orc cycles. Appl Energy 2012;97:601–8. [36] Clemente S, Micheli D, Reini M, Taccani R. Bottoming organic rankine cycle for a small scale gas turbine: a comparison of different solutions. Appl Energy 2013;106:355–64. [37] Moustapha H, Zelesky MF, Baines NC, Japikse D. Axial and radial turbines, concepts NREC; 2003. [38] Rodgers C. Mainline performance prediction for radial inflow turbine in small high pressure ratio turbine. Tech. rep., Von Karman Institute Lecture Series; 1987. [39] I. Concepts ETI, Rital, user guide. Tech. rep.; 2008. [40] Concepts-NREC, Axcent, user guide; 2009. [41] Peng D-Y, Robinson DB. Anew two-constant equation of state. Ind Eng Chem Fundam 1976;15(1):59–64. [42] Agrawal A, Cornelio AA, Limperich D. Investigation of cubic EOS models for HFO-1234yf refrigerant used in automotive applications. In: International refrigeration and air conditioning conference; 2012. [43] Ansys 13.0 CFX-solver theory guide. [44] Poling BE, Prausnitz JM, O’Connell JP. The properties of gases and liquids. McGraw-Hill; 2001. [45] Sauret E. Open design of high pressure ratio radial-inflow turbine for academic validation. In: ASME (Ed.), Proceedings of the ASME 2012 international mechanical engineering congress & exposition, IMECE 2012, November 9– 15, 2012, Houston, Texas, USA, ASME; 2012. [46] Brown JS. Predicting performance of refrigerants using the Peng–Robinson equation of state. Int J Refrig 2007;30:1319–28. [47] Lemmon EW, Huber ML, McLinden MO. NIST reference fluid thermodynamic and transport properties-REFPROP, version 8.0. Tech. rep., physical and chemical properties division, national institute of standards and technology; 2007.