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Research Papers: Gas Turbines: Turbomachinery

Centrifugal Turbines for Mini-Organic Rankine Cycle Power Systems

[+] Author and Article Information
Emiliano Casati

Propulsion and Power,
TU-Delft,
Kluyverweg 1,
Delft 2629 HS, Netherlands;
Laboratorio Fluidodinamica delle Macchine,
Dipartimento di Energia,
Politecnico di Milano,
Via La Masa 34,
Milano 20156, Italy
e-mail: E.I.M.Casati@tudelft.nl

Salvatore Vitale

Propulsion and Power,
TU-Delft,
Kluyverweg 1,
Delft 2629 HS, Netherlands
e-mail: S.Vitale@tudelft.nl

Matteo Pini

Assistant Professor
Propulsion and Power,
TU-Delft,
Kluyverweg 1,
Delft 2629 HS, Netherlands
e-mail: M.Pini@tudelft.nl

Giacomo Persico

Assistant Professor
Laboratorio Fluidodinamica delle Macchine,
Dipartimento di Energia,
Politecnico di Milano,
Via La Masa 34,
Milano 20156, Italy
e-mail: giacomo.persico@polimi.it

Piero Colonna

Professor
Propulsion and Power,
TU-Delft,
Kluyverweg 1,
Delft 2629 HS, Netherlands
e-mail: P.Colonna@tudelft.nl

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received May 6, 2014; final manuscript received June 3, 2014; published online July 15, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(12), 122607 (Jul 15, 2014) (11 pages) Paper No: GTP-14-1227; doi: 10.1115/1.4027904 History: Received May 10, 2014; Revised June 12, 2014

Organic Rankine cycle (ORC) power systems are rapidly diffusing as a technology for the conversion of thermal energy sources in the small-to-medium power range, e.g., from 150 kWe up to several MWe. The most critical component is arguably the expander, especially if the power capacity is small or very small, as it is the case for innovative high-potential applications such as waste heat recovery from truck engines, or distributed conversion of concentrated solar radiation. In these so-called high-temperature applications, the expansion ratio is very high; therefore, turbines are the expanders of choice. Recently, multistage radial-outflow turbines (ROT), a nonconventional turbine configuration, have been studied, and first commercial implementations in the MWe power range have been successful. The objective of this work is the evaluation of the radial-outflow arrangement for the turbine of high-temperature mini-ORC power systems, with power output of the order of 10 kWe. To this end, a method for the preliminary fluid-dynamic design is presented. It consists of an automated optimization procedure based on an in-house mean-line code for the one-dimensional preliminary design and efficiency estimation of turbines. It is first shown that usually adopted simplified design procedures, such as that of the so-called repeating-stage, cannot be extended to minicentrifugal turbines. The novel methodology is applied to the exemplary case of the 10 kWe turbine of an ORC power system for truck engine heat recovery documented in the literature. The expansion ratio is 45. The preliminary fluid-dynamic design of two miniturbines is presented, namely, a five-stage transonic and a three-stage slightly supersonic turbine. The outcome of the preliminary design leads to two turbine configurations whose fluid-dynamic efficiency exceeds 79% and 77%, respectively. The speed of revolution is around 12,400 and 15,400 RPM for the five-stage and the three-stage machine, respectively. These results show that the ROT configuration may allow for compact and efficient expanders for low power output applications.

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References

Figures

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Fig. 1

Centrifugal turbine schematic, adapted from Ref. [27]

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Fig. 2

Saturation line of siloxane D4 in the T–s diagram, showing the ORC and the inlet and outlet pressure and temperature of the exemplary turbine designs discussed here. Point CR indicates the liquid–vapor critical point of the fluid.

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Fig. 3

Schematic of the two-dimensional flow through a turbine stage of the repeating type. All the rows feature the same geometrical angles (BDA). The peripheral velocity is assumed to be constant along the machine, i.e., U2 = NU3. The stage reaction degree is 0.5, and the velocity triangles are thus symmetrical. The sign convention for the flow angles is also reported, adapted from Ref. [23].

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Fig. 4

Exemplary results obtained from the preliminary fluid-dynamic design of a 1 MWm ORC centrifugal turbine. The simplified design procedure is described in Sec. 4.1, i.e., fulfilling Eqs. (3)–(6). The design specifications are derived from the thermodynamic cycle parameters reported in Table 1. The Traupel loss estimation method [22] is adopted. The speed of revolution has been constrained to 3000 rpm, and the inlet diameter to 0.88 m. Figure 4(a) shows the velocity triangles, in black those referring to the rotor inlet section, in gray those referring to the rotor outlet. For the first rotor only, all the velocity components are detailed (see also Fig. 3). The corresponding meridional section is depicted in Fig. 4(b).

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Fig. 5

Diameter ratio for a centrifugal row (Din/Dout)row, i.e., term D in Eq. (14), as a function of the row diameter Din, row, and of the radial chord b

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Fig. 6

Results for the preliminary fluid-dynamic design of the five-stage transonic 10 kWm centrifugal turbine. The specifications are those reported in Table 1. The Traupel loss estimation method [22] has been selected. Figure 6(a) shows the velocity triangles, in black those referring to the rotor inlet section, in gray to the rotor outlet. For the first rotor only, the Mach numbers corresponding to the different velocity components are detailed, while for the subsequent rows only the values are reported (see also Fig. 3). The corresponding meridional section is depicted in Fig. 6(b).

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Fig. 7

Preliminary fluid-dynamic design results for the five-stage transonic 10 kWm turbine of Fig. 6. (a) Evolution of the load distribution among the stages, in terms of the aerodynamic loading expressed by the work coefficient Ψ = wstg/2U¯2 (with U¯ = (Uin+Uout)stg/2), and of the stage specific work w. (b) Row-by-row evolution of the kinetic energy loss coefficients ζp (solid lines), ζs (dashed–dotted lines), and ζl (dashed lines, plotted only for the rotors) accounting for profile-, secondary-, and tip leakage-losses, respectively. These results are obtained with the Traupel loss estimation method [22]. The loss coefficient is defined as ζ = 2ΔhS,loss/Vout2, where ΔhS,loss is the static enthalpy drop due to the considered loss, V = C for the stators, and V = W for the rotors.

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Fig. 8

Results of the preliminary fluid-dynamic design of the three-stage supersonic 10 kWm ORC turbine. Specifications are reported in Table 1. Figure 8(a) shows the velocity triangles, in black those referring to the rotor inlet section, in gray to the rotor outlet. For the first rotor only, the Mach numbers corresponding to the different velocity components are detailed, while for the subsequent rows only the values are reported (see also Fig. 3). The solid lines represent the results obtained with the Traupel loss estimation method [22], while the dashed ones those pertaining to the Craig–Cox model [16]. The corresponding meridional section is depicted in Fig. 8(b). In this case, the results of the two models are not distinguishable.

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Fig. 9

Results of the preliminary fluid-dynamic design of the three-stage supersonic 10 kWm ORC turbine of Fig. 8. (a) Evolution of the load distribution among the stages, in terms of the aerodynamic loading expressed by the work coefficient Ψ = wstg/2U¯2 (with U¯ = (Uin+Uout)stg/2), and of the stage specific work w. (b) Row-by-row evolution of the kinetic energy loss coefficients ζp (solid lines), ζs (dashed–dotted lines), and ζl (dashed lines, plotted only for the rotors) accounting for profile-, secondary-, and tip leakage-losses, respectively. The black lines represent the results obtained with the Traupel loss estimation method [22], while the gray ones those pertaining to the Craig and Cox one [16]. The loss coefficient is defined as ζ = 2ΔhS,loss/Vout2, where ΔhS,loss is the static enthalpy drop due to the considered loss, V = C for the stators, and V = W for the rotors.

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