Performance enhancement of a small-scale organic Rankine cycle radial-inflow turbine through multi-objective optimization algorithm

doi:10.1016/j.energy.2017.05.022

Energy

Volume 131, 15 July 2017, Pages 297-311

https://doi.org/10.1016/j.energy.2017.05.022 Get rights and content

Highlights

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Small-scale radial-inflow turbine was designed and optimized.
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ORC system modelling and optimization of radial-inflow turbine were integrated.
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The 3D optimization based on Multi-objective genetic algorithm was conducted.
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Higher turbine and thermal system efficiencies achieved with optimized turbine.

Abstract

An effective methodology that encompasses a mean-line design, three-dimensional CFD analysis and optimization and ORC system modelling of the small-scale ORC radial-inflow turbine is presented. Three-dimensional CFD analysis and a multi-objective optimization algorithm were achieved using ANSYS^®17 CFX and Design Exploration based on 3D RANS with a k-omega SST turbulence model. The 3D optimization technique combines a design of the experiment, a response surface method and multi-objective method. The optimization of the blade geometry was performed using 20 design points for both nozzle and rotor blades, based on the B-splines’ technique to represent the blade angles and thickness distribution. The number of blades and rotor tip clearance were included as design parameters. The isentropic efficiency and power output were introduced as an optimization objective with two organic working fluids, namely isopentane and R245fa. The results of the optimized geometry with R245fa showed that the turbine's and cycle's thermal efficiencies were higher by 13.95% and 17.38% respectively, compared with a base-line design with a maximum power output of 5.415 kW. Such methodology is proved to be effective as it allows the enhancing of the turbine's and the ORC's system performance throughout to find the optimum blade shape of the turbine stage.

Introduction

One of the major challenges in the world today is the increasing energy demand. Therefore, more attention is dedicated to energy saving and reduction of environmental pollution and fossil fuel consumption by exploiting renewable energy sources. The Organic Rankine Cycle (ORC) provides electricity from low-temperature heat sources including renewable energy (i.e. solar and geothermal) and low-grade waste heat. In this scenario, the ORC systems offer potential for generating electricity for wide range of applications including domestic and remote off-grid communities.

Many researches have been carried out regarding ORC system by focusing on thermodynamic analyses, optimization and the selection of a suitable working fluid for the cycle for low-temperature heat source applications, including solar thermal energy as reported in Refs. [1], [2], [3]. While, several studies focused on thermo-economic, and ORC system analysis driven by geothermal energy [4], [5], [6], [7]. In terms of low-grade waste heat sources, ORC thermodynamic analysis has been conducted in Refs. [8], [9], [10]. In aforementioned studies, the thermodynamic analysis model of ORC's system was performed based on the assumption of constant turbine isentropic efficiency for different working fluid and various operating conditions that lead inaccurate ORC performance.

In an ORC system, the turbine's efficiency has a significant influence on the ORC system's performance. For small-scale power generation using ORC, radial-inflow turbine is considered a suitable choice as reported in literature. A number of studies using radial-inflow turbine based on various approaches are summarized in Table 1 using the mean-line design approach and CFD analysis for developing radial-inflow turbine.

Although there have been a number of recent attempts to develop the turbine's performance using computational fluid dynamic techniques like ANSYS CFX/Fluent, a limited amount of work has involved using optimization techniques to optimize the blade geometry to improve both the turbine's and ORC's performance. Al Jubori et al. [28] presented a new methodology that coupled 1D, 3D CFD analysis and optimization of a small-scale axial turbine with ORC system modelling, based on a multi-objective genetic algorithm (MOGA) with six different working fluids. Their optimization results exhibited that the maximum turbine and cycle efficiencies and power output with R123 were about 88%, 10.5% and 6.3 kW respectively. Rahbar et al. [29] carried out 3D optimization of the transonic rotor of a two-stage radial-inflow turbine using a genetic algorithm (GA) with R245fa as the working fluid. Their optimization results showed that the maximum turbine isentropic efficiency was of 88% with a maximum power output of 26.35 kW and cycle efficiency about 14.8%, with a pressure ratio of 10 and total inlet temperature of 405.3 K.

There is limited literature concerning the design and 3D CFD analysis and optimization of small-scale radial-inflow turbine for ORC's system with power output around 5 kW for different power generation applications, such as small buildings, rural areas, off-grid zones and isolated installations. Therefore, three-dimensional CFD optimization using multi-objective optimization for a small-scale radial-inflow turbine stage (nozzle and rotor) is novel and has only received limited investigation previously. New methodology for integrating the mean-line design, 3D CFD analysis, and multi-objective optimization with ORC modelling has been presented for the small-scale radial-inflow turbine (RIT) stage. Furthermore, it seeks to fill the gap by investigating the turbine's performance in both design and off-design conditions for baseline and optimum design cases with two organic working fluids. The mean-line design of the RIT and ORC modelling is developed using the engineering equation solver (EES) software; ANSYS^®17-CFX is employed to predict the 3D viscous flow and turbine performance. The real gas formulation of the working fluids is applied to perform an accurate prediction of the real behaviour of the working fluids in a turbine/ORC model using the REFPROP database. The CFD baseline design of the RIT is optimized using the ANSYS^®17-Design Exploration package for 3D optimization purposes, based on a multi-objective genetic algorithm (MOGA). The optimized turbine performance (isentropic efficiency and power output) for each organic working fluid is inserted into the ORC model to determine the best cycle efficiency. The inclusion of constraints in the optimization technique allows for achieving the highest efficiency from optimized geometry without exceeding input operating conditions.

Section snippets

Working fluids selection and ORC system modelling

The selection of the organic working fluid is an essential aspect in the ORC system modelling and performance. According to their thermo-physical properties, the working fluids have a strong influence on the ORC system's efficiency, the expander's performance, the components' size, the system's stability, safety and economic feasibility and the environmental concerns [30]. Organic working fluids have large molecular weights and a low boiling temperature and pressure and are usually heavy

Radial-inflow turbine (RIT) design

The first and crucial step of the whole turbine design procedure is the preliminary mean-line design (PD) to create the correct aerodynamic design that delivers the desired output. The PD of the RIT is based on one-dimensional (1D) mean-line flow analysis. The mean-line model refers to the mid-span values of the blades' passage and only focuses on the inlet and outlet condition of each blade's passage. Its approach allows fast prediction for fluid-dynamic development and thermodynamic process

3D CFD analysis

The actual configuration of the flow inside the turbine stage is particularly complex; so it requires a high-fidelity model based on an adequately complex flow scheme. Therefore, the integrated methodology between the low-fidelity model (i.e. PD model) and the high-fidelity model (i.e. 3D CFD model) is essential to directly predict the most relevant flow features (3D, turbulent and unsteady flow etc.). Consequently, the main turbine stage's geometric characteristics from the mean-line design

Three-dimensional optimization methodology

The current optimization technique combines the design of experiment (DoE) technique, response surface method (RSM) and a multi-objective genetic algorithm (MOGA) through the ANSYS-Design of Exploration (DE) that is integrated with 3D CFD analysis. In this methodology, the DoE is used to fill the design space throughout to specify the location of sample design points that detects their space distribution for the blade geometry as design parameters in efficient way and then feed the response

ORC analysis results

Using the optimized turbine performance (i.e. isentropic efficiency and power output) at the design point (Table 3) and setting these as inputs to the ORC model (section 2) resulted in the system's thermal efficiency of 11.27%, compared with 9.56% at base-line design for R245fa as the working fluid, as shown in Fig. 20a. Also, Fig. 20a shows that the optimized ORC system's efficiency with isopentane as the working fluid was 9.69% compared with 8.07% at base-line design. Such results demonstrate

Conclusions

In this paper, 3D CFD optimization of the blade's geometry of a small-scale radial-inflow turbine stage (nozzle and rotor) for a low power ORC system, driven by a low-temperature heat source has been conducted to enhance the turbine's and the ORC system's performance. R245fa and isopentane were selected as working fluids with a temperature heat source of (≈90 °C). In multi-objective optimization algorithm, the turbine performance (isentropic efficiency and power output) was selected as an

Acknowledgement

The main author (Ayad M. Al Jubori) gratefully acknowledges the Iraqi ministry of higher education and scientific research for funding PhD scholarship at the University of Birmingham, UK which facilitates continuation of research on the modelling and 3D optimization of small-scale radial-inflow turbine.

Nomenclature

b₃, b₄, b₅: blade width (m)
C: absolute velocity (m/s)
d: diameter (m)
f: friction coefficient's (−)
h: specific enthalpy (kJ/kg)
$l$: length (m)
K: losses coefficient's (−)
k: specific turbulence kinetic energy (m²/s²)
$\dot{m}$: mass flow rate (kg/s)
M: meridional length (%)
p: pressure (bar)
$\dot{Q}$: heat (kW)
r: radius (m)
s: entropy (kJ/kg.K)
T: temperature (K)
t: time (s)
U: blade velocity (m/s)
w: relative velocity (m/s)
$\dot{W}$: power (kW)
Z: number of blades (−)

Greek symbols

α: absolute flow angle (degree)
β: relative flow angle (degree)
η: efficiency (%)
ρ: density (kg/m³)
ε: clearance (m)

References (45)

M. Wang et al.
Thermodynamic analysis and optimization of a solar-driven regenerative organic Rankine cycle (ORC) based on flat-plate solar collectors
Appl Therm Eng
(2013)
H. Hajabdollahi et al.
Thermo-economic optimization of RSORC (regenerative solar organic Rankine cycle) considering hourly analysis
Energy
(2015)
H.U. Helvaci et al.
Thermodynamic modelling and analysis of a solar organic Rankine cycle employing thermofluids
Energy Convers Manag
(2017)
X. Wang et al.
Parametric optimization and range analysis of Organic Rankine Cycle for binary-cycle geothermal plant
Energy Convers Manag
(2014)
Q. Liu et al.
Parametric optimization and performance analyses of geothermal organic Rankine cycles using R600a/R601a mixtures as working fluids
Appl Energy
(2015)
N. Kazemi et al.
Thermodynamic, economic and thermo-economic optimization of a new proposed organic Rankine cycle for energy production from geothermal resources
Energy Convers Manag
(2016)
M. Sadeghi et al.
Thermodynamic analysis and multi-objective optimization of various ORC (organic Rankine cycle) configurations using zeotropic mixtures
Energy
(2016)
D. Maraver et al.
Systematic optimization of subcritical and transcritical organic Rankine cycles (ORCs) constrained by technical parameters in multiple applications
Appl Energy
(2014)
Y. Feng et al.
Performance comparison of low-grade ORCs (organic Rankine cycles) using R245fa, pentane and their mixtures based on the thermoeconomic multi-objective optimization and decision makings
Energy
(2015)
Z. Ge et al.
Main parameters optimization of regenerative organic Rankine cycle driven by low-temperature flue gas waste heat
Energy
(2015)

E. Sauret et al.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Energy

(2011)

D. Hu et al.

Preliminary design and off-design performance analysis of an Organic Rankine Cycle for geothermal sources

Energy Convers Manag

(2015)

K. Rahbar et al.

Parametric analysis and optimization of a small-scale radial turbine for Organic Rankine Cycle

Energy

(2015)

D. Fiaschi et al.

Design and performance prediction of radial ORC turbo expanders

Appl Energy

(2015)

J. Song et al.

Influence of the radial-inflow turbine efficiency prediction on the design and analysis of the Organic Rankine Cycle (ORC) system

Energy Convers Manag

(2016)

L. Pan et al.

Improved analysis of Organic Rankine Cycle based on radial flow turbine

Appl Therm Eng

(2013)

S.Y. Cho et al.

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)

A. Al Jubori et al.

Development of micro-scale axial and radial turbines for low-temperature heat source driven organic Rankine cycle

Energy Convers Manag

(2016)

D. Fiaschi et al.

Design of micro radial turboexpanders for ORC power cycles: from 0D to 3D

Appl Therm Eng

(2016)

Y. Li et al.

Investigation of the organic Rankine cycle (ORC) system and the radial-inflow turbine design

Appl Therm Eng

(2016)

Y. Zheng et al.

Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method

Appl Therm Eng

(2017)

G. Pei et al.

Construction and dynamic test of a small-scale organic rankine cycle

Energy

(2011)

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