Hybrid method of optimization using of a swarm intelligence and Nelder-Mead's method as a method to improve efficiency of an ORC Microturbine

Interest in alternative energy resources has grown dramatically in the past decades. It is due to the increased environmental pollution and a threat of global warming. Burning of the fossil fuels is believed to be the main cause of a greenhouse effect. An important number of new solutions have been proposed to generate energy from low temperature heat sources. They are now applied to such diversified fields as solar thermal power, geothermal power, biomass combustion. The Organic Rankine Cycle is a very promising technology from point of view of renewable energy sources. A typical ORC system (Fig.1) consists of an evaporator, condenser, pump, regenerator and the heart of the system – turbine driving a generator. Optimization of the main part of the ORC system provides an increase of economic efficiency of the whole installation.

It is human nature to seek the best option among that are available. Nature, too, seems to be guided by optimization – many laws of nature have a vibrational character. Optimization has been a popular research topic for decades. There are many algorithms offered by different authors in the literature for this task. Among the swarm algorithms, the most popular are Ant Colony Optimization Artificial Bee Colony (ABC), Bee Colony Optimization (BCO). Interest in swarm algorithms has dynamically increased because they have demonstrated some promising results in solving tough optimization problems. In general, these algorithms tend to be flexible, efficient and highly adaptable, and yet easy to implement. All of these algorithms have one disadvantage - while solving complex problems good results such as a global extremum will be reached but the method needs a lot of time.

In 3D optimization of microturbine ORC it is very important to reduce the CPU time of the optimisation process. Therefore, 3D computational grids used during optimization are relatively coarse. One of the method of increasing the efficiency of the optimization algorithms is hybridization. Hybridization is a combination of two or more of algorithms so as to combine good features and eliminate drawbacks of particular algorithms.

The aim of the project is to elaborate a robust hybrid stochastic/deterministic method of optimization of the blading system for the ORC microturbine. The proposed method will draw on a combination of a swarm algorithm and the Nelder – Mead method of deformed polyhedron. The obtained results of optimization of the ORC microturbine blading system will be compared with the results obtained from other stochastic and deterministic optimizations algorithms.

Project cost: 106 400 zł (~24 918 Euro in 2016)

Project time: 36 months

Start date: 15.02.2016

Objective function and constraints

The isentropic total-to-static efficiency was selected as the objective function for the shape optimization of the flow channel . With this definition the exit kinetic energy losses are included in general losses of the stage. In order to secure global flow conditions constraint was imposed on the mass flow rate.

Procedure

The overall optimisation process consisted of two phases – iterative phase and verification. All stages of the iteration loop were managed by the script written in Matlab application. The geometry of the optimized stage was being created within the Matlab script. In order to perform the CFD analysis the next step was the generation of suitable computational grid. An automatic grid was created by means of Ansys Turbogrid software. The hexahedral meshes prepared for the numerical simulations consisted of about 20-60 thousand elements for every domain (single stator channel and single rotor channel with periodic condition). Special care was given to the edge length ratio, face angle, element volume ratio. During the optimisation the quality of the meshes was monitored. The RANS simulations were performed by means of a commercial code Ansys CFX. The numerical model used in the computations was similar to that used by other authors who simulated air turbine stages. The equations describing the flow were solved by means of the finite volume method. Second order discretization scheme was applied. As a turbulence model the k-w SST was selected. The imposed set of boundary conditions consisted of the total pressure and total temperature at the inlet, average static pressure at the outlet and the rotational speed of the rotor domain. In the verification phase the optimal geometry was tested on a fine grid (2-10 mln nodes for stage).

All 3D CFD simulations and optimizations are solved using an Intel® XEON® CPU E5-2640 v4@ 2.60 GHz (2 processors) with 64 GB RAM memory in parallel run with total 20 CPU cores.

Parametrization

The parametrization of the 3D radial inflow turbine (RIT) was based on changing the blade camber line at hub, medium height, and top, the thickness distribution on the same heights, and the meridional contour of fluid domain. The blade camber line was defined by the beta distribution. The beta distribution was parametrized by a Bezier curve with a few control points start with trailing edge and end on leading edge. Also the thickness distribution was defined by a Bezier curve and five control on three heights. The meridional contour were defined by hub and shroud curves. The coordinates of the control points were modified in axial, and radial direction.

The parameterization of the 3D one stagie axial turbine was based on several changing parameters: rotor twist angle, rotor simple circumferential lean, rotor simple circumferential lean, rotor compound circumferential lean, rotor simple axial lean, rotor compound axial lean and nozzle design parameters.