Method for the Preliminary Fluid Dynamic Design of High-Temperature Mini-Organic Rankine Cycle Turbines

Abstract

Widespread adoption of renewable energy technologies will arguably benefit from the availability of economically viable distributed thermal power conversion systems. For this reason, considerable efforts have been dedicated in recent years to R&D over mini-organic Rankine cycle (ORC) power plants, thus with a power capacity approximately in the 3–50 kW range. The application of these systems for waste heat recovery from diesel engines of long-haul trucks stands out because of the possibility of achieving economy of production. Many technical challenges need to be solved, as the system must be sufficiently efficient, light, and compact. The design paradigm is therefore completely different from that of conventional stationary ORC power plants of much larger capacity. A high speed turbine is arguably the expander of choice, if high conversion efficiency is targeted, thus high maximum cycle temperature. Given the lack of knowledge on the design of these turbines, which depends on a large number of constraints, a novel optimal design method integrating the preliminary design of the thermodynamic cycle and that of the turbine has been developed. The method is applicable to radial inflow, axial and radial outflow turbines, and to superheated and supercritical cycle configurations. After a limited number of working fluids are selected, the feasible design space is explored by means of thermodynamic cycle design calculations integrated with a simplified turbine design procedure, whereby the isentropic expansion efficiency is prescribed. Starting from the resulting design space, optimal preliminary designs are obtained by combining cycle calculations with a 1D mean-line code, subject to constraints. The application of the procedure is illustrated for a test case: the design of turbines to be tested in a new experimental setup named organic rankine cycle hybrid integrated device (ORCHID) which is being constructed at the Delft University of Technology, Delft, The Netherlands. The first turbine selected for further design and construction employs siloxane MM (hexamethyldisiloxane, C6H18OSi2), supercritical cycle, and the radial inflow configuration. The main preliminary design specifications are power output equal to 11.6 kW, turbine inlet temperature equal to 300 °C, maximum cycle pressure equal to 19.9 bar, expansion ratio equal to 72, rotational speed equal to 90 krpm, inlet diameter equal to 75 mm, minimum blade height equal to 2 mm, degree of reaction equal to 0.44, and estimated total-to-static efficiency equal to 77.3%. Results of the design calculations are affected by considerable uncertainty related to the loss correlations employed for the preliminary turbine design, as they have not been validated yet for this highly unconventional supersonic and transonic mini turbine. Future work will be dedicated to the extension of the method to encompass the preliminary design of heat exchangers and the off-design operation of the system.

One-Dimensional Annular Diffuser Model for Preliminary Turbomachinery Design

“…Specifically, Macchi and Perdichizzi [3] showed that the optimal design (maximum efficiency) of axial turbines depends on the amount of kinetic energy that can be recovered from the last stage. In addition, the work of Bahamonde et al [4] indicates that the discharge kinetic energy can be one of the main mechanisms of efficiency loss when the influence of the diffuser is not accounted during the preliminary design. Despite this, the impact of the diffuser on the overall performance of turbomachines is often neglected or modeled in a very simple way during the preliminary design (mean-line models).…”

Active subspaces for the optimal meanline design of unconventional turbomachinery

“…[6]. These models have been developed for conventional turbomachinery operating with fluids in the ideal gas state, and featuring subsonic flows and large Reynolds numbers.…”

“…A meanline code for the preliminary design of turbomachinery [6,26] is coupled with the in-house computational fluid library [21] in which fluid model (5) has been implemented. Among various inputs, the design model requires the turbine rotational speed X, the rotor inlet diameter D 2 , and the mass flow _ m. The successful application of the active subspaces method requires that the mathematical model is continuous and differentiable, therefore X; D 2 and _ m must be normalized, such that the input parameters are fluid independent.…”

“…Ultimately, based on our experience, see, e.g.,Ref. [6], achieving an optimum solution of the design problem might take from weeks The results of a previous study demonstrated that a reducedorder model allows to overcome these disadvantages [16]. Following such development, this paper presents an innovative design methodology employing a reduced-order model which integrates fluid selection, thermodynamic cycle calculation, and preliminary fluid dynamic design of the corresponding ORC turbine.…”

“…The fluid dynamic design strongly depends on the working fluid and on the cycle operating parameters, and is constrained by a considerable number of parameters related to feasibility, e.g., rotational speed, tip clearance, blade height, etc. For instance, for a turbine operating in a high-temperature mORC turbogenerator, the maximum pressure ratio, and thus the cycle thermal efficiency, might be constrained by the minimum blade height at the first-stage rotor inlet; this blade height is ultimately determined by a combination of factors like the fluid volumetric flow, the turbine degree of reaction, and the inlet diameter [6]. Moreover, for WHR systems on board of transportation vehicles, additional features to be considered are the weight and volume of the heat exchangers.…”