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Publication Title | Geometric Design of Scroll Expanders Optimized for Small Organic Rankine Cycles

Organic Rankine Cycle

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Matthew S. Orosz

e-mail: mso@mit.edu

Amy V. Mueller

e-mail: amym@mit.edu

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 15 Vassar St., 48-208, Cambridge, MA 02139

Bertrand J. Dechesne

Aerospace and Mechanical Engineering Department, University of Liege, Chemin des Chevreuils, 1, B-4000 Lie ́ge, Belgium e-mail: bertrand.dechesne@gmail.com

Harold F. Hemond

Professor Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 15 Vassar St., 48-425, Cambridge, MA 02139 e-mail: hfhemond@mit.edu

Introduction

The organic Rankine cycle (ORC) is an established technology for power generation from low temperature (<300 C) thermal sources (e.g., geothermal, solar, and industrial). Organic Rankine cycle applications are generally more economical as the scale of the thermal resource or potential load increases; however; as a result of rising energy costs and pressing environmental consider- ations, the minimum size for a commercially viable ORC unit is presently decreasing into the range of 1–10 kWs electrical output.

Whereas large ORC systems can use industrial turbomachinery similar to that widely used in common fossil-fuel-fired thermal power plants, the main challenge to developing ORC equipment in the range of 1–100 kW is in the selection of a suitable expander, given the absence of commercially available turbines at this scale. Furthermore, positive-displacement expanders may have certain advantages over small turbines, including lower rotational speeds, proportionally less windage loss, and potentially lower cost due to the availability of machines which can be adapted from HVAC applications, e.g., reversed scroll compressors. The primary draw- back of the latter approach is the low intrinsic volume ratio of commercially available scroll machines (typically 3) which lim- its the cycle operational temperature range or forces acceptance of under-expansion losses [1].

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 19, 2012; final manuscript received October 6, 2012; published online March 18, 2013. Assoc. Editor: Joost J. Brasz.

Development of a scroll expander optimized for the larger vol- ume ratios encountered at higher temperature ORC applications (3–15 or higher, depending on the temperature and working fluid) would promote the viability of ORC power generation from smaller distributed thermal resources. While several investigations of scroll expander models and validation experiments are described in the literature [2–7], discussion of the choice of the scroll geometry, the single feature upon which all other properties depend, is generally limited to the case of circle involutes in low volume ratio compressor applications [8,9]. In contrast, the pres- ent work explores the effect of varying the basic scroll geometry as a method for developing novel scroll machinery at the higher volume ratios needed for many ORC applications. The results demonstrate a computationally efficient process, based on thermo- dynamically relevant criteria, for converging on a set of near- optimal candidates for the scroll geometry. Details of the algo- rithm, along with a specific case study, are described in this publi- cation. The complete thermodynamic analysis of a particular scroll expander in an ORC application, such as that performed in Refs. [10,11], is not addressed in this paper but is further devel- oped from the results of this work in Refs. [12] and [13].

Method of Approach

The development of our design tool was based on the mathe- matical scroll model described by Gravesen and Henriksen [8], which was generalized for a wide range of scroll geometries and vectorized for implementation in Matlab. In the following sections

Geometric Design of Scroll Expanders Optimized for Small Organic Rankine Cycles

The application of organic Rankine cycles (ORCs) for small scale power generation is inhibited by a lack of suitable expansion devices. Thermodynamic and mechanistic con- siderations suggest that scroll machines are advantageous in kilowatt-scale ORC equip- ment, however, a method of independently selecting a geometric design optimized for high-volume-ratio ORC scroll expanders is needed. The generalized 8-dimensional pla- nar curve framework (Gravesen and Henriksen, 2001, “The Geometry of the Scroll Compressor,” Soc. Ind. Appl. Math., 43, pp. 113–126), previously developed for scroll compressors, is applied to the expansion scroll and its useful domain limits are defined. The set of workable scroll geometries is: (1) established using a generate-and-test algo- rithm with inclusion based on theoretical viability and engineering criteria, and (2) the corresponding parameter space is related to thermodynamically relevant metrics through an analytic ranking quantity fc (“compactness factor”) equal to the volume ratio divided by the normalized scroll diameter. This method for selecting optimal scroll geometry is described and demonstrated using a 3 kWe ORC specification as an example. Workable scroll geometry identification is achieved at a rate greater than 3 s 1 with standard desk- top computing, whereas the originally undefined 8-D parameter space yields an arbitra- rily low success rate for determining valid scroll mating pairs. For the test case, a maximum isentropic expansion efficiency of 85% is found by examining a subset of candi- dates selected the for compactness factor (volume expansion ratio per diameter), which is shown to correlate with the modeled isentropic efficiency (R2 1⁄4 0.88). The rapid com- putationally efficient generation and selection of complex validated scroll geometries ranked by physically meaningful properties is demonstrated. This procedure represents an essential preliminary qualification for intensive modeling and prototyping efforts nec- essary to generate new high performance scroll expander designs for kilowatt scale ORC systems. [DOI: 10.1115/1.4023112]

Keywords: scroll expander design, planar curves, volume ratio, compactness factor, isentropic efficiency kilowatt-scale organic Rankine cycle

JournalofEngineeringforGasTurbinesandPower

CopyrightVC 2013byASME

APRIL2013,Vol.135 / 042303-1

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