Research Papers: Gas Turbines: Microturbines and Small Turbomachinery

Geometric Design of Scroll Expanders Optimized for Small Organic Rankine Cycles

[+] Author and Article Information
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 Liége, Belgium
e-mail: bertrand.dechesne@gmail.com

Harold F. Hemond

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

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.

J. Eng. Gas Turbines Power 135(4), 042303 (Mar 18, 2013) (6 pages) Paper No: GTP-12-1018; doi: 10.1115/1.4023112 History: Received January 19, 2012; Revised October 06, 2012

The application of organic Rankine cycles (ORCs) for small scale power generation is inhibited by a lack of suitable expansion devices. Thermodynamic and mechanistic considerations suggest that scroll machines are advantageous in kilowatt-scale ORC equipment, however, a method of independently selecting a geometric design optimized for high-volume-ratio ORC scroll expanders is needed. The generalized 8-dimensional planar 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 algorithm 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 desktop computing, whereas the originally undefined 8-D parameter space yields an arbitrarily 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 candidates selected the for compactness factor (volume expansion ratio per diameter), which is shown to correlate with the modeled isentropic efficiency (R2 = 0.88). The rapid computationally 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 necessary to generate new high performance scroll expander designs for kilowatt scale ORC systems.

Copyright © 2013 by ASME
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Grahic Jump Location
Fig. 1

The expansion action of the scroll device works via a series of chambers defined by adjacent conjugate points. High pressure vapor enters at the inlet and expands against the orbiting scroll in an expanding chamber following the spiral. The orbit of radius R translates to rotation with a crank. The mating pairs of scroll curves are formed by reflection across the center point C, accounting for the wall thickness scalar d.

Grahic Jump Location
Fig. 2

Flow diagram for the design to development method

Grahic Jump Location
Fig. 3

Four example scroll distributions are plotted from within the 8-D planar curve parameter space. The color bar represents the value of the proposed “compactness factor” (volume ratio divided by normalized diameter) and gradients within the domains reveal the relationships of input parameters to this metric. White space indicates nonviability or practical constraint violation. The delineation of these domain envelopes, through the algorithm of Fig. 2, forms the basis for the equations in Table 1. The resulting avoidance of nonproductive parameter combinations conserves computation effort and accelerates the selection of optimal scroll geometries.

Grahic Jump Location
Fig. 4

Flow diagram for use of the design tool in an actual ORC application

Grahic Jump Location
Fig. 5

Right: A high “compactness factor” design for a noncircle involute scroll proposed for an ORC case study based on a RVP = 8.5. The chosen planar curve parameters are: c1 = 0, c2 = −0.44, c3 = 3.8, c4 = 0.3, c5 = −0.0027, N = 7.25, R = 28.8, d = 25.8. The scaling factor used to normalize to Vin = 245 cm3 is 3.1. Left: A standard constant wall thickness (circle involute) scroll achieving the same volume expansion. We note that the variance in throttling losses is expected, given the differential inlet port areas in this example. These have been normalized for the results of Fig. 6.

Grahic Jump Location
Fig. 6

Modeled [13] isentropic expander efficiency correlation to compactness factor fc for the test case ORC (RVP = 8.5) dataset; N = 13, R2 = 0.876. Circle involute cases with corresponding uniform wall thickness are indicated by arrows.



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