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Research Papers: Gas Turbines: Turbomachinery

Parameterizing Compact and Extensible Compressor Models Using Orthogonal Distance Minimization

[+] Author and Article Information
Xavier Llamas

Vehicular Systems,
Department of Electrical Engineering,
Linköping University,
Linköping SE-581 83, Sweden
e-mail: xavier.llamas.comellas@liu.se

Lars Eriksson

Vehicular Systems,
Department of Electrical Engineering,
Linköping University,
Linköping SE-581 83, Sweden
e-mail: lars.eriksson@liu.se

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 16, 2015; final manuscript received July 1, 2016; published online August 16, 2016. Assoc. Editor: Klaus Brun.

J. Eng. Gas Turbines Power 139(1), 012601 (Aug 16, 2016) (10 pages) Paper No: GTP-15-1569; doi: 10.1115/1.4034152 History: Received December 16, 2015; Revised July 01, 2016

A complete and compact control-oriented compressor model consisting of a mass flow submodel and an efficiency submodel is described. The final application of the model is a complete two-stroke mean value engine model (MVEM) which requires simulating the compressor operating at the low-flow and low-pressure ratio area. The model is based on previous research done for automotive-size compressors, and it is shown to be general enough to adapt well to the characteristics of the marine-size compressors. A physics-based efficiency model allows, together with the mass flow model, extrapolating to low-pressure ratios. The complexity of the model makes its parameterization a difficult task; hence, a method to efficiently estimate the 19 model parameters is proposed. The method computes analytic model gradients and uses them to minimize the orthogonal distances between the modeled speed lines (SpLs) and the measured points. The results of the parameter estimation are tested against nine different standard marine-size maps showing good agreement with the measured data. Furthermore, the results also show the importance of estimating the parameters of the mass flow and efficiency submodels at the same time to obtain an accurate model. The extrapolation capabilities to low-load regions are also tested using low-load measurements from an automotive-size compressor. It is shown that the model follows the measured efficiency trend down to low loads.

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References

Figures

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Fig. 1

Sketch of the three types of compressor maps: (I) normal maps, (II) full maps, and (III) extended maps

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Fig. 2

General characteristics of seven of the marine-size compressor maps used

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Fig. 3

Sketch of the main characteristics of the ellipse model. The SpLs are drawn in solid lines, with its vertical extension in the choked area as dashed lines. The ChL and ZSL are plotted in dashed-dotted lines. The dashed horizontal line situates where the pressure ratio is equal to unity. Note that the curvature increases with speed, and the lowest SpL corresponds to standstill.

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Fig. 4

Actual compression specific energy plotted against corrected mass flow for two different compressors. The measured data is plotted with dots connected with solid lines, and the linear fit is plotted in dashed lines. The data corresponds to marine-size normal maps. A good agreement with the linear assumption can be observed, as well as slight deviations for the high SpLs close to the choke region.

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Fig. 5

Actual compression specific energy plotted against corrected mass flow for the full automotive map. The measured data is plotted with dots connected with solid lines, and the linear fit is depicted with dashed lines. The right plot is a zoomed view of the first six SpLs seen in the left plot. More deviations from the linear assumption can be seen, in particular at low-pressure ratios and for the higher SpLs.

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Fig. 6

Orthogonal projection representation of the SpL measured points (crosses) to the modeled SpL curve in solid line. The gradient of the implicit model equation is used to find the orthogonal direction. The shaded area represents the zones where the orthogonal projection cannot be computed.

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Fig. 7

Orthogonal projection sketch in 3D for a given measured point (Y). The black solid curve defines the SpL, which is formed by the intersection of surfaces G and F̃. The orthogonal plane (N) is formed with the tangent vector to the SpL, n(X), and the measurement point (Y).

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Fig. 8

GAR GT Compressor pressure ratio versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points. The contour lines correspond to the efficiency values.

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Fig. 9

GAR GT Compressor efficiency versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points.

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Fig. 10

ABB VTR compressor pressure ratio versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points. The contour lines correspond to the efficiency values.

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Fig. 11

ABB VTR compressor efficiency versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points.

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Fig. 12

ABB VTR compressor efficiency versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points.

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Fig. 13

ABB TPS compressor efficiency versus mass flow. The dashed lines are the modeled SpLs; the solid lines connect the measured points.

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