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Research Papers

A Reduced Complexity Model for the Compressor Power of an Automotive Turbocharger

[+] Author and Article Information
Tao Zeng

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: zengtao2@msu.edu

Devesh Upadhyay

Ford Motor Company,
Dearborn, MI 48124
e-mail: dupadhya@ford.com

Guoming Zhu

Fellow ASME
Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: zhug@egr.msu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received October 11, 2016; final manuscript received January 17, 2018; published online March 27, 2018. Assoc. Editor: Azim Eskandarian.

J. Dyn. Sys., Meas., Control 140(6), 061018 (Mar 27, 2018) (10 pages) Paper No: DS-16-1496; doi: 10.1115/1.4039285 History: Received October 11, 2016; Revised January 17, 2018

Control-oriented models for automotive turbocharger (TC) compressors typically describe the compressor power assuming an isentropic thermodynamic process with fixed isentropic and mechanical efficiencies for power transmission between the turbine and the compressor. Although these simplifications make the control-oriented model tractable, they also introduce additional errors due to unmodeled dynamics. This is especially true for map-based approaches since the manufacture-provided maps tend to be sparse and often incomplete at the operational boundaries, especially at operational conditions with low mass flow rate and low speed. Extrapolation scheme is often used when the compressor is operated outside the mapped regions, which introduces additional errors. Furthermore, the manufacture-provided compressor maps, based on steady-flow bench tests, could be quite different from those under pulsating engine flow. In this paper, a physics-based model of compressor power is developed using Euler equations for turbomachinery, where the mass flow rate and the compressor rotational speed are used as model inputs. Two new coefficients, speed and power coefficients, are defined. As a result, this makes it possible to directly estimate the compressor power over the entire compressor operational range based on a single analytic relationship. The proposed modeling approach is validated against test data from standard TC flow bench tests, standard supercharger tests, steady-state, and certain transient engine dynamometer tests. Model validation results show that the proposed model has acceptable accuracy for model-based control design and also reduces the dimension of the parameter space typically needed to model compressor dynamics.

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Figures

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Fig. 1

Operating range deficit between mapped and desired engine operating range

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Fig. 2

Compressor geometry

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Fig. 3

Velocity triangles of a centrifugal compressor at the rotor inlet and outlet

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Fig. 4

Identification results for the generalized compressor-power model for compressors 1, 2, and 3: (a) flow bench test range for three compressors, (b) model identification under linear scale, and (c) model identification under log scale

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Fig. 5

Modeling error (27) for compressor power models

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Fig. 6

Identification results for the generalized compressor-power model for compressors 4, 5, and 6: (a) supercharger test ranges for three compressors, (b) model identification under linear scale, and (c) model identification under log scale

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Fig. 7

Comparison of Cpower model performance against calculated values based on flow bench data and engine steady-state dynamometer test data for compressor 1: (a) engine test range and flow bench test range, (b) comparison under linear scale, and (c) comparison under log scale

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Fig. 8

Model validation over US06 GT-Power transient simulation

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Fig. 9

Normalized measurements for mass flow rate, TC speed, and compressor downstream temperature for a load step

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Fig. 10

Model validation against transient engine test data for a FTP 75 cycle

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