A model-based methodology to predict the compressor behaviour for the simulation of turbocharged engines

Abstract

Modelling the flow and efficiency of turbochargers for engine system simulation and control applications is an established practice that relies on the steady-state maps provided by manufacturer suppliers. However, as often occurs in practice, only a limited fraction of data is available in the compressor and turbine operating domain. For this reason, several modelling techniques have been proposed to interpolate and extrapolate flow and efficiency data. Most of the modelling approaches, based on black-or grey-box approaches, have limited predictive ability and typically low accuracy in off-design conditions, such as at engine idle or low engine speed. The current paper presents a novel model-based approach for overcoming the sparse nature of the available compressor maps, characterizing the flow and efficiency outputs of automotive centrifugal compressors by using extrapolation methods that are physically consistent with the conservation principles and actual behaviour of the system. The approach relies on a predictive model based on the thermodynamic analysis of a centrifugal compressor stage. The model builds upon the mass, energy, and entropy balance equations for compressible fluids. Specific sub-models are then introduced to account for the effects of slip phenomena, incidence losses, friction, and heat transfer losses, leading to high fidelity and predictive ability in off-design conditions. A detailed analysis of the model calibration and validation process is presented, utilizing data from two different automotive compressors. Finally, the procedure described is applied to characterize the compressor performance in engine system simulation, in comparison with a conventional (data-driven) model.

Applicable and Comparative Research of Compressor Mass Flow Rate and Isentropic Efficiency Empirical Models to Marine Large-Scale Compressor

“…where ref T and ref p are the reference temperature and pressure, respectively, in T and in p are the temperature and pressure at the compressor inlet, respectively. The derivation of Equations (1) and (2) is based on the dimensional analysis of the compression process in a compressor [14]. For a compressor, its whole operating area is normally divided into three zones, as shown in Figure 1, i.e., design operating zone, surging zone, and choking zone.…”

“…In the field of automotive engines, several new types of turbocharging systems have emerged, such as electrically assisted turbocharging systems (E-Turbo), variable geometry turbochargers (VGTs), and variable geometry compressors (VGCs). It was revealed by many pieces of research that, compared with traditional turbocharging technology, these advanced technologies can not only effectively improve turbocharger performance at low loading conditions but also substantially extend the operating range [1,2]. Nowadays, large marine two-stroke diesel engines are generally equipped with a turbocharging system but they still lag behind automotive engines to some extent.…”

“…Aiming at this problem, some researchers have attempted to develop theoretical models to predict the working characteristics of compressors without the help of performance maps. These theoretical models can be divided into 3-D, 2-D, and 1-D models in order of decreasing complexity [2,11,[30][31][32]. Due to the large computational requirements, the 3-D and 2-D theoretical models are not suitable for control-and diagnostic-oriented dynamic simulations.…”

Dynamic steady-state allocation for over-actuated turbocharged diesel engines

“…The mass flow rate,ṁ t , and power, P t , are expressed by nonlinear functions of inputs and states [15]. The compressor model was derived using the methodology and the predictive first-principle compressor model described in [16]. In particular, the predictive model was first calibrated using manufacturer steady-state characteristic maps of a fixed-geometry compressor.…”

Characterization of the Performance of a Turbocharger Centrifugal Compressor by Component Loss Contributions

“…They considered the inlet, impeller and vaneless diffuser in the model. However they just applied the effect of slip, incidence, friction and heat loss in the impeller section with the results showing the accuracy of their model given in [15]. Zhuge et al developed a turbocharger simulation method, which models the compressor and turbine using two-zone and mean-line methods respectively.…”