Despite the importance of turbocharged engines with radial inflow dual-volute turbines, their characteristic maps and fully predictive modelling using 1D gas dynamic codes are not well established yet. The complexity of the unsteady flow and the unequal admission of these turbines, when operating with pulses of engine exhaust gas, makes them a challenging system. This is mainly due to the unequal flow admission, which generates an additional degree of freedom with respect to well-known single entry vanned or vaneless turbines. This paper has as a main novelty a simple procedure for characterizing experimentally and elaborating characteristic maps of these turbines with unequal flow conditions. This method of analysis allows for easy interpolation within the proposed characteristic maps or conceiving simple models for calculating and extrapolating full performance parameters of dual-volute turbines. Here, also described are two innovative 0D mean-line models that require a minimum quantity of experimental data for calibrating both: the mass flow parameter model and the isentropic efficiency model. Both models are predictive either in partial or unequal flow admission conditions using as inputs: the mass flow ratio between branches; the total temperature ratio between branches; the blade to jet speed ratio in each branch and the pressure ratio in each branch. These six inputs are generally instantaneously provided by 1D gas-dynamics codes. Therefore, the novelty of the model is its ability to be used in a quasi-steady way for dual-volute turbines performance prediction. This can be done instantaneously when turbines are calculated operating at turbocharged engines under pulsating and unequal flow conditions.

The variable geometry turbines (VGT) technology has been proved as beneficious for diesel engines turbocharging, becoming the standard for passenger car diesel engines when high boosting pressure and short transient response are pursued. It has not been until recent times that OEMs and turbocharger manufacturers are able to explore the advantages of VGTs in petrol engines. The high exhaust gases temperature and the low boost pressure prevented the introduction of petrol VGTs up to now. In modern direct injection petrol engines relevant fuel consumption benefits have been obtained from significant to moderate boosting pressure (thanks to downsizing strategies). This benefit joint with the advances in materials and turbocharger cooling technologies have fostered exploring the limits of VGT technology in petrol engines. Consequently, the 1-D and gas-dynamic modelling of turbocharged petrol engines for matching, benchmarking or analysis purposes has become a significantly more complex task. The reason is the energy loop interaction between VGT, petrol engine and compressor; which makes that all relevant system variables (boosting pressure, back-pressure, VGT inlet gas temperature, residuals, volumetric efficiency, etc) are coupled among them. In this case, a proper simulation strategy of the whole system with existing 1-D gas-dynamic codes, i.e.: avoiding excessive use of spurious-non-physical fitting coefficients, has not been enough explored either described in the literature yet. In addition, proper models of the turbocharger (both compressor and VGT) are more relevant now, since the VGT mechanism is a new variable with a first order influence. It can be destabilizing or tricking the whole system, depending on the engine operative conditions and turbo-model quality. In this paper, a systematic methodology, with physical perspective, for calibrating 1D codes of petrol engines with VGTs is clearly described. The methodology can be easily followed by other engineers or researchers in their modelling activities. In addition, the importance of the turbocharger sub-model for achieving successfully previous objectives is depicted. Standard characteristic maps used as look-up tables are shown to be a poor source of information when compared with pre-processed adiabatic and extrapolated maps. The focus is kept in low end torque at full load steady state and transient tip-in, for being the most challenging situations. Being, low-end torque simulation in steady state the baseline point for the transient simulation.

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