A statistical approach to the analysis of the surge phenomenon R. Bontempo, M. Cardone, M. Manna * , and G. Vorraro Dipartimento di Ingegneria Industriale, Universit` a degli Studi di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy Abstract The paper presents an innovative data processing methodology for the analysis of the surge phenomenon occurring in a compressor. Since the dynamic of the surge cycle does not have a deterministic character, its proper description can only be obtained through a statistical approach. To this aim, the temporally resolved traces of the pressure and mass flow rate signals are processed through a phase averaged decomposition technique. Furthermore, the shape of the oscillating surge cycle is detected and quantified by introducing the joint probability density function of the aforementioned signals which are reported in the pressure ratio versus mass flow rate plane. This probabilistic approach offers two significant advantages over the conventional deterministic approach, namely the possibility to quantify the time of residence of all individual unstable states in a statistical sense, as well as the possibility to carry out a proper code-to-experiments or experiments-to-experiments comparison of such an unstable phenomenon. In this paper, the proposed statistical approach is used to process the experimental data related to the surge phenomenon occurring in a small-sized free spool centrifugal compressor for automotive applications. However, the methodology can be applied both to numerical and experimental surge data from either centrifugal or axial compres- sors. Keywords: surge, compressor, turbocharger, turbocharger test rig. 1 Introduction Nowadays, the reduction of the engine displacement is one of the most widespread and successful technique used to reduce the fuel consumption and the pollutant emissions of internal combustion engines (ICE). How- ever, in order to preserve or even augment the delivered power, the ICE has to be charged, for example through a turbocharger (TC) [1–5]. In such a way the intake air density, the mass flow rate and consequently the power output are raised while retaining a small engine size. Further combustion advantages can be gained by tur- bocharging the ICE, such as an improved fuel atomiza- tion process [6] and a shorter fuel jet penetration length [7]. In spite of the aforementioned benefits, some draw- backs also exist. First of all, there are a few well-known shortcomings associated to the poor quality of the tran- sient response of turbocharged engines [8–11]. These problems are mainly associated to the mechanical in- ertia of the TC which induces significant delays in the charging effect during those maneuvers requiring a rapid increase of the delivered power. Another drawback can be caused by the occurrence of the critical surge phe- nomenon. Operating the compressor in surge regimes is not at all recommendable since it induces a signifi- cant drop down in the compressor efficiency, a proba- ble failure of the TC mechanical components, undesir- able noise, and, finally, a reduction of the vehicle drive- ability due to the oscillating power output. From the previous considerations, it is clearly understood that a proper characterization of the TC operating in the un- * Corresponding author: e-mail address: mar- cello.manna@unina.it; tel: +39-081-7683287 stable surge regime is very important. This is witnessed by the large amount of research papers dealing with this issue. For instance, in [12] the authors described a test bench specifically designed for the characterization of automotive TCs and used it to define a sound criterion for the surge limit definition. An experimental investi- gation of the effects of an inlet swirl generator to enlarge the surge margin is reported in [13]. Galindo et al. [14] developed a surge model in which the fluid inertia effects are taken into account. The model is validated against data measured in a specifically designed facility. An- dersen et al. [15] proposed a standardized measurement setup for the definition of the compressor surge limit. The effects of a pulsating flow at the compressor outlet are analyzed in [16] by experimental means. Specifically, the effects of the amplitude and frequency of the pres- sure oscillations upon the surge line have been described. The authors found that, for the typical frequencies char- acterising the pulsating flow in turbocharged engines, a surge margin enhancement is possible. Guillou et al. [17] carried out PIV measurements in the proximity of the centrifugal compressor (CC) inlet, both in stable and unstable regimes. In [18] a properly designed test bench is used to point out the dependence of the surge mar- gin from the piping configuration upstream and down- stream a CC. Finally, the design and prototyping of a new highly flexible hot gas generation system is reported in [19], while in [20] the collected experimental data are manipulated to estimate the effect of the thermal losses on the compressor efficiency, and to analyse the surge phenomenon. As proven by the above literature review, up to now the surge phenomenon has always been studied through 1 Energy, vol 124, pp 502-509, 2017 http://dx.doi.org/10.1016/j.energy.2017.02.026