The Role of Impeller Outflow Conditions on the Performance of Vaned Diffusers
Highly loaded impellers, typically used in turbocharger and gas turbine applications, exhaust an unsteady, transonic flow that is nonuniform across the span and pitch and swirling at angles approaching tangential. With the exception of the flow angle, conflicting data exist regarding whether these attributes have substantial influence on the performance of the downstream diffuser. This paper quantifies the relative importance of the flow angle, Mach number, nonuniformity, and unsteadiness on diffuser performance, through diffuser experiments in a compressor stage and in a rotating swirling flow test rig. This is combined with steady and unsteady Reynolds-averaged Navier–Stokes (RANS) computations. The test article is a pressure ratio 5 turbocharger compressor with an airfoil vaned diffuser. The swirling flow rig is able to generate rotor outflow conditions representative of the compressor except for the periodic pitchwise unsteadiness and fits a 0.86 scale diffuser and volute. In both rigs, the time-mean impeller outflow is mapped across a diffuser pitch using miniaturized traversing probes developed for the purpose. Across approximately two-thirds of the stage operating range, diffuser performance is well correlated to the average impeller outflow angle when the metric used is effectiveness, which describes the pressure recovery obtained relative to the maximum possible given the average inflow angle and Mach number and the vane exit metal angle. Utilizing effectiveness captures density changes through the diffuser at higher Mach numbers; a 10% increase in pressure recovery is observed as the inlet Mach number is increased from 0.5 to 1. Further, effectiveness is shown to be largely independent of the time-averaged spanwise and unsteady pitchwise nonuniformity from the rotor; this independence is reflective of the strong mixing processes that occur in the diffuser inlet region. The observed exception is for operating points with high time-averaged vane incidence. Here, it is hypothesized that temporary excursions into high-loss flow regimes cause a nonlinear increase in loss as large unsteady angle variations pass by from the rotor. Given that straight-channel diffuser design charts typically used in preliminary radial vaned diffuser design capture neither streamtube area changes from impeller exit to the diffuser throat nor vane incidence effects, their utility is limited. An alternative approach, utilizing effectiveness and vane leading edge incidence, is proposed.
Effect of Unsteadiness on the Performance of a Transonic Centrifugal Compressor Stage
Numerical and experimental investigations were conducted in a transonic centrifugal compressor stage composed of a backswept splittered unshrouded impeller and a vaned diffuser. The characteristic curves of the compressor stage resulting from the unsteady simulations and the experiments show a good agreement over the whole operating range. On the contrary, the total pressure ratio resulting from the steady simulations is clearly overestimated. A detailed analysis of the flow field at design operating point led to identify the physical mechanisms involved in the blade row interaction that underlie the observed shift in performance. Attention was focused on the deformation in shape of the vane bow shock wave due its interaction with the jet and wake flow structure emerging from the impeller. An analytical model is proposed to quantify the time-averaged effects of the associated entropy increase. The model is based on the calculation of the losses across a shock wave at various inlet Mach numbers corresponding to the moving of the jet and wake flow in front of the shock wave. The model was applied to the compressor stage performance calculated with the steady simulations. The resulting curve of the overall pressure ratio as a function of the mass flow is clearly shifted toward the unsteady results. The model, in particular, enhances the prediction of the choked mass flow.
DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES WITH MATHEMATICA OR MAPLE
The use of Computer Algebra Systems (CAS) in Mathematical Laboratories at Engineering Schools is increasing. Therefore, it has become necessary to undertake a new educational approach in the teaching of many mathematical topics. Obviously it is not possible to give the same lectures as in the 1950,s. The CAS allows us to experiment and teach in “a different way”. The students' mathematical knowledge at the beginning of their studies in the University is completely different. Moreover we have fewer credits assigned to Mathematical topics in engineering curriculum. The objective of he authors, professors of different Spanish Universities, is to try to demonstrate a new way to use the CAS, concretely Maple and Mathematica, as a support in the teaching of Differential Calculus of Several Variables. They take advantage of the computer's graphical capacities to sketch the graphs of surfaces defined in explicit, parametric or implicit form. They survey the general topics: limits, partial derivatives, differentiability, chain rule, implicit functions and extreme values. For each topic, they give a few basic instructions of the CAS used; afterwards they give several examples, in increasing order of difficulty, and finally the students must solve exercises and try to establish a general procedure for a quite general problem. In this paper we have included several examples used in this survey.