Computational predictions of the transient flow in multiple blade row turbomachinery configurations are considered. For cases with unequal numbers of blades/vanes in adjacent rows (“unequal pitch”) a computation over multiple passages is required to ensure that simple periodic boundary conditions can be applied. For typical geometries, a time accurate solution requires computation over a significant portion of the wheel. A number of methods are now available that address the issue of unequal pitch while significantly reducing the required computation time. Considered here are a family of related methods (“Transformation Methods”) which transform the equations, the solution or the boundary conditions in a manner that appropriately recognizes the periodicity of the flow, yet do not require solution of all or a large number of the blades in a given row. This paper will concentrate on comparing and contrasting these numerical treatments. The first method, known as “Profile Transformation”, overcomes the unequal pitch problem by simply scaling the flow profile that is communicated between neighboring blade rows, yet maintains the correct blade geometry and pitch ratio. The next method, known as the “Fourier Transformation” method applies phase shifted boundary conditions. To avoid storing the time history on the periodic boundary, a Fourier series method is used to store information at the blade passing frequency (BPF) and its harmonics. In the final method, a pitch-wise time transformation is performed that ensures that the boundary is truly periodic in the transformed space. This method is referred to as “Time Transformation”. The three methods have recently been added to a commercially-available CFD solver which is pressure based and implicit in formulation. The results are compared and contrasted on two turbine cases of engineering significance: a high pressure power turbine stage and a low pressure aircraft engine turbine stage. The relative convergence rates and solution times are examined together with the effect of non blade passing frequencies in the flow field. Transient solution times are compared with more conventional steady stage analyses, and in addition detailed flow physics such as boundary layer transition location are examined and reported.

The modern trends in automotive turbocharger applications are towards the boosting of smaller internal combustion engines and more advanced systems including two-stage, turbo-compounding and hybrid electric-motor assist. Off-the-shelf turbochargers will become a smaller share of the market and the choice of major parameters for the compressor and turbine, e.g. speed and diameter, will fall outside of the manufacturer’s knowledge base. The selection of the compressor and turbine may even be independent. The only certainty is that the turbomachinery will have to be small, cheap and efficient. To provide some guidance to the turbine designer, this paper presents the results of a study in which practical designs have been generated to cover the range of conceivable parameters, presented in non-dimensional terms to provide general applicability. All the designs are generated using a throughflow-based optimisation system in which the candidate geometries are assessed against mechanical as well as aerodynamic and inertia targets. Analysis of the results gives clues to the form of the basic empiricism that would be of use in the preliminary design of automotive turbocharger turbines.

Radial and mixed-flow turbine stages are an important component of turbochargers in automotive engines. The aerodynamic design of such turbines is generally compromised by the severe mechanical and manufacturing constraints to withstand the harsh motor environment with high stresses, high temperatures and unsteady operation. Conventionally, the designer deals with these constraints in the preliminary design stage by using a high degree of empiricism. This is then followed in the detailed design by extensive and time-consuming 3D CFD analysis and geometry optimisation. This paper describes a new approach to the preliminary design of radial turbine impellers using a quasi-3D throughflow method, which allows a more rapid consideration of the design issues before moving on to a full 3D CFD analysis. The paper describes the development of deviation models suitable for radial and mixed-flow turbines out of a range of CFD solutions in which a number of important features have been varied: aerodynamic loading, tip clearance and blade root thickness. The features of the deviation model are related to predicted features of the flow. The results of throughflow calculations including the deviation model are compared against the CFD predictions.

Automotive turbocharger radial inflow turbines are required to have both a high efficiency and a low inertia. In many cases this favours the use of a mixed-flow design. The inertia is minimised by scalloping the back-face, which removes a significant amount of material from the highest radius region of the hub. However, there is a concern that, for a mixed-flow geometry, the presence of a scallop introduces a forward-facing step to the inducer flow. This gives rise to the potential for an additional loss mechanism in the impeller. Two variants of a mixed-flow design, one having scallops and the other without, have been tested in a steady-state rig. The performance deltas are compared against the CFD representations. In reality there is the additional complexity of pulsing inlet conditions due to the operation of the exhaust valves of the piston engine. This causes severe variations in the inducer flow field. To assess whether the presence of a scallop might impair performance in an engine installation, a number of off-design CFD comparisons have been carried out using boundary conditions from a transient model covering a pulsing cycle.

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