This paper reports several CFD analyses of a centrifugal compressor stage with a vaned diffuser at high pressure ratio using different techniques to model the rotor-stator interaction. A conventional steady stage calculation with a mixing-plane type interface between the rotor and stator was used as a baseline. This simulation gave excellent agreement with the measured performance characteristics at design speed, demonstrating the ability of the particular steady simulation used to capture the essential features of the blockage interaction between the components. A full annulus simulation using a transient rotor-stator interaction (TRS) method was then used at the peak efficiency point to obtain a fully unsteady reference solution, and this predicted a small increase in peak efficiency. Finally, a computationally less expensive unsteady calculation using a Time Transformation (TT) method was carried out. This gave similar results to the fully transient calculation suggesting that this is an acceptable approach to estimate unsteady blade loading from the interaction. The impeller diffuser spacing was then reduced from 15 to 7% of the impeller tip radius using the more affordable TT approach. This identified an increase in efficiency of 1% and predicted unsteady pressure fluctuations in the impeller which were 116% higher with the closely spaced diffuser.
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.
Accurate and efficient prediction of blade damping is one essential element in the engineering of durable and reliable compressors and turbines. Over the years, a variety of empirical and linearized methods have been developed and used, and have served well. Recently, the development of efficient unsteady CFD methods combined with an expansion in available and affordable computing power has enabled CFD analysis of blade damping. This paper looks at the prediction of aerodynamic blade damping using some recently developed CFD methods. Unsteady CFD methods are used to predict the fluid flow in a transonic fan rotor, with tip Mach number of about 1.4. Deformation of the blade is determined from a mechanical pre-stressed modal analysis. In this investigation, blade motion for the first bending moments is prescribed in the CFD code, for a range of nodal diameters. After periodic unsteady solutions are obtained, damping coefficients are calculated based on the predicted blade forces and the specified blade motion. Traditional unsteady CFD methods require the simulation of many blades in a given row, depending on the nodal diameter. For instance, for a nodal diameter of four, a wheel with 22 blades would require simulation of eleven blades. Computational methods have been developed which now enable simulation of only a few (1 or 2) blades per row yet yield the full sector solution, thus providing considerable savings in computing time and machine resources. The properties of the available methods vary, but one method, the Fourier Transformation method, has the property that it is frequency preserving, and hence suitable for the present task. Fourier Transformation predictions, for a variety of nodal diameters, are compared with full sector predictions. Positive damping was predicted for this range of nodal diameters at design speed near peak efficiency operating condition indicating a stable system. The Fourier Transformation predictions for blade aerodynamic damping match very closely the reference full sector solutions. The Fourier transformation methods also provide solutions 3.5 times faster than average periodic reference cases.
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