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Research Papers

J. Turbomach. 2018;140(5):051001-051001-10. doi:10.1115/1.4038876.

This paper introduces a new approach for the preliminary design and aerothermal analysis of centrifugal impellers using a relative diffusion effectiveness parameter. The relative diffusion effectiveness is defined as the ratio of the achieved diffusion to the maximum available diffusion in an impeller. It represents the quality of the relative diffusion process in an impeller. This parameter is used to evaluate impeller performance by correlating the relative diffusion effectiveness with the impeller isentropic efficiency using the experimental data acquired on a single-stage centrifugal compressor (SSCC). By including slip, which is appropriate considering it is an inviscid effect that should be included in the determination of maximum available diffusion in the impeller, a linear correlation between impeller efficiency and relative diffusion effectiveness resulted for all operating conditions. Additionally, a new method for impeller preliminary design was introduced using the relative diffusion effectiveness parameter, in which the optimal design is selected to maximize relative diffusion effectiveness. While traditional preliminary design methods are based on empirical loss models or empirical knowledge for selection of diffusion factor (DF) in the impeller, the new method does not require any such models, and it also provides an analytical approach for the selection of DF that gives optimal impeller performance. Validation of the method was performed using three classic impeller designs available in the open literature, and very good agreement was achieved. Furthermore, a sensitivity study shows that the method is robust in that the resulting flow angles at the impeller inlet and exit are insensitive to a wide range of blockage factors and various slip models.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2018;140(5):051002-051002-13. doi:10.1115/1.4038871.

Shaped film cooling holes are used as a cooling technology in gas turbines to reduce metal temperatures and improve durability, and they generally consist of a small metering section connected to a diffuser that expands in one or more directions. The area ratio (AR) of these holes is defined as the area at the exit of the diffuser, divided by the area at the metering section. A larger AR increases the diffusion of the coolant momentum, leading to lower average momentum of the coolant jet at the exit of the hole and generally better cooling performance. Cooling holes with larger ARs are also more tolerant of high blowing ratio conditions, and the increased coolant diffusion typically better prevents jet lift-off from occurring. Higher ARs have traditionally been accomplished by increasing the expansion angle of the diffuser while keeping the overall length of the hole constant. The present study maintains the diffuser expansion angles and instead increases the length of the diffuser, which results in longer holes. Various ARs have been examined for two shaped holes: one with forward and lateral expansion angles of 7 deg (7-7-7 hole) and one with forward and lateral expansion angles of 12 deg (12-12-12 hole). Each hole shape was tested at numerous blowing ratios to capture trends across various flow rates. Adiabatic effectiveness measurements indicate that for the baseline 7-7-7 hole, a larger AR provides higher effectiveness, especially at higher blowing ratios. Measurements also indicate that for the 12-12-12 hole, a larger AR performs better at high blowing ratios but the hole experiences ingestion at low blowing ratios. Steady Reynolds-averaged Navier–Stokes simulations did not accurately predict the levels of adiabatic effectiveness, but did predict the trend of improving effectiveness with increasing AR for both hole shapes. Flowfield measurements with particle image velocimetry (PIV) were also performed at one downstream plane for a low and high AR case, and the results indicate an expected decrease in jet velocity due to a larger diffuser.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2018;140(5):051003-051003-11. doi:10.1115/1.4038872.

The estimation of boundary layer losses requires the accurate specification of the freestream velocity, which is not straightforward in centrifugal compressor blade passages. This challenge stems from the jet-wake flow structure, where the freestream velocity between the blades cannot be clearly specified. In addition, the relative velocity decreases due to adverse pressure gradient. Therefore, the common assumption of a single freestream velocity over the blade surface might not be valid in centrifugal compressors. Generally in turbomachinery, the losses in the blade cascade boundary layers are estimated, e.g., with different loss coefficients, but they often rely on the assumption of a uniform flow field between the blades. To give guidelines for the estimation of the mentioned losses in highly distorted centrifugal compressor flow fields, this paper discusses the difficulties in the calculation of the boundary layer thickness in the compressor blade passages, compares different freestream velocity definitions, and demonstrates their effect on estimated boundary layer losses. Additionally, a hybrid method is proposed to overcome the challenges of defining a boundary layer in centrifugal compressors.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2018;140(5):051004-051004-11. doi:10.1115/1.4038868.

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms, Tyler–Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. It was recently shown in literature that in multirow configurations, not only the next but also the next but one blade row is very important as it may create a large circumferential forcing variation, which is fixed in the rotating frame of reference. In the present paper, a study of these effects is performed on the basis of a quasi three-dimensional (3D) multirow and multipassage compressor configuration. For the analysis, a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler–Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map, the blade-to-blade forcing variation may change significantly. In addition, multirow flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2018;140(5):051005-051005-9. doi:10.1115/1.4038869.

The prediction of aerodynamic blade forcing is a very important topic in turbomachinery design. Usually, the wake from the upstream blade row and the potential field from the downstream blade row are considered as the main causes for excitation, which in conjunction with relative rotation of neighboring blade rows, give rise to dynamic forcing of the blades. In addition to those two mechanisms, the so-called Tyler–Sofrin (or scattered or spinning) modes, which refer to the acoustic interaction with blade rows further up- or downstream, may have a significant impact on blade forcing. In particular, they lead to considerable blade-to-blade variations of the aerodynamic loading. In Part I of the paper, a study of these effects is performed on the basis of a quasi-three-dimensional multirow and multipassage compressor configuration. Part II of the paper proposes a method to analyze the interaction of the aerodynamic forcing asymmetries with the already well-studied effects of random mistuning stemming from blade-to-blade variations of structural properties. Based on a finite element (FE) model of a sector, the equations governing the dynamic behavior of the entire bladed disk can be efficiently derived using substructuring techniques. The disk substructure is assumed as cyclically symmetric, while the blades exhibit structural mistuning and linear aeroelastic coupling. In order to avoid the costly multistage analysis, the variation of the aerodynamic loading is treated as an epistemic uncertainty, leading to a stochastic description of the annular force pattern. The effects of structural mistuning and stochastic aerodynamic forcing are first studied separately and then in a combined manner for a blisk of a research compressor without and with aeroelastic coupling.

Topics: Excitation , Blades , Disks
Commentary by Dr. Valentin Fuster

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