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J. Turbomach. 2016;138(6):061001-061001-16. doi:10.1115/1.4032359.

This paper elaborates on the theoretical development of an analytical approach, capable of modeling the effect of dynamic wake curvature on the aeroelastic response of open rotors with slender blades. The classical solution of incompressible, potential flow derived for a curved vortex tube of uniform vorticity strength is employed. The previously developed curved vortex tube analysis is mathematically generalized to account for arbitrary radial and circumferential variations of circulatory disk loading. An orthogonality analysis is carried out to obtain a finite set of inflow perturbation coefficients that describe the aerodynamic effect of wake curvature in a generalized manner. The end result is a set of integral expressions that provide the interharmonic coupling between the inflow perturbations on the rotor disk due to a curved trailing wake and the corresponding variations of disk loading. The obtained perturbation coefficients are subsequently superimposed upon an existing finite-state induced flow model that assumes a skewed, noncurved cylindrical wake. The developed mathematical approach for fluid mechanics is coupled with an unsteady blade element aerodynamics model, a rotor blade structural mechanics model, and a nonlinear rotor dynamics model. The combined formulation is implemented in an existing helicopter flight mechanics code. The overall method is initially employed to assess the effect of wake curvature on the dynamic response of a small-scale articulated rotor with a flap frequency ratio equal to unity. Subsequently, the integrated model is deployed to investigate the influence of wake curvature and inflow modeling fidelity on the predicted oscillatory blade loads and transient control response of a full-scale helicopter rotor. Comparisons are carried out with flight test measurements as well as with complex free-wake analysis methods. It is shown that including the effect of wake curvature is essential for predicting the transient control response of the investigated rotor. Good agreement is demonstrated between the proposed analytical model and nonlinear predictions carried out by resolving the complex wake geometry. The developed fluid mechanics formulation is a time-accurate method derived from first-principles and is applicable to both axial and nonaxial flow conditions.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061002-061002-10. doi:10.1115/1.4032360.

Turbocharger centrifugal compressors are equipped with a “ported shroud” to reduce flow instabilities at low mass flow rates. This passive stability control device using flow recirculation has been demonstrated to extend the surge margin of a compressor without substantially sacrificing performance. However, the actual working mechanisms of the system are not well understood. In this paper, the relationship between inlet flow recirculation and instability control is studied using stereoscopic particle image velocimetry (PIV) in conjunction with dynamic pressure transducers at the inlet of the turbocharger compressor with and without ported shroud. Both stable and unstable operational points are analyzed using phase-locked PIV measurements during surge. Detailed description of unstable flow in the centrifugal compressor is presented by reconstructing the complex flow structure evolution in the compressor inlet during surge. Rather than one-dimensional, the surge flow is characterized by a three-dimensional structure of both entering and exiting swirling flows, alternating in magnitude during a self-excited pressure cycle. The correlation between pressure and velocity measurements shows that the development of compressor unsteadiness is concurrent with swirling reversed flow at the impeller tip. The impact of the ported shroud on the inlet velocity flowfield is evidenced by the presence of localized flow recirculation. Stability improvement due to the ported shroud is thus a result of removing swirling backflow from the impeller inducer tip and recirculating it into the impeller inlet to increase the near shroud inlet blade loading and the incidence angle.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061003-061003-10. doi:10.1115/1.4032164.

This paper covers a comprehensive forced response analysis conducted on a multistage compressor and compared with the largest forced response experimental data set ever obtained in the field. The steady-state aerodynamic performance and stator wake predictions compare well with the experimental data, although losses are underestimated. Coupled and uncoupled unsteady simulations are conducted on the stator–rotor configuration. It is shown that the use of a decoupled method for forced response cannot yield accurate results for cases with strong inter-row interactions. The individual and combined contributions of the upstream and downstream stators are also assessed. The downstream stator is found to have a tremendous impact on the forced response predictions due to the constructive interactions of the two stator rows. Finally, predicted mistuned blade amplitudes are compared to mistuned experimental data. The average amplitudes match the experiments very well, while the maximum response amplitude is underestimated.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061004-061004-13. doi:10.1115/1.4032284.

The focus of the study presented here was to investigate the interaction between the blade and downstream vane of a stage-and-one-half transonic turbine via computation fluid dynamic (CFD) analysis and experimental data. A Reynolds-averaged Navier–Stokes (RANS) flow solver with the two-equation Wilcox 1998 k–ω turbulence model was used as the numerical analysis tool for comparison with all of the experiments conducted. The rigor and fidelity of both the experimental tests and numerical analysis methods were built through two- and three-dimensional steady-state comparisons, leading to three-dimensional time-accurate comparisons. This was accomplished by first testing the midspan and quarter-tip two-dimensional geometries of the blade in a linear transonic cascade. The effects of varying the incidence angle and pressure ratio on the pressure distribution were captured both numerically and experimentally. This was used during the stage-and-one-half post-test analysis to confirm that the target corrected speed and pressure ratio were achieved. Then, in a full annulus facility, the first vane itself was tested in order to characterize the flowfield exiting the vane that would be provided to the blade row during the rotating experiments. Finally, the full stage-and-one-half transonic turbine was tested in the full annulus cascade with a data resolution not seen in any studies to date. A rigorous convergence study was conducted in order to sufficiently model the flow physics of the transonic turbine. The surface pressure traces and the discrete Fourier transforms (DFT) thereof were compared to the numerical analysis. Shock trajectories were tracked through the use of two-point space–time correlation coefficients. Very good agreement was seen when comparing the numerical analysis to the experimental data. The unsteady interaction between the blade and downstream vane was well captured in the numerical analysis.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061005-061005-10. doi:10.1115/1.4032363.

A study examining the internal cooling of turbine blades by swirling flow is presented. The sensitivity of swirling flow is investigated with regard to Reynolds number, swirl intensity, and the common geometric features of blade-cooling ducts. The flow system consists of a straight and round channel that is attached to a swirl generator with tangential inlets. Different orifices and 180-deg bends are employed as channel outlets. The experiments were carried out with magnetic resonance velocimetry (MRV) for which water was used as flow medium. As the main outcome, it was found that the investigated flows are highly sensitive to the conditions at the channel outlet. However, it was also discovered that for some outlet geometries the flow field remains the same. The associated flow features a favorable topology for heat transfer; the majority of mass is transported in the annular region close to the channel walls. Together with its high robustness, it is regarded as an applicable flow type for the internal cooling of turbine blades. A large eddy simulation (LES) was conducted to analyze the heat transfer characteristic of the associated flow for S0=3 and Re=20,000. The simulation showed an averaged Nusselt number increase of factor 4.7 compared to fully developed flow. However, a pressure loss increase of factor 43 must be considered as well.

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061006-061006-10. doi:10.1115/1.4032285.

The capability of a linearized computational fluid dynamics (CFD) method for predicting turbine tone noise is investigated through comparison with measurements. To start with, a benchmark problem on flat plates is presented, and results are put together with those published by other authors. Then, numerical predictions are compared with measurements from two low-pressure turbines (LPTs), which have been tested in different facilities. The first specimen is a three-stage cold flow rig, noise tested in the Centro de Tecnologías Aeronáuticas (CTA) facility (Bilbao, Spain) in 2012 and funded by the Clean Sky EU Program. The second is the advanced near-term low emissions (ANTLE) LPT rig, full-scale, cold flow, noise tested in the twin shaft test facility (TSTF) in Rolls-Royce (Derby, UK) in 2005 and funded by the SILENCE(R) EU Funded Program. The comparison includes multistage effects, clocking sensitivities, and acoustic scattering through outlet guide vanes (OGVs).

Commentary by Dr. Valentin Fuster
J. Turbomach. 2016;138(6):061007-061007-12. doi:10.1115/1.4032306.

When the operating condition of a gas turbine engine changes from one steady-state to another, the cooling must ensure that the solid's temperatures never exceed the maximum allowable throughout the transient process. Exceeding the maximum allowable temperature is possible even though cooling is increased to compensate for the increase in heating because there is a time lag in how the solid responds to changes in its convective heating and cooling environments. In this paper, a closed-form solution (referred to as the 1D model) is derived to estimate the over temperature and its duration in a flat plate subjected to sudden changes in heating and cooling rates. For a given change in heating rate, the 1D model can also be used to estimate the minimum cooling needed to ensure that the new steady-state temperature will not exceed the maximum allowable. In addition, this model can estimate the temperature the material must be cooled to before imposing a sudden increase in heat load to ensure no over temperature throughout the transient process. Comparisons with the exact solutions show the 1D model to be accurate within 0.1%. This 1D model was generalized for application to problems in multidimensions. The generalized model was used to estimate the duration of over temperature in a two-dimensional problem involving variable heat transfer coefficient (HTC) on the cooled side of a flat plate and provided results that match the exact solution within 5%.

Commentary by Dr. Valentin Fuster

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