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A computational study of the multirow interaction mechanisms has been carried out for a one-and-a-half stage (NGV-rotor-stator) transonic turbine. In addition to measurable subharmonic unsteadiness on the rotor blades induced by two fundamental stator passing frequencies, a significant aperiodic ('mistuned') circumferential variation of unsteady forcing magnitude by about three times has been observed in the downstream stator blades. Further parametric studies with various stator blade counts illustrate that the circumferential variation pattern of the unsteady forcing is dictated by the NGV-stator blade count difference, while the local stator forcing magnitude is affected by its circumferential clocking position relative to the upstream NGV blades. The present work suggests that the circumferential clocking together with the choice of blade count should be considered as an aeromechanical design parameter For cases with stator-stator (or rotorrotor) blade counts resulting in a tuned (or nearly tuned) unsteady forcing pattern, the clocking position should be chosen to minimize the unsteady forcing. On the other hand, if the choice of blade counts leads to a significant aerodynamic aperiodicity (mistuning),the clocking-forcing analysis can be used to identify the most vulnerable blade that is subject to the maximum forcing.[DOI: 10.1115/1.1622711]

A nonlinear harmonic methodology is adopted to analyze interactions between adjacent stages in multi-stage compressors. Of particular interest are the effects of circumferential 'aperiodic' distributions and the relative circumferential positioning (`clocking') of blades. The main feature of the present approach is that both the aperiodic and clocking effects are very efficiently included with circumferential 'steady' harmonic disturbances. Consequently, a single run of the nonlinear harmonic solver using a single-passage domain can produce the whole annulus unsteady and aperiodic time-averaged flow field. In addition, performance variation at any clocking position can be obtained simply by post-processing the result. A case study is presented for a two-and-half-stage transonic compressor, and the present results show much stronger rotor-rotor interaction than stator-stator interaction. A mechanism leading to strong rotor-rotor interference seems to be the interaction between upstream rotor wakes and the downstream rotor passage shock waves. A rotor-rotor clocking study illustrates a qualitatively different loss variation with respect to clocking position in a transonic flow compared to that in a subsonic flow. [DOI: 10.1115/1.1508382]

Computations of unsteady flows due to inlet distortion driven blade vibrations, characterized by long circumferential wavelengths, typically need to be carried out in multi-passage/ whole-annulus domains. In the present work, a single-passage three-dimensional unsteady Navier-Stokes approach has been developed and applied to unsteady flows around vibrating blades of a transonic fan rotor (NASA Rotor-67) with inlet distortions. The phase-shifted periodic condition is applied using a Fourier series based method, 'shape-correction,' which enables a single-passage solution to unsteady flows under influences of multiple disturbances with arbitrary interblade phase angles. The computational study of the transonic fan illustrates that unsteady flow response to an inlet distortion varies greatly depending on its circumferential wavelength. The response to a long wavelength (whole-annulus) distortion is strongly nonlinear with a significant departure of its time-averaged flow from the steady state, while that at a short wavelength (two passages) behaves largely in a linear manner. Nevertheless, unsteady pressures due to blade vibration, though noticeably different under different inlet distortions, show a linear behavior. Thus, the nonlinearity of the flow response to inlet distortion appears to influence the aerodynamic damping predominantly by means of changing the time-averaged flow. Good agreements between single-passage solutions and multi-passage solutions are obtained for all the conditions considered, which clearly demonstrates the validity of the phase-shifted periodicity at a transonic nonlinear distorted flow condition. For the present cases, typical CPU time saving by a factor of 5-10 is achieved by the single-passage solutions. [DOI: 10.1115/1.1450567]

Unsteady flow around a linear oscillating turbine cascade has been experimentally and computationally studied, aimed at understanding the bubble type of flow separation and examining the predictive ability of a computational method. It was also intended to check the validity of the linear assumption under an unsteady viscous flow condition. Part 2 of the paper presents a computational study of the experimental turbine cascade that was discussed in Part 1. Numerical calculations were carried out for this case using an unsteady Navier-Stokes solver. The Baldwin-Lomax mixing length model was adopted for turbulence closure. The boundary layers on blade surfaces were either assumed to be fully turbulent or transitional with the unsteady transition subject to a quasi-steady laminar separation bubble model. The comparison between the computations and the experiment was generally quite satisfactory, except in the regions with the flow separation. It was shown that the behavior of the short bubble on the suction surface could be reasonably accounted for by using the quasi-steady bubble transition model. The calculation also showed that there was a more apparent mesh dependence of the results in the regions of flow separation. Two different kinds of numerical test were carried out to check the linearity of the unsteady flow and therefore the validity of the influence coefficient method. First, calculations using the same configurations as in the experiment were performed with different oscillating amplitudes. Second, calculations were performed with a tuned cascade model and the results were compared with those using the influence coefficient method. The present work showed that the nonlinear effect was quite small, even though for the most severe case in which the separated flow region covered about 60 percent of blade pressure surface with a large movement of the reattachment point. It seemed to suggest that the linear assumption about the unsteady flow behavior should be adequately acceptable for situations with bubble-type flow separation similar to the present case.

An experimental and computational study has been carried out on a linear cascade of low-pressure turbine blades with the middle blade oscillating in a torsion mode. The main objectives of the present work were to enhance understanding of the behavior of bubble-type flow separation and to examine the predictive ability of a computational method. In addition, an attempt was made to address a general modeling issue: Was the linear assumption adequately valid for such kind of flow? In Part 1 of this paper, the experimental work is described. Unsteady pressure was measured along blade surfaces using off-board mounted pressure transducers at realistic reduced frequency conditions. A short separation bubble on the suction surface near the trailing edge and a long leading-edge separation bubble on the pressure surface were identified. It was found that in the regions of separation bubbles, unsteady pressure was largely influenced by the movement of reattachment point, featured by an abrupt phase shift and an amplitude trough in the first harmonic distribution. The short bubble on the suction surface seemed to follow closely a laminar bubble transition model in a quasi-steady manner, and had a localized effect. The leading-edge long bubble on the pressure surface, on the other hand, was featured by a large movement of the reattachment point, which affected the surface unsteady pressure distribution substantially. As far as the aerodynamic damping was concerned, there was a destabilizing effect in the separated flow region, which was, however, largely balanced by the stabilizing effect downstream of the reattachment point due to the abrupt phase change.

A three-dimensional nonlinear time-marching method of solving the thin-layer Navier-Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the four-stage Runge-Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The three-dimensional unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established three-dimensional semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present three-dimensional unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable three-dimensional viscous flow features. The feasibility of solving the simplified thin-layer Navier-Stokes solver for oscillating blade flows at practical conditions is demonstrated.

A quasi-three-dimensional inviscid-viscous coupled approached has been developed for unsteady flows around oscillating blades, as described in Part 1. To validate this method, calculations for several steady and unsteady flow cases with strong inviscid-viscous interactions are performed, and the results are compared with the corresponding experiments. Calculated results for unsteady flows around a biconvex cascade and a fan tip section highlight the necessity of including viscous effects in predictions of turbomachinery blade flutter at transonic flow conditions.

An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi-3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multistep Runge-Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.

This paper documents an investigation conducted on the aerodynamic response of a turbine blade oscillating in a three-dimensional bending mode under massive tip separation. Flow separation near the tip of the blade was realized by use of a step placed upstream of the blade's leading edge. Extensive blade surface steady and unsteady pressure measurements were obtained from a test facility with clearly defined boundary conditions for a range of reduced frequency. The experiment is designed to produce detailed and reliable 3D test cases for aeroelastic applications. A complete set of steady and unsteady blade surface pressure measurements is provided for five spanwise sections at 10, 30, 50, 70, and 90 percent of span. In addition, the issue of linearity is addressed. Experimental results demonstrate a predominant linear behavior of the unsteady pressure response. [DOI: 10.1115/1.1370164]

The results of two investigations, concerning the aerodynamic response of a turbine blade oscillating in a three-dimensional bending mode, are presented in this paper. The first is an experimental and computational study, designed to produce detailed three-dimensional test cases for aeroelastic applications and examine the ability of a three-dimensional time-marching Euler method to predict the relevant unsteady aerodynamics. Extensive blade surface unsteady pressure measurements were obtained over a range of reduced frequency from a test facility with clearly defined boundary conditions (Bell and He, 1997). The test data indicate a significant three-dimensional effect, whereby the amplitude of the unsteady pressure response at different spanwise locations is largely insensitive to the local bending amplitude. The computational results, which are the first to be supported by detailed three-dimensional test data, demonstrate the ability of the inviscid method to capture the three-dimensional behavior exhibited by the experimental measurements and a good level of quantitative agreement is achieved throughout the range of reduced frequency. Additional computational solutions, obtained through application of the strip methodology, reveal inadequacies in the conventional quasi-three-dimensional approach to the prediction of oscillating blade flows. The issue of linearity is also considered, and both experimental and computational results indicate a linear behavior of the unsteady aerodynamics. The second, an experimental investigation, addresses the influence of tip leakage upon the unsteady aerodynamic response of an oscillating turbine blade. Results are provided for three settings of tip clearance. The steady flow measurements show marked increases in the size and strength of the tip leakage vortex for the larger settings of tip clearance and deviations are present in the blade loading toward the tip section. The changes in tip clearance also caused distinct trends in the amplitude of the unsteady pressure at 90 percent span, which are observed to correspond with localized regions where the tip leakage flow had a discernible impact on the steady flow blade loading characteristic. The existence of these trends in the unsteady pressure response warrants further investigation into the influence of tip leakage on the local unsteady flow and aerodynamic damping.

This is the second part of a two-part paper. First, the design-optimization system based on the adjoint gradient solution approach as described in Part I is introduced. Several test cases are studied for further validation and demonstration of the methodology and implementation. The base-line adjoint method as applied to realistic 3D configurations is demonstrated in the redesign of the NASA rotor 67 at a near-choke condition, leading to a 1.77% efficiency gain. The proposed adjoint mixing plane is applied to the redesign of a transonic compressor stage (DLR compressor stage) and an IGV-rotor-stator configuration of a Siemens industrial compressor at a single-operating point, both producing measurably positive efficiency gains. An examination on the choice of the operating mass flow condition as the basis for the performance optimization, however, highlights' the limitation of the single-point approach for practical applications. For the three-row compressor configuration, a near peak-efficiency point based redesign leads to a measurable reduction in the choke mass flow, while a near-choke point based redesign leads to a significant performance drop in other flow conditions. Subsequently, a parallel multipoint approach is implemented. The results show that a two-point design optimization can produce a consistently better performance over a whole range of mass flow conditions compared with the original design. In the final case, the effectiveness of the present method and system is demonstrated by a redesign applied to a seven-row industrial compressor at the design point, leading to a remarkable 2.4% efficiency gain. [DOI: 10.1115/1.3103928]

The adjoint method for blade design optimization will be described in this two-part paper. The main objective is to develop the capability of carrying out aerodynamic blading shape design optimization in a multistage turbomachinery environment. To this end, an adjoint mixing-plane treatment has been proposed. In the first part, the numerical elements pertinent to the present approach will be described. Attention is paid to the exactly opposite propagation of the adjoint characteristics against the physical flow characteristics, providing a simple and consistent guidance in the adjoint method development and applications. The adjoint mixing-plane treatment is formulated to have the two fundamental features of its counterpart in the physical flow domain: conservation and nonreflectiveness across the interface. The adjoint solver is verified by comparing gradient results with a direct finite difference method and through a 2D inverse design. The adjoint mixing-plane treatment is verified by comparing gradient results against those by the finite difference method for a 2D compressor stage. The redesign of the 2D compressor stage further demonstrates the validity of the adjoint mixing-plane treatment and the benefit of using it in a multi-bladerow environment. [DOI: 10.1115/1.3072498]

One of the most widely studied parameters in turbine blade shaping is blade lean, i.e., the tangential displacement of spanwise sections. However, there is a lack of published research that investigates the effect of blade lean under nonuniform temperature conditions (commonly referred to as a "hot-streak") that are present at the combustor exit. Of particular interest is the impact of such an inflow temperature profile on heat transfer when the nozzle guide vane (NGV) blades are shaped. In the present work, a computational study has been carried out for a transonic turbine stage using an efficient unsteady Navier-Stokes solver (HYDRA). The configurations with a nominal vane and a compound leaned vane under uniform and hot-streak inlet conditions are analyzed. After confirming the typical NGV loading and aeroloss redistributions as seen in previous literature on blade lean, the focus has been directed to the rotor aerothermal behavior. While the overall stage efficiencies for the configurations are largely comparable, the results show strikingly different rotor heat transfer characteristics. For a uniform inlet, a leaned NGV has a detrimental effect on the rotor heat transfer. However, once the hot-streak is introduced, the trend is reversed; the leaned NGV leads to favorable heat transfer characteristics in general and for the rotor tip region in particular. The possible causal links for the observed aerothermal features are discussed. The present findings also highlight the significance of evaluating NGV shaping designs under properly conditioned inflow profiles, rather than extrapolating the wisdom derived from uniform inlet cases. The results also underline the importance of including rotor heat transfer and coolability during the NGV design process. [ABSTRACT FROM AUTHOR]