A methodology for predicting the three-dimensional unsteady aerodynamics of the interaction between two turbomachinery blade rows that are in relative angular motion with one another is described. In this case, the kinematics of the blades introduce a chorochronic (space‐time) periodicity. This periodicity is analyzed in detail, and a mathematically straightforward methodology, based on Fourier series in µ (azimuth) and t (time), is presented for treating the interface between the two rows. These results are implemented in a computational method solving the three-dimensional Favre ‐Reynolds-averaged Navier ‐Stokes equations, with a near-wall wall-normalfree Reynolds-stress model. Only one blade passage per blade row is discretized. At the pitchwise boundaries, phase-lagged periodicity is applied using Fourier series in time. Both the pitchwise boundaries time harmonics and the interface chorochronic tµ harmonics are updated using a low-storage moving-averages technique. Computational results are presented and compared with measurements for a 1 1 -stage turbine, where the two stators have the same number of blades enabling the use of chorochronic periodicity. Sample results are also presented for a transonic inlet guide vane/rotor interaction, illustrating the ability of the interface treatment to handle shock waves.

Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations

Trends in turbomachinery turbulence treatments

Detailed flow measurements were taken in a centrifugal turbomachine model to investigate the aerodynamic influence of the vaned diffuser on the impeller flow. The model consists of an unshrouded centrifugal impeller with backswept blades and a rotatable vaned diffuser, which enables a continuous variation of the vaned diffuser location with respect to the measuring points. Phase-locked ensemble-averaged velocity components have been measured with hot-wire probes at the impeller outlet for 30 different relative positions of the probe with respect to the diffuser vanes. The data also include the distribution of the ensemble-averaged static pressure at the impeller front end, taken by means of miniature fast response pressure transducers flush-mounted at the impeller stationary casing. By circumferentially averaging the results obtained for the different circumferential probe locations, the periodically perturbed impeller flow has been split into a relative steady flow and a stator-generated unsteadiness. The results for the different probe positions have also been correlated in time to obtain instantaneous flow field images in the relative frame, which provide information on the various aspects of the diffuser vane upstream influence on the relative flow leaving the impeller.

An experimental investigation of stator induced unsteadiness on centrifugal impeller outflow

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of eight periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blademore » passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin.« less

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

This paper describes the time-varying aerodynamic interaction mechanisms that have been observed within a transonic high-pressure turbine stage; these are inferred from the time-resolved behavior of the rotor exit flow field. It contains results both from an experimental program in a turbine test facility and from numerical predictions. Experimental data was acquired using a fast-response aerodynamic probe capable of measuring Mach number, whirl angle, pitch angle, total pressure, and static pressure. A 3-D time-unsteady viscous Navier-Stokes solver was used for the numerical predictions. The unsteady rotor exit flowfield is formed from a combination of four flow phenomena: the rotor wake, the rotor trailing edge recompression shock, the tip-leakage flow, and the hub secondary flow. This paper describes the time-resolved behavior of each phenomenon and discusses the interaction mechanisms from which each originates. Two significant vane periodic changes (equivalent to a time-varying flow in the frame of reference of the rotor) in the rotor exit flowfield are identified. The first is a severe vane periodic fluctuation in flow conditions close to the hub wall and the second is a smaller vane periodic fluctuation occurring at equal strength over the entire blade span. These two regions of periodically varying flow are shown to be caused by two groups of interaction mechanisms. The first is thought to be caused by the interaction between the wake and secondary flow of the vane with the downstream rotor; and the second is thought to be caused by a combination of the interaction of the vane trailing edge recompression shock with the rotor, and the interaction between the vane and rotor potential fields.

Time-Resolved Vane-Rotor Interaction in a High-Pressure Turbine Stage

Detailed experimental and numerical studies have been performed in a subsonic, axial-flow turbine stage to investigate the secondary flow field, the aerodynamic loss generation, and the spanwise mixing under a stage environment. The experimental study includes measurements of the static pressure distribution on the rotor blade surface and the rotor exit flow field using three-dimensional hot-wire and pneumatic probes. The rotor exit flow field was measured with an unsteady hot-wire probe, which has high temporal and spatial resolution. Both steady and unsteady numerical analyses were performed with a three-dimensional Navier-Stokes code for the multiple blade rows. Special attention was focused on how well the steady multiple-blade-row calculation predicts the rotor exit flow field and how much the blade interaction affects the radial distribution of flow properties at the stage exit. Detailed comparisons between the measurement and the steady calculation indicate that the steady multiple-blade-row calculation predicts the overall time-averaged flow field very well. However, the steady calculation does not predict the secondary flow at the stage exit accurately. The current study indicates that the passage vortex near the hub of the rotor is transported toward the midspan due to the blade interaction effects. Also, the structure of the secondaryflowfield at the exit of the rotor is significantly modified by the unsteady effects. The time-averaged secondary flow field and the radial distribution of the flow properties, which are used for the design of the following stage, can be predicted more accurately with the unsteady flow calculation.

Endwall and unsteady flow phenomena in an axial turbine stage

Detailed experimental and numerical studies have been performed in a subsonic, axial-flow turbine stage to investigate the secondary flow field, the aerodynamic loss generation, and the spanwise mixing under a stage environment. The experimental study includes measurements of the static pressure distribution on the rotor blade surface and the rotor exit flow field using three-dimensional hot-wire and pneumatic probes. The rotor exit flow field was measured with an unsteady hot-wire probe which has high temporal and spatial resolution. Both steady and unsteady numerical analyses were performed with a three-dimensional Navier-Stokes code for the multiple blade rows. Special attention was focused on how well the steady multiple-blade-row calculation predicts the rotor exit flow field and how much the blade interaction affects the radial distribution of flow properties at the stage exit. Detailed comparisons between the measurement and the steady calculation indicate that the steady multiple-blade-row calculation predicts the overall time-averaged flow field very well. However, the steady calculation does not predict the secondary flow at the stage exit accurately. The current study indicates that the passage vortex near the hub of the rotor is transported toward the mid-span due to the blade interaction effects. And, the structure of the secondary flow field at the exit of the rotor is significantly modified by the unsteady effects. The time-averaged secondary flow field and the radial distribution of the flow properties, which are uses for the design of the following stage, can be predicted more accurately with the unsteady flow calculation.Copyright © 1994 by ASME

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Endwall and Unsteady Flow Phenomena in an Axial Turbine Stage

Detailed measurements have been performed in a subsonic, axial-flow turbine stage to investigate the structure of the secondary flow field and the loss generation. The data include the static pressure distribution on the rotor blade passage surfaces and radial-circumferential measurements of the rotor exit flow field using three-dimensional hot-wire and pneumatic probes. The flow field at the rotor outlet is derived from unsteady hot-wire measurements with high temporal and spatial resolution. The paper presents the formation of the tip clearance vortex and the passage vortices, which are strongly influenced by the spanwise nonuniform stator outlet flow. Taking the experimental values for the unsteady flow velocities and turbulence properties, the effect of the periodic stator wakes on the rotor flow is discussed.

Effects of stator wakes and spanwise nonuniform inlet conditions on the rotor flow of an axial turbine stage

Detailed measurements have been performed in a subsonic, axial-flow turbine stage to investigate the structure of the secondary flow field and the loss generation. The data in- cludes the static pressure distribution on the rotor blade passage surfaces and radial-cir- cumferential measurements of the rotor exit flow field using three-dimensional hot-wire and pneumatic probes. The flow field at the rotor outlet is derived from unsteady hot-wire measurements with high temporal and spatial resolution. The formation of the tip clearance vortex and the passage vortices is presented, which are strongly influenced by the spanwise non- uniform stator outlet flow. Taking the experi- mental values for the unsteady flow velocities and turbulence properties, the effect of the periodic stator wakes on the rotor flow is discussed. Nomenclature b, � axial chord Cvelocity, absolute frame hspan nshaft speed pstatic pressure p, total pressure schord tpitch ucircumferential speed u' random axial velocity fluctuation v' random radial velocity fluctuation wvelocity, relative frame w' random circumferential velocity fluctuation Zblade number aflow angle in circumferential direction, absolute frame 6� flow angle in circumferential direction, relative frame d, tip clearance tv, reduced frequency Subscripts

J. Zeschky

Papers

Endwall and unsteady flow phenomena in an axial turbine stage

Endwall and Unsteady Flow Phenomena in an Axial Turbine Stage

Effects of stator wakes and spanwise nonuniform inlet conditions on the rotor flow of an axial turbine stage

Effects of Stator Wakes and Spanwise Nonuniform Inlet Conditions on the Rotor Flow of an Axial Turbine Stage