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Research Papers

On the Impact of Geometric Variability on Fan Aerodynamic Performance, Unsteady Blade Row Interaction, and Its Mechanical Characteristics

[+] Author and Article Information
R. Schnell

German Aerospace Center e.V.—DLR,
Institute of Propulsion Technology,
Linder Hoehe,
Cologne 51147, Germany
e-mail: rainer.schnell@dlr.de

T. Lengyel-Kampmann, E. Nicke

German Aerospace Center e.V.—DLR,
Institute of Propulsion Technology,
Linder Hoehe,
Cologne 51147, Germany

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 17, 2013; final manuscript received March 10, 2014; published online April 18, 2014. Assoc. Editor: Seung Jin Song.

J. Turbomach 136(9), 091005 (Apr 18, 2014) (14 pages) Paper No: TURBO-13-1236; doi: 10.1115/1.4027218 History: Received October 17, 2013; Revised March 10, 2014; Accepted March 16, 2014

The focus of the present study is to assess and quantify the uncertainty in predicting the steady and unsteady aerodynamic performance as well as the major mechanical characteristics of a contrarotating turbofan, primarily due to geometric variations stemming from the manufacturing process. The basis of this study is the optically scanned blisk of the first rotor, for which geometric variations from blade to blade are considered. In a first step, selected profile sections of the first rotor were evaluated aerodynamically by applying the 2D coupled Euler/boundary-layer solver mises. Statistical properties of the relevant flow quantities were calculated firstly based on the results of the nine manufactured blades. In a second step, the geometric variations were decomposed into their corresponding eigenforms by means of principal component analysis (PCA). These modes were the basis for carrying out Monte Carlo (MC) simulations in order to analyze in detail the blade's aerodynamic response to the prescribed geometric variations. By means of 3D-computational fluid dynamics (CFD) simulations of the entire fan stage for all the nine scanned rotor 1 blade geometries, the variation of the overall stage performance parameters will be quantified. The impact of the instrumentation will be discussed, here partly doubling the standard deviation of the major performance indicators for the instrumented blades and also triggering a premature laminar/turbulent transition of the boundary layer. In terms of the unsteady blade row interaction, the standard deviation of the resulting blade pressure amplitude shall be discussed based on unsteady simulations, taking advantage of a novel harmonic balance approach. It will be shown that the major uncertainty in terms of the predicted blade pressure amplitude is in the aft part of the front rotor and results from upstream shock/blade interaction. Apart from the aerodynamic performance, an analysis of the mechanical properties in terms of Campbell characteristics and eigenfrequencies was carried out for each of the scanned blades of rotor 1, reflecting the frequency scattering of each eigenmode due to geometric variability.

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References

Figures

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Fig. 1

Contrarotating turbo fan rig CRTF2b installed at CIAM compressor test bed C-3 A [10]

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Fig. 2

Measured and calculated performance characteristic of the CRTF2b fan stage at 100%, 83%, and 54% rotational speed [19]

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Fig. 3

Strain gauge on the rotor of blisk 1 (left) and assembly of rotor 1 and 2 including the booster inlet guide vane (IGV) (right); the two blisks comprised of nine rotor 1 blades and 11 rotor 2 blades

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Fig. 4

Color-coded differences between manufactured and nominal geometry (in mm), including strain gauges' position and corresponding wiring

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Fig. 5

Surface-based CAD model of blade 04 including instrumentation and wiring on the pressure side as it was used for the 3D-CFD and CSM analysis of the real geometry (left) and nodewise distance between clean blade 03 and instrumented blade 04 to quantify sensor dimensions (right)

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Fig. 6

Leading-edge detail for different profile sections at 90% span: nominal (circles), all nine scanned blades of blisk 1 (solid lines), mean manufactured geometry, and ≈1000 geometries created based on PCA modes for MC simulations (solid light gray lines); the manufacturing tolerance band of ±0.1 mm is indicated by dashed circles at several locations along the profile

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Fig. 7

Mode shapes of the first four modes from principal component analysis and defined nondimensional parameters to characterize each mode

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Fig. 8

Outflow angles β2 at different incidence angles β1: results for the nominal geometry (solid line) and the mean manufactured geometry (dashed line) as well as results from Monte Carlo simulations based on PCA modes (plotted are the expectancy values as circles as well as corresponding uncertainties within ±2σ as error bars)

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Fig. 9

Empirical CDFs calculated from the nine samples (bullets) as well as from Monte Carlo simulations (solid lines) in comparison with the CDF from normal distribution (dashed line); the corresponding frequency distributions are shown in Figs. 8(a)8(c)

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Fig. 10

Various flow quantities and corresponding variation within ±2σ at different inflow incidence angles (90% span)

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Fig. 11

Relative standard deviation of different resulting flow parameters from MC simulations, each taking into account a different number of PCA modes to describe the geometric variability

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Fig. 12

Isentropic Mach number distribution at two different incidence angles and its variation due to the geometric variability (based on PCA modes as shown in Fig. 6) as a result from MC simulations; indicated is also the variation of the transition point at high flow incidence within a confidence interval of ±2σ (right)

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Fig. 13

Boundary layer edge velocity in the vicinity of the leading edge and calculated spike diffusion factors according to Ref. [16] for all scanned blade sections

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Fig. 14

Computational domain and grid details in an S1-plane on the hub for both rotors close to the leading edge (grid comprising of 6.2 × 106 cells in total, 141 cells in spanwise direction)

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Fig. 15

Rotor 1 isentropic efficiency at 100% rotational speed based on 3D-CFD full-stage simulations for all nine scanned rotor 1 blades and derived standard deviation (±2σ)

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Fig. 16

Rotor 1 total pressure ratio at 100% rotational speed based on 3D-CFD full-stage simulations for all nine scanned rotor 1 blades and derived standard deviation (±2σ)

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Fig. 17

Standard deviation of the rotor 1 isentropic efficiency at operating conditions 1–6 (see Fig. 16 for their definition on the 100% speed line)

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Fig. 18

Standard deviation of the mass flow rate at operating conditions 1–6 (see Fig. 16 for their definition on the 100% speed line)

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Fig. 19

Standard deviation of the rotor 1 total pressure at operating conditions 1–6 (see Fig. 16 for their definition on the 100% speed line); the error bars denote the standard error due to the limited number of samples O(σ/n1/2)

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Fig. 20

Boundary layer shape parameter H12 for all nine scanned blades at approximately 65% span (r = 180 mm) for the blade suction side (a) and pressure side (b); nondimensional displacement thickness δ1 as well as skin friction coefficient cf on the pressure side (c)

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Fig. 21

Comparison between stage and rotor isentropic efficiency standard deviation at three selected operating conditions

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Fig. 22

Instantaneous flow field at approximately 70% span highlighting the major interaction phenomena: upstream shock/blade interaction visualized by static pressure contours (left) and downstream wake/blade interaction visualized by contours of eddy viscosity (right)—results from HB computations with five harmonics

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Fig. 23

Blade-surface static pressure contours at design operating conditions for blade 01 (a), pressure fluctuations (amplitude of the first interaction harmonic) on both blades induced by wake/blade interaction (downstream) (b), and resulting pressure amplitude uncertainty (c)

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Fig. 24

Blade-surface static pressure amplitudes (first relative blade passing frequency (BPF) harmonic) resulting from unsteady blade-row interaction

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Fig. 25

Measured eigenfrequencies from blade excitation tests in comparison with FEM results as obtained in the present study (black bars, both average over all blades) and results with refined FEM model (permas), including the blade root/disk for the nominal geometry (see Ref. [19] for more details)

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Fig. 26

Campbell diagram for all nine scanned blades of the rotor 1 blisk; vertical dashed lines indicate test relevant operating conditions

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Fig. 27

Standard deviation of the eigenfrequency of the first four eigenmodes based on the results for all scanned blades

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Fig. 28

Standard deviation of the eigenfrequency of the first three eigenmodes—results from blade excitation tests (average over three positions) in comparison with FEM results

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