Research Papers

One-Dimensional and Three-Dimensional Design Strategies for Pressure Slope Optimization of High-Flow Transonic Centrifugal Compressor Impellers

[+] Author and Article Information
A. Hildebrandt

MAN Energy Solutions SE,
Steinbrinkstraße 1,
Oberhausen 46145, Germany
e-mail: andre.hildebrandt@man-es.com

T. Ceyrowsky

MAN Energy Solutions SE,
Steinbrinkstraße 1,
Oberhausen 46145, Germany

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 22, 2018; final manuscript received October 31, 2018; published online January 21, 2019. Editor: Kenneth Hall.

J. Turbomach 141(5), 051002 (Jan 21, 2019) (11 pages) Paper No: TURBO-18-1135; doi: 10.1115/1.4041907 History: Received June 22, 2018; Revised October 31, 2018

This paper deals with the numerical and theoretical investigations of the effect of geometrical dimensions and one-dimensional (1D)-design parameters on the impeller pressure slope of a transonic centrifugal compressor stage for industrial process application. A database being generated during the multi-objective and multipoint design process of a high flow coefficient impeller, comprising 545 computational fluid dynamics (CFD) designs is investigated in off-design and design conditions by means of Reynolds-averaged Navier–Stokes (RANS) simulation of an impeller with vaneless diffuser. For high flow coefficients of 0.16 < ϕdes < 0.18, the CFD-setup has been validated against measurement data regarding stage and impeller performance taken from MAN test rig experimental data for a centrifugal compressor stage of similar flow coefficient. This paper aims at answering the question how classical design parameter, such as the impeller blade angle distribution, impeller suction diameter, and camber line length affect the local and total relative diffusion and pressure slope toward impeller stall operation. A second-order analysis of the CFD database is performed by cross-correlating the CFD data with results from impeller two-zone 1D modeling and a rapid loading calculation process by Stanitz and Prian. The statistical covariance of first-order 1D-analysis parameters such as the mixing loss of the impeller secondary flow, the slip factor, impeller flow incidence is analyzed, thereby showing strong correlation with the design and off-design point efficiency and pressure slope. Finally, guide lines are derived in order to achieve either optimized design point efficiency or maximum negative pressure slope characteristics toward impeller stall operation.

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Fig. 1

Compressor map showing six operational points for analysis

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Fig. 2

(a) Pareto front of objective function and (b) work input versus design point efficiency

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Fig. 3

(a) At flow coefficient Φnorm = 0.85, slope of pressure coefficient as function of work-input and efficiency derivatives and (b) slope of pressure coefficient as function of work-input and efficiency derivatives at Φnorm = 0.88

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Fig. 4

(a) Impeller inlet optimization (1D: lines, CFD: circles) and (b) normalized choke flow margin versus CFD work-input and pressure slope

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Fig. 5

(a) 1D-stage efficiency and (b) CFD-stage efficiency as function of swirl angle λ and impeller exit

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Fig. 6

Sensitivity analysis of shroud blade angle distribution on design point efficiency; big circles: DOE-, small circles: opt. samples

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Fig. 7

(a) Incidence correlated with design point efficiency and slope and (b) pressure slope correlated with derivatives of mixing loss ω24 and flow angle α2 at ϕnorm = 85%

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Fig. 8

(a) Pressure slope and (b) design point efficiency as function of mixing loss ω24 and flow angle α2 at ϕdes

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Fig. 9

(a) Pressure slope as function of CFD-calculated impeller slip factors and (b) pressure slope as function of relative diffusion ratio and shroud camber length

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Fig. 10

(a) Geometry domain for Stanitz and Prian impeller flow calculation and (b) example of blade loading calculation result on mean radius

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Fig. 11

Pressure slope at ϕnorm = 85% as function of the impeller loading and relative diffusion at 10%, 15%, 20%, and 30% camber length

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Fig. 12

(a) Pressure slope as function of relative velocity at 15% camber length and (b) global diffusion ratio and slope of relative diffusion at 12% camber length

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Fig. 13

(a) Design point efficiency and (b) pressure slope at ϕnorm = 0.93 as function of relative velocity and blade loading at 10% camber length

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Fig. 14

Comparison Spearman and Pearson 1D-correlations for pressure slope at ϕnorm = 0.85

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Fig. 15

Computational fluid dynamics calculated characteristic maps of five selected samples (AE) from the slope-efficiency Pareto-Front

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Fig. 16

Computational fluid dynamics impeller static pressure rise on 95% span at ϕdes

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Fig. 17

Computational fluid dynamics calculated relative Mach number at impeller exit (S3 plane) at ϕdes

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Fig. 18

Computational fluid dynamics results of the optimized new stage design “impeller sample C” versus old (reference) impeller design @Mau2 = 1.1 at impeller exit (curve 02), diffuser inlet (curve 03) and diffuser outlet (curve 04), calculated with a vaned diffuser

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Fig. 19

Computational fluid dynamics model for the analysis showing the impeller exit section and the diffuser inlet section (for stage evaluation)

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Fig. 20

Test rig setup for aerodynamic measurements of the reference design



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