Research Papers

Numerical Study of Deterministic Fluxes in Compressor Passages

[+] Author and Article Information
Feng Wang

Department of Engineering Science,
Oxford Thermofluids Institute,
University of Oxford,
Oxford OX2 0ES, UK
e-mail: feng.wang@eng.ox.ac.uk

Mauro Carnevale

Department of Mechanical Engineering,
University of Bath,
Bath BA2 7AY, UK
e-mail: m.carnevale@bath.ac.uk

Luca di Mare

Department of Engineering Science,
Oxford Thermofluids Institute,
University of Oxford,
Oxford OX2 0ES, UK
e-mail: luca.dimare@eng.ox.ac.uk

1Corresponding author.

2The deterministic stress appears in the momentum equation, and for compressible flows, there are also terms which appear in the energy equation. Together, they will be called deterministic fluxes in the following text.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 12, 2018; final manuscript received September 5, 2018; published online September 28, 2018. Editor: Kenneth Hall.

J. Turbomach 140(10), 101005 (Sep 28, 2018) (11 pages) Paper No: TURBO-18-1158; doi: 10.1115/1.4041450 History: Received July 12, 2018; Revised September 05, 2018

Computational fluid dynamics (CFD) has been widely adopted in the compressor design process, but it remains a challenge to predict the flow details, performance, and stage matching for multistage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and unsteady RANS (URANS) calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious values of flow quantities (e.g., whirl angle). The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore, the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS mixing plane solutions. The magnitudes of divergence of Reynolds stresses (RS) and deterministic stresses (DS) are compared. The effect of deterministic fluxes is demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes is also observed. The effect of deterministic fluxes is confirmed via the nonlinear harmonic (NLH) method which includes the deterministic fluxes in the mean flow, and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Jelly, T. O. , Day, I. J. , and di Mare, L. , 2017, “ Phase-Averaged Flow Statistics in Compressors Using a Rotated Hot-Wire Technique,” Exp. Fluids, 58, p. 48. [CrossRef]
Adamczyk, J. , 1984, “ Model Equation for Simulating Flows in Multistage Turbomachinery,” Technical Report, NASA, Washington, DC, Report No. NASA-TM-86869.
Wilcox, D. C. , 1988, “ Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA J., 26(11), pp. 1299–1310. [CrossRef]
Menter, F. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Menter, F. , Garbaruk, A. , and Egorov, Y. , 2012, “ Explicit Algebraic Reynolds Stress Models for Anisotropic Wall-Bounded Flows,” Progress in Flight Physics, 3, pp. 89–104.
Adamczyk, J. J. , 1999, “ Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design,” ASME J. Turbomach., 122(2), pp. 189–217. [CrossRef]
He, L. , and Ning, W. , 1998, “ Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines,” AIAA J., 36(11), pp. 2005–2012. [CrossRef]
Vasanthakumar, P. , 2003, “ Three Dimensional Frequency-Domain Solution Method for Unsteady Turbomachinery Flows,” Ph.D. thesis, Durham University, Durham, UK.
Hall, K. C. , Thomas, J. P. , and Clark, W. S. , 2002, “ Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique,” AIAA J., 40(5), pp. 879–886. [CrossRef]
He, L. , 2010, “ Fourier Methods for Turbomachinery Applications,” Prog. Aerosp. Sci., 46(8), pp. 329–341. [CrossRef]
Hall, K. C. , Ekici, K. , Thomas, J. P. , and Dowell, E. H. , 2013, “ Harmonic Balance Methods Applied to Computational Fluid Dynamics Problems,” Int. J. Comput. Fluid Dyn., 27(2), pp. 52–67. [CrossRef]
Denton, J. , 1992, “ The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines,” ASME J. Turbomach., 114(1), pp. 18–26. [CrossRef]
Wang, F. , Carnevale, M. , di Mare, L. , and Gallimore, S. , 2017, “ Simulation of Multi-Stage Compressor at Off-Design Conditions,” ASME J. Turbomach., 140(2), p. 021011. [CrossRef]
Smith, L. , 1966, “ Wake Dispersion in Turbomachines,” ASME J. Basic Eng., 88(3), pp. 688–690. [CrossRef]
Van Zante, D. E. , Adamczyk, J. J. , Strazisar, A. J. , and Okiishi, T. H. , 2002, “ Wake Recovery Performance Benefit in a High-Speed Axial Compressor,” ASME J. Turbomach., 124(2), pp. 275–284. [CrossRef]
Denton, J. , 2010, “ Some Limitations of Turbomachinery CFD,” ASME Paper No. GT2010-22540.
Cumpsty, N. A. , 2010, “ Some Lessons Learned,” ASME J. Turbomach., 132(4), p. 041018. [CrossRef]
Chen, T. , Vasanthakumar, P. , and He, L. , 2001, “ Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach,” J. Propul. Power, 17(3), pp. 651–658. [CrossRef]
di Mare, L. , Kulkarni, D. Y. , Wang, F. , Romanov, A. , Ramar, P. R. , and Zachariadis, Z. I. , 2011, “ Virtual Gas Turbine: Geometry and Conceptual Description,” ASME Paper No. GT2011-46437.
Wang, F. , Carnevale, M. , Lu, G. , di Mare, L. , and Kulkarni, D. , 2016, “ Virtual Gas Turbine: Pre-Processing and Numerical Simulations,” ASME Paper No. GT2016-56227.
Carnevale, M. , Green, J. S. , and Di Mare, L. , 2014, “ Numerical Studies Into Intake Flow for Fan Forcing Assessment,” ASME Paper No. GT2014-25772.
Carnevale, M. , Wang, F. , Green, J. S. , and Mare, L. D. , 2016, “ Lip Stall Suppression in Powered Intakes,” J. Propul. Power, 32(1), pp. 161–170. [CrossRef]
Hadade, I. , Wang, F. , Carnevale, M. , and di Mare, L. , 2018, “ Some Useful Optimisations for Unstructured Computational Fluid Dynamics Codes on Multicore and Manycore Architectures,” Comput. Phys. Commun. (in press).
Saxer, A. P. , and Giles, M. B. , 1993, “ Quasi-Three-Dimensional Nonreflecting Boundary Conditions for Euler Equations Calculations,” J. Propul. Power, 9(2), pp. 263–271. [CrossRef]
Wang, F. , and di Mare, L. , 2017, “ Mesh Generation for Turbomachinery Blade Passages With Three-Dimensional Endwall Features,” J. Propul. Power, 33(6), pp. 1459–1472. [CrossRef]
Giles, M. , 1988, “ UNSFLO: A Numerical Method for Unsteady Inviscid Flow in Turbomachinery,” Technical Report,” MIT, Cambridge, MA, Report No. 195.
Gallimore, S. , and Cumpsty, N. , 1986, “ Spanwise Mixing in Multistage Axial Flow Compressors—Part I: Experimental Investigation,” ASME J. Turbomach., 108(1), pp. 2–9. [CrossRef]


Grahic Jump Location
Fig. 1

Triple decomposition of a velocity signal

Grahic Jump Location
Fig. 2

Schematic of bladerow coupling for the implemented NLH

Grahic Jump Location
Fig. 3

Schematic of the 2D duct case

Grahic Jump Location
Fig. 4

Comparison of mixed-out and time-averaged variables under different Mach numbers, wake orientations, and velocity deficits

Grahic Jump Location
Fig. 5

Geometry and mesh details of the front stages

Grahic Jump Location
Fig. 6

Predicted whirl angle downstream of IGV

Grahic Jump Location
Fig. 7

Axial velocity signal at S1 inlet around middle span using different time steps. The data of two revolutions are shown.

Grahic Jump Location
Fig. 8

Entropy around the middle span section for the front stages

Grahic Jump Location
Fig. 9

Entropy at the IGV exit

Grahic Jump Location
Fig. 10

Left: whirl angle on both sides of the mixing plane. Right: pressure ratio along the span of R1.

Grahic Jump Location
Fig. 11

DS divergence at three axial planes in R1

Grahic Jump Location
Fig. 12

Schematic of the planes to extract deterministic and Reynolds stress divergence

Grahic Jump Location
Fig. 13

Projections of DS and RS divergence on ur around 20% span

Grahic Jump Location
Fig. 14

Projections of DS and RS divergence on ut around 20% span

Grahic Jump Location
Fig. 15

Total pressure profiles in front of S1 and S2 leading edges. The values are normalized by their corresponding values at the middle span.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In