Pump CFD - performance prediction: a tutorial

1. Pump CFD - performance prediction: a tutorial Niels P. KruytEngineering Fluid Dynamics, Department of Mechanical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlandsn.p.kruyt@utwente.nl www.ts.wb.utwente.nl/kruyt/ 5th International Symposium on Pumping Machinery, 2005 ASME Fluids Engineering Division Summer Meeting and Exhibition, 19-23 June, Houston, TX, USA

2. CFD for pump design: pitfalls and opportunities CFD for pump design: a magic bullet? Pump CFD - performance prediction

3. Overview of tutorial • Why is fluid dynamics important for pump design? • What is Computational Fluid Dynamics (CFD)? • Opportunities provided by CFD • Components of CFD • Essential fluid dynamics • Examples of performance prediction • Trends • “Do’s” and “don’t’s” of CFD

4. Characteristics of centrifugal pumps

5. Basics of pump design/analysis • One-dimensional flow model • Euler pump relation • Slip factor is empirical • Hydraulic efficiency is empirical

6. What is Computational Fluid Dynamics (CFD)? Determination of flow: • Analytical ® impossible • Experiments ® expensive • Numerical ® CFD(“computer test-rig”)

7. Benefits of CFD for pump design • Improved designs • More reliable design methods • Cheaper design process

8. Design phases • Conceptual design • Preliminary design • Detailed design • Use different CFD-methods for different design phases!

9. Components of CFD • Model formulation • geometry • flow model • boundary conditions • Grid/mesh generation • Discretisation of governing equations • Solution of discretised equations • Interpretation

10. Selection of modelled geometry • Single channel of impeller • Full pump: impeller & volute/diffusor • steady • unsteady • Leakage-flow region • Piping system / pump intake • Single stage vs. multi-stage

11. Turbulent flow

12. Closure problem • Averaging over time ® Reynolds-averaged Navier-Stokes equations (RANS) • Contains ‘Reynolds stresses’ • Extra quantities in equations ® ‘closure’ problem • Model required for Reynolds stresses in terms of time-averaged velocities

13. Turbulence models “Turbulent viscosity” • Mixing-length model • k-e models (k-w) • Reynolds-stress models • ¼ Increasing complexity Pope (2000); Bradshaw (1996)

14. Flow models • Stream-surface methods • Potential-flow model • Euler flow model • RANS-based models • Large-eddy simulations (LES) • Direct Navier-Stokes simulations (DNS) Increasing complexity

15. Boundary layers • High Reynolds numbers • Main flow is inviscid • Boundary-layer flow is viscous • Boundary-layer is thin • Large variation of velocity in direction normal to wall Re = 107: L = 25 cm; d = 0.4 cmL = 9.8 in; d = 0.1 in

16. Logarithmic layer • Large variation of velocity perpendicular to wall ® many grid points • ‘Universal’ behaviour near wall ® “logarithmic layer” • “Wall functions” in RANS-based CFD-methods ® boundary conditions Craft et al. (2002); Pope (2000)

17. Separation Attached boundary-layer Separated boundary-layer

18. Grid/mesh (1) Structured Unstructured

19. Structured multi-block Viscous accuracy Unstructured Easeof use Grid/mesh (2) Baker (2005)

20. Discretisation • Replace partial differential equations by a finite set of equations • Finite difference method • Finite volume method • Finite element method • Discretisation error solution depends on grid/mesh size!

21. Sources of errors in CFD-predictions • Modelling errors • Geometrical uncertainties • Limited validity of adopted flow model • Uncertain boundary conditions • Numerical errors • Discretisation error due to finite grid-size • Lack of convergence in iterative solution process • Insufficient mesh/grid quality • User/programmer errors

22. DNS Cost RSM k, e Potential& B.L. Potential 1D Accuracy Choice of flow model ‘Around’ design point

23. Performance prediction with potential-flow model van Esch & Kruyt (2001)

24. RAE101 wing Inviscid-viscous interaction methods • Outer flow ® inviscid flow equations • Boundary-layer flow ® boundary-layer equations • Coupled solution ® mildy separated flows Milewski (1997)

25. Comparison of RANS-predictions • Different machines • Many contributors • Draft tube • Wing/body

26. Turbine draft tube Turbine draft tube flow; Engström et al. (2001) Experimental

27. Wing/body DLR F6 wing/body study Baker (2005)

28. Differences CFDpump «aerospace applications • Compressibility effects are absent; no shock waves • Cavitation is important • Rotating/stationary parts • More boundary layers need to be resolved • Flow separation more important for off-design conditions • Effect rotation and curvature on turbulence

29. Implementation of CFD in pump-design process • Integrate CFD in all design phases • Different CFD-models for each design phase • Simple models give more insight • Tune model parameters from database • RANS-methods require intense use • Set accuracy targets clearly • Be cautious of designs from CFD that deviate strongly from experience

30. Trends • Maturing of commercial/general-purpose CFD-packages • Main problem remains turbulence modelling • Multi-phase CFD-methods • Adaptive mesh refinement • Open-source CFD-methods (“GNU-CFD”) • Verification of CFD-methods ® “blind” tests • Design-oriented CFD-methods • Optimisation methods • Inverse-design methods

31. Inverse-design method • Specified • meridional plane • duty • “blade loading” • Obtained • Blade angles Westra et al. (2005) [Click on figure to start movie]

32. “Don’t’s” of CFD • Use CFD-package as a black-box tool • Forget that turbulence needs to be modelled • Use RANS-methods for all design phases

33. “Do’s” of CFD • Choose right tool for the task • Analyse and interpret results • Use common-sense • Use/develop knowledge of fluid dynamics • Check grid/mesh convergence • Check sensitivity of results to model parameters

34. Conclusions • CFD is not a “magic bullet” • CFD is a powerful tool • Many pitfalls; many opportunities • CFD does not replace a smart designer • CFD provides great potential for improved pump-design process • CFD is (still) an art

35. Questions and comments • Thank you for your attention! • Questions and comments? • Presentation can be downloaded from: www.ts.wb.utwente.nl/kruyt/asme2005.pps • E-mail: n.p.kruyt@utwente.nl

36. Literature • Baker, T.J. (2005). “Mesh generation: art or science”, Progress in Aerospace Sciences 41 29-63. • Craft, T.J. & Gerasimov, A.V. & Iacovides, H. & Launder, B.E. (2002). “Progress in the generalization of wall-function treatments”, International Journal of Heat and Fluid Flow 23 148-160. • Bradshaw, P. (1996). “Turbulence modelling with application to turbomachinery”, Progress in Aerospace Sciences 32 575-624. • Engström, T.F. & Gustavsson, L.H. & Karlsson, R.I. (2001). “Proceedings of Turbine 99 – Worskshop 2. The second ERCOFTAC Workshop on draft tube flow”, http://www.sirius.luth.se/strl/Turbine-99/. • Esch, B.P.M. van & Kruyt, N.P. (2001). “Hydraulic performance of a mixed-flow pump: unsteady inviscid computations and loss models”, Journal of Fluids Engineering 123256-264. • Jameson, A. (2001). “A perspective on computational algorithms for aerodynamic analysis and design”, Progress in Aerospace Sciences 37 197-243. • Milewski, W.M. (1997). “Three-dimensional viscous flow computations using the integral boundary-layer equations simultaneously coupled with a low-order panel method”, Ph.D. Thesis, MIT, Cambridge, USA. • Westra, R.W. & Kruyt, N.P. & Hoeijmakers, H.W.M. (2005). “An inverse-design method for centrifugal pump impellers”, 2005 ASME 5th International Symposium on Pumping Machinery, Paper FEDSM2005-77283. • Pope, S.B. (2000). “Turbulent flows”, Cambridge University Press, Cambridge, UK.

37. Notes