Tomasz Michałek, Tomasz A. Kowalewski

1. Tomasz Michałek, Tomasz A. Kowalewski NUMERICAL BENCHMARK BASED ON NATURAL CONVECTION OF FREEZING WATER Institute of Fundamental Technological Research Polish Academy of Sciences, Dept. of Mechanics and Physics of Fluids, Poland.

2. Building confidence to CFD results Verification Validation Code/Program verification Verification of Calculation Validation of Idealized problems Validation of actual configuration • Method of • manufactured solution [Roache] • Analytical solutions • Numerical benchmarks • [Ghia, de Vahl Davis, • Le Quere,…] • Unit problems • Benchmark cases • Simplified/Partial • Flow Path • Actual Hardware • [Sindir et al.] • Richardson extrapolation (RE) • Generalized RE • [Stern at all.] • Grid Convergence Index (GCI) [Roache] sensitivity analysis

3. BENCHMARK DEFINITION FOR THERMAL AND VISCOUS FLOWS • 2D viscous, incompressible flow driven by natural convection • Navier – Stokes equations with non-linear buoyancy term (water) coupled with heat transfer • Temperature gradient ΔT = 10ºC • Verified programs: Th = 10C Tc = 0C • FRECON (FDM) • FLUENT (FVM) • FIDAP (FEM) • SOLVSTR (FDM) • SOLVMEF (MEF) Ra = 1.5 · 106 Pr = 13.31

4. VERIFICATION PROCEDURE Compare profiles (not points!) CALCULATE: SOLUTION S , SOLUTION UNCERTAINTY USN Error indicator for code comparisons Reference solution

5. INTER-CODE COMPARISONS using selected profiles FRECON3V (FRE) FLUENT 6.1. (FLU) FIDAP 8.7.0.(FID) SOLVSTR (STR) Details of the reference solutions w(x) Michalek T., Kowalewski T.A., Sarler B. ”Natural Convection for Anomalous Density Variation of Water: Numerical Benchmark” Progress in Computational Fluid Dynamics, 5 (3-5),pp 158-170,2005 Error U,W along Y=0.5L Error U,W along X=0.5L Error U,W along X=0.9L Mesh sensitivity

6. SENSITIVITY ANALYSISParameters and control points COMP. RESULTS INITIAL PARAMETERS Boundary conditions TH, TC, Text, Q1, Q2, Q3 Initial conditions Tinit. ,vinit Material properties ,,,,cp MODEL OUTPUT SENSITIVITY MEASURES 1. Fundamental parameters for validation procedure 2. Precision of measurements necessary to validate calculations

7. EXPERIMENTAL SET-UP light sheet

8. CAVITY DETAILSControl points for monitoring internal and external temperatures T14 PLEXIGLASS WALL T7 T10 Th Tc ALUMINIUM WALL ALUMINIUM WALL TL TP PLEXIGLASS WALL T15 CENTRAL CROS-SECTION TE1 TE2

9. EXPERIMENTAL TECHNIQUES • Particle Image Velocimetry (PIV) • Particle Image Thermometry (PIT) • 2D Visualization • Point temperature measurements correlation F(t0) F(t0+t)

10. ESTIMATION OF EXP. UNCERAINTY UD • PIV Avg. Fields N – length of series Std. Dev. Std. Dev. Error Experimental Data Uncertainty • PIT

11. EXPERIMENTAL BENCHMARK DEFINEDDifferent liquid crystal tracers to cover entire color range PIT - temperature Ra = 1.5*106 Pr = 11.78 PIV – velocity Th = 10 C Tc = 0 C

12. EXPERIMENTAL BENCHMARK DEFINEDSelected velocity and temperature profiles 2D Temp. Field Temp. along X = 0.9L Temp. along Y = 0.5L W along Y = 0.5L U along X = 0.5L W along X = 0.9L

13. EXPERIMENTAL UNCERTAINTY ESTIMATION N = 40, t = 1s • PIV • PIT • two sets of tracers

14. VALIDATION METHODOLOGY Stern et all., Comprehensive approach to verification and validation of CFD simulations – Part 1: Methodology and procedures Journal of Fluids Engineering – Transactions of ASME, 123 (4), pp. 793-802,2001. • Validation error • Validation metric In our example: for water

15. TUNNING NUMERICAL SOLUTIONEffect of fluid variable properties and thermal boundary conditions Simulation A Variable liquid properties (T),(T),cp (T) Simulation B Const. liquid properties ,,cp = const. Simulation C Adiabatic and isothermal walls ,,cp = const Temperature fields Velocity fields

16. THERMAL BOUNDARY CONDITIONValidation of the selected numerical model for Tc=-2oC Computational Simulation Tc= - 2C Th=10C Experiment

17. THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=-1oC Computational Simulation Tc = -1C Th=10C Experiment

18. THERMAL BOUNDARY CONDITIONValidation of the selected numerical model for Tc=+1oC Computational Simulation Tc=1C Th=10C Experiment

19. THERMAL BOUNDARY CONDITIONValidation of the selected numerical model for Tc=+2oC Computational Simulation Tc=2C Th=10C Experiment

20. VALIDATION – QUANTITATIVE COMPARISONS WITH THE EXPERIMENTAL BENCHMARK Y=0.5L X=0.5L X=0.9L Temperature profiles Velocity profiles

21. NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER Th = 27.33 C Tc = 6.87 C PIV PIT with two TLCs Th = 27.21 C Tc = 6.77 C

22. NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER Ra = 3.107 control points and area selected for velocity measurements Ra = 4.4.108

23. HIGH RAYLEIGH NUMBERVelocity field statistics Ra = 3x107 Ra = 1.5x108 Turbulence Intensity Ra = 4.4x108 Ra = 1.8x108 N = 150 t = 100 ms t = 15 sec

24. HIGH RAYLEIGH NUMBERVelocity histogram and time series Ra = 3x107 N=150 t = 100 ms

25. HIGH RAYLEIGH NUMBERVelocity histogram and time series Ra = 4.4x108 N=138 t = 100 ms

26. CONCLUSIONS Numerical benchmark based on natural convection of freezing water defined A sensitivity analysis proposed to evaluate effects of initial parameters and to identify fundamental (crucial) parameters => determination of measurement’s precision needed in the validation procedure. Experimental benchmark defined 2D Temperature field, 2D Velocity fieldobtained for defined configuration Uncertainty of experimental data assessed Validation procedure performed in order to assess modeling errors. High Rayleigh number natural convection resolved experimentally – Numerical solution … pending

27. Thank you for your attention!