Tomasz Michałek

1. Tomasz Michałek HIGH RAYLEIGH NUMBER NATURAL CONVECTION IN A CUBIC ENCLOSURE Institute of Fundamental Technological Research Polish Academy of Sciences, Dept. of Mechanics and Physics of Fluids, Poland.

2. Outline 1. Experimental benchmark • Sensitivity Analysis Towards Benchmark Definition • Experimental measurements • Results for moderate Ra Numbers • Experimental Benchmark (Ra = 1.5*106, Pr =11.78) 2. Towards high Ra Numbers and transition regime • 2D full velocity & temperature fields • Statistics of velocity fields • Time series of velocities • Validation of computational results

3. Building credibility 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,…] • Richardson extrapolation (RE) • Generalized RE • [Stern at all.] • Grid Convergence Index (GCI) [Roache] • Unit problems • Benchmark cases • Simplified/Partial • Flow Path • Actual Hardware • [Sindir et al.] sensitivity analysis

4. 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 model 2. Precision of measurements necessary to validate calculations

5. EXPERIMENTAL SET-UP light sheet

6. 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

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

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

9. 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

10. 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

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

12. NATURAL CONVECTION Ra ~ 3.0x107 Th = 18.0C Tc = 4.0C PIV Th = 23.2C Tc = 9.0C

13. NATURAL CONVECTION Ra = 1.5x108 Th = 27.3 C Tc = 6.8 C PIV PIT with two TLCs Th = 27.2 C Tc = 6.8C

14. NATURAL CONVECTION Ra = 1.8x108 Th = 36.4C Tc = 10.2C PIV PIT with two TLCs Tc = 10.2C Th = 36.4C

15. NATURAL CONVECTION Ra = 4.4x108 Th = 45.8C Tc = 14.2C PIV PIT with two TLCs Tc = 14.0C Th = 45.8C

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

17. HIGH RAYLEIGH NUMBERMean velocity fields Ra = 3x107 Ra = 1.5x108 Avg. Horizontal Velocity Ra = 4.4x108 Ra = 1.8x108 N = 150 t = 100 ms t = 15 sec

18. HIGH RAYLEIGH NUMBERMean velocity fields Ra = 1.5x108 Ra = 3x107 Avg. Vertical Velocity Ra = 4.4x108 Ra = 1.8x108 N = 150 t = 100 ms t = 15 sec

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

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

21. 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

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

23. HIGH RAYLEIGH NUMBERVelocity histogram and time series Ra = 1.5x108 N=120 t = 100 ms

24. HIGH RAYLEIGH NUMBERVelocity histogram and time series Ra = 1.8x108 N=134 t = 100 ms

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

26. 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 examples: for water

27. VALIDATION : Ra ~ 3 x 107 Experiment FD method (SOLVSTR) Condition does not hold

28. VALIDATION : Ra ~ 3 x 107 Experiment FV method (Fluent) Condition does not hold

29. VALIDATION : Ra ~ 1.3 x 108 Experiment FD method (SOLVSTR) Condition does not hold

30. VALIDATION : Ra ~ 1.3 x 108 Experiment FV method (Fluent) Condition does not hold

31. CONCLUSIONS The sensitivity analysis was used to identify fundamental (crucial) parameters for considered configuration. Experimental benchmark was defined for moderate Ra numbers. Agreement between computational results and experimental data was achieved. 2D Temperature fields, 2D Velocity fields were determined for high Ra numbers in the central cross-section of the box cavity heated from the side. Uncertainty of experimental data was assessed. Velocity fluctuations were observed in these experiments for high Ra number below Rac. Numerical simulations were performed for Ra = 3x107, 1.3x108 (FV,FD). Validation procedure was performed in order to assess modeling errors. Velocity fluctuations were not reproduced by computational results. These fluctuations were attributed to non-uniformity of thermal boundary conditions along the bottom wall.

32. Thank you for your attention!