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

Building confidence to CFD results VerificationValidation Code/Program verification Verification of Calculation Validation of Idealized problems 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] sensitivity analysis Unit problems Benchmark cases Simplified/Partial Flow Path Actual Hardware [Sindir et al.] Validation of actual configuration

 FRECON (FDM)  FLUENT (FVM)  FIDAP (FEM)  SOLVSTR (FDM)  SOLVMEF (MEF) Ra = 1.5 · 10 6 Pr = 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: T h = 10  CT c = 0  C

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

INTER-CODE COMPARISONS using selected profiles Error U,W along Y=0.5LError U,W along X=0.5LError U,W along X=0.9L 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 ,2005 FRECON3V (FRE) FLUENT 6.1. (FLU) FIDAP (FID) SOLVSTR (STR) Mesh sensitivity

SENSITIVITY ANALYSIS Parameters and control points Boundary conditions T H, T C, T ext, Q 1, Q 2, Q 3 Initial conditions T init., v init Material properties , , , ,c p MODEL COMP. RESULTS INITIAL PARAMETERS SENSITIVITY MEASURES OUTPUT 1. Fundamental parameters for validation procedure 2. Precision of measurements necessary to validate calculations

EXPERIMENTAL SET-UP light sheet

CAVITY DETAILS Control points for monitoring internal and external temperatures CENTRAL CROS-SECTION ALUMINIUM WALL PLEXIGLASS WALL T7T7 T 10 T 14 T 15 ThTh TLTL TPTP TcTc T E1 T E2

Particle Image Velocimetry (PIV) Particle Image Thermometry (PIT) 2D Visualization Point temperature measurements EXPERIMENTAL TECHNIQUES correlation F(t 0 ) F(t 0 +  t )

ESTIMATION OF EXP. UNCERAINTY U D PIV Avg. FieldsN – length of series Std. Dev. Std. Dev. Error Experimental Data Uncertainty PIT Halcrest Inc. BM100 Temp. range [  C] HueColor UD[C]UD[C] Red Yellow Green Blue1.5

EXPERIMENTAL BENCHMARK DEFINED Different liquid crystal tracers to cover entire color range T h = 10  C T c = 0  C PIV – velocity PIT - temperature Ra = 1.5*10 6 Pr = 11.78

EXPERIMENTAL BENCHMARK DEFINED Selected velocity and temperature profiles 2D Temp. Field Temp. along Y = 0.5L Temp. along X = 0.9L W along Y = 0.5LU along X = 0.5LW along X = 0.9L

EXPERIMENTAL UNCERTAINTY ESTIMATION N = 40,  t = 1s Mix C Temp. range [  C] HueColor UD[C]UD[C] Red Yellow Green Blue3.0 BM Red Yellow Green Blue1.5 PIV PIT two sets of tracers

Validation error Validation metric 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 ,2001. In our example: for water

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

THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=-2 o C T h =10  C T c = - 2  C Computational Simulation Experiment

THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=-1 o C Computational Simulation Experiment T h =10  C T c = -1  C

THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=+1 o C T h =10  C T c =1  C Computational Simulation Experiment

THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=+2 o C T h =10  C T c =2  C Computational Simulation Experiment

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

VALIDATION – QUANTITATIVE COMPARISONS ExperimentComp. Sim. AComp. Sim. B YDUDUD SU SN |E||E|UVUV S |E||E|Uv ExperimentComp. Sim. AComp. Sim. B YDUDUD SU SN |E||E|UVUV S |E||E|Uv Validation error was assessed for both simulations Assessed discrepancy are solely due to modeling errors Comp. Sim. A. turned out to be closer to experimental results than comp. Sim. B according to applied validation technique

NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER T h =  C T c = 6.87  C T h =  C T c = 6.77  C RaPr 13* * * * PIV PIT with two TLCs

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

Ra = 4.4x10 8 Ra = 1.5x10 8 Ra = 1.8x10 8 Ra = 3x10 7 Avg. Horizontal Velocity N = 150  t = 100 ms t = 15 sec HIGH RAYLEIGH NUMBER Mean velocity fields

Avg. Vertical Velocity N = 150  t = 100 ms t = 15 sec Ra = 4.4x10 8 Ra = 1.5x10 8 Ra = 1.8x10 8 Ra = 3x10 7 HIGH RAYLEIGH NUMBER Mean velocity fields

Skewness N = 150  t = 100 ms t = 15 sec Ra = 4.4x10 8 Ra = 1.5x10 8 Ra = 1.8x10 8 Ra = 3x10 7 HIGH RAYLEIGH NUMBER Velocity field statistics

Kurtozis N = 150  t = 100 ms t = 15 sec Ra = 4.4x10 8 Ra = 1.5x10 8 Ra = 1.8x10 8 Ra = 3x10 7 HIGH RAYLEIGH NUMBER Velocity field statistics

Turbulence Intensity N = 150  t = 100 ms t = 15 sec Ra = 4.4x10 8 Ra = 1.5x10 8 Ra = 1.8x10 8 Ra = 3x10 7 HIGH RAYLEIGH NUMBER Velocity field statistics

Ra = 3x10 7 N=150  t = 100 ms HIGH RAYLEIGH NUMBER Velocity histogram and time series

Ra = 1.5x10 8 N=120  t = 100 ms HIGH RAYLEIGH NUMBER Velocity histogram and time series

Ra = 1.8x10 8 N=134  t = 100 ms HIGH RAYLEIGH NUMBER Velocity histogram and time series

Ra = 4.4x10 8 N=138  t = 100 ms HIGH RAYLEIGH NUMBER Velocity histogram and time series

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. Uncertainty of experimental data assessed 2D Temperature field, 2D Velocity field obtained for defined configuration Validation procedure performed in order to assess modeling errors. Experimental benchmark defined High Rayleigh number natural convection resolved experimentally – Numerical solution … pending

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