Tomasz Michaek Tomasz A Kowalewski NUMERICAL BENCHMARK BASED

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.

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

BENCHMARK DEFINITION FOR THERMAL AND VISCOUS FLOWS • 2 D 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: q FRECON (FDM) q FLUENT (FVM) q FIDAP (FEM) q SOLVSTR (FDM) q SOLVMEF (MEF) Th = 10 C Tc = 0 C Ra = 1. 5 · 106 Pr = 13. 31

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

INTER-CODE COMPARISONS using selected profiles 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. 5 L Error U, W along X=0. 5 L Mesh sensitivity FRECON 3 V (FRE) FLUENT 6. 1. (FLU) FIDAP 8. 7. 0. (FID) SOLVSTR (STR) Error U, W along X=0. 9 L

SENSITIVITY ANALYSIS Parameters and control points COMP. RESULTS INITIAL PARAMETERS Boundary conditions TH, TC, Text, Q 1, Q 2, Q 3 Initial conditions Tinit. , vinit Material properties , , cp OUTPUT 1. Fundamental parameters for validation procedure 2. Precision of measurements necessary to validate calculations MODEL SENSITIVITY MEASURES

EXPERIMENTAL SET-UP light sheet

CAVITY DETAILS Control points for monitoring internal and external temperatures CENTRAL CROS-SECTION TE 1 TE 2 T 14 PLEXIGLASS WALL Tc WALL Th ALUMINIUM TL T 10 ALUMINIUM WALL T 7 PLEXIGLASS WALL T 15 TP

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

ESTIMATION OF EXP. UNCERAINTY UD • PIV Avg. Fields N – length of series Std. Dev. Error Experimental Data Uncertainty Halcrest Inc. BM 100 • PIT Temp. range [ C] Hue Color UD[ C] 5. 5 6. 4 0. 12 0. 28 Red 1. 0 6. 4 6. 5 0. 28 0. 35 Yellow 0. 5 6. 5 7. 5 0. 35 0. 55 Green 1. 0 7. 5 9. 5 0. 55 0. 70 Blue 1. 5

EXPERIMENTAL BENCHMARK DEFINED Different 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

EXPERIMENTAL BENCHMARK DEFINED Selected velocity and temperature profiles 2 D Temp. Field Temp. along Y = 0. 5 L W along Y = 0. 5 L U along X = 0. 5 L Temp. along X = 0. 9 L W along X = 0. 9 L

EXPERIMENTAL UNCERTAINTY ESTIMATION N = 40, t = 1 s • PIV Temp. range [ C] Mix C • PIT two sets of tracers Hue Color UD[ C] BM 100 0. 0 3. 0 0. 11 0. 18 Red 1. 0 3. 5 0. 18 0. 25 Yellow 0. 5 3. 9 0. 25 0. 48 Green 0. 5 3. 9 8. 0 0. 48 0. 66 Blue 3. 0 5. 5 6. 4 0. 12 0. 28 Red 1. 0 6. 4 6. 5 0. 28 0. 35 Yellow 0. 5 6. 5 7. 5 0. 35 0. 55 Green 1. 0 7. 5 9. 5 0. 55 0. 70 Blue 1. 5

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

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

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

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

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

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

Velocity profiles Temperature profiles VALIDATION – QUANTITATIVE COMPARISONS WITH THE EXPERIMENTAL BENCHMARK Y=0. 5 L X=0. 9 L

3*107 9. 53 2 1. 5 *108 7. 01 3 1. 8*108 7. 01 4 4. 4*108 5. 41 PIV PIT with two TLCs Tc = 6. 87 C 1 Tc = 6. 77 C Pr Th = 27. 21 C Ra Th = 27. 33 C NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER

NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER Ra = 3. 107 control points and area selected for velocity measurements Ra = 4. 4. 108

HIGH RAYLEIGH NUMBER Velocity field statistics Turbulence Intensity Ra = 3 x 107 Ra = 1. 8 x 108 N = 150 t = 100 ms t = 15 sec Ra = 1. 5 x 108 Ra = 4. 4 x 108

HIGH RAYLEIGH NUMBER Velocity histogram and time series Ra = 3 x 107 N=150 t = 100 ms

HIGH RAYLEIGH NUMBER Velocity histogram and time series Ra = 4. 4 x 108 N=138 t = 100 ms

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 2 D Temperature field, 2 D Velocity field obtained 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

Thank you for your attention!