tomasz michałek, tomasz a. kowalewski institute of fundamental technological research polish...
Post on 11-Jan-2016
222 Views
Preview:
TRANSCRIPT
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
Verification Validation
Code/Program verification
Verification of Calculation
Validation ofIdealized 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/PartialFlow Path
• Actual Hardware[Sindir et al.]
Validation ofactual
configuration
FRECON (FDM) FLUENT (FVM) FIDAP (FEM) SOLVSTR (FDM) SOLVMEF (MEF)
Ra = 1.5 · 106 Pr = 13.31
BENCHMARK DEFINITIONFOR 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 = 10C Tc = 0C
VERIFICATION PROCEDURECompare profiles (not points!)
Reference solution
Error indicator for code comparisons
N
iii xwxf
Nf
1
2)()(1
CALCULATE: SOLUTION S , SOLUTION UNCERTAINTY USN
N
iii xwxf
Nf
1
2)()(1
INTER-CODE COMPARISONSusing selected profiles
Error U,W along Y=0.5L Error U,W along X=0.5L Error 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 158-170,2005
FRECON3V (FRE) FLUENT 6.1. (FLU)FIDAP 8.7.0.(FID) SOLVSTR (STR)
Mesh sensitivity
SENSITIVITY ANALYSISParameters and control points
Boundary conditionsTH, TC, Text, Q1, Q2, Q3
Initial conditionsTinit. ,vinit
Material properties,,,,cp
MODEL
COMP. RESULTSINITIAL PARAMETERS
i
NiNii
i
pppFpppFDF
,...,,...,,...,,..., 11
Ni
NiNiid pppF
pppFpppFF
,...,,...,
,...,,...,,...,,...,)(
1
11
SENSITIVITY MEASURESOUTPUT
1. Fundamental parameters for validation procedure
2. Precision of measurements necessary to validate
calculations
EXPERIMENTAL SET-UP
light sheet
CAVITY DETAILSControl points for monitoring internal and external temperatures
CENTRAL CROS-SECTION
AL
UM
INIU
M
W
AL
L
AL
UM
INIU
M
W
AL
L
PLEXIGLASS WALL
PLEXIGLASS WALL
T7 T10
T14
T15
Th
TL TP
Tc
TE1 TE2
Particle Image Velocimetry (PIV)
Particle Image Thermometry (PIT)
2D VisualizationPoint temperature measurements
EXPERIMENTAL TECHNIQUES
correlationF(t0)
F(t0+t)
Niiavg v
Nv
..1
1
21
..1
2
1
1
Ni
avgiN vvN
ESTIMATION OF EXP. UNCERAINTY UD
21
..1
2
11
Niavgi vv
NNs
• PIVAvg. Fields N – length of series
Std. Dev.
Std. Dev. Error
Experimental Data Uncertainty
• PIT
svsvUvUv avgavgDavgDavg 3;3;
sUD 3
Halcrest Inc. B
M100
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
Th = 10 C Tc = 0 C
PIV – velocity
PIT -temperature
Ra = 1.5*106
Pr = 11.78
EXPERIMENTAL BENCHMARK DEFINEDSelected velocity and temperature profiles
2D Temp. Field Temp. along Y = 0.5L Temp. along X = 0.9L
W along Y = 0.5L U along X = 0.5L W along X = 0.9L
EXPERIMENTAL UNCERTAINTY ESTIMATION
Niiavg v
Nv
..1
1
21
..1
2
11
Niavgi vv
NNs
smmyxs /18.080,0:3max
N = 40, t = 1s
Mix C
Temp. range [C] Hue Color UD[C]
0.0 3.0 0.11 0.18 Red 1.0
3.0 3.5 0.18 0.25 Yellow 0.5
3.5 3.9 0.25 0.48 Green 0.5
3.9 8.0 0.48 0.66 Blue 3.0
BM
100
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
• PIV
• PITtwo sets of tracers
s
• Validation error
• Validation metric
SDE
VALIDATION METHODOLOGY
Stern et all., Comprehensive approach to verification and validation of CFD simulations – Part 1: Methodology and proceduresJournal of Fluids Engineering – Transactions of ASME, 123 (4), pp. 793-802,2001.
5.0222SPDSNDV UUUUE
5.0222SPDSNDV UUUU
sUD 3 SSSU extSN
21
..1
2
11
Niavgi vv
NNs
0SPDU
Niiavg v
Nv
..1
1 cfext SSS 33.033.1
In our example:
for water
TUNNING NUMERICAL SOLUTIONEffect of fluid variable properties and thermal boundary conditions
Simulation AVariable liquid properties
(T),(T),cp (T)
Simulation BConst. liquid properties
,,cp = const.
Simulation CAdiabatic and isothermal walls
,,cp = const
Tem
pera
ture
fie
lds
Vel
ocity
fie
lds
THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=-2oC
Th=
10C
Tc=
- 2C
Computational Simulation
Experiment
extwii TTQ
121 10 KWm
122 2400 KWm
123 1000 KWm
THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=-1oC
Computational Simulation
ExperimentT
h=
10C
Tc
= -
1C
extwii TTQ
121 10 KWm
122 2400 KWm
123 1000 KWm
THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=+1oC
Th=
10C
Tc=
1C
Computational Simulation
Experiment
extwii TTQ
121 10 KWm
122 2400 KWm
123 1000 KWm
THERMAL BOUNDARY CONDITION Validation of the selected numerical model for Tc=+2oC
Th=
10C
Tc=
2C
Computational Simulation
Experiment
extwii TTQ
121 10 KWm
122 2400 KWm
123 1000 KWm
VALIDATION – QUANTITATIVE COMPARISONS WITH THE EXPERIMENTAL BENCHMARK
Tem
per
atu
re p
rofi
les
Vel
oci
ty p
rofi
les
Y=0.5L X=0.5L X=0.9L
NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER
Th
= 2
7.33
C
Tc
= 6
.87 C
Th
= 2
7.21
C
Tc
= 6
.77 C
Ra Pr1 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
Ra = 3.107
Ra = 4.4.108
NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER
control points and area selectedfor velocity measurements
avg
N
vI
21
..1
2
1
1
Ni
avgiN vvN
Niiavg v
Nv
..1
1
Turbulence Intensity
N = 150
t = 100 ms
t = 15 sec
Ra = 4.4x108
Ra = 1.5x108
Ra = 1.8x108
Ra = 3x107
HIGH RAYLEIGH NUMBERVelocity field statistics
Ra = 3x107
N=150 t = 100 ms
HIGH RAYLEIGH NUMBERVelocity histogram and time series
Ra = 4.4x108
N=138 t = 100 ms
HIGH RAYLEIGH NUMBERVelocity 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
Thank you for your attention!
top related