tomasz michałek
DESCRIPTION
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. Outline. 1. Experimental benchmark - PowerPoint PPT PresentationTRANSCRIPT
Tomasz Michałek
Institute of Fundamental Technological Research
Polish Academy of Sciences, Dept. of Mechanics and Physics of Fluids, Poland.
HIGH RAYLEIGH NUMBER NATURAL CONVECTION IN A CUBIC ENCLOSURE
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
Building credibility 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
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 model
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
2
1
..1
2
1
1
Ni
avgiN vvN
ESTIMATION OF EXP. UNCERAINTY UD
2
1
..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
2
1
..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
NATURAL CONVECTION Ra ~ 3.0x107
Th
= 1
8.0 C
Tc
= 4
.0 C
Th
= 2
3.2 C
Tc
= 9
.0 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
NATURAL CONVECTION Ra = 1.5x108
Th
= 2
7.3 C
Tc
= 6
.8 C
Th
= 2
7.2 C
Tc
= 6
.8 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
NATURAL CONVECTION Ra = 1.8x108
Th
= 3
6.4 C
Tc
= 1
0.2 C
Th
= 3
6.4 C
Tc
= 1
0.2 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
NATURAL CONVECTION Ra = 4.4x108
Th
= 4
5.8 C
Tc
= 1
4.2 C
Th
= 4
5.8 C
Tc
= 1
4.0 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
Ra = 4.4x108
Ra = 1.5x108
Ra = 1.8x108
Ra = 3x107
Avg. Horizontal Velocity
N = 150
t = 100 ms
t = 15 sec
HIGH RAYLEIGH NUMBERMean velocity fields
Avg. Vertical Velocity
N = 150
t = 100 ms
t = 15 sec
Ra = 4.4x108
Ra = 1.5x108
Ra = 1.8x108
Ra = 3x107
HIGH RAYLEIGH NUMBERMean velocity fields
Ni
avgiN
N vvN
S..1
3
31
1
Skewness
N = 150
t = 100 ms
t = 15 sec
Ra = 4.4x108
Ra = 1.5x108
Ra = 1.8x108
Ra = 3x107
HIGH RAYLEIGH NUMBERVelocity field statistics
Ni
avgiN
N vvN
K..1
4
41
1
Kurtozis
N = 150
t = 100 ms
t = 15 sec
Ra = 4.4x108
Ra = 1.5x108
Ra = 1.8x108
Ra = 3x107
HIGH RAYLEIGH NUMBERVelocity field statistics
avg
N
vI
2
1
..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 = 1.5x108
N=120 t = 100 ms
HIGH RAYLEIGH NUMBERVelocity histogram and time series
Ra = 1.8x108
N=134 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
• 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
2
1
..1
2
11
Niavgi vv
NNs
0SPDU
Niiavg v
Nv
..1
1 cfext SSS 33.033.1
In our examples:
for water
VALIDATION : Ra ~ 3 x 107
Experiment Comp. Results FD (SOLVSTR)
Variable D UD S USN E UV
T7 18,22 0,48
17,99 0,07 0,23 0,49
T10 17,76 0,63
17,17 0,07 0,59 0,63
Umin -0,66 0,24
-0,65 0,01 0,01 0,24
Umax 0,69 0,24
0,65 0,01 0,04 0,24
Vmin -2,60 0,24
-2,40 0,09 0,20 0,26
Vmax 2,42 0,24
2,40 0,09 0,02 0,26
VP1 -2,48 0,58
-1,99 0,04 0,49 0,58
VP2 -1,85 0,42
-1,71 0,04 0,14 0,42
UP3 -0,24 0,09
-0,22 0,01 0,02 0,09
VP3 -0,75 0,21
-1,05 0,02 0,30 0,21
UP4 -0,58 0,14
-0,39 0,01 0,19 0,14
UP5 -0,60 0,16
-0,42 0,02 0,18 0,16
FD method (SOLVSTR)
Experiment
VUE Conditiondoes not hold
VALIDATION : Ra ~ 3 x 107
Experiment Comp. Results (Fluent)
Variable D UD S USN E UV
T12 18,67 0,38 18,92 0,02 0,25 0,38
T16 4,05 0,38 3,83 0,02 0,22 0,38
T7 18,22 0,48 18,39 0,02 0,17 0,48
T10 17,76 0,63 17,64 0,02 0,12 0,63
Umin -0,66 0,24 -0,73 0,01 0,07 0,24
Umax 0,69 0,24 0,68 0,01 0,01 0,24
Vmin -2,6 0,24 -2,22 0,05 0,38 0,25
Vmax 2,42 0,24 2,22 0,05 0,20 0,25
VP1 -2,48 0,58 -1,99 0,01 0,49 0,58
VP2 -1,85 0,42 -1,77 0,02 0,08 0,42
UP3 -0,24 0,09 -0,29 0,02 0,05 0,09
VP3 -0,75 0,21 -1,29 0,01 0,54 0,21
UP4 -0,58 0,14 -0,4 0,01 0,18 0,14
UP5 -0,6 0,16 -0,42 0,01 0,18 0,16
FV method (Fluent)
Experiment
VUE Conditiondoes not hold
Experiment Comp. Results (SOLVSTR)
Variable D UD S USN E UV
T7 25,51 0,18 25,64 0,09 0,13 0,20
T10 24,40 0,21 24,57 0,11 0,17 0,24
Umin -1,12 0,76 -1,23 0,04 0,11 0,76
Umax 0,97 0,76 1,23 0,04 0,26 0,76
Vmin -6,11 1,16 -5,29 0,06 0,82 1,16
Vmax 6,19 1,16 5,29 0,06 0,90 1,16
VP1 -4,55 1,59 -3,03 0,02 1,52 1,59
VP2 -3,58 1,28 -2,53 0,07 1,05 1,28
UP3 -0,55 0,24 -0,36 0,02 0,19 0,24
VP3 -1,98 0,75 -1,97 0,06 0,01 0,75
UP4 -0,94 0,45 -0,52 0,01 0,46 0,45
UP5 -1,04 0,40 -0,58 0,02 0,46 0,40
VALIDATION : Ra ~ 1.3 x 108
Experiment
FD method (SOLVSTR)
VUE Conditiondoes not hold
VALIDATION : Ra ~ 1.3 x 108
Experiment
FV method (Fluent)
Experiment Comp. Results (Fluent)
Variable D UD S USN E UV
T12 27,23 0,24 27,27 0,02 0,04 0,24
T16 6,76 0,18 6,58 0,03 0,18 0,18
T7 25,51 0,18 25,40 0,02 0,11 0,18
T10 24,40 0,21 24,69 0,04 0,29 0,21
T15 25,08 0,33 24,82 0,02 0,26 0,33
Umin -1,12 0,76 -1,01 0,01 0,11 0,76
Umax 0,97 0,76 1,01 0,01 0,04 0,76
Vmin -6,11 1,16 -3,65 0,05 2,46 1,16
Vmax 6,19 1,16 3,65 0,05 2,54 1,16
VP1 -4,55 1,59 -2,39 0,01 2,16 1,59
VP2 -3,58 1,28 -2,19 0,02 1,39 1,28
UP3 -0,55 0,24 -0,36 0,02 0,19 0,24
VP3 -1,98 0,75 -1,68 0,01 0,30 0,75
UP4 -0,94 0,45 -0,48 0,01 0,46 0,45
UP5 -1,04 0,40 -0,49 0,01 0,55 0,40VUE
Conditiondoes not hold
CONCLUSIONS
The sensitivity analysis was used to identify fundamental (crucial) parameters for considered configuration.
Uncertainty of experimental data was assessed.
2D Temperature fields, 2D Velocity fields were determined for high Ra numbersin the central cross-section of the box cavity heated from the side.
Validation procedure was performed in order to assess modeling errors.
Velocity fluctuations were observed in these experiments for high Ra number below Rac.
Velocity fluctuations were not reproduced by computational results.
Numerical simulations were performed for Ra = 3x107, 1.3x108 (FV,FD).
These fluctuations were attributed to non-uniformity of thermal boundary conditions along the bottom wall.
Experimental benchmark was defined for moderate Ra numbers. Agreement between computational results and experimental data was achieved.
Thank you for your attention!