tomasz michałek

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!