Progress Report

Qian Wentao

24/05/2011

Content

Mesh Independence Study

Taylor-Couette Validation

Wavy Taylor Validation

Turbulent Validation

Thermal Validation

Simple Model Test

Plans for Next Period

Mesh Independence Study

100 60 120 100 60 180 100 60 250 100 60 400

Taylor-Couette Validation

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.21

2

4

8

16

32

64

Experiment DataSimulation Data

Wavelength

T/T

c

Full Length

Wavy Taylor Validation

η(a/b) a(cm)b(cm

) h(cm)R(11R

c)Ω(rad/

s)Upper Bound

circum radial axial

0.868 2.2052.54

010.05

01266.

117.222

42 Free 100 30 250

Fundamental angular frequencyω=17.279s=ω/(m Ω)=0.334

Wavy Taylor Validation

η(a/b) a(cm)b(cm

) h(cm)R(11R

c)Ω(rad/

s)Upper Bound

circum radial axial

0.900 2.2862.54

0 7.6201447.

625.050

61 Free 100 25 190

Two fundamental frequenciesω=27.227s=ω/(m Ω)=0.362

Wavy Taylor Validation

η(a/b) a(cm)b(cm

) h(cm)R(11R

c)Ω(rad/

s)Upper Bound

circum radial axial

0.950 5.6495.94

6 8.9102036.

112.194

13 Free 200 25 200

Fundamental angular frequencyω=50.265s=ω/(m Ω)=0.458

Comparing with Experiment Data

η(a/b) Computed S1

Measured S1

0.868 0.334 0.320±0.005

0.900 0.362 0.360±0.010

0.950 0.458 0.450±0.001

The difference is located in the reasonable region of uncertainty

Need to be calculated longer.

Turbulent Validation

Comparison of normalized mean angular momentum profiles between presentsimulation (Re=8000) and the experiment of Smith & Townsend (1982).

uθ Azimuthal VelocityR1 Radius of Inner CylinderR2 Radius of Outer CylinderU0 Tangential Velocity of Inner Cylinderr Distance from Centre Axis

Boundary Conditions

R1 = 0.1525 mR2 = 0.2285 mΩ = 22.295 rad/s (Re=17295)Height = 1.80 m

End walls are free surfaces

k- epsilon and k- omega were chosen to compare

Measure points are located along the mid-height of the gap

Mesh DensityAxial = 400Circle = 100Radial = 60

Comparing with Experiment Data

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2

0.3

0.4

0.5

0.6

0.7

0.8

Experiment DataSimulation Data k-epsilonSimulation Data k-omega

z/d

U*r

/(U

1*R

1)

Possible Reasons for Difference

Flow time interval is not enough

ΔTepsilon=27.68s ΔTomega=20.48s

Sampling frequency

fexperiment=10kHz fsimulation=200Hz

Mesh density

Tip: 文章名称 used k-epsilon as the turbulent model

Thermal Validation

Keq= -h*r*ln(R1/R2)/kRe = Ω* (R1-R2)*R1/ν

h Convective Heat Transfer CoefficientR1 Radius of Inner CylinderR2 Radius of Outer CylinderK Thermal Conductivityν Kinematic Viscosityr Distance from Centre Axis

Fluid is air

Boundary Conditions

Keq= -h*r*ln(R1/R2)/kRe = Ω* (R1-R2)*R1/ν

R1 = 1.252 cmR2 = 2.216 cmHeight = 50.64 Gr= 1000 ΔT= 7.582 KTi = 293K To= 300.582KEnd walls are fixed and insulated

Re=[40 120 280]Ω=[5.008 15.023 35.054] rad/s

Since for η=0.565 Rec= 70,All the three cases are in laminar mode.

Mesh DensityAxial = 1000Circle = 100Radial = 60

Comparing with Experiment Data

Re2 h(w/m2k) keq Experiment Data Residue

1600 5.639 1.568 1.080 9.8e-04

14400 9.721 2.704 1.500 2.0e-03

78400 16.022 4.456 2.120 1.8e-03

Comparing with Experiment Data

Possible Reasons for Difference

Boundary condition set-up

ideal gas, pressure based, real apparatus error (axial temperature gradient, end walls effect)

Wrong understanding of the experiment

Simple Model Test

R1 = 96.85 mmR2 = 97.5 mmHeight = 140 mm Q=4 L/min Vin= 0.000168 m/sTin = 308K Tout= 551KΩ=29.311 rad/sEnd walls are fixed and insulated

Measure points are located in the vertical lines close to the inner cylinder.

Since for η=0.975 Rec= 260.978,In this case Re=1837.075So, it is in laminar mode.

Important Tips

Combined flows in annular space not only on the operating point (axial Reynolds and Taylor numbers), but also e and strongly e on geometry and, to a lesser degree, on parietal thermal conditions.

Plans for Next Period

Keep running both of the turbulent cases

Finish the thermal validation

Couette flow validation

Repeat Taylor-couette validation with full length

Wavy validation should be finished with running 0.95 case long enough

More validation of the thermal part (optional)

Keep turbulent case running

Finish simple model test

Check geometry related paper