2. Content  Mesh Independence Study  Taylor-Couette Validation  Wavy Taylor Validation  Turbulent Validation  Thermal Validation  Simple Model Test  Plans for Next Period

3. Mesh Independence StudyMesh Independence Study 100 60 120100 60 180100 60 250100 60 400

4. Taylor-Couette ValidationTaylor-Couette Validation Wavelength T/Tc Full Length

5. Wavy Taylor ValidationWavy Taylor Validation η (a/b)a(cm)b(cm)h(cm)R(11Rc) Ω (rad/s) Upper Boundcircumradialaxial 0.8682.2052.54010.0501266.117.22242Free10030250 Fundamental angular frequency ω =17.279 s= ω /(m Ω )=0.334

6. Wavy Taylor ValidationWavy Taylor Validation η (a/b)a(cm)b(cm)h(cm)R(11Rc) Ω (rad/s) Upper Boundcircumradialaxial 0.9002.2862.5407.6201447.625.05061Free10025190 Two fundamental frequencies ω =27.227 s= ω /(m Ω )=0.362

7. Wavy Taylor ValidationWavy Taylor Validation η (a/b)a(cm)b(cm)h(cm)R(11Rc) Ω (rad/s) Upper Boundcircumradialaxial 0.9505.6495.9468.9102036.112.19413Free20025200 Fundamental angular frequency ω =50.265 s= ω /(m Ω )=0.458

8. Comparing with Experiment Data η (a/b)Computed S1Measured S1 0.8680.3340.320±0.005 0.9000.3620.360±0.010 0.9500.4580.450±0.001 The difference is located in the reasonable region of uncertainty Need to be calculated longer.

9. Turbulent ValidationTurbulent Validation Comparison of normalized mean angular momentum profiles between present simulation (Re=8000) and the experiment of Smith & Townsend (1982). u θ Azimuthal Velocity R 1 Radius of Inner Cylinder R 2 Radius of Outer Cylinder U 0 Tangential Velocity of Inner Cylinder r Distance from Centre Axis

10. Boundary ConditionsBoundary Conditions R 1 = 0.1525 m R 2 = 0.2285 m Ω = 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 Density Axial = 400 Circle = 100 Radial = 60

11. Comparing with Experiment Data

12. Possible Reasons for Difference  Flow time interval is not enough ΔT epsilon =27.68s ΔT omega =20.48s  Sampling frequency f experiment =10kHz f simulation =200Hz  Mesh density Tip: 文章名称 used k-epsilon as the turbulent model

13. Thermal ValidationThermal Validation K eq = -h*r*ln(R 1 /R 2 )/k Re = Ω* (R 1 -R 2 )*R 1 /ν h Convective Heat Transfer Coefficient R 1 Radius of Inner Cylinder R 2 Radius of Outer Cylinder K Thermal Conductivity ν Kinematic Viscosity r Distance from Centre Axis Fluid is air

14. Boundary ConditionsBoundary Conditions K eq = -h*r*ln(R 1 /R 2 )/k Re = Ω* (R 1 -R 2 )*R 1 /ν R 1 = 1.252 cm R 2 = 2.216 cm Height = 50.64 Gr= 1000 ΔT= 7.582 K Ti = 293K To= 300.582K End walls are fixed and insulated Re=[40 120 280] Ω=[5.008 15.023 35.054] rad/s Since for η=0.565 Re c = 70, All the three cases are in laminar mode. Mesh Density Axial = 1000 Circle = 100 Radial = 60

15. Comparing with Experiment Data Re 2 h(w/m 2 k)k eq Experiment DataResidue 16005.6391.5681.0809.8e-04 144009.7212.7041.5002.0e-03 7840016.0224.4562.1201.8e-03

16. Comparing with Experiment Data

17. 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

18. Simple Model TestSimple Model Test R 1 = 96.85 mm R 2 = 97.5 mm Height = 140 mm Q=4 L/min V in = 0.000168 m/s T in = 308K T out = 551K Ω=29.311 rad/s End walls are fixed and insulated Measure points are located in the vertical lines close to the inner cylinder. Since for η=0.975 Re c = 260.978, In this case Re=1837.075 So, it is in laminar mode.

19. Important TipsImportant Tips  Combined fl ows 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.

21. Plans for Next PeriodPlans 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