3. Free convection small when Nusselt Number

4. for m = 0 and substituting expressions above for N u and q c For gas flows with nearly constant P r

6. For example 2 Another alternative is to construct a Alternatives to King’s Law

7. velocity vector cooling a hot-wire or hot-film sensor Jorgensen’s cooling law

8. In the laboratory coordinate system Relating the two decompositions of V

9. Two component X- or V-array probes

10. 12-Sensor Hot-Wire Probe Dimensions in mm Vukoslavčević & Wallace. (1996) Meas. Sci & Tech. 10

11. Taylor’s series expansion of velocity components about probe cross-stream plane centroid to center of the jth sensor over the measured distances, C j and D j. 12 Cooling equations for each of the j sensors in terms of the three velocity components at the probe centroid and the six velocity gradients in the cross-stream plane. System of equations solved by minimizing the error function ∑ f j =0 iteratively at each time step. 12-sensor Probe Data Processing for Simultaneous velocity vector and velocity gradient tensor measurements 120 calibration coefficients, A ij and k ij to be determined. is a polynomial of the measured voltages, Ej.

12. System of equations for 12-sensor probe in terms of error function f j

13. to determine streamwise gradients Streamwise wavenumber approximated from frequency setting the acceleration equal to zero in the N-S equations

16. Virtual experiment Virtual probe with S y = 8 ∆y over the numerical grid where ∆y is 1 viscous length Study of Spatial Resolution Effects using DNS

17. DNS database High and low speed streaks at an instant in time, in a plane parallel to the wall at y+=14 Ratio of Kolmogorov to viscous length scale  data from KMM -- present DNS

18. Velocity Statistics - RMS ♦ DNS y+ = 15 = 150 ■ S+=2 → 1.2 η → 0.6 η ▲ S+=4 → 2.4 η → 1.2 η x S+=8 → 4.8 η → 2.4 η + S+=12 → 7.2 η → 3.6 η

19. ♦ DNS y+ = 15 = 150 ■ S+=2 → 1.2 η → 0.6 η ▲ S+=4 → 2.4 η → 1.2 η x S+=8 → 4.8 η → 2.4 η + S+=12 → 7.2 η → 3.6 η Velocity Skewness

20. Vorticity Statistics - RMS ♦ DNS y+ = 15 = 150 ■ S+=2 → 1.2 η → 0.6 η ▲ S+=4 → 2.4 η → 1.2 η x S+=8 → 4.8 η → 2.4 η + S+=12 → 7.2 η → 3.6 η

21. Vorticity Spectra @ y + = 20 Probe scale S + = 8 __ DNS y+ = 15 = 150 __ S+ = 2 → 1.2 η → 0.6 η __ S+ = 4 → 2.4 η → 1.2 η __ S+ = 8 → 4.8 η → 2.4 η __ S+ = 12 → 7.2 η → 3.6 η

22. Plus and square configuration of 12- sensor probes to measure velocity and velocity gradient properties of turbulent flows Dimensions in mm 12-sensor hot-wire probes

23. Turbulent Kinetic Energy Production & Dissipation and Reynolds shear stress ♦ DNS y + = 15 = 150 + □ S + =2 → 1.2 η → 0.6 η + □ S + =4 → 2.4 η → 1.2 η + □ S + =8 → 4.8 η → 2.4 η + □ S + =12 → 7.2 η → 3.6 η -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 2040 60 80 100 120140160180200220240 260 280 300 320 340360380400 y + -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 20 40 6080 100120140160 180200 220240260280300 320340 360380400 y + uv/u   uv/u  2