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Table 2. Uncertainties of U, T, u’, v’, t', wv, ut, and vt in the Transitional Region

Table 2 Uncertainties of U, T, u’, v’, t', wv, ut, and vt in the Transitional Region

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The rectangular test section is 0.15 m wide, 2.4 m long, and 0.92 m high and has an aspect ratio of 6 to reduce the effects of three-dimensionality. The rectangular test wall (2.4 X 0.92 m) is composite in nature and was designed and constructed to be flexible so that it can be bent to varying degrees of streamwise curvature for future efforts. The support wall is a 4.68-mm-thick polycarbonate sheet. The back of this polycarbonate sheet is covered with 0.25-m-thick R-30 fiberglass wool to minimize back- conduction loss to the room. Attached to the inside of the polycarbonate support wall is a 1.5-mm-thick heater patch.
The rectangular test section is 0.15 m wide, 2.4 m long, and 0.92 m high and has an aspect ratio of 6 to reduce the effects of three-dimensionality. The rectangular test wall (2.4 X 0.92 m) is composite in nature and was designed and constructed to be flexible so that it can be bent to varying degrees of streamwise curvature for future efforts. The support wall is a 4.68-mm-thick polycarbonate sheet. The back of this polycarbonate sheet is covered with 0.25-m-thick R-30 fiberglass wool to minimize back- conduction loss to the room. Attached to the inside of the polycarbonate support wall is a 1.5-mm-thick heater patch.
angle from the wire axis (Fig. 3); this ensures that both of the X-wires can touch the wall simultaneously. This de- sign, which doesn’t involve bending the prongs, provides a 50% reduction in the manufacturing cost. Due to the 10° inclined angle, the cross-wires have respective slant angles of 35° and —55° relative to the probe axis, instead of the +45° of traditional X-wires. However, these X-wires are
angle from the wire axis (Fig. 3); this ensures that both of the X-wires can touch the wall simultaneously. This de- sign, which doesn’t involve bending the prongs, provides a 50% reduction in the manufacturing cost. Due to the 10° inclined angle, the cross-wires have respective slant angles of 35° and —55° relative to the probe axis, instead of the +45° of traditional X-wires. However, these X-wires are
Figure 4. Free-stream turbulence. (a) Intensities and length scales; (b) spectral distribution. The free-stream turbulence intensity (FSTI), calculated from three components of velocity fluctuations, is shown in Fig. 4a to have a value of about 0.5% for a free-stream velocity of 13 m/s. The ratios of v'/u' and w'/u’' in the free stream, also shown in Fig. 4a, are not isotropic; the values varied between 2.0 and 1.6 for v'/u' and between
Figure 4. Free-stream turbulence. (a) Intensities and length scales; (b) spectral distribution. The free-stream turbulence intensity (FSTI), calculated from three components of velocity fluctuations, is shown in Fig. 4a to have a value of about 0.5% for a free-stream velocity of 13 m/s. The ratios of v'/u' and w'/u’' in the free stream, also shown in Fig. 4a, are not isotropic; the values varied between 2.0 and 1.6 for v'/u' and between
Table 1. Reynolds Numbers at Onset and End of Transition
Table 1. Reynolds Numbers at Onset and End of Transition
Figure 5. Mean velocity profiles, U* vs. Y*.
Figure 5. Mean velocity profiles, U* vs. Y*.
Figure 6. Skin friction coefficient and centerline Stanton number distributions. The correlations are from Kays and Crawford [27].
Figure 6. Skin friction coefficient and centerline Stanton number distributions. The correlations are from Kays and Crawford [27].
The boundary layer thickness and integral parameters are shown in Fig. 9 along with the appropriate laminar and turbulent solutions. The turbulent solutions have been adjusted to account for the virtual origin of the turbulent boundary layer beginning at x,. The boundary layer thick- ness observed in Fig. 9 can be explained using this ap- proach. The boundary layer thickness follows the laminar boundary layer values up to the point of transition and
The boundary layer thickness and integral parameters are shown in Fig. 9 along with the appropriate laminar and turbulent solutions. The turbulent solutions have been adjusted to account for the virtual origin of the turbulent boundary layer beginning at x,. The boundary layer thick- ness observed in Fig. 9 can be explained using this ap- proach. The boundary layer thickness follows the laminar boundary layer values up to the point of transition and
Figure 7. Reynolds analogy factor, 2 St/C,, distribution.
Figure 7. Reynolds analogy factor, 2 St/C,, distribution.
to y/6 = 0.3, with a value larger than the wall shear. The peak of uv, still staying at around y/6 = 0.3, continued to grow to a maximum at station 7 of about twice the magnitude of the wall shear. The magnitude of uv decayed after station 7 across the whole boundary layer and reached equilibrium between stations 9 and 13. In order to see more clearly the behavior of uv near the wall, four selected uv profiles at stations 4, 7, 8, and 13 have been replotted in wall coordinates (Y*) in Fig. 13. An almost constant turbulent shear stress appears in a region of Y*= 20-40 at station 4. This indicates that the turbulent shear communicated well near the wall in the boundary layer in the early stage of the transition when the turbu- lence production was not high. Somehow, this communica- tion could not keep up with the vigorous generation of turbulent shear stress that occurred around Y*= 70-100 at station 7. The localized high shear, with a magnitude twice that of the wall shear, took a little while to commu- nicate with the wall until a relatively uniform distribution
to y/6 = 0.3, with a value larger than the wall shear. The peak of uv, still staying at around y/6 = 0.3, continued to grow to a maximum at station 7 of about twice the magnitude of the wall shear. The magnitude of uv decayed after station 7 across the whole boundary layer and reached equilibrium between stations 9 and 13. In order to see more clearly the behavior of uv near the wall, four selected uv profiles at stations 4, 7, 8, and 13 have been replotted in wall coordinates (Y*) in Fig. 13. An almost constant turbulent shear stress appears in a region of Y*= 20-40 at station 4. This indicates that the turbulent shear communicated well near the wall in the boundary layer in the early stage of the transition when the turbu- lence production was not high. Somehow, this communica- tion could not keep up with the vigorous generation of turbulent shear stress that occurred around Y*= 70-100 at station 7. The localized high shear, with a magnitude twice that of the wall shear, took a little while to commu- nicate with the wall until a relatively uniform distribution
Figure 11. Cross-stream velocity fluctuation distributions.
Figure 11. Cross-stream velocity fluctuation distributions.
Figure 12. Reynolds shear stress distributions.
Figure 12. Reynolds shear stress distributions.
Despite the difficulty in accurately measuring vt in the transitional boundary layer, the measurements of ut are clean and without any ambiguities because the value of u
Despite the difficulty in accurately measuring vt in the transitional boundary layer, the measurements of ut are clean and without any ambiguities because the value of u
Figure 15. Streamwise evolution of rms temperature profiles.
Figure 15. Streamwise evolution of rms temperature profiles.
Figure 16. Cross-stream Reynolds heat flux distributions.
Figure 16. Cross-stream Reynolds heat flux distributions.
Figure 17. Streamwise Reynolds heat flux distributions.
Figure 17. Streamwise Reynolds heat flux distributions.
Figure 18. Streamwise evolution of eddy viscosity, diffusivity, and turbulent Prandtl number profiles.
Figure 18. Streamwise evolution of eddy viscosity, diffusivity, and turbulent Prandtl number profiles.
Related topics:
EngineeringBoundary LayersLow Reynolds NumberTransitional FlowSkin Friction
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