TY - JOUR

T1 - New scaling for compressible wall turbulence

AU - Pei, Jie

AU - Chen, Jun

AU - Fazle, Hussain

AU - She, Zhensu

N1 - Funding Information:
This work was supported by the National Nature Science Foundation of China (Grant Nos. 90716008, 10572004 and 11172006) and the National Basic Research Program of China (Grant No. 2009CB724100). The authors would like to thank Prof. LI XinLiang of Chinese Academy of Sciences for the help in computations.

PY - 2013/9

Y1 - 2013/9

N2 - Classical Mach-number (M) scaling in compressible wall turbulence was suggested by van Driest (Van Driest E R. Turbulent boundary layers in compressible fluids. J Aerodynamics Science, 1951, 18(3): 145-160) and Huang et al. (Huang P G, Coleman G N, Bradshaw P. Compressible turbulent channel flows: DNS results and modeling. J Fluid Mech, 1995, 305: 185-218). Using a concept of velocity-vorticity correlation structure (VVCS), defined by high correlation regions in a field of two-point cross-correlation coefficient between a velocity and a vorticity component, we have discovered a limiting VVCS as the closest streamwise vortex structure to the wall, which provides a concrete Morkovin scaling summarizing all compressibility effects. Specifically, when the height and mean velocity of the limiting VVCS are used as the units for the length scale and the velocity, all geometrical measures in the spanwise and normal directions, as well as the mean velocity and fluctuation (r.m.s) profiles become M-independent. The results are validated by direct numerical simulations (DNS) of compressible channel flows with M up to 3. Furthermore, a quantitative model is found for the M-scaling in terms of the wall density, which is also validated by the DNS data. These findings yield a geometrical interpretation of the semi-local transformation (Huang et al., 1995), and a conclusion that the location and the thermodynamic properties associated with the limiting VVCS determine the M-effects on supersonic wall-bounded flows.

AB - Classical Mach-number (M) scaling in compressible wall turbulence was suggested by van Driest (Van Driest E R. Turbulent boundary layers in compressible fluids. J Aerodynamics Science, 1951, 18(3): 145-160) and Huang et al. (Huang P G, Coleman G N, Bradshaw P. Compressible turbulent channel flows: DNS results and modeling. J Fluid Mech, 1995, 305: 185-218). Using a concept of velocity-vorticity correlation structure (VVCS), defined by high correlation regions in a field of two-point cross-correlation coefficient between a velocity and a vorticity component, we have discovered a limiting VVCS as the closest streamwise vortex structure to the wall, which provides a concrete Morkovin scaling summarizing all compressibility effects. Specifically, when the height and mean velocity of the limiting VVCS are used as the units for the length scale and the velocity, all geometrical measures in the spanwise and normal directions, as well as the mean velocity and fluctuation (r.m.s) profiles become M-independent. The results are validated by direct numerical simulations (DNS) of compressible channel flows with M up to 3. Furthermore, a quantitative model is found for the M-scaling in terms of the wall density, which is also validated by the DNS data. These findings yield a geometrical interpretation of the semi-local transformation (Huang et al., 1995), and a conclusion that the location and the thermodynamic properties associated with the limiting VVCS determine the M-effects on supersonic wall-bounded flows.

KW - Morkovin's hypothesis

KW - coherent structures

KW - compressible channel flow

KW - correlation structures

UR - http://www.scopus.com/inward/record.url?scp=84883160617&partnerID=8YFLogxK

U2 - 10.1007/s11433-013-5147-9

DO - 10.1007/s11433-013-5147-9

M3 - Article

AN - SCOPUS:84883160617

VL - 56

SP - 1770

EP - 1781

JO - Science China: Physics, Mechanics and Astronomy

JF - Science China: Physics, Mechanics and Astronomy

SN - 1674-7348

IS - 9

ER -