Effect of mean pressure gradient on the turbulent wall pressure–velocity correlations

Two-point correlations of the wall fluctuating pressure and turbulent pressure and velocities in the flow field are computed in three dimensions using direct numerical simulation (DNS) databases. The mean pressure gradient in the flow has strong influence on these correlations. The DNS () in a converging/diverging channel with streamwise curvature near the lower wall is used to compute the statistics. The correlations in favourable pressure gradient and adverse pressure gradient are compared with the correlation in flat channel flow DNS (). The results show that these pressure–pressure and pressure–velocity correlations are not only sensitive to the local pressure gradient and wall curvature, but also to the pressure gradient history.

[1]  Ronald L. Panton,et al.  Wall pressure spectra calculations for equilibrium boundary layers , 1974, Journal of Fluid Mechanics.

[2]  Alexander J. Smits,et al.  A turbulent flow over a curved hill Part 1. Growth of an internal boundary layer , 1987 .

[3]  M. Bull.  Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow , 1967, Journal of Fluid Mechanics.

[4]  D. Chase.  Modeling the wavevector-frequency spectrum of turbulent boundary layer wall pressure , 1980 .

[5]  H. Sung,et al.  Structures in turbulent boundary layers subjected to adverse pressure gradients , 2009, Journal of Fluid Mechanics.

[6]  Y. Kobashi,et al.  Wall pressure and its relation to turbulent structure of a boundary layer , 1986 .

[7]  Michel Stanislas,et al.  Decelerating Boundary Layer: A New Scaling and Mixing Length Model , 2003 .

[8]  P. Alfredsson,et al.  Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers , 2007, Journal of Fluid Mechanics.

[9]  John Kim,et al.  On the structure of wall‐bounded turbulent flows , 1983 .

[10]  P. Chou.  On velocity correlations and the solutions of the equations of turbulent fluctuation , 1945 .

[11]  Philippe R. Spalart,et al.  Experimental and numerical study of a turbulent boundary layer with pressure gradients , 1993, Journal of Fluid Mechanics.

[12]  Javier Jiménez,et al.  Scaling of the energy spectra of turbulent channels , 2003, Journal of Fluid Mechanics.

[13]  K. Squires,et al.  Numerical investigation of the turbulent boundary layer over a bump , 1998, Journal of Fluid Mechanics.

[14]  G. Maidanik,et al.  A wavenumber analysis of the coupling of a structural mode and flow turbulence , 1990 .

[15]  Arne V. Johansson,et al.  On the generation of high-amplitude wall-pressure peaks in turbulent boundary layers and spots , 1987, Journal of Fluid Mechanics.

[16]  Wall pressure fluctuations in a turbulent boundary layer over a bump , 2004 .

[17]  Ben Thornber,et al.  Physics of the single-shocked and reshocked Richtmyer–Meshkov instability , 2012 .

[18]  M. Bull,et al.  On the role of wall-pressure fluctuations in deterministic motions in the turbulent boundary layer , 1983, Journal of Fluid Mechanics.

[19]  Relationships Between Turbulent Wall Pressure and Velocity Field Sources , 1998 .

[20]  J. Wallace.  Highlights from 50 years of turbulent boundary layer research , 2012 .

[21]  Uwe Ehrenstein,et al.  Instability of streaks in wall turbulence with adverse pressure gradient , 2011, Journal of Fluid Mechanics.

[22]  Uwe Ehrenstein,et al.  On the relation between kinetic energy production in adverse-pressure gradient wall turbulence and streak instability , 2012 .

[23]  Hyung Jin Sung,et al.  Wall pressure fluctuations and flow-induced noise in a turbulent boundary layer over a bump , 2006, Journal of Fluid Mechanics.

[24]  Hill,et al.  TURBULENT FLOW OVER A CURVED HILL , 2003 .

[25]  W. Willmarth,et al.  Pressure Fluctuations Beneath Turbulent Boundary Layers , 1975 .

[26]  Jean-Philippe Laval,et al.  Direct numerical simulation of a separated channel flow with a smooth profile , 2007, 0710.3729.

[27]  Parviz Moin,et al.  The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation , 1998, Journal of Fluid Mechanics.

[28]  H. Sung,et al.  EFFECTS OF ADVERSE PRESSURE GRADIENT ON A TURBULENT BOUNDARY LAYER , 2008, Proceeding of Fifth International Symposium on Turbulence and Shear Flow Phenomena.

[29]  J. Eaton,et al.  Turbulence characteristics of a boundary layer over a two-dimensional bump , 1996 .

[30]  Jean-Philippe Laval,et al.  Direct Numerical Simulations of Converging–Diverging Channel Flow , 2011 .

[31]  G. Corcos.  Resolution of Pressure in Turbulence , 1963 .

[32]  M. Wang,et al.  Hydroacoustic forcing function modeling using DNS database , 1996 .

[33]  William K. Blake,et al.  Turbulent boundary-layer wall-pressure fluctuations on smooth and rough walls , 1970, Journal of Fluid Mechanics.

[34]  W. Willmarth,et al.  Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer , 1962, Journal of Fluid Mechanics.

[35]  F. Fahy,et al.  Mechanics of flow-induced sound and vibration , 1989 .

[36]  M. Bull.  WALL-PRESSURE FLUCTUATIONS BENEATH TURBULENT BOUNDARY LAYERS: SOME REFLECTIONS ON FORTY YEARS OF RESEARCH , 1996 .