Wall pressure fluctuations of a turbulent separated and reattaching flow affected by an unsteady wake

The spatio-temporal characteristics of the wall-pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated through pressure-velocity joint measurements carried out using multiple-arrayed microphones and split-film probes. A spoke-wheel-type wake generator was installed upstream of the backward-facing step. The flow structure at the effective forcing frequency (St_f=0.2) was found to be well organized in terms of wall pressure spectrum, cross-correlation, wavenumber-frequency spectrum, and wavelet auto-correlation. Introduction of the unsteady wake (St_f=0.2) reduced the reattachment length by 10%. In addition, the unsteady wake enhanced the turbulence intensity near the separation edge and, as a consequence, enhanced the quadrupole sound sources; however, the turbulence intensity near the reattachment region was weakened and the overall flow noise was attenuated. The greater organization of the flow structure induced by the unsteady wake led to a weakening of the dipole sound sources, which are the dominant sound sources in this system. The dipole sound sources generated by wall pressure fluctuations were calculated using Curles integral formula.Abbreviations AR Aspect ratio - SBF Spatial box filteringRoman symbols C_p Wall pressure fluctuation coefficient, p/0.5U² - H Step height of backward-facing step (mm) - H_s Shape factor (H_s=^*/) - R_s Distance from acoustic source point to observation point (m) - Re_H Reynolds number,UH/ - St The reduced frequency,fH/U - St_f Normalized forcing frequency by unsteady wake, f_pH/U - T Vortex shedding period (s) - U Free-stream velocity (m/s) - a Speed of sound (m/s) - f Frequency (Hz) - f_p Wake passing frequency (Hz) - k Turbulent kinetic energy (m²/s²) - k_x Streamwise wave number (1/m) - k_z Spanwise wave number (1/m) - l_j Cosine of angle - p Instantaneous wall pressure (Pa) - p_rms Root-mean-square of wall pressure (Pa) - p_SBF Spatial box filtered wall pressure (Pa) - p_d Dipole sound source (Pa) - p_w Conditionally-averaged wall pressure (Pa) - q Dynamic pressure, 0.5U²(Pa) - r Distance from origin to observation point (mm) - u_c Convection velocity (m/s) - u_max Root-mean-square of streamwise velocity (m/s) - x_R Time-mean reattachment length (mm)Greek symbols _p Forward-flow time fraction - Auto-correlation of pressure atx₀ - Two-dimensional cross-correlation of pressure with streamwise separation interval , spanwise separation interval , and time delay , at (x₀,z₀) - Boundary layer thickness (mm,_99%) - ^* Displacement thickness (mm, ) - _ij Kroneckers delta function - Phase angle (°) - Wavelength (mm) - Momentum thickness (mm, ) - Angle between vertical axis and observation point (°) - Density (kg/m³) - Time delay (s) - Streamwise separation interval (m) - Spanwise separation interval (m) - _p(f;x₀) Autospectrum of pressure measured atx₀ (Pa²s) - _pp(, ;x₀) Streamwise cross spectrum of pressure atx₀ (Pa²s) - _pp(, , ; x₀,z₀) Streamwise and spanwise cross spectrum of pressure at (x₀,z₀) (Pa²s) - _pp(kx, ; x₀) Streamwise wavenumber-frequency spectrum of pressure at x₀(Pa²s) - _pp(kx, kz, ;x₀,z₀) Two-dimensional wavenumber-frequency spectrum of pressure at (x₀,z₀) (Pa²s)